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A global sensitivity analysis framework for hybrid simulation
Abstract
Hybrid Simulation is a dynamic response simulation paradigm that merges physical experiments and computational models into a hybrid model. In earthquake engineering, it is used to investigate the response of structures to earthquake excitation. In the context of response to extreme loads, the structure, its boundary conditions, damping, and the ground motion excitation itself are all subjected to large parameter variability. However, in current seismic response testing practice, Hybrid Simulation campaigns rely on a few prototype structures with fixed parameters subjected to one or two ground motions of different intensity. While this approach effectively reveals structural weaknesses, it does not reveal the sensitivity of structure’s response. This thus far missing information could support the planning of further experiments as well as drive modeling choices in subsequent analysis and evaluation phases of the structural design process.
This paper describes a Global Sensitivity Analysis framework for Hybrid Simulation. This framework, based on Sobol’ sensitivity indices, is used to quantify the sensitivity of the response of a structure tested using the Hybrid Simulation approach due to the variability of the prototype structure and the excitation parameters. Polynomial Chaos Expansion is used to surrogate the hybrid model response. Thereafter, Sobol’ sensitivity indices are obtained as a by-product of polynomial coefficients, entailing a reduced number of Hybrid Simulations compared to a crude Monte Carlo approach. An experimental verification example highlights the excellent performance of Polynomial Chaos Expansion surrogates in terms of stable estimates of Sobol’ sensitivity indices in the presence of noise caused by random experimental errors.
... parallel to the leg axis of the VPP model (·) 0 . . . initial value (at t = 0 s) (·) 1 . . . final value (t ! 1) ...
... The experimental part typically comprises critical components from which the correct function should be verified or parts that are cumbersome to model (e.g. due to 1 The terms part, substructure and component are used interchangeably. ...
... For the last decades, RTHS has mainly be considered from a deterministic perspective. Over the last few years, the focus shifts to frameworks including parameter uncertainty and the investigation of uncertainty/error propagation through the RTHS loop [1][2][3]192]. A further research topic is about distributed RTHS, where experimental parts are at different laboratories around the world and RTHS tests are performed. ...
Real-Time Hybrid Substructuring (RTHS) is a cyber-physical testing method to analyze complex dynamical systems. This thesis covers three research topics related to RTHS: (i) an actuator control scheme is proposed that achieves high test fidelity and maintains test stability also for RTHS with contact (ii) a fidelity measure is established that is based on an experimental sensitivity analysis and (iii) an RTHS setup to test prosthetic feet is presented, where the amputee is modeled.
... In this regard, surrogate modeling is proposed to perform global sensitivity analysis (GSA) of a quantity of interest (QoI) hybrid model response with respect to a set of input parameters originating from both substructures and excitation [16,17]. GSA aims to quantitatively determine the degree each input parameter affects the selected QoI of the hybrid model response. ...
... Monte Carlo simulations can be used to estimate Sobol' indices. Nonetheless, for each index estimation, O(10 3 ) model evaluations would be required [16]. To alleviate this burden, surrogate models of the QoI response can be developed. ...
... As explained in [16], PCE is used to surrogate the hybrid model response and to then compute the Sobol' indices. This study extends the GSA framework proposed in [16] by utilizing multiple and different surrogate modeling techniques to conduct GSA via Sobol' indices in HS. ...
Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation is extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation are conceived as being deterministic. However, associated uncertainties are present, whilst simulation deviation, due to their presence, could be significant. In this regard, global sensitivity analysis based on Sobol’ indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol’ sensitivity indices requires an unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques using machine learning data-driven regression are utilized to alleviate this burden. This study extends the current global sensitivity analysis practices in hybrid simulation by employing various different surrogate modeling methodologies as well as providing comparative results. In particular, polynomial chaos expansion, Kriging and polynomial chaos Kriging are used. A case study encompassing a virtual hybrid model is employed, and hybrid model response quantities of interest are selected. Their respective surrogates are developed, using all three aforementioned techniques. The Sobol’ indices obtained utilizing each examined surrogate are compared with each other, and the results highlight potential deviations when different surrogates are used.
... An exhaustive exploration of all possible load cases is clearly not an option given the experimental cost associated with a single hybrid model evaluation. Accordingly, Abbiati et al. (2021) proposed surrogate modeling to compute the variance-based global sensitivity analysis (GSA) of the response quantity of interest (QoI) of a given hybrid model with respect to a set of input parameters that characterize both substructures and loading excitations. In detail, polynomial chaos expansion (PCE) was used to construct a surrogate model (a.k.a. ...
... As a result, uncertainty, both aleatory or epistemic, always affects the PS structural behavior. This paper extends the GSA framework for HS proposed in Abbiati et al. (2021) to the case of PSs with non-deterministic behavior. Similar to the original framework, the idea is to surrogate the hybrid model response as a function of the input parameters that can be controlled by the experimenter and originate from substructures and loading (physical and numerical). ...
... Variance-based sensitivity analysis has been extensively studied and successfully developed in the context of deterministic models (Abbiati et al. (2021); Saltelli (2008)). For a random vector X with independent components, any deterministic mapping Y M s (X) with Var[Y] < + ∞ can be decomposed as (Sobol', 1993): ...
Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.
... An exhaustive exploration of all possible load cases is clearly not an option given the experimental cost associated with a single hybrid model evaluation. Accordingly, Abbiati and co-workers [9] proposed surrogate modeling to compute the variance-based global sensitivity analysis (GSA) of the response quantity of interest (QoI) of a given hybrid model with respect to a set of input parameters that characterize both substructures and loading excitations. In detail, polynomial chaos expansion (PCE) was used to construct a surrogate model (a.k.a. ...
... This paper extends the GSA framework for HS proposed in [9] to the case of PSs with non-deterministic behavior. Similarly to the original framework, the idea is to surrogate the hybrid model response as a function of the input parameters that can be controlled by the experimenter and originate from substructures and loading (physical and numerical). ...
... Variance-based sensitivity analysis has been extensively studied and successfully developed in the context of deterministic models [9,16]. For a random vector with independent components, any deterministic mapping = M ( ) with Var [ ] < +∞ can be decomposed as [22] ...
Hybrid simulation is used to investigate the experimental dynamic response of a component or sub-assembly of a prototype structure using a hybrid model. The latter comprises both physically-tested and numerically-simulated substructures interacting with each other in a real-time feedback loop. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol' sensitivity indices are computed for substructure quantity of interest response quantiles. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.
... We choose to target the bending motion of a cantilever beam with two degrees of freedom at the interface; torsional effects are ignored. While tests have been conducted on two or more interface degrees-of-freedom and on lightly damped structures (see, for instance, [27,28,29]), both of these combined with the direct force measurement challenge makes this a particularly difficult type of test. ...
... In dynamic substructuring, the original structure is divided into two or more substructures and the dynamics of each of them is studied separately and subsequently assembled [30]. In the context of hybrid testing, although the case of multiple substructures has been treated [27], the most common setup consists of only two substructures, the numerical one (NS) and the physical one (PS), which will be denoted in the following by the subscripts N and P respectively. The original structure is split into two at an interface that contains one or more degrees of freedom. ...
In this paper, an iterative method for real-time hybrid testing (RTHT) is proposed. The method seeks to iteratively balance the interface conditions between the physical and numerical substructures by controlling the periodic demand of the actuators. It is then suitable for RTHT of structures undergoing a periodic response, e.g. structures excited at resonance. We demonstrate the capabilities of the method on a cantilever beam in bending motion with two degrees of freedom at the interface, which we use as a prototype for future testing of aircraft wings. We show that a number of challenges arise in these settings, such as the difficulty in measuring interface forces while controlling a continuous structure and the instability of the hybrid test for small time delays. Classical RTHT strategies could produce inaccurate or unstable outcomes, whereas the proposed method is able to attain very good interface synchronisation in a wide range of tested scenarios.
... In addition, the parameter variations in nonlinear systems are also uncertain, e.g., model form error, initial and boundary conditions, and operation wear [15]. Global sensitivity analysis can be applied to identify the main sources of uncertainty in the model inputs, especially when the model under consideration is nonlinear and the uncertainty level of model inputs is large [16,17]. Therefore, the sensitivity analysis method has been developed to quantitatively analyze the influence between the inputs and outputs of the nonlinear systems. ...
... end for 16. ...
Based on the direct differentiation method, sensitivity analysis of transient responses with respect to local nonlinearity is developed in this paper. Solutions of nonlinear equations and time-domain integration are combined to compute the response sensitivities, which consist of three steps: firstly, the nonlinear differential equations of motion are solved using Newton–Raphson iteration to obtain the transient response; secondly, the algebraic equations of the sensitivity are obtained by differentiating the incremental equation of motion with respect to nonlinear coefficients; thirdly, the nonlinear transient response sensitivities are determined using the Newmark-β integration in the interested time range. Three validation studies, including a Duffing oscillator, a nonlinear multiple-degrees-of-freedom (MDOF) system, and a cantilever beam with local nonlinearity, are adopted to illustrate the application of the proposed method. The comparisons among the finite difference method (FDM), the Poincaré method (PCM), the Lindstedt–Poincaré method (LPM), and the proposed method are conducted. The key factors, such as the parameter perturbation step size, the secular term, and the time step, are discussed to verify the accuracy and efficiency. Results show that parameter perturbation selection in the FDM sensitivity analysis is related to the nonlinear features depending on the initial condition; the consistency of the transient response sensitivity can be improved based on the accurate nonlinear response when a small time step is adopted in the proposed method.
... The response function (x) of DAR is defined in the unit hypercube = { |0 ≤ ≤ 1}. The high-dimensional model representations of the response function (x) can be uniquely expressed as follows [41,42]: ...
... The high-dimensional model representations of the response function f (x) can be uniquely expressed as follows [41,42]: ...
The modeling of compliant bridge-type displacement amplification mechanisms has challenges due to the intrinsic coupling of kinematic and mechanical behaviors. A structure load performance integrated model method for the bridge-type displacement amplification mechanism is presented. The established modeling based on Castigliano’s second theorem considers the deformations of all members, the effect of external load and the nonlinear shear effect. Compared to the finite element model (FEM) and existing models, the established modeling precisely predicts significant nonlinearity of the displacement amplification ratio (DAR) with the driving force, strong sensitivity of DAR to the external load and corresponding relationships of structural parameters with DAR, which is the closest to the FEM result over existing models. The variance-based sensitivities of structural parameters to DAR are thoroughly analyzed, indicating that sensitive structure parameters need to be focused on. Modeling applications further prove the reliability and expandability of the proposed model method. The proposed model method can provide support for the design, optimization and control of compliant systems with bridge-type displacement amplification mechanisms.
... Global sensitivity analysis is a statistical tool that has been receiving great attention in the analysis of many engineering systems, providing a comprehensive approach on how an input variation can affect the underlying system response [4]. An application of these idea in the context of energy harvesting can be seen in the recent work of Aloui et al. [5]. ...
... which is an orthogonal decomposition in terms of conditional expectations as defined by [4]. In this way, first-order Sobol' indices are defined as for chaotic behavior (see [3] for details). ...
This work deals with a global sensitivity analysis in the nonlinear dynamics of a bistable piezo-magneto-elastic energy harvester. The objective is to evaluate the degree of influence of each input parameter variation, as well as their joint effect, on the system response. The global sensitivity analysis method used is the Sobol index, which is based on the idea of orthogonally decompose the total variance of the system response into a sum of conditional variances. The Monte Carlo-based analysis provides a detailed overview about the influence of the physical parameters on the energy recovering process in periodic and chaotic dynamic regimes.
... Among these sensitivity measures, the Sobol' indices [16] have shown the largest accuracy in most cases and hence they will be incorporated in this study. Using the Sobol' indices, Abiatti et al. [17] evaluated the sensitivity of the probabilistic response of a structure due to the uncertainty of the structure and of the excitation parameters. Zeighami et al. [18] studied the Sobol' sensitivity of the stochastic mechanical behavior of a seismic meta-barrier with respect to its uncertain mechanical parameters. ...
A novel numerical framework for the Sobol' sensitivity analysis of 1D stochastic elasto-plastic wave propagation is proposed and evaluated. The forward propagation of uncertain input motions through uncertain elasto-plastic soils and structures is often conducted using the finite element method (FEM) together with the Monte Carlo simulation. However, it is computationally much more efficient to use the stochastic elasto-plastic FEM (SEPFEM) instead. Hence the developed framework is based on the SEPFEM. The backward propagation of uncertainties, that is, the determination of relative influences of individual uncertain input motions and uncertain material properties on the resulting uncertain seismic wave propagation, is known as the global sensitivity analysis. A global sensitivity analysis, namely, the Sobol' sensitivity analysis, is included in the proposed framework. Uncertain input, bedrock motions are obtained using the ground motion prediction equations of Fourier amplitude spectra and Fourier phase derivative, and they are modeled as a non-stationary random process. Stochastic elasto-plastic soil properties are represented as heterogeneous random fields. The random process and the random fields are discretized in the probabilistic space using an orthogonal Hermite polynomial chaos (PC) basis. The probabilistic system response is obtained efficiently using the Galerkin stochastic FEM. The Sobol' sensitivity analysis is conducted for the PC-represented uncertain system response. The benefits of the presented framework to the site-specific probabilistic seismic hazard analysis are discussed. The novel approach enables to take into account the uncertainty in both, seismic load and elasto-plastic material parameters, and to assess their individual influences on the overall uncertainty in the resulting wave field accurately and efficiently. The presented framework has been implemented into Real-ESSI Simulator and, here, it is evaluated and demonstrated to be very useful for the seismic site response analysis.
... Therefore, when the difference is small, the influence of parameter interactions is negligible. 57 When K and V are taken as the target parameters, the S i and S Ti of parameters D 1 , L 1 , d 2 , and P on K and V are shown in Fig. 30. ...
In this study, a series dual-chamber self-excited oscillation nozzle (SDSON) for atomization was developed for photodecomposition of oily wastewater. In order to address the computational complexity associated with optimizing this nozzle, a surrogate model that integrates computational fluid dynamics simulation is proposed. By employing a multi-objective optimization algorithm that combines Genetic Algorithm and Non-dominated Sorting Genetic Algorithm II, significant improvements in atomization performance have been achieved. The influencing factors of atomization and their interactions on the nozzle's atomization performance have been analyzed. The entropy weight method was employed in conjunction with gray theory to rank the optimal solutions based on weighted correlation evaluation, resulting in the determination of the most favorable design solutions. The optimized design exhibited significant enhancements in turbulence kinetic energy and gas volume fraction at the nozzle outlet. Atomization experiments confirmed that the optimized SDSON generated smaller and more uniformly sized droplets under identical inlet pressure conditions, thereby greatly improving atomization performance.
... A promising approach to allow detailed global sensitivity analysis on computationally expensive simulations is the introduction of a surrogate model to approximate the full system. Polynomial chaos expansion (PCE) models are becoming increasingly popular for this purpose (e.g., Sudret, 2008;Le Gratiet et al., 2017;Abbiati et al., 2021;Eldred and Burkardt, 2009). They span the full uncertainty domain with a set of orthogonal polynomials. ...
Uncertainty quantification (UQ) is a well-established category of methods to estimate the effect of parameter variations on a quantity of interest based on a solid mathematical foundation. In the wind energy field most UQ studies focus on the sensitivity of turbine loads. This article presents a framework, wrapped around a modern Python UQ library, to analyze the impact of uncertain turbine properties on aeroelastic stability. The UQ methodology applies a polynomial chaos expansion surrogate model. A comparison is made between different wind turbine simulation tools on the engineering model level (alaska/Wind, Bladed, HAWC2/HAWCStab2, and Simpack). Two case studies are used to demonstrate the effectiveness of the method to analyze the sensitivity of the aeroelastic damping of an unstable turbine mode to variations of structural blade cross-section parameters. The code-to-code comparison shows good agreement between the simulation tools for the reference model, but also significant differences in the sensitivities.
... parameters and analyzing their impact on the system output, SA enables us to identify and prioritize the most influential factors in the design process (Abbiati et al., 2021). There are two types into which SA techniques can be classified: local and global. ...
... Gray-box models take a more comprehensive approach by acknowledging that the computational model may not fully capture the system's complexity and thus, incorporating both knowledgedriven and data-driven elements. As an example, hybrid simulation, which combines physical and numerical substructures to create a hybrid model (Schellenberg et al., 2009;Abbiati et al., 2021), follows a gray-box modeling paradigm. Recently, machine learning approaches using physics-informed neural networks (Raissi et al., 2019) have been employed to perform gray-box modeling, e.g. in the work of Yan et al. (2022). ...
Computer simulations (a.k.a. white-box models) are more indispensable than ever to model intricate engineering systems. However, computational models alone often fail to fully capture the complexities of reality. When physical experiments are accessible though, it is of interest to enhance the incomplete information offered by computational models. Gray-box modeling is concerned with the problem of merging information from data-driven (a.k.a. black-box) models and white-box (i.e., physics-based) models. In this paper, we propose to perform this task by using multi-fidelity surrogate models (MFSMs). A MFSM integrates information from models with varying computational fidelity into a new surrogate model. The multi-fidelity surrogate modeling framework we propose handles noise-contaminated data and is able to estimate the underlying noise-free high-fidelity function. Our methodology emphasizes on delivering precise estimates of the uncertainty in its predictions in the form of confidence and prediction intervals, by quantitatively incorporating the different types of uncertainty that affect the problem, arising from measurement noise and from lack of knowledge due to the limited experimental design budget on both the high- and low-fidelity models. Applied to gray-box modeling, our MFSM framework treats noisy experimental data as the high-fidelity and the white-box computational models as their low-fidelity counterparts. The effectiveness of our methodology is showcased through synthetic examples and a wind turbine application.
... To reduce the computational time of high-fidelity simulations, surrogate models have been developed. Classical methods, such as Gaussian processes, Kriging, Polynomial chaos, etc., depend on a limited set of parameters [4,5,6,7,8]. Uncertainty quantification has benefited from the development of neural networks which account for a larger number of parameters and reduce the a priori selection of influential variables. ...
... A promising approach to allow detailed global sensitivity analysis on computationally expensive simulations, is the introduction of a surrogate 30 model to approximate the full system. Polynomial Chaos Expansion (PCE) models are becoming increasingly popular for this purpose (e.g., Sudret, 2008;Le Gratiet et al., 2017;Abbiati et al., 2021;Eldred and Burkardt, 2009). PCE models span the full uncertainty domain with a set of orthogonal polynomials. ...
Uncertainty quantification (UQ) is a well-established category of methods to estimate the effect of parameter variations on a quantity of interest, based on a solid mathematical fundament. In the wind energy field most UQ studies were focused on the sensitivity of turbine loads. This article presents a framework, wrapped around a modern Python UQ library, to analyze the impact of uncertain turbine properties on aeroelastic stability. The UQ methodology applies a polynomial chaos expansion surrogate model to increase the numerical efficiency. A comparison is made between different wind turbine simulation tools on the engineering model level (alaska/Wind, Bladed, HAWC2/HAWCStab2 and Simpack). Two case studies are used to demonstrate the effectiveness of the method to analyze the sensitivity of the aeroelastic damping of an unstable turbine mode to variations of structural blade cross section parameters. The code-to-code comparison shows a good agreement between the simulation tools for the reference model, but also significant differences in the sensitivities.
... It can also used to determine which parameters have a greater impact on the system or model. [21][22][23][24][25][26][27] Greco and Trentadue 28 proposed a reliability sensitivity evaluation model using the time domain covariance theory, through which the sensitivity statistics of different quantities of dynamic response with respect to structural parameters can be achieved. Zhang et al. 29 studied the sensitivity analysis based on the frequency reliability theory and Sobol' theory. ...
The sensitivity analysis model is frequently used to express the influence of conditional elements on structural reliability. However, the traditional sensitivity analysis model is limited to a few influencing factors, and has a small scope of application. In this paper, a modified sensitivity model is proposed by combining the optimal polynomial response surface function with the Sobol sensitivity algorithm. And the sensitivity calculation approach was combined with coupling factor test design, range verification, multi-body dynamics analysis and structural statics analysis, which enables to achieve the quantitative sensitivity value of the influence of conditional factors on structural reliability. Finally, a typical harvester structure is selected as a case, to verify the evaluation accuracy and effectiveness of the revised model. The results show that the sensitivity of threshing drum speed has the greatest influence, while the sensitivity of granary load has the least influence. The average quantitative prediction accuracy of revised approach is up to 97.36%. The revised model can accurately evaluate the sensitivity value of coupled influencing factors for industrial equipment.
... Gradient interpretability has also been studied for this purpose in [259][260][261]. In [262], a GSA framework for hybrid surrogates that merge physical and numerical substructures is presented and applied to a structural dynamic problem modeled by a PCE-based surrogate. ...
The use of Machine Learning (ML) has rapidly spread across several fields of applied sciences, having encountered many applications in Structural Dynamics and Vibroacoustic (SD&V). An advantage of ML algorithms compared to traditional techniques is that physical phenomena can be modeled using only sampled data from either measurements or simulations. This is particularly important in SD&V when the model of the studied phenomenon is either unknown or computationally expensive to simulate. This paper presents a survey on the application of ML algorithms in three classical problems of SD&V: structural health monitoring, active control of noise and vibration, and vibroacoustic product design. In structural health monitoring, ML is employed to extract damage-sensitive features from sampled data and to detect, localize, assess, and forecast failures in the structure. In active control of noise and vibration, ML techniques are used in the identification of state-space models of the controlled system, dimensionality reduction of existing models, and design of controllers. In vibroacoustic product design, ML algorithms can create surrogates that are faster to evaluate than physics-based models. The methodologies considered in this work are analyzed in terms of their strength and limitations for each of the three considered SD&V problems. Moreover, the paper considers the role of digital twins and physics-guided ML to overcome current challenges and lay the foundations for future research in the field.
... For GSA, lain hypercube sampling of a parametric range is considered, where sensitivity analysis values are averaged at the end. Other approaches for GSA, such as Sobol's sensitivity indices can be used with a surrogate model minimizing the repeated solution of the hybrid model(Abbiati et al., 2021). Parameter significance can be measured based on sensitivity indices ranging from 0 to 1(Tsipa et al., 2018).4.3 | Mapping the black-box component and architecture4.3.1 | ANN-based hybrid modelsThough there is a range of data-driven modeling approaches to map the black-box part of a hybrid model, ANNs are most widely adopted for nonlinear, complex systems to predict multiple responses simultaneously, whilst taking multiple independent predictors as input(Noll & Henkel, 2020). ...
Hybrid modeling, with an appropriate blend of the mechanistic and data‐driven framework, is increasingly being adopted in bioprocess modeling, model‐based experimental design (digital‐twin), identification of critical process parameters, and optimization. However, the development of a hybrid model from experimental data is an inherently complex workflow, involving designed experiments, selection of the data‐driven process, identification of model parameters, assessment fitness, and generalization capability. Depending on the complexity of the process system and purpose, each piece of these modules can flexibly be incorporated into the puzzle. However, this extra flexibility can be a cause of concern to trace an “optimal” model structure. In this paper, the development of hybrid models in a common bioprocess system, selection of data‐driven components and their mapping to states, choice of parameter identification techniques, and model quality assurance are revisited. The challenges associated with hybrid‐model development, and corrective actions have also been reviewed. The review also suggests the lack of data, and code sharing in communal repositories can be a hurdle in the exploration, and expansion of those tools in a bioprocess system.
... Hence, the exact purpose of these tools is to prioritize the important data and eliminate the trivial data to optimize the system and reduce over-design (Cacuci et al., 2005). Thus, a sensitivity analysis (SA) is used in different sciences and engineering fields (Toufiq and Hadid, 2018;Ranjbar and Saffar, 2016;Tian, 2012;Zhang et al., 2020aZhang et al., , 2020bAbbiati et al., 2021). In general, the SA methods are divided into local and global methods; the first category is known as one-at-a-time methods, i.e. ...
Purpose
This paper aims to introduce the usage of sensitivity analysis (SA) for the problem of faults identification in three-phase induction motors (IMs). These motors are susceptible to different kinds of faults that should be detected in a proper time to keep the systems working in a safety environment.
Design/methodology/approach
One of the effective approaches for faults identifications, which is presented in the literature, is a model-based strategy. This strategy mainly depends on using a software model to make an identification decision. Therefore, this work intends to examine the model sensitivity towards variables’ variation. The SA toolbox of Matlab R2017b package is used for this purpose since the Matlab software is a well-known environment, and it is easy for a nonstatistical person to deal with it. As a study case, open-circuit and stator inter-turn faults in the stator windings of a three-phase IM have been chosen.
Findings
The results show that the model-based strategy is considerably speed up by up to 30% when neglecting the trivial model’s parameters with the same accurate identification decision as compared with the results of this strategy without using the SA.
Originality/value
The novelty of this work is summarized in devoting the usage of SA in the field of faults identification to enhance the speed of final decision.
... effects are computed [44][45][46]. Univariate effects can be defined as the conditional expectation of a quantity of interest as a function of a single parameter, where expectations are taken over all other parameters: ...
The mechanical properties of 3D printed materials produced with additive manufacturing depend on the printing process, which is controlled by several tuning parameters. This paper focuses on Binder Jet technology and studies the influence of printing resolution, activator percentage, droplet mass, and printing speed on the compressive and flexural strength, as well as on the Young’s modulus of the bulk printed material. As the number of tests required using a one factor at a time approach is not time efficient, a Design of Experiments approach was applied and optimal points in the 4-dimensional parameter space were selected. Then Sobol’ sensitivity indices were calculated for each mechanical property through polynomial chaos expansion. We found that the mechanical properties are primarily controlled by the binder content of the bulk material, namely printing resolution and droplet mass. A smaller dependence on the activator percentage was also found. The printing speed does not affect the mechanical properties studied. In parallel, curing of the specimens at 80–115 °C for 30–120 min increases their strength.
... To reduce the computational time of high-fidelity simulations, surrogate models have been developed. Classical methods, such as Gaussian processes, Kriging, Polynomial chaos, etc., depend on a limited set of parameters [4,5,6,7,8]. Uncertainty quantification has benefited from the development of neural networks which account for a larger number of parameters and reduce the a priori selection of influential variables. ...
With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks (CNN) or Physics-Informed Neural Networks (PINN), are restricted to the prediction of solutions in a predefined configuration. With neural operators, one can learn the general solution of Partial Differential Equations, such as the elastic wave equation, with varying parameters. There have been very few applications of neural operators in seismology. All of them were limited to two-dimensional settings, although the importance of three-dimensional (3D) effects is well known. In this work, we apply the Fourier Neural Operator (FNO) to predict ground motion time series from a 3D geological description. We used a high-fidelity simulation code, SEM3D, to build an extensive database of ground motions generated by 30,000 different geologies. With this database, we show that the FNO can produce accurate ground motion even when the underlying geology exhibits large heterogeneities. Intensity measures at moderate and large periods are especially well reproduced. We present the first seismological application of Fourier Neural Operators in 3D. Thanks to the generalizability of our database, we believe that our model can be used to assess the influence of geological features such as sedimentary basins on ground motion, which is paramount to evaluating site effects.
... As such, variance-based global sensitivity analysis is conducted in this section for the FE-predicted load capacity with and without considering model uncertainty. To this end, this section adopts the polynomial chaos expansion (PCE)-based Sobol indices (Sudret 2008), which has been previously employed as a sensitivity measure in different fields such as geotechnical earthquake engineering (Abbiati et al. 2021) and structural dynamics (Hariri-Ardebili et al. 2021). ...
Inherent uncertainties associated with masonry structures result in large scatter in experimentally or analytically predicted behavior. Rigorous investigation of uncertainties in the structural behavior of masonry structures is of paramount importance to lay down the basis for reliable structural design. In this study, the probabilistic behavior of reinforced masonry walls under out-of-plane (OOP) loading was investigated. Uncertainties in material and geometric properties were incorporated in finite-element (FE) models for probabilistic structural analysis. The individual and combined effect of different uncertain input parameters on the overall probabilistic behavior was evaluated. Furthermore, the relative importance of uncertain variables to the load and deformation capacities was assessed using variance-based sensitivity analysis. The model uncertainty in FE-predicted load capacity was quantified to characterize the model error. The results indicate that model uncertainty contributes to the variance in lateral load capacity more than all the other uncertainties in material and geometric properties.
... metamodel), representing the outputs of the model by a polynomial function of its inputs [28,29]. It is proven to be a powerful surrogate technique used in a wide variety of engineering contexts to replicate the dynamic response of complex high-dimensional models [30][31][32][33][34][35]. Hence, it can be seen as a promising technique for MOR of NS in HS. ...
Hybrid simulation is used to investigate the dynamic response of a system by combining numerical and physical substructures. To ensure high fidelity results, it is necessary to conduct hybrid simulation in real-time. One challenge in real-time hybrid simulation originates from high-dimensional nonlinear numerical substructures and, in particular, from the computational cost linked to the accurate computation of their dynamic responses. When the computation takes longer than the actual simulation time, time delays are introduced distorting the simulation timescale. In such cases, the only viable solution for performing hybrid simulation in real-time is to reduce the order of such complex numerical substructures. In this study, a model order reduction framework is proposed for real-time hybrid simulation, based on polynomial chaos expansion and feedforward neural networks. A parametric case study is used to validate the framework. Selected numerical substructures are substituted with their respective reduced-order models. To determine the framework’s robustness, parameter sets are defined covering the design space of interest. Comparisons between the full- and reduced-order hybrid model response are delivered. The attained results demonstrate the performance of the proposed framework.
... Literature [41,42,43,44] can quantitatively realize the sensitivity relationship between influencing parameters and structural reliability. However it lacks the consideration of global sensitivity, without considering the integrated effects of external influencing parameters [45,46,47,48,49,50,51]. It is challenging to evaluate the structural reliability under complex conditions precisely. ...
The sensitivity analysis model is widely used to describe the impacts of condition parameters on structural reliability. However, the classical sensitivity analysis model is limited to the small number of influence parameters and has no high prediction accuracy. Integrating the response surface function - Kriging model with Sobol sensitivity algorithm, a revised sensitivity model is proposed in this paper. And the quantitative sensitivity analysis for the influence of condition parameters on structural reliability are achieved through combining the revised sensitivity model with the experimental design of coupling parameters, range verification, the multi-body dynamics analysis and the structural statics analysis. The proposed analysis model is mainly applied in large structures with multiple influence parameters. Finally, a typical port crane is adopted to verify the accuracy and effectiveness of the proposed model. The results reveal that among the multiple parameters, the biggest sensitivity influence is the trolley position, while the least one is the lifting speed. The average prediction accuracy of the quantitative structural reliability index for the influencing parameters is up to 95.91%. The revised sensitivity model enables the accurate assessment of structural relativity with plenty of coupling condition parameters.
... The metamodeling technique presents a promising alternative to reduce the computational costs in uncertainty quantification such as polynomial chaos expansion (PCE) (Blatman and Sudret 2010), support vector regression (SVR) (Smola and Schölkopf 2004), artificial neural network (ANN) (Abebe and Price 2004), and kriging (Matheron 1963). Among these methods, PCE uses a set of multivariate orthogonal polynomials of the input variables to approximate the model response and therefore presents a global method to comprehensively evaluate the structural response (Wan and Karniadakis 2005;Gerritsma et al. 2010;Abbiati et al. 2015Abbiati et al. , 2021; meanwhile, kriging provides an accurate surrogate for the points attached to the training points (Dimitrov et al. 2018). Efforts have been devoted to integrating the surrogate technique with nonlinear autoregressive with exogenous input (NARX) modeling to account for the potential uncertainties with lower computational cost (Spiridonakos and Chatzi 2015;Mai 2016;Gao et al. 2021). ...
Real-time hybrid simulation (RTHS) provides an efficient and effective experimental technique for rate-dependent energy-dissipation devices in seismic hazard mitigation. The structure under investigation is generally divided into analytical and physical substructures to enable large-scale experiments for system behavior. Accurate modeling of analytical substructures is critical for truthful structural response replication through RTHS. This presents challenges to laboratory practice of RHTS such as capability of specialized finite-element software to replicate complex nonlinear behavior, and the equipment capacity to accommodate large-scale finite-element modeling to be executed in a real-time manner. This study explores the use of a polynomial chaos nonlinear autoregressive with exogenous input (PC-NARX) model to conduct RTHS in laboratories using existing equipment and general-purpose finite-element analysis (FEA) software readily available in earthquake engineering research. The NARX model can be trained using any existing FEA software for a good representation of structural dynamics. Polynomial chaos expansion (PCE) is then introduced to surrogate NARX model coefficients to account for ground motion uncertainties. Laboratory tests of a self-centering viscous damper were conducted as proof of concept to experimentally demonstrate the effectiveness of RTHS with PC-NARX metamodeling approach. The results were further compared with the kriging surrogate technique for NARX model coefficients to explore a better technique to account for uncertainties in RTHS.
... Sensitivity analysis (SA) is a tool that has been recently receiving increasing attention in the analysis of many engineering systems since it offers a comprehensive evaluation of how the system properties can affect the system's response [1]. It allows for identifying the most critical parameters that affect the energy harvesting dynamic response. ...
Parametric variability is inevitable in actual energy harvesters. It can significantly affect crucial aspects of the system performance, especially in harvesting systems that present geometric parameters, material properties, or excitation conditions that are susceptible to small perturbations. This work aims to develop an investigation to identify the most critical parameters in the dynamic behavior of asymmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation properties. For this purpose, a global sensitivity analysis based on orthogonal variance decomposition, employing Sobol indices, is performed to quantify the effect of the harvester parameters on the variance of the recovered power. This technique quantifies the variance concerning each parameter individually and collectively regarding the total variation of the model. The results indicate that the frequency and amplitude of excitation, asymmetric terms and electrical proprieties of the piezoelectric coupling are the most critical parameters that affect the mean power harvested. It is also shown that the order of importance of the parameters can change according to the stability of the harvester’s dynamic response. In this way, a better understanding of the system under analysis is obtained since the study allows the identification of vital parameters that rule the change of dynamic behavior and therefore constitutes a powerful tool in the robust design, optimization, and response prediction of nonlinear harvesters.
... Although the RF surrogate presents bias and smoothing effects, Chai et al. [151] showed an overall good agreement of the sensitivity indexes obtained by the Fourier amplitude sensitivity test (FAST) and OOBbased method and highlighted that the latter can be more easily interpreted. Abbiati et al. [152] show a framework to do global sensitivity analysis in hybrid surrogates, which merge physical and numerical substructures, showing an application in a structural dynamic problem modeled by polynomial chaos expansion surrogates. With a similar method, Abbiati et al. [84] creates a hybrid model for buckling failure reliability analysis using a GP classifier, obtaining a failure surface prediction with good accuracy against experimental and analytical references. ...
The use of Machine Learning (ML) has rapidly spread across several fields, having encountered many applications in Structural Dynamics and Vibroacoustic (SD&V). The increasing capabilities of ML to unveil insights from data, driven by unprecedented data availability, algorithms advances and computational power, enhance decision making, uncertainty handling, patterns recognition and real-time assessments. Three main applications in SD&V have taken advantage of these benefits. In Structural Health Monitoring (SHM), ML detection and prognosis lead to safe operation and optimized maintenance schedules. System identification and control design are leveraged by ML techniques in Active Noise Control (ANC) and Active Vibration Control (AVC). Finally, the so-called ML-based surrogate models provide fast alternatives to costly simulations, enabling robust and optimized product design. Despite the many works in the area, they have not been reviewed and analyzed. Therefore, to keep track and comprehend this ongoing integration of fields, we intend to make the first survey of ML applications in SD&V analyses, shedding light on the current state of implementation and emerging opportunities. For each of the three applications mentioned, we identified the main methodologies, advantages, limitations, and recommendations based on scientific knowledge. Moreover, we discuss the role of Digital Twins and Physics Guided ML to overcome current challenges and power future research progress. As a result, the survey provides a broad overview of the present landscape of ML applied in SD&V and guides the reader to an advanced understanding of progress and prospects in the field.
... HS is a desirable dynamic response testing technique, and it is widely used across different engineering applications [3][4][5][6][7][8][9][10], since it combines the versatility and risk-free testing of numerical simulations along with the realism of experimental campaigns. However, ensuring high fidelity of hybrid dynamic response simulations of a loading-rate-sensitive prototype often necessitates performing HS in real-time. ...
Hybrid simulation is used to obtain the dynamic response of a system whose components consist of physical and numerical substructures. The coupling of these substructures is achieved by actuation systems, which are commanded in closed-loop control setting. To ensure high fidelity of such hybrid simulations, performing them in real-time is necessary. However, real-time hybrid simulation poses challenges since the inherent dynamics of the actuation system introduce time delays, thus modifying the dynamic response of the investigated system. Therefore, a tracking controller is required to adequately compensate for such time delays. In this study, a novel tracking controller is proposed for dynamics compensation in real-time hybrid simulations. It is based on adaptive model predictive control, a linear time-varying Kalman filter, and a real-time model identification algorithm. Within the latter, auto-regressive exogenous polynomial models are identified in real-time to estimate the changing plant dynamics. A parametric virtual case study, encompassing a virtual motorcycle, is used to validate the performance and robustness of the proposed controller. Results demonstrate the effectiveness of the proposed controller for real-time hybrid simulations.
... This is the so-called lowdata regime. Sparse PCE techniques, which aim to compute an expansion involving only few terms, have proven especially powerful and cost-efficient for real-world engineering problems such as, among many others, surrogate-assisted robust design optimization (Chatterjee et al., 2019), hybrid simulation for earthquake engineering (Abbiati et al., 2021), dam engineering (Guo et al., 2019;Hariri-Ardebili and Sudret, 2020), and wind turbine design (Slot et al., 2020). Note that real-world applications are typically not exactly sparse; however, sparse regression-based PCE is a useful tool to find good approximations at low computational cost. ...
... Sensitivity analysis is an advantageous tool to study the influence of various independent variables on a given dependent variable under a set of assumptions (Orta and Bartlett, 2020;Abbiati et al., 2021). Therefore, the goal here is to determine what are the impacts of vertical force and transversal tension on the SIFs in the vicinity of the crack tip. ...
Civil engineering structures play an important role in any country for improving the economy together with the social and environmental welfare. An unwanted failure might cause significant impacts at different levels for the structure owner and for users. Fatigue is one of the main degradation processes on steel structures that causes structural failure before the end of the designed service life. To avoid unexpected failures due to fatigue, a comprehensive structural Life Cycle Management (LCM) is required to minimize the life-cycle cost and maximize the structural service life. One of the main objectives within the LCM can be related to optimizing the structural maintenance planning. Achieving this goal is a challenging task which requires to address some challenges such as predicting the structural performance under uncertainty, employing Structural Health Monitoring (SHM) data to reduce uncertainties, taking into account crack propagation behavior for given components, reliability and cost-informed decision making, and effect of maintenance actions among others. Accordingly, following contributions are considered in this research to improve the capabilities of structural LCM which are explained shortly in the sequel.Developing a new time-dependent reliability method for fatigue reliability analysis.Investigating the effectiveness of advanced crack propagation tools to study unwanted fatigue cracking problems and characterizing some possible repair actions on a real case study.Introducing the assumptions and simplification steps required to integrate the proposed time-dependent reliability method with crack propagation models to approximate the time-dependent fatigue reliability.As the first contribution of this thesis, a new time-dependent reliability method called AK-SYS-t is proposed. This method provides an efficient and accurate tool to evaluate time-dependent reliability of a component compared to other available methods. AK-SYS-t relates the time-dependent reliability to system reliability problems and tries to exploit the efficient system reliability methods such as AK-SYS towards time-dependent reliability analysis. It is worth mentioning that time-dependent reliability analysis is necessary in this context since the performance deterioration (such as fatigue) is a time-dependent process associated with time-dependent parameters such as fatigue loading.Another related topic is the study of crack propagation phenomenon with advanced modeling tools such as Finite Element Method (FEM) and eXtended Finite Element Method (XFEM). For illustration purposes, the crack in the root of a fillet weld is considered (common fatigue detail in bridges with orthotropic deck plates). One important issue investigated herein is the influence of the transversal tension in the deck plate on the direction of the crack propagation. It is shown how increasing the transversal tension in the deck plate may change the crack propagation towards the deck plate. Such cracks are considered dangerous since they are hard to inspect and detect. In the end, XFEM is used to investigate the effectiveness of two possible repair solutions.A supplementary contribution is related to introducing the required steps in order to integrate the newly developed time-depend reliability method with crack propagation problems through some applicational examples. This is a challenging task since performing the time-dependent reliability analysis for such problems requires a cycle-by-cycle calculation of stress intensity factors which requires huge computational resources. Therefore, the aim here is to introduce the assumptions and simplification steps in order to adopt the AK-SYS-t for fatigue reliability analysis. Accordingly, two examples are considered. (...)
... metamodel), representing the outputs of the model by a polynomial function of its inputs [28,29]. It is proven to be a powerful surrogate technique used in a wide variety of engineering contexts to replicate the dynamic response of complex high-dimensional models [30,31,32,33]. Hence, it can be seen as a promising technique for MOR of NS in HS. ...
Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario by combining numerical and physical substructures. To ensure high fidelity of the simulation results, it is often necessary to conduct hybrid simulation in real-time. One of the challenges arising in real-time hybrid simulation originates from high-dimensional nonlinear numerical substructures and, in particular, from the computational cost linked to the computation of their dynamic responses with sufficient accuracy. It is often the case that the simulation time-step must be decreased to capture the dynamic behavior of numerical substructures, thus resulting in longer computation. When such computation takes longer than the actual simulation time, time delays are introduced and the simulation timescale becomes distorted. In such a case, the only viable solution for doing hybrid simulation in real-time is to reduce the order of such complex numerical substructures.In this study, a model order reduction framework is proposed for real-time hybrid simulation, based on polynomial chaos expansion and feedforward neural networks. A parametric case study encompassing a virtual hybrid model is used to validate the framework. Selected numerical substructures are substituted with their respective reduced-order models. To determine the robustness of the framework, parameter sets are defined to cover the design space of interest. A comparison between the full- and reduced-order hybrid model response is delivered. The attained results demonstrate the performance of the proposed framework.
... In other words, it may aid in finding the parameters that most affect the system response. In this way, it has been receiving increasing attention in many engineering systems, giving a comprehensive approach to how an input data variation can affect the underlying system response [1]. ...
Parametric variability is inevitable in actual energy harvesters and can define crucial aspects of the system performance, especially in susceptible systems to small perturbations. In this way, this work aims to identify the most critical parameters in the dynamics of (a)symmetric bistable energy harvesters with nonlinear piezoelectric coupling, considering the variability of their physical and excitation parameters. For this purpose, a global sensitivity analysis based on the Sobol' indices is performed by an orthogonal decomposition in terms of conditional variances to access the dependence of the recovered power concerning the harvester parameters. This technique quantifies the variance concerning each parameter individually and jointly regarding the total variation of the model. The results indicate that the frequency and amplitude of excitation, asymmetric bias angle, and piezoelectric coupling at the electrical domain are the most influential parameters that affect the mean power harvested. It has also been shown that the order of importance of the parameters can change from stable conditions. In possession of this, a better understanding of the system under analysis is obtained, identifying vital parameters that rule the change of dynamic behavior and constituting a powerful tool in the robust design and prediction of nonlinear harvesters.
... A recent version of Kriging, known as the polynomial-chaos-Kriging (PC-Kriging; Kersaudy et al., 2015;Schobi et al., 2015), uses the PCE result as the trend term of Kriging and, thus, inherits the attributes of both the PCE and Kriging methods, although more unknown parameters increase the risk of over-fitting. When a reliable surrogate model is built up, uncertainty propagation with any assumption of uncertain parameter distribution and GSA can be rapidly computed; the variance-based sensitivity analysis (often referred to as the Sobol method or Sobol index) is a powerful tool to analyze the global sensitivity of each uncertain parameter (Abbiati et al., 2021;Saltelli et al., 2008Saltelli et al., , 2010Sobol, 1993Sobol, , 2001). ...
Accurate simulation of pipe transient wave is crucial for the design, reliability assessment, and defect detection of water supply systems. However, this is a difficult task since the wave propagation media in pipeline systems are often highly complex and involve a range of uncertainties. Experimental data show that key parameters such as valve closure time, wave speed, and pipe material coefficients are strongly uncertain and stochastic that may vary in a wide range. To analyze the transient behavior in such complex environments, surrogate models are built to realize the fast computation of uncertainty propagation. Three surrogate modeling methods, i.e., the polynomial‐chaos‐expansion, ordinary‐Kriging, and polynomial‐chaos‐Kriging, are tested and compared in terms of transient wave forecast accuracy. The global sensitivity is then analyzed via the Sobol index method, by which the most influential uncertainty sources on various transient signal features are identified.
... Before HFT starts, the coordination algorithm solves the hybrid model response with no thermal and mechanical loading until actuator restoring forces approach zero. Fig. 2 shows the experimental setup (see Ref. [3] for more details). ...
Fire testing of large-scale structural prototypes is costly and requires highly specialized facilities. For this reason, most of the research on the structural response to fire loading relies on cheaper single-component experiments. However, such experiments do not reproduce the internal force redistribution in a realistic assembly, which plays a pivotal role in determining the failure mode of every component. Hybrid fire testing overcomes this limitation by harnessing fire experiments and numerical simulations in a closed feedback loop. Specifically, the boundary conditions of the tested specimen are updated on-the-fly to match those of a numerically simulated subassembly. In order to test gypsum-plasterboard-based wall assemblies under realistic loading scenarios, the Danish Institute of Fire and Security Technology has recently implemented hybrid fire testing. This paper describes the developed hybrid testing setup and the results of a demonstrative experimental campaign.
... Due to its closed-loop nature, a successful RTHS framework needs to control the delays and noises in the interfacing actuator and sensor systems, as they tend to bring destabilizing effect into RTHS, causing large experimental error or even failure (Christenson et al., 2014;Maghareh et al., 2014;Hayati and Song, 2017). Research studies have also been conducted to quantify uncertainties in RTHS due to experimental errors (Sauder et al., 2019) and modeling choices (Abbiati et al., 2021). ...
As an attractive renewable energy source, offshore wind plants are becoming increasingly popular for energy production. However, the performance assessment of offshore wind turbine (OWT) structure is a challenging task due to the combined wind-wave loading and difficulties in reproducing such loading conditions in laboratory. Real-time hybrid simulation (RTHS), combining physical testing and numerical simulation in real-time, offers a new venue to study the structural behavior of OWTs. It overcomes the scaling incompatibilities in OWT scaled model testing by replacing the rotor components with an actuation system, driven by an aerodynamic simulation tool running in real-time. In this study, a RTHS framework for monopile OWTs is proposed. A set of sensitivity analyses is carried out to evaluate the feasibility of this RTHS framework and determine possible tolerances on its design. By simulating different scaling laws and possible error contributors (delays and noises) in the proposed framework, the sensitivity of the OWT responses to these parameters are quantified. An example using a National Renewable Energy Lab (NREL) 5-MW reference OWT system at 1:25 scale is simulated in this study to demonstrate the proposed RTHS framework and sensitivity analyses. Three different scaling laws are considered. The sensitivity results show that the delays in the RTHS framework significantly impact the performance on the response evaluation, higher than the impact of noises. The proposed framework and sensitivity analyses presented in this study provides important information for future implementation and further development of the RTHS technology for similar marine structures.
... Cross-fertilization between the two disci-1 plines is nowadays the norm, rather than an exception, and for good reasons. Physics-informed neural networks are reaching unprecedented approximation power in UQ applications (see, e.g., (Raissi et al., 2019;Pang et al., 2019)), while sparse polynomial chaos expansions are used as denoising regressors in Torre et al. (2019a), as high-dimensional regression tools in Lataniotis et al. (2020), and on real-world experimental data in Abbiati et al. (2021). UQ-born Gaussian process modeling Santner et al. (2003); Rasmussen and Williams (2006) is now a staple tool in ML Rasmussen and Williams (2006), while support vector machines (Vapnik, 2013) found their way in rare event estimation (Bourinet, 2016;Moustapha et al., 2018). ...
Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models such as kriging or polynomial chaos expansions tend to struggle with highly nonlinear, localized, or nonstationary computational models. We hereby propose a novel sequential adaptive surrogate modeling method based on recursively embedding locally spectral expansions. It is achieved by means of disjoint recursive partitioning of the input domain, which consists in sequentially splitting the latter into smaller subdomains, and constructing simpler local spectral expansions in each, exploiting the trade-off complexity vs. locality. The resulting expansion, which we refer to as "stochastic spectral embedding" (SSE), is a piecewise continuous approximation of the model response that shows promising approximation capabilities, and good scaling with both the problem dimension and the size of the training set. We finally show how the method compares favorably against state-of-the-art sparse polynomial chaos expansions on a set of models with different complexity and input dimension.
Extensive simulations of complex computational models are typically required to acquire accurate prediction of structural responses under seismic loading. Traditional mechanics-based or phenomenological models however often struggle to capture the behavior of complex components. This study proposes integrating real-time hybrid simulation (RTHS) with deep gated recurrent units (GRU) network for accurate dynamic response prediction of structural systems with parts challenging for modeling. The GRU network, trained using RTHS data, enables accurate assessments of structural responses. To optimize training of the GRU network, a cross-validation (CV)-Voronoi adaptive sampling method is introduced to minimize the number of RTHS experiments. A two-story steel frame equipped with self-centering viscous dampers (SC-VD) is designed as a proof-of-concept to validate the proposed method. To account for the effects of uncertainty, a non-stationary stochastic earthquake ground motion model is used to generate the seismic waves for training. The final GRU network is then validated against additional tests. The results demonstrate that the proposed method holds promise for efficient and accurate prediction of dynamic response of structural systems.
Sensitivity analysis is used to quantify the contribution of the uncertainty of input variables to the uncertainty of systematic output responses. For tolerance design in manufacturing and assembly, sensitivity analysis is applied to help designers allocate tolerances optimally. However, different sensitivity indices derived from different sensitivity analysis methods will always lead to conflicting results. It is necessary to find a sensitivity index suitable for tolerance allocation to transmission mechanisms so that the sensitivity results can truly reflect the effects of tolerances on kinematic and dynamic performances. In this paper, a variety of sensitivity indices are investigated and compared based on hybrid simulation. Firstly, the hybrid simulation model of the crank-slider mechanism is established. Secondly, samples of the kinematic and dynamic responses of the mechanism with joint clearances and link length errors are obtained, and the surrogate model established using polynomial chaos expansion (PCE). Then, different sensitivity indices are calculated based on the PCE model and are further used to evaluate the effect of joint clearances and link length errors on the output response. Combined with the tolerance-cost function, the corresponding tolerance allocation schemes are obtained based on different sensitivity analysis results. Finally, the kinematic and dynamic responses of the mechanism adopting different tolerance allocation schemes are simulated, and the sensitivity index corresponding to the optimal response is determined as the most appropriate index.
Most of hybrid simulation platforms (HSPs) that use OpenSees for structural hybrid testing research are developed based on OpenFresco framework software. Although OpenFresco is mature and reliable, it can only communicate with specific hydraulic servo actuator control systems, which limits the diversity and flexibility of HSP development. Matlab has powerful independent development functions, and has a wide range of communication interface advantages with many finite element software and actuator control systems. Therefore, Matlab can be used as the communication medium between OpenSees and actuator control system in this study. Firstly, the controller-extensible HSP based on Matlab-OpenSees frameworks is developed. Then, the core establishment details of HSP, including core architecture, hardware system, and DELTA-Matlab-OpenSees system, are analyzed and described in detail. Next, the dynamic loading tests on the spring components are carried out when the HSP is subjected to continuously changing working conditions in the wide frequency domain and displacement amplitude domain. The comparative analysis results on the target displacement curve and the measured displacement curve verify the accuracy and robustness of the inner control loop of HSP. Next, the hybrid tests on a three-story reinforced concrete frame structure with linear springs are implemented under different seismic wave excitations. The comparative research on the hybrid test results and time-history analysis results verifies the accuracy and robustness of the developed HSP (outer control loop) in this study. Lastly, on this basis, a series of hybrid tests on viscoelastically damped frame structures are conducted under different seismic wave excitations. The test results truly reveal the control rule on the seismic response of reinforced concrete frame structures affected by viscoelastic dampers.
Modeling uncertainty in structural models can greatly affect the reliability of nonlinear time history results, which are central to performance‐based earthquake engineering. A crucial source of modeling uncertainty is the uncertainty in the parameters of constitutive models, which simulate the hysteretic behavior of key structural components. In current research and engineering practice, it is assumed that the accuracy of a nonlinear structural model is achieved by component calibration, which is conducted by trying to best match the response of a numerical model of a component to test results under a standardized quasi‐static loading regime. However, previous research has shown that even a very well‐fitted component‐level calibration might result in considerable errors in the system‐level structural dynamic response. This study is an initial attempt to investigate calibration relevance incorporating a rigorous uncertainty quantification framework. In the proposed framework, parameters of a constitutive model are considered as random inputs. Calibration error at the component level and global error at the system level are quantified based on the discrepancies between the simulation models with probabilistic inputs and reference models. Polynomial chaos expansions (PCEs) metamodels are implemented to conduct sensitivity analysis and investigate calibration relevance. Three buckling restrained braced frames (BRBFs) with different heights are investigated using the proposed framework. Four calibration methods’ relevance with global errors based on three engineering demand parameters (EDPs) are studied. The results allow for the identification of optimum hyperparameters to achieve peak calibration relevance and to evaluate different calibration methods for several EDPs for the three BRBFs.
In this research, a hybrid of surrogate model and Multi-island genetic algorithm (MIGA) is proposed for optimization and compensation of steady-state flow force on water hydraulic high-speed on-off valve (HSV) driven by voice coil motor. Firstly, a dynamic model on the spool of HSV is established, and the effects of spool displacement, spool half-cone angle, valve stem diameter and inlet pressure on the steady-state flow force of HSV are analyzed through the CFD simulation. Secondly, a quadratic response surface model is set up based on design of experiment (DOE) to analyze interactions of key parameters on steady-state flow force. MIGA is proposed to optimise the structural parameters of HSV, and the optimization results are analysed and verified by CFD simulations. Simulation results demonstrate that the steady-state flow force is reduced significantly. Finally, the steady-state flow force in the optimized structure of HSV is also verified experimentally. The experiment results exhibit that the optimized spool can compensate about 71% for the steady-state flow force, then reduce about 15% the energy consumption of HSV. This research will provide the guide for the design and engineering application of HSV.
Cemented tailings backfill (CTB) is widely adopted to ensure the safety of underground goafs and mitigate environmental risks. Fly ash (FA) and calcium formate (CF) are common industrial by-products that improve the mechanical performance of CTB. How the coupling of the two components affects the strength development is not yet well-understood. Neural network modelling was conducted to predict the strength development, including the static indicator of uniaxial compressive strength (UCS) and the dynamic indicator of ultrasonic pulse velocity (UPV). Sobol’ sensitivity analysis was carried out to reveal the contributions of FA, CF and curing time to CTB strength. SEM microstructure investigation on CTB samples was implemented to reveal the mechanism of strength development and justify the predictions by neural network modelling and sensitivity analysis. Results show that the combination of FA content, CF content and curing time can be used to predict both UCS and UPV while providing adequate accuracy. The maximum of UCS of 6.1215 MPa is achieved at (FA content, CF content, curing time) = (13.78 w%, 3.76 w%, 28 days), and the maximum of UPV of 2.9887 km/s is arrived at (FA content, CF content, curing time) = (11.67 w%, 3.08 w%, 10 days). It is also implicated that prediction of UCS using UPV alone, although common in field application is not recommended. However, UPV measurement, in combination with the information of FA dosage, CF dosage and curing time, could be used to improve UCS prediction. The rank of variable significance for UCS is curing time > FA content > CF content, and for UPV is FA content > curing time > CF content; variable interaction is strongest for FA with CF for UCS development, and for FA with curing time for UPV evolution. Influence of FA on CTB strength development is due to improved polymerisation and consumption of Ca(OH)2. Influence of CF on strength development is a result of accelerated hydration and increased combined-water content in calcium silicate hydrate (CSH). Effect of curing time is attributed to the evolution of CSH product and pore-water content during cement hydration.
This technical note presents the experimental validation of a hybrid fire testing coordination algorithm recently developed by some of the authors. For the first time, the algorithm is applied to solve the static response of a multiple-degrees-of-freedom hybrid model.
Communities and their supporting civil infrastructure systems can be viewed as an assembly of, often numerous, interacting components. Tools that can identify components relevant for community disaster resilience can help to efficiently allocate limited resources to reach community resilience goals. We use Sobol’ indices to measure the importance of vulnerability and recoverability of components for disaster resilience of communities with interdependent civil infrastructure systems. The initial component importance analysis requires no prior knowledge regarding component’s vulnerability and recoverability. We first rank components based on their importance, using their Sobol’ indices. Secondly, we illustrate how the results of the component importance analysis can be used to improve community disaster resilience. Finally, we use component importance to show how model complexity can be reduced by abstracting less important components.
The preform architectures and the variability of the constituents of carbon fiber reinforced polymer (CFRP) composites materials can affect their mechanical behaviors significantly. This paper describes a systematic analysis of the low-velocity impact response and energy absorption capacity of biomimetic architected CFRP laminates. High-fidelity multiscale Finite Element (FE) models considering constituent material property uncertainties are developed to evaluate the effect of pitch angles on the impact performance of Bouligand architected composite laminates. Experimental results extracted from open literature have been used to validate the low velocity impact response of the CFRPs predicted by the numerical model. Constituent material property uncertainties are identified as parametric variables, and the peak impact load and energy absorption responses of the bio-inspired CFRPs are obtained with the verified numerical models. The main effect sensitivity indices of the parameters are then calculated based on a variance-based global sensitivity analysis model. The presented studies clearly shows that smaller pitch angles and larger fiber longitudinal elastic modulus achieve more desirable impact resistance and better energy-absorption characteristics. This study aim to open up new possibilities for improving low velocity impact performance of CFRP composite laminates by adopting bionic design approach and considering constituent materials effect.
Sparse polynomial chaos expansions (PCEs) are an efficient and widely used surrogate modeling method in uncertainty quantification. Among the many contributions aiming at computing an accurate sparse PCE while using as few model evaluations as possible, basis adaptivity is a particularly interesting approach. It consists in starting from an expansion with a small number of polynomial terms, and then parsimoniously adding and removing basis functions in an iterative fashion. We describe several state-of-the-art approaches from the recent literature and extensively benchmark them on a large set of computational models representative of a wide range of engineering problems. We investigate the synergies between sparse regression solvers and basis adaptivity schemes, and provide recommendations on which of them are most promising for specific classes of problems. Furthermore, we explore the performance of a novel cross-validation-based solver and basis adaptivity selection scheme, which consistently provides close-to-optimal results.
We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive computational model subject to random inputs with an inexpensive-to-evaluate polynomial function. The metamodel obtained enables a reliable estimation of the statistics of the output, provided that a suitable probabilistic model of the input is available. Machine learning (ML) regression is a research field that focuses on providing purely data-driven input-output maps, with the focus on pointwise prediction accuracy. We show that a PCE metamodel purely trained on data can yield pointwise predictions whose accuracy is comparable to that of other ML regression models, such as neural networks and support vector machines. The comparisons are performed on benchmark datasets available from the literature. The methodology also enables the quantification of the output uncertainties, and is robust to noise. Furthermore, it enjoys additional desirable properties, such as good performance for small training sets and simplicity of construction, with only little parameter tuning required.
We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum depending on the six cosmological parameters ' ‰ b, ' ‰ m, n s, h, w 0, and σ 8. It is constructed using the uncertainty quantification software UQLab using a spectral decomposition method called polynomial chaos expansion. All steps in its construction have been tested and optimized: the large high-resolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers kapprox 5, h, rm Mpc -1 for redshifts z ≤ 5. The emulator is based on 100 input cosmologies simulated in boxes of (1250 Mpc/h) 3 using 2048 3 particles. We show that by creating mock emulators it is possible to successfully predict and optimize the performance of the final emulator prior to performing any N-body simulations. The absolute accuracy of the final nonlinear power spectrum is as good as one obtained with N-body simulations, conservatively, sim 1 per cent for klesssim 1, h, rm Mpc -1 and z 2 1. This enables efficient forward modelling in the nonlinear regime, allowing for estimation of cosmological parameters using Markov Chain Monte Carlo methods. EuclidEmulator has been compared to HALOFIT, CosmicEmu, and NGenHalofit, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations, and investigate higher dimensional cosmological parameter spaces. © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.
We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance-decomposition-based Sobol' indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the state-of-the-art approach of constructing a polynomial chaos expansion of the model, from which Sobol' indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real-business-cycle model and compare it to traditional local sensitivity analysis approaches. The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities.
Tunnels are constructed increasingly close to existing buried structures, including pile foundations. This poses a serious concern, especially for tunnels built beneath piles. Current understanding of the global tunnel-soil-pile-building interaction effects is lacking, which leads to designs which may be overly conservative or the adoption of expensive measures to protect buildings. This paper presents outcomes from 24 geotechnical centrifuge tests that aim to investigate the salient mechanisms that govern piled building response to tunnelling. Centrifuge test data include greenfield tunnelling, pile loading, and tunnelling beneath single piles and piled frames, all within sand. The global tunnel-piled frame interaction scenario is investigated using a newly developed real-time hybrid testing technique, wherein a numerical model is used to simulate a building frame, a physical (centrifuge) model is used to replicate the tunnel-soil-foundation system and structural loads, and coupling of data between the numerical and physical models is achieved using a real-time load-control interface. The technique enables, for the first time, a realistic redistribution of pile loads (based on the superstructure characteristics) to be modelled in the centrifuge. The unique dataset is used to quantify the effects of several factors which have not previously been well defined, including the pile installation method, initial pile safety factor, and superstructure characteristics. In particular, results illustrate that pile settlement and failure mechanisms are highly dependent on the pre-tunnelling loads and the load redistribution that occurs between piles during tunnel volume loss, which are related to structure weight and stiffness. The paper also provides insight as to how pile capacity should be dealt with in a tunnel-pile interaction context.
We present a fundamentally new approach to laboratory acoustic and seismic wave experimentation that enables full immersion of a physical wave propagation experiment within a virtual numerical environment. Using a recent theory of immersive boundary conditions that relies on measurements made on an inner closed surface of sensors, the output of numerous closely spaced sources around the physical domain is continuously varied in time and space. This allows waves to seamlessly propagate back and forth between both domains, without being affected by reflections at the boundaries between both domains, which enables us to virtually expand the size of the physical laboratory and operate at much lower frequencies than previously possible (sonic frequencies as low as 1 kHz). While immersive boundary conditions have been rigorously tested numerically, here we present the first proof of concept for their physical implementation with experimental results from a one-dimensional sound wave tube. These experiments demonstrate the performance and capabilities of immersive boundary conditions in canceling boundary reflections and accounting for long-range interactions with a virtual domain outside the physical experiment. Moreover, we introduce a unique high-performance acquisition, computation, and control system that will enable the real-time implementation of immersive boundary conditions in three dimensions. The system is capable of extrapolating wave fields recorded on 800 simultaneous inputs to 800 simultaneous outputs, through arbitrarily complex virtual background media with an extremely low total system latency of 200 μs. The laboratory allows studying a variety of long-standing problems and poorly understood aspects of wave physics and imaging. Moreover, such real-time immersive experimentation opens up exciting possibilities for the future of laboratory acoustic and seismic experiments and for fields such as active acoustic cloaking and holography.
Performing hydrodynamic model testing of ultra-deep water floating systems at a reasonable scale is challenging, due to the limited space available in existing laboratories and to the large spatial extent of the slender marine structures that connect the floater to the seabed. In this paper, we consider a method based on real-time hybrid model testing, namely the active truncation of the slender marine structures: while their upper part is modelled physically in an ocean basin, their lower part is simulated by an adequate numerical model. The control system connecting the two substructures inevitably introduces artefacts, such as noise, biases and time delays, whose probabilistic description is assumed to be known. We investigate specifically how these artefacts influence the fidelity of the active truncation setup, that is its capability to reproduce correctly the dynamic behaviour of the system under study. We propose a systematic numerical method to rank the artefacts according to their influence on the fidelity of the test. The method is demonstrated on the active truncation of a taut polyester mooring line.
Successful online hybrid (numerical/physical) dynamic substructuring simulations have shown their potential in enabling realistic dynamic analysis of almost any type of non-linear structural system (e.g., an as-built/isolated viaduct, a petrochemical piping system subjected to non-stationary seismic loading, etc.). Moreover, owing to faster and more accurate testing equipment, a number of different offline experimental substructuring methods, operating both in time (e.g. the impulse-based substructuring) and frequency domains (i.e. the Lagrange multiplier frequency-based substructuring), have been employed in mechanical engineering to examine dynamic substructure coupling. Numerous studies have dealt with the above-mentioned methods and with consequent uncertainty propagation issues, either associated with experimental errors or modelling assumptions. Nonetheless, a limited number of publications have systematically cross-examined the performance of the various Experimental Dynamic Substructuring (EDS) methods and the possibility of their exploitation in a complementary way to expedite a hybrid experiment/numerical simulation. From this perspective, this paper performs a comparative uncertainty propagation analysis of three EDS algorithms for coupling physical and numerical subdomains with a dual assembly approach based on localized Lagrange multipliers. The main results and comparisons are based on a series of Monte Carlo simulations carried out on a five-DoF linear/non-linear chain-like systems that include typical aleatoric uncertainties emerging from measurement errors and excitation loads. In addition, we propose a new Composite-EDS (C-EDS) method to fuse both online and offline algorithms into a unique simulator. Capitalizing from the results of a more complex case study composed of a coupled isolated tank-piping system, we provide a feasible way to employ the C-EDS method when nonlinearities and multi-point constraints are present in the emulated system.
Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol’ indices is based on Monte Carlo simulation, which is not affordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Then the surrogate can be used to compute the sensitivity indices in negligible time. In this chapter an introduction to each technique is given, with an emphasis on their strengths and limitations in the context of global sensitivity analysis. In particular, Sobol’ (resp. total Sobol’) indices can be computed analytically from the PCE coefficients. In contrast, confidence intervals on sensitivity indices can be derived straightforwardly from the properties of GPs. The performance of the two techniques is finally compared on three well-known analytical benchmarks (Ishigami, G-Sobol’, and Morris functions) as well as on a realistic engineering application (deflection of a truss structure).
We present a global sensitivity analysis that quantifies the impact of parameter uncertainty on model outcomes. Specifically, we propose variance-decomposition-based Sobol’ indices to establish an importance ranking of parameters and univariate effects to determine the direction of their impact. We employ the state-of-the-art approach of constructing a polynomial chaos expansion of the model, from which Sobol’ indices and univariate effects are then obtained analytically, using only a limited number of model evaluations. We apply this analysis to several quantities of interest of a standard real-business-cycle model and compare it to traditional local sensitivity analysis approaches.
The results show that local sensitivity analysis can be very misleading, whereas the proposed method accurately and efficiently ranks all parameters according to importance, identifying interactions and nonlinearities.
Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol' indices is based on Monte Carlo simulation, which is not affordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Then the surrogate can be used to compute the sensitivity indices in negligible time. In this chapter an introduction to each technique is given, with an emphasis on their strengths and limitations in the context of global sensitivity analysis. In particular, Sobol' (resp. total Sobol') indices can be computed analytically from the PCE coefficients. In contrast, confidence intervals on sensitivity indices can be derived straightforwardly from the properties of GPs. The performance of the two techniques is finally compared on three well-known analytical benchmarks (Ishigami, G-Sobol and Morris functions) as well as on a realistic engineering application (deflection of a truss structure).
The UQLab "Sensitivity Analysis" module is a powerful and flexible tool for performing sensitivity analysis with a number of different techniques. This user manual includes a review of several advanced sensitivity analysis methods and algorithms available in UQLab, also serving as an overview of the relevant up-to-date literature. It also provides an in-depth, example-driven user guide to help new users to properly set up and solve sensitivity analysis problems with the techniques described. Finally, a comprehensive reference list of the methods and functions available in the UQLab sensitivity module is given at the end of the manual.
Polynomial Chaos Expansions (PCE) are a powerful metamodeling tool that has important
applications in many engineering and applied mathematics fields. These include structural
reliability, sensitivity analysis, Monte Carlo simulation and others. Due to the underlying
complexity of its formulation, however, this technique has seen relatively little use outside of
these fields.
UQLAB metamodelling tools provide an efficient, flexible and easy to use PCE module that
allows one to apply state-of-the-art algorithms for non-intrusive, sparse and adaptive PCE on
a variety of applications. This manual for the polynomial chaos expansion metamodelling
module is divided into three parts:
• A short introduction to the main concepts and techniques behind PCE, with a selection
of references to the relevant literature;
• A detailed example-based guide, with the explanation of most of the available options
and methods;
• A comprehensive reference list detailing all the available functionalities in UQLAB.
A hybrid simulation approach is used to evaluate the traffic performance of a typical California highway overpass bridge after a major earthquake. The prototype bridge used in this study is a five-span single-column-bent reinforced concrete overpass. A hybrid model, composed of the physical column specimen and the OpenSees model of the remainder of the bridge, was assembled using the OpenFresco framework. Two hybrid simulation tests were performed on the same bridge for the same recorded ground motion scaled to represent two levels of seismic intensity: moderate and high. After the earthquake, loads corresponding to a heavy truck placed in the most critical positions on the bridge were applied on the hybrid model. The data obtained from these tests show that a typical California overpass bridge has the capacity to carry heavy truck loads immediately after a major earthquake event. (C) 2014 American Society of Civil Engineers.
The present study makes use of polynomial chaos expansions to compute Sobol'
indices in the frame of a global sensitivity analysis of hydro-dispersive
parameters in a synthetic multi-layered hydrogeological model. The model
introduced in this paper is a simplified vertical cross-section of a segment of
the subsurface of the Paris Basin. This 15-layer numerical model is aimed at
exploring the behavior of groundwater and solute fluxes when accounting for
uncertain advective and dispersive parameters. Applying conservative ranges,
the uncertainty in the input variables is propagated upon the mean lifetime
expectancy of water molecules departing from a specific location within a
highly confining layer situated in the middle of the numerical model. The
sensitivity analysis indicates that the variability in the mean lifetime
expectancy can be sufficiently explained by the uncertainty in the petrofacies,
\ie the sets of porosity and hydraulic conductivity, of only a few layers of
the model.
Uncertainty quantification is a rapidly growing field in computer simulation-based scientific applications. The UQLAB project aims at the development of a MATLAB-based software framework for uncertainty quantification. It is designed to encourage both academic researchers and field engineers to use and develop advanced and innovative algorithms for uncertainty quantification, possibly exploiting modern distributed computing facilities. Ease of use, extendibility and handling of non-intrusive stochastic methods are core elements of its development philosophy. The modular platform comprises a highly optimized core probabilistic modelling engine and a simple programming interface that provides unified access to heterogeneous high performance computing resources. Finally, it provides a content-management system that allows users to easily develop additional custom modules within the framework. In this contribution, we intend to demonstrate the features of the platform at its current development stage.
Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol' indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate variance-based sensitivity indices. Indeed, their computation is analytically derived from the expansion coefficients but without error estimators of the meta-model approximation. In order to evaluate the reliability of these indices, we propose to build confidence intervals by bootstrap re-sampling on the experimental design used to estimate the polynomial chaos approximation. Since the evaluation of the sensitivity indices is obtained with confidence intervals, it is possible to find a design of experiments allowing the computation of sensitivity indices with a given accuracy.
The stochastic finite element method allows to solve stochastic boundary value problems where material properties and loads are random. The method is based on the expansion of the mechanical response onto the so-called polynomial chaos. In this paper, a non intrusive method based on a least-squares minimization procedure is presented. This method is illustrated by the study of the settlement of a foundation. Different analysis are proposed: the computation of the statistical moments of the response, a reliability analysis and a parametric sensitivity analysis.
Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate.To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained (sparse representation), which may be obtained at a reduced computational cost compared to the classical “full” PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 − 500 random variables, respectively.
Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol’ indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol’ indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression-based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2–3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol’ indices.
We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.
Hybrid simulation reproduces the experimental response of large‐ or even full‐scale structures subjected to a realistic excitation with reduced costs compared with shake table testing. A real‐time control system emulates the interaction between numerical substructures, which replace subparts having well‐established computational models, and physical substructures tested in the laboratory. In this context, state‐space modeling, which is quite popular in the community of automatic control, offers a computationally cheaper alternative to the finite‐element method for implementing nonlinear numerical substructures for fast‐time hybrid simulation, that is, with testing timescale close to one. This standpoint motivated the development of a computational framework based on partitioned time integration, which is well suited for hard real‐time implementations. Partitioned time integration, which relies on a dual assembly of substructures, enables coupling of state‐space equations discretized with heterogeneous time step sizes. In order to avoid actuators stopping at each simulation step, the physical substructure response is integrated with the same rate of control system, whereas a larger time step size is allowed on the numerical substructure compatibly with available computational resources. Fast‐time hybrid simulations of a two‐pier reinforced concrete bridge tested at the EUCENTRE Experimental Laboratory of Pavia, Italy, are presented as verification example.
A procedure to generate horizontal pairs of synthetic near-fault ground motion components for specified earthquake source and site characteristics is presented. Some near-fault ground motions contain a forward directivity pulse; others do not, even when the conditions for such a pulse are favorable. The proposed procedure generates pulse-like and non-pulse-like motions in appropriate proportions. We use our recent stochastic models of pulse-like and non-pulse-like near-fault ground motions that are formulated in terms of physically meaningful parameters. The parameters of these models are fitted to databases of recorded pulse-like and non-pulse-like motions. Using these empirical “observations,” predictive relations are developed for the model parameters in terms of the earthquake source and site characteristics (type of faulting, earthquake magnitude, depth to top of rupture plane, source-to-site distance, site characteristics, and directivity parameters). The correlation coefficients between the model parameters are also estimated. For a given earthquake scenario, the probability of occurrence of a directivity pulse is first computed; pulse-like and non-pulse-like motions are then simulated according to the predicted proportions using the empirical predictive models. The resulting time series are realistic and reproduce important features of recorded near-fault ground motions, including the natural variability. Moreover, the statistics of their elastic response spectra agree with those of the NGA-West2 dataset, with the additional feature of distinguishing between pulse-like and non-pulse-like cases and between forward and backward directivity scenarios. The synthetic motions can be used in addition to or in place of recorded motions in performance-based earthquake engineering, particularly when recorded motions are scarce.
This article presents a novel approach to model validation and to the calibration of complex structural systems, through the adoption of heterogeneous (numerical/physical) simulation based on dynamic substructuring (HDS). HDS isolates the physical sub-system (PS) that contains the key region of nonlinear behavior of interest and is tested experimentally, separate from the remainder of the system, i.e. the numerical sub-system (NS), which is numerically simulated. A parallel partitioned time integrator based on the finite element tearing and interconnecting (FETI) method plays a central role in solving the coupled system response, enabling a rigorous and stable synchronization between sub-systems and a realistic interaction between PS and NS response. This feature enhances the quality of benchmarks for validation and calibration of low-discrepancy models through virtual structural testing. As a proof of concept, we select an old reinforced concrete viaduct, subjected to seismic loading. Several HDS were conducted at the European Laboratory for Structural Assessment in Ispra (Italy) considering two physical piers and related concave sliding bearings as PSs of the heterogeneous system. As a result, the benefit of employing HDS to set benchmarks for model validation and calibration is highlighted, by developing low-discrepancy FE models of critical viaduct components.
A new thermomechanical hybrid simulation method is proposed that extends the mechanical hybrid simulation method by including thermal degrees of freedom and temperature loads. The thermomechanical hybrid simulation method was implemented in the OpenSees and OpenFresco frameworks. Modifications to enable this new capability centered on incorporating the temperature degrees of freedom in the hybrid model domain, and on developing new OpenFresco objects and a test execution strategy to simultaneously control the structural elements of the experimental setup, the thermal loads, and the mechanical loads. The implementation of the thermomechanical method at the ETH Zürich IBK Structural Testing Laboratory was verified and validated using a simple two-element hybrid model. The responses of the model to a force ramp, applied to the full structure, and a scaled version of the ISO 834 standard fire curve, applied to the experimental element, were obtained in two simulations - one conducted using an explicit and the other using an implicit integration scheme. The tests yield very similar results, and both simulations closely match the theoretical solution.
SUMMARY The last decade of performance-based earthquake engineering (PBEE) research has seen a rapidly increasing emphasis placed on the explicit quantification of uncertainties. This paper examines uncertainty consideration in input ground-motion and numerical seismic response analyses as part of PBEE, with particular attention given to the physical consistency and completeness of uncertainty consideration. It is argued that the use of the commonly adopted incremental dynamic analysis leads to a biased representation of the seismic intensity and that when considering the number of ground motions to be used in seismic response analyses, attention should be given to both reducing parameter estimation uncertainty and also limiting ground-motion selection bias. Research into uncertainties in system-specific numerical seismic response analysis models to date has been largely restricted to the consideration of ‘low-level’ constitutive model parameter uncertainties. However, ‘high-level’ constitutive model and model methodology uncertainties are likely significant and therefore represent a key research area in the coming years. It is also argued that the common omission of high-level seismic response analysis modelling uncertainties leads to a fallacy that ground-motion uncertainty is more significant than numerical modelling uncertainty. The author's opinion of the role of uncertainty analysis in PBEE is also presented. Copyright © 2013 John Wiley & Sons, Ltd.
External coupling software based on the coupling algorithm proposed by Prakash and Hjelmstad (PH method) is compared to the previous external coupling software based on the GC (Gravouil and Combsecure) method. The salient features of multi-time-step partitioning methods are presented: they involve non-overlapping partitions and follow a dual Schur approach by enforcing the velocity continuity at the interface with Lagrange multipliers. The main difference between the two methods lies in the time scale at which the interface problem is solved: the micro-time scale for the GC algorithm and macro-time scale for the PH algorithm. During the multi-time-step co-computations involving two finite element codes (explicit and implicit FE codes), the tasks carried out by the coupling software PH-CPL, based on a variant of the PH algorithm, are illustrated and compared to the coupling software GC-CPL based on the GC algorithm. The advantage of the new coupling PH-CPL software is highlighted in terms of parallel capabilities. In addition, the PH-CPL coupling software alleviates the dissipative drawback of the GC method at the interface between the subdomains. Academic cases are investigated to check the energy features and the accuracy order for the GC and PH algorithms. Finally, explicit/implicit multi-time-step co-computations with GC-CPL and PH-CPL software are conducted for two engineering applications under the assumption of linear elastic materials: a reinforced concrete frame structure under blast loading striking its front face and a flat composite stiffened panel subjected to localised loads applied to its central frame.
A wave propagation laboratory is proposed which enables the study of the interaction of broadband signals with complex materials. A physical experiment is dynamically linked to a numerical simulation in real time through transmitting and recording transducer surfaces surrounding the target. The numerical simulation represents an arbitrarily larger domain, allowing experiments to be performed in a total environment much greater than the laboratory experiment itself. Specific applications include the study of non-linear effects or wave propagation in media where the physics of wave propagation is not well understood such as the effect of fine scale heterogeneity on broadband propagating waves.
Magneto-rheological (MR) fluid dampers have been identified as a particularly promising type of semiactive control device for hazard mitigation in civil engineering structures. Large-scale experimental testing is important to verify the performance of MR fluid dampers for seismic protection of civil structures. Real-time hybrid testing, where only the critical components of the system are physically tested while the rest of the structure is simulated, can provide a cost-effective means for large-scale testing of semiactive controlled structures. This paper describes the real-time hybrid simulation experimental setup for multiple large-scale MR fluid dampers and demonstrates the capability at the University of Colorado at Boulder shared-use Fast Hybrid Test facility to conduct real-time hybrid testing within the Network for Earthquake Engineering Simulation.
Hybrid simulation is an effective structural test technique combining the numerical simulation of substructures with predictable behavior, and experimental testing of complex components that are difficult to model. Consequently, hybrid simulation is prone to both numerical and experimental errors. In this paper, the dominant sources of numerical and experimental errors that can contaminate the results of a hybrid simulation are examined. It is shown that linearized analytical stability and accuracy limits for algorithms and test procedures used in a hybrid simulation may fail to adequately predict the results due to errors and nonlinearities of actual tests. An alternative approach based on monitoring the energy balance of the structural system is proposed to capture the effects of both experimental and numerical errors. This method extends an existing experimental error indicator to also account for (a) errors resulting from modification of experimental measurements by iterative corrections in numerical integrators or other signal correction procedures, and (b) numerical errors in the integration algorithm including equilibrium errors and kinematic relations between displacement, velocity and acceleration. The effectiveness of the proposed energy error indicator in predicting severity of errors is demonstrated through numerical and experimental simulations using various integration procedures.
Advanced Implementation of Hybrid Simuation
- A H Shellenberg
- S A Mahin
F. G., A.H. Shellenberg, S.A. Mahin, Advanced Implementation of Hybrid Simuation, Tech. Rep. 104, Pacific Earthquake Engineering Research Center,
2009..
- B Iooss
- P Lemaıtre
B. Iooss, P. Lemaıtre, A review on global sensitivity analysis methods, arXiv:1404.2405 [math, stat]ArXiv: 1404.2405.
Thermo-mechanical virtualization of hybrid flax/carbon fiber composite for spacecraft structures
- G Abbiati
- V Hey
- J Rion
- B Stojadinovic
G. Abbiati, V. Hey, J. Rion, B. Stojadinovic, Thermo-mechanical virtualization of hybrid flax/carbon fiber composite for spacecraft structures. thermics
project, final report., 2018..