Sankaran Mahadevan

• Vanderbilt University

This paper investigates a novel approach to efficiently construct and improve surrogate models in problems with high-dimensional input and output. In this approach, the principal components and corresponding features of the high-dimensional output are first identified. For each feature, the active subspace technique is used to identify a correspond...

Surrogate models are employed in engineering analysis to replace detailed physics-based models to achieve computational efficiency in problems that require multiple evaluations of the model. The accuracy of the surrogate model depends on the quality and quantity of data collected from the expensive model. This paper investigates surrogate modeling...

The uncertainty in the stochastic unit commitment (UC) problem for a real-world power grid is driven by a large number of stochastic input variables. This article develops a method for estimating the contribution of uncertainty in different input variables to the uncertainty in the quantities of interest (QoIs) corresponding to a unit commitment de...

Model validation for real-world systems involves multiple sources of uncertainty, multivariate model outputs, and often a limited number of measurement samples. These factors preclude the use of many existing validation metrics, or at least limit the ability of the practitioner to derive insights from computed metrics. This paper seeks to extend th...

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision- and policy-making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series o...

Bulk power systems, commonly referred to as power grids, need to be safely operated under uncertainty in load demand and power generation as well as unplanned loss of system elements. In recent years, increasing participation of variable generators, like wind and solar generators, has significantly increased the system uncertainty, and therefore, i...

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of...

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally...

This paper pursues a probabilistic digital twin methodology for designing component health- and stress-aware system control, and demonstrates the proposed methodology for the problem of rotorcraft maneuver control. The probabilistic digital twin uses sensor data to infer up-to-date knowledge regarding the component’s current health state and the as...

This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve compu...

This paper develops a physics-informed machine learning approach for response prediction in dynamic systems, by augmenting a physics-based model with a machine learning model for model error; both models are probabilistic. The physics-based dynamic system model has discrepancy in the predicted output (due to incomplete physics or model form error i...

In a grid with a significant share of renewable generation, operators will need additional tools to evaluate the operational risk due to the increased volatility in load and generation. The computational requirements of the forward uncertainty propagation problem, which must solve numerous security-constrained economic dispatch (SCED) optimizations...

Errors in formulating the system physics model, due to inability to rigorously account for nonlinear behavior, boundary conditions, and multi-component and multi-physics interactions result in discrepancies between model predictions of system responses and the corresponding experimentally measured values. In our previous work, we have developed a B...

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of...

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of...

This paper proposes a multi-level Bayesian calibration approach that fuses information from heterogeneous sources and accounts for uncertainties in modeling and measurements for time-dependent multi-component systems. The developed methodology has two elements: quantifying the uncertainty at component and system levels, by fusing all available info...

Collisions during airport surface operations can create risk of injury to passengers, crew or airport personnel and damage to aircraft and ground equipment. A machine learning model that is able to predict the trajectories of ground objects can help to diminish the occurrences of such collision events. In this paper, we pursue this objective by bui...

Recorded aircraft trajectory data may vary significantly from predictions based on physics-informed models. This discrepancy may be attributed to inadequacies in the trajectory prediction models, including errors in modeling aircraft dynamics, and omission of inputs such as weather data, equipment malfunctions, and pilot errors. In this work, we re...

Computer simulation of the additive manufacturing (AM) process involves multi-physics, multi-scale models. These sophisticated higher fidelity (HF) AM models, though more accurate, are computationally very expensive. On the other hand, AM process simulation using lower fidelity (LF) analytical models with simplified physics is fast but has signific...

This paper proposes a detailed methodology for constructing an AM digital twin, for the laser powder bed fusion (LPBF) process. An important aspect of the proposed digital twin is the incorporation of model uncertainty and process variability. A virtual representation of the LPBF process is first constructed using a physics-based model. To enable f...

Landing is generally cited as one of the riskiest phases of a flight, as indicated by the much higher accident rate than other flight phases. In this paper, we focus on the hard landing problem (which is defined as the touchdown vertical speed exceeding a predefined threshold), and build a probabilistic predictive model to forecast the aircraft’s v...

This paper develops a methodology to compute variance-based sensitivity indices for dynamic systems with time series inputs and outputs, while accounting for both aleatory and epistemic uncertainty sources, and both random process and random variable inputs. We present semi-analytical methods for computing sensitivity indices for linear systems wit...

The poor explainability of deep learning models has hindered their adoption in safety and quality-critical applications. This paper focuses on image classification models and aims to enhance the explainability of deep learning models through the development of an uncertainty quantification-based framework. The proposed methodology consists of three...

This study develops a probabilistic simulation methodology for the en-route safety assessment of multiple aircraft flying within an airspace sector. This assessment is affected by multiple sources of uncertainty, such as external inputs such as wind gust, internal factors such as aircraft component failure, and model errors (e.g., in the aircraft d...

This paper investigates the utility of physics-informed machine learning models for vibro-acoustic modulation (VAM)–based damage localization in concrete structures. Vibro-acoustic modulation is a nonlinear dynamics-based non-destructive testing method, which was initially developed to perform damage detection and later extended to accomplish damag...

Rotorcraft components experience different stress levels based on the flight parameters and intensity of the rotorcraft mission, which in turn dictates the maintenance schedule as well as life expectancy for the component. To improve the resilience of a rotorcraft to safely complete a mission, the rotorcraft’s maneuvers can be designed to minimize...

Engineering analysis using finite element models of complex aerospace structural components is computationally expensive and consists of multiple inputs and outputs. The analysis becomes more demanding when the system inputs and outputs vary over space and time, and the problem becomes very high-dimensional. Surrogate models are often employed to r...

This paper reviews the state of the art in applying uncertainty quantification (UQ) methods to additive manufacturing (AM). Physics-based as well as data-driven models are increasingly being developed and refined in order to support process optimization and control objectives in AM, in particular to maximize the quality and minimize the variability...

This work presents a data-driven methodology for multi-objective optimization under uncertainty of process parameters in the fused filament fabrication (FFF) process. The proposed approach optimizes the process parameters with the objectives of minimizing the geometric inaccuracy and maximizing the filament bond quality of the manufactured part. Fi...

This paper proposes a Digital Twin approach for the monitoring and prognosis of vessel-specific fatigue damage. During design, fatigue damage estimates are based on conservative assumptions regarding operational conditions and structural response. However, variability in the vessel-specific operations from those assumed during design needs to be co...

This work presents a Bayesian methodology for layer-by-layer predictive quality control of an additively manufactured part by integrating physics-based simulation with online monitoring data. The model and the sensor data are first used to infer porosity in the printed layers, prediction of porosity in future layers, and adjustment of process param...

This article describes a novel method for detecting flaws in curing FRP composite materials while they are being manufactured. Such a method can improve the efficiency of the manufacturing process by minimizing, or potentially eliminating, the need for post-manufacturing inspection. The method utilizes a Kalman filter, a heat conduction model, and...

In this paper, we apply a set of data-mining and sequential deep learning techniques to accident investigation reports published by the National Transportation Safety Board (NTSB) in support of the prognosis of adverse events. Our focus is on learning with text data that describes the sequences of events. NTSB creates post-hoc investigation reports...

Recent technological advancements in computing, sensing and communication have led to the development of cyber-physical manufacturing processes, where a computing subsystem monitors the manufacturing process performance in real-time by analyzing sensor data and implements the necessary control to improve the product quality. This paper develops a p...

Full-scale system tests are often prohibitively expensive, therefore experiments on simpler configurations are used in engineering to gain insights that can be applied to the behavior prediction of the full-scale system. However, the transfer of information from the experimental configuration to the prediction configuration is not trivial. In this...

When computational models (either physics-based or data-driven) are used for the sensitivity analysis of engineering systems, the sensitivity estimate is affected by the accuracy and uncertainty of the model. This paper considers global sensitivity analysis (GSA) for situations where both a physics-based model and experimental observations are avai...

The objective of multifidelity modeling is to achieve both accurate and efficient predictions by combining high- and low-fidelity models. A flexible approach considering additive, multiplicative, and input correction factors is proposed to improve the low-fidelity model using high-fidelity data. The correction factors are estimated using a Bayesian...

Digital Twin is one of the promising digital technologies being developed at present to support digital transformation and decision making in multiple industries. While the concept of a Digital Twin is nearly 20 years old, it continues to evolve as it expands to new industries and use cases. This has resulted in a continually increasing variety of...

Rotorcraft components experience different stress levels based on the flight parameters and intensity of the rotorcraft mission. The stress history experienced by a mechanical component can have significant effect on the wear and tear of a given component, which in turn dictates the maintenance schedule as well as life expectancy for the component....

Surrogate models are often employed in engineering analysis to replace a detailed model with complicated geometry, loading, material properties and boundary conditions, in order to achieve computational efficiency. The accuracy of the surrogate model depends on the quality and quantity of data collected from the expensive physics model. This paper...

Safety assurance is of paramount importance in the air transportation system. In this paper, we analyze the historical passenger airline accidents that happened from 1982 to 2006 as reported in the National Transportation Safety Board (NTSB) aviation accident database. A four-step procedure is formulated to construct a Bayesian network to capture t...

This paper presents a novel surrogate modeling approach that enables the application of Bayesian calibration to a gas turbine disc finite element (FE) heat transfer model. The surrogate modeling process begins with two transformations of the FE model predictions: first, principal components analysis “rotates” the multivariate FE model outputs into...

The digital twin paradigm aims to fuse information obtained from sensor data, physics models, and operational data for a mechanical component in use to make well-informed decisions regarding health management and operations of the component. In this work, we discuss a methodology for digital-twin-based operation planning in mechanical systems to en...

This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-phys...

The digital twin paradigm that aims to integrate the information obtained from sensor data, physics models, operational data and inspection/maintenance/repair history of the system or component of interest, can potentially be used to optimize operational parameters that achieve a desired performance or reliability goal. In this paper, we discuss su...

This paper develops a computational framework to optimize the process parameters such that the bond quality between extruded polymer filaments is maximized in fused filament fabrication (FFF). A transient heat transfer analysis providing an estimate of the temperature profile of the filaments is coupled with a sintering neck growth model to assess...

Resilience is an important capability for many complex systems to mitigate the impact of extreme events as well as timely restoration of system performance in the aftermath of a disruptive event. In this paper, we investigate a bi-level pre-disaster resilience-based design optimization approach for the configuration of logistics service centers. In...

Despite the desirable characteristics of fiber-reinforced polymer (FRP) composites, their utilization in high volume production industries is limited by a lack of efficient manufacturing techniques. Monitoring the curing process of these composites can help with improving the quality and efficiency of the manufacturing process. This article discuss...

This work presents a novel process design optimization framework for additive manufacturing (AM) by integrating physics-informed computational simulation models with experimental observations. The proposed framework is implemented to optimize the process parameters such as extrusion temperature, extrusion velocity, and layer thickness in the fused...

A novel approach to surrogate modeling motivated by recent advancements in parameter dimension reduction is proposed. Specifically, the approach aims to speed-up surrogate modeling for mapping multiple input variables to a field quantity of interest. Computational efficiency is accomplished by first identifying principal components (PC) and corresp...

This paper presents a methodology to estimate the discrepancy in the model output of untested coupled multiphysics systems, based on tests on related systems. Model predictions often exhibit discrepancy with respect to experimental observations, due to assumptions and approximations in the model. Bayesian approaches for estimating discrepancy in si...

Safety, as the most important concern in civil aviation, needs to be maintained at an acceptable level at all times in the air transportation system. This paper aims to increase en-route flight safety through the development of deep learning models for trajectory prediction, where model prediction uncertainty is characterized following a Bayesian a...

This article investigates the application of vibro-acoustic modulation testing for diagnosing damage in concrete structures. The vibro-acoustic modulation technique employs two excitation frequencies on a structure. The interaction of these excitations in the measured response indicates damage through the presence of sidebands in the frequency spec...

Control room operators respond to abnormal situations through a series of cognitively demanding activities, e.g., monitoring, detection, diagnosis, and response. However, variability among operators in terms of prior experience and current operational context affects their response to the malfunction. A machine learning framework was employed to in...

This paper proposes a probability-space surrogate modeling approach for computationally efficient multidisciplinary design optimization under uncertainty. This paper uses a probability-space surrogate as opposed to an algebraic surrogate so that the probability distributions of the required outputs at a given design input can naturally be obtained...

This paper studies a multifidelity resource optimization methodology for simulation and data collection in the calibration of dynamics model parameters. Nonlinear dynamics systems require high-fidelity modeling; however, expensive high-fidelity simulations cannot be used in Bayesian model calibration: Markov chain Monte Carlo sampling requires thou...

Vibro‐acoustic modulation (VAM) is a nonlinear dynamics‐based method for detecting damage in mechanical and structural components. Past studies have shown that VAM can be used for detecting contact acoustic nonlinearities and for mapping the extent of delamination or impact damage in thin composite plates. However, the suitability of VAM for mappin...

Dempster’s rule of combination can only be applied to independent bodies of evidence. This paper proposes a new rule to combine dependent bodies of evidence. The rule is based on the concept of joint belief distribution, and can be seen as a generalization of Dempster’s rule. When the bodies of evidence are independent, the new combination rule wil...

Coupled aerothermoelastic analysis is required to predict the response of a hypersonic vehicle panel. The required computational effort of the coupled multidisciplinary analysis, interactions between multiple failure modes, and the spatio-temporal variability of the response create significant challenges to the reliability analysis of such structur...

We focus on an efficient approach for quantification of uncertainty in complex chemical reaction networks with a large number of uncertain parameters and input conditions. Parameter dimension reduction is accomplished by computing an active subspace that predominantly captures the variability in the quantity of interest (QoI). In the present work,...

The complicated metal-based additive manufacturing (AM) process involves various sources of uncertainty, leading to variability in AM products. For comprehensive uncertainty quantification (UQ) of AM processes, we present a physics-informed data-driven modeling framework, in which multilevel data-driven surrogate models are constructed based on ext...

Model predictions often exhibit discrepancy with respect to experimental observations, due to assumptions and approximations in the model. Bayesian approaches for estimating discrepancy in single models have been studied in the past. In this paper, we approach the problem of discrepancy estimation in coupled models (especially multi-disciplinary mo...

Reliable methodologies that help diagnose flaws in structural components of nuclear power plants play a crucial role in a plant’s operational and maintenance decision process. In this work, we focus on degradation in concrete structures caused by the alkali-silica reaction (ASR): a chemical reaction between the cement and certain aggregates contain...

Surrogate modeling has become a critical component of scientific computing in situations involving expensive model evaluations. However, training a surrogate model can be remarkably challenging and even computationally prohibitive in the case of intensive simulations and large-dimensional systems. We develop a systematic approach for surrogate mode...

Evacuating residents out of affected areas is an important strategy for mitigating the impact of natural disasters. However, the resulting abrupt increase in the travel demand during evacuation causes severe congestions across the transportation system, which thereby interrupts other commuters' regular activities. In this article, a bilevel mathema...

Uncertainty quantification (UQ) has an important role to play in the quality control of additively manufactured products. With a focus on laser direct metal deposition (LDMD), this work presents a systematic UQ framework to quantify the uncertainty of grain morphology due to various sources of uncertainty in the LDMD simulation process. The LDMD pr...

This paper develops an efficient methodology for both forward and inverse problems in uncertainty quantification with respect to molecular dynamics simulation. Specifically, our objectives are to investigate the impact of uncertainty in the Stillinger-Weber (SW) potential parameters on NEMD-based predictions of bulk thermal conductivity of silicon...

The objectives of this ongoing research project focus on health monitoring and data analytics of concrete slabs containing reactive aggregates and thus subjected to degradation due to alkali-silica reaction (ASR). A controlled concrete slab with four pockets of reactive aggregates (pure silica, and reactive aggregates from three different quarries)...

With the spectacular growth of air traffic demand expected over the next two decades, the safety of the air transportation system is of increasing concern. In this paper, we facilitate the "proactive safety" paradigm to increase system safety with a focus on predicting the severity of abnormal aviation events in terms of their risk levels. To accom...

This research is concerned with how to use available experimental data from tests of lower complexity to inform the prediction regarding a complicated system where no test data is available. Typically, simpler test configurations are used to infer the unknown parameters of an engineering system. Then the calibration results are propagated through t...

Current structural health monitoring techniques face significant difficulties in damage diagnosis for heterogeneous materials such as concrete. In this article, we propose a damage diagnosis methodology that overcomes such difficulties and is capable of detecting and localizing the damage, using linear swept and harmonic vibration tests with swept...

Existing methods for the computation of global sensitivity indices are challenged by both number of input-output samples required and the presence of dependent or correlated variables. First, a methodology is developed to increase the efficiency of sensitivity computations with independent variables by incorporating optimal space-filling quasi-rand...

Bulk thermal conductivity estimates based on predictions from non-equilibrium molecular dynamics (NEMD) using the so-called direct method are known to be severely under-predicted since finite simulation length-scales are unable to mimic bulk transport. Moreover, subjecting the system to a temperature gradient by means of thermostatting tends to imp...

This paper presents a probability model-based global sensitivity analysis (PM-GSA) framework, to compute various Sobol’ indices when only input-output data are available. The PM-GSA framework consists of two main elements, namely data extraction and probability model training. The data extraction step extracts data of the variables of interest (VoI...

Bayesian networks (BNs) represent a promising approach for the aggregation of multiple uncertainty sources in manufacturing networks and other engineering systems for the purposes of uncertainty quantification, risk analysis, and quality control. A standardized representation for BN models will aid in their communication and exchange across the web...

We focus on an efficient approach for quantification of uncertainty in complex chemical reaction networks with a large number of uncertain parameters. Parameter dimension reduction is accomplished by computing an active subspace that predominantly captures the variability in the quantity of interest (QoI). In the present work, we compute the active...

The safety of the air transportation system is affected by a variety of uncertainties arising from multiple sources. This paper investigates a diagnosis and prognosis approach to detect anomalies in the flight trajectory, diagnose root causes, and then perform prognosis regarding the risk of occurrence of adverse events, in the presence of various...