Chao Dang

• Dr.-Ing.
• Postdoc Position at TU Dortmund University

Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation,...

Estimation of the response probability distributions of computer simulators subject to input random variables is a crucial task in many fields. However, achieving this task with guaranteed accuracy remains an open computational challenge, especially for expensive-to-evaluate computer simulators. In this work, a Bayesian active learning perspective...

The well-established Bayesian failure probability inference (BFPI) framework offers a solid foundation for developing new Bayesian active learning reliability analysis methods. However, there remains an open question regarding how to effectively leverage the posterior statistics of the failure probability to design the two key components for Bayesi...

The Bayesian failure probability inference (BFPI) framework provides a sound basis for developing new Bayesian active learning reliability analysis methods. However, it is still computationally challenging to make use of the posterior variance of the failure probability. This study presents a novel method called ‘semi-Bayesian active learning quadr...

The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by takin...

Effectively estimating output probability distributions in stochastic static and dynamic systems with a limited number of simulations is a significant challenge, especially for complex distributions with multi-modality and heavy tails. To address this challenge, this work explores the potential of the Laplace Transform (LT) and its inversion. First...

Engineering structures are inherently subject to various uncertainties, including geometric variations and stochastic external loads, which can significantly impact their performance and, in extreme cases, lead to failure. Structural uncertainty quantification (UQ) encompasses methods such as uncertainty modeling, simulation, propagation, reliabili...

Time-dependent reliability analysis has received increasing attention for assessing the performance and safety of engineered components and systems subject to both random and time-varying dynamic factors. However, many existing methods may prove insufficient when applied to real-world problems, particularly in terms of applicability, efficiency and...

To alleviate the intensive computational burden of reliability analysis, a new parallel active learning reliability method is proposed from the multi-point look-ahead paradigm. First, in the framework of probability density evolution method, a global measure of epistemic uncertainty about Kriging-based failure probability estimation, referred to as...

Bayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical pro...

The stochastic dynamic analysis of high-dimensional nonlinear systems is a critical concern in engineering fields, especially when considering the reliability analysis of low-probability events. To address this challenge, the dimension-reduced probability density evolution equation (DR-PDEE) method has recently emerged as a promising tool. The DR-P...

Structural reliability analysis stands as an essential tool for assessing the capacity of engineering structures to fulfill their designated functions in various disciplines, such as civil engineering, mechanical engineering, and aerospace engineering. Significant advances in methodology and computational tools have been achieved over the last few...

The assessment of structural reliability is crucial when it comes to ensuring the safety and durability of engineering systems, especially in areas such as civil engineering, aerospace and mechanical engineering. In this paper, an approach is presented using a probabilistic load model derived from environmental processes, such as seismic events. Th...

Bayesian updating reduces epistemic uncertainty for more reliable predictions, but characterizing the distribution of conditional failure probability with measurement data is complex. This study proposes an efficient and accurate method to fully describe the probabilistic characteristics of the updated conditional failure probability. It formulates...

Estimation of the response probability distributions of computer simulators in the presence of randomness is a crucial task in many fields. However, achieving this task with guaranteed accuracy remains an open computational challenge, especially for expensive-to-evaluate computer simulators. In this work, a Bayesian active learning perspective is p...

Buildings and structures in many regions of the world are exposed to environmental factors that can cause damage or failure, making it essential to model these factors accurately in engineering. Stochastic dynamics are crucial for modelling environmental processes, such as earthquake ground motions and wind loads, which can be characterised by a po...

Line sampling (LS) is a powerful stochastic simulation method for structural reliability analysis, especially for assessing small failure probabilities. To further improve the performance of traditional LS, a Bayesian active learning idea has been successfully pursued. This work presents another Bayesian active learning alternative, called `Bayesia...

A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility fu...

Structural reliability analysis is essential for evaluating the ability of engineering structures to perform their intended functions, including safety, serviceability, and durability. Although numerous methods have been developed for structural reliability analysis over the past few decades, traditional methods are still inefficient and/or inaccur...

Bayesian active learning methods have emerged for structural reliability analysis, showcasing more attractive features compared to existing active learning methods. The parallel adaptive Bayesian quadrature (PABQ) method, as a representative of them, allows to efficiently assessing small failure probabilities but faces the problem of empirically sp...

The concept of Bayesian active learning has recently been introduced from machine learning to structural reliability analysis. Although several specific methods have been successfully developed, significant efforts are still needed to fully exploit their potential and to address existing challenges. This work proposes a quasi-Bayesian active learni...

In stochastic dynamics, ensuring the structural reliability of buildings and structures is of paramount importance, especially when subjected to environmental loads such as wind or earthquakes. To adequately address these loads and the uncertainties associated with them, it is often necessary to utilise advanced load models, frequently expressed us...

Bayesian active learning methods have emerged for structural reliability analysis and shown more attractive features than existing active learning methods. However, it remains a challenge to actively learn the failure probability by fully exploiting its posterior statistics. In this study, a novel Bayesian active learning method termed ‘Parallel Ba...

Uncertainty quantification (UQ) involves quantitatively characterizing all sources ofuncertainties arising from both computational and real-world applications. It plays apivotal role in various scientific and engineering domains, particularly in situationswhere decisions or product designs hinge on imperfectly known system aspects dueto a lack of i...

In engineering analysis, propagating parametric probability boxes (p-boxes) remains a challenge since a computationally expensive nested solution scheme is involved. To tackle this challenge, this paper proposes a novel optimization-integration method to propagate parametric p-boxes, mainly focusing on estimating the lower and upper bounds of struc...

Line sampling has been demonstrated to be a promising simulation method for structural reliability analysis, especially for assessing small failure probabilities. However, its practical performance can still be significantly improved by taking advantage of, for example, Bayesian active learning. Along this direction, a recently proposed `partially...

Random and interval variables can coexist in a single structural reliability analysis problem. The existing methods for such hybrid reliability analysis, however, cannot balance the computational cost and accuracy well. In this paper, a fully decoupled approach based on Bayesian active learning is developed to estimate the failure probability funct...

This paper aims at approximating the bounds of the static response of structures with interval uncertainties. Such task is often challenging due to the large number of computationally intensive response evaluations required. To address this challenge, we propose an efficient non-intrusive method, namely, parallel Bayesian interval optimization (PBI...

Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, l...

Near-fault pulse-like ground motions attract increasing attention in engineering because they tend to cause more severe damage to structures than ordinary ground motions. Landslides, as the most common natural hazard triggered by earthquakes, pose a critical threat to life and infrastructure safety. However, the seismic reliability assessment of sl...

Evaluating the large reliability index of an-implicit and nonlinear performance function (PF) is still a challenging problem in practical engineering. To overcome this problem, an efficient method by using multiple techniques is proposed. A strategy is proposed to select the optimal transformation parameter (OTP) that makes the transformed PF appro...

First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is...

This work proposes a Bayesian updating approach, called parallel Bayesian optimization and quadrature (PBOQ). It is rooted in Bayesian updating with structural reliability methods (BUS) and offers a coherent Bayesian approach for the BUS analysis by assuming Gaussian process priors. The first step of the method, i.e., parallel Bayesian optimization...

Spatial uncertainty of soil parameters has a significant impact on the analysis of slope stability. Interval field analysis is emerging as a complementary tool of the conventional random field method that can take spatial uncertainty into account, which, however, has not been investigated in slope stability analysis. The present paper proposes a ne...

First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed 'fractional moments-based mixture distribution', to address such challenge. This approach is impleme...

Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of resp...

The paper presents an efficient method for quantification of extreme response statistics of stochastic dynamic systems from a small number of samples. Specifically, the fractional moment as a generalized concept of the traditional statistical moment is of interest. To strike a trade-off between efficiency and accuracy, a sequential sampling strateg...

First-passage probability estimation of stochastic dynamic systems is an important but still challenging problem in various science and engineering fields. This paper proposes a novel parametric approach, termed 'fractional moments-based mixture distribution' (FMs-MD), to address this challenge. Such method is based on capturing the extreme value d...

Multiple types of uncertainty characterization models usually coexist within a single practical uncertainty quantification (UQ) problem. However, efficient propagation of such hybrid uncertainties still remains one of the biggest computational challenges to be tackled in the UQ community. In this study, a novel Bayesian approach, termed 'Parallel B...

Both random and interval variables can coexist in a single reliability problem. Such cases could pose a serious challenge for existing reliability analysis methods. In this paper, we present a parallel active learning Kriging method for hybrid reliability analysis under both random and interval variables. The key contribution of the proposed method...

Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilist...

This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive black-box function over a prescribed hyper-rectangle. On this basis, a novel non-intrusive method, calle...

In practical engineering, experimental data is not fully in line with the true system response due to various uncertain factors, e.g., parameter imprecision, model uncertainty, and measurement errors. In the presence of mixed sources of aleatory and epistemic uncertainty, stochastic model updating is a powerful tool for model validation and paramet...

Surrogate modelling has emerged as a useful technique to study complex physical and engineering systems in various disciplines, especially for engineering analysis. Previous studies mostly focused on developing new surrogate models and/or applying existing surrogate models to practical problems. Despite the computational efficiency, the surrogate f...

Imprecise probabilities have gained increasing popularity for quantitatively modelling uncertainty under incomplete information in various fields. However, it is still a computationally challenging task to propagate imprecise probabilities since a double-loop procedure is usually involved. In this contribution, a fully decoupled method, termed as `...

Efficient assessment of small first-passage failure probabilities of nonlinear structures with uncertain parameters under stochastic seismic excitations is an important but still challenging problem. In principle, the first-passage failure probabilities can be evaluated once the extreme value distribution (EVD) of studied structural response become...

The seismic reliability assessment (SRA) of complex nonlinear structures which possess structural and seismic uncertainty is an open challenge for academics and practical engineers. This paper proposes an improved maximum entropy method (IMEM) for the SRA of nonlinear structures. Non-stationary ground motions are first generated via a random-functi...

The first-order reliability method (FORM) is a prevalent method in the structural reliability community. However, when solving the high-dimensional problem with a highly nonlinear limit state function, FORM usually encounters non-convergence or divergence. In this study, an improved FORM combining Harris Hawks Optimization (HHO-FORM) is presented f...

In this paper, a novel hybrid cubature formula is proposed for moment-based uncertainty propagation analysis. First, the contribution-degree analysis is performed to classify the input random vector of the response function into two separate parts, i.e. the more important one and less important one. In this regard, the statistical moment of the res...

In this paper, an efficient approach is proposed for seismic reliability analysis of nonlinear structures with random parameters subjected to non-stationary stochastic ground motions. First, the first-passage reliability problem is equivalently transformed to the evaluation of the extreme value distribution (EVD) of the response. A mixture of inver...

The first‐order reliability method (FORM) is well recognized as an efficient approach for reliability analysis. Rooted in considering the reliability problem as a constrained optimization of a function, the traditional FORM makes use of gradient‐based optimization techniques to solve it. However, the gradient‐based optimization techniques may resul...

High-dimensional reliability analysis is still an open challenge in structural reliability community. To address this problem, a new sampling approach, named the good lattice point method based partially stratified sampling is proposed in the fractional moments-based maximum entropy method. In this approach, the original sample space is first parti...

As is known, there are many unavoidable uncertainties inherent in the engineering structure systems, so the use of deterministic analysis methods may often lead to severe consequences. Structural reliability analysis provides theoretical basis and computational approaches for the propagation and quantification of uncertainty in structural engineeri...

This paper proposes a novel algorithm to reconstruct an unknown distribution by fitting its first-four moments to a proper parametrized probability distribution (PPD) model. First, a PPD system containing three previously developed PPD models is suggested to approximate the unknown distribution, rather than empirically adopting a single distributio...

This paper presents a new bivariate dimension reduction method (BDRM) for statistical moments evaluation and structural reliability analysis with accuracy and efficiency. A high-order unscented transformation (HUT) is introduced to evaluate the two-dimensional integrals involved in BDRM, and the free parameter involved in HUT is suggested. In this...

The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficie...