Pengfei Wei

• Doctor of Philosophy
• Professor (Associate) at Northwestern Polytechnical University

(All the codes are attached. Please feel free to download and use them. If you have any question, don't hesitate to contact me.) Uncertainty propagation through the simulation models is critical for computational mechanics engineering to provide robust and reliable design in the presence of polymorphic uncertainty. This set of companion papers pres...

The combination of active learning with surrogate model (e.g., Gaussian Process Regression, GPR) for structural reliability analysis has been extensively studied and proved to be of superiority due to the high efficiency. The performance of an active learning algorithm is determined by the utilized acquisition function, to a great extent, as it dom...

This document is adapted from a reading guide document for the students of our team, and it presents a brief introduction to some of our selected papers published within five years, in the directions of Model Verification, Validation & Uncertainty Quantification (VV&UQ), Bayesian Computation, Structural Reliability Analysis and Design optimization,...

Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly...

As a main task of inverse problem, model updating has received more and more attention in the area of inspection, sensing, and monitoring technologies during the recent decades, where the estimation of posterior probability density function (PDF) of unknown model parameters is still challenging for expensive-to-evaluate models of interest. In this...

Efficient estimation of small failure probability subjected to multiple failure domains is one of the central and challenging issues in structural reliability analysis and other rare event analysis tasks, especially in case where the computational resource is quite limited but high accuracy is required. A new active learning scheme, named as Transi...

Calculating statistical moments of the response of mechanical systems in the presence of various uncertainties still remains one of the main topics in stochastic mechanics. To mitigate the "curse of dimensionality" of the existing direct numerical integration methods, the bivariate dimension-reduction method (BDRM) can be invoked. The original BDRM...

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...

This study bridges the concepts of subset simulation with asymptotic approximation theory inmultinormal integrals for the estimation of small probabilities. To meet this aim, for a sequence ofscaled limit state functions (LSFs) with failure probabilities higher than the original LSF, it isfound that the proposed asymptotic approximation and subset...

Uncertainty quantification (UQ) is essential for understanding and mitigating the impact of pervasive uncertainties in engineering systems, playing a crucial role in modern engineering practice. As engineering products grow increasingly complex and the demand for highly accurate UQ results intensifies, the need for efficient UQ methods has become p...

Calibration of computational models with experimental or operational data to achieve desired prediction accuracy has been widely recognized as a crucial problem in reliability engineering. Bayesian model updating (BMU) has been developed as an appealing methodology framework to achieve this goal, but the existing methods range from very approximate...

Accurate and efficient estimation of small failure probability subjected to high-dimensional and multiple failure domains is still a challenging task in structural reliability engineering. In this paper, we propose a stratified beta-spheres sampling method (SBSS) to tackle this task. Initially, the whole support space of random input variables is d...

Accurate and efficient estimation of small failure probability subjected to high-dimensional and multiple failure domains is still a challenging task in structural reliability engineering. In this paper, we propose a stratified beta-spheres sampling method (SBSS) to tackle this task. Initially, the whole support space of random input variables is d...

As a main task of inverse problem, model updating has received more and more attention in the area of inspection, sensing, and monitoring technologies during the recent decades, where the estimation of posterior probability density function (PDF) of unknown model parameters is still challenging for expensive-to-evaluate models of interest. In this...

Time-dependent reliability-oriented sensitivity analysis (ROSA) is a potent technique utilized to assess the impact of uncertain random input variables on the time-dependent reliability of planar linkage mechanisms. However, in cases where these random variables exhibit significant correlation behavior, the existing time-dependent ROSA indices will...

Estimating the small failure probability is a crucial task in structural engineering, and directional sampling has long been recognized as one of the most promising stochastic simulation method for problems with multiple disconnected failure domains. However, when applied to problems with expensive-to-evaluate and highly nonlinear limit state funct...

Engineering structures are inherently susceptible to a multitude of uncertainties, ranging from geometric variations to external stochastic loads. These uncertainties wield significant influence over structural performance and, in severe cases, can lead to structural failure. Thus, structural uncertainty quantification, which encompasses uncertaint...

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample...

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...

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample...

Purpose Bayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integrati...

For efficiently solving the Reliability-Based Design Optimization (RBDO) problem with multi-modal, highly nonlinear and expensive-to-evaluate limit state functions (LSFs), a sequential sampling-based Bayesian active learning method is developed in this work. The penalty function method is embedded to transform the constrained optimization problem i...

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...

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...

Estimating the failure probability is one of the core problems in reliability engineering. However, the existence of epistemic uncertainties, which result from the incomplete information of the input parameters, prevents us from learning the true value of the failure probability with high confidence. Thus, quantifying the influence of the input epi...

This chapter investigates the regression models and methods for machine learning in engineering computations, from both non-Bayesian and Bayesian perspectives. The non-Bayesian regression models, including the least square regression, ridge regression, and support vector regression, equipped or not equipped with kernel trick, are first examined as...

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...

Estimating the design points with high accuracy is a historical and key issue for many reliability analysis and reliability-based design optimization methods. Indeed, it is still a challenge especially when the limit state functions (LSFs) show highly nonlinear behaviors, and/or the reliability index is large, and/or the gradients of LSF are not av...

Uncertainty quantification (UQ) has been widely recognized as of vital importance for reliability-oriented analysis and design of engineering structures, and three groups of mathematical models, i.e., the probability models, the imprecise probability models and the non-probabilistic models, have been developed for characterizing uncertainties of di...

Uncertainty quantification has been realized as of vital importance in structural reliability engineering to achieve credible results especially when the available information is scarce, incomplete, imprecise, etc., and it is also recognized that the aleatory and epistemic uncertainties need to be distinguished and separated and characterized throu...

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...

This article describes a new adaptive Kriging method combined with adaptive importance sampling approximating the optimal auxiliary by iteratively building a Gaussian mixture distribution. The aim is to iteratively reduce both the modeling and sampling errors simultaneously, thus avoiding limitations in cases of very rare failure events. At each it...

The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when app...

The time-dependent reliability analysis aims at estimating the probability of failure, occurring within a specified time period, of a structure subjected to stochastic and dynamic loads or stochastic degradation of performance. Development of efficient numerical algorithms with accuracy assurance for solving this problem, although has been investig...

This paper deals with the issue on metamodelling (a.k.a. surrogate modelling) of nonlinear stochastic dynamical systems, which are often with multiple input uncertainties Θ∈Rn, viz., the dimension n may range from low to high (e.g., n≥10). In this paper, to circumvent the problem of “curse of dimensionality” of high-dimensional input uncertainties,...

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,...

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...

This article describes a new adaptive Kriging method designed to alleviate the limitations of other related approaches encounter in cases of extremely rare failure events. The main idea is to iteratively reduce both surrogate modelling error and sampling error. To do so the adaptive Kriging framework is associated with the multiple adaptive importa...

Probabilistic engineering computation involves two groups of models, i.e., the probability model for characterizing the randomness of input variables, and the physic model (usually described as a set of PDEs) for describing the behavior of a physic system. The probabilistic analysis aims at propagating the probability models through the physic one,...

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...

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...

Estimating the failure probabilities of multiple failure modes is a challenging task in structural reliability analysis. The conventional sequential importance sampling (conventional SIS) fails to estimate all the failure probabilities in a single run, leading to high computational expense and low efficiency. To address this issue, this study provi...

With this item, we are announcing "The First Sino-German Workshop on Reliability of Complex Systems", to be held on November 5-6, 2021, in Xi'an, China, in virtual form, with Prof. Michael Beer and Assoc. Prof. Pengfei Wei as chairs. Enclosed please find the workshop programme where the online room information is also given. Six keynote lectures fr...

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 `...

In this work, the reliability of complex systems under consideration of imprecision is addressed. By joining two methods coming from different fields, namely, structural reliability and system reliability, a novel methodology is derived. The concepts of survival signature, fuzzy probability theory and the two versions of non-intrusive stochastic si...

Variance-based sensitivity indices play an important role in scientific computation and data mining, thus the significance of developing numerical methods for efficient and reliable estimation of these sensitivity indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this article, the estimation of these sen...

This paper proposes a new non-probabilistic time-dependent reliability model for evaluating the kinematic reliability of mechanisms when the input uncertainties are characterized by intervals. Based on the introduction of the non-probabilistic interval process of motion error, the most probable point of an outcrossing is defined to transform the co...

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 efficient propagation of imprecise probabilities through expensive simulators has emerged to be one of the great challenges for mixed uncertainty quantification in computational mechanics. An active learning method, named Collaborative and Adaptive Bayesian Optimization (CABO), is developed for tackling this challenge by combining Bayesian Prob...

This contribution proposes an approach for the assessment of the failure probability associated with a particular class of series systems. The type of systems considered involves components whose response is linear with respect to a number of Gaussian random variables. Component failure occurs whenever this response exceeds prescribed deterministic...

Imprecise probability allows quantifying the level of safety of a system taking into account the effect of both aleatory and epistemic uncertainty. The practical estimation of an imprecise probability is usually quite demanding from a numerical viewpoint, as it is necessary to propagate separately both types of uncertainty, leading in practical cas...

This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying alpha-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is co...

published version available at: https://authors.elsevier.com/a/1bdRW39%7Et0VLw3. Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack...

Line Sampling (LS) has been widely recognized as one of the most appealing stochastic simulation algorithms for rare event analysis, but when applying it to many real-world engineering problems, improvement of the algorithm with higher efficiency is still required. This paper aims to improve both the efficiency and accuracy of LS by active learning...

Published version available at https://authors.elsevier.com/a/1bcOfAQEIt1QG. The efficient estimation of the failure probability function of rare failure events is a challenging task in the structural safety analysis when the input variables are characterized by imprecise probability models due to insufficient information on these variables. The re...

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the req...

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the req...

Probabilistic integration is a Bayesian inference technique for numerical integration, and has received much attention in the community of scientific and engineering computations. The most appealing advantages are the ability to improve the integration accuracy by making full use of the spatial correlation information among the design points, and t...

Fuzzy probability offers a framework for taking into account the effects of both aleatoric and epistemic uncertainty on the performance of a system, quantifying its level of safety, for example, in terms of a fuzzy failure probability. However, the practical application of fuzzy probability is often challenging due to increased numerical efforts ar...

The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges: small failure probability (typical less than 10-5) and time-demanding mechanical models. This paper proposes an improved active learning surrogate model method, which combines the advantages of the classical Acti...

Invited presentation given on CIVIL-COMP 2019, 16-19 September 2019 | Riva del Garda, near Lake Garda, Italy.

Uncertainty characterization and propagation through computational models are the two key basic problems in risk and reliability analysis of structures and systems. Commonly used methods are mostly based on precise probability models, which are effective for characterizing the aleatory uncertainty. In real-world applications, the available data of...

Non-intrusive Imprecise Stochastic Simulation (NISS) is a recently developed general methodological framework for efficiently propagating the imprecise probability models and for estimating the resultant failure probability functions and bounds. Due to the simplicity, high efficiency, stability and good convergence, it has been proved to be one of...

The tendency of uncertainty analysis has promoted the transformation of sensitivity analysis from the deterministic sense to the stochastic sense. This work proposes a stochastic sensitivity analysis framework using the Bhattacharyya distance as a novel uncertainty quantification metric. The Bhattacharyya distance is utilised to provide a quantitat...

Two challenges may exist in the reliability analysis of highly reliable structures in, e.g., aerospace engineering. The first one is that, the failure probability may be extremely small (typically, smaller than 1e-6), which commonly prevents us from generating accurate estimation with acceptable computational costs by using the available methods. T...

Here is the Matlab tool to calculate the Bhattacharyya distance between two random sample sets. As elaborated in the paper, the calculation employs the Probability Mass Function (PMF) estimated from each sample sets. The Matlab tool is universal for different problems with different numbers of outputs (i.e. multiple dimensional problems). Now, on...

This package provides Matlab codes for the algorithm "AK-MCMC" for efficiently and robustly estimating the extremely small failure probability, developed in the paper entitled "Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods". For more details, please fir...

If you have any questions on either methods or codes, please feel free to contact me at pengfeiwei@nwpu.edu.cn. This package provides Matlab codes of the "Non-intrusive imprecise stochastic simulation (NISS)" methodology framework for efficiently propagating the imprecise probability models. The codes are developed for the methods developed in the...

If you have any questions on either methods or codes, please feel free to contact me at pengfeiwei@nwpu.edu.cn. This package provides Matlab codes of the "Non-intrusive imprecise stochastic simulation (NISS)" methodology framework for efficiently propagating the imprecise probability models. The codes are developed for the methods developed in the...

The aim of this paper is to study the reliability analysis, parametric reliability sensitivity (PRS) analysis and global reliability sensitivity (GRS) analysis of structures with extremely rare failure events. Firstly, the GRS indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying ea...

The computational models in real-world applications commonly have multivariate dependent outputs of interest, and developing global sensitivity analysis techniques, so as to measure the effect of each input variable on each output as well as their dependence structure, has become a critical task. In this paper, a new moment-independent sensitivity...

This is a draft version of an invited chapter which has been published in the Chinese book"李杰, 陈建兵, 彭永波. 随机振动理论与应用新进展(第Ⅱ辑). 上海：同济大学出版社, 2018". It focuses on reviewing the recent developments on uncertainty quantification models and sensitivity analysis under uncertainty environment. Unfortunately, only Chinese version is available. 本文是关于不确定性量化模型和敏感...

(All the codes are attached. Please feel free to download and use them. If you have any question, don't hesitate to contact me.) Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stoc...

In many disciplines involving high-dimensional data, permutation variable importance measure (PVIM) based on random forest is widely used for importance ranking of model inputs. This work extends the traditional PVIM to investigate the regional effects of the internal value range of model inputs. The PVIM function is firstly defined to measure the...

This paper develops a new global sensitivity analysis (GSA) framework for computational models with input variables being characterized by second-order probability models due to epistemic uncertainties. Firstly, two graphical tools, called individual effect (IE) function and total effect (TE) function, are defined for identifying the influential an...

In the context of structural system reliability, quantifying the relative importance of random input variables and failure modes is necessary for improving system reliability and simplifying the reliability-based design problems. We firstly introduce the reliability-based variable importance analysis (VIA) indices to structural systems for quantify...

Identifying the parameters that substantially affect the time-dependent reliability is critical for reliability-based design of motion mechanism. The time-dependent local reliability sensitivity and global reliability sensitivity are the two effective techniques for this type of analysis. This work extends the first-passage method and PHI2 method,...