Pengfei Wei

Northwestern Polytechnical University | NWPU · School of Power and Energy

(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...

(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...

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...

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...

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...

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...

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...

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...

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...

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...

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,...

The ubiquitous uncertainties presented in the input factors (e.g., material properties and loads) commonly lead to occasional failure of mechanical systems, and these input factors are generally characterized as random variables or stochastic processes. For identifying the contributions of the uncertainties presented in the input factors to the tim...

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters...

The kinematic failure of a mechanism is commonly caused by the random input errors such as the errors of component dimensions and motion inputs. For identifying the main source of the failure probability, the global reliability sensitivity analysis is introduced. The method is based on decomposing the variance of the failure domain indicator functi...

Permutation variable importance measure (PVIM) based on random forest and Morris' screening design are two effective techniques for measuring the variable importance in high dimensions. The former technique is developed in the machine learning discipline and widely used in bioinformatics, while the latter technique is popular in scientific computin...

Measuring variable importance for computational models or measured data is an important task in many applications. It has drawn our attention that the variable importance analysis (VIA) techniques were developed independently in many disciplines. We are strongly aware of the necessity to aggregate all the good practices in each discipline, and comp...

Nowadays, utilizing the Monte Carlo estimators for variance-based sensitivity analysis has gained sufficient popularity in many research fields. These estimators are usually based on n+2 sample matrices well designed for computing both the main and total effect indices, where n is the input dimension. The aim of this paper is to use such n+2 sample...

Global sensitivity analysis techniques for computational models with precise random inputs have been studied widely in the past few decades. However, in real engineering application, due to the lack of information, the distributions of input variables cannot be specified uniquely, and other models such as probability-box (p-box) need to be introduc...

Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1)assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2)identifying the opt...

The variance ratio function, derived from the contribution to sample variance (CSV) plot, is a regional sensitivity index for studying how much the output deviates from the original mean of model output when the distribution range of one input is reduced and to measure the contribution of different distribution ranges of each input to the variance...

Combined with advantages of moving least squares approximation, a new method for estimating higher-order conditional moment is established, which is useful for application in importance analysis and provides a supplement of the standard variance-based importance analysis. On the other hand, after obtaining the first four-order moments, the probabil...

A new set of variance-based sensitivity indices, called W-indices, is proposed. Similar to the Sobol's indices, both main and total effect indices are defined. The W-main effect indices measure the average reduction of model output variance when the ranges of a set of inputs are reduced, and the total effect indices quantify the average residual va...

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts effi...

In risk assessment, the moment-independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire di...

Through several decades of development, global sensitivity analysis has been developed as a very useful guide tool for assessing scientific models and has gained pronounced attention in environmental science. However, standard global sensitivity analysis aims at measuring the contribution of input variables to model output uncertainty on average by...

In the design of engineering structure, uncertainties can be modeled as randomness or fuzziness depending on the amount of information available. In this article, the estimation of failure probability of structural system with multiple failure modes and mixed (random and fuzzy) inputs is considered. We firstly review the addition law of failure pro...

In order to explore the contributions by correlated input variables to the variance of the model output, the contribution decomposition of the correlated input variables based on Mara's definition is investigated in detail. By taking the quadratic polynomial output without cross term as an illustration, the solution of the contribution decompositio...

The moment-independent sensitivity analysis (SA) is one of the most popular SA techniques. It aims at measuring the contribution of input variable(s) to the probability density function (PDF) of model output. However, compared with the variance-based one, robust and efficient methods are less available for computing the moment-independent SA indice...