Evidence Theory-Based Reliability Analysis and Optimization in Engineering Design

2007 ◽  
Author(s):  
Li Du ◽  
Liping He ◽  
Hong-Zhong Huang
Keyword(s):  
Reliability Analysis ◽  
Engineering Design ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Theoretical Research ◽  
Future Research ◽  
Sufficient Information ◽  
Computationally Efficient ◽  
Input Uncertainty ◽  
Analysis And Design

Engineering design under uncertainty has gained considerable attention in recent years. There exist two different types of uncertainties in practical engineering applications: aleatory uncertainty that is classified as objective and irreducible uncertainty with sufficient information on input uncertainty data and epistemic uncertainty that is a subjective and reducible uncertainty that is caused by the lack of knowledge on input uncertainty data. Among several alternative tools to handle uncertainty, evidence theory has proved to be computationally efficient and stable tool for reliability analysis and design optimization under aleatory and/or epistemic uncertainty involved in engineering systems. This paper attempts to give a better understanding of uncertainty in engineering design with a general overview. The overview includes theoretical research, computational development, and performable ability consideration of evidence theory during recent years. At last, perspectives on future research are stated.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Hybrid reliability analysis for energy-absorbing composite structures based on evidence theory

2014 ◽  
Vol 33 (22) ◽  
pp. 2095-2105 ◽  
Author(s):  
Shuyong Duan ◽  
Xujing Yang ◽  
Yourui Tao ◽  
Zhangping Hu ◽  
Yunbiao Chen
Keyword(s):  
Reliability Analysis ◽  
Composite Structures ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Analysis Model ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Hybrid Reliability ◽  
Energy Absorbing ◽  
Composite Energy

It is important to investigate the uncertain modeling and reliability analysis for the crashworthiness capacity of composite energy-absorbing structures (CEAS) in which there are random and epistemic uncertainty. A probability-evidence theory hybrid uncertainty model and a corresponding efficient reliability analysis method for the crashworthiness capacity of CEAS are presented in this paper. In this method, evidence theory is introduced to address the difficulties in the epistemic uncertain modeling due to the lack of experimental samples, which expand greatly the applicability of reliability analysis technology in the crashworthiness capacity of CEAS research. Moreover, the probability theory is applied to address the random uncertainty. Based on the traditional equivalence normalization method, a probability-evidence theory hybrid reliability analysis model for the crashworthiness capacity of CEAS is developed. An explicit finite element analysis is used to calculate the peak crushing force and the specific energy absorption of CEAS which are presented by the quadratic response surface. Two numerical examples of CEAS are presented for verification of the validity of the proposed method.

Computationally Efficient Imprecise Uncertainty Propagation in Engineering Design and Decision Making

2012 ◽  
Author(s):  
Dipanjan D. Ghosh ◽  
Andrew Olewnik
Keyword(s):  
Decision Making ◽  
Engineering Design ◽  
Computational Efficiency ◽  
Design Problem ◽  
Uncertainty Propagation ◽  
Future Research ◽  
Parameter Estimates ◽  
Design Decision ◽  
Computationally Efficient ◽  
Imprecise Uncertainty

Modeling uncertainty through probabilistic representation in engineering design is common and important to decision making that considers risk. However, representations of uncertainty often ignore elements of “imprecision” that may limit the robustness of decisions. Further, current approaches that incorporate imprecision suffer from computational expense and relatively high solution error. This work presents the Computationally Efficient Imprecise Uncertainty Propagation (CEIUP) method which draws on existing approaches for propagation of imprecision and integrates sparse grid numerical integration to provide computational efficiency and low solution error for uncertainty propagation. The first part of the paper details the methodology and demonstrates improvements in both computational efficiency and solution accuracy as compared to the Optimized Parameter Sampling (OPS) approach for a set of numerical case studies. The second half of the paper is focused on estimation of non-dominated design parameter spaces using decision policies of Interval Dominance and Maximality Criterion in the context of set-based sequential design-decision making. A gear box design problem is presented and compared with OPS, demonstrating that CEIUP provides improved estimates of the non-dominated parameter range for satisfactory performance with faster solution times. Parameter estimates obtained for different risk attitudes are presented and analyzed from the perspective of Choice Theory leading to questions for future research. The paper concludes with an overview of design problem scenarios in which CEIUP is the preferred method and offers opportunities for extending the method.

A Reliability-Based Multidisciplinary Design Optimization Method with Evidence Theory and Probability Theory

2018 ◽  
Vol 25 (01) ◽  
pp. 1850003 ◽  
Author(s):  
Chen Guoqiang ◽  
Tan Jianping ◽  
Tao Yourui
Keyword(s):  
Probability Theory ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Computational Efficiency ◽  
Multidisciplinary Design Optimization ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Optimization Method ◽  
Multidisciplinary Design ◽  
Multidisciplinary System

Uncertainties, including aleatory and epistemic uncertainties, always exist in multidisciplinary system. Due to the discontinuous nature of epistemic uncertainty and the complex coupled relation among subsystems, the computational efficiency of reliability-based multidisciplinary design optimization (RBMDO) with mixed aleatory and epistemic uncertainties is extremely low. A novel RBMDO procedure is presented in this paper based on combined probability theory and evidence theory (ET) to deal with hybrid-uncertainties and improve the computational efficiency. Firstly, based on Bayes method, a novel method to define the probability density function of the aleatory variables is proposed. Secondly, the conventional equivalent normal method (J-C method) is modified to reliability analysis with hybrid-uncertainties. Finally, a novel RBMDO procedure is suggested by integrating the modified J-C method into the frame of sequence optimization and reliability analysis (SORA). Numerical examples and engineering example are applied to demonstrate the performance of the proposed method. The examples show the excellence of the RBMDO method both in computational efficiency and accuracy. The proposed method provides a practical and effective reliability design method for multidisciplinary system.

Uncertainty Analysis With Probability and Evidence Theories

2006 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Probability Theory ◽  
Uncertainty Analysis ◽  
Physical System ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Future Research ◽  
Aleatory Uncertainty ◽  
Maximum Probability ◽  
Reliability Method ◽  
Input Parameters

Both aleatory and epistemic uncertainties exist in engineering applications. Aleatory uncertainty (objective or stochastic uncertainty) describes the inherent variation associated with a physical system or environment. Epistemic uncertainty, on the other hand, is derived from some level of ignorance or incomplete information about a physical system or environment. Aleatory uncertainty associated with parameters is usually modeled by probability theory and has been widely researched and applied by industry, academia, and government. The study of epistemic uncertainty in engineering has recently started. The feasibility of the unified uncertainty analysis that deals with both types of uncertainties is investigated in this paper. The input parameters with aleatory uncertainty are modeled with probability distributions by probability theory, and the input parameters with epistemic uncertainty are modeled with basic probability assignment by evidence theory. The effect of the mixture of both aleatory and epistemic uncertainties on the model output is modeled with belief and plausibility measures (or the lower and upper probability bounds). It is shown that the calculation of belief measure or plausibility measure can be converted to the calculation of the minimum or maximum probability of failure over each of the mutually exclusive subsets of the input parameters with epistemic uncertainty. A First Order Reliability Method (FORM) based algorithm is proposed to conduct the unified uncertainty analysis. Two examples are given for the demonstration. Future research directions are derived from the discussions in this paper.

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

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