Iterative Most Probable Point Search Method for Problems With Mixture of Random and Interval Variables

2017 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi
Keyword(s):  
Reliability Analysis ◽  
Performance Measure ◽  
Search Method ◽  
Additional Function ◽  
Most Probable Point ◽  
Mixed Variables ◽  
Mathematical Correlation ◽  
Interval Variables ◽  
Inverse Reliability Analysis ◽  
Mixed Variable

To represent input variability accurately, input distribution model for random variables should be constructed using many observations or data. However, for certain input variables, engineers may have only their bounds which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. For the applications, to consider both input variability and uncertainty, inverse reliability analysis should be carried out considering the mixed variables and their mathematical correlation in performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed variable problem. The random and interval variables update procedures are developed considering the features of mixed variable in the inverse reliability analysis. Both variable update methods proceed one iteration simultaneously to consider the mathematical correlation. An interpolation method is introduced to find better candidate MPP without additional function evaluations. Mixed variable design optimization (MVDO) has been formulated to obtain cost effective and reliable design in the presence of the mixed variables. In addition, the design sensitivity of probabilistic constraint has been developed for effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds accurate MPP more efficiently than generic optimization method. In addition, it is verified that the developed method enables MVDO process with small number of function evaluations.

Iterative Most Probable Point Search Method for Problems With a Mixture of Random and Interval Variables

2019 ◽  
Vol 142 (7) ◽  
Author(s):  
Hyunkyoo Cho ◽  
Kyung K. Choi ◽  
Jaekwan Shin
Keyword(s):  
Reliability Analysis ◽  
Performance Measure ◽  
Search Method ◽  
Additional Function ◽  
Most Probable Point ◽  
Mixed Variables ◽  
Mathematical Correlation ◽  
Interval Variables ◽  
Inverse Reliability Analysis ◽  
Mixed Variable

Abstract To represent input variability accurately, an input distribution model for random variables should be constructed using many data. However, for certain input variables, engineers may have only their intervals, which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. To consider both input variability and uncertainty, inverse reliability analysis should be carried out considering both random and interval variables—mixed variables—and their mathematical correlation in a performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed-variable problem. The update procedures for MPP search are developed considering the features of mixed variables in the inverse reliability analysis. MPP search for random and interval variables proceed simultaneously to consider the mathematical correlation. An interpolation method is introduced to find a better candidate MPP without additional function evaluations. Mixed-variable design optimization (MVDO) has been formulated to obtain cost-effective and reliable design in the presence of mixed variables. In addition, the design sensitivity of a probabilistic constraint has been developed for an effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds an accurate MPP more efficiently than the generic optimization method does. In addition, it is verified that the developed method enables the MVDO process with a small number of function evaluations.

Interval Reliability Analysis

2007 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Performance Characteristic ◽  
Extreme Values ◽  
Probability Distributions ◽  
Probability Of Failure ◽  
Interval Reliability ◽  
Interval Variables ◽  
Inverse Reliability Analysis ◽  
Reliability Method ◽  
A Performance

Traditional reliability analysis uses probability distributions to calculate reliability. In many engineering applications, some nondeterministic variables are known within intervals. When both random variables and interval variables are present, a single probability measure, namely, the probability of failure or reliability, is not available in general; but its lower and upper bounds exist. The mixture of distributions and intervals makes reliability analysis more difficult. Our goal is to investigate computational tools to quantify the effects of random and interval inputs on reliability associated with performance characteristics. The proposed reliability analysis framework consists of two components — direct reliability analysis and inverse reliability analysis. The algorithms are based on the First Order Reliability Method and many existing reliability analysis methods. The efficient and robust improved HL-RF method is further developed to accommodate interval variables. To deal with interval variables for black-box functions, nonlinear optimization is used to identify the extreme values of a performance characteristic. The direct reliability analysis provides bounds of a probability of failure; the inverse reliability analysis computes the bounds of the percentile value of a performance characteristic given reliability. One engineering example is provided.

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

Confidence-Based Design Optimization Under Data Uncertainty Using Most Probable Point-Based Approach

2019 ◽  
Author(s):  
Yongsu Jung ◽  
Hyunkyoo Cho ◽  
Ikjin Lee
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Performance Measure ◽  
Cumulative Distribution ◽  
Data Uncertainty ◽  
Normal Space ◽  
Most Probable Point ◽  
Input Distribution ◽  
Design Variables ◽  
Distribution Parameters

Abstract An accurate input statistical model has been assumed in most of reliability-based design optimization (RBDO) to concentrate on variability of random variables. However, only limited number of data are available to quantify the input statistical model in practical engineering applications. In other words, irreducible variability and reducible uncertainty due to lack of knowledge exist simultaneously in random design variables. Therefore, the uncertainty in reliability induced by insufficient data has to be accounted for RBDO to guarantee confidence of reliability. The uncertainty of input distributions is successfully propagated to a cumulative distribution function (CDF) of reliability under normality assumptions, but it requires a number of function evaluations in double-loop Monte Carlo simulation (MCS). To tackle this challenge, reliability measure approach (RMA) in confidence-based design optimization (CBDO) is proposed to handle the randomness of reliability following the idea of performance measure approach (PMA) in RBDO. Input distribution parameters are transformed to the standard normal space for most probable point (MPP) search with respect to reliability. Therefore, the reliability is approximated at MPP with respect to input distribution parameters. The proposed CBDO can treat confidence constraints employing the reliability value at the target confidence level that is approximated by MPP in P-space. In conclusion, the proposed method can significantly reduce the number of function evaluations by eliminating outer-loop MCS while maintaining acceptable accuracy.

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