Structural Reliability Evaluation Using Enhanced HDMR

2008 ◽  
Author(s):  
B. N. Rao ◽  
Rajib Chowdhury
Keyword(s):  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Statistical Simulation ◽  
Higher Order ◽  
Complex Model ◽  
High Dimensional ◽  
Approximation Technique ◽  
High Dimensional Model Representation ◽  
Model Assessment

This paper presents a new computational tool for predicting failure probability of randomly parametered structural/mechanical systems based on high dimensional model representation (HDMR) generated from low order function components. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. When first-order HDMR approximation of the original high dimensional implicit limit state/performance function is not adequate to provide desired accuracy to the predicted failure probability, this paper presents an enhanced HDMR (eHDMR) method to represent the higher order terms of HDMR expansion by expressions similar to the lower order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input-output samples without directly invoking the determination of second- and higher order HDMR terms. This study aims to assess how accurately and efficiently eHDMR approximation technique can capture complex model output uncertainty. As a part of this effort, the efficacy of HDMR approximation, which is recently applied to reliability analysis, is also demonstrated. Once the approximate form of implicit response function is defined using HDMR/eHDMR, the failure probability can be obtained by statistical simulation.

Structural Reliability Analysis with Multi-Failure Models Using High-Dimensional Model Representation

2013 ◽  
Vol 351-352 ◽  
pp. 1648-1651
Author(s):  
Wei Tao Zhao ◽  
Lei Jia ◽  
Cheng Kui Niu
Keyword(s):  
Failure Probability ◽  
Parallel System ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
State Function ◽  
Model Assessment ◽  
Series System ◽  
Dimensional Model ◽  
Failure Models

Based on the high dimensional model representation (HDMR) and Monte Carlo simulation (MCS), this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models. The HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. Once the limit state function is defined by using the HDMR, the failure probability can be obtained by using the MCS without increasing computational efforts. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the HDMR are both high in terms of series system and parallel system, the accuracy can be acceptable with respect to series system, and the accuracy can not be acceptable with respect to parallel system.

A Method of Multi-Failure Models Based on Response Surfaces Method-High Dimensional Model Representation on Structural Reliability Analysis

2015 ◽  
Vol 724 ◽  
pp. 3-6
Author(s):  
Lei Jia ◽  
Fa Cai Guan
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Structural Reliability ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Dimensional Model ◽  
Surface Method ◽  
Failure Models

The response surface method (RSM) is widely adopted for structural reliability analysis because of its numerical efficiency. However, the RSM is time consuming for large-scale applications and sometimes shows large errors in the calculation of the sensitivity of the reliability index with respect to random variables. In order to overcome these problems, this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models which is based on the high dimensional model representation (HDMR) and response surface method (RSM).Once the limit state function is defined, the design point can be found by using HDMR method, through which the response surface can be established to calculate the failure probability. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the RSM-HDMR are both high in terms of series system and parallel system.

MEMBERSHIP FUNCTION OF FAILURE PROBABILITY USING MULTICUT-HIGH DIMENSIONAL MODEL REPRESENTATION

2012 ◽  
Vol 19 (04) ◽  
pp. 1250018
Author(s):  
A. S. BALU ◽  
B. N. RAO
Keyword(s):  
Reliability Analysis ◽  
Membership Function ◽  
Failure Probability ◽  
Structural Reliability ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Dimensional Model ◽  
Convolution Integral ◽  
Fuzzy Variables ◽  
Uncertain Variables

The structural reliability analysis in the presence of mixed uncertain variables demands more computation as the entire configuration fuzzy variables needs to be explored. Moreover the existence of multiple design points deviate the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this paper a novel uncertainty analysis method for estimating the membership function of failure probability of structural systems involving multiple design points in the presence of mixed uncertain variables is presented. The proposed method involves Multicut-High Dimensional Model Representation technique for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability analysis involving any number of fuzzy and random variables. The accuracy and efficiency of the proposed method is demonstrated through three examples.

Alternative Kriging-HDMR optimization method with expected improvement sampling strategy

2017 ◽  
Vol 34 (6) ◽  
pp. 1807-1828 ◽  
Author(s):  
Enying Li ◽  
Fan Ye ◽  
Hu Wang
Keyword(s):  
Standard Deviation ◽  
Sampling Strategy ◽  
Suggested Method ◽  
Expected Improvement ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Analysis Tool ◽  
Model Assessment ◽  
Content Type ◽  
Kriging Predictor

Purpose The purpose of study is to overcome the error estimation of standard deviation derived from Expected improvement (EI) criterion. Compared with other popular methods, a quantitative model assessment and analysis tool, termed high-dimensional model representation (HDMR), is suggested to be integrated with an EI-assisted sampling strategy. Design/methodology/approach To predict standard deviation directly, Kriging is imported. Furthermore, to compensate for the underestimation of error in the Kriging predictor, a Pareto frontier (PF)-EI (PFEI) criterion is also suggested. Compared with other surrogate-assisted optimization methods, the distinctive characteristic of HDMR is to disclose the correlations among component functions. If only low correlation terms are considered, the number of function evaluations for HDMR grows only polynomially with the number of input variables and correlative terms. Findings To validate the suggested method, various nonlinear and high-dimensional mathematical functions are tested. The results show the suggested method is potential for solving complicated real engineering problems. Originality/value In this study, the authors hope to integrate superiorities of PFEI and HDMR to improve optimization performance.

An adaptive SVR-HDMR model for approximating high dimensional problems

2015 ◽  
Vol 32 (3) ◽  
pp. 643-667 ◽  
Author(s):  
Zhiyuan Huang ◽  
Haobo Qiu ◽  
Ming Zhao ◽  
Xiwen Cai ◽  
Liang Gao
Keyword(s):  
Support Vector Regression ◽  
Direct Method ◽  
Model Representation ◽  
Computational Time ◽  
High Dimensional ◽  
Support Vector ◽  
High Dimensional Model Representation ◽  
Model Assessment ◽  
Dimensional Model ◽  
Content Type

Purpose – Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. The purpose of this paper is to use support vector regression with high dimensional model representation (SVR-HDMR) model to obtain accurate metamodels for high dimensional problems with a few sampling points. Design/methodology/approach – High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. Support vector regression (SVR) method can approximate the underlying functions with a small subset of sample points. Dividing Rectangles (DIRECT) algorithm is a deterministic sampling method. Findings – This paper proposes a new form of HDMR by integrating the SVR, termed as SVR-HDMR. And an intelligent sampling strategy, namely, DIRECT method, is adopted to improve the efficiency of SVR-HDMR. Originality/value – Compared to other metamodeling techniques, the accuracy and efficiency of SVR-HDMR were significantly improved. The SVR-HDMR helped engineers understand the essence of underlying problems visually.

Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

2013 ◽  
Author(s):  
Zhonglai Wang ◽  
Zissimos P. Mourelatos ◽  
Jing Li ◽  
Amandeep Singh ◽  
Igor Baseski
Keyword(s):  
Stochastic Processes ◽  
Dynamic Systems ◽  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Reliability Estimation ◽  
Time Dependent ◽  
Cumulative Distribution ◽  
High Dimensional ◽  
Subset Simulation

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work addresses systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.

Efficient Assessment of Structural Reliability in Presence of Random and Fuzzy Uncertainties

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
A. S. Balu ◽  
B. N. Rao
Keyword(s):  
Function Approximation ◽  
Structural Reliability ◽  
Limit State ◽  
Reliability Estimation ◽  
High Dimensional Model Representation ◽  
State Function ◽  
Convolution Integral ◽  
Possibility Distribution ◽  
Fuzzy Variables ◽  
Uncertain Variables

This paper presents an efficient uncertainty analysis for estimating the possibility distribution of structural reliability in presence of mixed uncertain variables. The proposed method involves high dimensional model representation for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In this methodology, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods, thus the computational efficiency is accomplished. The proposed method is applicable for structural reliability estimation involving any number of fuzzy and random variables with any kind of distribution.

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