Stochastic Response Surface Method Based on Weighted Regression and Its Application to Fatigue Reliability Analysis of Crankshaft

2009 ◽  
Author(s):  
Yi Fei Sun ◽  
Hao Bo Qiu ◽  
Liang Gao ◽  
Ke Lin ◽  
Xue Zheng Chu
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Limit State ◽  
Weighted Regression ◽  
Normal Equation ◽  
Fatigue Reliability ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method

Response surface method (RSM) is widely used in structural reliability analysis with implicit performance function (PF) which requires formidable computational effort. The ill conditioned coefficient matrix of normal equation in classical RSM prevents it from being used in high order conditions. The stochastic response surface method (SRSM), deriving from classical RSM, offers one alternative to solve this problem. Yet the regression method of conventional SRSM is based on normal least square method which ignores the different significance of each sample point through which the response surface function (RSF) is formed. To yield RSF close to the limit state which leads to better estimation of probability of failure, this paper introduces the weighted regression into SRSM and several examples with hypothetic explicit PF are given to test the performance of SRSM. In addition, we use this method in the fatigue reliability analysis of crankshaft with implicit PF. All these examples demonstrate the advantages of the proposed method.

scholarly journals Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Qinghai Zhao ◽  
Xiaokai Chen ◽  
Zheng-Dong Ma ◽  
Yi Lin
Keyword(s):  
Topology Optimization ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Computational Efficiency ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Grid Design

A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis

2019 ◽  
Vol 16 (05) ◽  
pp. 1840017 ◽  
Author(s):  
Amit Kumar Rathi ◽  
P. V. Sudhi Sharma ◽  
Arunasis Chakraborty
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Moving Least Square ◽  
Stochastic Response Surface Method ◽  
Reliability Based Design ◽  
Surface Method ◽  
Grid Scheme

The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.

Fuzzy Reliability Analysis of Nonlinear Structural System Based on Stochastic Response Surface Method

2014 ◽  
Vol 912-914 ◽  
pp. 1268-1271 ◽  
Author(s):  
Yun Ji
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Systems ◽  
State Function ◽  
Fuzzy Reliability ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Highly Nonlinear

Response surface method (RSM) is widely accepted as an efficient method for reliability analysis, especially when the limit state function (LSF) is supposed to be highly nonlinear or closed-form mechanical models to describe the complex structural systems are not available. However, the selection of different response surface functions may result in different computational accuracy and computing time. In this paper, stochastic response surface method (SRSM), in which Hermite polynomials are employed to approximate the real LSF, is adopted in this paper to analyze the fuzzy reliability of structural systems. With a beam presented as an example, traditional methods, such as FORM, JC method and sequence response surface method, and the method raised in the context are compared in case of the study on solving the reliability. The results show that fuzzy reliability analysis with SRSM is relatively much more efficient and less time-consuming, thus the method raised is more suitable for the analysis of this kind of problems.

An Efficient Method for Structural Reliability Analysis

2012 ◽  
Vol 204-208 ◽  
pp. 3044-3047
Author(s):  
Liu Ying
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Analysis Method ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Comparative Accuracy ◽  
The Mean

An efficient reliability analysis method has been proposed in the paper, which based on stochastic response surface method. The key advantage of the stochastic response surface method is that the collocation points are selected for minimizing the mean square error, and from high probability regions, thus leading to fewer function evaluations for high accuracy. Compared with Monte Carlo method, the proposed technique can be more efficiency while achieve comparative accuracy.

Sign in / Sign up

Export Citation Format

Share Document