A new sampling strategy for Kriging-based response surface method and its application in structural reliability

2016 ◽  
Vol 20 (4) ◽  
pp. 564-581 ◽  
Author(s):  
Buyu Jia ◽  
XiaoLin Yu ◽  
QuanSheng Yan
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Iterative Process ◽  
Structural Reliability ◽  
Interpolation Method ◽  
Limit State ◽  
Sampling Strategy ◽  
Surface Method ◽  
Number Theoretic Method ◽  
Process Strategy

A new sampling strategy is proposed to improve the robustness and efficiency of the Kriging-based response surface method. In the initial stage, the number-theoretic method is utilized to generate deterministic initial design samples, which are further optimized by an interpolation method. In the sequential iterative process, a new sampling criterion called reliability infill sampling criterion is proposed. Besides, a more reasonable two-process strategy is suggested where the iterative process is divided into two sub-processes using different sampling criteria. The proposed method ensures that the approximation can be accurately and efficiently fitted near the limit state. The numerical examples and the applications in structural reliability indicate the improved accuracy and efficiency of the proposed method.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

Reliability Analysis of Self-Anchored Suspension Bridge by Improved Response Surface Method

2011 ◽  
Vol 90-93 ◽  
pp. 869-873 ◽  
Author(s):  
Xiao Lin Yu ◽  
Quan Sheng Yan
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Suspension Bridge ◽  
Support Vector ◽  
Surface Method ◽  
Reliability Method ◽  
Improved Response Surface Method

The response surface method (RSM) developed in recent years is an effective way to solve the structural reliability problems with implicit performance function. In order to improve the computational efficiency and make RSM suitable well to large and complex engineering structures, the reliability analysis method based on uniform design method (UDM) and support vector machine (SVM) was proposed. UDM is adopted to select training data and SVM is used as response surface. Structural reliability index is calculated in combination with the traditional reliability analysis methods (such as, the first-order reliability method (FORM), the second-order reliability method (SORM) or Monte Carlo simulation method (MCSM)). Numerical examples show that sampled with the UDM can greatly reduce the number of samples required for training by SVM model, and a very good approximation of the limit state surface can be obtained to get the failure probability. The reliability analysis of the under serviceability limit-state of a typical self-anchored suspension bridge——Sanchaji Bridge was carried out with the improved response surface method.

A modified downhill simplex algorithm interpolation response surface method for structural reliability analysis

2019 ◽  
Vol 37 (4) ◽  
pp. 1423-1450
Author(s):  
Hailiang Su ◽  
Fengchong Lan ◽  
Yuyan He ◽  
Jiqing Chen
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Simplex Algorithm ◽  
Content Type ◽  
Structural Reliability Analysis ◽  
Surface Method ◽  
Downhill Simplex

Purpose Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM). Design/methodology/approach In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis. Findings The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy. Originality/value This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

A new response surface method based on the adaptive bivariate cut-HDMR

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenliang Fan ◽  
Wei Shen ◽  
Qingbin Zhang ◽  
Alfredo H.-S. Ang
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Limit State ◽  
Sampling Technique ◽  
Content Type ◽  
Surface Method ◽  
Wide Range ◽  
Cross Terms ◽  
Order Polynomial ◽  
Component Function

Purpose The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness. Design/methodology/approach By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state. Findings The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points. Originality/value This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Application of a new local effective constrained response surface method in structural reliability optimization design

2019 ◽  
Vol 36 (3) ◽  
pp. 1055-1078 ◽  
Author(s):  
Hailiang Su ◽  
Fengchong Lan ◽  
Yuyan He ◽  
Jiqing Chen
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Optimization Design ◽  
Structural Reliability ◽  
Reliability Optimization ◽  
Content Type ◽  
Meta Model ◽  
Proxy Model ◽  
Surface Method ◽  
Sampling Points

Purpose Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model. Design/methodology/approach The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated. Findings The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations. Originality/value This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.

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