Reliability-Based Structural Optimization Using Sequential Response Surface Method

2012 ◽  
Vol 532-533 ◽  
pp. 1503-1506
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Structural Optimization ◽  
Response Surface ◽  
Response Surface Method ◽  
Computational Efficiency ◽  
Limit State ◽  
Computational Cost ◽  
Random Variables ◽  
State Function ◽  
Limit State Function ◽  
Surface Method

A design method of reliability-based structural optimization has a powerful advantage because some random variables can be considered. However, the sensitivity analysis of reliability with respect to random variables is very complicated and its computational cost is very expensive. Thus, a response surface method is adopted for approximating the limit state function to improve computational efficiency. An iterative strategy is used to determine a response surface that is able to fit the limit state function in the neighborhood of the design point. A sequential response surface method is performed to satisfy the demand of accuracy in the process of reliability-based structural optimization. A numerical example is presented to demonstrate the computational 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.

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.

Reliability Research of Building Fire Based on Numerical Simulation and Uniform Design

2011 ◽  
Vol 368-373 ◽  
pp. 665-672
Author(s):  
Su Fen Huang ◽  
Zhi Gang Song ◽  
Bin Li
Keyword(s):  
Numerical Simulation ◽  
Response Surface ◽  
Response Surface Method ◽  
Reliability Index ◽  
Limit State ◽  
Uniform Design ◽  
State Function ◽  
Limit State Function ◽  
Building Fire ◽  
Surface Method

Existing safety study of building fire is mainly based on the ISO834 temperature-time curve, which is a theoretical curve and not fully reflect the influencing factors of fire such as the distribution of fuel and ventilation of the building. Secondly, the reliability analysis of building fire lacks explicit limit state function, especially when the reliability calculation considers the internal force redistribution of the structure. Direct Monte Carlo simulation has no requirement of explicit limit state function, but it needs huge calculation efforts. To solve these two problems, the response surface method is proposed from the view point of numerical simulation and experiment design. Using the fire modeling software CFAST the actual result of temperature and thickness of smoke layer can be obtained. On this basis, the reliability index can be calculated with the response surface method，which can solve the problem of lacking explicit limit state function by regressing multi-variable function based on the inputs and outputs. Uniform design (UD) method can allocate more parameters without greatly increasing the calculation efforts. Using a case the calculation process is explained with. The results show that this method can quickly obtain the reliability index in the premise of less calculation.

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>

scholarly journals Reliability Evaluation of Bridges Based on Nonprobabilistic Response Surface Limit Method

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Xuyong Chen ◽  
Qian Chen ◽  
Xiaoya Bian ◽  
Jianping Fan
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Reliability Index ◽  
Limit State ◽  
Iteration Process ◽  
Evaluation Process ◽  
Reliability Evaluation ◽  
State Function ◽  
Interval Model ◽  
Surface Method

Due to many uncertainties in nonprobabilistic reliability assessment of bridges, the limit state function is generally unknown. The traditional nonprobabilistic response surface method is a lengthy and oscillating iteration process and leads to difficultly solving the nonprobabilistic reliability index. This article proposes a nonprobabilistic response surface limit method based on the interval model. The intention of this method is to solve the upper and lower limits of the nonprobabilistic reliability index and to narrow the range of the nonprobabilistic reliability index. If the range of the reliability index reduces to an acceptable accuracy, the solution will be considered convergent, and the nonprobabilistic reliability index will be obtained. The case study indicates that using the proposed method can avoid oscillating iteration process, make iteration process stable and convergent, reduce iteration steps significantly, and improve computational efficiency and precision significantly compared with the traditional nonprobabilistic response surface method. Finally, the nonprobabilistic reliability evaluation process of bridge will be built through evaluating the reliability of one PC continuous rigid frame bridge with three spans using the proposed method, which appears to be more simple and reliable when lack of samples and parameters in the bridge nonprobabilistic reliability evaluation is present.

scholarly journals Reliability Analysis on Structures Based on a Modified Iterative Response Surface Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yanxu Wei ◽  
Guangchen Bai ◽  
Bowei Wang ◽  
Bin Bai
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
State Function ◽  
Cycle Fatigue ◽  
Computational Accuracy ◽  
Surface Method ◽  
Turbine Disc

In order to improve the computational accuracy and efficiency of response surface method for reliability analysis on structures, a modified iterative response surface method (called as NDIRSM) is proposed. Firstly, a new starting center point, which is closer to design point, is calculated out as the starting center point instead of the point at mean values of input variables and a dynamic factor vector f1, which is inversely proportional to the change rate of performance function with respect to variance, is calculated out for the first iteration. Then the arbitrary factors fk are determined according to the design matrix condition number for the subsequent iteration. Thus the sample points are close to limit state function and the response surface function can approximate the limit state function accurately and efficiently. Two examples are employed to validate the advantages of NDIRSM and the results show that NDIRSM improves the computational accuracy and efficiency of response surface method. At last, NDIRSM is applied to the reliability analysis on low cycle fatigue life of a gas turbine disc, which provides a useful reference for reliability analysis on low cycle fatigue life of gas turbine disc and demonstrates the high computational accuracy and efficiency of NDIRSM.

Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS

2014 ◽  
Vol 578-579 ◽  
pp. 1449-1453
Author(s):  
Chun Xue Song ◽  
Yi Zhang ◽  
Ying Yi Cao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Design System ◽  
State Function ◽  
Surface Method

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

scholarly journals High Dimension Model Representation-Based Response Surface for Reliability Analysis of Tunnel

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hongbo Zhao
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Reliability Index ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Implicit Function ◽  
Surface Method ◽  
Reliability Method ◽  
Rock Tunnel

Uncertainty is an important prosperity to rock tunnel. Reliability analysis is widely used to deal with the uncertainty. But it is difficult to be adopted in rock tunnel using the traditional reliability method because the limit state function is an implicit function. High dimension model representation (HDMR) can approximate the high dimensional, nonlinear, and implicit function using the low dimensional function. In this study, the HDMR method was adapted to approximate the limit state function through combining with response surface method (RSM). A new reliability analysis approach of HDMR-based response surface method, combined with the first-order reliability method (FORM), is developed to calculate the reliability index of tunnel, and implementation of the method is explained briefly. A circular tunnel with analytical solution and horseshoe tunnel with numerical solution are used to demonstrate the proposed method. The obtained reliability index is in excellent agreement with Low and Tang’s (2007) method and traditional RSM. It shows that HDMR-based response surface can approximate well the limit state function, and the proposed method is an efficient and effective approach for reliability analysis in tunnel engineering. It is very useful for reliability analysis of practical large-scale rock engineering.

Reliability Analysis of Composite Laminate Structures by Moving Kriging Interpolation Response Surface Method

2015 ◽  
Vol 744-746 ◽  
pp. 222-225
Author(s):  
Wei Zhao ◽  
Yang Yang Chen ◽  
Qiu Wei Yang ◽  
Xue Yan Li
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Composite Laminate ◽  
Limit State ◽  
Kriging Interpolation ◽  
State Function ◽  
Moving Kriging Interpolation ◽  
Surface Method ◽  
Reliability Method

A response surface method (RSM) for composite laminate structures is proposed in this paper, which is based on the moving Kriging interpolation. The substitute limit state function for failure criteria is discussed and constructed on series of deterministic finite element analysis. Combined with first order reliability method, reliabilities of composite laminate structures are subsequently obtained. Reliability analysis of a composite laminate plate, as a numerical example, is illustrated by the proposed method. The results demonstrate the practicability of the 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.

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