scholarly journals Improved Reliability-Based Optimization with Support Vector Machines and Its Application in Aircraft Wing Design

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Yu Wang ◽  
Xiongqing Yu ◽  
Xiaoping Du
Keyword(s):  
Support Vector Machines ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Wing Design ◽  
Aircraft Wing ◽  
Vector Machines

A new reliability-based design optimization (RBDO) method based on support vector machines (SVM) and the Most Probable Point (MPP) is proposed in this work. SVM is used to create a surrogate model of the limit-state function at the MPP with the gradient information in the reliability analysis. This guarantees that the surrogate model not only passes through the MPP but also is tangent to the limit-state function at the MPP. Then, importance sampling (IS) is used to calculate the probability of failure based on the surrogate model. This treatment significantly improves the accuracy of reliability analysis. For RBDO, the Sequential Optimization and Reliability Assessment (SORA) is employed as well, which decouples deterministic optimization from the reliability analysis. The improved SVM-based reliability analysis is used to amend the error from linear approximation for limit-state function in SORA. A mathematical example and a simplified aircraft wing design demonstrate that the improved SVM-based reliability analysis is more accurate than FORM and needs less training points than the Monte Carlo simulation and that the proposed optimization strategy is efficient.

Iterative Algorithm for Structure Reliability Analysis Based on Support Vector Classification Method

2007 ◽  
Vol 353-358 ◽  
pp. 1009-1012
Author(s):  
Chao Ma ◽  
Zhen Zhou Lu
Keyword(s):  
Reliability Analysis ◽  
Iterative Algorithm ◽  
Limit State ◽  
Sampling Procedure ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Structure Reliability ◽  
Important Region ◽  
Actual Limit

For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the present method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the proposed rational iteration and sampling procedure, the constructed support vector classification machine can converge to the actual limit state function at the important region, which contributes to the failure probability significantly. Then the precision of the reliability analysis is improved. The implementation of the presented method is given in detail, and the feasibility and the efficiency are demonstrated by the illustrations.

Reliability Analysis Method Based on Support Vector Machines Classification and Adaptive Sampling Strategy

2012 ◽  
Vol 544 ◽  
pp. 212-217 ◽  
Author(s):  
Hong Yan Hao ◽  
Hao Bo Qiu ◽  
Zhen Zhong Chen ◽  
Hua Di Xiong
Keyword(s):  
Reliability Analysis ◽  
Adaptive Sampling ◽  
Limit State ◽  
Computational Cost ◽  
Sampling Strategy ◽  
Support Vector ◽  
State Function ◽  
Analysis Method ◽  
Design Problems ◽  
Vector Machines

For probabilistic design problems with implicit limit state functions encountered in practical application, it is difficult to perform reliability analysis due to the expensive computational cost. In this paper, a new reliability analysis method which applies support vector machine classification(SVM-C) and adaptive sampling strategy is proposed to improve the efficiency. The SVM-C constructs a model defining the boundary of failure regions which classifies samples as safe or failed using SVM-C, then this model is used to replace the true limit state function,thus reducing the computational cost. The adaptive sampling strategy is applied to select samples along the constraint boundaries. It can also improves the efficiency of the proposed method. In the end, a probability analysis example is presented to prove the feasible and efficient of the proposed method.

Adaptive Virtual Support Vector Machine for the Reliability Analysis of High-Dimensional Problems

2011 ◽  
Author(s):  
Hyeongjin Song ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liang Zhao ◽  
David Lamb
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Decision Function ◽  
High Dimensional ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Response Surface Methods ◽  
Virtual Samples ◽  
Virtual Support

In this study, an efficient classification methodology is developed for reliability analysis while maintaining the accuracy level similar to or better than existing response surface methods. The sampling-based reliability analysis requires only the classification information — a success or a failure – but the response surface methods provide real function values as their output, which requires more computational effort. The problem is even more challenging to deal with high-dimensional problems due to the curse of dimensionality. In the newly proposed virtual support vector machine (VSVM), virtual samples are generated near the limit state function by using linear or Kriging-based approximations. The exact function values are used for approximations of virtual samples to improve accuracy of the resulting VSVM decision function. By introducing the virtual samples, VSVM can overcome the deficiency in existing classification methods where only classified function values are used as their input. The universal Kriging method is used to obtain virtual samples to improve the accuracy of the decision function for highly nonlinear problems. A sequential sampling strategy that chooses a new sample near the true limit state function is integrated with VSVM to maximize the accuracy. Examples show the proposed adaptive VSVM yields better efficiency in terms of the modeling time and the number of required samples while maintaining similar level or better accuracy especially for high-dimensional problems.

A novel adaptive support vector machine method for reliability analysis

2021 ◽  
pp. 1748006X2110033
Author(s):  
Zhaoyin Shi ◽  
Zhenzhou Lu ◽  
Xiaobo Zhang ◽  
Luyi Li
Keyword(s):  
Support Vector Machine ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Adaptive Learning ◽  
Limit State ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Learning Function ◽  
Svm Model

For the structural reliability analysis, although many methods have been proposed, they still suffer from substantial computational cost or slow convergence rate for complex structures, the limit state function of which are highly non-linear, high dimensional, or implicit. A novel adaptive surrogate model method is proposed by combining support vector machine (SVM) and Monte Carlo simulation (MCS) to improve the computational efficiency of estimating structural failure probability in this paper. In the proposed method, a new adaptive learning method is established based on the kernel function of the SVM, and a new stop criterion is constructed by measuring the relative position between sample points and the margin of SVM. Then, MCS is employed to estimate failure probability based on the convergent SVM model instead of the actual limit state function. Due to the introduction of adaptive learning function, the effectiveness of the proposed method is significantly higher than those that employed random training set to construct the SVM model only once. Compared with the existing adaptive SVM combined with MCS, the proposed method avoids information loss caused by inconsistent distance scales and the normalization of the learning function, and the proposed convergence criterion is also more concise than that employed in the existing method. The examples in the paper show that the proposed method is more efficient and has broader applicability than other similar surrogate methods.

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.

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