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.

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.

Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Henry Arenbeck ◽  
Samy Missoum ◽  
Anirban Basudhar ◽  
Parviz Nikravesh
Keyword(s):  
Multibody Systems ◽  
Adaptive Sampling ◽  
Design Space ◽  
Limit State ◽  
Uniform Design ◽  
Probability Of Failure ◽  
Support Vector ◽  
State Function ◽  
Nominal System ◽  
Truncated Normal

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Improved Line Sampling Reliability Analysis Method and its Application

2007 ◽  
Vol 353-358 ◽  
pp. 1001-1004 ◽  
Author(s):  
Shu Fang Song ◽  
Zhen Zhou Lu
Keyword(s):  
Markov Chain ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Computational Cost ◽  
State Function ◽  
Line Sampling ◽  
Failure Region ◽  
Important Direction

For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in failure region. In the presented method, Markov Chain is employed to simulate the samples located at failure region, and the important direction of line sampling is obtained from these simulated samples. Simultaneously, the simulated samples can be used as the samples for line sampling to evaluate the failure probability. Since the Markov Chain samples are recycled for both determination of the important direction and calculation of the failure probability, the computational cost of the line sampling is reduced greatly. The practical application in reliability analysis for low cycle fatigue life of an aeronautical engine turbine disc structure under 0-takeoff-0 cycle load shows that the presented method is rational and feasible.

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.

A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Dynamic Properties ◽  
Limit State ◽  
Quadratic Function ◽  
State Function ◽  
Analysis Method ◽  
Engineering Structures ◽  
Reliability Problem ◽  
Time Invariant

Abstract Due to the uncertainties and the dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. This paper proposes a novel time-variant reliability analysis method using failure processes decomposition to transform the time-variant reliability problems to the time-invariant problems for dynamic structures under uncertainties. The transformation is achieved via a two-stage failure processes decomposition. First, the limit state function with high dimensional input variables and high order temporal parameters is transformed to a quadratic function of time based on the optimized time point in the first-stage failure processes decomposition. Second, based on the characteristics of the quadratic function and reliability criterion, the time-variant reliability problem is then transformed to a time-invariant system reliability problem in the second-stage failure processes decomposition. Then, the kernel density estimation (KDE) method is finally employed for the system reliability evaluation. Several examples are used to verify the effectiveness of the proposed method to demonstrate its efficiency and accuracy.

RCA-PCK: A new structural reliability analysis method based on PC-Kriging and radial centralized adaptive sampling strategy

2020 ◽  
pp. 095440622095771
Author(s):  
Zhenliang Yu ◽  
Zhili Sun ◽  
Runan Cao ◽  
Jian Wang ◽  
Yutao Yan
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Adaptive Sampling ◽  
Structural Reliability ◽  
Sampling Strategy ◽  
Kriging Model ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Structural Reliability Analysis ◽  
Training Samples

To improve the efficiency and accuracy of reliability assessment for structures with small failure probability and time-consuming simulation, a new structural reliability analysis method (RCA-PCK) is proposed, which combines PC-Kriging model and radial centralized adaptive sampling strategy. Firstly, the PC-Kriging model is constructed by improving the basis function of Kriging model with sparse polynomials. Then, the sampling region which contributes a great impact on the failure probability is constructed by combining the radial concentration and important sampling technology. Subsequently, the k-means++ clustering technology and learning function LIF are adopted to select new training samples from each subdomains in each iteration. To avoid the sampling distance in one subdomain or the distance between the new training samples in two subdomains being too small, we construct a screening mechanism to ensure that the selected new training samples are evenly distributed in the limit state. In addition, a new convergence criterion is derived based on the relative error estimation of failure probability. Four benchmark examples are given to illustrate the convergence process, accuracy and stability of the proposed method. Finally, the transmission error reliability analysis of thermal-elastic coupled gears is carried out to prove the applicability of the proposed method RCA-PCK to the structures with strong nonlinearity and time-consuming simulation.

A Time-Variant Reliability Analysis Method Based on Stochastic Process Discretization

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
C. Jiang ◽  
X. P. Huang ◽  
X. Han ◽  
D. Q. Zhang
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Complex Structure ◽  
Random Variable ◽  
State Function ◽  
Analysis Method ◽  
Reliability Problem ◽  
Reliability Method

Time-variant reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant reliability analysis method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant reliability problem into a conventional time-invariant system reliability problem. By linearizing the limit-state function with the first-order reliability method (FORM) and furthermore, introducing a new random variable, the converted system reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

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