An active learning reliability method with multiple kernel functions based on radial basis function

Shi, Lingjian; Sun, Baozhi; Ibrahim, Dauda Sh.

doi:10.1007/s00158-019-02210-0

Cited by 42 publications

(14 citation statements)

References 47 publications

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“…Since it is difficult to obtain the physical equation of the device uncertainty parameter and its response, the key is to obtain the relationship between the uncertainty parameter and its response, that is, the proxy model. Currently, the most widely used proxy models are polynomial response surface proxy model [11], Kriging proxy model [12][13][14], radial basis function proxy model [15,16], and BP neural network proxy model [17][18][19]. Among them, the BP neural network proxy model significantly improved the robustness of the overall design of the mechanical structure with its low calculation cost and high noise processing capability [17].…”

Section: Reliability Analysis Methods Based On Cpso-br-bp Neural Network Proxy Modelmentioning

confidence: 99%

“…Currently, the most widely used proxy models are polynomial response surface proxy model [11], Kriging proxy model [12][13][14], radial basis function proxy model [15,16], and BP neural network proxy model [17][18][19]. Among them, the BP neural network proxy model significantly improves the robustness of the overall design of the mechanical structure with low calculation cost and high noise processing capability.…”

Section: Introductionmentioning

confidence: 99%

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Motion Reliability Analysis of Unlocking Trigger Device Based on CPSO-BR-BP Neural Network with Uncertain Parameters

Tian

Fan

Zhang

et al. 2021

Mathematical Problems in Engineering

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Aiming at overcoming the problem that the mechanism function of the unlocking trigger device is difficult to obtain and the corresponding reliability analysis cannot be performed, a motion reliability analysis method based on the CPSO-BR-BP neural network proxy model is proposed. Firstly, the particle swarm algorithm is optimized through the chaotic sequence, and the back-propagation (BP) neural network is optimized using Chaos Particle Swarm Optimization (CPSO) and Bayesian Regularization (BR) algorithm. The CPSO-BR-BP neural network proxy model is established, and the reliability of shape memory alloys (SMA) wire unlocking based on the structural function is calculated. Moreover, according to the structural function of the separation process, the motion reliability based on the proxy model and the improved membership function is calculated. Finally, a series reliability model is established based on the unlocking process and the separation process to calculate the reliability of the whole machine. The reliability of the unlocking trigger device is analyzed by the proposed method. Results show that the proposed method is computationally efficient with the calculated reliability of 0.9987.

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Section: Reliability Analysis Methods Based On Cpso-br-bp Neural Network Proxy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Motion Reliability Analysis of Unlocking Trigger Device Based on CPSO-BR-BP Neural Network with Uncertain Parameters

Tian

Fan

Zhang

et al. 2021

Mathematical Problems in Engineering

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“…Therefore, in order to improve the computational efficiency and to avoid a large of simulation cost in engineering reliability analysis, more recent attention has focused on surrogate model-based method, which aims to replace original performance function with approximate numerical model. Up to now, various surrogate models are widely used to balance accuracy and efficiency, such as response surface method (RSM), 17,18 neural network (NN), 19 radial basis function (RBF), 20,21 support vector machine (SVM), 22,23 Kriging model, 24–28 polynomial chaos expansion (PCE), 29 polynomial chaos kriging (PCK), 30 and deep neural network (DNN), 31 etc. Generally, to construct a surrogate model, one-shot sampling and sequential sampling are two typical methods.…”

Section: Introductionmentioning

confidence: 99%

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

You

Zhang

Tang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Reducing the surrogate model-based method computation without loss of prediction accuracy remains a significant challenge in structural reliability analysis. The unbalanced probability density, important information in critical region and information redundancy of added sample points are ignored in most of traditional surrogate-based methods, resulting in heavy computational burden. In this work, an active learning combining adaptive Kriging method and weighted penalty (AK-WP) is proposed to analyze the reliability of engineering structures. Firstly, an active learning and weighted penalty function (WPLF) is the result of integrating active learning method, weighted function and penalty function, which is proposed to find the most probable point (MPP). Meanwhile, to avoid redundant information, the best suitable MPP is determined by a proposed distance law established between the found MPP and the existing design of experiment (DoE). Secondly, the Kriging model is refined according to best suitable MPP in each iteration. Thirdly, the failure probability is estimated by the Monte Carlo sample points from the n-ball domain until the convergence condition is satisfied. The accuracy and efficiency of the proposed method are demonstrated by some numerical examples including the highly nonlinear, the small probability problems and implicit function, as well as a real engineering application.

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“…The classic metamodels include artificial neural network (ANN) [15]- [17], support vector machine (SVM) [18]- [19], Kriging model [20]- [21], radial basis function [22]- [23] (RBF) and exponential surrogate model [24]. Among them, as one of accurate interpolation methods, RBF can efficiently deal with high dimensional problems with exponentially converge rate [25]- [27] and the Gaussian function-based augmented RBF (ARBF) is one of the most widely used RBF, which can make full use of all the samples and possesses potentials to accomplish an accurate approximation [28]. So it had been widely applied in reliability evaluation and design fields [22], [25]- [28].…”

Section: Introductionmentioning

confidence: 99%

“…Among them, as one of accurate interpolation methods, RBF can efficiently deal with high dimensional problems with exponentially converge rate [25]- [27] and the Gaussian function-based augmented RBF (ARBF) is one of the most widely used RBF, which can make full use of all the samples and possesses potentials to accomplish an accurate approximation [28]. So it had been widely applied in reliability evaluation and design fields [22], [25]- [28].…”

Section: Introductionmentioning

confidence: 99%

A Novel Reliability Analysis Approach With Collaborative Active Learning Strategy-Based Augmented RBF Metamodel

2020

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Metamodels in lieu of time-demanding performance functions can accelerate the reliability analysis effectively. In this paper, we propose an efficient collaborative active learning strategy-based augmented radial basis function metamodel (CAL-ARBF), for reliability analysis with implicit and nonlinear performance functions. For generating the suitable samples, a CAL function is first designed to constrain the new samples being generated in sensitivity region, near limit state surface and keep certain distances mutually. Then by adjusting the adjustment coefficient of CAL function, the CAL-ARBF is mathematically modeled and the corresponding reliability analysis theory is developed. The effectiveness of the proposed approach is validated by four numerical samples, including global nonlinear problem, local nonlinear problem, nonlinear oscillator and truss structure. Through comparison of several state-of-the-art methods, the proposed CAL-ARBF is demonstrated to possess the computational advantages in efficiency and accuracy for reliability analysis.

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An active learning reliability method with multiple kernel functions based on radial basis function

Cited by 42 publications

References 47 publications

Motion Reliability Analysis of Unlocking Trigger Device Based on CPSO-BR-BP Neural Network with Uncertain Parameters

Motion Reliability Analysis of Unlocking Trigger Device Based on CPSO-BR-BP Neural Network with Uncertain Parameters

An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis

A Novel Reliability Analysis Approach With Collaborative Active Learning Strategy-Based Augmented RBF Metamodel

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