An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method

Shayanfar, Mohsen Ali; Barkhordari, Mohammad Ali; Roudak, Mohammad Amin

doi:10.1016/j.cnsns.2016.11.021

Cited by 43 publications

(15 citation statements)

References 24 publications

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“…The failure probability obtained by MCS is 2.1 × 10 −8 . This data is duplicated from Reference 9, where a method combines the traditional response surface method with the IS method (RSM + IS) was proposed. The performance function is very simple and a pretty accurate result can be obtained by FORM.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Yuan

Cheng

2020

Numerical Meth Engineering

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A novel method which combines the active learning Kriging (ALK) model with important sampling is proposed in this paper. The main aim of the proposed method is to solve problems with very small failure probability and multiple failure regions. A surrogate limit state surface (LSS) which strikes a balance between the Kriging mean and variance is proposed. In each iteration, important samples of the surrogate LSS are generated, optimal training points are chosen, the Kriging model is updated and the surrogate LSS is refined. After several iterations, the surrogate LSS will converge to the true LSS. To obtain all the local and global most probable points (MPPs) on the surrogate LSS in each iteration, a recently proposed evolutionary algorithm from the field of multimodal optimization is introduced. In this way, none of the potential failure regions is missed and the unbiasedness of the proposed method is guaranteed. The contribution factor of each MPP is defined and a weighted multimodal instrumental sampling density is formulated. In this way, more attention is paid to the more important failure regions and training points are further saved. The performance of the proposed method is verified by six case studies.

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Section: Numerical Examplesmentioning

confidence: 99%

“…6. If Ratio ≥ 0.98 and m ≥ N min , which means the Kriging model has been accurate enough, go to step (9). Otherwise, set N Seq = 0 and prepare to enrich the DoE.…”

Section: Obtain the Contribution Factor Of Each Mpp And Build An Ipdfmentioning

confidence: 99%

Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Yuan

Cheng

2020

Numerical Meth Engineering

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“…Three process selection models have been carried out and the best model for response surface is quadratic, then a variety analysis is performed. Shayanfar et al (2017) state the main criteria for accuracy were based on testing the Lack of Fit. The model was considered appropriate if, after the test, the model's inaccuracy was statistically insignificant and considered inappropriate to explain a problem from an analysis examined if the inaccuracy of the model is significant.…”

Section: Viscositymentioning

confidence: 99%

Optimization of NaOH concentration and trichloroacetic acid in bacterial carboxymethylation cellulose

Santosa¹,

Wignyanto²,

Hidayat³

et al. 2019

Food Res.

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The aims of this study were to obtain the optimal concentration of NaOH and trichloroacetic acid in the process of making CMC from bacterial cellulose. The experimental design used is response surface method. In the present study, NaOH as the variable X1 is concentration with a minimum limit (-1) of 30%, optimal limit (0) of 35% while the maximum limit (+1) of 40%. Variable X2 is the trichloroacetic acid concentration with a minimum limit (-1) of 25%, an optimal limit (0) of 30% and a maximum limit (+1) of 35%. Based on calculations using the program, expert design combination of treatments was obtained by 13 samples. The selection of the treatment above is based on the fact that in making CMC the alkalization process and carboxymethylation play an important role. The results showed variable optimum points of NaOH and Trichloroacetic Acid concentrations were 35.95% and 30.87%. The optimum point of the independent variable, the optimum response value of the substitution degree obtained was 0.897, water content of 20.08%, pH of 10.04 and viscosity of 17. 26%. In conclusion, that the best treatment of NaOH concentration on 35.95%, trichloroacetic acid on 30.87%, substitution degrees on 0.93, water content on 19.86%, pH on 10.17, and viscosity on 17.39 cPs.

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“…Obtain the Allowed LCF Life of the Gas Turbine Disc according to Reliability Probability. After the LCF life of the gas turbine disc f ( ) is calculated out with (18), the PF of the gas turbine disc LCF life can be expressed as (19) allow denotes the allowed LCF life of the gas turbine disc. The reliability probability value of the LCF life of gas turbine disc should be greater than or equal to 99.87% and the corresponding reliability index is 3.0115 which is obtained by = Φ(− ).…”

Section: Probabilistic Analysis On Low Cycle Fatigue Life Ofmentioning

confidence: 99%

“…Goswami et al [18] proposed an improved RSM with the moving leastsquares method, which can reduce the number of iteration. Shayanfar et al [19] proposed a new efficient RSM, which is combined with the importance sampling concepts. The vicinity of the design point is located with the method of the concepts of importance sampling and an effective twostep updating role, through which a suitable seedbed for the subsequent iteration of RSM is obtained.…”

Section: Introductionmentioning

confidence: 99%

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

Wei

Bai

Wang

et al. 2018

Mathematical Problems in Engineering

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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.

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An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method

Cited by 43 publications

References 24 publications

Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Active learning method combining Kriging model and multimodal‐optimization‐based importance sampling for the estimation of small failure probability

Optimization of NaOH concentration and trichloroacetic acid in bacterial carboxymethylation cellulose

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

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