Sequential importance sampling for structural reliability analysis

Papaioannou, Iason; Papadimitriou, Costas; Straub, Daniel

doi:10.1016/j.strusafe.2016.06.002

Cited by 186 publications

(107 citation statements)

References 32 publications

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“…N is the total number of data points in the dataset and h D is the size of the volume. Thus, to search for the peaks, we must calculate the densities of all of the different data points using Equation (8). However, this is computationally expensive: Another method fixes h and applies a kernel density estimator [31].…”

Section: Preliminary Investigationsmentioning

confidence: 99%

“…However, as we mentioned in Section 3, the form of probability function p(x) is not known, and it can instead be represented by an approximate probability function, which is f (x) in Algorithm 1 line 4. Therefore, in this paper, we use Equation (8) to calculate the approximate probability function, which we use in the proposed algorithm. Equation (8) is simpler and more practical for finding dataset peaks.…”

Section: The Algorithmmentioning

confidence: 99%

“…Bayesian optimization is typically used for hyper-parameter optimizations; to the best of our knowledge, our approach is the first to use BO to improve clustering. Moreover, other Bayesian theorem based algorithms, such as [8][9][10][11], are also appropriate optimization strategies for training online and offline machine learning algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian-Optimization-Based Peak Searching Algorithm for Clustering in Wireless Sensor Networks

Zhang

Zhao

Shin

et al. 2018

JSAN

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Abstract:We propose a new peak searching algorithm (PSA) that uses Bayesian optimization to find probability peaks in a dataset, thereby increasing the speed and accuracy of clustering algorithms. Wireless sensor networks (WSNs) are becoming increasingly common in a wide variety of applications that analyze and use collected sensing data. Typically, the collected data cannot be directly used in modern data analysis problems that adopt machine learning techniques because such data lacks additional information (such as data labels) specifying its purpose of users. Clustering algorithms that divide the data in a dataset into clusters are often used when additional information is not provided. However, traditional clustering algorithms such as expectation-maximization (EM) and k-means algorithms require massive numbers of iterations to form clusters. Processing speeds are therefore slow, and clustering results become less accurate because of the way such algorithms form clusters. The PSA addresses these problems, and we adapt it for use with the EM and k-means algorithms, creating the modified PSEM and PSk-means algorithms. Our simulation results show that our proposed PSEM and PSk-means algorithms significantly decrease the required number of clustering iterations (by 1.99 to 6.3 times), and produce clustering that, for a synthetic dataset, is 1.69 to 1.71 times more accurate than it is for traditional EM and enhanced k-means (k-means++) algorithms. Moreover, in a simulation of WSN applications aimed at detecting outliers, PSEM correctly identified the outliers in a real dataset, decreasing iterations by approximately 1.88 times, and PSEM was 1.29 times more accurate than EM at a maximum.

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Section: Preliminary Investigationsmentioning

confidence: 99%

Section: The Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian-Optimization-Based Peak Searching Algorithm for Clustering in Wireless Sensor Networks

Zhang

Zhao

Shin

et al. 2018

JSAN

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“…Structural reliability analysis has been extensively studied, and various methods have been proposed to estimate failure probability (FP) for complex structures, including the Advanced First Order Second Moment (AFOSM) (Hasofer and Lind), the moment method (Zhao and Ono), the second order reliability method (Hohenbichler and Rackwitz), the Monte Carlo simulation (MCS) (Liu), the importance sampling (IS) (Melchers, Tang et al, Dai et al, and Papaioannou et al), the subset simulation (Au and Beck and Li and Au), the line sampling (LS) (Schuëller et al and Depina et al), the directional sampling (Jinsuo and Ellingwood), the response surface method (RSM) (Rajashekhar and Ellingwood and Zhou et al), the dimension reduction (Xu and Rahman, Rahman and Wei, Wei and Rahman, and Li and Ma), the polynomial chaos expansion (Sudret and Der Kiureghian and Berveiller), the eigenvector dimension reduction (Byeng et al), the asymptotic sampling (Bucher, Tang et al, and Tang et al), the hierarchical clustering (Yin and Ahsan Kareem), and many other techniques. These methods have considerably promoted the state‐of‐the‐art in the structural reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

A surrogate‐based iterative importance sampling method for structural reliability analysis

Tang

Xia

2018

Quality & Reliability Eng

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In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF.

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“…We use sequential importance sampling (SIS, [2]) to approximate integral (3) efficiently. SIS generates samples from a sequence of distributions {h i (Θ), i = 0, .…”

mentioning

confidence: 99%

Efficient Conditional Reliability Updating with Sequential Importance Sampling

Ehre

Papaioannou

Straub

2018

Proc Appl Math and Mech

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Data on the performance of engineering systems can and should be used to learn system parameters and update the system reliability estimate. This can be achieved in a Bayesian framework. In order to capture the dependence of the reliability estimate on the data used, we consider the probability of failure conditional on the updating variables, i.e. those variables on which data is available. Thus, the probability of failure becomes a random variable itself. In practice, the distribution of the conditional probability of failure may be obtained by solving a reliability problem at several samples from the updating variable space which causes a considerable increase in required computational effort. To address this challenge, we devise a procedure for the fast re-computation of failure probabilities within a sequential sampling method. We exploit the similarity of reliability problems with small distance in a suitable norm by sequentially initializing computations with failure samples of similar problem solutions.

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Sequential importance sampling for structural reliability analysis

Cited by 186 publications

References 32 publications

Bayesian-Optimization-Based Peak Searching Algorithm for Clustering in Wireless Sensor Networks

Bayesian-Optimization-Based Peak Searching Algorithm for Clustering in Wireless Sensor Networks

A surrogate‐based iterative importance sampling method for structural reliability analysis

Efficient Conditional Reliability Updating with Sequential Importance Sampling

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