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Two-stage stochastic model updating approach based on Bayesian framework and hybrid multi-population migrant genetic-metropolis-hastings algorithm for heavy-haul railway bridges

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ENGINEERING OPTIMIZATION 2024年

作者： Yang, Hongyin Wu, Nanhao Cao, Hongyou Zhang, Wei Wuhan Inst Technol Sch Civil Engn & Architecture Wuhan Peoples R China Fujian Prov Univ Engn Res Ctr Disaster Prevent & Mitigat Southeast Putian Peoples R China Wuhan Univ Technol Sch Civil Engn & Architecture Wuhan Peoples R China

This study proposes a stochastic model updating approach using an improved multi-population migrant genetic algorithm (MMGA) with the metropolis-hastings (MH) algorithm based on the Bayesian inference approach. To enhance the search capacity of the genetic algorithm (GA), the MMGA introduces heuristic: the promotion and elimination mechanisms of urban population migration. The stochastic model updating approach includes two stages. The optimal values identified by the MMGA without considering the parameter uncertainties in the first stage are used as the initial values for the MH algorithm to accelerate Bayesian inference for uncertain parameters in the second stage. A practical application, the Yellow River Bridge with a heavy-haul railway line, demonstrates that the proposed approach offers an increased probability of gaining the global optimum, and predictions of displacements and frequencies provided by the updated finite element model are comparable to those obtained from the field tests.

关键词： Two-stage stochastic model updating Bayesian framework improved multi-population migrant genetic algorithms metropolis-hastings algorithm

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Note on the sampling distribution for the metropolis-hastings algorithm

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2003年第4期32卷 775-789页

作者： Geweke, J Tanizaki, H Kobe Univ Grad Sch Econ Kobe Hyogo 6578501 Japan Univ Iowa Dept Econ Iowa City IA 52242 USA

The metropolis-hastings algorithm has been important in the recent development of Bayes methods. This algorithm generates random draws from a target distribution utilizing a sampling (or proposal) distribution. This article compares the properties of three sampling distributions-the independence chain, the random walk chain, and the Taylored chain suggested by Geweke and Tanizaki (Geweke, J., Tanizaki, H. (1999). On Markov Chain Monte-Carlo methods for nonlinear and non-Gaussian state-space models. Communications in Statistics, Simulation and. Computation 28(4):867-894, Geweke, J., Tanizaki, H. (2001). Bayesian estimation of state-space model using the metropolis-hastings algorithm within Gibbs sampling. Computational Statistics and Data Analysis 37(2):151-170).

关键词： metropolis-hastings algorithm sampling distribution taylored chain

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Bayesian estimation of state-space models using the metropolis-hastings algorithm within Gibbs sampling

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2001年第2期37卷 151-170页

作者： Geweke, J Tanizaki, H Univ Iowa Dept Econ Iowa City IA 52242 USA Kobe Univ Grad Sch Econ Nada Ku Kobe Hyogo 6578501 Japan

In this paper, an attempt is made to show a general solution to nonlinear and/or non-Gaussian state-space modeling in a Bayesian framework, which corresponds to an extension of Carlin et al. (J. Amer. Statist. Assoc. 87(418) (1992) 493-500) and Carter and Kohn (Biometrika 81(3) (1994) 541-553;Biometrika 83(3) (1996) 589-601). Using the Gibbs sampler and the metropolis-hastings algorithm, an asymptotically exact estimate of the smoothing mean is obtained from any nonlinear and/or non-Gaussian model. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed Bayes estimator. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： state-space model Bayesian estimation Markov chain Monte Carlo Gibbs sampler metropolis-hastings algorithm proposal density nonlinear and/or non-Gaussian smoothing

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Damage Identification of Frame Structure Based on Approximate metropolis-hastings algorithm and Probability Density Evolution Method

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2022年第3N04期22卷 2240014-2240014页

作者： Yang, Y. Ling, Y. Tan, X. K. Wang, S. Wang, R. Q. Chongqing Univ MOE Key Lab New Technol Construct Cities Mt Area Chongqing 400045 Peoples R China Chongqing Univ Sch Civil Engn Chongqing 400045 Peoples R China Power China Chongqing Engn Corp Ltd Chongqing 400060 Peoples R China

This paper proposes a new method to identify local damages in frame structures based on approximate metropolis-hastings (AMH) algorithm and statistical moment. By analyzing the sensitivity of different statistical moment-based damage indices, the fusion index of fourth-order displacement moment and eighth-order acceleration moment is selected. Then the local damages in frame structures are primarily evaluated by AMH algorithm, where Gibbs sampling is adopted. Finally, the uncertainty of identified local damages is analyzed by using probability density evolution method (PDEM). Numerical simulations have been conducted to compare the proposed method with other similar damage detection methods, showing that the proposed method is more time-saving due to the involvement of Gibbs sampling and more accurate in assessing the damage severity. Experimental study of a 12-story benchmark frame testing has also been carried out, further validating the effectiveness of the proposed method.

关键词： Statistical moment damage detection metropolis-hastings algorithm Gibbs sampling frame structures

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Modified metropolis-hastings algorithm with delayed rejection

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PROBABILISTIC ENGINEERING MECHANICS 2011年第3期26卷 405-412页

作者： Zuev, K. M. Katafygiotis, L. S. HKUST Dept Civil Engn Hong Kong Hong Kong Peoples R China

The development of an efficient MCMC strategy for sampling from complex distributions is a difficult task that needs to be solved for calculating the small failure probabilities encountered in the high-dimensional reliability analysis of engineering systems. Usually different variations of the metropolis-hastings algorithm (MH) are used. However, the standard MH algorithm does not generally work in high dimensions, since it leads to very frequent repeated samples. In order to overcome this deficiency one can use the Modified metropolis-hastings algorithm (MMH) proposed in Au and Beck (2001)[1]. Another variation of the MH algorithm, called the metropolis-hastings algorithm with delayed rejection (MHDR) has been proposed by Tierney and Mira (1999)[7]. The key idea behind the MHDR algorithm is to reduce the correlation between states of the Markov chain. In this paper we combine the ideas of MMH and MHDR and propose a novel modification of the MH algorithm, called the Modified metropolis-hastings algorithm with delayed rejection (MMHDR). The efficiency of the new algorithm is demonstrated with a numerical example where MMHDR is used together with Subset simulation for computing small failure probabilities in high dimensions. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Reliability metropolis-hastings algorithm Markov chains Markov chain Monte Carlo Variance reduction techniques Subset simulation Dynamic analysis

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Density estimation for the metropolis-hastings algorithm

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SCANDINAVIAN JOURNAL OF STATISTICS 2003年第4期30卷 699-718页

作者： Sköld, M Roberts, GO Lund Univ Ctr Math Sci SE-22100 Lund Sweden Univ Lancaster Lancaster LA1 4YW England

Kernel density estimation is an important tool in visualizing posterior densities from Markov chain Monte Carlo output. It is well known that when smooth transition densities exist, the asymptotic properties of the estimator agree with those for independent data. In this paper, we show that because of the rejection step of the metropolis-hastings algorithm, this is no longer true and the asymptotic variance will depend on the probability of accepting a proposed move. We find an expression for this variance and apply the result to algorithms for automatic bandwidth selection.

关键词： density estimation metropolis-hastings algorithm

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Modified metropolis-hastings algorithm with reduced chain correlation for efficient subset simulation

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PROBABILISTIC ENGINEERING MECHANICS 2011年第2期26卷 331-341页

作者： Santoso, A. M. Phoon, K. K. Quek, S. T. Natl Univ Singapore Dept Civil Engn Singapore 117576 Singapore

Simulation of Markov chain samples using the metropolis-hastings algorithm is useful for reliability estimation. Subset simulation is an example of the reliability estimation method utilizing this algorithm. The efficiency of the simulation is governed by the correlation between the simulated Markov chain samples. The objective of this study is to propose a modified metropolis-hastings algorithm with reduced chain correlation. The modified algorithm differs from the original in terms of the transition probability. It has been verified that the modified algorithm satisfies the reversibility condition and therefore the simulated samples follow the target distribution for the correct theoretical reasons. When applied to subset simulation, the modified algorithm produces a more accurate estimate of failure probability as indicated by a lower coefficient of variation and a lower mean square error. The advantage is more significant for small failure probability. Examples of soil slope with spatially variable properties were presented to demonstrate the applicability of the proposed modification to reliability estimation of engineering problems. It was found that the modified algorithm produces a more accurate estimator over the range of random dimensions studied. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： metropolis-hastings algorithm Markov chain Subset simulation Chain correlation Reliability estimation

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A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm

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PSYCHOMETRIKA 1998年第3期63卷 271-300页

作者： Arminger, G Berg Univ Gesamthsch Wuppertal Dept Econ D-42097 Wuppertal Germany Univ Calif Los Angeles Grad Sch Educ & Informat Studies Los Angeles CA 90024 USA

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Monte Carlo methods such as the Gibbs sampler and the metropolis-hastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a non-linear model for the dependence of performance on task complexity and goal specificity using empirical data.

关键词： Gibbs sampler LISREL model metropolis-hastings algorithm non-linear functions of latent regressors

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DOES WASTE RECYCLING REALLY IMPROVE THE MULTI-PROPOSAL metropolis-hastings algorithm? AN ANALYSIS BASED ON CONTROL VARIATES

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JOURNAL OF APPLIED PROBABILITY 2009年第4期46卷 938-959页

作者： Delmas, Jean-Francois Jourdain, Benjamin Univ Paris Est Paris France

The waste-recycling Monte Carlo (WRMC) algorithm introduced by physicists is a modification of the (multi-proposal) metropolis-hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) metropolis-hastings algorithm uses only the accepted proposals. In this paper we extend the WRMC algorithm to a general control variate technique and exhibit the optimal choice of the control variate in terms of the asymptotic variance. We also give an example which shows that, in contradiction to the intuition of physicists, the WRMC algorithm can have an asymptotic variance larger than that of the metropolis-hastings algorithm. However, in the particular case of the metropolis-hastings algorithm called the Boltzmann algorithm, we prove that the WRMC algorithm is asymptotically better than the metropolis-hastings algorithm. This last property is also true for the multiproposal metropolis-hastings algorithm. In this last framework we consider a linear parametric generalization of WRMC, and we propose an estimator of the explicit optimal parameter using the proposals.

关键词： metropolis-hastings algorithm multi-proposal algorithm Monte Carlo Markov chain variance reduction control variates ergodic theorem central limit theorem

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Efficient implementation of the metropolis-hastings algorithm, with application to the Cormack-Jolly-Seber model

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ENVIRONMENTAL AND ECOLOGICAL STATISTICS 2008年第1期15卷 79-87页

作者： Link, William A. Barker, Richard J. USGS Patuxent Wildlife Res Ctr Laurel MD 20708 USA Univ Otago Dept Math & Stat Dunedin New Zealand

Judicious choice of candidate generating distributions improves efficiency of the metropolis-hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution;this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack-Jolly-Seber model and its extensions.

关键词： Cormack-Jolly-Seber model Mark-recapture analysis Markov chain Monte Carlo metropolis-hastings algorithm

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