Identification of Bouc–Wen type models using the Transitional Markov Chain Monte Carlo method

Ortiz, Gilberto A.; Álvarez, Diego A.; Bedoya-Ruíz, Daniel

doi:10.1016/j.compstruc.2014.10.012

Cited by 61 publications

(33 citation statements)

References 42 publications

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“…In Refs. [14,15,16], a Bayesian framework was exploited to quantify uncertainty in Bouc-Wen identification. Specialised NARX [17], neural network [18] and Hammerstein [19] models were also developed to address Bouc-Wen systems.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear state-space approach to hysteresis identification

Noël

Esfahani

Kerschen

et al. 2017

Mechanical Systems and Signal Processing

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Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.

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Section: Introductionmentioning

confidence: 99%

A nonlinear state-space approach to hysteresis identification

Noël

Esfahani

Kerschen

et al. 2017

Mechanical Systems and Signal Processing

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“…The method tries to overcome the aforementioned issues of MCMC by gradually pushing the samples from the prior to the posterior distribution. The method has become popular in both research and practice: recent contributions include [25], [15], [17], [13], [2]. In addition to the posterior samples generated by TMCMC, the method returns an estimate of the evidence of the Bayesian model class, which is needed for Bayesian model class selection and Bayesian model averaging [16,24].…”

Section: Introductionmentioning

confidence: 99%

Transitional Markov Chain Monte Carlo: Observations and Improvements

2016

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The Transitional Markov Chain Monte Carlo (TMCMC) method is a widely used method for Bayesian updating and Bayesian model class selection. The method is based on successively sampling from a sequence of distributions that gradually approach the posterior target distribution. The samples of the intermediate distributions are used to obtain an estimate of the evidence, which is needed in the context of Bayesian model class selection. We discuss the properties of the TMCMC method and propose the following three modifications to the TMCMC method: (1) The sample weights should be adjusted after each MCMC step. (2) A burn-in period in the MCMC sampling step can improve the posterior approximation. (3) The scale of the proposal distribution of the MCMC algorithm can be selected adaptively to achieve a near-optimal acceptance rate. We compare the performance of the proposed modifications with the original TMCMC method by means of three example problems. The proposed modifications reduce the bias in the estimate of the evidence, and improve the convergence behavior of posterior estimates.

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“…In this paper, we show that such uneven chain lengths lead to bias in the resulting posterior sample set that is accumulated from each resampling step. Such a problem has not been recognized and explicitly studied in spite of its applications in many engineering problems [12][13][14][15]. We propose a simple remedy to this bias by adjusting the uniformity of the length for each MCMC chain, which found its root in some of the previous studies in SMC [11].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

Angelikopoulos

Papadimitriou

et al. 2017

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

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The transitional Markov chain Monte Carlo (TMCMC) is one of the efficient algorithms for performing Markov chain Monte Carlo (MCMC) in the context of Bayesian uncertainty quantification in parallel computing architectures. However, the features that are associated with its efficient sampling are also responsible for its introducing of bias in the sampling. We demonstrate that the Markov chains of each subsample in TMCMC may result in uneven chain lengths that distort the intermediate target distributions and introduce bias accumulation in each stage of the TMCMC algorithm. We remedy this drawback of TMCMC by proposing uniform chain lengths, with or without burn-in, so that the algorithm emphasizes sequential importance sampling (SIS) over MCMC. The proposed Bayesian annealed sequential importance sampling (BASIS) removes the bias of the original TMCMC and at the same time increases its parallel efficiency. We demonstrate the advantages and drawbacks of BASIS in modeling of bridge dynamics using finite elements and a disk-wall collision using discrete element methods.

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Identification of Bouc–Wen type models using the Transitional Markov Chain Monte Carlo method

Cited by 61 publications

References 42 publications

A nonlinear state-space approach to hysteresis identification

A nonlinear state-space approach to hysteresis identification

Transitional Markov Chain Monte Carlo: Observations and Improvements

Bayesian Annealed Sequential Importance Sampling: An Unbiased Version of Transitional Markov Chain Monte Carlo

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