Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

Vakilzadeh, Majid Khorsand; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

doi:10.1016/j.ymssp.2016.02.024

Cited by 33 publications

(30 citation statements)

References 28 publications

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“…If there is no analytical solution for Equation , Laplace's approximation method can be used when the model class is globally identifiable based on the available data

{bold-italic bold-scriptD}_{N}

(e.g., Beck and Yuen ; Beck ). When the chosen class of models is unidentifiable or locally identifiable based on the data

{bold-italic bold-scriptD}_{N}

so that there are multiple MLEs ( maximum likelihood estimates ) (Beck and Katafygiotis, ), only stochastic simulation methods are practical to calculate the model class evidence, such as the Transitional Markov chain Monte Carlo simulation (MCMC) method (Ching and Chen, ) or the Approximate Bayesian Computation method (Chiachio et al., ; Vakilzadeh et al., ). When the posterior probability of each model class,

P (M_{m} | {bold-italic bold-scriptD}_{N}, boldM)

, has been calculated, the Total Probability Theorem can be applied to produce the posterior hyper‐robust predictive models that combine the predictions of all plausible model classes in a specified set (Beck, ).…”

Section: Bayesian System Identificationmentioning

confidence: 99%

“…In addition to SHM, the goals of such data-informed modeling might also include providing a better understanding of the structural system's behavior and allowing more accurate predictions of its future response to specified excitations. Despite a long history, the development of algorithms for system identification continues to be an active area of research in structural dynamics (e.g., Green et al, 2015;Shan et al, 2016;Perez-Ramirez et al, 2016;Huang et al, 2017b;Vakilzadeh et al, 2017;Oh et al, 2017;Li et al, 2017;Amezquita-Sanchez et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Full Gibbs Sampling Procedure for Bayesian System Identification Incorporating Sparse Bayesian Learning with Automatic Relevance Determination

Huang

Beck

2018

Computer aided Civil Eng

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Bayesian system identification has attracted substantial interest in recent years for inferring structural models and quantifying their uncertainties based on measured dynamic response in a structure. The relative plausibility of each structural model in a specified model class is quantified by its posterior probability from Bayes’ Theorem. The relative plausibility of each model class within a set of candidate model classes for the structure can also be assessed via Bayes’ Theorem. Computation of this posterior probability over all candidate model classes automatically applies a quantitative Ockham's razor that trades off a data‐fit measure with an information‐theoretic measure of model complexity, which penalizes model classes that “over‐fit” the data. In this article, we first present a general Bayesian system identification framework and point out that combining it with sparse Bayesian learning (SBL) is an effective strategy to implement the Bayesian Ockham razor. Then we review our recent progress in exploring SBL with the automatic relevance determination likelihood concept to detect and quantify spatially sparse substructure stiffness reductions. To characterize the full posterior uncertainty for this problem, an improved Gibbs sampling procedure for SBL is then developed. Finally, illustrative results are provided to compare the performance and validate the capability of the presented SBL algorithms for structural system identification.

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“…If there is no analytical solution for Equation , Laplace's approximation method can be used when the model class is globally identifiable based on the available data

{bold-italic bold-scriptD}_{N}

(e.g., Beck and Yuen ; Beck ). When the chosen class of models is unidentifiable or locally identifiable based on the data

{bold-italic bold-scriptD}_{N}

P (M_{m} | {bold-italic bold-scriptD}_{N}, boldM)

Section: Bayesian System Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Full Gibbs Sampling Procedure for Bayesian System Identification Incorporating Sparse Bayesian Learning with Automatic Relevance Determination

Huang

Beck

2018

Computer aided Civil Eng

Self Cite

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“…In the study by Vakilzadeh et al (2017), an ABC technique (Approximate Bayesian Computation, an offline parameter estimation method that does not require explicit knowledge of the likelihood function, contrary to MCMC schemes) is used on several problems which exhibit various identifiability properties, and one can observe that this offline technique is indeed able to capture non-Gaussian, possibly multimodal posterior pdfs. In this paper, we study the behavior of online algorithms to parameter identification in systems that also show different identifiability characteristics, some of them adapted from the study by Vakilzadeh et al (2017).…”

Section: A Challenge To Parameter Estimation: Parameter Identifiabilitymentioning

confidence: 99%

“…In this paper, we study the behavior of online algorithms to parameter identification in systems that also show different identifiability characteristics, some of them adapted from the study by Vakilzadeh et al (2017). The idea is to provide an insight into the kind of behavior to expect from fast online parameter learning algorithms, depending on the problem at hand, thus guiding the choice of algorithm for future users.…”

Section: A Challenge To Parameter Estimation: Parameter Identifiabilitymentioning

confidence: 99%

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On the Performance of Online Parameter Estimation Algorithms in Systems with Various Identifiability Properties

Olivier

Smyth

2017

Front. Built Environ.

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In recent years, Bayesian inference has been extensively used for parameter estimation in non-linear systems; in particular, it has proved to be very useful for damage detection purposes. The problem of parameter estimation is inherently correlated with the issue of identifiability, i.e., is one able to learn uniquely the parameters of the system from available measurements? The identifiability properties of the system will govern the complexity of the posterior probability density functions (pdfs), and thus the performance of learning algorithms. Offline methods such as Markov Chain Monte Carlo methods are known to be able to estimate the true posterior pdf, but can be very slow to converge. In this paper, we study the performance of online estimation algorithms on systems that exhibit challenging identifiability properties, i.e., systems for which all parameters cannot be uniquely identified from the available measurements, leading to complex, possibly multimodal posterior pdfs. We show that online methods are capable of correctly estimating the posterior pdfs of the parameters, even in challenging cases. We also show that a good trade-off can be obtained between computational time and accuracy by correctly selecting the right algorithm for the problem at hand, thus enabling fast estimation and subsequent decision-making.

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Bayesian Estimation of Acoustic Emission Arrival Times for Source Localization

Madarshahian

Ziehl

Todd

2019

Model Validation and Uncertainty Quantification, Volume 3

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The onset time of an Acoustic Emission (AE) signal is an important feature for source localization. Due to the large volume of data, manually identifying the onset times of AE signals is not possible when AE sensors are used for health monitoring of a structure. Numerous algorithms have been proposed to autonomously obtain the onset time of an AE signal, with diering levels of accuracy. While some methods generally seem to outperform others (even compared to traditional visual inspection of the time signals), this is not true for all signals, even within the same experiment. In this paper, we propose the use of an inverse Bayesian source localization model to develop an autonomous framework to select the most accurate onset time among several competitors. Without loss of generality, three algorithms of Akaike Information Criterion (AIC), Floating Threshold, and Reciprocal-based picker are used to illustrate the capabilities of the proposed method.Data collected from a concrete specimen are used as an input of the proposed technique. Results show that the proposed technique can select the best onset time candidates from the three mentioned algorithms, automatically.The picked onset time is comparable with manual selection, and accordingly has better accuracy for source localization when compared to any of the single methods.

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Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

Cited by 33 publications

References 28 publications

Full Gibbs Sampling Procedure for Bayesian System Identification Incorporating Sparse Bayesian Learning with Automatic Relevance Determination

Full Gibbs Sampling Procedure for Bayesian System Identification Incorporating Sparse Bayesian Learning with Automatic Relevance Determination

On the Performance of Online Parameter Estimation Algorithms in Systems with Various Identifiability Properties

Bayesian Estimation of Acoustic Emission Arrival Times for Source Localization

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