gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approac...

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Autores principales:	Filippo Landi, Francesca Marsili, Noemi Friedman, Pietro Croce
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	bayesian inversion gPCE surrogate model uncertainty quantification non-linear filter parameter identification Technology T
Acceso en línea:	https://doaj.org/article/e26667696919492baf7d90941c77e856
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spelling	oai:doaj.org-article:e26667696919492baf7d90941c77e8562021-11-25T17:58:51ZgPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective10.3390/infrastructures61101582412-3811https://doaj.org/article/e26667696919492baf7d90941c77e8562021-11-01T00:00:00Zhttps://www.mdpi.com/2412-3811/6/11/158https://doaj.org/toc/2412-3811In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.Filippo LandiFrancesca MarsiliNoemi FriedmanPietro CroceMDPI AGarticlebayesian inversiongPCEsurrogate modeluncertainty quantificationnon-linear filterparameter identificationTechnologyTENInfrastructures, Vol 6, Iss 158, p 158 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bayesian inversion gPCE surrogate model uncertainty quantification non-linear filter parameter identification Technology T
spellingShingle	bayesian inversion gPCE surrogate model uncertainty quantification non-linear filter parameter identification Technology T Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
description	In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.
format	article
author	Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce
author_facet	Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce
author_sort	Filippo Landi
title	gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
title_short	gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
title_full	gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
title_fullStr	gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
title_full_unstemmed	gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective
title_sort	gpce-based stochastic inverse methods: a benchmark study from a civil engineer’s perspective
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e26667696919492baf7d90941c77e856
work_keys_str_mv	AT filippolandi gpcebasedstochasticinversemethodsabenchmarkstudyfromacivilengineersperspective AT francescamarsili gpcebasedstochasticinversemethodsabenchmarkstudyfromacivilengineersperspective AT noemifriedman gpcebasedstochasticinversemethodsabenchmarkstudyfromacivilengineersperspective AT pietrocroce gpcebasedstochasticinversemethodsabenchmarkstudyfromacivilengineersperspective
_version_	1718411773505175552

gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

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