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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Infrastructures |
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| Online Access: | https://www.mdpi.com/2412-3811/6/11/158 |
| _version_ | 1797509960917057536 |
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| author | Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce |
| author_facet | Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce |
| author_sort | Filippo Landi |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:25:07Z |
| format | Article |
| id | doaj.art-e26667696919492baf7d90941c77e856 |
| institution | Directory Open Access Journal |
| issn | 2412-3811 |
| language | English |
| last_indexed | 2024-03-10T05:25:07Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Infrastructures |
| spelling | doaj.art-e26667696919492baf7d90941c77e8562023-11-22T23:46:05ZengMDPI AGInfrastructures2412-38112021-11-0161115810.3390/infrastructures6110158gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s PerspectiveFilippo Landi0Francesca Marsili1Noemi Friedman2Pietro Croce3Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56122 Pisa, ItalyFederal Waterways Engineering and Research Institute, Kußmaulstraße 17, 76187 Karlsruhe, GermanyInstitute for Computer Science and Control, Kende u. 13, 1111 Budapest, HungaryDepartment of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56122 Pisa, ItalyIn 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.https://www.mdpi.com/2412-3811/6/11/158bayesian inversiongPCEsurrogate modeluncertainty quantificationnon-linear filterparameter identification |
| spellingShingle | Filippo Landi Francesca Marsili Noemi Friedman Pietro Croce gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective Infrastructures bayesian inversion gPCE surrogate model uncertainty quantification non-linear filter parameter identification |
| title | 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_short | 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 |
| topic | bayesian inversion gPCE surrogate model uncertainty quantification non-linear filter parameter identification |
| url | https://www.mdpi.com/2412-3811/6/11/158 |
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