Published 6 issues per year
ISSN Print: 2152-5080
ISSN Online: 2152-5099
Indexed in
PRIOR AND POSTERIOR ROBUST STOCHASTIC PREDICTIONS FOR DYNAMICAL SYSTEMS USING PROBABILITY LOGIC
ABSTRACT
An overview is given of a powerful unifying probabilistic framework for treating modeling uncertainty, along with input uncertainty, when using dynamic models to predict the response of a system during its design or operation. This framework uses probability as a multivalued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the system's uncertain behavior are specified by the choice of a stochastic system model class: a set of input–output probability models for the system and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parametrized deterministic system model by stochastic embedding which utilizes Jaynes' principle of maximum information entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if response data are available, by its posterior probability from Bayes' theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes' theorem. This higher-level application of Bayes' theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over high-dimensional spaces that usually must be evaluated numerically by Laplace's method of asymptotic approximation or by Markov chain Monte Carlo methods. These computational tools are demonstrated in an illustrative example involving the vertical dynamic response of a car being driven along a rough road.
-
Zuev Konstantin M., Beck James L., Global optimization using the asymptotically independent Markov sampling method, Computers & Structures, 126, 2013. Crossref
-
Medina Juan Camilo, Taflanidis Alexandros, Probabilistic measures for assessing appropriateness of robust design optimization solutions, Structural and Multidisciplinary Optimization, 51, 4, 2015. Crossref
-
Hadjidoukas P.E., Angelikopoulos P., Papadimitriou C., Koumoutsakos P., Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models, Journal of Computational Physics, 284, 2015. Crossref
-
Jia Gaofeng, Taflanidis Alexandros A., Beck James L., Non-parametric stochastic subset optimization for design problems with reliability constraints, Structural and Multidisciplinary Optimization, 52, 6, 2015. Crossref
-
Farrell Kathryn, Oden J. Tinsley, Faghihi Danial, A Bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems, Journal of Computational Physics, 295, 2015. Crossref
-
Wu S., Angelikopoulos P., Papadimitriou C., Moser R., Koumoutsakos P., A hierarchical Bayesian framework for force field selection in molecular dynamics simulations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374, 2060, 2016. Crossref
-
Esmaili Omid, Grant Ludwig Lisa, Zareian Farzin, Improved performance-based seismic assessment of buildings by utilizing Bayesian statistics, Earthquake Engineering & Structural Dynamics, 45, 4, 2016. Crossref
-
Zhang J., Taflanidis A.A., Medina J.C., Sequential approximate optimization for design under uncertainty problems utilizing Kriging metamodeling in augmented input space, Computer Methods in Applied Mechanics and Engineering, 315, 2017. Crossref
-
Vakilzadeh Majid K., Yaghoubi Vahid, Johansson Anders T., Abrahamsson Thomas J.S., Stochastic finite element model calibration based on frequency responses and bootstrap sampling, Mechanical Systems and Signal Processing, 88, 2017. Crossref
-
Papadimitriou Costas, Bayesian Uncertainty Quantification and Propagation (UQ+P): State-of-the-Art Tools for Linear and Nonlinear Structural Dynamics Models, in Identification Methods for Structural Health Monitoring, 567, 2016. Crossref
-
Yuen Ka-Veng, Ortiz Gilberto A., Multiresolution Bayesian nonparametric general regression for structural model updating, Structural Control and Health Monitoring, 25, 2, 2018. Crossref
-
Ruiz Rafael O, Meruane Viviana, Uncertainties propagation and global sensitivity analysis of the frequency response function of piezoelectric energy harvesters, Smart Materials and Structures, 26, 6, 2017. Crossref
-
Oden John Tinsley, Babuška Ivo, Faghihi Danial, Predictive Computational Science: Computer Predictions in the Presence of Uncertainty, in Encyclopedia of Computational Mechanics Second Edition, 2017. Crossref
-
Oden J. Tinsley, Adaptive multiscale predictive modelling, Acta Numerica, 27, 2018. Crossref
-
Karathanasopoulos Nikolaos, Arampatzis Georgios, Ganghoffer J.-Francois, Unravelling the viscoelastic, buffer-like mechanical behavior of tendons: A numerical quantitative study at the fibril-fiber scale, Journal of the Mechanical Behavior of Biomedical Materials, 90, 2019. Crossref
-
Hubert Paulo, Padovese Linilson, Stern Julio, A Sequential Algorithm for Signal Segmentation, Entropy, 20, 1, 2018. Crossref
-
Wang Zhiyi, Zentner Irmela, Zio Enrico, A Bayesian framework for estimating fragility curves based on seismic damage data and numerical simulations by adaptive neural networks, Nuclear Engineering and Design, 338, 2018. Crossref
-
San Martin Gabriel, López Droguett Enrique, Meruane Viviane, das Chagas Moura Márcio, Deep variational auto-encoders: A promising tool for dimensionality reduction and ball bearing elements fault diagnosis, Structural Health Monitoring, 18, 4, 2019. Crossref
-
Peralta Patricio, Ruiz Rafael O., Meruane Viviana, Experimental study of the variations in the electromechanical properties of piezoelectric energy harvesters and their impact on the frequency response function, Mechanical Systems and Signal Processing, 115, 2019. Crossref
-
Peralta Patricio, Ruiz Rafael O., Meruane Viviana, Maia N., Dimitrovová Z., A Bayesian updating procedure for the electromechanical properties of piezoelectric energy harvesters, MATEC Web of Conferences, 211, 2018. Crossref
-
Sedehi Omid, Papadimitriou Costas, Katafygiotis Lambros S., Probabilistic hierarchical Bayesian framework for time-domain model updating and robust predictions, Mechanical Systems and Signal Processing, 123, 2019. Crossref
-
Zhang J., Taflanidis A. A., Multi-objective optimization for design under uncertainty problems through surrogate modeling in augmented input space, Structural and Multidisciplinary Optimization, 59, 2, 2019. Crossref
-
Taflanidis Alexandros A., Medina Juan Camilo, Simulation-Based Optimization in Design-Under-Uncertainty Problems Through Iterative Development of Metamodels in Augmented Design/Random Variable Space, in Simulation and Modeling Methodologies, Technologies and Applications, 402, 2015. Crossref
-
Zhang J., Taflanidis A. A., Evolutionary Multi-Objective Optimization Under Uncertainty Through Adaptive Kriging in Augmented Input Space, Journal of Mechanical Design, 142, 1, 2020. Crossref
-
Jensen Hector, Papadimitriou Costas, Bayesian Finite Element Model Updating, in Sub-structure Coupling for Dynamic Analysis, 89, 2019. Crossref
-
Karathanasopoulos Nikolaos, Ganghoffer Jean-Francois, Exploiting Viscoelastic Experimental Observations and Numerical Simulations to Infer Biomimetic Artificial Tendon Fiber Designs, Frontiers in Bioengineering and Biotechnology, 7, 2019. Crossref
-
Li Dian-Qing, Wang Lin, Cao Zi-Jun, Qi Xiao-Hui, Reliability analysis of unsaturated slope stability considering SWCC model selection and parameter uncertainties, Engineering Geology, 260, 2019. Crossref
-
Peralta Patricio, Ruiz Rafael O., Taflanidis Alexandros A., Bayesian identification of electromechanical properties in piezoelectric energy harvesters, Mechanical Systems and Signal Processing, 141, 2020. Crossref
-
Sedehi Omid, Papadimitriou Costas, Katafygiotis Lambros S., Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework, Probabilistic Engineering Mechanics, 60, 2020. Crossref
-
Zheng Shuo, Zhu Yu-Xin, Li Dian-Qing, Cao Zi-Jun, Deng Qin-Xuan, Phoon Kok-Kwang, Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning, Geoscience Frontiers, 12, 1, 2021. Crossref
-
Villani Luis G. G., Silva Samuel da, Cunha Americo, Application of a Stochastic Version of the Restoring Force Surface Method to Identify a Duffing Oscillator, in Nonlinear Dynamics of Structures, Systems and Devices, 2020. Crossref
-
Patsialis Dimitrios, Kyprioti Aikaterini P., Taflanidis Alexandros A., Bayesian calibration of hysteretic reduced order structural models for earthquake engineering applications, Engineering Structures, 224, 2020. Crossref
-
Parida Siddharth S., Nikellis Alexandros, Sett Kallol, Singla Puneet, Model‐data fusion for seismic performance evaluation of an instrumented highway bridge, Earthquake Engineering & Structural Dynamics, 49, 14, 2020. Crossref
-
Poblete Alejandro, Peralta Patricio, Ruiz Rafael O., Tuning Nonlinear Model Parameters in Piezoelectric Energy Harvesters to Match Experimental Data, ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg, 7, 1, 2021. Crossref
-
Wang Lin, Tang Libin, Wang Zhenyu, Liu Hanlong, Zhang Wengang, Probabilistic characterization of the soil-water retention curve and hydraulic conductivity and its application to slope reliability analysis, Computers and Geotechnics, 121, 2020. Crossref
-
Zhang Jize, Taflanidis Alexandros A., Adaptive Kriging Stochastic Sampling and Density Approximation and Its Application to Rare-Event Estimation, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 4, 3, 2018. Crossref
-
De Subhayan, Brewick Patrick T., Johnson Erik A., Wojtkiewicz Steven F., Investigation of Model Falsification Using Error and Likelihood Bounds with Application to a Structural System, Journal of Engineering Mechanics, 144, 9, 2018. Crossref
-
Jia Gaofeng, Taflanidis Alexandros A., Beck James L., A New Adaptive Rejection Sampling Method Using Kernel Density Approximations and Its Application to Subset Simulation, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 3, 2, 2017. Crossref
-
De Subhayan, Johnson Erik A., Wojtkiewicz Steven F., Brewick Patrick T., Computationally Efficient Bayesian Model Selection for Locally Nonlinear Structural Dynamic Systems, Journal of Engineering Mechanics, 144, 5, 2018. Crossref
-
Jia Xinyu, Sedehi Omid, Papadimitriou Costas, Katafygiotis Lambros S., Moaveni Babak, Hierarchical Bayesian modeling framework for model updating and robust predictions in structural dynamics using modal features, Mechanical Systems and Signal Processing, 170, 2022. Crossref
-
Poblete Alejandro, Ruiz Rafael O., Jia Gaofeng, Hierarchical Bayesian Approach for Model Parameter Updating in Piezoelectric Energy Harvesters, Mechanical Systems and Signal Processing, 172, 2022. Crossref
-
Céspedes S., Boroschek R., Ruiz R. O., Strong Motion Models for Duration and Arias Intensity for Strong Motion Records in Chile, Journal of Earthquake and Tsunami, 16, 04, 2022. Crossref