000013243 001__ 13243
000013243 005__ 20161114160333.0
000013243 04107 $$aeng
000013243 046__ $$k2009-06-22
000013243 100__ $$aBeck J., L.
000013243 24500 $$aUsing model classes in system identification for robust response predictions

000013243 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013243 260__ $$bNational Technical University of Athens, 2009
000013243 506__ $$arestricted
000013243 520__ $$2eng$$aThe goal of system identification for dynamic systems is to use experimental data to improve mathematical models of the input-output behavior of a dynamic system so that they make more accurate predictions of the system response to a prescribed excitation. A common approach is to take a parameterized model of the system and then use system data to estimate the value of the uncertain model parameters. This parameter estimation must be done with great care, however, because it is unrealistic to expect any model to be an exact representation of the system behavior and so one cannot expect true parameter values, and often the estimation gives non-unique results. Furthermore, in order to make more robust predictions, the uncertainties in modelling the system, as well as in modelling the future system input, should be explicitly treated; in particular, because of the approximate nature of any system model, one should explicitly treat the uncertain prediction error (the difference between the outputs or state of the real system and those of the system model). Probability logic with Bayesian updating has emerged in recent years as a rigorous approach to address these points. This paper first present an overview of probability logic, which provides a multi-valued propositional logic for plausible reasoning and which gives a meaning for the "probability of a model" as a measure of the relative plausibility of the model within a proposed set of models; this plausibility is quantified by a probability distribution for the model parameter values which is conditional on specified information. A summary is then given of the application of probability logic to quantifying modelling uncertainty for robust predictive analysis of systems. Instead of using system data to estimate the model parameters, Bayes’ Theorem is used to update the relative plausibility of each model in a model class, which is a parameterized set of predictive input-output probability models for the system behavior together with a prior probability distribution over this set that expresses the initial plausibility of each model. Then to produce robust predictive analyses, the entire model class is used with the probabilistic predictions of each model being weighted by its posterior probability, in accordance with the Total Probability Theorem. An additional level of robustness can be performed by combining the robust predictions of each model class in a set of candidate model classes for the system, where each contribution is weighted by the posterior probability of the corresponding model class. These robust analyses involve integrals over high-dimensional parameter spaces that usually cannot be evaluated analytically. Useful computational tools for these evaluations are Laplace's method of asymptotic approximation and Markov Chain Monte Carlo methods.

000013243 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013243 653__ $$aSystem Identification, Probability Logic, Bayesian Analysis, Robust Predictions, Model Class Selection, Markov Chain Monte Carlo Simulation Abstract. The goal of system identification for dynamic systems is to use experimental data to improve mathematical models of the input-output behavior of a dynamic system so that they make more accurate predictions of the system response to a prescribed excitation. A common approach is to take a parameterized model of the system and then use system data to estimate the value of the uncertain model parameters. This parameter estimation must be done with great care, however, because it is unrealistic to expect any model to be an exact representation of the system behavior and so one cannot expect true parameter values, and often the estimation gives non-unique results. Furthermore, in order to make more robust predictions, the uncertainties in modelling the system, as well as in modelling the future system input, should be explicitly treated; in particular, because of the approximate nature of any system model, one should explicitly treat the uncertain prediction error (the difference between the outputs or state of the real system and those of the system model). Probability logic with Bayesian updating has emerged in recent years as a rigorous approach to address these points. This paper first present an overview of probability logic, which provides a multi-valued propositional logic for plausible reasoning and which gives a meaning for the "probability of a model" as a measure of the relative plausibility of the model within a proposed set of models; this plausibility is quantified by a probability distribution for the model parameter values which is conditional on specified information. A summary is then given of the application of probability logic to quantifying modelling uncertainty for robust predictive analysis of systems. Instead of using system data to estimate the model parameters, Bayes’ Theorem is used to update the relative plausibility of each model in a model class, which is a parameterized set of predictive input-output probability models for the system behavior together with a prior probability distribution over this set that expresses the initial plausibility of each model. Then to produce robust predictive analyses, the entire model class is used with the probabilistic predictions of each model being weighted by its posterior probability, in accordance with the Total Probability Theorem. An additional level of robustness can be performed by combining the robust predictions of each model class in a set of candidate model classes for the system, where each contribution is weighted by the posterior probability of the corresponding model class. These robust analyses involve integrals over high-dimensional parameter spaces that usually cannot be evaluated analytically. Useful computational tools for these evaluations are Laplace's method of asymptotic approximation and Markov Chain Monte Carlo methods.

000013243 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013243 720__ $$aBeck J., L.
000013243 8560_ $$ffischerc@itam.cas.cz
000013243 8564_ $$s315644$$uhttps://invenio.itam.cas.cz/record/13243/files/CD360.pdf$$yOriginal version of the author's contribution as presented on CD, section: Semi-plenary lectures.
000013243 962__ $$r13074
000013243 980__ $$aPAPER