Numerical identification of a linear oscillator stiffness using Bayesian inference and Markov chain Monte Carlo
Keywords:
Bayesian Inference; Maximum Likelihood; Markov Chain Monte Carlo (MCMC); Inverse problem; Parameters estimation; Dynamic system.Abstract
Inverse problem techniques have been used in different engineering application aiming to convert observed measurements or data acquired together to the prior knowledge of the system into information about material properties, geometry, locations of anomalies, e.g. cracks and structural damage, excitation force, among others. The present papers aim to estimate parameters of a dynamic system with the inverse problem using Bayesian Inference technique. Multiples studies are presented to analyse the statistical significance of the catches for the settings, making a critical analysis between a solution via Bayesian Inference linked to minimising the objective function with stochastic methods. It applied through stochastic strategies as the Maximum Likelihood (MLE), Least Squares (LSE) and Markov Chains Monte Carlo (MCMC), implemented with the Metropolis-Hastings algorithm (MH). In the estimation, the random parameters assumed distribution inference of Gaussian and Uniform types for different standard deviations. The results demonstrated the efficacy of Bayesian inference to estimates parameter of the oscillator systems from its dynamic response and the statistical parameter information.
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