BAYESIAN DESIGN OF EXPERIMENT FOR THE ESTIMATION OF VISCOELASTIC PARAMETERS

Josiele Da Silva Teixeira,Anilton Do Nascimento Viana,Leonardo Tavares Stutz,Diego Campos Knupp,Antônio José Da Silva Neto

doi:10.21575/25254782rmetg2020vol5n21163

Josiele Da Silva Teixeira, Anilton Do Nascimento Viana + Show 3 more

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https://doi.org/10.21575/25254782rmetg2020vol5n21163

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Abstract

The present work has as its main objective the formulation and solution of inverse problems aiming at the estimation of viscoelastic parameters of a discrete mechanical system. Its application potential covers several areas in the most varied segments of engineering and industry. For the formulation and solution of the direct problem, a discrete mechanical system with viscoelastic damping is considered. The parameter estimation problem is then formulated as an inverse problem, whose objective is to estimate the viscoelastic properties of a discrete system using a Bayesian approach. First, a Bayesian design of experiment its carried out in order to identify optimal experimental conditions for solving the inverse problem, taking into account the positioning of the sensors and actuators. To solve the parameter estimation inverse problem, an Adaptive Monte Carlo Markov Chain Method is employed.

Highlights

Mechanical structures are subject to dynamic loading, which, under certain conditions, can generete excessive levels of vibration and may even cause structural failures, causing great damage to society
The present work proposes the application of the Bayesian approach for the formulation and solution of the inverse problem of estimation of viscoelastic parameters of discrete mechanical systems
The present work had as its main objective the application of the Bayesian experimental project in the determination of an optimal experimental design/arrangement for the estimation of viscoelastic parameters of a mechanical system of two degrees of freedom

Summary

Introduction

Mechanical structures are subject to dynamic loading, which, under certain conditions, can generete excessive levels of vibration and may even cause structural failures, causing great damage to society. It is essential to develop techniques for the construction of mechanical systems with adequate vibration control and isolation, allowing their applications in various engineering areas, for example, in the development of viscoelastic dampers used to control vibrations in machines, aeronautical structures and energy dissipation mechanisms in buildings, protecting them against earthquakes damage These measures have a direct impact on reducing operating costs and maintaining adequate structural functioning. In addition to allowing a priori information to be incorporated into the model, the ease of incorporating it into a formal decision context, the explicit treatment of problem uncertainties and the ability to assimilate new information in adaptive contexts are some of its advantages (COSTA, 2004) In this approach, the variables of problem are modeled as random variables and Probability Density Functions (PDF) are used to incorporate, in the estimation process, prior information about the parameters to be estimated. At the end of the process, an approximation of the a posteriori probability density function of the parameters of interest is obtained (TEIXEIRA et al, 2016)

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