Bayesian parameter estimation and model selection in nonlocal viscoelastic models

doi:10.1016/j.ymssp.2024.111237

2024-04-01

PRE

Leonardo Tavares Stutz

Daniel A. Castello *

DOI：10.1016/j.ymssp.2024.111237

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摘要

En 中文

Uncertainties regarding heterogeneous materials are common in engineering applications. In the special case of nanomaterials and nanostructures, the heterogeneity may stem from technical difficulties in their manufacturing process, as well as from imperfections and defects in their molecular structure. In the present paper, a nonlocal viscoelastic plate model with spatially varying viscoelastic parameters is derived. The model was built based on the assumptions of the Kirchhoff plate, together with the Eringen's nonlocal theory to account for the small scale effects and the use of internal variables for the description of the viscoelastic dissipation mechanism. Further, the viscoelastic parameters of the nanoplate are modeled as spatial random fields and represented by means of the Karhunen-Loeve expansion. Different model classes are defined according to the number of internal variables used to describe the viscoelastic behavior. To properly handle uncertainties underlying experimental data as well the ones associated to the physical properties of the system, inverse analyses of model calibration and model class selection are formulated within the Bayesian framework. Numerical analyses are presented considering synthetic modal data. To avoid inverse crimes, synthetic modal data are provided by a spatially heterogeneous reference model, whereas homogeneous models are considered in the inverse analyses. The Transitional Markov Chain Monte Carlo method is used to sample the posterior probability density functions and also to provide the evidence for each model class. Numerical results show that the proposed approach succeeded in ranking model classes, within a specified set of model classes, balancing data-fitting capability against model complexity. Further, the proposed approach was also able to accurately estimate the model parameters and quantify their associated uncertainties.

Keyword:

Nanoplates

Viscoelasticity

Nonlocal elasticity

Random fields

Karhunen-Loeve expansion

Bayesian inference

Transitional Markov Chain Monte Carlo