Comparison of Bayesian Methods on Parameter Identification for a Viscoplastic Model with Damage

Abstract

<jats:p>The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified by minimization of the difference between model response and experimental data. However, the measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article, the focus is on the identification of material parameters of a viscoplastic damaging material using a stochastic simulation technique to generate artificial data which exhibit the same stochastic behavior as experimental data. It is proposed to use Bayesian inverse methods for parameter identification and therefore the model and damage parameters are identified by applying the Transitional Markov Chain Monte Carlo Method (TMCMC) and Gauss-Markov-Kalman filter (GMKF) approach. Identified parameters by using these two Bayesian approaches are compared with the true parameters in the simulation and with each other, and the efficiency of the identification methods is discussed. The aim of this study is to observe which one of the mentioned methods is more suitable and efficient to identify the model and damage parameters of a material model, as a highly non-linear model, using a limited surface displacement measurement vector and see how much information is indeed needed to estimate the parameters accurately.</jats:p>

Bayesian Parameter Determination of a CT-Test Described by a Viscoplastic-Damage Model Considering the Model Error

“…However, the uncertainty associated with the material model predictions can have a significant impact on the decision-making process in design, control, and health monitoring process. Following the other paper of the authors [77] where random walk approach methods, in specific transitional Markov Chain Monte Carlo method, and Gauss Markov Kalman filter (GMKF) approach are throughly compared on the simple academic examples, in this paper using the outcome of the previous paper of the authors, the sequential GMKF (SGMKF) is selected to apply on real structure examples to not only evaluate the efficiency the method on real structure examples, but also to check if this method is applicable for the very time consuming finite element updating models. Furthermore, the authors would have wanted to check if the combination of SGMKF and functional approximation, in specific polynomial chaos expansion (PCE), could be a possible approach as a tool for the purpose of health monitoring of real structures and also to check if the proposed method is able to detect the damage before any collapsing damages happen and to prevent them.…”

“…given in rate formulation. More details are given in this paper [77]. The Chaboche model allows for isotropic and kinematic hardening, which is considered in order to describe the Bauschinger effect observed at steel material under high cyclic loadings, see Simo and Hughes [81].…”

“…Moreover the polynomial chaos expansion is also used along with the ensemble Kalman filter (EnKF) [78,89] in order to be completely independent from any time consuming computational implementations such as Monte Carlo method. This leads to the Gauss-Markov-Kalman filter [78,79] which is discussed in this section and more details are provided in this paper [77].…”

“…In this paper, a viscoplastic model of Chaboche with damage is studied. The model contains five material parameters and three damage parameters which have to be determined from experimental data by using a modified version of Gauss-Markov-Kalman filter approach [78,79] so-called sequential Gauss-Markov-Kalman filter approach [77,80]. The results of this method is discussed and different aspects of method's efficiency are evaluated.…”

Comparison of Bayesian methods on parameter identification for a viscoplastic model with damage

“…In order to predict the behavior of mechanically loaded metallic materials, constitutive models are applied, which present a mathematical frame for the description of elastic and inelastic deformation. All inelastic constitutive models contain parameters which have to be identified for a given material from experiments [1].…”