Viscoplastic-Damage Model Parameter Identification via Bayesian Methods

Abstract

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 thesis, 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. To do so, two steps are considered, solving the forward and the inverse problem. Therefore, first the propagation of the a priori parametric uncertainty through the model including hardening behavior and damage describing the behavior of a steel structure is studied. A non-intrusive stochastic finite element method based on polynomial chaos is applied. From the forward model, material parameters can be identified using measurement data such as displacement via Bayesian approaches. In this thesis, two methods are applied. The first one is a Transitional Markov chain Monte Carlo method that generates the samples of the posterior probability distribution functions. The second one is a linear approximation of the conditional expectation, the so-called Gauss-Markov-Kalman filter, which is a modification of the Kalman filter, by using the polynomial chaos expansion as the spectral approximation. The applicability of these methods on the desired model is evaluated and the results of both these methods are studied. Further, the efficiency of these identification methods is discussed. Moreover, the evaluated efficient approach is applied to a well-known CT-Test to identify its model parameters by using the data from a pure surface measurement of strain. As the damage parameters can also be determined by considering a minor damage, i.e. not a collapsing damage, the selected Bayesian approach can be proposed for the purpose of structure health monitoring for mechanical material models considering real tests.