System identification of large-scale linear and nonlinear structural dynamicmodels
Doktorsavhandling, 2016

System identification is a powerful technique to build a model from measurement data by using methods from different fields such as stochastic inference, optimization and linear algebra. It consists of three steps: collecting data, constructing a mathematical model and estimating its parameters. The available data often do not contain enough information or contain too much noise to enable an estimation of all uncertain model parameters with a good-enough precision. These are examples of challenges in the field of system identification. To construct a mathematical model, one should decide upon a model structure and then estimate its associated parameters. This model structure could be built with clear physical interpretation of its parameters like a parameterized finite element model, or be built just to fit to test data like general state-space or modal model. Each such model class has its own identification challenges. For the former, the complexity of finite element models can create an obstacle because of their time-consuming simulation. Furthermore, if a linear model does not represent the data with reasonable accuracy, nonlinear models need to be engaged and their modeling and parameterization impose even bigger challenges. For the latter, selecting a proper model order is a challenge and the physical relevance of identified states is an important issue. Deciding upon the physical relevance of states is presently a highly judgmental task and to instead do a classification based on physical relevance in an automated fashion is a formidable challenge. In-depth studies of such modeling and computational challenges are presented here and proper tools are suggested. They specifically target problems encountered in identification of large-scale linear and nonlinear structures. An experimental design strategy is proposed to increase the information content of test data for linear structures. By combining some new correlation metrics with a bootstrap data resampling technique, an automated procedure is developed that gives a proper model order that represent test data. The procedure’s focus is on the physical relevance of identified states and on uncertainty quantification of parameter estimates. A method for stochastic parameter calibration of linear finite element models is developed by using a damping equalization method. Bootstrapping is used also here to estimate the uncertainty on the model parameters and response predictions. For identification of nonlinear systems a method is developed in which the information content of the data is increased by incorporating multiple harmonics of the response spectra. The parameter uncertainty is here estimated by employing a cross-validation technique. A fast higher-order time-integration method is developed which combines the well-known pseudo-force method with exponential time-integration methods. High-order-hold interpolation schemes are derived to increase the methods stability. As an alternative, to speed up the computations for large-scale linear models, a surrogate model for frequency response functions is developed based on sparse Polynomial Chaos Expansion.

Finite element model

Surrogate modeling

Bootstrapping

Polynomial chaos expansion

System identification

Exponential integration

Uncertainty quantification

EA, Hörsalsvägen 11
Opponent: Prof. Randall J. Allemang

Författare

Vahid Yaghoubi Nasrabadi

Chalmers, Tillämpad mekanik, Dynamik

Ämneskategorier

Teknisk mekanik

Sannolikhetsteori och statistik

Signalbehandling

ISBN

978-91-7597-377-7

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie

EA, Hörsalsvägen 11

Opponent: Prof. Randall J. Allemang