COMPREHENSIVE IDENTIFICATION OF NONLINEAR STRUCTURAL SYSTEMS WITH THE LOW NUMBER AND NON-HOMOGENEOUS SENSING USING MODERN BAYESIAN METHODS

In this paper, a general framework is presented to estimate the unknown parameters of structures. The unknown parameters can consist of a vast range of variables, such as the dynamical parameters of structure, the motivation inputs, the responses of other degree of freedoms (DOFs) except un-sensed ones, etc. Engineering problems can be widely classified into four general areas: 1. Direct problem: The system matrices, the initial conditions, and the external forces are the inputs of problem and the output variables should be calculated. 2. Inverse problem: The system matrices as well as some measurements related to the DOFs are the inputs of problem and the external forces and initial conditions should be determined. 3. System identification problems: The external forces and initial conditions together with some measurements related to the DOFs are the inputs of problem and the system matrices or some components of them should be determined. 4. Research problems: Some measurements related to the DOFs are taken as the inputs of problem and the system matrices, external forces, initial conditions, and remaining DOFs are the outputs. Apparently, the last case is the most difficult as compared with other ones, which the attentions are focused on this case in this study. For this purpose, two general approaches, including off-line and on-line methods, are available in the technical literature. In the off-line methods, identification process can be initiated just after completing the sensing operation. In the otherwords, in these methods, all sensed data are necessary for the analysis. The most popular off-line method is Tikhonov regularization that includes the dynamic programming and L-curve techniques in its structure. The dynamic programming is a technique used to determine the optimal solution that consists of backward and forward processes. For tuning the parameters of these processes, some smoothness methods, such as L-curve technique, should be employed. In the recent years, many researchers and engineers have used the off-line methods in different engineering applications and the results are almost satisfying. However, these methods have some drawbacks. First, these methods are acutely weak to handle the problems with large number of variables. In fact, off-line methods use the optimization basics in their solving process, in which, the complexity of problem is drastically increased with increasing the number of variables. The second weakness of these methods is the difficulty to handle the nonlinear problems. Although, some new tricks are used in recent years, but all of them solve a part of the model nonlinearity, while the observation processes of them are different.

Keywords:

System identification , Particle filter , Unscented Kalman filter , Bayesian methods , Inverse Problem