VIBRATION BASED DAMAGE IDENTIFICATION OF TIME-VARYING DYNAMICAL SYSTEMS

This thesis develops and explores two new kinds of vibration-based damage identification methodologies suitable for dynamical systems with periodically time-varying coefficients; 1) a Floquet based method (Methodology I) and, 2) a Sideband Frequency Response Function (FRF) method (Methodology II). One important class of dynamical systems where periodic time-varying parametric terms naturally arise is rotordynamic systems. For the case of a flexible shaft-rotor system with multiple open cracks, this thesis explores a new Least Squares damage identification approach based on Floquet theory with iterative eigenvector estimate updating. It is found that this method is able to detect the location and severity of multiple cracks with the assistance of control inputs from an Active Magnetic Bearing (AMB). However, it is also found that this method could not effectively identify the crack angle. To overcome this shortcoming, the new Sideband FRF based methodology is developed which utilizes the measured changes in transfer function magnitude and phase due to structural damage at the primary and side-band frequencies of the damaged periodically time-varying dynamical system. This method provides the advantages of arbitrary interrogation frequency and multiple inputs/outputs which greatly enriches the dataset for damage identification. This damage identification algorithm utilizes an iterative least square approach combined with a Newton-Raphson technique to estimate the damage parameters. The effectiveness of this method is thoroughly explored for a flexible rotor system and a planar truss both with breathing cracks. In each case, damage estimation is performed using time-domain vibration data taken from full nonlinear simulations of the cracked structures. The results show that this new method successfully estimated the crack depths, locations and angles for the case of multiple simultaneous damages

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems

In this paper, the identification of a class of multiscale spatio-temporal dynamical sys-tems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a B-spline wavelet multi-resolution analysis (MRA). The resulting identified models of the spatio-temporal evolution form a system of partial differential equations with different spatial scales. Examples are provided to demonstrate the efficiency of the proposed method