Studies On Structural System Identification And Optimal Sensor Placement Methods In Time Domain

Structural health monitoring and condition assessment on important civil engineering structures is an active area of research. Structural system identification including parameter identification and force identification plays an important role in structural health monitoring and condition assessment. Much attention has been devoted to this area over the last decades and various methods have been proposed, which are either in the frequency domain or time domain. Increasing interests have been focused on time domain methods in recent years, because comparing to frequency domain methods, time domain methods can directly use the measured signal and they are much easier for practical application. However, duo to the complexity of the structure and influences of environmental perturbations, there are still some problems needed to be solved, e.g. incomplete measurement data, multiple uncertainties such as noise and model errors and ill-conditioning of the identification equation etc., have adverse effects on identification accuracy. Moreover, dynamic tests should be carried out before structural system identification, and the degrees of freedom (DOFs) with sensors are limited comparing to the DOFs of the whole structure. Thus, the accuracy of system identification may vary significantly with different spatial location of the response measurements.The methods of algorithm optimization and optimal sensor placement for structural system identification including force identification and damage identification in time domain are presented in this dissertation. The main contents and achievements are as follows:(1) A new criterion for optimal sensor placement is presented based on the ill-conditioning analysis of the force identification equation in state space, and it is called criterion of the minimization of ill-conditioning. Two different sensor placement methods with determined number of sensor based on the proposed criterion are presented. The first one is based on direct computation of the condition number of the system Markov parameter matrix, and it would be time consuming when a large number of candidate combinations of sensor locations is considered. The second approach is based on the correlation analysis of the system Markov parameter matrix. A sensor correlation matrix is defined and the correlation criterion, which can indicate the ill-conditioning of the Markov parameter matrix, is introduced. Results from numerical simulations reveal that the performances of both methods are similar when the number of candidate combination of sensors is small. However, when there are a large number of candidate combinations, the method based on correlation analysis of the Markov parameter matrix performs better with consistently good sensor placement for force identification and much less computation effort.(2) Dynamic force identification in state space is transformed to structural dynamic response reconstruction. The unmeasured structural responses can be reconstructed from limited measured responses. A new two-step sensor placement method is proposed for better prediction of the dynamic response reconstruction. In the first step, the system Markov parameter matrix corresponding to candidate sensor locations are singular value decomposed with One-sided Jacobi-transformation and QR decomposition methods. Sensor locations with non-zero singular values are combined as the initial sensor combination. In the second step, a measurement noise effect index is defined and the number and locations for the final sensor placement can be obtained from a heuristic forward sequential sensor placement algorithm based on the minimization of the noise effect index. Results of numerical simulations reveal that the sensors selected from the proposed method would lead to acceptable error of response reconstruction even with measurement noise.(3) Damage identification equation based on sensitivity approach from the dynamic responses is ill-conditioned and is usually solved with regularization method. When the structural system contains measurement noise and model errors, the identification results from Tikhonov Regularization method often diverge after several iterations. A Modified Tikhonov Regularization method is presented to solve the above problem. New side conditions with limits on the identification of physical parameters allow for the presence of model errors and ensure the physical meanings of the identified parameters. The L-curve method for determining the regularized parameter is revised. Chebyshev polynomial is applied to approximate the acceleration response for moderation of measurement noise. Results from numerical simulations reveal that the proposed method can lead the identified physical parameter converge to a relative correct direction and it has superior performance than the traditional Tikhonov Regularization method.(4) A new sensor placement method with multiple objectives is proposed for damage identification based on sensitivity approach from dynamic response. The covariance matrices of the identification error caused by the model errors, measurement noise and errors in the exciting forces are calculated separately. The sensor placement problem is then formulated as a multi-objective optimization problem of finding the Pareto optimal sensor combinations that compromise the criteria which are defined separately based on the covariance matrices corresponding to the three different kinds of uncertainties. A heuristic algorithm for Pareto optimal sensor placement is applied to solve the multi-objective problem. Results from numerical simulations reveal that the sensors selected from the proposed method would lead to acceptable errors of damage identification even with multi-uncertainties.