Statistical damage assessment of structures using parameter estimation from modal response

Abstract

This thesis investigates the statistical damage assessment method for structures with members consisting of one or more parameters. The parameters under consideration may comprise of the axial, shear or bending stiffness parameters. The proposed method takes into account the problem of noise contamination in the measured response of the structures. For the single-parameter structural members, three distinct statistical methods were introduced: (1) the Monte-Carlo simulation method; (2) the optimum sensitivity-based method; and (3) the sensitivity-based method. The underlying principle of these methods is to compare the statistical distribution of the estimated parameters for the damaged structure with the undamaged structure. A numerical integration scheme can then be used to compute the probability of damage for each structural member as a function of the level of damage. It was found from the current study that the performance of the proposed damageassessment scheme for the single-parameter structural members depends considerably upon the quality of the estimated system parameters. In the present study, the regularization technique was adopted to reduce the degree of instabilities of solutions to the parameter estimation problem in the presence of the measurement noise. The level of success for the damage assessment is identified by the statistical identification error index that approaches zero when the assessment is considered effective. To identify damage in the multi-parameter structural members, a baseline function was proposed to identify whether a structural member is in the "healthy state" or the "damaged state." The boundary separating these two states is referred to as the "limit state." The probability of damage can then be computed as a function of the distance of the limit-state line to the origin of the reduced-variate space which approaches the unit value when the damage can be assessed effectively.