Unit Modal Strain Energy Sensitivity And Its Application In Structural Damage Identification

Sensitivity analysis can be used to ascertain how a given model output depends upon the input parameters, which is the basis of modeling and model analysis. Such a sensitivity analysis has extensive applications in many fields of structural engineering such as system identification, vibration control, structural design optimization, dynamic model updating and damage detection et al. Recently, modal strain energy as a new modal index has drawn worldwide attention for its application in damage detection. Therefore, how to calculate the sensitivity of modal strain energy has become one of the crucial issues. However, work in this aspect is still lack. In this dissertation, the element modal strain energy sensitivity equation is derived based on an efficient algebraic method. The properties of element modal strain energy sensitivity to different input parameters are discussed in details, and then they are applied in structural damage detection. Finally, a statistical damage identification algorithm based on element modal strain energy is developed. The main work and conclusions are:1. The first-order and the second-order sensitivity formulae of the element modal strain energy for a real symmetric undamped structure are derived based on an efficient algebraic method. The formulae are simple and compact, and it is easy to program. Moreover, it only requires one eigenvector to be known, which does not result in the problem of mode truncation.2. Via numerical parametric studies, the behavior of element modal strain energy sensitivity to different input parameters has been investigated. The general properties of the sensitivity coefficients with respect to possible damage parameters have been examined and the effect of noise to these sensitivity coefficients has also been discussed. It is demonstrated that element modal strain energy for the lower modes will be the most likely to indicate the structural damage and it is less affected by noise than that for the higher modes.3. Based on the efficient algebraic solution of element modal strain energy sensitivity, an element modal strain energy-based damage detection method is proposed for detecting damage location and severity. A solution technique incorporated with the singular value decomposition-based regularization algorithm is used to ensure the right solutions. It is demonstrated that the proposed method is efficient in a one-step (non-iterative) procedure.4. The proposed method has been verified by a number of simulated damage scenarios for a simply supported beam and a continuous beam. The problem of noise in the modal data and the influence on damage identification accuracy are discussed. Results indicate that the present method is able to find the exact severity of the damaged elements under noise-free and mild noise environment.5. A statistical damage identification algorithm based on element modal strain energy is developed to estimate the probability of damage existence, which accounts for the effects of random noise in both the vibration data and finite element model. A numerical beam is used to demonstrate the applicability of proposed method. The effects of noise level and damage level on damage identification results are also presented.