Damage Identification of Structures Based on Smooth Orthogonal Decomposition and Improved Beetle Antennae Search Algorithm

A novel damage identification method that utilizes the smooth orthogonal decomposition (SOD) combined with the improved beetle antennae search algorithm (BAS) presented by previous scholars is proposed. Firstly, the damage index which can track the curvature changing of mode shape identified by the SOD method is generated by an adaptive polynomial fit method. The locations of structure damages are determined according to the damage index. Thus, the number of possible damaged elements needed to be taken into account can be reduced when calculating the degree of damage. Then, the reduction in the stiffness at the damage location of the structure is calculated by the improved BAS in which the fitness function is constructed by calculated frequencies of the damaged structure in each iteration and the modal frequencies obtained by SOD. The BAS algorithm is improved through a fusion strategy of simulated annealing theory. Thus, the improved BAS algorithm is efficient and adaptive. The effect of this combined application in damage identification has been verified by numerical examples of a simply supported beam with single damage and a cantilever beam with double damage. The numerical results show that this combined algorithm exhibits high reliability in damage identification of beam-like structures.

Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

The smooth orthogonal decomposition method (SOD) is an efficient algorithm that can be used to extract modal matrix and frequencies of lightly damped vibrating systems. It uses the covariance matrices of output-only displacement and velocity responses to form a generalized eigenvalues problem (EVP). The mode shape vectors are estimated by the eigenvectors of the EVP. It is stated in this work that the accuracy of the SOD method is mainly affected by the correlation characteristic of modal coordinate responses. For the damped vibration systems, biases will be contained in the results of using the SOD. Therefore, an iterative smooth orthogonal decomposition (ISOD) method is proposed to identify modal parameters of the damped system from the covariance matrices of the displacement, velocity, and acceleration responses. The modal matrix given by the SOD method is updated in each iteration step using a transformation matrix. The transformation matrix can be efficiently computed using a set of analytical formulations. Meanwhile, natural frequencies and damping ratios are obtained by using a simple search method. The performance of the proposed ISOD method is verified by numerical and experimental studies. The results demonstrate that, by considering the correlation of modal responses, the ISOD method can be used to extract accurately the modal information of vibration systems with coupled modes.

Empirical Mode Decomposition for Dynamic AFM Microcantilevers in Air and Liquid Environment

The modal decomposition of tapping mode atomic force microscopy microcantilevers in air and liquid environment was experimentally investigated to identify their complex responses. In experiment, the flexible microcantilevers and a flat HOPG sample were used. The responses of the microcantilevers were obtained to extract the linearized modes and orthogonal values using the methods for the proper orthogonal decomposition and the smooth orthogonal decomposition. The influence of the tapping setpoints and the hydrodynamic damping forces were investigated with the multi-mode response of microcantilevers. The results show that the first mode is dominant under normal operating conditions in tapping mode. However, at lower setpoint, the flexible microcantilever behaved uncertain modal distortion near the tip on the sample. The dynamics tapping effect and the damping between microcantilever and liquid influenced their responses.

Extended Smooth Orthogonal Decomposition for Modal Analysis

The smooth orthogonal decomposition (SOD) is an output-only modal analysis method, which has simple structure and gives good results for undamped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate various measurements that contain the displacement, the velocity, the acceleration, and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the undamped vibration system. These different methods are called extended smooth orthogonal decomposition (ESOD) methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different from each other. Thus, a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the single-degree-of-freedom (SDOF) vibration systems, it is effective for the multi-degrees-of-freedom (MDOF) vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for undamped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.