Inverse Analysis of Crack in Fixed-Fixed Structure by Neural Network with the Aid of Modal Analysis

In this research, dynamic response of a cracked shaft having transverse crack is analyzed using theoretical neural network and experimental analysis. Structural damage detection using frequency response functions (FRFs) as input data to the back-propagation neural network (BPNN) has been explored. For deriving the effect of crack depths and crack locations on FRF, theoretical expressions have been developed using strain energy release rate at the crack section of the shaft for the calculation of the local stiffnesses. Based on the flexibility, a new stiffness matrix is deduced that is subsequently used to calculate the natural frequencies and mode shapes of the cracked beam using the neural network method. The results of the numerical analysis and the neural network method are being validated with the result from the experimental method. The analysis results on a shaft show that the neural network can assess damage conditions with very good accuracy. 1. Introduction Vibration-based methods for detection of cracks offer some advantages over conventional methods. This methodology can help to determine the location and size of the cracks from the vibration data collected from the cracked beam structure. Development of cracks in a vibrating structure leads to reduction in the stiffness and increase in its damping [1] which, in turn, gives rise to a change in natural frequencies and mode shapes. So it may be possible to estimate the location and size of the cracks by measuring changes in the vibration parameters. Tada et al. [2] have proposed the basis for calculation of compliance matrix for different types of beams. Sekhar and Prabhu [3] have derived a method to calculate the vibration characteristics using a model based on finite element. Paviglianiti et al. [4] have devised a scheme for detecting and isolating sensor faults in industrial robot manipulators. They have adopted a procedure for decoupling of the disturbance effect from the effect of the fault generated in the system. The dynamics of the proposed scheme has been improved by using radial basis functions neural network. Behera et al. [5] have studied the vibration characteristics of a shaft with two open cracks rotating in a fluid medium by using the influence coefficient method to find frequency of the cracked shaft and frequency contours with respect to crack depths and locations. Wang et al. [6] have investigated the bending and torsional vibration of a fiber reinforced composite cantilever with a surface crack. They have suggested that the coupling of bending and torsion is the result of