Damage prediction in mechanical and structural systems is establishing a prominent role in modern engineering. Unlike conventional NDT methods, vibration based damage methods give ample flexibility to understand the extent of expected damages in the system. Measurement of vibration characteristics like natural frequencies and mode shapes, Fourier responses and transient responses can help in comprehending the present status of a system either by comparing with their baseline equivalents or by formulating residual functions. Current damage- detection methods are varied like visual or localized experimental methods such as acoustic or ultrasonic methods, magnetic field methods, radiograph, eddy- current methods and thermal field methods.The book in that direction, assumes vital importance in the contemporary vibration technology. In this procedure the minimization of residues is carried out using non-conventional optimization techniques like genetic algorithms. Residual functions are developed with various types of outputs and effectiveness is verified.