This study performed an inverse detection of fiber stiffness degradation that occurs due to damages in free vibrating composite structures. Five unknown parameters are considered to determine the fiber stiffness which is a modified form of the bivariate Gaussian distribution function. The proposed approach is more feasible than the conventional element-based damage detection method from the computational efficiency because a finite element analysis coupled with a genetic algorithm using a small number of unknown parameters is performed. The numerical examples show that the proposed technique is a feasible and practical method, which can prove the location of a damaged region as well as inspect the distribution of deteriorated fiber stiffness although there is a small difference in dynamic characteristics between damaged and undamaged structures.

In this paper, statistical distribution functions are developed for distance determination of stellar groups. This method depends on the assumption that absolute magnitudes and apparent magnitudes follow a Gaussian distribution function. Due to the limits of the integrands of the frequency function of apparent and absolute magnitudes, we introduce Case A, B, and C Gaussian distributions. The developed approaches have been implemented to determine distances to some clusters and stellar associations. The comparison with the distances derived by different authors reveals good agreement.