Random Vibration Sensitivity Analysis Based On Pseudo-excitation And Its Application

Sensitivity analysis is an active research area. It is widely used in fields of engineering computation, such as structural optimization, model updating, damage identification and reliability evaluation. With the widespread application of random vibration in practical engineering, when the random excitation is taken into consideration, the sensitivities of random responses usually need to be calculated in many fields above. A method is proposed for sensitivity analysis of stationary random vibration within the framework of pseudo excitation method (PEM). The proposed method is then applied to researches of structural model updating using test data of power spectral density (PSD) and composite random vibration problem. The work is summarized as follows:Firstly, a method is proposed for sensitivity analysis of stationary random response on the basis of PEM. The stationary random vibration analysis is transformed into harmonic vibration analysis by PEM. Hence, the sensitivity analysis of stationary random responses is transformed into sensitivity analysis of pseudo responses of structures subjected to pseudo harmonic excitation. Using PEM, the formulae are derived to calculate the sensitivities of random responses of PSD and variance from sensitivities of pseudo responses. The method for high order sensitivity analysis of random responses is proposed by extending the first order sensitivity analysis method. For large complicated structures, the sensitivities of pseudo responses are solved by mode superposition method. They are transformed into modal coordinates and then calculated in modal coordinates, so the computational efficiency is greatly improved.Secondly, a method is presented for model updating using test data of PSD of stationary random vibration. The model updating equations are established from the identity between model analytical PSD and test PSD. The model updating equations have no solution because of the noise errors in test data. Hence, the model updating problem is an ill-posed problem. The model updating problem is solved by means of trust region type L-M algorithm. The sensitivities of random responses in the Jacobi matrix are solved during iterations by the proposed sensitivity analysis method. The model updating of a plan truss is numerically simulated by the proposed model updating method. The influence of noise is discussed. It is shown that the proposed method has good results, and it can be easily applied to large complex engineering structures.Finally, the pseudo excitation perturbation method (PEPM) is presented for probabilistic information prediction of stochastic dynamic response of structures with uncertain parameters subjected to stationary stochastic excitation. The perturbation expressions of structural random responses are deduced by Taylor series expansion. The statistical characteristics of stationary random responses are derived from the perturbation expressions. A high order pseudo excitation perturbation method is presented by high order perturbation expressions. The proposed method is applied to a space truss and a cable-stayed bridge with uncertain structural parameters, and the mean values and standard deviations of the variances of stationary random responses are calculated. The results from this method are compared with those obtained from Monte Carlo simulation. It is shown that this method has satisfactory accuracy. It provides an effective way for composite random vibration analysis of large complex structures in practical engineering.