IMPORTANCE SAMPLING METHOD BASED ON RESPONSE POWER SPECTRUM FOR STRUCTURAL DYNAMIC RELIABILITY ESTIMATIONS

Based on response spectrum, the paper proposed importance sampling method for structural dynamic reliability estimation under random earthquake excitations. In order to improve the calculation efficiency of dynamic reliability estimations, the paper uses power spectrum with importance sampling method to increase the variances of input random excitation amplitudes. The power spectral density of the response usually has some significant peaks which indicate the corresponding frequency ranges with the most contribution to the total variance of the response. Hence, the importance sampling density should be adapted for those amplitudes assigned to frequencies near the peaks of the spectrum. According to random vibration theory, the power spectral density of stationary random response is similar to the expectation of square of the absolute value of response in frequency domain, which can be easily calculated by Fourier transform and can also be used to increase the variances of input random excitation amplitudes. The importance sampling density function can be expressed as multiplications of elements of excitation amplitudes, and the variances of input random excitation amplitudes in importance sampling density function can be obtained by structural analysis for several times. Calculations of a three degree-of-freedom linear structure and a ten degree-of-freedom random structure indicate that the proposed method is an effective method for improving the dynamic reliability calculation efficiency and for estimating dynamic reliability of random structures.