| Simulation of non-stationary stochastic process is the basis of stochastic dynamic response analysis and reliability calculation of engineering structures by using Monte Carlo method.Based on the theory of spectral representation,a new method is proposed to simulate non-stationary stochastic processes using generalized harmonic wavelet,which is combined with stochastic harmonic function to improve the simulation efficiency then.Research contents include:Firstly,the relationship between the evolutionary power spectrum of non-stationary processes and the generalized harmonic wavelet coefficients is derived,and the formula for estimating the evolutionary power spectrum is obtained,and the time-frequency modulation function is assumed to be a slow variable function relative to the time-holding function.According to the evolutionary power spectrum estimation formula based on generalized harmonic wavelet,the generalized harmonic wavelet coefficients in the inverse transformation of generalized harmonic wavelet are expressed by the evolutionary power spectrum,and the formula of using generalized harmonic wavelet to simulate non-stationary processes is derived.In the numerical example,the formula is used to simulate the nonstationary ground motion of a given evolutionary power spectrum,the convergence and accuracy of the proposed method are proved.In order to reduce the number of random variables,the stochastic harmonic function is introduced into the generalized harmonic wavelet simulation method of non-stationary processes.The idea of stochastic harmonic function is introduced into the formula of using generalized harmonic wavelet to simulate non-stationary process.Besides the random phase angles,the frequency and time translation factors in the formula are also defined as random variables that obey uniform distribution,and the dimensionality reduction expression of using generalized harmonic wavelet to simulate non-stationary process is obtained.The relationship between amplitude and probability density function is derived by using autocorrelation function and variance.In the numerical example,it is proved that the proposed method can further reduce the amount of simulation calculation while meeting the requirement of the accuracy of the evolutionary power spectrum by reconstructing the target evolutionary power spectrum.Finally,two examples of non-stationary stochastic processes simulated by generalized harmonic wavelet are analyzed.In the first example,the method proposed in this paper is used to simulate a real ground motion.The consistency of the non-stationary characteristics between the simulated time history and the actual record is proved by using the nonstationary evaluation index of ground motion.In the second example,the generalized harmonic wavelet method is compared with the spectral representation method from the perspective of component energy distribution.Through the analysis of the results,it can be concluded that the component energy of the method using generalized harmonic wavelet to simulate the non-stationary process is more concentrated,so the specified accuracy can be reached faster.The results of two application examples show that the method proposed in this paper can ensure the simulation effect and improve the computational efficiency.The results of this paper can be used to simulate dynamic disasters such as earthquake,strong wind and sea wave in stochastic response analysis and reliability calculation of structures. |
