A two-step density estimation method and its applications Tao, Wei-Feng; Li, Jie
Probability density evolution method (PDEM) provides a feasible approach for dynamic responses analysis of nonlinear stochastic structures. The key issue of PDEM is to solve a generalized density evolution equation (GDEE). Previously, finite difference method (FDM) is resorted to solve GDEE, thus getting the probability density function (PDF) result directly. In this paper, a two-step method that improves the result of FDM by means of nonlinear wavelet density estimation is proposed. By taking advantage of the property of multi-resolution of wavelet, the proposed method tends to give a more accurate result. An 8-story reinforced concrete shear frame with Bouc-Wen hysteretic restoring forces subjected to seismic excitation is investigated. The result shows that the proposed method performs better than FDM.
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