The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution ...The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.展开更多
In the present paper the approximate functions for certain periodic functions of several variables are constructed by means of the number-theoretic method.
In this paper, we propose a new approach to the test of elliptical symmetry based on theprojection pursuit (P.P.) technique, the number-theoretic method, skewness and kurtosis. Thelimiting null distributions of the ne...In this paper, we propose a new approach to the test of elliptical symmetry based on theprojection pursuit (P.P.) technique, the number-theoretic method, skewness and kurtosis. Thelimiting null distributions of the new statistics are derived. The powers of the tests against sixalternatives are calculated by simulation, which shows that the new t.st's are acceptable.展开更多
基金the National Natural Science Foundation of Chinafor Innovative Research Groups Under Grant No.50621062the National Natural Science Foundation of China forYoung Scholars Under Grant No.10402030
文摘The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.
文摘In the present paper the approximate functions for certain periodic functions of several variables are constructed by means of the number-theoretic method.
文摘In this paper, we propose a new approach to the test of elliptical symmetry based on theprojection pursuit (P.P.) technique, the number-theoretic method, skewness and kurtosis. Thelimiting null distributions of the new statistics are derived. The powers of the tests against sixalternatives are calculated by simulation, which shows that the new t.st's are acceptable.
