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
The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measu...The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.展开更多
This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and po...This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.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.
基金Supported by the National Natural Science Foundation of China （No. 60736006 and 60875019）
文摘The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.
基金supported by the National Program on Key Basic Research Project(Grant No.2014CB046805)National Natural Science Foundation of China(Grant No.11372211).
文摘This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.
