In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of s...In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.展开更多
When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed...When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed modeling strategy of multi-dimensional stochastic earthquakes is addressed in this study.This improved seismic model has several merits that enable it to better provide seismic analyses of structures.Specifically,at first,the ground motion model is compatible with the design response spectrum.Secondly,the evolutionary power spectrum involved in the model and the design response spectrum are constructed accordingly with sufficient consideration of the correlation between different seismic components.Thirdly,the random function-based dimension-reduction representation is applied,by which seismic modeling is established,with three elementary random variables.Numerical simulations of multi-dimensional stochastic ground motions in a specific design scenario indicate the effectiveness of the proposed modeling strategy.Moreover,the multi-dimensional seismic response and the global reliability of a high-rise frame-core tube structure is discussed in detail to further illustrate the engineering applicability of the proposed method.The analytical investigations demonstrate that the suggested stochastic model of multi-dimensional ground motion is available for accurate seismic response analysis and dynamic reliability assessment of complex engineering structures for performance-based seismic resistance design.展开更多
With the development of space rendezvous and proximity operations(RPO)in recent years,the scenarios with noncooperative spacecraft are attracting the attention of more and more researchers.A method based on the costat...With the development of space rendezvous and proximity operations(RPO)in recent years,the scenarios with noncooperative spacecraft are attracting the attention of more and more researchers.A method based on the costate normalization technique and deep neural networks is presented to generate the optimal guidance law for free-time orbital pursuit-evasion game.Firstly,the 24-dimensional problem given by differential game theory is transformed into a three-parameter optimization problem through the dimension-reduction method which guarantees the uniqueness of solution for the specific scenario.Secondly,a close-loop interactive mechanism involving feedback is introduced to deep neural networks for generating precise initial solution.Thus the optimal guidance law is obtained efficiently and stably with the application of optimization algorithm initialed by the deep neural networks.Finally,the results of the comparison with another two methods and Monte Carlo simulation demonstrate the efficiency and robustness of the proposed optimal guidance method.展开更多
We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation,to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables a...We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation,to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and highdimensional microscopic variables.In the present work,we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization.The numbers of Maxwell boundary condition required for well-posedness are studied.The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed.By solving several benchmark problems,we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.展开更多
文摘In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.
基金National Natural Science Foundation of China under Grant Nos.51978543,52108444,and 51778343Plan of Outstanding Young and Middle-aged Scientific and Technological Innovation Team in the Universities of Hubei Province with Project No.T2020010Natural Science Foundation of Hebei Province under Grant No.E2021512001。
文摘When evaluating the seismic safety and reliability of complex engineering structures,it is a critical problem to reasonably consider the randomness and multi-dimensional nature of ground motions.To this end,a proposed modeling strategy of multi-dimensional stochastic earthquakes is addressed in this study.This improved seismic model has several merits that enable it to better provide seismic analyses of structures.Specifically,at first,the ground motion model is compatible with the design response spectrum.Secondly,the evolutionary power spectrum involved in the model and the design response spectrum are constructed accordingly with sufficient consideration of the correlation between different seismic components.Thirdly,the random function-based dimension-reduction representation is applied,by which seismic modeling is established,with three elementary random variables.Numerical simulations of multi-dimensional stochastic ground motions in a specific design scenario indicate the effectiveness of the proposed modeling strategy.Moreover,the multi-dimensional seismic response and the global reliability of a high-rise frame-core tube structure is discussed in detail to further illustrate the engineering applicability of the proposed method.The analytical investigations demonstrate that the suggested stochastic model of multi-dimensional ground motion is available for accurate seismic response analysis and dynamic reliability assessment of complex engineering structures for performance-based seismic resistance design.
基金supported by the National Defense Science and Techn ology Innovation(18-163-15-LZ-001-004-13)。
文摘With the development of space rendezvous and proximity operations(RPO)in recent years,the scenarios with noncooperative spacecraft are attracting the attention of more and more researchers.A method based on the costate normalization technique and deep neural networks is presented to generate the optimal guidance law for free-time orbital pursuit-evasion game.Firstly,the 24-dimensional problem given by differential game theory is transformed into a three-parameter optimization problem through the dimension-reduction method which guarantees the uniqueness of solution for the specific scenario.Secondly,a close-loop interactive mechanism involving feedback is introduced to deep neural networks for generating precise initial solution.Thus the optimal guidance law is obtained efficiently and stably with the application of optimization algorithm initialed by the deep neural networks.Finally,the results of the comparison with another two methods and Monte Carlo simulation demonstrate the efficiency and robustness of the proposed optimal guidance method.
基金supported in part by the National Basic Research Program of China(2011CB309704)the National Natural Science Foundation of China(NSFC91330205)+2 种基金supported by the Hong Kong Research Council GRF grant(PolyU 2021/12P)the Hong Kong Polytechnic University grant(A-PL61)supported by the Hong Kong RGC grant PolyU 2017/10P during their visits to the Hong Kong Polytechnic University。
文摘We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation,to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and highdimensional microscopic variables.In the present work,we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization.The numbers of Maxwell boundary condition required for well-posedness are studied.The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed.By solving several benchmark problems,we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.
