This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is establi...This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.展开更多
A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OW...A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.展开更多
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 fuzzy comfortability of a wind-sensitive super-high tower crane is critical to guarantee occupant health and improve construction efficiency.Therefore,the wind-resistant fuzzy comfortability of a super-high tower ...The fuzzy comfortability of a wind-sensitive super-high tower crane is critical to guarantee occupant health and improve construction efficiency.Therefore,the wind-resistant fuzzy comfortability of a super-high tower crane in the Ma’anshan Yangtze River(MYR)Bridge site is analyzed in this paper.First,the membership function model that represents fuzzy comfortability is introduced in the probability density evolution method(PDEM).Second,based on Fechner’s law,the membership function curves are constructed according to three acceleration thresholds in ISO 2631.Then,the fuzzy comfortability for the super-high tower crane under stochastic wind loads is assessed on the basis of different cut-set levelsλ.Results show that the comfortability is over 0.9 under the required maximum operating wind velocity.The low sensitivity toλcan be observed in the reliability curves of ISOⅡandⅢmembership functions.The reliability of the ISOⅠmembership function is not sensitive toλwhenλ<0.7,whereas it becomes sensitive toλwhenλ>0.7.展开更多
针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定...针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定理,求解了覆冰输电导线起舞临界风速;其次,基于概率密度演化法,发展了一种覆冰输电导线起舞概率评估框架,并进行覆冰输电导线起舞概率的计算与分析;最后,获得了某单跨覆冰导线算例的起舞概率并进行了参数分析。分析结果表明:本研究方法可准确计算该单跨输电导线的起舞概率,在计算效率上相比拉丁超立方抽样-蒙特卡洛模拟法(Latin hypercube sampling-Monte Carlo simulation,简称LHS-MCS)具有显著优势;档距、初始水平张力与初始风攻角对该单跨输电导线的起舞概率影响较大。展开更多
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochas...This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.展开更多
Herein, a typhoon hazard assessment method at the site-specific scale is proposed. This method integrates the nonlinear threedimensional wind field model and the probability density evolution method. At the site-speci...Herein, a typhoon hazard assessment method at the site-specific scale is proposed. This method integrates the nonlinear threedimensional wind field model and the probability density evolution method. At the site-specific scale, the track of a typhoon near the engineering site is approximated via a straight line. The wind field model is utilized to calculate the wind speed at the surface given the gradient wind field at the top of the boundary layer. A comparison between the simulated and observed wind histories for Typhoon Hagupit that made landfall in Guangdong Province demonstrates the fidelity of the wind field model. The probability density evolution method is utilized to calculate the propagation of the randomness from the basic random variables toward the extremities of the typhoon surface wind. To model the probability distribution of the basic random variables, several candidate distributions are considered to fit the observations. Akaike information criterion and Anderson-Darling distance are used for selecting the preferred probability distribution model. The adequacy of the probability density evolution method in assessing typhoon hazards is verified by comparing the results with those generated by Monte Carlo simulations. The typhoon wind hazards estimated by the present study are compared with those proposed by other studies and the design code, and the differences are analyzed and discussed. The results of the proposed method provide the reasonable probabilistic model for the assessment of the structural reliability and the improvement of community resilience in the typhoon-prone areas.展开更多
To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Base...To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.展开更多
基金the National Natural Science Foundation of China(Grant No.11472137).
文摘This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.
基金This research is supported by the National Natural Science Foundation of China(Grant No.51578444)Key Science Research Program of Education Department of Shaanxi Province(Grant No.20JY032).
文摘A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.
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The National Natural Science Foundation of China(No.52108274,52208481,52338011)State Scholarship Fund of China Scholarship Council(No.202306090285).
文摘The fuzzy comfortability of a wind-sensitive super-high tower crane is critical to guarantee occupant health and improve construction efficiency.Therefore,the wind-resistant fuzzy comfortability of a super-high tower crane in the Ma’anshan Yangtze River(MYR)Bridge site is analyzed in this paper.First,the membership function model that represents fuzzy comfortability is introduced in the probability density evolution method(PDEM).Second,based on Fechner’s law,the membership function curves are constructed according to three acceleration thresholds in ISO 2631.Then,the fuzzy comfortability for the super-high tower crane under stochastic wind loads is assessed on the basis of different cut-set levelsλ.Results show that the comfortability is over 0.9 under the required maximum operating wind velocity.The low sensitivity toλcan be observed in the reliability curves of ISOⅡandⅢmembership functions.The reliability of the ISOⅠmembership function is not sensitive toλwhenλ<0.7,whereas it becomes sensitive toλwhenλ>0.7.
文摘针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定理,求解了覆冰输电导线起舞临界风速;其次,基于概率密度演化法,发展了一种覆冰输电导线起舞概率评估框架,并进行覆冰输电导线起舞概率的计算与分析;最后,获得了某单跨覆冰导线算例的起舞概率并进行了参数分析。分析结果表明:本研究方法可准确计算该单跨输电导线的起舞概率,在计算效率上相比拉丁超立方抽样-蒙特卡洛模拟法(Latin hypercube sampling-Monte Carlo simulation,简称LHS-MCS)具有显著优势;档距、初始水平张力与初始风攻角对该单跨输电导线的起舞概率影响较大。
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No.50321803 & 50621062National Natural Science Foundation of China Under Grant No.50808113 & 10872148
文摘This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
基金supported by the National Natural Science Foundation of China (Grant No. 51538010)。
文摘Herein, a typhoon hazard assessment method at the site-specific scale is proposed. This method integrates the nonlinear threedimensional wind field model and the probability density evolution method. At the site-specific scale, the track of a typhoon near the engineering site is approximated via a straight line. The wind field model is utilized to calculate the wind speed at the surface given the gradient wind field at the top of the boundary layer. A comparison between the simulated and observed wind histories for Typhoon Hagupit that made landfall in Guangdong Province demonstrates the fidelity of the wind field model. The probability density evolution method is utilized to calculate the propagation of the randomness from the basic random variables toward the extremities of the typhoon surface wind. To model the probability distribution of the basic random variables, several candidate distributions are considered to fit the observations. Akaike information criterion and Anderson-Darling distance are used for selecting the preferred probability distribution model. The adequacy of the probability density evolution method in assessing typhoon hazards is verified by comparing the results with those generated by Monte Carlo simulations. The typhoon wind hazards estimated by the present study are compared with those proposed by other studies and the design code, and the differences are analyzed and discussed. The results of the proposed method provide the reasonable probabilistic model for the assessment of the structural reliability and the improvement of community resilience in the typhoon-prone areas.
基金supported by the National Natural Science Foundation of China(Grant Nos NSFC1057211,50875213)New Century Excellent Talents in University of China(Grant No NCET-05-0868)+2 种基金Aviation Science Foundation of China(Grant No 2007ZA53012)National High Technology Research and Development Program of China(Grant No 2007AA04Z401)the Important National Science&Technology Specific Projects(Grant No 2009ZX04014-015-03)
文摘To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.
