In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems...In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.展开更多
FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at doc...FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at dock like other kinds of ships, the reliability of FPSO hull girder during the whole service should be focused. Based on latest corrosion database and rational corrosion model, the ultimate strength of one FPSO is calculated under the conditions of slight, moderate and severe corrosion. The results not only provide the reliabihty under different corrosion conditions, but also do well for further inspection and maintenance research. The results provide necessary foundation for deciding inspection intervals and maintenance measure, which has practical sense to improve the general safety level of ocean engineering.展开更多
Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Meth...Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.展开更多
A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis ...A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.展开更多
A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, t...A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.展开更多
Wavelets are a useful tool for analyzing the time-frequency of a non-stable series and are widely applied in many fields. The process of earthquake preparation and occurrence is a non-linear process. In the paper, the...Wavelets are a useful tool for analyzing the time-frequency of a non-stable series and are widely applied in many fields. The process of earthquake preparation and occurrence is a non-linear process. In the paper, the wavelet method is used to analyze the series of earthquake data for the time period from 1900 to 2003 in the west of the Chinese mainland and its adjacent area (WCMAA), and to obtain the characteristic information for different time scales. In the past 103 years, there were four primary periods of regional earthquake activity in the area with durations of 42, 22, 7 and 14 years, respectively and the intensity of earthquake activity changing with time. It doesn’t make sense to talk about active or quiet periods of earthquake activity unless it is based on a specific time scale. In addition, the tendency analysis of earthquake activity using the primary period of seismic activity and wavelet coefficients of varied time scales indicates that the earthquake activity in this region will be high in the forthcoming years.展开更多
Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model,accuracy of the long-wavelength part of gravity field model recovered by them are poor,whi...Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model,accuracy of the long-wavelength part of gravity field model recovered by them are poor,which leads to only a few applications in time-variable gravity investigation.The reason is that some factors limit the accuracy of the gravity field recovered using gradient data,including accuracy of the gravity gradient observations,measurement bandwidth(MBW)of gradiometer,satellite inclination,etc.This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations.Firstly,for arbitrary satellite orbit inclination,we give the frequency distributions of all the components of gravity gradients(i.e.Txx;Tyy;Tzz;Txy;Txz and Tyz,).The results show that the maximum frequency of each component of the gravity gradients is the same,i.e.l=Ts(l is degree of the gravity field model,Ts is the orbital periods),and it is not influenced by the inclination of the satellite orbits.Secondly,the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps.Big polar gaps are experimented by a numerical test with inclination of 45°.Finally,considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer(SGG)compared to gradiometer used in Gravity field and steadystate Ocean Circulation Explorer(GOCE),the possibility of detecting time-variable gravity using gravity gradient observations is discussed.The results show that the SGG creates errors in MBW with magnitude of 0.014 m E,which is smaller than the magnitude of the time-variable gravity gradient signals(i.e.,0.02 m E)derived from Gravity Recovery and Climate Experiment(GRACE)gravity field models.This indicates the potential of SGG in time-variable gravity detection.展开更多
The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and proce...The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.展开更多
The stability analysis and stabilization problems of the wireless networked control systems(WNCSs) with signal transmission deadbands were considered. The deadbands were respectively set up at the sensor to the contro...The stability analysis and stabilization problems of the wireless networked control systems(WNCSs) with signal transmission deadbands were considered. The deadbands were respectively set up at the sensor to the controller and the controller to the actor sides in the WNCS, which were used to reduce data transmission, furthermore, to decrease the network collision and node energy consumption. Under the consideration of time-varying delays and signal transmission deadbands, the model for the WNCS was presented. A novel Lyapunov functional which took full advantages of the network factors was exploited. Meanwhile, new stability analysis and stabilization conditions for the WNCS were proposed, which described the relationship of the delay bounds, the transmission deadband bounds and the system stability. Two examples were used to demonstrate the effectiveness of the proposed methods. The results show that the proposed approach can guarantee asymptotical stability of the system and reduce the data transmission effectively.展开更多
Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm.Precision analysis and computation efficiency of new algorithm are implemented.The following co...Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm.Precision analysis and computation efficiency of new algorithm are implemented.The following conclusions can be got.Choosing matrixes M,G and K is certainly flexible.We can place left side of nonlinear terms of vibration equations of time-varying system into right side of equations in precise integration algorithms.The key of transformation from vibration equations of time-varying system to first order differential equations is to form matrix H,which should be assured to be nonsingular.With suitable disposal,precision and computation efficiency of precise integration algorithms are greatly larger than those of general methods.展开更多
Recently, several approaches have been proposed to discover the causality of the time-independent or fixed causal model. However, in many realistic applications, especially in economics and neuroscience, causality amo...Recently, several approaches have been proposed to discover the causality of the time-independent or fixed causal model. However, in many realistic applications, especially in economics and neuroscience, causality among variables might be time-varying. A time-varying linear causal model with non-Gaussian noise is considered and the estimation of the causal model from observational data is focused. Firstly, an independent component analysis(ICA) based two stage method is proposed to estimate the time-varying causal coefficients. It shows that, under appropriate assumptions, the time varying coefficients in the proposed model can be estimated by the proposed approach, and results of experiment on artificial data show the effectiveness of the proposed approach. And then, the granger causality test is used to ascertain the causal direction among the variables. Finally, the new approach is applied to the real stock data to identify the causality among three stock indices and the result is consistent with common sense.展开更多
Using Time-Varying AR (TVAR) model and adaptive notch filter is a new method for the non-stationary jammer suppression in Direct Sequence Spread Spectrum (DSSS). The performance of TVAR model for Instantaneous Frequen...Using Time-Varying AR (TVAR) model and adaptive notch filter is a new method for the non-stationary jammer suppression in Direct Sequence Spread Spectrum (DSSS). The performance of TVAR model for Instantaneous Frequency (IF) estimation will be affected by some factors such as basis functions. Focusing on this problem, the optimal basis function of TVAR model for the IF estimation of the LFM signal is obtained in this paper. Besides the depth and width of notching, the phase properties of notch filter affect the Signal-to-Interference plus-Noise Ratio (SINR) of correlation output to the narrowband jammer suppression in DSSS, in response to the problem the closed solution of correlation output SINR improvement has been derived when a single frequency jammer passes through direct IIR notch filter, and its performance has been compared with those of five coefficient FIR filters. Later, a novel method for LFM jammer suppression based on Fourier basis TVAR model and direct IIR notch filter is proposed. The simulation results show the effectiveness of the proposed method.展开更多
In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis (TCA)...In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.展开更多
基金partially supported by the National Natural Science Foundation of China(52375238)Science and Technology Program of Guangzhou(202201020213,202201020193,202201010399)GZHU-HKUST Joint Research Fund(YH202109).
文摘In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.
基金This research was financially supported by the National Natural Science Foundation of China (Grant No50323004)
文摘FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at dock like other kinds of ships, the reliability of FPSO hull girder during the whole service should be focused. Based on latest corrosion database and rational corrosion model, the ultimate strength of one FPSO is calculated under the conditions of slight, moderate and severe corrosion. The results not only provide the reliabihty under different corrosion conditions, but also do well for further inspection and maintenance research. The results provide necessary foundation for deciding inspection intervals and maintenance measure, which has practical sense to improve the general safety level of ocean engineering.
文摘Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.
基金supported by National Natural Science Foundation of China(Project No.11572229)Shanghai Chenguang Plan(Project No.14CG18)Fundamental Research Funds for the Central Universities(Project No.22120180063).
文摘A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.
文摘A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.
文摘Wavelets are a useful tool for analyzing the time-frequency of a non-stable series and are widely applied in many fields. The process of earthquake preparation and occurrence is a non-linear process. In the paper, the wavelet method is used to analyze the series of earthquake data for the time period from 1900 to 2003 in the west of the Chinese mainland and its adjacent area (WCMAA), and to obtain the characteristic information for different time scales. In the past 103 years, there were four primary periods of regional earthquake activity in the area with durations of 42, 22, 7 and 14 years, respectively and the intensity of earthquake activity changing with time. It doesn’t make sense to talk about active or quiet periods of earthquake activity unless it is based on a specific time scale. In addition, the tendency analysis of earthquake activity using the primary period of seismic activity and wavelet coefficients of varied time scales indicates that the earthquake activity in this region will be high in the forthcoming years.
基金funded by National Natural Science Foundation of China(No.41674026,41404019,41774089)Fundamental Research Funds for the Central University(No.2652018027)+2 种基金China Geological Survey(DD20191006)Open Research Fund of Qian Xuesen Laboratory of Space Technology,CAST(No.GZZKFJJ2020006)Open Research Fund of Key Laboratory of Space Utilization,Chinese Academy of Sciences(LSU-KFJJ201902)
文摘Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model,accuracy of the long-wavelength part of gravity field model recovered by them are poor,which leads to only a few applications in time-variable gravity investigation.The reason is that some factors limit the accuracy of the gravity field recovered using gradient data,including accuracy of the gravity gradient observations,measurement bandwidth(MBW)of gradiometer,satellite inclination,etc.This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations.Firstly,for arbitrary satellite orbit inclination,we give the frequency distributions of all the components of gravity gradients(i.e.Txx;Tyy;Tzz;Txy;Txz and Tyz,).The results show that the maximum frequency of each component of the gravity gradients is the same,i.e.l=Ts(l is degree of the gravity field model,Ts is the orbital periods),and it is not influenced by the inclination of the satellite orbits.Secondly,the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps.Big polar gaps are experimented by a numerical test with inclination of 45°.Finally,considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer(SGG)compared to gradiometer used in Gravity field and steadystate Ocean Circulation Explorer(GOCE),the possibility of detecting time-variable gravity using gravity gradient observations is discussed.The results show that the SGG creates errors in MBW with magnitude of 0.014 m E,which is smaller than the magnitude of the time-variable gravity gradient signals(i.e.,0.02 m E)derived from Gravity Recovery and Climate Experiment(GRACE)gravity field models.This indicates the potential of SGG in time-variable gravity detection.
基金supported by the National Natural Science Foundation of China(6087405361034006)
文摘The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.
基金Project(61104106)supported by the National Natural Science Foundation of ChinaProject(201202156)supported by the Natural Science Foundation of Liaoning Province,ChinaProject(LJQ2012100)supported by the Program for Liaoning Excellent Talents in University(LNET),China
文摘The stability analysis and stabilization problems of the wireless networked control systems(WNCSs) with signal transmission deadbands were considered. The deadbands were respectively set up at the sensor to the controller and the controller to the actor sides in the WNCS, which were used to reduce data transmission, furthermore, to decrease the network collision and node energy consumption. Under the consideration of time-varying delays and signal transmission deadbands, the model for the WNCS was presented. A novel Lyapunov functional which took full advantages of the network factors was exploited. Meanwhile, new stability analysis and stabilization conditions for the WNCS were proposed, which described the relationship of the delay bounds, the transmission deadband bounds and the system stability. Two examples were used to demonstrate the effectiveness of the proposed methods. The results show that the proposed approach can guarantee asymptotical stability of the system and reduce the data transmission effectively.
基金Project(50078006) supported by the National Natural Science Foundation of China
文摘Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm.Precision analysis and computation efficiency of new algorithm are implemented.The following conclusions can be got.Choosing matrixes M,G and K is certainly flexible.We can place left side of nonlinear terms of vibration equations of time-varying system into right side of equations in precise integration algorithms.The key of transformation from vibration equations of time-varying system to first order differential equations is to form matrix H,which should be assured to be nonsingular.With suitable disposal,precision and computation efficiency of precise integration algorithms are greatly larger than those of general methods.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61573014)
文摘Recently, several approaches have been proposed to discover the causality of the time-independent or fixed causal model. However, in many realistic applications, especially in economics and neuroscience, causality among variables might be time-varying. A time-varying linear causal model with non-Gaussian noise is considered and the estimation of the causal model from observational data is focused. Firstly, an independent component analysis(ICA) based two stage method is proposed to estimate the time-varying causal coefficients. It shows that, under appropriate assumptions, the time varying coefficients in the proposed model can be estimated by the proposed approach, and results of experiment on artificial data show the effectiveness of the proposed approach. And then, the granger causality test is used to ascertain the causal direction among the variables. Finally, the new approach is applied to the real stock data to identify the causality among three stock indices and the result is consistent with common sense.
基金Supported by the Natural Science Foundation of Hebei Province (F2010000442)
文摘Using Time-Varying AR (TVAR) model and adaptive notch filter is a new method for the non-stationary jammer suppression in Direct Sequence Spread Spectrum (DSSS). The performance of TVAR model for Instantaneous Frequency (IF) estimation will be affected by some factors such as basis functions. Focusing on this problem, the optimal basis function of TVAR model for the IF estimation of the LFM signal is obtained in this paper. Besides the depth and width of notching, the phase properties of notch filter affect the Signal-to-Interference plus-Noise Ratio (SINR) of correlation output to the narrowband jammer suppression in DSSS, in response to the problem the closed solution of correlation output SINR improvement has been derived when a single frequency jammer passes through direct IIR notch filter, and its performance has been compared with those of five coefficient FIR filters. Later, a novel method for LFM jammer suppression based on Fourier basis TVAR model and direct IIR notch filter is proposed. The simulation results show the effectiveness of the proposed method.
基金supported by the Natural Science Foundation of China under Grant No.51175423
文摘In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.