It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating varie...It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.展开更多
A knowledge representation has been proposed using the state space theory of Artificial Intelligence for Dynamic Programming Model, in which a model can be defined as a six tuple M=(I,G,O,T,D,S). A building block mode...A knowledge representation has been proposed using the state space theory of Artificial Intelligence for Dynamic Programming Model, in which a model can be defined as a six tuple M=(I,G,O,T,D,S). A building block modeling method uses the modules of a six tuple to form a rule based solution model. Moreover, a rule based system has been designed and set up to solve the Dynamic Programming Model. This knowledge based representation can be easily used to express symbolical knowledge and dynamic characteristics for Dynamic Programming Model, and the inference based on the knowledge in the process of solving Dynamic Programming Model can also be conveniently realized in computer.展开更多
Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stabil...Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stability and passenger safety.Since wheel/rail contact forces of high-speed train are very difficult to measure directly,a new estimation process for wheel/rail contact forces was introduced in this work.Based on the state space equation,dynamic programming methods and the Bellman principle of optimality,the main theoretical derivation of the inversion mathematical model was given.The new method overcomes the weakness of large fluctuations which exist in current inverse techniques.High-speed vehicle was chosen as the research object,accelerations of axle box as input conditions,10 degrees of freedom vertical vibration model and 17 degrees of freedom lateral vibration model were established,respectively.Under 250 km/h,the vertical and lateral wheel/rail forces were identified.From the time domain and frequency domain,the comparison of the results between inverse and SIMPACK models were given.The results show that the inverse mathematical model has high precision for inversing the wheel/rail contact forces of an operation high-speed vehicle.展开更多
文摘It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.
文摘A knowledge representation has been proposed using the state space theory of Artificial Intelligence for Dynamic Programming Model, in which a model can be defined as a six tuple M=(I,G,O,T,D,S). A building block modeling method uses the modules of a six tuple to form a rule based solution model. Moreover, a rule based system has been designed and set up to solve the Dynamic Programming Model. This knowledge based representation can be easily used to express symbolical knowledge and dynamic characteristics for Dynamic Programming Model, and the inference based on the knowledge in the process of solving Dynamic Programming Model can also be conveniently realized in computer.
基金Project(2009BAG12A04-A11)supported by the National Key Technology R&D Program in the"11-th Five-year Plan"of ChinaProjects(51275432,51005190)supported by the National Natural Science Foundation of ChinaProject(SWJTU09ZT23)supported by University Doctor Academics Particularly Science Research Fund,China
文摘Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stability and passenger safety.Since wheel/rail contact forces of high-speed train are very difficult to measure directly,a new estimation process for wheel/rail contact forces was introduced in this work.Based on the state space equation,dynamic programming methods and the Bellman principle of optimality,the main theoretical derivation of the inversion mathematical model was given.The new method overcomes the weakness of large fluctuations which exist in current inverse techniques.High-speed vehicle was chosen as the research object,accelerations of axle box as input conditions,10 degrees of freedom vertical vibration model and 17 degrees of freedom lateral vibration model were established,respectively.Under 250 km/h,the vertical and lateral wheel/rail forces were identified.From the time domain and frequency domain,the comparison of the results between inverse and SIMPACK models were given.The results show that the inverse mathematical model has high precision for inversing the wheel/rail contact forces of an operation high-speed vehicle.
