In order to grasp the evolution of flight conflict amount accurately and to forecast the amount, chaos in flight conflicts is studied. Firstly, a fault tree of flight conflicts is established based on the man-machine-...In order to grasp the evolution of flight conflict amount accurately and to forecast the amount, chaos in flight conflicts is studied. Firstly, a fault tree of flight conflicts is established based on the man-machine-environ- ment system engineering theory. The chaotic characteristics of flight conflict are analyzed from the qualitative point of view. Secondly, an improved chaotic algorithm for the largest Lyapunov exponent is proposed based on the small-data method and the wavelet de-noising theory. Chaos in flight conflict time series is identified by the improved chaotic algorithm from the quantitative point of view. Finally, a case study by the chaos forecasting al- gorithm is performed and the results are evaluated by the gray error checking ： Correlative value of posterior error is 0. 220 9〈0. 35, and micro-error probability is 0. 985 3〉0.95. Such results show the chaos forecasting algo- rithm is effective, thus it is feasible to analyze and forecast flight conflict by chaotic theory.展开更多
The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It...The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It is found that the estimated local largest Lyapunov exponent is positive in all cases and the profile is similar to that of the local fractal dimension in this reactor. The positive largest Lyapunov exponent shows that the reactor is a nonlinear chaotic system. The obvious distribution indicates that the local nonlinear characteristic parameters such as the Lyapunov exponent and the fractal dimension could be applied to further study the flow characteristics such as the flow regine transitions and flow structures of the multi phase reactors.展开更多
The stretching and folding of fluid element during chaotic mixing field is studied using numerical method. The chaotic mixing process is caused by periodic secondary flow in a twisted curved pipe. Using the nonlinea...The stretching and folding of fluid element during chaotic mixing field is studied using numerical method. The chaotic mixing process is caused by periodic secondary flow in a twisted curved pipe. Using the nonlinear discrete velocity field as the dynamical system, the present study connects the fluid particle's stretching along its trajectory in one period to a linearized time-varying variational equation. After numerical approximation of the variational equation, fluid stretching is calculated on the whole cross section. The stretching distribution shows an exponential fluid stretching and folding, which indicates an excellent mixing performance.展开更多
An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were ex...An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.展开更多
基金Supported by the Joint Funds of National Natural Science Foundation of China(61039001)~~
文摘In order to grasp the evolution of flight conflict amount accurately and to forecast the amount, chaos in flight conflicts is studied. Firstly, a fault tree of flight conflicts is established based on the man-machine-environ- ment system engineering theory. The chaotic characteristics of flight conflict are analyzed from the qualitative point of view. Secondly, an improved chaotic algorithm for the largest Lyapunov exponent is proposed based on the small-data method and the wavelet de-noising theory. Chaos in flight conflict time series is identified by the improved chaotic algorithm from the quantitative point of view. Finally, a case study by the chaos forecasting al- gorithm is performed and the results are evaluated by the gray error checking ： Correlative value of posterior error is 0. 220 9〈0. 35, and micro-error probability is 0. 985 3〉0.95. Such results show the chaos forecasting algo- rithm is effective, thus it is feasible to analyze and forecast flight conflict by chaotic theory.
文摘The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It is found that the estimated local largest Lyapunov exponent is positive in all cases and the profile is similar to that of the local fractal dimension in this reactor. The positive largest Lyapunov exponent shows that the reactor is a nonlinear chaotic system. The obvious distribution indicates that the local nonlinear characteristic parameters such as the Lyapunov exponent and the fractal dimension could be applied to further study the flow characteristics such as the flow regine transitions and flow structures of the multi phase reactors.
基金Supported by the National Natural Science Foundation of China(No.29776039).
文摘The stretching and folding of fluid element during chaotic mixing field is studied using numerical method. The chaotic mixing process is caused by periodic secondary flow in a twisted curved pipe. Using the nonlinear discrete velocity field as the dynamical system, the present study connects the fluid particle's stretching along its trajectory in one period to a linearized time-varying variational equation. After numerical approximation of the variational equation, fluid stretching is calculated on the whole cross section. The stretching distribution shows an exponential fluid stretching and folding, which indicates an excellent mixing performance.
基金Supported by National Natural Science Foundation of China (No.50578108) .
文摘An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.
