In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decompo...In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.展开更多
Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual info...Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.展开更多
Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have mac...Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have macro spatiotemporal characteristics and micro chaotic characteristics. The key to improving the model prediction accuracy is to fully extract the macro and micro characteristics of traffic flow time sequences. However, traditional prediction model by only considers time features of traffic data, ignoring spatial characteristics and nonlinear characteristics of the data itself, resulting in poor model prediction performance. In view of this, this research proposes an intelligent combination prediction model taking into account the macro and micro features of chaotic traffic data. Firstly, to address the problem of time-consuming and inefficient multivariate phase space reconstruction by iterating nodes one by one, an improved multivariate phase space reconstruction method is proposed by filtering global representative nodes to effectively realize the high-dimensional mapping of chaotic traffic flow. Secondly, to address the problem that the traditional combinatorial model is difficult to adequately learn the macro and micro characteristics of chaotic traffic data, a combination of convolutional neural network(CNN) and convolutional long short-term memory(ConvLSTM) is utilized for capturing nonlinear features of traffic flow more comprehensively. Finally,to overcome the challenge that the combined model performance degrades due to subjective empirical determined network parameters, an improved lightweight particle swarm is proposed for improving prediction accuracy by optimizing model hyperparameters. In this paper, two highway datasets collected by the Caltrans Performance Measurement System(PeMS)are taken as the research objects, and the experimental results from multiple perspectives show that the comprehensive performance of the method proposed in this research is superior to those of the prevalent methods.展开更多
It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochas- tic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time se...It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochas- tic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.展开更多
In order to realize the prediction of a chaotic time series of mine water discharge,an approach incorporating phase space reconstruction theory and statistical learning theory was studied.A differential entropy ratio ...In order to realize the prediction of a chaotic time series of mine water discharge,an approach incorporating phase space reconstruction theory and statistical learning theory was studied.A differential entropy ratio method was used to determine embedding parameters to reconstruct the phase space.We used a multi-layer adaptive best-fitting parameter search algorithm to estimate the LS-SVM optimal parameters which were adopted to construct a LS-SVM prediction model for the mine water chaotic time series.The results show that the simulation performance of a single-step prediction based on this LS-SVM model is markedly superior to that based on a RBF model.The multi-step prediction results based on LS-SVM model can reflect the development of mine water discharge and can be used for short-term forecasting of mine water discharge.展开更多
This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed ...This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.展开更多
To realize real-time monitoring and short-term forecasting and forewarning of coalmine ventilation systems(CVS), in this paper, we first established a joint surface and underground CVS safety management system consist...To realize real-time monitoring and short-term forecasting and forewarning of coalmine ventilation systems(CVS), in this paper, we first established a joint surface and underground CVS safety management system consisting of main ventilation fan, safety-partition linked passageways, and air-required locations. We then applied chaos theory to identify the air quantity and gas concentration of underground partition boundaries, and adopted a fixed data quantity, multi-step progressive, weighted first-order local-domain method to setup a chaos prediction model and a CVS safety forecasting and forewarning system formed by the normal change level, orange forewarning level, and red alarm level. We next conduct the on-field application of the system in a coalmine in Jining, Shandong, China. The results showed that (1) in the statistical scale of 5 min, the changes in both air quantity and gas concentration along CVS partition airflow boundaries were characteristic of chaos and could be used for short-term chaos prediction, and the latter was more chaotic than the former;(2) the setup chaos prediction model had a higher prediction precision and the established safety prediction system could not only predict the variation in CVS stability but also reflect the rationality of underground mining intensity. Thus, this CVS safety forecasting and forewarning system is of better application value.展开更多
基金supported by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2010J01210 and T0750008)
文摘In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.
文摘Chaotic characteristics of traffic flow time series is analyzed to further investigate nonlinear characteristics of air traffic system.Phase space is reconstructed both by time delay which is built through mutual information,and by embedding dimension which is based on false nearest neighbors method.In order to analyze chaotic characteristics of time series,correlation dimensions and the largest Lyapunov exponents are calculated through Grassberger-Procaccia(G-P)algorithm and small-data method.Five-day radar data from the control center in Guangzhou area are analyzed and the results show that saturated correlation dimensions with self-similar structures exist in time series,and the largest Lyapunov exponents are all equal to zero and not sensitive to initial conditions.Air traffic system is affected by multiple factors,containing inherent randomness,which lead to chaos.Only grasping chaotic characteristics can air traffic be predicted and controlled accurately.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62063014)the Natural Science Foundation of Gansu Province, China (Grant No. 22JR5RA365)。
文摘Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have macro spatiotemporal characteristics and micro chaotic characteristics. The key to improving the model prediction accuracy is to fully extract the macro and micro characteristics of traffic flow time sequences. However, traditional prediction model by only considers time features of traffic data, ignoring spatial characteristics and nonlinear characteristics of the data itself, resulting in poor model prediction performance. In view of this, this research proposes an intelligent combination prediction model taking into account the macro and micro features of chaotic traffic data. Firstly, to address the problem of time-consuming and inefficient multivariate phase space reconstruction by iterating nodes one by one, an improved multivariate phase space reconstruction method is proposed by filtering global representative nodes to effectively realize the high-dimensional mapping of chaotic traffic flow. Secondly, to address the problem that the traditional combinatorial model is difficult to adequately learn the macro and micro characteristics of chaotic traffic data, a combination of convolutional neural network(CNN) and convolutional long short-term memory(ConvLSTM) is utilized for capturing nonlinear features of traffic flow more comprehensively. Finally,to overcome the challenge that the combined model performance degrades due to subjective empirical determined network parameters, an improved lightweight particle swarm is proposed for improving prediction accuracy by optimizing model hyperparameters. In this paper, two highway datasets collected by the Caltrans Performance Measurement System(PeMS)are taken as the research objects, and the experimental results from multiple perspectives show that the comprehensive performance of the method proposed in this research is superior to those of the prevalent methods.
文摘It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochas- tic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.
基金supported by the Science and Research projects for Ph.D. candidates in the faculty of Xuzhou Normal University (No.08XLR12)Natural Science Foundation of Xuzhou Normal University (No.09XLA10)
文摘In order to realize the prediction of a chaotic time series of mine water discharge,an approach incorporating phase space reconstruction theory and statistical learning theory was studied.A differential entropy ratio method was used to determine embedding parameters to reconstruct the phase space.We used a multi-layer adaptive best-fitting parameter search algorithm to estimate the LS-SVM optimal parameters which were adopted to construct a LS-SVM prediction model for the mine water chaotic time series.The results show that the simulation performance of a single-step prediction based on this LS-SVM model is markedly superior to that based on a RBF model.The multi-step prediction results based on LS-SVM model can reflect the development of mine water discharge and can be used for short-term forecasting of mine water discharge.
基金supported in part by the National Natural Science Foundation of China (Grant No.60774088)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20090031110029)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin (Grant No.08JCZDJC21900)
文摘This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.
基金supported by the National Natural Science Foundation of China(Nos.51304128 and 51674158)the Natural Science Foundation of Shandong Province(No.ZR2013EEQ015)
文摘To realize real-time monitoring and short-term forecasting and forewarning of coalmine ventilation systems(CVS), in this paper, we first established a joint surface and underground CVS safety management system consisting of main ventilation fan, safety-partition linked passageways, and air-required locations. We then applied chaos theory to identify the air quantity and gas concentration of underground partition boundaries, and adopted a fixed data quantity, multi-step progressive, weighted first-order local-domain method to setup a chaos prediction model and a CVS safety forecasting and forewarning system formed by the normal change level, orange forewarning level, and red alarm level. We next conduct the on-field application of the system in a coalmine in Jining, Shandong, China. The results showed that (1) in the statistical scale of 5 min, the changes in both air quantity and gas concentration along CVS partition airflow boundaries were characteristic of chaos and could be used for short-term chaos prediction, and the latter was more chaotic than the former;(2) the setup chaos prediction model had a higher prediction precision and the established safety prediction system could not only predict the variation in CVS stability but also reflect the rationality of underground mining intensity. Thus, this CVS safety forecasting and forewarning system is of better application value.
