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CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction
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作者 Xiao-Qian Lu Jun Tian +2 位作者 Qiang Liao Zheng-Wu Xu Lu Gan 《Journal of Electronic Science and Technology》 EI CAS CSCD 2024年第2期77-90,共14页
To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)pre... To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR. 展开更多
关键词 chaotic time series Incremental attention mechanism Phase-space reconstruction
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A prediction comparison between univariate and multivariate chaotic time series 被引量:3
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作者 王海燕 朱梅 《Journal of Southeast University(English Edition)》 EI CAS 2003年第4期414-417,共4页
The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic tim... The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error. 展开更多
关键词 multivariate chaotic time series phase space reconstruction PREDICTION neural networks
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Local polynomial prediction method of multivariate chaotic time series and its application 被引量:1
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作者 方芬 王海燕 《Journal of Southeast University(English Edition)》 EI CAS 2005年第2期229-232,共4页
To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the p... To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series. 展开更多
关键词 chaotic time series phase space reconstruction local polynomial prediction stock market
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New prediction of chaotic time series based on local Lyapunov exponent 被引量:9
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作者 张勇 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期191-197,共7页
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in stat... A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. 展开更多
关键词 chaotic time series prediction of chaotic time series local Lyapunov exponent least squaresmethod
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Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network 被引量:7
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作者 马千里 郑启伦 +2 位作者 彭宏 钟谭卫 覃姜维 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期536-542,共7页
This paper proposes a co-evolutionary recurrent neural network (CERNN) for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structu... This paper proposes a co-evolutionary recurrent neural network (CERNN) for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by coevolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets: the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series. 展开更多
关键词 chaotic time series multi-step-prediction co-evolutionary strategy recurrent neural networks
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Regular nonlinear response of the driven Duffng oscillator to chaotic time series 被引量:3
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作者 袁野 李月 +1 位作者 Danilo P.Mandic 杨宝俊 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第3期958-968,共11页
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, m... Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated. 展开更多
关键词 Duffing oscillator chaotic time series phase plane diagram largest Lyapunov exponent
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Chaotic time series prediction using fuzzy sigmoid kernel-based support vector machines 被引量:2
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作者 刘涵 刘丁 邓凌峰 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第6期1196-1200,共5页
Support vector machines (SVM) have been widely used in chaotic time series predictions in recent years. In order to enhance the prediction efficiency of this method and implement it in hardware, the sigmoid kernel i... Support vector machines (SVM) have been widely used in chaotic time series predictions in recent years. In order to enhance the prediction efficiency of this method and implement it in hardware, the sigmoid kernel in SVM is drawn in a more natural way by using the fuzzy logic method proposed in this paper. This method provides easy hardware implementation and straightforward interpretability. Experiments on two typical chaotic time series predictions have been carried out and the obtained results show that the average CPU time can be reduced significantly at the cost of a small decrease in prediction accuracy, which is favourable for the hardware implementation for chaotic time series prediction. 展开更多
关键词 support vector machines chaotic time series prediction fuzzy sigmoid kernel
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Neural Volterra filter for chaotic time series prediction 被引量:2
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作者 李恒超 张家树 肖先赐 《Chinese Physics B》 SCIE EI CAS CSCD 2005年第11期2181-2188,共8页
A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system i... A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter (SOVF). The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective. 展开更多
关键词 chaotic time series adaptive neural Volterra filter conjugate gradient algorithm
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The improved local linear prediction of chaotic time series 被引量:2
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作者 孟庆芳 彭玉华 孙佳 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第11期3220-3225,共6页
Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously... Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method. 展开更多
关键词 local linear prediction Bayesian information criterion state space reconstruction chaotic time series
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PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL 被引量:1
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作者 马军海 王志强 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第1期7-14,共8页
The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques, but also discusses prediction techniques of chaotic time series and its applications based on... The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques, but also discusses prediction techniques of chaotic time series and its applications based on chaotic data noise reduction. In the paper, we first decompose the phase space of chaotic time series to range space and null noise space. Secondly we restructure original chaotic time series in range space. Lastly on the basis of the above, we establish order of the nonlinear model and make use of the nonlinear model to predict some research. The result indicates that the nonlinear model has very strong ability of approximation function, and Chaos predict method has certain tutorial significance to the practical problems. 展开更多
关键词 chaotic time series noise reduction essential characteristic extraction nonlinear model predict technology
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Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression 被引量:1
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作者 YEMei-Ying WANGXiao-Dong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第1期102-106,共5页
A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction... A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction of chaotic time series. The effectiveness of themethod is demonstrated by applying it to the Henon map. This study also compares nu-support vectormachine with back propagation (BP) networks in order to better evaluate the performance of theproposed methods. The experimental results show that the nu-support vector machine regressionobtains lower root mean squared error than the BP networks and provides an accurate chaotic timeseries prediction. These results can be attributable to the fact that nu-support vector machineimplements the structural risk minimization principle and this leads to better generalization thanthe BP networks. 展开更多
关键词 chaotic time series phase space PREDICTION support vector machines
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Multimodality Prediction of Chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model 被引量:1
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作者 周亚同 樊煜 +1 位作者 陈子一 孙建成 《Chinese Physics Letters》 SCIE CAS CSCD 2017年第5期22-26,共5页
The contribution of this work is twofold: (1) a multimodality prediction method of chaotic time series with the Gaussian process mixture (GPM) model is proposed, which employs a divide and conquer strategy. It au... The contribution of this work is twofold: (1) a multimodality prediction method of chaotic time series with the Gaussian process mixture (GPM) model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. (2) An effective sparse hard-cut expec- tation maximization (SHC-EM) learning algorithm for the GPM model is proposed to improve the prediction performance. SHO-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval SHC-EM outperforms the traditional variational 1earning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning. 展开更多
关键词 GPM Multimodality Prediction of chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model EM SHC
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Genetic programming-based chaotic time series modeling 被引量:1
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作者 张伟 吴智铭 杨根科 《Journal of Zhejiang University Science》 EI CSCD 2004年第11期1432-1439,共8页
This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) ... This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling. 展开更多
关键词 chaotic time series analysis Genetic programming modeling Nonlinear Parameter Estimation (NPE) Particle Swarm Optimization (PSO) Nonlinear system identification
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Stabilization of Chaotic Time Series by Proportional Pulse in the System Variable Based on Genetic Algorithm 被引量:1
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作者 Qing Li Deling Zheng Jianlong Zhou(Information Engineering School, University of Science and Technology Beijing, Beijing 100083, China)(Handan iron and Steel Co., Handan 056015, China) 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 1999年第3期228-229,共2页
The PPSV (Proportional Pulse in the System Variable) algorithm is a convenient method for the stabilization of the chaotic time series. It does not require any previous knowledge of the system. The PPSV method also ha... The PPSV (Proportional Pulse in the System Variable) algorithm is a convenient method for the stabilization of the chaotic time series. It does not require any previous knowledge of the system. The PPSV method also has a shortcoming, that is, the determination off. is a procedure by trial and error, since it lacks of optimization. In order to overcome the blindness, GA (Genetic Algorithm), a search algorithm based on the mechanics of natural selection and natural genetics, is used to optimize the λi The new method is named as GAPPSV algorithm. The simulation results show that GAPPSV algorithm is very efficient because the control process is short and the steady-state error is small. 展开更多
关键词 STABILIZATION chaotic time series genetic algorithm
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Complex Networks from Chaotic Time Series on Riemannian Manifold
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作者 孙建成 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第10期28-31,共4页
Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliabl... Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliable method for constructing complex networks from chaotic time series. We first estimate the covariance matrices, then a geodesic-based distance between the covariance matrices is introduced. Consequently the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and geodesic-based distance, respectively. The proposed method provides us with an intrinsic geometry viewpoint to understand the time series. 展开更多
关键词 of IS Complex Networks from chaotic Time Series on Riemannian Manifold from into been on for that
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Prediction and analysis of chaotic time series on the basis of support vector
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作者 Li Tianliang He Liming Li Haipeng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第4期806-811,共6页
Based on discussion on the theories of support vector machines (SVM), an one-step prediction model for time series prediction is presented, wherein the chaos theory is incorporated. Chaotic character of the time ser... Based on discussion on the theories of support vector machines (SVM), an one-step prediction model for time series prediction is presented, wherein the chaos theory is incorporated. Chaotic character of the time series is taken into account in the prediction procedure; parameters of reconstruction-detay and embedding-dimension for phase-space reconstruction are calculated in light of mutual-information and false-nearest-neighbor method, respectively. Precision and functionality have been demonstrated by the experimental results on the basis of the prediction of Lorenz chaotic time series. 展开更多
关键词 support vector machines chaotic time series prediction model FUNCTIONALITY
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KLT-based local linear prediction of chaotic time series
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作者 Meng Qingfang Peng Yuhua Chen Yuehui 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第4期694-699,共6页
In the reconstructed phase space, based on the Karhunen-Loeve transformation (KLT), the new local linear prediction method is proposed to predict chaotic time series. & noise-free chaotic time series and a noise ad... In the reconstructed phase space, based on the Karhunen-Loeve transformation (KLT), the new local linear prediction method is proposed to predict chaotic time series. & noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction. 展开更多
关键词 Karhunen-Loeve transformation local linear prediction phase space reconstruction chaotic time series.
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A method to improve the precision of chaotic time series prediction by using a non-trajectory
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作者 闫华 魏平 肖先赐 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第8期3287-3294,共8页
Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems, the error of chaotic time series prediction increases with the prediction st... Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems, the error of chaotic time series prediction increases with the prediction step. This paper provides a method to improve the prediction precision by adjusting the predicted value in the course of iteration according to the evolution information of small intervals on the left and right sides of the predicted value. The adjusted predicted result is a non-trajectory which can provide a better prediction performance than the usual result based on the trajectory. Numerical simulations of two typical chaotic maps demonstrate its effectiveness. When the prediction step gets relatively larger, the effect is more pronounced. 展开更多
关键词 non-trajectory chaotic time series PREDICTION
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Research on Optimize Prediction Model and Algorithm about Chaotic Time Series
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作者 JIANGWei-jin XUYu-sheng 《Wuhan University Journal of Natural Sciences》 CAS 2004年第5期735-739,共5页
We put forward a chaotic estimating model, by using the parameter of the chaotic system, sensitivity of the parameter to inching and control the disturbance of the system, and estimated the parameter of the model by u... We put forward a chaotic estimating model, by using the parameter of the chaotic system, sensitivity of the parameter to inching and control the disturbance of the system, and estimated the parameter of the model by using the best update option. In the end, we forecast the intending series value in its mutually space. The example shows that it can increase the precision in the estimated process by selecting the best model steps. It not only conquer the abuse of using detention inlay technology alone, but also decrease blindness of using forecast error to decide the input model directly, and the result of it is better than the method of statistics and other series means. Key words chaotic time series - parameter identification - optimal prediction model - improved change ruler method CLC number TP 273 Foundation item: Supported by the National Natural Science Foundation of China (60373062)Biography: JIANG Wei-jin (1964-), male, Professor, research direction: intelligent compute and the theory methods of distributed data processing in complex system, and the theory of software. 展开更多
关键词 chaotic time series parameter identification optimal prediction model improved change ruler method
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AN ANALYTIC AND APPLICATION TO STATE SPACE RECONSTRUCTION ABOUT CHAOTIC TIME SERIES
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作者 马军海 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第11期1237-1245,共9页
The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibso... The state space, reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: AT. H. Packard, F. Takens, M. Casdagli, J. F. Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time tau were identified. The influence for state space reconstruction of lag time tau was discussed. The result tells us that is a good practical method for state space reconstruction. 展开更多
关键词 chaotic time series state space reconstruction Legendre coordinates?
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