Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environme...Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.展开更多
To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase spa...To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.展开更多
A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to de...A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay,which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement(AD)in AD algorithm.Thereafter,by means of the iterative algorithm of multiple autocorrelation andΓtest,the near-optimum parameters of embedding dimension and delay time are estimated.This algorithm is provided with a sound theoretic basis,and its computing complexity is relatively lower and not strongly dependent on the data length.The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4%when using conventional algorithm to 1.06%when using this algorithm.The accuracy of invariants in phase space reconstruction is greatly improved.展开更多
Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various ...Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various image processing,signal processing,and machine-learning based techniques are employed to analyze epilepsy,using spatial and temporal features.The nervous system that generates the EEG signal is considered nonlinear and the EEG signals exhibit chaotic behavior.In order to capture these nonlinear dynamics,we use reconstructed phase space(RPS) representation of the signal.Earlier studies have primarily addressed seizure detection as a binary classification(normal vs.ictal) problem and rarely as a ternary class(normal vs.interictal vs.ictal)problem.We employ transfer learning on a pre-trained deep neural network model and retrain it using RPS images of the EEG signal.The classification accuracy of the model for the binary classes is(98.5±1.5)% and(95±2)% for the ternary classes.The performance of the convolution neural network(CNN) model is better than the other existing statistical approach for all performance indicators such as accuracy,sensitivity,and specificity.The result of the proposed approach shows the prospect of employing RPS images with CNN for predicting epileptic seizures.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
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
A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space...A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.展开更多
Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to ...Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.展开更多
In this work,a comparative study is performed to investigate the influence of time-varying normal forces on the friction properties and friction-induced stick-slip vibration(FIV)by experimental and theoretical methods...In this work,a comparative study is performed to investigate the influence of time-varying normal forces on the friction properties and friction-induced stick-slip vibration(FIV)by experimental and theoretical methods.In the experiments,constant and harmonic-varying normal forces are applied,respectively.The measured vibration signals under two loading forms are compared in both time and frequency domains.In addition,mathematical tools such as phase space reconstruction and Fourier spectra are used to reveal the science behind the complicated dynamic behavior.It can be found that the friction system shows steady stick-slip vibration,and the main frequency does not vary with the magnitude of the constant normal force,but the size of limit cycle increases with the magnitude of the constant normal force.In contrast,the friction system under the harmonic normal force shows complicated behavior,for example,higher-frequency larger-amplitude vibration occurs and looks chaotic as the frequency of the normal force increases.The interesting findings offer a new way for controlling FIV in engineering applications.展开更多
The machining accuracy of computer numerical control machine tools has always been a focus of the manufacturing industry.Among all errors,thermal error affects the machining accuracy considerably.Because of the signif...The machining accuracy of computer numerical control machine tools has always been a focus of the manufacturing industry.Among all errors,thermal error affects the machining accuracy considerably.Because of the significant impact of Industry 4.0 on machine tools,existing thermal error modeling methods have encountered unprecedented challenges in terms of model complexity and capability of dealing with a large number of time series data.A thermal error modeling method is proposed based on bidirectional long short-term memory(BiLSTM)deep learning,which has good learning ability and a strong capability to handle a large group of dynamic data.A four-layer model framework that includes BiLSTM,a feedforward neural network,and the max pooling is constructed.An elaborately designed algorithm is proposed for better and faster model training.The window length of the input sequence is selected based on the phase space reconstruction of the time series.The model prediction accuracy and model robustness were verified experimentally by three validation tests in which thermal errors predicted by the proposed model were compensated for real workpiece cutting.The average depth variation of the workpiece was reduced from approximately 50μm to less than 2μm after compensation.The reduction in maximum depth variation was more than 85%.The proposed model was proved to be feasible and effective for improving machining accuracy significantly.展开更多
Based on reconstructing the phase space and calculating the largest Lyapunov exponent, an improved method of detecting chaotic motion is presented for rotor-bearing systems. The method is an improvement to the Wolf me...Based on reconstructing the phase space and calculating the largest Lyapunov exponent, an improved method of detecting chaotic motion is presented for rotor-bearing systems. The method is an improvement to the Wolf method and the Rosenstein algorithm. The improved method introduces the correlation integral function method to estimate the embedding dimension and the reconstruction delay simultaneously, and it makes tracks for the evolutions of every pair of the nearest neighbors to improve the utilization of the reconstructed phase space. Numerical calculation and experimental verification show that the improved method can estimate the proper reconstruction parameters and detect chaotic motion of rotor-bearing systems accurately. In addition, the analytical results show that the current approach is robust to variations of the embedding dimension and the reconstruction delay, and it is applicable to small data sets.展开更多
基金The National Natural Science Foundation of China under contract No.62275228the S&T Program of Hebei under contract Nos 19273901D and 20373301Dthe Hebei Natural Science Foundation under contract No.F2020203066.
文摘Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.
基金Sponsored by the National Eleventh Five year Plan Key Project of Ministry of Science and Technology of China (Grant No. 2006BAJ03A05-05)
文摘To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.
文摘A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction.It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay,which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement(AD)in AD algorithm.Thereafter,by means of the iterative algorithm of multiple autocorrelation andΓtest,the near-optimum parameters of embedding dimension and delay time are estimated.This algorithm is provided with a sound theoretic basis,and its computing complexity is relatively lower and not strongly dependent on the data length.The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4%when using conventional algorithm to 1.06%when using this algorithm.The accuracy of invariants in phase space reconstruction is greatly improved.
文摘Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various image processing,signal processing,and machine-learning based techniques are employed to analyze epilepsy,using spatial and temporal features.The nervous system that generates the EEG signal is considered nonlinear and the EEG signals exhibit chaotic behavior.In order to capture these nonlinear dynamics,we use reconstructed phase space(RPS) representation of the signal.Earlier studies have primarily addressed seizure detection as a binary classification(normal vs.ictal) problem and rarely as a ternary class(normal vs.interictal vs.ictal)problem.We employ transfer learning on a pre-trained deep neural network model and retrain it using RPS images of the EEG signal.The classification accuracy of the model for the binary classes is(98.5±1.5)% and(95±2)% for the ternary classes.The performance of the convolution neural network(CNN) model is better than the other existing statistical approach for all performance indicators such as accuracy,sensitivity,and specificity.The result of the proposed approach shows the prospect of employing RPS images with CNN for predicting epileptic seizures.
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(51374035)supported by the National Natural Science Foundation of ChinaProject(2012BAB08B02)supported by the National“Twelfth Five”Science and Technology,ChinaProject(NCET-13-0669)supported by New Century Excellent Talents in University of Ministry of Education of China
文摘A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.
文摘Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.
基金The authors would like to acknowledge the support from the National Natural Science Foundation of China(11672052 and 51822508)111 Project(B20008)and Natural Science Foundation of Zhejiang province(LQ22E050012).
文摘In this work,a comparative study is performed to investigate the influence of time-varying normal forces on the friction properties and friction-induced stick-slip vibration(FIV)by experimental and theoretical methods.In the experiments,constant and harmonic-varying normal forces are applied,respectively.The measured vibration signals under two loading forms are compared in both time and frequency domains.In addition,mathematical tools such as phase space reconstruction and Fourier spectra are used to reveal the science behind the complicated dynamic behavior.It can be found that the friction system shows steady stick-slip vibration,and the main frequency does not vary with the magnitude of the constant normal force,but the size of limit cycle increases with the magnitude of the constant normal force.In contrast,the friction system under the harmonic normal force shows complicated behavior,for example,higher-frequency larger-amplitude vibration occurs and looks chaotic as the frequency of the normal force increases.The interesting findings offer a new way for controlling FIV in engineering applications.
基金sponsored by the National Natural Science Foundation of Major Special Instruments(Grant No.51527806)the National Natural Science Foundation Projects of the People’s Republic of China(Grant No.51975372).
文摘The machining accuracy of computer numerical control machine tools has always been a focus of the manufacturing industry.Among all errors,thermal error affects the machining accuracy considerably.Because of the significant impact of Industry 4.0 on machine tools,existing thermal error modeling methods have encountered unprecedented challenges in terms of model complexity and capability of dealing with a large number of time series data.A thermal error modeling method is proposed based on bidirectional long short-term memory(BiLSTM)deep learning,which has good learning ability and a strong capability to handle a large group of dynamic data.A four-layer model framework that includes BiLSTM,a feedforward neural network,and the max pooling is constructed.An elaborately designed algorithm is proposed for better and faster model training.The window length of the input sequence is selected based on the phase space reconstruction of the time series.The model prediction accuracy and model robustness were verified experimentally by three validation tests in which thermal errors predicted by the proposed model were compensated for real workpiece cutting.The average depth variation of the workpiece was reduced from approximately 50μm to less than 2μm after compensation.The reduction in maximum depth variation was more than 85%.The proposed model was proved to be feasible and effective for improving machining accuracy significantly.
基金the National Basic Research Program (973) of China (No. 2009CB724302)
文摘Based on reconstructing the phase space and calculating the largest Lyapunov exponent, an improved method of detecting chaotic motion is presented for rotor-bearing systems. The method is an improvement to the Wolf method and the Rosenstein algorithm. The improved method introduces the correlation integral function method to estimate the embedding dimension and the reconstruction delay simultaneously, and it makes tracks for the evolutions of every pair of the nearest neighbors to improve the utilization of the reconstructed phase space. Numerical calculation and experimental verification show that the improved method can estimate the proper reconstruction parameters and detect chaotic motion of rotor-bearing systems accurately. In addition, the analytical results show that the current approach is robust to variations of the embedding dimension and the reconstruction delay, and it is applicable to small data sets.
