In order to predict electromechanical equipments＇ nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on...In order to predict electromechanical equipments＇ nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on chaos theory. The predict method of chaos time series and two methods of proposing f and F are dis- cussed. The arithmetic of max prediction time of chaos time series is provided. Aiming at the key part of large rotating mechanical equipments-bearing, used this prediction method the simulation experiment is carried out. The result shows that this method has excellent performance for condition trend prediction.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
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical syste...A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.展开更多
Efficient use of industrial equipment, increase its availability, safety and economic issues spur strong research on maintenance programs based on their operating conditions. Machines normally operate in a linear rang...Efficient use of industrial equipment, increase its availability, safety and economic issues spur strong research on maintenance programs based on their operating conditions. Machines normally operate in a linear range, but when malfunctions occur, nonlinear behavior might set in. By studying and comparing five nonlinear features, which listed in decreasing order by their damage detection capability are： LLE （largest Lyapunov exponent）, embedded dimension, Kappa determinism, time delay and cross error values; i.e., LLE performs best. Using somewhat similar ideas from Chaos control, i.e., vary the ＂mass imbalance＂ forcing parameters, we aim to stabilize the Lorenz equation. Quite interestingly, for certain imbalance excitation values, the system is stabilized. The previous even when paradigmatically chaotic parameters for Lorenz system are used （plus our forcing terms）. This quasi-control approach is validated studying signals obtained from the previously mentioned lab test. Finally, it is concluded that analyzing and comparing nonlinear features extracted from baseline vs. malfunction condition （test acquired）, one might increase the efficiency and the performance of machine condition monitoring.展开更多
Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas f...Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）展开更多
Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressur...Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.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
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
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
In recent years, the phenomenon of a critical slowing down has demonstrated its major potential in discovering whether a complex dynamic system tends to abruptly change at critical points. This research on the Pacific...In recent years, the phenomenon of a critical slowing down has demonstrated its major potential in discovering whether a complex dynamic system tends to abruptly change at critical points. This research on the Pacific decadal oscillation(PDO) index has been made on the basis of the critical slowing down principle in order to analyze its early warning signal of abrupt change. The chaotic characteristics of the PDO index sequence at different times are determined by using the largest Lyapunov exponent(LLE). The relationship between the regional sea surface temperature(SST) background field and the early warning signal of the PDO abrupt change is further studied through calculating the variance of the SST in the PDO region and the spatial distribution of the autocorrelation coefficient, thereby providing the experimental foundation for the extensive application of the method of the critical slowing down phenomenon. Our results show that the phenomenon of critical slowing down, such as the increase of the variance and autocorrelation coefficient, will continue for six years before the abrupt change of the PDO index. This phenomenon of the critical slowing down can be regarded as one of the early warning signals of an abrupt change. Through calculating the LLE of the PDO index during different times, it is also found that the strongest chaotic characteristics of the system occurred between 1971 and 1975 in the early stages of an abrupt change(1976), and the system was at the stage of a critical slowing down, which proves the reliability of the early warning signal of abrupt change discovered in 1970 from the mechanism. In addition, the variance of the SST,along with the spatial distribution of the autocorrelation coefficient in the corresponding PDO region, also demonstrates the corresponding relationship between the change of the background field of the SST and the change of the PDO.展开更多
Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks ...Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.展开更多
The principal resonance of a visco_elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitu...The principal resonance of a visco_elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco_elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results.展开更多
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of...The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.展开更多
The main research motive is to analysis and to veiny the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/f^β and periodic characteristics.The p...The main research motive is to analysis and to veiny the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/f^β and periodic characteristics.The priraeipal compohems analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts.So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear be havior and can be characterized by its power spectral density,principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.展开更多
Nonlinear methods are used to analyze current signal of spot welding and the minimum embedding dimension, correlation dimension, the optimal time delay and the largest Lyapunav exponent of current signal time series a...Nonlinear methods are used to analyze current signal of spot welding and the minimum embedding dimension, correlation dimension, the optimal time delay and the largest Lyapunav exponent of current signal time series are calculated in this paper. The chaotic character of current signal time series is discovered. Then a chaotic neural network is built and used to predict the future current signal. Means of residual error out of the network are used as eigenvalue of current signal during spot welding. It is shown that spatter can greatly affect the means of residual error of spot welding after analysis, the mean values of output errors of signal contaminated by spatter noise are more than 0. 08, but the mean values of output errors of the signal with no spatter noise are less than 0. 04, so mean of residual errors can be employed as the character of spatter.展开更多
The nonlinear dynamics of permanent-magnet synchronous motor(PMSM) with v/f control signals is investigated intensively.First,the equilibria and steady-state characteristics of the system are formulated by analytical ...The nonlinear dynamics of permanent-magnet synchronous motor(PMSM) with v/f control signals is investigated intensively.First,the equilibria and steady-state characteristics of the system are formulated by analytical analysis.Then,some of its basic dynamical properties,such as characteristic eigenvalues,Lyapunov exponents and phase trajectories are studied by varying the values of system parameters.It is found that when the values of the system parameters are smaller,the PMSM operates in stable domains,no matter what the values of control gains are.With the values of parameters increasing,the unstability appears and PMSM falls into chaotic operation.Furthermore,the complex dynamic behaviors are verified by means of simulation.展开更多
A method is proposed to chaotify a class of complex networks via impulsive control, when the orbits of the impulsive systems are confined in a bounded area. Based on computing the largest Lyapunov exponent, theoretica...A method is proposed to chaotify a class of complex networks via impulsive control, when the orbits of the impulsive systems are confined in a bounded area. Based on computing the largest Lyapunov exponent, theoretical results and algorithmic analysis are given in details. Finally, numerical simulations are presented to illustrate the effectiveness of the method.展开更多
The goal of this paper is to analyze the Finnish gross domestic product(GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series p...The goal of this paper is to analyze the Finnish gross domestic product(GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series possible. At first we estimated the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space reconstruction.Subsequently, we computed the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we calculated the 0-1 test for chaos. Finally we computed the Hurst exponent by rescaled range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end, we executed a recurrent analysis and displayed recurrence plots of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.展开更多
基金Sponsored by Key Funding Project for Science and Technology under the Beijing Municipal Education Commission(KZ200910772001)
文摘In order to predict electromechanical equipments＇ nonlinear and non-stationary condition effectively, max Lyapunov exponent is introduced to the fault trend prediction of large rotating mechanical equipments based on chaos theory. The predict method of chaos time series and two methods of proposing f and F are dis- cussed. The arithmetic of max prediction time of chaos time series is provided. Aiming at the key part of large rotating mechanical equipments-bearing, used this prediction method the simulation experiment is carried out. The result shows that this method has excellent performance for condition trend prediction.
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.
文摘A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
文摘Efficient use of industrial equipment, increase its availability, safety and economic issues spur strong research on maintenance programs based on their operating conditions. Machines normally operate in a linear range, but when malfunctions occur, nonlinear behavior might set in. By studying and comparing five nonlinear features, which listed in decreasing order by their damage detection capability are： LLE （largest Lyapunov exponent）, embedded dimension, Kappa determinism, time delay and cross error values; i.e., LLE performs best. Using somewhat similar ideas from Chaos control, i.e., vary the ＂mass imbalance＂ forcing parameters, we aim to stabilize the Lorenz equation. Quite interestingly, for certain imbalance excitation values, the system is stabilized. The previous even when paradigmatically chaotic parameters for Lorenz system are used （plus our forcing terms）. This quasi-control approach is validated studying signals obtained from the previously mentioned lab test. Finally, it is concluded that analyzing and comparing nonlinear features extracted from baseline vs. malfunction condition （test acquired）, one might increase the efficiency and the performance of machine condition monitoring.
文摘Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）
文摘Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.
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.
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supported by the National Natural Science Foundation of China (Grant Nos 40574051 and 40774054)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.41175067 and 41305056)the National Basic Research Program of China(Grant No.2012CB955901)+1 种基金the Special Scientific Research Project for Public Interest of China(Grant No.GYHY201506001)the Special Fund for Climate Change of China Meteorological Administration(Grant No.CCSF201525)
文摘In recent years, the phenomenon of a critical slowing down has demonstrated its major potential in discovering whether a complex dynamic system tends to abruptly change at critical points. This research on the Pacific decadal oscillation(PDO) index has been made on the basis of the critical slowing down principle in order to analyze its early warning signal of abrupt change. The chaotic characteristics of the PDO index sequence at different times are determined by using the largest Lyapunov exponent(LLE). The relationship between the regional sea surface temperature(SST) background field and the early warning signal of the PDO abrupt change is further studied through calculating the variance of the SST in the PDO region and the spatial distribution of the autocorrelation coefficient, thereby providing the experimental foundation for the extensive application of the method of the critical slowing down phenomenon. Our results show that the phenomenon of critical slowing down, such as the increase of the variance and autocorrelation coefficient, will continue for six years before the abrupt change of the PDO index. This phenomenon of the critical slowing down can be regarded as one of the early warning signals of an abrupt change. Through calculating the LLE of the PDO index during different times, it is also found that the strongest chaotic characteristics of the system occurred between 1971 and 1975 in the early stages of an abrupt change(1976), and the system was at the stage of a critical slowing down, which proves the reliability of the early warning signal of abrupt change discovered in 1970 from the mechanism. In addition, the variance of the SST,along with the spatial distribution of the autocorrelation coefficient in the corresponding PDO region, also demonstrates the corresponding relationship between the change of the background field of the SST and the change of the PDO.
文摘Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.
文摘The principal resonance of a visco_elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco_elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results.
文摘The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.
基金Supported by the National Natural Science Founda-tion of China (60132030)
文摘The main research motive is to analysis and to veiny the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/f^β and periodic characteristics.The priraeipal compohems analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts.So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear be havior and can be characterized by its power spectral density,principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.
基金National Natural Science Foundation of China(No50575159)project of Chinese Ministry of Education(No106049,20060056058)Natural Science Foundation of Tianjin (06YFJMJC03400)
文摘Nonlinear methods are used to analyze current signal of spot welding and the minimum embedding dimension, correlation dimension, the optimal time delay and the largest Lyapunav exponent of current signal time series are calculated in this paper. The chaotic character of current signal time series is discovered. Then a chaotic neural network is built and used to predict the future current signal. Means of residual error out of the network are used as eigenvalue of current signal during spot welding. It is shown that spatter can greatly affect the means of residual error of spot welding after analysis, the mean values of output errors of signal contaminated by spatter noise are more than 0. 08, but the mean values of output errors of the signal with no spatter noise are less than 0. 04, so mean of residual errors can be employed as the character of spatter.
基金Supported by the Key Program of National Natural Science Foundation of China under Grant No. 50937001the National Natural Science Foundation of China under Grant Nos. 10947011,11262004,61263021,and 50877028
文摘The nonlinear dynamics of permanent-magnet synchronous motor(PMSM) with v/f control signals is investigated intensively.First,the equilibria and steady-state characteristics of the system are formulated by analytical analysis.Then,some of its basic dynamical properties,such as characteristic eigenvalues,Lyapunov exponents and phase trajectories are studied by varying the values of system parameters.It is found that when the values of the system parameters are smaller,the PMSM operates in stable domains,no matter what the values of control gains are.With the values of parameters increasing,the unstability appears and PMSM falls into chaotic operation.Furthermore,the complex dynamic behaviors are verified by means of simulation.
基金supported by the National Natural Science Foundation of China under Grant No.60573005the Key Scientific Research Project for Colleges and Universities of Henan Province under Grant No.15A120022Doctor Scientific Research Fund of Zhengzhou University of Light Industry under Grant No.2014BSJJ047
文摘A method is proposed to chaotify a class of complex networks via impulsive control, when the orbits of the impulsive systems are confined in a bounded area. Based on computing the largest Lyapunov exponent, theoretical results and algorithmic analysis are given in details. Finally, numerical simulations are presented to illustrate the effectiveness of the method.
文摘The goal of this paper is to analyze the Finnish gross domestic product(GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series possible. At first we estimated the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space reconstruction.Subsequently, we computed the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we calculated the 0-1 test for chaos. Finally we computed the Hurst exponent by rescaled range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end, we executed a recurrent analysis and displayed recurrence plots of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.
