Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the c...Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the conditional nonlinear optimal perturbations （CNOPs）, which are the nonlinear generalization of the linear singular vectors （LSVs）, is adopted. The numerical results indicate that the linearly stable grassland and desert states are nonlinearly unstable to large enough initial perturbations on the condition that the moisture index # satisfies 0.3126 〈 μ 〈 0.3504. The perturbations represent some kind of anthropogenic influence and natural factors. The results obtained by CNOPs, LSVs and Lyapunov vectors （LVs） are compared to analyze the nonlinear feature of the transition between the grassland state and the desert state. Besides this, it is shown that the five-variable model is superior to the three-variable model in providing more visible signals when the transitions occur.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
The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature informa...The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man＇s participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay r by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D; Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of Poincare map, and the non-circle degree Dnc and non-order degree Dno of quasi-phase orbit. Chaos features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.展开更多
Strong mechanical vibration and acoustical signals of grinding process contain useful information related to load parameters in ball mills. It is a challenge to extract latent features and construct soft sensor model ...Strong mechanical vibration and acoustical signals of grinding process contain useful information related to load parameters in ball mills. It is a challenge to extract latent features and construct soft sensor model with high dimensional frequency spectra of these signals. This paper aims to develop a selective ensemble modeling approach based on nonlinear latent frequency spectral feature extraction for accurate measurement of material to ball volume ratio. Latent features are first extracted from different vibrations and acoustic spectral segments by kernel partial least squares. Algorithms of bootstrap and least squares support vector machines are employed to produce candidate sub-models using these latent features as inputs. Ensemble sub-models are selected based on genetic algorithm optimization toolbox. Partial least squares regression is used to combine these sub-models to eliminate collinearity among their prediction outputs. Results indicate that the proposed modeling approach has better prediction performance than previous ones.展开更多
To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the ...To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the nonlin-earity of wind waves are studied by using bispectral and statistical analysis of surface elevations. The relations between bispectra and nonlinear apparent characteristics of wind waves are established and confirmed.展开更多
An extended ocean-atmosphere coupled characteristic system including thermodynamic physical processes in ocean mixed layer is formulated in order to describe SST explicitly and remove possible limitation of ocean-atmo...An extended ocean-atmosphere coupled characteristic system including thermodynamic physical processes in ocean mixed layer is formulated in order to describe SST explicitly and remove possible limitation of ocean-atmosphere coupling assumption in hydrodynamic ENSO models. It is revealed that there is a kind of abrupt nonlinear characteristic behaviour, which relates to rapid onset and intermittency of El Nino events, on the second order slow time scale due to the nonlinear interaction between a linear unstable low-frequency primary eigen component of ocean-atmosphere coupled Kelvin wave and its higher order harmonic components under a strong ocean-atmosphere coupling background. And, on the other hand, there is a kind of finite amplitude nonlinear characteristic behaviour on the second order slow time scale due to the nonlinear interaction between the linear unstable primary eigen component and its higher order harmonic components under a weak ocean-atmosphere coupling background in this model system.展开更多
基金Funding was provided by grants from the state Key Development Program for Basic Research(Grant No.2006CB400503)the KZCX3-SW-230 of the Chinese Academy of Sciences(CAS)and National Natural Science Foundation of China(Grant No.40675030).
文摘Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the conditional nonlinear optimal perturbations （CNOPs）, which are the nonlinear generalization of the linear singular vectors （LSVs）, is adopted. The numerical results indicate that the linearly stable grassland and desert states are nonlinearly unstable to large enough initial perturbations on the condition that the moisture index # satisfies 0.3126 〈 μ 〈 0.3504. The perturbations represent some kind of anthropogenic influence and natural factors. The results obtained by CNOPs, LSVs and Lyapunov vectors （LVs） are compared to analyze the nonlinear feature of the transition between the grassland state and the desert state. Besides this, it is shown that the five-variable model is superior to the three-variable model in providing more visible signals when the transitions occur.
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The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man＇s participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay r by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D; Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of Poincare map, and the non-circle degree Dnc and non-order degree Dno of quasi-phase orbit. Chaos features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.
基金Supported partially by the Post Doctoral Natural Science Foundation of China(2013M532118,2015T81082)the National Natural Science Foundation of China(61573364,61273177,61503066)+2 种基金the State Key Laboratory of Synthetical Automation for Process Industriesthe National High Technology Research and Development Program of China(2015AA043802)the Scientific Research Fund of Liaoning Provincial Education Department(L2013272)
文摘Strong mechanical vibration and acoustical signals of grinding process contain useful information related to load parameters in ball mills. It is a challenge to extract latent features and construct soft sensor model with high dimensional frequency spectra of these signals. This paper aims to develop a selective ensemble modeling approach based on nonlinear latent frequency spectral feature extraction for accurate measurement of material to ball volume ratio. Latent features are first extracted from different vibrations and acoustic spectral segments by kernel partial least squares. Algorithms of bootstrap and least squares support vector machines are employed to produce candidate sub-models using these latent features as inputs. Ensemble sub-models are selected based on genetic algorithm optimization toolbox. Partial least squares regression is used to combine these sub-models to eliminate collinearity among their prediction outputs. Results indicate that the proposed modeling approach has better prediction performance than previous ones.
基金This study was supported in part by the National Natural Science Fundation of China
文摘To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the nonlin-earity of wind waves are studied by using bispectral and statistical analysis of surface elevations. The relations between bispectra and nonlinear apparent characteristics of wind waves are established and confirmed.
文摘An extended ocean-atmosphere coupled characteristic system including thermodynamic physical processes in ocean mixed layer is formulated in order to describe SST explicitly and remove possible limitation of ocean-atmosphere coupling assumption in hydrodynamic ENSO models. It is revealed that there is a kind of abrupt nonlinear characteristic behaviour, which relates to rapid onset and intermittency of El Nino events, on the second order slow time scale due to the nonlinear interaction between a linear unstable low-frequency primary eigen component of ocean-atmosphere coupled Kelvin wave and its higher order harmonic components under a strong ocean-atmosphere coupling background. And, on the other hand, there is a kind of finite amplitude nonlinear characteristic behaviour on the second order slow time scale due to the nonlinear interaction between the linear unstable primary eigen component and its higher order harmonic components under a weak ocean-atmosphere coupling background in this model system.
