AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES

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.

Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine

Some problems in using v-support vector machine(v-SVM)for the prediction of nonlinear time series arediscussed.The problems include selection of various net parameters,which affect the performance of prediction,mixtureof kernels,and decomposition cooperation linear programming v-SVM regression,which result in improvements of thealgorithm.Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation andLorenz equation provide some improved results.

A Prediction Method Based on Improved Echo State Network for COVID-19 Nonlinear Time Series

This paper proposes a prediction method based on improved Echo State Network for COVID-19 nonlinear time series, which improves the Echo State Network from the reservoir topology and the output weight matrix, and adopt the ABC (Artificial Bee Colony) algorithm based on crossover and crowding strategy to optimize the parameters. Finally, the proposed method is simulated and the results show that it has stronger prediction ability for COVID-19 nonlinear time series.

LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES

An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.

Ergodicity of a Class of Nonlinear Time Series Models in Random Environment Domain

In this paper, we study the problem of a variety of p, onlinear time series model Xn＋ 1= TZn＋1（X（n）, … ,X（n - Zn＋l）, en＋1（Zn＋1）） in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en（i）} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.

Small-time scale network traffic prediction based on a local support vector machine regression model

In this paper we apply the nonlinear time series analysis method to small-time scale traffic measurement data. The prediction-based method is used to determine the embedding dimension of the traffic data. Based on the reconstructed phase space, the local support vector machine prediction method is used to predict the traffic measurement data, and the BIC-based neighbouring point selection method is used to choose the number of the nearest neighbouring points for the local support vector machine regression model. The experimental results show that the local support vector machine prediction method whose neighbouring points are optimized can effectively predict the small-time scale traffic measurement data and can reproduce the statistical features of real traffic measurements.

A new method of determining the optimal embedding dimension based on nonlinear prediction

A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.

Monthly and seasonal streamflow forecasting of large dryland catchments in Brazil

Streamflow forecasting in drylands is challenging.Data are scarce,catchments are highly humanmodified and streamflow exhibits strong nonlinear responses to rainfall.The goal of this study was to evaluate the monthly and seasonal streamflow forecasting in two large catchments in the Jaguaribe River Basin in the Brazilian semi-arid area.We adopted four different lead times:one month ahead for monthly scale and two,three and four months ahead for seasonal scale.The gaps of the historic streamflow series were filled up by using rainfall-runoff modelling.Then,time series model techniques were applied,i.e.,the locally constant,the locally averaged,the k-nearest-neighbours algorithm(k-NN)and the autoregressive(AR)model.The criterion of reliability of the validation results is that the forecast is more skillful than streamflow climatology.Our approach outperformed the streamflow climatology for all monthly streamflows.On average,the former was 25%better than the latter.The seasonal streamflow forecasting(SSF)was also reliable(on average,20%better than the climatology),failing slightly only for the high flow season of one catchment(6%worse than the climatology).Considering an uncertainty envelope(probabilistic forecasting),which was considerably narrower than the data standard deviation,the streamflow forecasting performance increased by about 50%at both scales.The forecast errors were mainly driven by the streamflow intra-seasonality at monthly scale,while they were by the forecast lead time at seasonal scale.The best-fit and worst-fit time series model were the k-NN approach and the AR model,respectively.The rainfall-runoff modelling outputs played an important role in improving streamflow forecasting for one streamgauge that showed 35%of data gaps.The developed data-driven approach is mathematical and computationally very simple,demands few resources to accomplish its operational implementation and is applicable to other dryland watersheds.Our findings may be part of drought forecasting systems and potentially help allocating water months in advance.Moreover,the developed strategy can serve as a baseline for more complex streamflow forecast systems.

Cross and joint ordinal partition transition networks for multivariate time series analysis

We propose the construction of cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is a prototypical scenario in dynamical systems. We systematically show that cross and joint ordinal pattern transition networks are sensitive to phase synchronization. Furthermore, we find that some particular missing ordinal patterns play crucial roles in forming the detailed structures in the parameter space, whereas the calculations of permutation entropy measures often do not. We conclude that cross and joint ordinal partition transition network approaches provide complementary insights into the traditional symbolic analysis of synchronization transitions.

Detecting Lags in Nonlinear Models Using General Mutual Information

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.

THE EXISTENCE OF MOMENTS OF NONLINEAR AUTOREGRESSIVE MODEL

In this paper we examine the existence of higher-order moments for the following nonlinearautoregressive model

Unknown fault detection for EGT multi-temperature signals based on self-supervised feature learning and unary classification

Intelligent tpower systems scanimprove operational efficiency by installing a large number of sensors.Data-based methods of supervised learning have gained popularity because of available Big Data and computing resources.However,the common paradigm of the loss function in supervised learning requires large amounts of labeled data and cannot process unlabeled data.The scarcity of fault data and a large amount of normal data in practical use pose great challenges to fault detection algorithms.Moreover,sensor data faults in power systems are dynamically changing and pose another challenge.Therefore,a fault detection method based on self-supervised feature learning was proposed to address the above two challenges.First,self-supervised learning was employed to extract features under various working conditions only using large amounts of normal data.The self-supervised representation learning uses a sequence-based Triplet Loss.The extracted features of large amounts of normal data are then fed into a unary classifier.The proposed method is validated on exhaust gas temperatures(EGTs)of a real-world 9F gas turbine with sudden,progressive,and hybrid faults.A comprehensive comparison study was also conducted with various feature extractors and unary classifiers.The results show that the proposed method can achieve a relatively high recall for all kinds of typical faults.The model can detect progressive faults very quickly and achieve improved results for comparison without feature extractors in terms ofF1 score.

Confidence Intervals of Variance Functions in Generalized Linear Model

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.

Shape-constrained semiparametric additive stochastic volatility models

Nonparametric stochastic volatility models,although providing great flexibility for modelling thevolatility equation,often fail to account for useful shape information.For example,a model maynot use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases.We propose a class of additive stochasticvolatility models that allow for different shape constraints and can incorporate the leverageeffect–asymmetric impact of positive and negative return shocks on volatilities.We developa Bayesian fitting algorithm and demonstrate model performance on simulated and empiricaldatasets.Unlike general nonparametric models,our model sacrifices little when the true volatility equation is linear.In nonlinear situations we improve the model fit and the ability to estimatevolatilities over general,unconstrained,nonparametric models.

Asymptotic Properties of Wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.