Phase Space Reconstruction Parameters Research Articles

Research on Real-Time Prediction Method of Photovoltaic Power Time Series Utilizing Improved Grey Wolf Optimization and Long Short-Term Memory Neural Network

This paper proposes a novel method for the real-time prediction of photovoltaic (PV) power output by integrating phase space reconstruction (PSR), improved grey wolf optimization (GWO), and long short-term memory (LSTM) neural networks. The proposed method consists of three main steps. First, historical data are denoised and features are extracted using singular spectrum analysis (SSA) and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Second, improved grey wolf optimization (GWO) is employed to optimize the key parameters of phase space reconstruction (PSR) and long short-term memory (LSTM) neural networks. Third, real-time predictions are made using LSTM neural networks, with dynamic updates of training data and model parameters. Experimental results demonstrate that the proposed method has significant advantages in both prediction accuracy and speed. Specifically, the proposed method achieves a mean absolute percentage error (MAPE) of 3.45%, significantly outperforming traditional machine learning models and other neural network-based approaches. Compared with seven alternative methods, our method improves prediction accuracy by 15% to 25% and computational speed by 20% to 30%. Additionally, the proposed method exhibits excellent prediction stability and adaptability, effectively handling the nonlinear and chaotic characteristics of PV power.

A new compound structure combining DAWNN with modified water cycle algorithm-based synchronous optimization for wind speed forecasting

With the aims to improve the forecasting performance, a novel hybrid model based on variational mode decomposition (VMD), phase space reconstruction (PSR), improved water cycle algorithm (WCA) and double activation function wavelet neural network (DAWNN) is established for wind speed forecasting. In the proposed wind speed forecasting model, VMD is firstly employed to decompose the original wind speed time series into different modes and PSR is utilized to construct appropriate input matrix of each mode for DAWNN. To take advantage of different activation functions, DAWNN with optimal combination of Mexican hat function and Morlet wavelet function is constructed to make short-term wind speed forecasting. Then, the proposed improved WCA based on the chaos initialization of population, exploration–exploitation synergy optimization strategy and adaptively adjusting the search intensity, is developed to optimize the reconstruction parameters of PSR, hidden node number and the weighted coefficients in DAWNN synchronously. To confirm and evaluate the forecasting performance of the proposed hybrid model, two sets of historical wind speed samples from a wind farm in China are employed to make multi-step short-term wind speed forecasting. The experimental results illustrate that the proposed compound structure is effective when applying in wind speed forecasting.

Multi-step wind speed forecasting model using a compound forecasting architecture and an improved QPSO-based synchronous optimization

The intermittency and randomness of wind speed time series influence the forecasting accuracy. To figure out this problem and enhance the forecasting performance, a novel compound structure is developed for short-term wind speed forecasting. The developed compound method firstly eliminates the inherent noise from the original empirical wind speed time series using wavelet packet decomposition (WPD) and subsequently constructs appropriate input matrix by phase space reconstruction (PSR) for multi-kernel least square support vector machine (MKLSSVM). To take advantage of different kernel function, MKLSSVM with optimal combination of radial basis kernel function, polynomial kernel function and linear kernel function is constructed to make wind speed forecasting. Then, the proposed improved quantum particle swarm optimization algorithm (QPSO) based on the chaos initialization, Gaussian distribution local attraction points, precocity judgment, and disturbance operator, namely ADQPSO, is employed to optimize the decomposition level of WPD, reconstruction parameters of PSR, kernel parameters and weighted coefficients in MKLSSVM synchronously. To evaluate the forecasting performance of the proposed hybrid model, four sets of historical wind speed data samples from Weihai wind farm in China are utilized to make multi-step short-term wind speed forecasting tests. The experimental results illustrate that the proposed hybrid model outperforms the compared single and new recently developed forecasting models, thus, the proposed WPD-PSR-ADQPSO-MKLSSVM is an effective method for short-term wind speed forecasting.

Online prediction of ultra-short-term photovoltaic power using chaotic characteristic analysis, improved PSO and KELM

Accurate photovoltaic (PV) power prediction can guarantee the stable operation of a power system. However, complex environmental factors contribute to the chaotic nature of PV power sequences, consequently affecting the prediction accuracy. In this paper, an online PV power prediction model is proposed based on chaotic characteristic analysis, improved particle swarm optimization (PSO), and kernel-based extreme learning machine (KELM). The proposed method includes data pre-processing, offline parameters extraction and online prediction. At first, historical data are classified according to the degree of fluctuation of PV power and seasonal characteristics. The PV power sequences are filtered by singular spectrum analysis (SSA) to eliminate noise and outliers. Then, extracted parameters include the decomposing modes of variational mode decomposition (VMD) and the ideal parameters of phase space reconstruction (PSR) and KELM. The ideal parameters are searched by improved PSO. Finally, during the online prediction process, the training data needs to be reconstructed using VMD and PSR to update the network of KELM at each point prediction. Chaotic characteristic analysis is reflected in the application of SSA, VMD and PSR. Compared with the other seven different prediction methods, the experimental results verify that the proposed method is effective with higher accuracy.

A Study on Methods for Determining Phase Space Reconstruction Parameters

Abstract Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chen's attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex autocorrelation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex autocorrelation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified by combing the application of the correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

Modeling of Robot's Low-Speed Motion Nonlinear Dynamics Based on Phase Space Reconstruction Neural Network

Abstract In order to improve the accuracy of the robot dynamics model, a low-speed motion nonlinear dynamics modeling method of industrial robot based on phase space reconstruction neural network is proposed. It is confirmed in advance by the largest Lyapunov exponent of joint motor torque data that the robot has chaotic characteristics at low-speed motion. Therefore, experimental data and chaos theory is used to analyze low-speed motion nonlinear dynamics, instead of considering each factor that may cause the robot's nonlinear dynamics separately. The phase space reconstruction parameters of each joint are determined by autocorrelation method and false nearest neighbor method. Through data preprocessing and analysis, some joint position derivatives related to the changing law of torque data are determined. The phase space reconstruction values of these derivatives are chosen as the inputs of neural network. Then the neural network and curve fitting method are combined to compensate for the nonlinear joint torque. Experimental results show that the proposed method can better describe the robot's low-speed motion nonlinear dynamics, and has smaller errors compared with ordinary back propagation (BP) neural network in the case of single joint rotation.

Improved phase space warping method for degradation tracking of rotating machinery under variable working conditions

Health Indicators (HI) that can effectively track the degradation state and are insensitive to the change of working conditions are of great significance to the process of Prognostic and Health Management (PHM). Based on the rapidly changing one-dimensional vibration signal to reconstruct the phase space, the Phase Space Warping (PSW) method was used to quantify the small curvature of the phase space trajectory caused by the damage, and then the HI that can represent the evolution process of the slow-changing damage could be obtained with the curvature. However, there are still several problems with the PSW method that need to be solved urgently. Firstly, it does not provide clear optimization criteria and adaptive determination strategies for the two key parameters of phase space reconstruction, which are, time delay and embedded dimension. Secondly, the HI extracted based on the PSW is greatly affected by noise and lacks a proper feature fusion strategy. Aiming at these problems, the Improved Phase Space Warping (IPSW) method is proposed in this paper. The contribution of IPSW is as follows: (1) IPSW considers the degree of comprehensive mutual information between multi-dimensional components, and uses comprehensive mutual information entropy as an optimization index, and gives clear guidelines on how to select optimal parameters; (2) IPSW introduces the correlation analysis method to fuse the acquired multi-modal trend components and then obtains the HI that can characterize the damage degradation trend. The simulation and experimental signal verification results of bearing fault degradation under the condition of variable speed show that the HI extracted based on the IPSW method can reduce the influence of variable speed and track the bearing damage degradation trend effectively.

A compound framework for wind speed forecasting based on comprehensive feature selection, quantile regression incorporated into convolutional simplified long short-term memory network and residual error correction

A reliable wind speed forecasting framework can contribute to handling rational dispatching and safe operation for power system effectively. For this purpose, a novel compound framework coupling decomposition technique, subseries aggregation, synchronous optimization, improved deep network and residual error correction (REC) is investigated in this study. To begin with, time varying filter-based empirical mode decomposition (TVF-EMD) is employed to decompose the raw series into a set of subseries, which are further aggregated based on fuzzy entropy (FE) theory and approximation criterion. Then the synchronous optimization implemented by blended coding-based Harris hawks optimization (HHO) is adopted to optimize the parameters of phase space reconstruction (PSR) and applicable features for each aggregated subseries. Subsequently, quantile regression (QR) is incorporated into an improved deep network, namely convolutional simplified long short-term memory network (QRConvSLSTM), to deduce conditional quantiles for each aggregated subseries, in which the optimized arguments obtained above are applied to construct the optimal input matrixes. Later, the initial point forecasting results can be calculated on the basis of accumulating the conditional quantiles of all the aggregated subseries, while the corresponding error series is deduced therewith. Then the conditional quantiles of the error series are estimated by QRConvSLSTM in the light of REC strategy, after which the final conditional quantiles are calculated by summating the conditional quantiles of the raw series and the error series. Finally, kernel density estimation (KDE) is employed to estimate probabilistic density functions (PDF) of wind speed series in accordance to the final conditional quantiles. To validate the efficiency and effectiveness of the proposed compound framework, nine relevant models are performed on three datasets for comparative experiments, among which the results of point, interval and probability prediction are comprehensively demonstrated and analyzed. The experimental results illustrate that: (1) data preprocessing strategy integrating TVF-EMD and FE-based subseries aggregation contributes to balancing forecasting performance and timing computation properly; (2) the applicable deterministic and uncertainty forecasting results can be obtained by the improved deep network, namely QRConvSLSTM; (3) appropriate parameters of PSR and feature selection can be effectively optimized by the proposed synchronous optimization; (4) the application of REC possesses positive effects on further compensating the ultimate forecasting results.

A composite framework coupling multiple feature selection, compound prediction models and novel hybrid swarm optimizer-based synchronization optimization strategy for multi-step ahead short-term wind speed forecasting

Accurate wind speed prediction plays a vital role in power system in terms of rational dispatching and safe operation. For this purpose, a novel composite framework integrating time varying filter-based empirical mode decomposition (TVF-EMD), fuzzy entropy (FE) theory, singular spectrum analysis (SSA), phase space reconstruction (PSR), compound prediction models adopting kernel-based extreme learning machine (KELM) and convolutional long short-term memory network (ConvLSTM) as well as mutation and hierarchy-based hybrid optimization algorithm, is proposed in this paper. Among the supplementary strategies, TVF-EMD, FE and SSA are employed to achieve non-stationary raw series attenuation, aggregation for approximate IMFs as well as separation of dominant and residuary ingredients from the aggregated IMFs, respectively. Besides, parameters of PSR and KELM as well as wrapper method-based feature selection (FS) for input combination are synchronously optimized by the newly developed swarm optimizer integrating Harris hawks optimization (HHO) and grey wolf optimizer (GWO) with mutation operator and hierarchy strategy. Meanwhile, such hybrid structure is adopted to predict the preprocessed high-frequency components, while the remaining component is predicted by ConvLSTM cells-based deep learning network. Subsequently, the ultimate forecasting results of the raw wind speed are calculated by superimposing the predicted values of all components. Four datasets collected from various sites with two different time intervals and nine relevant contrastive models are carried out to evaluate the proposed approach, where the corresponding results demonstrate that: (1) data preprocessing strategy applying TVF-EMD and FE theory can significantly reduce the time consumption of the entire model without decreasing forecasting performance; (2) SSA-based dominant ingredients extraction can further improve the forecasting capability of combined model; (3) the proposed MHHOGWO can synchronously accomplish parameters optimization and FS effectively, thus improving the forecasting effectiveness of the entire model significantly; (4) the proposed compound prediction models based on KELM and ConvLSTM can exert the capabilities of each model adequately as well as ulteriorly reducing computational requirements.

A hybrid approach for measuring the vibrational trend of hydroelectric unit with enhanced multi-scale chaotic series analysis and optimized least squares support vector machine

Accurate vibrational trend measuring for hydroelectric unit (HEU) is of great significance for safe and economic operation of unit. For this purpose, a novel hybrid approach based on variational mode decomposition (VMD), singular value decomposition (SVD)-based phase space reconstruction (PSR) and least squares support vector machine (LSSVM) improved with adaptive sine cosine algorithm optimization (ASCA) is proposed. Firstly, the raw vibration signal is preprocessed into several components with different scales by VMD, while the residual of VMD is defined as an additional component. Then, SVD with median filtering is utilized to unearth the dominating characteristic ingredients of each component, with which the chaotic series analysis will be effectively implemented. Moreover, the optimal parameters of PSR for each original component are determined by applying grid search on the corresponding dominating component. Later, LSSVM improved by ASCA are established for all the components, whose inputs and outputs are obtained by performing PSR with the optimal parameters. Finally, the measuring results of vibration trend are deduced by accumulating the prediction values of all the components. Furthermore, five related methods are employed to evaluate the effectiveness of the proposed approach. The results illustrate that: (1) the VMD-based models obtained better evaluation indexes compared with the relevant models through significantly weakening the non-stationarity of the original signal; (2) the proposed SVD-based PSR enhanced efficiency of chaotic system restoration, thus to improve the measuring accuracy effectively; (3) the proposed ASCA optimization algorithm could effectively search the parameters of LSSCVM, which contributes to improving model performance.

Research on optimal identification method of circuit breaker defect type based on phase space reconstruction and SVM

The vibration signals generated by the transmission and impact of circuit breaker mechanical components have chaotic characteristics and using conventional signal processing method is difficult to distinguish the abnormal operation process quickly and accurately. Based on the mutual information method and the Cao algorithm, the delay time and the embedding dimension of the phase space reconstruction parameters are calculated and optimized according to the chaotic characteristics of the vibration signals. The singular value order energy (SVOE) and the singular value energy entropy (SVEE) are obtained by decomposing the phase space reconstruction matrix, which is determined by the optimal phase space reconstruction parameters, and the support vector machines (SVM) are used to identify the states of the circuit breaker in operation. The experimental results show that the combination phase space reconstruction and singular value decomposition (PSR‐SVD) can accurately extract the characteristics of the vibration signal of the circuit breaker, and the genetic algorithm (GA)‐improved SVM can quickly and effectively identify the circuit breaker defect types, which solves the problems of path distortions, energy leaks, modal aliasing, and lack of samples in existing diagnostic methods. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Parameter optimization of phase space reconstruction based on differential entropy

This paper presents a differential entropy optimization method for phase space reconstruction parameters. The degree of differential entropy can be used to describe the complexity of the system. By establishing the relationship between the differential entropy and the embedded dimension and the delay time, the objective function is obtained. The constraints of embedding dimension and delay time is established by describing the global features of the system through autocorrelation function. By using the improved particle swarm algorithm to solve the model, the minimum differential entropy is obtained and the best embedded dimension and delay time is obtained. Therefore, the reconstructed phase space not only maintains its independence but also maintains its dynamic characteristics. Finally, through the prediction of the annual data of sunspots and the simulation data from Lorenz system and, it is verified that the method can determine the appropriate embedding dimension and delay time.

Chaos-based multigene genetic programming: A new hybrid strategy for river flow forecasting

Chaos theory is integrated with Multi-Gene Genetic Programming (MGGP) engine as a new hybrid model for river flow forecasting. This is to be referred to as Chaos-MGGP and its performance is tested using daily historic flow time series at four gauging stations in two countries with a mix of both intermittent and perennial rivers. Three models are developed: (i) Local Prediction Model (LPM); (ii) standalone MGGP; and (iii) Chaos-MGGP, where the first two models serve as the benchmark for comparison purposes. The Phase-Space Reconstruction (PSR) parameters of delay time and embedding dimension form the dominant input signals derived from original time series using chaos theory and these are transferred to Chaos-MGGP. The paper develops a procedure to identify global optimum values of the PSR parameters for the construction of a regression-type prediction model to implement the Chaos-MGGP model. The inter-comparison of the results at the selected four gauging stations shows that the Chaos-MGGP model provides more accurate forecasts than those of stand-alone MGGP or LPM models.

Application of EEMD and high‐order singular spectral entropy to feature extraction of partial discharge signals

Feature extraction of partial discharge (PD) signals is a key step in the pattern recognition and fault diagnosis of power equipment. The theory of singular spectral entropy analysis (SSEA) is introduced in order to study the complexity and irregularity degree of PD signals, but it cannot reflect the inherent nonlinear characteristics. The fourth‐order cumulant of PD signals is used instead of the covariance matrix of SSEA, and the ensemble empirical mode decomposition (EEMD) method is applied to realize multiple scales. The proposed multi‐scale high‐order singular spectral entropy analysis (M‐HSSEA) is applied to the simulated PD signals. Noise is effectively suppressed in the extracted entropy eigenvectors, and the robustness of phase space reconstruction parameters can be enhanced as well. Three kinds of typical defect models are designed. The entropy eigenvectors of the PDs detected by the ultra high frequency (UHF) method are extracted. The radial basis function neural network (RBF‐NN) classifier is used for pattern recognition. An ideal accuracy can be obtained, which verifies the validity and applicability of the proposed method. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Selection of Phase Space Reconstruction Parameters for EMG Signals of the Uterus

Abstract Biological time series have a finite number of samples with noise included in them. Because of this fact, it is not possible to reconstruct phase space in an ideal manner. One kind of biomedical signals are electrohisterographical (EHG) datasets, which represent uterine muscle contractile activity. In the process of phase space reconstruction, the most important thing is suitable choice of the method for calculating the time delay τ and embedding dimension d, which will reliably reconstruct the original signal. The parameters used in digital signal processing are key to arranging adequate parameters of the analysed attractor embedded in the phase space. The aim of this paper is to present a method employed for phase space reconstruction for EHG signals that will make it possible for their further analysis to be carried out.

An integrated chaotic time series prediction model based on efficient extreme learning machine and differential evolution

In this paper, an integrated model based on efficient extreme learning machine (EELM) and differential evolution (DE) is proposed to predict chaotic time series. In the proposed model, a novel learning algorithm called EELM is presented and used to model the chaotic time series. The EELM inherits the basic idea of extreme learning machine (ELM) in training single hidden layer feedforward networks, but replaces the commonly used singular value decomposition with a reduced complete orthogonal decomposition to calculate the output weights, which can achieve a much faster learning speed than ELM. Moreover, in order to obtain a more accurate and more stable prediction performance for chaotic time series prediction, this model abandons the traditional two-stage modeling approach and adopts an integrated parameter selection strategy which employs a modified DE algorithm to optimize the phase space reconstruction parameters of chaotic time series and the model parameter of EELM simultaneously based on a hybrid validation criterion. Experimental results show that the proposed integrated prediction model can not only provide stable prediction performances with high efficiency but also achieve much more accurate prediction results than its counterparts for chaotic time series prediction.

Chaos time series prediction based on membrane optimization algorithms.

This paper puts forward a prediction model based on membrane computing optimization algorithm for chaos time series; the model optimizes simultaneously the parameters of phase space reconstruction (τ, m) and least squares support vector machine (LS-SVM) (γ, σ) by using membrane computing optimization algorithm. It is an important basis for spectrum management to predict accurately the change trend of parameters in the electromagnetic environment, which can help decision makers to adopt an optimal action. Then, the model presented in this paper is used to forecast band occupancy rate of frequency modulation (FM) broadcasting band and interphone band. To show the applicability and superiority of the proposed model, this paper will compare the forecast model presented in it with conventional similar models. The experimental results show that whether single-step prediction or multistep prediction, the proposed model performs best based on three error measures, namely, normalized mean square error (NMSE), root mean square error (RMSE), and mean absolute percentage error (MAPE).

Chaotic behavior of light-assisted physical aging in arsenoselenide glasses.

The theory of strange attractors is shown to be adequately applicable for analyzing the kinetics of light-assisted physical aging revealed in structural relaxation of Se-rich As-Se glasses below glass transition. Kinetics of enthalpy losses is used to determine the phase space reconstruction parameters. Observed chaotic behaviour (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, false nearest neighbours, etc.) reconstructed via the TISEAN program package is treated within a microstructure model describing multistage aging behaviour in arsenoselenide glasses. This simulation testifies that photoexposure acts as an initiating factor only at the beginning stage of physical aging, thus facilitating further atomic shrinkage of a glassy backbone.

Natural physical aging in glassy As–Se: A comparative study of chaotic behavior with enhanced results analysis

Theory of chaos is shown to be adequately applied to analyze kinetics of natural physical aging revealed in structural relaxation of Se-rich As–Se glasses below glass transition. Kinetics of enthalpy losses induced by prolonged storage in natural conditions is used to determine phase space reconstruction parameters. The observed chaotic behavior (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, and false nearest neighbors) reconstructed via TISEAN is treated within potential energy landscape as diversity of multiple transitions between different basins–metabasins towards more thermodynamically equilibrium state, minimizing the free energy of the system. Natural physical aging, facilitates further atomic shrinkage of the glass backbone.

Short-Term Wind Power Prediction Based on Phase Space Reconstruction Theory

The accession of large scale wind power will impact the planning and construction, analytical control, operation of the economy, as well as power quality of the power grid. More accurate wind power prediction can help reduce the quantity of spinning reserve and provide the grid dispatching operation a reliable foundation. Wind power has chaotic characteristic. This paper proposed a method of chaotic time series prediction based on chaotic phase space reconstruction. The forecast precision depends largely on the choice of the model parameters. In order to improve the forecast precision and generalization ability of the prediction model, this article computed with the method of C-C to optimize the phase space reconstruction parameters comprehensive. Forecasting model used weighting first-order local field method. To test the approach, the data from a wind farm of Inner Mongolia were used. Practical examples showed that the integrated approach has a very good forecast precision and good practicability.