Phase Space Reconstruction Technique Research Articles

A novel crude oil price forecasting model using decomposition and deep learning networks

Crude oil prices are susceptible to a variety of elements, including military, political, financial, and diplomatic forces, resulting in price fluctuations that are random, abrupt, and chaotic. Based on the chaotic nature of crude oil price series, this paper proposes a model for predicting crude oil prices that incorporates variational modal decomposition algorithm (VMD), phase space reconstruction technique (PSR), convolutional neural network (CNN), and bidirectional long and short-term memory network (BiLSTM). Specifically, the noises in the original data are removed using VMD. Next, the crude oil price is reconstructed using PSR. Then the reconstructed and denoised phase space is fed into the CNN-BiLSTM model for multi-step predictions. The empirical results show that the proposed model achieves the lowest MAPEs as 0.662%, 2.283%, 3.829%, and 4.44% and the lowest MSEs as 0.335, 3.942, 10.047 and 13.681. The Diebold Mariano (DM) test also demonstrates the proposed model’s superiority in the domain of crude oil price forecasting.

Specific Emitter Identification Based on Attractor Feature Space of System under Blind Equalization

In the process of the individual identification of radiation sources, the effective extraction of fine features of target radiation sources can be regarded as being crucial for the subsequent individual identification. However, in the complex electromagnetic environment, the effective extraction of the radiation source features is still facing great challenges. To solve this problem, we propose an algorithm for constructing the attractor feature space of the radiation source system based on blind equalization to solve this problem. Firstly, we use blind equalization to process the target signal. Secondly, we use the phase-space reconstruction technique to construct the system attractor feature space of the target signal processed, and explore the adaptive relationship between feature-space-embedding dimensions, the delay time and the neural network, finding the optimal values. Finally, the feature space is used as the input of the neural network for the subsequent individual discrimination decision. Experimentally, it is proved that our proposed algorithm improves the individual recognition rate of the target radiation source under the complex electromagnetic environment to a certain extent, which is of practical application value.

A new fault diagnosis of rolling bearing based on phase-space reconstruction and convolutional neural network

PurposeTo solve the problem that the traditional methods miss key information in the process of bearing fault identification, this paper aims to apply the phase-space reconstruction (PSR) theory and intelligent diagnosis techniques to extend the one-dimensional vibration signal to the high-dimensional phase space to reveal the system information implied in the univariate time series of the vibration signal.Design/methodology/approachIn this paper, a new method based on the PSR technique and convolutional neural network (CNN) is proposed. First, the delay time and the embedding dimension are determined by the C-C method and the false nearest neighbors method, respectively. Through the coordinate delay reconstruction method, the two-dimensional signal is constructed, and this information is saved in a set of gray images. Then, a simple and efficient convolutional network is proposed. Finally, the phase diagrams of different states are used as samples and input into a two-dimensional CNN for learning modeling to construct a PSR-CNN fault diagnosis model.FindingsThe proposed PSR-CNN model is tested on two data sets and compared with support vector machine (SVM), k-nearest neighbor (KNN) and Markov transition field methods, and the comparison results showed that the method proposed in this paper has higher accuracy and better generalization performance.Originality/valueThe method proposed in this paper provides a reliable solution in the field of rolling bearing fault diagnosis.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2023-0113/

Topological EEG Nonlinear Dynamics Analysis for Emotion Recognition

Emotional recognition through exploring the electroencephalography (EEG) characteristics has been widely performed in recent studies. Nonlinear analysis and feature extraction methods for understanding the complex dynamical phenomena are associated with the EEG patterns of different emotions. The phase space reconstruction is a typical nonlinear technique to reveal the dynamics of the brain neural system. Recently, the topological data analysis (TDA) scheme has been used to explore the properties of space, which provides a powerful tool to think over the phase space. In this work, we proposed a topological EEG nonlinear dynamics analysis approach using the phase space reconstruction (PSR) technique to convert EEG time series into phase space, and the persistent homology tool explores the topological properties of the phase space. We perform the topological analysis of EEG signals in different rhythm bands to build emotion feature vectors, which shows high distinguishing ability. We evaluate the approach with two well-known benchmark datasets, the DEAP and DREAMER datasets. The recognition results achieved accuracies of 99.37% and 99.35% in arousal and valence classification tasks with DEAP, and 99.96%, 99.93%, and 99.95% in arousal, valence, and dominance classifications tasks with DREAMER, respectively. The performances are supposed to be outperformed current state-of-art approaches in DREAMER (improved by 1% to 10% depends on temporal length), while comparable to other related works evaluated in DEAP. The proposed work is the first investigation in the emotion recognition oriented EEG topological feature analysis, which brought a novel insight into the brain neural system nonlinear dynamics analysis and feature extraction.

Multi-stage hybrid energy management strategy for reducing energy abandonment and load losses among multiple microgrids

This paper proposes a multi-stage hybrid energy management strategy for multiple microgrids (MMGs) to reduce energy abandonment and load losses. The proposed energy management model consists of three stages including a decentralized autonomy stage, a coordinated operation stage, and a reserve reallocation stage, respectively. First, in the decentralized autonomy stage, a day-ahead energy management model is established with the objective of minimizing the comprehensive management cost of individual microgrids. Especially, the uncertainty from renewable energy and load demands are quantified by interval forecast algorithm, phase space reconstruction technique, machine learning, and kernel density estimation, which simplifies the forecasting processes while capturing multivariate data more comprehensively. Second, the coordinated operation stage aims to encourage the power interaction among MMGs to achieve maximize the benefit of MMGs while suppressing the power fluctuations of the tie line between the MMGs and the main grid. Then, in the reserve reallocation stage, taking the actual values of energy abandonment and load losses of a week before the management day as the dataset, machine learning algorithms are applied to predict energy abandonment and load losses. Meanwhile, the actual energy abandonment and load losses are reduced by dispatching reserve resources. Finally, simulations on an MMGs system containing four microgrids are conducted to testify the rationality and validity of the proposed energy management strategy.

A short-term wind energy hybrid optimal prediction system with denoising and novel error correction technique

As an important part of system operation and wind power station planning, wind energy forecasting is significantly affected by the strong volatility, intermittency and variability of the wind speed sequence itself. Therefore, to improve forecast accuracy and stability, the complex new energy forecasting problem is analyzed, and a research plan including denoising processing, input data feature optimization, model optimization selection and error correction is proposed. Apply the wavelet soft thresholding algorithm (WSTD) to sequence denoising, remove redundant information, and determine the best predictive model and model input for the sequence based on a new model selection principle (MSP) and phase space reconstruction technique (PSR), simultaneously, introduce the bayesian optimization (BO) to design the optimal reference search strategy to improve the learning efficiency of the model. Then, in order to avoid losing prediction information, a decomposition-segment error correction (DSEC) technique is proposed to enhance the veracity and adaptability of wind speed prediction. Based on 3 different data, the improved percentage of mean absolute percentage error is 7.366%, 7.514% and 10.649% respectively compared with the best performing comparative model, which verifies the effectiveness and applicability of the proposed framework and can provide strong support for smart grid planning.

RF Fingerprint Extraction Method Based on CEEMDAN and Multidomain Joint Entropy

Specific emitter identification (SEI) can distinguish communication radio emitters with the fingerprint features carried by the received signal, and this technology has been widely used in military and civilian fields. However, in the real electromagnetic environment, the number of communication radio emitters is large and the signal-to-noise ratio (SNR) is low, which leads to poor nonlinear fingerprint analysis of SEI in a single domain. Therefore, combining the exploration of multiple domains of electromagnetic spatial information resources, this paper proposed a radio frequency (RF) fingerprint extraction method based on complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multidomain joint entropy. The proposed method is an attempt and exploration further extraction of nonlinear fingerprint features in multiple domains. Firstly, considering the nonstationarity of the communication signal, this article adopts the CEEMDAN method to decompose the signal to multiple intrinsic mode functions (IMF). Then, the decomposed signal is represented in multiple spaces by a multidimensional phase space reconstruction technique. Nonlinear analysis of the original signal is performed in multiple spaces: multidimensional differential approximate entropy space, singular spectral entropy space, and power spectral entropy space. Finally, the support vector machine (SVM) is adopted in the classification stage. To demonstrate the robustness of the method, the method is verified on the universal software radio peripheral (USRP) dataset and the Northeastern University public dataset. In terms of the identification accuracy, the proposed method performs with 98.5% accuracy on the 5-class USRP dataset. It also performs with 94.7% accuracy on the 16-class public dataset. The experimental results show that the proposed method has a stable identification performance and has a more than 85% recognition rate in the SNR above 5dB.

Effluent ammonia nitrogen prediction using a phase space reconstruction method combining pipelined recurrent wavelet neural network

In wastewater treatment processes (WWTPs), the effluent ammonia nitrogen (NH4-N) concentration is a significant index to measure effluent quality. Recently, the soft computing methods have been widely used to measure effluent NH4-N concentration. However, the performance of soft computing method is closely related with its input variables, which is difficult to choose. As an alternative, the time series prediction method PSR-PRWNN is proposed, which combines phase space reconstruction (PSR) technique and pipelined recurrent wavelet neural network (PRWNN). Different from soft computing methods, the time series prediction method is a method which predicts the effluent NH4-N concentration by using its history data rather than other variables data. Firstly, the chaotic characteristics of effluent NH4-N time series is proved by using the correlation dimension method. Based on chaotic characteristics, the phase space of effluent NH4-N concentration is reconstructed by PSR technique. Then, the relationship model between inputs and output of the reconstructed phase space is established by PRWNN. Thirdly, the parameters of PRWNN are trained by an online gradient algorithm with adaptive learning rates. Finally, the experimental results indicate that the PSR-PRWNN can obtain better training results and prediction accuracy than other algorithms.

Parameter Prediction of Marine Seawater Cooling System Based on Chaos-Elman Combined Model

To improve the accuracy of short-term prediction of marine seawater cooling system parameters and reduce the accuracy loss caused by chaotic data, a combined prediction model combining chaos theory and Elman feedback neural network was proposed in this paper. Firstly, the C-C algorithm and G-P algorithm were used to calculate the two reconstruction parameters respectively, and according to the properties of the maximum Lyapunov exponent, it could be determined that the original one-dimensional time series had chaotic characteristics. Secondly, phase space reconstruction technique was used to map the one-dimensional seawater outlet temperature time series of intercooler to the high-dimensional space to find its chaotic phase trajectory, and the number of adjacent points was determined by HQ (Hannan Quinn) information criterion. Finally, the Chaos-Elman combined prediction model was used to train and test 300 sets of seawater outlet temperature data of intercooler, and the accuracy of prediction was compared with that of single structure model. The experimental results were as follows: the average prediction accuracy based on chaos theory was 95.5%, the prediction accuracy of Elman neural network was 95.1%, and the prediction accuracy of Chaos-Elman combined model could reach 98.7%. In this study, the Chaos-Elman combined model has better prediction accuracy than the single model. It can be concluded that the Chaos-Elman combined model can be used for the short-term prediction of seawater cooling system parameters, and the prediction accuracy and reliability are high.

An analytical approach of behavior change for concrete dam by panel data model

The behavior variation of concrete dam is investigated, based on a new method for analyzing the data model of concrete dam in service process for the limitation of wavelet transform for solving concrete dam service process model. The study takes into account the time and position of behavior change during the process of concrete dam service. There is no dependence on the effect quantity for overcoming the shortcomings of the traditional identification method. The panel data model is firstly proposed for analyzing the behavior change of composite concrete dam. The change-point theory is used to identify whether the behavior of concrete dams changes during service. The phase space reconstruction technique is used to reconstruct the phase plane of the trend effect component. The time dimension method is used to solve the construction of multi-transformation model of composite panel data. An existing 76.3-m-high dam is used to investigate some key issues on the behavior change. Emphasis is placed on conversion time and location for three time periods consistent with the practical analysis report for evaluating the validity of the analysis method of the behavior variation of concrete dams presented in this paper.

A Vector Angle Method of Rolling Bearing Fault Classification by Phase-Space Reconstruction Technique

Abstract A fault classification method is developed by the phase-space reconstruction technique for a rotor system with a rolling bearing fault. Based on the nonlinear time series analysis, proper choices on time delay and embedding dimension are firstly discussed to accomplish the phase-space reconstruction from an arbitrarily one-dimensional time series, then the vector angle calculation is derived for each point in the reconstructed trajectory of an illustrating artificial signal, from which the vector angles of the points are composed of 90° and non-90° ones. To perform the fault feature analysis of the rolling bearing, an experimental rig of the rotor-bearing system and dynamical model of the system are established to collect the one-dimensional acceleration signals of three types of rolling bearing faults, and the topology of the reconstructed trajectory in three-dimensional phase space is characterized. It is interesting to find that the effects of various rolling bearing faults on the reconstructed trajectories are different, and the fault features can be extracted successfully by the distribution percentage of 90° and non-90° vector angles of the points in the reconstructed trajectory in three-dimensional phase space, which cannot be identified by the traditional attractor reconstruction method. Moreover, the higher the fault frequency, the lower proportion the healthy points.

Point and interval forecasting for carbon price based on an improved analysis-forecast system

Effective analysis and forecasting of carbon prices, which is an essential endeavor for the carbon trading market, is still considered a difficult task because of the nonlinearity and nonstationarity inherent in carbon prices. Previous studies have failed at the analysis and interval prediction of carbon prices and are limited to point forecasts. Therefore, an improved carbon price analysis and forecasting system that consists of an analysis module and a forecasting module is established in this study; more importantly, the forecasting module includes point forecasting and interval forecasting as well. Aimed at investigating the characteristics of the carbon price series, a chaotic analysis based on the maximum Lyapunov exponent is performed, the determination of appropriate distribution functions based on our newly proposed hybrid optimization algorithm is conducted, and different distribution functions are effectively designed in the analysis module. Furthermore, in the point forecasting model, the phase space reconstruction technique is applied to reconstruct the sequences decomposed by variational mode decomposition due to the chaotic characteristics of the carbon price series, and the reconstructed sequences are considered as the optimal input–output variables of the forecasting model. Then, an adaptive neuro-fuzzy inference system model is trained by the newly proposed hybrid optimization algorithm, which is developed for the first time in the domain of carbon price point forecasting. Moreover, based on the results of point forecasting and the distribution function of the carbon price series determined by the analysis module, the interval forecasting results can be obtained and implemented to provide more reliable information for decision making. Empirical results based on the carbon price data of the European Union Emissions Trading System and Shenzhen of China demonstrate that the proposed system achieves better results than other benchmark models in point forecasting as well as interval forecasting.

Phase Space Reconstruction Based CVD Classifier Using Localized Features

This paper proposes a generalized Phase Space Reconstruction (PSR) based Cardiovascular Diseases (CVD) classification methodology by exploiting the localized features of the ECG. The proposed methodology first extracts the ECG localized features including PR interval, QRS complex, and QT interval from the continuous ECG waveform using features extraction logic, then the PSR technique is applied to get the phase portraits of all the localized features. Based on the cleanliness and contour of the phase portraits CVD classification will be done. This is first of its kind approach where the localized features of ECG are being taken into considerations unlike the state-of-art approaches, where the entire ECG beats have been considered. The proposed methodology is generic and can be extended to most of the CVD cases. It is verified on the PTBDB and IAFDB databases by taking the CVD including Atrial Fibrillation, Myocardial Infarction, Bundle Branch Block, Cardiomyopathy, Dysrhythmia, and Hypertrophy. The methodology has been tested on 65 patients’ data for the classification of abnormalities in PR interval, QRS complex, and QT interval. Based on the obtained statistical results, to detect the abnormality in PR interval, QRS complex and QT interval the Coefficient Variation (CV) should be greater than or equal to 0.1012, 0.083, 0.082 respectively with individual accuracy levels of 95.3%, 96.9%, and 98.5% respectively. To justify the clinical significance of the proposed methodology, the Confidence Interval (CI), the p-value using ANOVA have been computed. The p-value obtained is less than 0.05, and greater F-statistic values reveal the robust classification of CVD using localized features.

Phase Space Reconstruction of EEG Signals for Classification of ADHD and Control Adults.

Attention deficit hyperactivity disorder (ADHD) is a childhood behavioral disorder that can persist into adulthood. Electroencephalography (EEG) plays a significant role in assessing the neurophysiology of ADHD because of its ability to reveal complex brain activity. The present study proposes an EEG-based diagnosis system using the phase space reconstruction technique to classify ADHD and control adults. Electric activity is recorded for 47 ADHD and 50 control adults during the eyes-open, eyes-closed, and Continuous Performance Test (CPT) condition. Various statistical features are extracted from Euclidean distances based on phase space reconstruction of signals. The proposed system is evaluated with 2 feature selection methods (correlation-based feature selection and particle swarm optimization) and 5 machine learning methods (neural dynamic classifier, support vector machine, enhanced probabilistic neural network, k-nearest neighbor, and naive-Bayes classifier). Experimental results showed the highest testing accuracy of 93.3% under the eyes-open, 90% under the eyes-closed, and 100% under the CPT condition. This study focused on the utility of phase space reconstruction of brain signals to discriminate between ADHD and control adults.

Classifying Power Quality Disturbances Based on Phase Space Reconstruction and a Convolutional Neural Network

This paper presents a hybrid approach combining phase space reconstruction (PSR) with a convolutional neural network (CNN) for power quality disturbance (PQD) classification. Firstly, a PSR technique is developed to transform a 1D voltage disturbance signal into a 2D image file. Then, a CNN model is developed for the image classification. The feature maps are extracted automatically from the image file and different patterns are derived from variables in CNN. A set of synthetic signals, as well as operational measurements, are used to validate the proposed method. Moreover, the test results are also compared with existing methods, including empirical mode decomposition (EMD) with balanced neural tree (BNT), S-transform (ST) with neural network (NN) and decision tree (DT), hybrid ST with DT, adaptive linear neuron (ADALINE) with feedforward neural network (FFNN), and variational mode decomposition (VMD) with deep stochastic configuration network (DSCN). Based on deep learning algorithms, the proposed method is capable of providing more accurate results without any human intervention for PQDs. It also enables the planning of PQ remedy actions.

Bifurcation Analysis and Vibration Signal Identification for a Motorized Spindle with Random Uncertainty

A nonparametric model is established to investigate the vibration characteristics of a motorized spindle system, where the bearing restoring force, the unbalanced magnetic pull, and the external bounded noise excitation are taken into account. Based on the Monte Carlo simulation, several numerical examples are used to study the effect of dispersion parameters from model uncertainty and strength of external bounded noise excitation on the whirl frequency and bifurcation behavior of the spindle. It is shown that the whirl frequency fluctuates due to the random uncertainty, and the fluctuation range grows wider as the dispersion parameters increase as anticipated. In the randomly uncertain case, the vibration of the spindle also exhibits periodic-dominant and bifurcation phenomena, of particular interest is the delay of bifurcation point following the increase of the rotation speed. Towards the vibration condition monitoring on the spindle system, the phase space reconstruction technique is also applied to identify the vibration signals by comparing the reconstructed deterministic phase-space orbits with those from the random uncertainty and the bounded noise excitation, and the inherent dynamical behavior can be revealed from the irregular one-dimension time series effectively.

Lyapunov exponent analysis for the evaluation of hybrid laser double-arc welding process stability.

Hybrid laser double-arc welding is a complicated process with many random and uncertain influencing factors because of the interactions of energy, forces, and fields. The wire spacing is one of the main factors affecting the coupling behavior of laser and arc plasma and the stability of welding process. However, it is difficult to establish a precise mathematical model for evaluation of welding stability. In this paper, the largest Lyapunov exponent (LLE) of characteristic currents during the welding process under different wire-wire distances were numerically evaluated by the phase space reconstruction technique. Synchronous high-speed photography was adopted to observe arc shape and droplet transfer. The experimental and calculated results indicate that hybrid laser double-pulsed arc welding is a complex process of chaos. The LLE can provide a criterion for welding stability and can agree well with the observation of electrical signal, arc shape, and droplet transfer. Research results are needed to understand the welding process and to guarantee a stable and safe joining.

Multi-Step Ahead Wind Power Generation Prediction Based on Hybrid Machine Learning Techniques

Accurate generation prediction at multiple time-steps is of paramount importance for reliable and economical operation of wind farms. This study proposed a novel algorithmic solution using various forms of machine learning techniques in a hybrid manner, including phase space reconstruction (PSR), input variable selection (IVS), K-means clustering and adaptive neuro-fuzzy inference system (ANFIS). The PSR technique transforms the historical time series into a set of phase-space variables combining with the numerical weather prediction (NWP) data to prepare candidate inputs. A minimal redundancy maximal relevance (mRMR) criterion based filtering approach is used to automatically select the optimal input variables for the multi-step ahead prediction. Then, the input instances are divided into a set of subsets using the K-means clustering to train the ANFIS. The ANFIS parameters are further optimized to improve the prediction performance by the use of particle swarm optimization (PSO) algorithm. The proposed solution is extensively evaluated through case studies of two realistic wind farms and the numerical results clearly confirm its effectiveness and improved prediction accuracy compared to benchmark solutions.

Multiscale Analysis of Time Irreversibility Based on Phase-Space Reconstruction and Horizontal Visibility Graph Approach

Time irreversibility is an important property of nonequilibrium dynamic systems. A visibility graph approach was recently proposed, and this approach is generally effective to measure time irreversibility of time series. However, its result may be unreliable when dealing with high-dimensional systems. In this work, we consider the joint concept of time irreversibility and adopt the phase-space reconstruction technique to improve this visibility graph approach. Compared with the previous approach, the improved approach gives a more accurate estimate for the irreversibility of time series, and is more effective to distinguish irreversible and reversible stochastic processes. We also use this approach to extract the multiscale irreversibility to account for the multiple inherent dynamics of time series. Finally, we apply the approach to detect the multiscale irreversibility of financial time series, and succeed to distinguish the time of financial crisis and the plateau. In addition, Asian stock indexes away from other indexes are clearly visible in higher time scales. Simulations and real data support the effectiveness of the improved approach when detecting time irreversibility.

Multi-step ahead wind speed forecasting using an improved wavelet neural network combining variational mode decomposition and phase space reconstruction

Accurate wind speed forecasting is crucial to reliable and secure power generation system. However, the intermittent and unstable nature of wind speed makes it very difficult to be predicted accurately. This paper proposes a novel hybrid model based on variational mode decomposition (VMD), phase space reconstruction (PSR) and wavelet neural network optimized by genetic algorithm (GAWNN) for multi-step ahead wind speed forecasting. In the proposed model, VMD is firstly applied to disassemble the original wind speed series into a number of components in order to improve the overall prediction accuracy. Then, the multi-step ahead forecasting for each component is conducted using GAWNN model in which the input-output sample pairs are determined by PSR technique. Finally, the ultimate forecast series of wind speed is obtained by aggregating the forecast result of each component. The proposed model is tested using two real-world wind speed series collected respectively in spring and autumn from a wind farm located in Xinjiang, China. The experimental results show that the proposed model outperforms all other comparison models including persistence method, PSR-BPNN, PSR-WNN, PSR-GAWNN and EEMD-PSR-GAWNN models adopted in this paper, which demonstrates that the proposed model has superior performances for multi-step ahead wind speed forecasting.