Phase Space Reconstruction Research Articles

Nonlinear dynamic characteristics of self-excited thermoacoustic instabilities in premixed swirling flames

The nonlinear behavior of thermoacoustic oscillation for premixed swirl flames fueled with CH4/air mixtures is experimentally studied by changing the equivalence ratio Φ, combustor inlet bulk velocity Uin and swirl number S. The nonlinear dynamic characteristics of the system are analyzed by the methods of phase space reconstruction, recurrence plot, Poincaré section and 0–1 test for chaos. Five kinds of flame modes are observed in the combustion system with the change of Φ, Uin, and S, which are lean/rich blow-off, stable combustion, quasi-periodic oscillation, and limit cycle oscillation. Subcritical Hopf bifurcation of the oscillation is captured either by changing Φ or Uin, and Φ and Uin are found to have similar effects on the flame mode transition under specific operating conditions. It is observed that the appearance of flame in the outer circulation zone (ORZ) and the enhancement of its burning intensity are matched with the occurrence of quasi-periodic and limit cycle oscillations, respectively. It is examined that the lean/rich blow-off limits and oscillation range are extended with a larger S, and the stable combustion regime is wider with a smaller S. This study contributes to understanding the nonlinear thermoacoustic instability of swirl flames under broad flame conditions, which helps to develop effective instability prediction and control methods in stable, efficient, and low-emission gas turbines.

Cumulative Diversity Pattern Entropy (CDEn): A High-Performance, Almost-Parameter-Free Complexity Estimator for Nonstationary Time Series

Tedious parameter settings and poor performances seriously affect the entropy estimation's effectiveness in time series analysis. To solve these limits, we propose a conceptually novel definition, cumulative diversity pattern entropy (CDEn), focusing on eliminating parameter selections and improving quantization accuracy, stability, and robustness. The CDEn algorithm consists of three steps: (1) improved phase-space reconstruction (IPSR) with constant embedding dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{m\ }} = {\bm{\ }}2$</tex-math></inline-formula> and time delay <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{\tau \ }} = {\bm{\ }}1$</tex-math></inline-formula> ; (2) diversity pattern partition generated by the cosine similarity between adjacent vectors; and (3) entropy calculation based on the normalized cumulative probability distribution. Numerical experiments are performed using 7 synthetic datasets and 15 baseline entropy methods for comparative validation. The results confirm CDEn's best description of chaotic/stochastic dynamics with the highest quantization accuracy and the lowest error rate of 2.04%. The coefficient of variation (CV) results also verify CDEn's excellent quantization stability with CV lower than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . The relative change rate (RCR) results demonstrate that CDEn achieves the best robustness to data length and noise. Finally, the entropy algorithms are applied to a real-world dataset, i.e., neonatal sleep EEG analysis. The results further confirm that suggested CDEn outperforms the state-of-the-art entropy methods, with the minimum outliers and best statistical significance (highest mean of effect size, 1.22) in characterizing the neurodynamics of different sleep stages.

A Mechanical Defect Localization and Identification Method for High-Voltage Circuit Breakers Based on the Segmentation of Vibration Signals and Extraction of Chaotic Features.

To address the problem of mechanical defect identification in a high-voltage circuit breaker (HVCB), this paper studies the circuit breaker vibration signal and proposes a method of feature extraction based on phase-space reconstruction of the vibration substages. To locate mechanical defects in circuit breakers, vibration signals are divided into different substages according to the time sequence of the parts of the circuit breakers. The largest Lyapunov exponent (LLE) of the vibration signals' substages is calculated, and then the substages are reconstructed in high-dimensional phase space. The geometric features of the phase trajectory mean center distance (MCD) and vector diameter offset (VDO) are calculated, and the LLE, MCD, and VDO are selected as the three fault identification features of the vibration substages. The eigenvalue anomaly rate of each substage of the vibration signal under defect state are calculated and analyzed to locate the vibration substage of the mechanical defect. Finally, a fault diagnosis model is constructed by a support vector machine (SVM), and the common mechanical defects of circuit breakers simulated in the laboratory are effectively identified.

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/

Analysis and classification of gait patterns in osteoarthritic and asymptomatic knees using phase space reconstruction, intrinsic time-scale decomposition and neural networks

Analysis and classification of gait patterns in osteoarthritic and asymptomatic knees using phase space reconstruction, intrinsic time-scale decomposition and neural networks

A compound framework incorporating improved outlier detection and correction, VMD, weight-based stacked generalization with enhanced DESMA for multi-step short-term wind speed forecasting

Precise wind speed forecasting contributes to wind power consumption and power grid schedule as well as promotes the implementation of global carbon neutrality policy. However, in existing research, the negative impact of outliers on forecasting models is ignored and the inherent shortcomings of the single predictors have not been taken seriously. Moreover, the intrinsic parameters of predictors are set by manual and empirical methods in some research, leading to difficulties in achieving optimal forecasting performance. To solve the shortcomings of existing research, a multi-step short-term wind speed forecasting framework is proposed by incorporating boxplot-medcouple (MC), variational mode decomposition (VMD), phase space reconstruction (PSR), weight-based stacked generalization with enhanced differential evolution slime mold algorithm (DESMA). Firstly, boxplot-MC is employed to achieve outlier detection and correction for preprocessing original wind speed data by analyzing values and trends. Then, the modified data is further adaptively decomposed into multiple subsequences by VMD, after which each subsequence is constructed into feature matrices through PSR. Subsequently, weight-based multi-model fusion strategy in layer-1 of stacked generalization is proposed to integrate the predicting values acquired by three primary learners, of which the weight coefficients are calculated with the error between actual values and predicting values. After that, kernel extreme learning machine (KELM) in layer-2 of stacked generalization is applied to predict the fusion result to obtain forecasting value corresponding to each subsequence. Meanwhile, an enhanced DESMA based on slime mold algorithm (SMA) and differential evolution (DE) is proposed to calibrate the parameters of KELM. Eventually, the final wind speed forecasting results are attained by summing the prediction values of all subsequences. Furthermore, comparative experiments from different aspects are undertaken on real datasets to ascertain the availability of the proposed framework. The experimental results are clarified as follows: (1) outlier detection and correction employing boxplot-MC is dedicated to analyzing values and trends effectively, with which the negative impact of outliers can be weakened while retaining valid data significantly; (2) VMD can prominently reduce the non-smoothness and volatility of wind speed data; (3) weight-based stacked generalization is conducive to exploiting the advantages of individual primary learners, contributing to compensating for instability; (4) DESMA enhances prediction accuracy by optimizing the parameters of KELM. Additionally, the code has been made available at https://github.com/fyc233/a-multi-step-short-term-wind-speed-forecasting-framework.git.

What can phone attractors in RPS tell us? A study of dynamic information in speech signals for phone classification purposes

The speech production system is time-varying, multidimensional, and nonlinear. Most techniques for spoken feature extraction (SFE), which are tools for extracting information from speech signals, rely on the linear aspects of this system. In the past two decades, several techniques have been developed to account for the nonlinear characteristics of the system using embedded speech attractors in the reconstructed phase space (RPS). However, despite the clear benefits of speech representation in the RPS domain, only a few studies have successfully applied it for classification purposes. The main goal of this study is to develop an RPS-based framework that uses dynamic information of the embedded speech attractors in the RPS domain and outperforms the time-domain SFE techniques. The extracted features are based on multivariate linear prediction models of phone trajectories that show the dynamic information of the embedded speech attractor in the RPS. Several experiments on the FARSDAT and TIMIT databases test the phone classification accuracy of the proposed framework and show that the dynamic information of the phone attractors can significantly improve phone classification accuracy.

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling.

Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.

Sea Clutter Amplitude Prediction via an Attention-Enhanced Seq2Seq Network

Sea clutter is a kind of ubiquitous interference in sea-detecting radars, which will definitely influence target detection. An accurate sea clutter prediction method is supposed to be beneficial while existing prediction methods are based on the one-step-ahead prediction. In this paper, a sea clutter prediction network (SCPNet) is proposed to achieve the k-step-ahead prediction based on the characteristics of sea clutter. The SCPNet takes a sequence-to-sequence (Seq2Seq) structure as the backbone, and a simple self-attention module is employed to enhance the ability of adaptive feature selections. The SCPNet takes the normalized amplitudes of sea clutter as inputs and is capable of predicting an output sequence with a length of k; the phase space reconstruction theory is also used to find the optimized input length of the sea clutter sequence. Results with the sea-detecting radar data-sharing program (SDRDSP) database show the mean square error of the proposed method is 1.48 × 10−5 and 8.76 × 10−3 in the one-step-ahead prediction and the eight-step-ahead prediction, respectively. Compared with four existing methods, the proposed method achieves the best prediction performance.

Characterising the variability in ocean data using fractal and correlation dimension analysis

Understanding the variability of ocean data is essential for predicting its behaviour in time domain. This study aims to examine the usability of several nonlinear time series analysis techniques for diagnosing the complexity of the underlying dynamics of various ocean data. For such purpose, one-year data from an offshore platform and two-year data from a weather buoy were collected and analysed. The results indicate that all the ocean data considered here are chaotic in nature, reflected by the unfolded structure in the reconstructed phase space. In general, the surface currents speed possess the largest fractal dimension (or lowest Hurst exponent) and correlation dimension, while the significant wave height has the lowest values. This implies that the dynamics associated with surface currents speed tend to be the most complex, which can lead to more random and unpredictable temporal behaviour. The fractal analysis shows that the fluctuation of these ocean data are mostly persistent, and the dependence of fractal properties on window length appears to vary amongst different ocean data. Overall, the results derived from various analysis techniques are consistent, which confirms the potential of using chaotic time series analysis technique for characterizing ocean data variability.

Multistep Wind Power Prediction Using Time-Varying Filtered Empirical Modal Decomposition and Improved Adaptive Sparrow Search Algorithm-Optimized Phase Space Reconstruction–Echo State Network

Accurate wind power prediction is vital for improving grid stability. In order to improve the accuracy of wind power prediction, in this study, a hybrid prediction model combining time-varying filtered empirical modal decomposition (TVFEMD), improved adaptive sparrow search algorithm (IASSA)-optimized phase space reconstruction (PSR) and echo state network (ESN) methods was proposed. First, the wind power data were decomposed into a set of subsequences by using TVFEMD. Next, PSR was used to construct the corresponding phase space matrix for sequences, which were then divided into training sets, validation sets, and testing sets. Then, ESN was used for subsequence prediction. Finally, the predicted values of all the subseries were used to determine the final predicted power. To enhance the model performance, the sparrow search algorithm was improved in terms of the discoverer position update strategy, the follower position update strategy, and the population structure. IASSA was employed to synchronously optimize multiple parameters of PSR-ESN. The results revealed that the proposed model has higher applicability and prediction accuracy than existing models.

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.

Integrated approach to diagnose structural behaviour of dam

The objectives of this study are to: (1) develop an approach for extracting representative information from dam behaviour data and (2) diagnose deformation and crack opening behaviour by integrating techniques in transfer entropy (TE), chaos theory and wavelet transform (WT). First, TE is employed to map the information flow between measuring points to select the representative measuring point. The phase space reconstruction of observation data on dam behaviour is implemented, where lag time τ and embedding dimension m are identified by the statistical C–C method. The non-linear structural dynamical behaviour of the dam is then quantified in the form of the largest Lyapunov exponent representing system chaoticity. In addition, a moving window formula is employed to scan along the observation data to ensure an on-line continuous diagnosis. WT may be employed to assist in detecting the time where significant changes occur. A simple 4 degrees of freedom spring-mass-damper (K-M-C) system is employed to illustrate the performance of the proposed approach. The approach is then applied to an actual dam using monitoring data. From the deformation and crack opening behaviour, it is concluded that the studied dam is performing with no significant changes in behaviour over time. HIGHLIGHTS Transfer entropy is applied to map the information flow between measuring points. The representative information on structural behaviour of an actual dam is identified. TE and chaos theory are combined to diagnose the dam behaviour. A moving window is adopted to facilitate online statistical diagnosis.

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication.

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

Machine learning models combined with wavelet transform and phase space reconstruction for groundwater level forecasting

Reliable forecasting of groundwater levels plays an important role in water resource management and the prevention of environmental problems. This study aims to introduce a novel hybrid model combining machine learning with wavelet transform (WT) and phase space reconstruction (PSR) for groundwater level forecasting. The development of the proposed hybrid model consists of two levels. Firstly, a popular data-driven nonlinear artificial neural network (ANN) model was selected as the base model. Thereafter, the WT is used to decompose the groundwater level time series. In addition, the PSR method is further adopted to select the suitable sub-series components resulting from the WT decomposition processes. At the first level, the hybrid model only combines the WT with ANN (WT-ANN). At the second level, a two-step preprocessing process, WT coupled with PSR, is implemented before the ANN, namely WT-PSR-ANN. Meanwhile, three mother wavelets (Daubechies, Symlets, and Dmeyer) are selected to further investigate the effect of wavelet type. Finally, the model's performance is evaluated using visual analysis and statistical metrics (root means square error, correlation coefficient, and the Nash-Sutcliffe efficiency coefficient). The results show that the WT-ANN model outperformed the vanilla ANN model. Furthermore, the WT-PSR-ANN model achieved the best accuracy for all selected mother wavelets. The most suitable mother wavelet is specific to each well, and there is no one-size-fits-all answer. This study highlights the effectiveness of PSR combined with WT as a data preprocessing step when the ANN model is applied for groundwater level forecasting.

Inatorial forecasting method considering macro and micro characteristics of chaotic traffic flow

Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have macro spatiotemporal characteristics and micro chaotic characteristics. The key to improving the model prediction accuracy is to fully extract the macro and micro characteristics of traffic flow time sequences. However, traditional prediction model by only considers time features of traffic data, ignoring spatial characteristics and nonlinear characteristics of the data itself, resulting in poor model prediction performance. In view of this, this research proposes an intelligent combination prediction model taking into account the macro and micro features of chaotic traffic data. Firstly, to address the problem of time-consuming and inefficient multivariate phase space reconstruction by iterating nodes one by one, an improved multivariate phase space reconstruction method is proposed by filtering global representative nodes to effectively realize the high-dimensional mapping of chaotic traffic flow. Secondly, to address the problem that the traditional combinatorial model is difficult to adequately learn the macro and micro characteristics of chaotic traffic data, a combination of convolutional neural network (CNN) and convolutional long short-term memory (ConvLSTM) is utilized for capturing nonlinear features of traffic flow more comprehensively. Finally, to overcome the challenge that the combined model performance degrades due to subjective empirical determined network parameters, an improved lightweight particle swarm is proposed for improving prediction accuracy by optimizing model hyperparameters. In this paper, two highway datasets collected by the Caltrans Performance Measurement System (PeMS) are taken as the research objects, and the experimental results from multiple perspectives show that the comprehensive performance of the method proposed in this research is superior to those of the prevalent methods.

Short-Term Passenger Flow Forecasting for Rail Transit considering Chaos Theory and Improved EMD-PSO-LSTM-Combined Optimization

This paper proposes a prediction method based on chaos theory and an improved empirical-modal-decomposition particle-swarm-optimization long short-term-memory (EMD-PSO-LSTM)-combined optimization process for passenger flow data with high nonlinearity and dynamic space-time dependence, using EMD to process the original passenger flow data and generate several eigenmodal functions (IMFs) and residuals with different characteristic scales. Based on the chaos theory, each component of the PSO algorithm was improved by introducing an inertia factor to facilitate the adjustment of its search capability to improve optimization. Each subsequence of the phase-space reconstruction was built into an improved PSO-LSTM prediction model, and the output of each prediction model was summed to determine the final output. Experimental studies were performed using data from the North Railway Station of Chengdu Rail Transit, and the results showed that the proposed model can generate better prediction results. The proposed model obtained root mean square error (RMSE) and mean absolute error (MAE) of 16.0908 and 11.3704, respectively. Compared with the LSTM, the improved PSO-LSTM, the improved EMD-PSO-LSTM, and the model proposed in this paper improved the RMSE values by 25.53%, 29.97%, and 58.76%, respectively, and the MAE values by 30.41%, 40.13%, and 63.08%, respectively, of the prediction results.

Improved Long Short-Term Memory: Statistical Regression Model for High Precision SOC Estimation of Lithium-Ion Batteries Adaptive to Complex Current Variation Conditions

Lithium battery health management is of great significance to promote its wide application. Its accurate battery modeling and state prediction can ensure the safe start-up and stable operation of battery management system. A new method for estimating the charge state of lithium-ion batteries based on phase space reconstruction was proposed by combining long and short term memory network and statistical regression. Compared with the traditional method, the improved LSTM improves the accuracy of prediction by adding data feature dimension through phase space reconstruction, and the segmentation prediction reduces the complexity of data and improves the learning speed. By combining neural network with Kalman filter, it is more consistent with the continuity of lithium battery SOC and further improves the prediction accuracy. Finally, in order to verify the accuracy of the algorithm, an estimation test is carried out using ternary lithium battery. The results show that in BBDST conditions, the prediction ability of the proposed method is significantly improved compared with other algorithms. After 400 cycles of charge and discharge, the prediction error is less than 2.21%, which further indicates that this method has good estimation ability.

Optimal Choices of Reconstruction Parameters United Improved C-C Algorithm and Improved G-P Algorithm

For the phase space reconstruction of chaotic time series, the precise selection of delay and embedding dimension is indispensable. Therefore, this paper makes an in-depth study on the selection of reconstruction parameters, and puts forward some suggestions for improving the theoretical defects of the original C-C algorithm and G-P algorithm. The modified C-C algorithm optimizes the intermediate determination parameters of delay time and embedded window of the original algorithm, and makes the selection of delay time and embedded window more accurate. The improved G-P algorithm optimizes the range of neighborhood radius and the selection of scale-free interval, and improves the calculation accuracy of embedding dimension. On the theoretical basis, Lorenz sequence and Rossler sequence are used to verify, and the simulation results can be obtained. The improved algorithm can select parameters more accurately. Finally, the parameters obtained by the two improved algorithms are compared, and it is considered that the phase space reconstruction can be better by using the improved C-C algorithm to solve the delay and the improved G-P algorithm to solve the embedding dimension.

Multivariate variational mode decomposition & phase space reconstruction based motor imagery EEG classification

Electroencephalogram signals have gained much attention in recent years as these signals help in decoding a person's intentions for performing various actions using the Brain Computer Interface system. However, it is challenging to accurately classify human intentions as the electroencephalogram signals are non-linear and non-stationary. This work proposes a novel methodology for feature extraction and classification of motor imagery electroencephalogram signals. The proposed methodology is based on Multivariate Variational Mode Decomposition and Phase Space Reconstruction. A number of statistical and non-linear features are extracted and classified using the Ensemble Support Vector Machine model. The efficiency of the methodology is evaluated on BCI competition-IV(2a) dataset. The evaluation results conclude that the proposed methodology is able to classify both binary and multi-class electroencephalogram data with an average classification accuracy of 96.76% and 84.22%, respectively. Hence, the proposed methodology can be utilized in designing a real-time Brain Computer interface system.