Phase Space Reconstruction Research Articles

Short-term Traffic Flow Prediction：A Method of MEA-LSTM Model Based on Chaotic Characteristics Analysis

To effectively improve the accuracy of short-term traffic flow prediction, an improved Long Short-Term Memory (LSTM) method is proposed using the Mind Evolution Algorithm (MEA). Firstly, to address the issues of abnormal and missing traffic flow data, a Neighborhood Stacked Denoising AutoEncoder (NSDAE) is used for data repair. Then, the maximum Lyapunov exponent is used to determine the chaotic characteristics. Meanwhile, based on Bayesian estimation theory, the features of three-parameter sequences are fused in high-dimensional space using phase space reconstruction technique to obtain reconstructed multi-parameter fused traffic flow data. Finally, by taking advantage of the fact that MEA can divide the data into several subpopulations for optimal search separately, a prediction model based on MEA to improve LSTM is proposed. The results show that compared to the other two traditional data restoration methods, the NSDAE has higher accuracy, with the lowest average values of RMSE, MAE, and MAPE. Through the phase space reconstruction technique, the feature fusion of three parameters of traffic flow is realized in high-dimensional space, which makes up for the insufficiency of a single time-series data that cannot comprehensively levy the characteristics of traffic flow. The MEA-LSTM model outperforms the LSTM model in terms of prediction accuracy, computational efficiency, and generalization ability, and its RMSE, MEA, and MAPE are reduced by 24.3%, 28.9%, and 30.1%, respectively.

Transportation characteristics analysis of the dense-phase gas-solid two-phase flow based on phase space reconstruction

The operational efficiency and safety of the dense phase pneumatic conveying system is deeply influenced by the transportation characteristics of the dense-phase gas-solid two-phase flow in conveying pipelines. This paper presents a framework for analyzing the transport characteristics of the gas-solid two-phase flow based on the phase space reconstruction. The framework explores the transport characteristics by reconstructing the state evolution trajectories of the two-phase flow system in state space. The main goal is to enhance the interpretability of feature analysis. By employing the phase space reconstruction method to process the output signals of an electrostatic sensor, the evolution trajectory of the dynamic state of the gas-solid two-phase flow system was reconstructed in phase space.This provides an effective entry point for extracting the essential dynamic characteristics of the gas-solid two-phase flow system. Furthermore, a series of feature values were proposed, including the average speed of the trajectory, Shannon entropy of the trajectory, and the average distance between state points in phase space, which were used to respectively evaluate important transportation characteristics such as flowability, stability, and particle aggregation degree of the gas-solid two-phase flow. Moreover, through comparative analysis with visualization images that represent actual conveying conditions, the effectiveness of these proposed feature values in evaluating these transportation characteristics was verified.

Multivariable financial time series forecasting based on phase space reconstruction compensation

Multivariable financial time series forecasting based on phase space reconstruction compensation

Learning global and local features of power load series through transformer and 2D-CNN: An image-based multi-step forecasting approach incorporating phase space reconstruction

As modern power systems continue to evolve, accurate power load forecasting remains a critical issue in energy management. The phase space reconstruction (PSR) method can effectively retain the inner chaotic property of power load from a system dynamics perspective and thus is a promising knowledge-based method for power load forecasting. To fully leverage the PSR method’s capability in modeling this high-dimensional, non-stationary characteristics of power load data, and to address the challenges faced by its classical mathematical prediction algorithms in effectively solving contemporary prediction scenarios characterized by massive volumes of data. This study proposes a novel learning-based multi-step forecasting approach that utilizes an image-based modeling perspective for the reconstructed phase trajectories. Firstly, the feature engineering approach that simultaneously utilizes dynamic evolution features and temporal locality features in the trajectory image is proposed. Through mathematical derivation, the equivalent characterization of the PSR method and another time series modeling approach, patch segmentation (PS), is demonstrated for the first time. Building on this prior knowledge, a novel image-based modeling perspective incorporating a global and local feature extraction strategy is introduced to fully leverage these valuable features. Subsequently, within this framework, a novel deep learning model, termed PSR-GALIEN, is designed for end-to-end processing. This model employs a Transformer Encoder and 2D convolutional neural networks (CNNs) to extract global and local patterns from the image, while a multi-layer perceptron (MLP)-based predictor is utilized for efficient correlation modeling. Extensive experiments on five real-world datasets show that PSR-GALIEN consistently outperforms six state-of-the-art deep learning models in short-term load forecasting scenarios with varying characteristics, demonstrating its great robustness. Ablation studies further confirm that the image-based modeling approach captures more relevant features than traditional sequential methods, improving the overall forecasting accuracy. Additionally, the attributions of the forecasting results of PSR-GALIEN can be explained through the proposed visualization-based method, which significantly enhances its interpretability.

Enhanced probabilistic damage localization for composite plate based on joint recurrence plots

Localizing damage is a key aspect of monitoring composite laminate structural health. To address the problem of generating the damage index (DI) of composite laminates using Lamb waves, a reconstruction approach for probabilistic damage inspection (RAPID) based on joint recurrence plots (JRP) was proposed. First, the dynamics of the Lamb wave signals are analyzed using phase space reconstruction. Second, the damage information in each sensing path is represented using JRP, and the DI based on the JRP is built with variational auto-encoder (VAE). Finally, the relative magnitude of the DI was employed to modify RAPID’s weight distribution function, allowing for composite plate damage localization detection. The findings of finite element modeling and experiment data reveal that the approach can achieve accurate localization imaging of the composite plate’s interior damage while also properly identifying the damage under 20 dB and 10 dB noise interference. The approach does not require an understanding of Lamb wave dispersion characteristics and involve the extraction of complicated wave packet signals, making it promising for structural health monitoring based on damage index.

Correlation change analysis and NDVI prediction in the Yellow River Basin of China using complex networks and GRNN-PSRLSTM.

The Normalized Difference Vegetation Index (NDVI) is affected by various environmental factors, and its relationship with these factors is complex. In order to explore the complex relationship between NDVI and environmental factors, this paper adopts the complex network method to construct a correlation fluctuation network and analyze the interaction between them. It is found that temperature, precipitation, soil moisture, sunshine duration, and PM2.5 are all correlated with NDVI to varying degrees, and their combined correlation with NDVI varies over time. The correlation typically takes 3 to 6months to change, and it tends to persist to some extent. Moreover, we fuse a generalized regression neural network (GRNN) with a long-short-term memory (LSTM) network combining phase space reconstruction (PSR) to propose a GRNN-PSRLSTM prediction model. The model achieves the prediction of monthly NDVI using the five environmental factors of the fluctuation network. The results indicate that the averages of root mean squared error (RMSE) and mean absolute percentage error (MAPE) predicted by the GRNN-PSRLSTM model in the nine provinces are 0.0232 and 0.0564 respectively. This model performs better in the assessment metrics for monthly NDVI forecasts. These findings are significant for evaluating vegetation changes and have some theoretical value for the ecological protection of the Yellow River Basin.

Long-time prediction of multi-indicator water quality based on the improved WaveNet under time series decomposition and phase space reconstruction

Abstract Long–time prediction of water quality indicator such as chlorophyll–a (Chl–a) is crucial for water process engineering and environmental management. In order to capture the characteristics of long–time series and reduce the limitations of traditional long–time prediction strategies, this paper proposes a novel hybrid model by combining data decomposition, phase space reconstruction, feature fusion and improved WaveNet. Firstly, the original data is decomposed into several subsequences through time series decomposition. Then, the subsequences with chaotic characteristics are integrated with multiple features for phase space reconstruction. Next, the decomposed and reconstructed subsequences are fed back into the improved WaveNet model separately. Finally, the prediction results are obtained by summing the predicted values of the subsequences. In this paper, the reliability of the method is assessed using the dissolved oxygen, water temperature, pH and Chl–a data of a monitoring station in the Beihai coastal sea area, ablation experiments are conducted to demonstrate the effectiveness of each module in the proposed model, and comparisons with multiple benchmark and hybrid models show that the proposed model exhibits better performance in long–time prediction of coastal water quality in the next fourteen days.

Chaotic laser time series prediction based on an improved logistic mapping algorithm echo state network

Chaos synchronization plays vital functions in the fields of optical chaos secure communication. The synchronization performance can be significantly degraded by parameter mismatches between the chaotic transmitter and receiver. In this paper, the Deep-Logistical Mapping Echo State Network (D-LMESN) is proposed to enhance the performance of chaos synchronization. The network is upgraded by using an improved logical mapping algorithm and a deep reserve pool structure with phase space reconstruction. Results show that D-LMESN exhibits better performance in the prediction of chaotic time series, thanks to the adaptive parameter adjustment, which increases the ability to capture the dynamic characteristics of complex systems. Compared with ESN, the mean square error of this model is reduced by 55% and 72%, respectively, in chaotic laser simulation and actual data experiments. This provides a new possibility, to our knowledge, for the development of chaotic secure communication.

Effects of the kinematic variable, time delay and data length on test-retest reliability of the maximal Lyapunov exponent of human walking.

The maximal Lyapunov exponent (MLE) has been used to quantify the dynamic stability of human locomotion. The method for estimating MLE requires selecting a proper time series of kinematic variables and reconstructing phase space using proper time delay. The data length also affects the reliability of the measured MLE. However, there has been no criterion for the choice of the time series, time delay or data length. Here, we quantified the effect of these factors on the test-retest reliability of MLE estimations. We recruited 15 young and healthy adults and let them walk on a treadmill three times. We calculated MLE employing various lengths of time series of 18 frequently used kinematic variables and two typical choices of time delay: fixed delay and delay selected by average mutual information algorithm. Then, we measured the intraclass correlation coefficient (ICC) of the measured MLE under each condition. Our results show that the choice of time delay does not affect reliability. Five among the 18 kinematic variables enabled excellent reliability with ICC above 0.9 within 450 strides and also enabled ICC above 0.75 even with 60 or less strides. These findings can contribute to establishing the criteria for measuring the dynamic stability of human walking.

A novel and effective method for characterizing time series correlations based on martingale difference correlation.

Analysis of correlation between time series is an essential step for complex system studies and dynamical characteristics extractions. Martingale difference correlation (MDC) theory is mainly concerned with the correlation of conditional mean values between response variables and predictor variables. It is the generalization and deepening of the Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, and other statistics. In this paper, on the basis of phase space reconstruction, the generalized dependence index (GDI) is proposed by using MDC and martingale difference divergence matrix theories, which can measure the degree of dependence between time series more effectively. Moreover, motivated by the theoretical framework of the refined distance correlation method, the corresponding dependence measure (DE) is employed in this paper to construct the DE-GDI plane, so as to comprehensively and intuitively distinguish different types of data and deeply explore the operating mechanism behind the relevant time series and complex systems. According to the performances tested by the different simulated and real-world data, our proposed method performs relatively reasonably and reliably in dependence measuring and data distinguishing. The proposal of this complex data clustering method can not only recognize the features of complex systems but also distinguish them effectively so as to acquire more relevant detailed information.

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Next-generation accelerator concepts, which hinge on the precise shaping of beam distributions, demand equally precise diagnostic methods capable of reconstructing beam distributions within six-dimensional position-momentum spaces. However, the characterization of intricate features within six-dimensional beam distributions using current diagnostic techniques necessitates a substantial number of measurements, using many hours of valuable beam time. Novel phase space reconstruction techniques are needed to reduce the number of measurements required to reconstruct detailed, high-dimensional beam features in order to resolve complex beam phenomena and as a feedback in precision beam shaping applications. In this study, we present a novel approach to reconstructing detailed six-dimensional phase space distributions from experimental measurements using generative machine learning and differentiable beam dynamics simulations. We demonstrate that this approach can be used to resolve six-dimensional phase space distributions from scratch, using basic beam manipulations and as few as 20 two-dimensional measurements of the beam profile. We also demonstrate an application of the reconstruction method in an experimental setting at the Argonne Wakefield Accelerator, where it is able to reconstruct the beam distribution and accurately predict previously unseen measurements 75× faster than previous methods. Published by the American Physical Society 2024

Innovative load identification with Res-UNet: Integrating phase space reconstruction and physics-informed deep learning

This study developed a specialized load identification model for a specific ocean platform that integrates advanced deep learning techniques with the unique physical characteristics of marine engineering. Key achievements include high-dimensional mapping of data features using phase space reconstruction (PSR) techniques to enhance the predictive capacity of the model through chaos system theory; optimization of ResNet and UNet deep learning networks with attention mechanisms to boost performance; calculation of stiffness, mass, and damping matrices using finite element software; establishment of corresponding state-space equations; and integration of structural dynamics equations with the deep learning network loss function to significantly improve load identification accuracy. In addition, proprietary structural equations for ocean platform structures were developed, underscoring the uniqueness and applicability of the algorithm. The proposed physics-informed Res-UNet model exhibited excellent performance in identifying both periodic and random loads. These improvements were validated through training with finite element simulated data and subsequent experimental applications, demonstrating the effectiveness of the proposed innovative methods.

Application of cross-channel multiscale permutation entropy in measuring multichannel data complexity.

Entropy is a pivotal concept in nonlinear dynamics, revealing chaos, self-organization, and information transmission in complex systems. Permutation entropy, due to its computational efficiency and lower data length requirements, has found widespread use in various fields. However, in the age of multi-channel data, existing permutation entropy methods are limited in capturing cross-channel information. This paper presents cross-channel multiscale permutation entropy algorithm, and the proposed algorithm can effectively capture the cross-channel information of multi-channel dataset. The major modification lies in the concurrent frequency counting of specific events during the calculation steps. The algorithm improves phase space reconstruction and mapping, enhancing the capability of multi-channel permutation entropy methods to extract cross-channel information. Simulation and real-world multi-channel data analysis demonstrate the superiority of the proposed algorithm in distinguishing different types of data. The improvement is not limited to one specific algorithm and can be applied to various multi-channel permutation entropy variants, making them more effective in uncovering information across different channels.

Unlocking Predictive Capability and Enhancing Sensing Performances of Plasmonic Hydrogen Sensors via Phase Space Reconstruction and Convolutional Neural Networks.

This study innovates plasmonic hydrogen sensors (PHSs) by applying phase space reconstruction (PSR) and convolutional neural networks (CNNs), overcoming previous predictive and sensing limitations. Utilizing a low-cost and efficient colloidal lithography technique, palladium nanocap arrays are created and their spectral signals are transformed into images using PSR and then trained using CNNs for predicting the hydrogen level. The model achieves accurate predictions with average accuracies of 0.95 for pure hydrogen and 0.97 for mixed gases. Performance improvements observed are a reduction in response time by up to 3.7 times (average 2.1 times) across pressures, SNR increased by up to 9.3 times (average 3.9 times) across pressures, and LOD decreased from 16 Pa to an extrapolated 3 Pa, a 5.3-fold improvement. A practical application of remote hydrogen sensing without electronics in hydrogen environments is actualized and achieves a 0.98 average test accuracy. This methodology reimagines PHS capabilities, facilitating advancements in hydrogen monitoring technologies and intelligent spectrum-based sensing.

Wind Speed Forecasting Based on Phase Space Reconstruction and a Novel Optimization Algorithm

The wind power generation capacity is increasing rapidly every year. There needs to be a corresponding development in the management of wind power. Accurate wind speed forecasting is essential for a wind power management system. However, it is not easy to forecast wind speed precisely since wind speed time series data are usually nonlinear and fluctuant. This paper proposes a novel combined wind speed forecasting model that based on PSR (phase space reconstruction), NNCT (no negative constraint theory) and a novel GPSOGA (a hybrid optimization algorithm that combines global elite opposition-based learning strategy, particle swarm optimization and the genetic algorithm) optimization algorithm. SSA (singular spectrum analysis) is firstly applied to decompose the original wind speed time series into IMFs (intrinsic mode functions). Then, PSR is employed to reconstruct the intrinsic mode functions into input and output vectors of the forecasting model. A combined forecasting model is proposed that contains a CBP (cascade back propagation network), RNN (recurrent neural network), GRU (gated recurrent unit), and CNNRNN (convolutional neural network combined with recurrent neural network). The NNCT strategy is used to combine the output of the four predictors, and a new optimization algorithm is proposed to find the optimal combination parameters. In order to validate the performance of the proposed algorithm, we compare the forecasting results of the proposed algorithm with different models on four datasets. The experimental results demonstrate that the forecasting performance of the proposed algorithm is better than other comparison models in terms of different indicators. The DM (Diebold–Mariano) test, Akaike’s information criterion and the Nash–Sutcliffe efficiency coefficient confirm that the proposed algorithm outperforms the comparison models.

HM–GDM: Hybrid Measures and Graph-Dependent Modeling for Environmental Sound Classification

One of the upcoming areas of research is the automated environmental sound classification, as its application is highly utilized in criminal investigations scenarios, surveillance systems, biomedical fields, radio navigation systems, etc. The procedure of environmental sound classification deals with standardized techniques such as feature extraction and feature selection, followed by classification with machine learning or deep learning techniques. In this work, five feature extraction techniques are used initially such as the discrete wavelet transform (DWT)-based empirical mode decomposition (EMD) technique, phase space reconstruction (PSR), kernel principal component analysis (KPCA), variational mode decomposition (VMD) and tunable Q-wavelet transform (TQWT). The extracted features are then selected through seven feature selection techniques, out of which two have been proposed newly and five have already existed. The proposed feature selection techniques are stratified clustered collective technique (SCCT) and fuzzy-based template shape clustering (FTSC). The other feature selection techniques used are the generalized discriminant analysis (GDA), ReliefF, Fisher discriminant criterion (FDC), Kruskal–Wallis test and coati optimization algorithm (COA). The selected features are then classified through the proposed swarm intelligence-based hybrid Adaboost – random forest termed as SIHAR classifier and the selected features are classified with the less explored sparse representation classifier (SRC) along with eight other traditionally used machine learning classifiers. The work also proposes graph-dependent modeling for the environmental sounds where the rhythms are extracted for the similarity assessment and later the decision-making is done using hypothesis testing. The work is tested on Firat ESC-50 dataset and the best results are produced in terms of a high classification accuracy of 87.48% which is obtained for the TQWT + SCCT + SIHAR combination.

Dynamic chaos unveiled: enhancing ship’s attitude time series prediction through spatiotemporal embedding and improved transformer model

Abstract During ship operations at sea, the vessel's attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship's attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a
Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.

Zero-shot fault diagnosis of high-voltage circuit breakers: fusion of phase space reconstruction and attribute embedding methods

Zero-shot fault diagnosis of high-voltage circuit breakers: fusion of phase space reconstruction and attribute embedding methods

Fractional-order state space reconstruction: a new frontier in multivariate complex time series

This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks.

An adaptive feature mode decomposition-guided phase space feature extraction method for rolling bearing fault diagnosis

Abstract The extraction of fault features from rolling bearings is a challenging and highly important task. Since they have complex operating conditions and are usually under a strong noise background. In this study, a novel approach termed phase space feature extraction guided by an adaptive feature mode decomposition (AFMDPSFE) is proposed to detect subtle faults in rolling bearings. Initially, a new method using Kullback-Leiber divergence is introduced to automatically select the optimal mode number and filter length for the decomposition of vibration signals, facilitating the automatic extraction of optimal components and ensuring efficient screening. This eliminates the need for manual configuration of feature mode decomposition parameters. Furthermore, a criterion that could determine two crucial parameters to capture system dynamics characteristics in phase space reconstruction is embedded into AFMDPSFE algorithm. Subsequently, a series of high-dimensional independent components is derived. The envelope spectrum of the principal component exhibiting the highest kurtosis value is computed to achieve fault identification, consequently enhancing the separation of signal from noise. Both simulations and experimental results confirm the effectiveness of AFMDPSFE approach. A comparison analysis shows the excellent performance of AFMDPSFE in extracting fault features from significant noise interference.