Phase Space Reconstruction Theory Research Articles

Chaotic characterization and chaotic prediction modelling of HFSWR ionospheric echoes excited by typhoon

ABSTRACT This research explores the intricate-coupling relationship between typhoons and the ionosphere by the high-frequency surface wave radar’s (HFSWR) over-the-horizon capabilities. This letter describes the gravity wave features in travelling ionospheric disturbances (TIDs) and ionospheric drift information. Further discussion is raised on the chaotic properties of gravity wave features using the Lyapunov exponents and chaotic attractors, particularly as they are influenced by typhoon. To predict these gravity wave features more accurately, a new model is developed by synergizing phase space reconstruction theory and statistical learning theory, a chaotic prediction model for gravity wave features constructed on a third-order Volterra filter. The experimental findings confirm that the gravity waves features detected via HFSWR present the hyperchaotic behaviour. More importantly, the innovative gravity wave prediction model based on chaotic attractor can capture the dynamics of the original chaotic system. Notably, the model’s prediction accuracy has been improved by 98.6% after the introduction of phase space reconstruction modelling.

Chaotic index analysis of ethanol-based graphene nanofluid pulsating heat pipe

Pulsating heat pipes utilizing ethanol-based graphene nanofluids hold significant promise for cooling large electronic devices. However, traditional methods fall short in fully characterizing their properties due to internal phase transitions, latent heat, multiphase flow, and multi-field coupling. To address this, nonlinear chaotic analysis methods are introduced. This study constructs a vertical closed-loop pulsating heat pipe platform and applies Takens embedding theorem, phase space reconstruction theory, mutual information recursive selection method, and associative dimensionality algorithm to analyze ethanol-based graphene nanofluids with various concentrations. The investigation focuses on correlation dimensions and Kolmogorov entropy to provide numerical feedback on nanofluid concentration. Notably, ethanol-based graphene nanofluids concentrations between 0.04 wt% and 0.07 wt% exhibit an average heat transfer thermal resistance of approximately 0.74 K/W, corresponding to correlation dimension and Kolmogorov entropy values of 1.36 and 0.035, respectively. Additionally, reconstructed three-dimensional Singular Attractor phase diagrams offer morphological feedback on the pulsating heat pipe's working conditions. As the ethanol-based graphene nanofluids concentration reaches 0.35 wt%, an increase in the number of free vector points within the three-dimensional coordinate Attractor indicates localized unstable conditions in the heat pipe. Employing a wavelet noise reduction method with a soft threshold of 80 preserves the macroscopic vector flow pattern while eliminating irrelevant local information. Overall, this paper introduces novel approaches for analyzing heat transfer characteristics of graphene nanofluids in pulsating heat pipes.

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.

Enterprise Supply Chain Risk Assessment Based on the Support Vector Machine Algorithm and Fuzzy Model

In systems with uncertain information, ambiguity must be taken into account. In this paper, fuzzy set theory concepts are incorporated into support vector machines (SVM). This ensemble preserves the benefits of SVM regression models and fuzzy regression models, where SVM learning theory describes the properties of learning machines that enable them to generalize well, and fuzzy set theory offers an efficient method for capturing the approximate, imprecise properties of the real world. In accordance with the phase space reconstruction theory of dynamical systems, a fuzzy model for enterprise supply chain risk assessment is proposed using the robust nonlinear mapping capability of support vector machines and the characteristic of fuzzy logic that makes it easy to combine prior system knowledge into fuzzy rules. The results demonstrate that the prediction model can not only automatically acquire knowledge from learning data to generate fuzzy rules but can also extract support vectors that can represent the inherent laws of enterprise supply chain risks, drastically reduce the number of support vectors, and accurately predict. Future risk can be accurately predicted. This conclusion suggests that the support vector machine based on a fuzzy model is an effective method for analyzing enterprise supply chain risk.

Improved Hybrid Model for Predicting Concrete Crack Openings Based on Chaos Theory

Conventional statistical models provide inaccurate predictions of concrete crack openings because they do not consider the nonlinear temperature response and the residual characteristics of concrete. To address this problem, this study introduces a nonlinear temperature factor and develops an improved statistical model of crack openings. The chaotic characteristics of residual time series of the improved statistical model are analyzed based on chaos theory and phase-space reconstruction theory. These theories are integrated with back-propagation (BP) artificial neural networks and genetic algorithms (GAs) to establish a GA-BP neural network model for predicting residuals. Finally, a hybrid model is developed for predicting the concrete crack opening behavior. The predictions of the conventional statistical model, the statistical model considering nonlinear temperature component, and the hybrid model are compared using the case study on the crack openings of a regulating sluice. The results show that the proposed hybrid model in this study for predicting concrete crack openings is significantly more accurate than the conventional statistical model and the statistical model considering nonlinear temperature component.

LA-LMRBF: Online and Long-Term Web Service QoS Forecasting

We propose a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</u> ong-term Quality of Service (QoS) forecasting approach using <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u> dvertisement and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</u> evenberg- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</u> arquardt improved <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> adial <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</u> asis <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</u> unction (LA-LMRBF)—a novel online QoS forecasting approach. LA-LMRBF aims to accurately predict QoS attributes of Web services in the form of multivariate time series via three stages. First, the phase space reconstruction theory is employed to restore multi-dimensional and nonlinear relations among the multivariate QoS attributes. Second, short-term QoS advertisement data is incorporated to enable long-term QoS forecasting. Finally, an optimized Radial Basis Function (RBF) neural network is constructed to forecast long-term multivariate QoS values, where the Affinity Propagation clustering algorithm is used to determine the number of hidden nodes and the Levenberg-Marquardt (LM) algorithm is utilized to dynamically update some parameters of the RBF neural network. A series of experiments are performed on a mixture of public and self-collected data sets. The results show that LA-LMRBF is superior to the other approaches and more suitable for long-term QoS forecasting.

A novel approach of dependence measure for complex signals

The distance correlation (DC) statistics is capable of describing the nonlinear correlation between random variables, which is the extension and reinforcement of the existing Pearson correlation coefficient, Spearman rank correlation coefficient, Kendall coefficient of concordance, etc. However, there are difficulties in using the DC statistics to measure the dynamical features of complex signals directly. So in this work, we introduce the refined distance correlation (RDC). Motivated by the cross-sample entropy (CSE), a state-of-the-art measure, we propose the dependence measure (DM) based on the RDC and the phase space reconstruction theory, aiming to capture linear and nonlinear dynamical features from various kinds of complex signals with higher accuracy. The RDC also includes the modified version of distance dependence statistics that overcomes the natural defect of the original DC. We first apply the RDC and the DM into simulation signals to testify whether they are effective in detecting different dynamical features. Afterward, we apply our methods to analyze real-world data. We affirm that our methods are capable of obtaining more detailed information by comparing it to the CSE. Finally, we combine the DM and the CSE to construct the DM–CSE plane. By applying it to the existing data, more distinctive and rational clustering results of complex systems are obtained.

Traffic Flow Characteristics mining of Time Series Data Based on Phase Space Reconstruction Using Complex Networks

Traffic flow time series is vital for mining the traditional statistical characteristics by using the theory of statistics and machine learning when its identity is a special time series. The network analysis of the traffic flow time series, who uses the complex network of time series analysis method, is designed to inquire into the special law of traffic flow time series which uses its visualization characteristics. Through the network analysis of traffic data flow, the connotation of traffic data flow can be revealed, and the relationship between all data and some data can be further studied. Therefore, it is constructed by combination with the phase space reconstruction theory. The phase space trajectory may be squeezed and the structure of attractor may change. We need to use C-C method to estimate the time delay according to the characteristics of integral parameters, and use G-P algorithm to estimate the embedding dimension to avoid it. This study can effectively reveal the motion law of the system. After constructing the complex network of traffic flow time series with various traffic parameters, the degree distribution, clustering coefficient and modularization of the representative critical threshold corresponding network are statistically analysed. The analysis results show that the new networked structure of traffic flow time series proposed in this study has strong advantages, and its core is phase space reconstruction, which can well reflect the information space of traffic dynamic fluctuation. The time series networking method based on phase space reconstruction has become a new approach to inquire into the characteristics of traffic flow time series. The degree distribution of the actual multi-traffic parameter time series construction network satisfies the characteristics of a Gaussian distribution. Their average clustering coefficients have attenuation characteristics, and their modularization degree is obvious.

A multiple-parameter approach for short-term traffic flow prediction

This study proposes a short-term traffic flow prediction approach based on multiple traffic flow basic parameters, in which the chaos theory and support vector regression are utilized. First, a high-dimensional variable space can be obtained according to the traffic flow fundamental function. Then, a maximum conditional entropy method is proposed to determine the embedding dimension. And multiple time series are reconstructed based on the phase space reconstruction theory using the time delay obtained by mutual information method and the embedding dimension captured by the maximum conditional entropy method. Finally, the reconstructed phase space is used as the input and the support vector regression optimized by the genetic algorithm is utilized to predict the traffic flow. Numerical experiments are performed and the results show that the approach proposed has strong fitting capability and better prediction accuracy.

Network Public Opinion Prediction and Control Based on Edge Computing and Artificial Intelligence New Paradigm

In this paper, an adaptive edge service placement mechanism based on online learning and a predictive edge service migration method based on factor graph model are proposed to solve the edge computing service placement problem from the edge computing dimension. First, the time series of the development of online chaotic public opinion is a platform for vectorized collection of keyword index trends using the theory of chaotic phase space reconstruction. Secondly, it is necessary to use the main index method to judge whether the time series has the chaotic characteristics of the network public opinion data. The simulation results show that network public opinion is the development characteristic of chaotic time series. Finally, the prediction model is improved by using complex network topology. Through the simulation experiment of network public opinion and chaotic time series, the results show that the improved model has the advantages of accuracy, rapidity, and self‐adaptability and can be applied to other fields.

Prediction of Sea Clutter Based on Recurrent Neural Network

As radar sea clutter has chaotic characteristics, a prediction model can be established to predict sea clutter according to short-term predictability of chaotic time series. Therefore, this paper proposes a sea clutter amplitude prediction model based on LSTM, Stacked LSTM and Nested LSTM. This paper first obtains the best state space for sea clutter prediction according to the phase space reconstruction theory and establishes the prediction equation, then uses three networks to predict the sea clutter amplitude, and finally compares the effects of the three neural networks and analyzes the factors that affect the prediction precision. The experimental results on the IPIX radar data and P-band radar data show that, the model used in this paper has a smaller prediction error than RBF, and the prediction performance is better. The model can achieve high-precision and high-efficiency prediction of sea clutter and has verified the effectiveness of the method.

Monthly Streamflow Prediction Based on Random Forest Algorithm and Phase Space Reconstruction Theory

In order to find an effective time series forecasting method, a random forest prediction model based on phase space reconstruction theory is proposed in this paper. The Cao method and mutual information function method are used to reconstruct the phase space, and the parameters of the random forest (RF) model are discussed. The feasibility of the model is verified by analyzing the monthly runoff data of Pingshan hydrological station in Jinsha River Basin. Compared with BP neural network (BPnet) model and traditional support vector machine (SVM) model which optimizes parameters by grid algorithm, random forest model has higher prediction accuracy and less calculation in dealing with complex nonlinear hydrological time series as shown by the result.

Performance Degradation Prediction Based on a Gaussian Mixture Model and Optimized Support Vector Regression for an Aviation Piston Pump.

Performance degradation prediction plays a key role in realizing aviation pump health management and condition-based maintenance. Thus, this paper proposes a new approach that combines a Gaussian mixture model (GMM) and optimized support vector regression (SVR) to predict aviation pumps’ degradation processes based on the pump outlet pressure signals. Different from other feature extraction methods in which the information of intrinsic mode functions (IMFs) is not fully utilized, some useful IMF components are firstly chosen, and the corresponding multi-domain features are extracted from each selected component. Considering that it is not the case that all features are equally sensitive to degradation assessment, PCA is used to select more sensitive degradation features. Since the distribution of these extracted features is a stochastic process in feature space, meanwhile, self-information quantity can describe the uncertainty of system by measuring the average information quantity contained in the probability distribution, self-information quantity based on GMM is defined as degradation index (DI) to describe the degradation degree of the pump quantitatively. Finally, an SVR model is constructed to predict the degradation status of the pump. To achieve higher prediction accuracy, phase space reconstruction theory is first employed to determine the number of the inputs of the SVR model, then a new method combining particle swarm optimization (PSO) with grid search (GS) is developed to optimize the parameters of the SVR model. Finally, both the online data and historical data are utilized for the construction of the SVR model, respectively. The effectiveness of the proposed approach is validated by full life cycle data collected from an aviation pump test rig. The results demonstrate that the DI extracted from pump outlet pressure signals can effectively identify and track the current deterioration stage, and the established SVR model has better prediction ability when compared with previously published methods.

Nonlinear Dynamic Feature Extraction Based on Phase Space Reconstruction for the Classification of Speech and Emotion

Due to the shortcomings of linear feature parameters in speech signals, and the limitations of existing time- and frequency-domain attribute features in characterizing the integrity of the speech information, in this paper, we propose a nonlinear method for feature extraction based on the phase space reconstruction (PSR) theory. First, the speech signal was analyzed using a nonlinear dynamic model. Then, the model was used to reconstruct a one-dimensional time speech signal. Finally, nonlinear dynamic (NLD) features based on the reconstruction of the phase space were extracted as the new characteristic parameters. Then, the performance of NLD features was verified by comparing their recognition rates with those of other features (NLD features, prosodic features, and MFCC features). Finally, the Korean isolated words database, the Berlin emotional speech database, and the CASIA emotional speech database were chosen for validation. The effectiveness of the NLD features was tested using the Support Vector Machine classifier. The results show that NLD features not only have high recognition rate and excellent antinoise performance for speech recognition tasks but also can fully characterize the different emotions contained in speech signals.

Short-term traffic volume prediction using GA-BP based on wavelet denoising and phase space reconstruction

Accurate traffic volume prediction can help traffic managers to control traffic well,and can also provide convenient travel routes for passengers. In order to better describe the non-stationary, complex and spatial correlation of traffic volume, the traffic prediction model is proposed based on wavelet denoising and phase space reconstruction (WD-PSR-GA-BP). Pure traffic volume is firstly preprocessed by wavelet denoising method. Subsequently, the prediction model is built by BP neural network, which is optimized by genetic algorithm. In addition, one-dimensional traffic volume is mapped to high-dimensional space by the theory of phase space reconstruction. The inputsof the prediction model are obtained by the reconstructed traffic volume datasets. In order to verify the effectiveness of the proposed model, two groups of datasets and different models are studied in the experiment of Section 4. The experimental results show that the proposed model is superior to all other competitors in terms of MAPE, RMSE, and MAE.

Time series prediction based on deep confidence network

The timing deep belief network model (T-DBN) is proposed to solve the problems of gradient dispersion, local minimum, poor long-term prediction performance of nonlinear time series prediction and high complexity of high-dimensional sequence data in traditional computer neural networks. In the pre-training stage, the improved greedy pre-training algorithm is adopted. In the pre-training process, the gradient fixing parallel tempering (GFPT) algorithm is used to determine the depth of network by reconstruction error. In the stage of reverse adjustment, the quasi-newton method (BFGS) is adopted to obtain more accurate prediction performance. Combined with the theory of phase space reconstruction and BP (back propagation) neural network, the total power of agricultural machinery in Jiangxi province of China from 2016 to 2020 is predicted. For the highly nonlinear stock data, the characteristics of the Shanghai stock exchange index from 1990-12-20 to 2018-03-30 are extracted from the stock data of Tonghuashun software. T-DBN, DBN and long short-term memory (LSTM) models areused for stock forecasting with the prediction accuracy of 79.3%, 77.9% and 74.6%, respectively. The experimental results demonstrate the better prediction performance of T-DBN model in comparison with DBN and LSTM models.

Research of Mapping Element Space Method for Uncertain Lurie System Stability Diagnosis

A new diagnosis method of Lurie system stability by using Chaotic time series data was proposed in order to solve stability analysis of flight control system with fault and uncertain. Firstly, the reasons for the instability of the nonlinear system of Ruri leaf was analyzed by using the small gain theory and linear matrix inequalities in the robust control theory. And the stability conditions of Rui leaf system under the condition of uncertainty and failure were proved theoretically. In order to quantify the stability of nonlinear systems in complex Ruri leaves, based on the theory of phase space reconstruction, the nonlinear Ruri system with continuous discrete characteristics was converted into an approximate time discrete equation, mapping it to a low dimensional primitive space, by introducing Q Gauss function into Kernel function, the generalization ability of neural networks are enhanced, realizing the stability analysis method based on the characteristic of primitive migration, which is suitable for various fault and uncertainty conditions, and the relative quantized stability norm can be given. The simulation shows that the present method can effectively solve the stability analysis and determination of flight control system under various factors.

Exploring the fluctuant transmission characteristics of Air Quality Index based on time series network model

Abstract Although many works have focused on the issues related to Air Quality Index (AQI) from the perspective of statistics or economics, the dynamic and temporal characteristics of AQI time series remain unclear. The main reason is that AQI time series has both non-linearity and complexity, which cannot be characterized by conventional ways. The inherent transmission laws of AQI volatility are of great importance for environment monitoring and management system. Thus, this paper has endeavored to address the issue from the interdisciplinary perspective of complex network theory. First, we collect the annual and the total AQI data of three cities (Shanghai, Wuhan and Guangzhou) in China from January 1, 2015 to December 31, 2017. Then the coarse graining method is employed in combination with the theory of phase space reconstruction to convert AQI time series into complex network. The coarse graining method is used to transform yearly and total AQI time series into the corresponding symbol sequences. In accordance with the theory of phase space reconstruction, we adopt C C method and false nearest neighbor algorithm to estimate the optimal time delay and embedding dimension of AQI time series, respectively. The optimal time delay is integrated with the embedding dimension to map symbol sequences into AQI complex network. Based on complex network theory, we investigate the transmission of AQI fluctuation by the temporal characteristics and dynamics of yearly AQI networks (YAN) and total AQI networks (TAN), which include node strength, betweenness centrality and community structure. The empirical results show: (1) the AQI networks of various periods display small-world effect; (2) network evolution tends to be more complex and the modality in YAN has less alternative transformation paths than that in TAN; (3) the node strength and betweenness centrality in measuring the importance of nodes achieve a relative consistency; (4) the three cities have the same dominant fluctuation modalities both in YAN and in TAN; (5) the uneven distribution of transmission ability between clusters implies a preferential transmission whether in YAN or TAN. These findings not only help us to interpret the frequent volatility of AQI and control some extreme short-term AQI fluctuation, but also contribute to the reliability assessment of AQI and the prediction of AQI fluctuation. In summary, this paper not only reveals the temporal dynamic properties of AQI time series, but also provides some policy recommendations for environmental monitoring and management.

Nonlinear dynamics model for social popularity prediction based on multivariate chaotic time series

In online social network, it is of great significance in the popularity perception of social topics. Aiming to deeply analyze the nonlinear dynamics mechanism in the propagation process of social topics, the chaotic characteristics of information dissemination are thoroughly explored in this paper, and Bayesian estimation theory is employed to integrate the cross-platform factors affecting the topic popularity. Firstly, the time series of topic popularity from different platforms are redefined. And Principal Component Analysis (PCA) method is introduced to quantize the redefined time series and receive the main components affecting popularity. Secondly, this paper focuses on specific topics and performs small-data method to calculate the maximum Lyapunov exponent, which can be found that there are chaotic characteristics in time series of topic popularity. Then, the main components affecting popularity are reconstructed based on the phase space reconstruction theory, and the chaotic attractor is recovered in the high-dimensional reconstructed phase space. Smoothly, the evolution regularities and properties of complex system are restored to perceive the propagating situation of topic popularity. At the same time, the novel and fused phase space is obtained by using the Bayesian estimation theory to optimally fuse multiple variables in the same high-dimensional space. Finally, RBF (Radial Basis Function) neural network is employed to predict the fused popularity due to its strong ability to approximate nonlinear functions. Experiments show that the prediction approach can not only merge topic popularity from multiple social platforms, but also can improve the prediction accuracy to some degree. In the meanwhile, the developing trend of topics can be perceived from a more fine-grained perspective.

Mechanical behaviors and acoustic emission fractal characteristics of coal specimens with a pre-existing flaw of various inclinations under uniaxial compression

To study the influence of hydraulic slotting inclination on the mechanical behaviors of coal seam during mining process, uniaxial compression experiments on coal specimens with a single pre-existing flaw inclined at 0°, 15°, 30°, 45°, 60°, 75°, 90° and intact specimens were conducted. Acoustic emission (AE) signals in the loading process were monitored, and fractal analysis method was introduced to investigate the AE characteristics. Additionally, the laboratory experiments were simulated by a finite element code. Both the experimental and numerical results show that the existence of a flaw reduces the mechanical properties of coal. The uniaxial compressive strength and modulus of elasticity increase polynomially and linearly with the increase of inclination angle, respectively. When the coal specimen ruptures finally, the fewer the surface secondary cracks or the more the sudden drops of stress, the smaller the peak value of AE count. According to the stress–strain curve, the loading process is divided into five stages: (I) compaction stage; (II) linear elastic stage; (III) stable crack propagation stage; (IV) accelerating crack propagation stage; (V) post peak and residual stage. AE fractal characteristics in various stages of each specimen were determined by Grassberger and Procaccia algorithm based on phase space reconstruction theory. AE count show fractal characteristics from stage III. The fractal dimension declines rapidly in stage IV, and continues to decline further or rise slightly in stage V, but both are lower than that in stage III. Therefore, the changing rule of AE fractal dimension in different loading stages can be used as a precursor to coal and rock dynamic disasters.