Heterogeneous information phase space reconstruction and stability prediction of filling body–surrounding rock combination

Traditional research believes that the filling body can effectively control stress concentration while ignoring the problems of unknown stability and the complex and changeable stress distribution of the filling body–surrounding rock combination under high-stress conditions.Current monitoring data processing methods cannot fully consider the complexity of monitoring objects,the diversity of monitoring methods,and the dynamics of monitoring data.To solve this problem,this paper proposes a phase space reconstruction and stability prediction method to process heterogeneous information of backfill–surrounding rock combinations.The three-dimensional monitoring system of a large-area filling body–surrounding rock combination in Longshou Mine was constructed by using drilling stress,multipoint displacement meter,and inclinometer.Varied information,such as the stress and displacement of the filling body–surrounding rock combination,was continuously obtained.Combined with the average mutual information method and the false nearest neighbor point method,the phase space of the heterogeneous information of the filling body–surrounding rock combination was then constructed.In this paper,the distance between the phase point and its nearest point was used as the index evaluation distance to evaluate the stability of the filling body–surrounding rock combination.The evaluated distances(ED)revealed a high sensitivity to the stability of the filling body–surrounding rock combination.The new method was then applied to calculate the time series of historically ED for 12 measuring points located at Longshou Mine.The moments of mutation in these time series were at least 3 months ahead of the roadway return dates.In the ED prediction experiments,the autoregressive integrated moving average model showed a higher prediction accuracy than the deep learning models(long short-term memory and Transformer).Furthermore,the root-mean-square error distribution of the prediction results peaked at 0.26,thus outperforming the no-prediction method in 70%of the cases.

Classification of power quality combined disturbances based on phase space reconstruction and support vector machines

Power Quality (PQ) combined disturbances become common along with ubiquity of voltage flickers and harmonics. This paper presents a novel approach to classify the different patterns of PQ combined disturbances. The classification system consists of two parts, namely the feature extraction and the automatic recognition. In the feature extraction stage, Phase Space Reconstruction (PSR), a time series analysis tool, is utilized to construct disturbance signal trajectories. For these trajectories, several indices are proposed to form the feature vectors. Support Vector Machines (SVMs) are then implemented to recognize the different patterns and to evaluate the efficiencies. The types of disturbances discussed include a combination of short-term dis-turbances (voltage sags, swells) and long-term disturbances (flickers, harmonics), as well as their homologous single ones. The feasibilities of the proposed approach are verified by simulation with thousands of PQ events. Comparison studies based on Wavelet Transform (WT) and Artificial Neural Network (ANN) are also reported to show its advantages.

Prediction of elevator traffic flow based on SVM and phase space reconstruction

To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.

Degradation Process of Coated Tinplate by Phase Space Reconstruction Theory

The degradation process of organosol coated tinplate in beverage was investigated by electrochemical noise (EN) technique combined with morphology characterization.EN data were analyzed using phase space reconstruction theory.With the correlation dimensions obtained from the phase space reconstruction,the chaotic behavior of EN was quantitatively evaluated.The results show that both electrochemical potential noise (EPN) and electrochemical current noise (ECN) have chaotic properties.The correlation dimensions of EPN increase with corrosion extent,while those of ECN seem nearly unchanged.The increased correlation dimensions of EPN during the degradation process are associated with the increased susceptibility to local corrosion.

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Study on resource quantity of surface water based on phase space reconstruction and neural network

Proposed a new method to disclose the complicated non-linearity structure of the water-resource system, introducing chaos theory into the hydrology and water resources field, and combined with the chaos theory and artificial neural networks. Training data construction and networks structure were determined by the phase space reconstruction, and establishing nonlinear relationship of phase points with neural networks, the forecasting model of the resource quantity of the surface water was brought forward. The keystone of the way and the detailed arithmetic of the network training were given. The example shows that the model has highly forecasting precision.

Analysis of dynamic of two-phase flow in small channel based on phase space reconstruction combined with data reduction sub-frequency band wavelet

A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems(Lorenz and Rssler) to examine the anti-noise ability for complex systems. Results show that the nonlinear dynamic system analysis method resists noise and reveals the internal dynamics of a weak signal from noise pollution. On this basis, the vertical upward gas–liquid two-phase flow in a 2 mm × 0.81 mm small rectangular channel is investigated. The frequency and energy distributions of the main oscillation mode are revealed by analyzing the time–frequency spectra of the pressure signals of different flow patterns. The positive power spectral density of singular-value frequency entropy and the damping ratio are extracted to characterize the evolution of flow patterns and achieve accurate recognition of different vertical upward gas–liquid flow patterns(bubbly flow:100%, slug flow: 92%, churn flow: 96%, annular flow: 100%). The proposed analysis method will enrich the dynamics theory of multi-phase flow in small channel.

Transverse phase space reconstruction study in Shanghai soft X-ray FEL facility

Phase space is one of the most important parameters used to describe beam properties. Computer tomography, as a method for reconstructing phase space and measuring beam emittance, has been used in many accelerators over the past few decades. In this paper, we demonstrate a transverse phase space reconstruction study in the Shanghai soft X-ray free electron laser facility. First,we discuss the basic principles of phase space reconstruction and the advantage of reconstructing beam distribution in normalized phase space. Then, the phase space reconstruction results by different computer tomography methods based on the maximum entropy(MENT) algorithm and the filtered back projection algorithm in normalized phase space are presented. The simulation results indicate that,with proper configuration of the phase advance between adjacent screens, the MENT algorithm is feasible and has good efficiency. The beam emittance and Twiss parameters are also calculated using the reconstructed phase space.

A Phase Space Reconstruction Based Approach to Throughput Prediction in Semiconductor Wafer Fabrication System

In order to manage and control semiconductor wafer fabrication system (SWFS) more effectively,the daily throughput prediction data of wafer fab are often used in the planning and scheduling of SWFS.In this paper,an artificial neural network (ANN) prediction method based on phase space reconstruction (PSR) and ant colony optimization (ACO) is presented,in which the phase space reconstruction theory is used to reconstruct the daily throughput time series,the ANN is used to construct the daily throughput prediction model,and the ACO is used to train the connection weight and bias values of the neural network prediction model.Testing with factory operation data and comparing with the traditional method show that the proposed methodology is effective.

PARAMETERS DETERMINATION METHOD OF PHASE-SPACE RECONSTRUCTION BASED ON DIFFERENTIAL ENTROPY RATIO AND RBF NEURAL NETWORK

Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.

SELECTION OF PROPER EMBEDDING DIMENSION IN PHASE SPACE RECONSTRUCTION OF SPEECH SIGNALS

In phase space reconstruction of time series, the selection of embedding dimension is important. Based on the idea of checking the behavior of near neighbors in the reconstruction dimension, a new method to determine proper minimum embedding dimension is constructed. This method has a sound theoretical basis and can lead to good result. It can indicate the noise level in the data to be reconstructed, and estimate the reconstruction quality. It is applied to speech signal reconstruction and the generic embedding dimension of speech signals is deduced.

Application of phase space reconstruction and v-SVR algorithm in predicting displacement of underground engineering surrounding rock

A new method for predicting the trend of displacement evolution of surroundingrock was presented in this paper.According to the nonlinear characteristics of displace-ment time series of underground engineering surrounding rock,based on phase spacereconstruction theory and the powerful nonlinear mapping ability of support vector ma-chines,the information offered by the time series datum sets was fully exploited and thenon-linearity of the displacement evolution system of surrounding rock was well described.The example suggests that the methods based on phase space reconstruction and modi-fied v-SVR algorithm are very accurate,and the study can help to build the displacementforecast system to analyze the stability of underground engineering surrounding rock.

Prediction of seawater pH by bidirectional gated recurrent neural network with attention under phase space reconstruction:case study of the coastal waters of Beihai,China

Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.

Deep learning approach to detect seizure using reconstructed phase space images

Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various image processing,signal processing,and machine-learning based techniques are employed to analyze epilepsy,using spatial and temporal features.The nervous system that generates the EEG signal is considered nonlinear and the EEG signals exhibit chaotic behavior.In order to capture these nonlinear dynamics,we use reconstructed phase space(RPS) representation of the signal.Earlier studies have primarily addressed seizure detection as a binary classification(normal vs.ictal) problem and rarely as a ternary class(normal vs.interictal vs.ictal)problem.We employ transfer learning on a pre-trained deep neural network model and retrain it using RPS images of the EEG signal.The classification accuracy of the model for the binary classes is(98.5±1.5)% and(95±2)% for the ternary classes.The performance of the convolution neural network(CNN) model is better than the other existing statistical approach for all performance indicators such as accuracy,sensitivity,and specificity.The result of the proposed approach shows the prospect of employing RPS images with CNN for predicting epileptic seizures.

Neural network forecasting model based on phase space re-construction in water yield of mine

The neutral network forecasting model based on the phase space reconstruction was proposed. First, through reconstructing the phase space, the time series of single variable was done excursion and expanded into multi- dimension series which included the ergodic information and more rich information could be excavated. Then, on the basis of the embedding dimension of the time series, the structure form of neutral network was constructed, of which the node number in input layer was the embedding dimension of the time series minus 1, and the node number in output layers was 1. Finally, as an example, the model was applied for water yield of mine forecasting. The result shows that the model has good fitting accuracy and forecasting precision.

融合核极限学习机与PSR的混沌交通流预测

传统短时交通流预测精度低、稳定性差,提出一种结合改进蝴蝶算法优化核极限学习机与相空间重构的短时交通流预测模型。结合量子自适应种群初始化、邻域扰动和惯性权重对蝴蝶算法改进,利用改进蝴蝶算法对核极限学习机超参寻优。利用混沌理论确定样本时序最佳延迟时间和嵌入维数,利用PSR对样本重构,利用优化核极限学习机建立短时混沌交通流预测模型。采用郑州市某主干路口车流实测数据进行实证分析,其结果表明,改进模型能够有效降低预测误差,实现混沌交通流实时准确预测。

基于MPSR和IRBM的电力系统中长期负荷预测

针对电力系统中长期负荷波动大及不确定因素导致负荷预测误差较大的问题,提出了一种基于多变量相空间重构(MPSR)和改进受限波尔兹曼机(IRBM)的电力系统中长期负荷预测方法。首先,利用多元线性回归分析方法分析天气因素与电负荷之间的相关性,并将其与电负荷序列组成多变量时间序列;然后,利用C-C法确定每一时间序列的最优嵌入维数和时间延迟,实现多变量相空间重构;最后,采用多变量相空间重构建立的数据集训练电力系统负荷预测模型,同时利用梯度优化法对参数进行优化,得到预测模型。结果表明:相比长短期记忆神经网络和粒子群优化BP神经网络,所提出的预测方法有较高的精准度。

基于PSR和SVM方法的化工过程单变量故障诊断

基于相空间重构(PSR)和支持向量机(SVM)算法本文提出了一种利用单一变量进行化工过程故障诊断的方法。首先进行变量筛选,然后对筛选出的关键变量进行相空间重构,再利用SVM对重构后的数据进行故障分类。通过对TE(Tennessee Eastman)过程几类故障进行仿真测试,结果表明在单一故障和多故障情况下,本方法均可实现化工过程的单变量故障诊断;与传统SVM方法相比,相空间重构可有效提高诊断正确率。此方法可为建立简单而有效的单变量故障诊断系统提供理论依据。

基于PSRT与Elman神经网络的短期负荷多步预测

短期负荷预测(short-term load forcastings,STLF)对电力系统的经济和安全运行有着重要的作用。为提高短期负荷预测的精度,根据短期负荷的基本特性,提出了一种将相空间重构理论(phase space reconstruction space,PSRT)与Elman神经网络相结合的短期负荷多步预测模型。首先利用PSRT重构相空间的吸引子,然后用Elman神经网络来拟合相空间吸引子的多步演化,其中利用空间欧氏距离来选取Elman网络的输入样本。通过对广西电网短期负荷预测的分析表明,该多步预测方法是有效可行的。

安全预测的EEMD-PSR-Elman建模方法及应用

为分析安全预测中时间序列的非平稳特性并提高预测精度,提出基于集合经验模态分解（EEMD）、相空间重构（PSR）及神经网络的预测建模方法。首先应用EEMD方法将时间序列分解成若干具有不同周期性或趋势性的分量,通过C-C方法计算各分量的最佳嵌入维数和延迟时间;然后分别进行相空间重构;再应用Elman神经网络对各分量进行训练并建立预测模型;最后将各分量预测结果叠加得到最终预测值。用该方法分析反映煤矿安全生产的关键性指标——煤炭生产百万吨死亡率。结果得到具有长期趋势性和周期性波动的5个分量,预测相对误差为-0.11%~0.20%;外推预测表明,中国煤炭生产百万吨死亡率将保持持续下降趋势,至2020年将下降到0.05以下。