Laws of strata energy release and corresponding safety warning system in metal mine

The strata deformation in mining area was monitored in Dabaoshan copper-iron mine,and an analytical method of strata energy release was put forward.On the basis of chaotic theory,by reconstructing the phase space for time series data of strata energy release,the saturated embedding dimension and the correlation dimension of the dynamic system were obtained to be 4 and 1.212 8,respectively,and the evolution laws of distances between phase points of strata energy release in the phase space were revealed.With grey theory,a prediction model of strata energy release was set up,the maximum error of which was less than 6.7%.The results show that there are chaotic characters in strata energy release during mining;after reconstructing phase space,the subtle changing characteristics of energy release can be magnified,and the internal rules can be fully demonstrated.According to the laws,a warning system for strata stability in mining area was established to provide a technical safeguard for safe mining.

基于VMD与MOGOA-LSTM的短期负荷预测模型

为了提高短期负荷预测的准确度,降低非平稳信号对模型预测造成的影响,提出一种集数据挖掘和多目标优化网络于一体的短期负荷预测模型。该方法将电力负荷数据通过变分模态分解技术分解成若干个不同频率的模态分量,采用相间重构方法动态确定人工神经网络的训练测试比和神经元设置,采用长短期记忆神经网络对各分量进行模型搭建,并在长短期记忆神经网络的基础上加入多目标蝗虫智能优化算法来优化网络内部参数,累加所有分量模型预测的值,实现短期负荷预测。仿真结果表明,与统计学方和混合模型相比,本文提出的模型在短期预测方面的预测精度较高、泛化能力更强。

CHARACTERISTICS OF FAN STALLING BASED ON CORRELATED DIMENSIONS

Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.

Local polynomial prediction method of multivariate chaotic time series and its application

To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.

Optimization of support vector machine power load forecasting model based on data mining and Lyapunov exponents

According to the chaotic and non-linear characters of power load data,the time series matrix is established with the theory of phase-space reconstruction,and then Lyapunov exponents with chaotic time series are computed to determine the time delay and the embedding dimension.Due to different features of the data,data mining algorithm is conducted to classify the data into different groups.Redundant information is eliminated by the advantage of data mining technology,and the historical loads that have highly similar features with the forecasting day are searched by the system.As a result,the training data can be decreased and the computing speed can also be improved when constructing support vector machine(SVM) model.Then,SVM algorithm is used to predict power load with parameters that get in pretreatment.In order to prove the effectiveness of the new model,the calculation with data mining SVM algorithm is compared with that of single SVM and back propagation network.It can be seen that the new DSVM algorithm effectively improves the forecast accuracy by 0.75%,1.10% and 1.73% compared with SVM for two random dimensions of 11-dimension,14-dimension and BP network,respectively.This indicates that the DSVM gains perfect improvement effect in the short-term power load forecasting.

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.

Short-term traffic flow prediction with PSR-XGBoostconsidering chaotic characteristics

To improve the level of active traffic management,a short-term traffic flow prediction model is proposed by combining phase space reconstruction(PSR)and extreme gradient boosting(XGBoost)algorithms.Firstly,the traditional data preprocessing method is improved.The new method uses hierarchical clustering to determine the traffic flow state and fills in missing and abnormal data according to different traffic flow states.Secondly,one-dimensional data are mapped into a multidimensional data matrix through PSR,and the time series complex network is used to verify the data reconstruction effect.Finally,the multidimensional data matrix is inputted into the XGBoost model to predict future traffic flow parameters.The experimental results show that the mean square error,average absolute error,and average absolute percentage error of the prediction results of the PSR-XGBoost model are 5.399%,1.632%,and 6.278%,respectively,and the required running time is 17.35 s.Compared with mathematical-statistical models and other machine learning models,the PSR-XGBoost model has clear advantages in multiple predictive indicators,proving its feasibility and superiority in short-term traffic flow prediction.

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.

Human action recognition based on chaotic invariants

A new human action recognition approach was presented based on chaotic invariants and relevance vector machines(RVM).The trajectories of reference joints estimated by skeleton graph matching were adopted for representing the nonlinear dynamical system of human action.The C-C method was used for estimating delay time and embedding dimension of a phase space which was reconstructed by each trajectory.Then,some chaotic invariants representing action can be captured in the reconstructed phase space.Finally,RVM was used to recognize action.Experiments were performed on the KTH,Weizmann and Ballet human action datasets to test and evaluate the proposed method.The experiment results show that the average recognition accuracy is over91.2%,which validates its effectiveness.

Mine water discharge prediction based on least squares support vector machines

In order to realize the prediction of a chaotic time series of mine water discharge,an approach incorporating phase space reconstruction theory and statistical learning theory was studied.A differential entropy ratio method was used to determine embedding parameters to reconstruct the phase space.We used a multi-layer adaptive best-fitting parameter search algorithm to estimate the LS-SVM optimal parameters which were adopted to construct a LS-SVM prediction model for the mine water chaotic time series.The results show that the simulation performance of a single-step prediction based on this LS-SVM model is markedly superior to that based on a RBF model.The multi-step prediction results based on LS-SVM model can reflect the development of mine water discharge and can be used for short-term forecasting of mine water discharge.

A Neural Network based Method for Detection of Weak Underwater Signals

Detection of weak underwater signals is an area of general interest in marine engineering.A weak signal detection scheme was developed; it combined nonlinear dynamical reconstruction techniques, radial basis function (RBF) neural networks and an extended Kalman filter (EKF).In this method chaos theory was used to model background noise.Noise was predicted by phase space reconstruction techniques and RBF neural networks in a synergistic manner.In the absence of a signal, prediction error stayed low and became relatively large when the input contained a signal.EKF was used to improve the convergence rate of the RBF neural network.Application of the scheme to different experimental data sets showed that the algorithm can detect signals hidden in strong noise even when the signal-to-noise ratio (SNR) is less than -40d B.

Nonlinear characteristics and functional analysis of masseter electromyography

The C-C method was adopted to analyze the nonlinear characteristics of masseter electromyography （EMG） signals and the chaotic degree by the largest Lyapunov exponent （LLE） of different genders and sides. First, the embedding dimension and the delay time were obtained through this method, then the phase space was reconstructed to resume the chaotie attractor and determine the LLE. The result shows that the trajectory of attractor is denser than Chen＇s attractor, and the LLE is positive, which means that not only the signal has the character of chaos, but also the chaotic degree of masseter EMG is relatively high. According to the value of the LLE, the chaotic degree of men＇s masseter EMG is higher than that of women＇s; when the dentition is normal, the chaotic degree of two sides is almost the same. Then, a conclusion can be deduced that if the LLE of both sides are in great difference, the unilateral mastication is likely to exist, which means that the nonlinear characteristics of masseter EMG can be applied to predict the unilateral mastication.

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.

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.

Multi-scale prediction of MEMS gyroscope random drift based on EMD-SVR

To improve the prediction accuracy of micro-electromechanical systems(MEMS)gyroscope random drift series,a multi-scale prediction model based on empirical mode decomposition(EMD)and support vector regression(SVR)is proposed.Firstly,EMD is employed to decompose the raw drift series into a finite number of intrinsic mode functions(IMFs)with the frequency descending successively.Secondly,according to the time-frequency characteristic of each IMF,the corresponding SVR prediction model is established based on phase space reconstruction.Finally,the prediction results are obtained by adding up the prediction results of all IMFs with equal weight.The experimental results demonstrate the validity of the proposed model in random drift prediction of MEMS gyroscope.Compared with a single SVR model,the proposed model has higher prediction precision,which can provide the basis for drift error compensation of MEMS gyroscope.

Generic reconstruction technology based on RST for multivariate time series of complex process industries

In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate time series was originally reconstructed by a classical reconstruction technology.Then,the original decision-table of rough set theory was set up according to the embedding dimensions and time-delays of the original reconstruction phase space,and the rough set reduction was used to delete the redundant dimensions and irrelevant variables and to reconstruct the generic phase space,Finally,the input vectors for the prediction of multivariate time series were extracted according to generic reconstruction results to identify the parameters of prediction model.Verification results show that the developed reconstruction method leads to better generalization ability for the prediction model and it is feasible and worthwhile for application.

DATA-MINING BASED FAULT DETECTION

This paper presents a fault-detection method based on the phase space reconstruction and data mining approaches for the complex electronic system. The approach for the phase space reconstruction of chaotic time series is a combination algorithm of multiple autocorrelation and F-test, by which the quasi-optimal embedding dimension and time delay can be obtained. The data mining algorithm, which calculates the radius of gyration of unit-mass point around the centre of mass in the phase space, can distinguish the fault parameter from the chaotic time series output by the tested system. The experimental results depict that this fault detection method can correctly detect the fault phenomena of electronic system.

Approximate Entropy Analysis of Electroencephalogram

Based on the time-delayed embedding method of phase space reconstruction, a new method to compute the approximate entropy （ApEn） of electroencephalogram （EEG） is proposed. The computational results show that there are signiticant differences between epileptic： EEG and normal EEG in the approximate entropy with the variance of embedding dimension. This conclusion is helpful to analyze the dynamical behavior of difibrent EEGs by entropy.

Complex network theory-based condition recognition of electromechanical system in process industry

In order to recognize the different operating conditions of a distributed and complex electromechanical system in the process industry,this work proposed a novel method of condition recognition by combining complex network theory with phase space reconstruction.First,a condition-space with complete information was reconstructed based on phase space reconstruction,and each condition in the space was transformed into a node of a complex network.Second,the limited penetrable visibility graph method was applied to establish an undirected and un-weighted complex network for the reconstructed condition-space.Finally,the statistical properties of this network were calculated to recognize the different operating conditions.A case study of a real chemical plant was conducted to illustrate the analysis and application processes of the proposed method.The results showed that the method could effectively recognize the different conditions of electromechanical systems.A complex electromechanical system can be studied from the systematic and cyber perspectives,and the relationship between the network structure property and the system condition can also be analyzed by utilizing the proposed method.