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.

Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space

We study thermodynamics of charged AdS black hole surrounded by quintessence in a new formalism which is called the restricted phase space thermodynamics.This context is based on Visser’s holographic thermodynamics with a fixed antide Sitter radius and a variable Newton constant.The conjugate variables,central charge C and the chemical potential m,are introduced as a new pair of thermodynamic variables.We find that the iso-e-charge T-S curve becomes non-monotonic when Q<Q_(c).Correspondingly,the F-T curve exhibits a swallow tail structure.This behavior is considered as a van der Waals-like phase transition.As the value of b related to the energy density of Kiselev’s fluid becomes larger,the critical temperature T_(c)will decrease.Thus,the van derWaals-like phase transition will occur at lower temperature.There is always a non-quilibrium transition from a small unstable black hole to a large stable black hole state in the isocoltage T-S process.There exist a maximum and a Hawking-Page phase transition points in theμ-C plane.As the value of b related to Kiselev’s fluid becomes larger,the Hawking-Page phase transition will occur at lower temperature in the isovoltageμ-T process.For other values of the state parameterω,there also exists van der Waals-like phase transition.

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.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

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.

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.

New conserved quantities of Noether-Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.

Noether-Mei Symmetry of Mechanical System in Phase Space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i,e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the Bpplication of the results.

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.

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.

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.

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.

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.

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.

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.

Perturbation to Noether-Mei Symmetry and Adiabatic Invariants for Nonholonomic Mechanical Systems in Phase Space

Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction of chaotic time series. The effectiveness of themethod is demonstrated by applying it to the Henon map. This study also compares nu-support vectormachine with back propagation (BP) networks in order to better evaluate the performance of theproposed methods. The experimental results show that the nu-support vector machine regressionobtains lower root mean squared error than the BP networks and provides an accurate chaotic timeseries prediction. These results can be attributable to the fact that nu-support vector machineimplements the structural risk minimization principle and this leads to better generalization thanthe BP networks.

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.

THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV'S TYPE IN PHASE SPACE

The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.