High-dimensional Phase Space Research Articles

Data Mining in the Vibration Signal of the Trip Mechanism in Circuit Breakers Based on VMD-PSR

To address the difficulty in characterizing early mechanical faults in the trip mechanism of circuit breakers, a data mining method based on variational mode decomposition (VMD) and phase space reconstruction (PSR) method was proposed. First, the vibration signal in the trip stage was separated from the whole according to the current features. Then, it was decomposed using the VMD algorithm to obtain the intrinsic mode functions (IMFs) and these sub signals were mapped to high-dimensional phase space based on the PSR algorithm. Then, the features of the attractor trail shape and the recurrence plot matrixes were extracted. In order to judge the fault in the trip mechanism, a fault simulation test was carried out and the characteristic under different faults was analyzed. Based on these samples, a fault identification model is established by support vector machine (SVM) and the effectiveness is verified by other test samples. The accuracy of the SVM model is 98%, which is higher than that of the BPNN and KNN clustering models. This research supplements the existing method for condition evaluation of the trip mechanism and can provide a reference for circuit breaker fault diagnosis.

Double-layer robust broad logistic regression for detecting weak pulse signal in chaotic interference

Owing to the extreme complexity of detecting weak signals submerged in chaotic interference, traditional neural network detection methods based on hypothesis testing are difficult to sufficiently portray the data and chaotic noise evolution characterization for achieving high effective training, and the hypothesis test usually has the shortcomings of poor generalization performance. In this article, a double-layer robust broad logistic regression (DRBLR) is proposed to overcome the aforementioned issues and achieve highly accurate detection. The proposed method reconstructs the observation signal into a high-dimensional phase space with fixed-size tuples, and it extracts both the chaotic evolution trend and nonlinear structure from these spatiotemporal sequences by broad enhancement and manifold embedding operation of the Robust Manifold Broad Learning System. After that, the weights in Logistic Regression with two layers can be trained based on the obtained features and their corresponding pulse signal labels. The strategy of the DRBLR model leads to a robust learning paradigm and obtains better generalization performance. Experiments to detect weak pulse signals are conducted using Lorenz and sunspot datasets. Simulation results illustrate that the proposed method can better capture the characteristics of the chaotic interference evolution and effectively detect the weak pulse signal in the chaotic noise background.

Multi-Scale Recurrence Quantification Measurements for Voice Disorder Detection

Due to the complexity and non-stationarity of the voice generation system, the nonlinearity of speech signals cannot be accurately quantified. Recently, the recurrence quantification analysis method has been used for voice disorder detection. In this paper, multiscale recurrence quantification measures (MRQMs) are proposed. The signals are reconstructed in the high-dimensional phase space at the equivalent rectangular bandwidth scale. Recurrence plots (RPs) combining the characteristics of human auditory perception are drawn with an appropriate recurrence threshold. Based on the above, the nonlinear dynamic recurrence features of the speech signal are quantized from the recurrence plot of each frequency channel. Furthermore, this paper explores the recurrence quantification thresholds that are most suitable for pathological voices. Our results show that the proposed MRQMs with support vector machine (SVM), random forest (RF), Bayesian network (BN) and Local Weighted Learning (LWL) achieve an average accuracy of 99.45%, outperforming traditional features and other complex measurements. In addition, MRQMs also have the potential for multi-classification of voice disorder, achieving an accuracy of 89.05%. This study demonstrates that MRQMs can characterize the recurrence characteristic of pathological voices and effectively detect voice disorders.

Hybrid quantum-classical reservoir computing of thermal convection flow

We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with three and eight degrees of freedom by a hybrid quantum-classical reservoir computing model. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. A comparison of the quantum reservoir computing model with its classical counterpart shows that the same prediction and reconstruction capabilities of classical reservoirs with thousands of perceptrons can be obtained by a few strongly entangled qubits. We demonstrate that the mean squared error between model output and ground truth in the test phase of the quantum reservoir computing algorithm increases when the reservoir is decomposed into separable subsets of qubits. Furthermore, the quantum reservoir computing model is implemented on a real noisy IBM quantum computer for up to seven qubits. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.

Non-linear feature analysis of public emotion evolution for online teaching during the COVID-19 pandemic

PurposeNowadays, the breakout of the COVID-19 pandemic has caused an important change in teaching models. The emotional experience of this change has an important impact on online teaching. This paper aims to explore its time evolution characteristics and provide reference for the development of online teaching in the post epidemic era.Design/methodology/approachThe article firstly crawls the online teaching-related comment text data on Zhihu platform and performs emotional calculation to obtain a one-dimensional time series of daily average emotional values. Then, by using non-linear time-series analysis, this paper reconstructs the daily average emotion value time series in high-dimensional phase space, calculates the maximum Lyapunov exponent and correlation dimension and finally, explores the feature patterns through recurrence plot and recurrence quantification analysis.FindingsIt was found that the sequence has typical non-linear chaotic characteristics; its correlation dimension indicates that it contains obvious fractal characteristics; the public emotional evolution shows a cyclical rise and fall. By text mining and temporal evolution analysis, this paper explores the evolution law over chronically of the daily average emotion value time series, provides feasible strategies to improve students' online learning experience and quality and continuously optimizes this new teaching model in the era of pandemic.Originality/valueBased on social knowledge sharing platform of Q&A, this paper models and analyzes users interaction data under online teaching-related topics. This paper explores the evolution law over a long time period of the daily average emotion value time series using text mining and temporal evolution analysis. It then offers workable solutions to enhance the quality and experience of students' online learning, and it continuously improves this new teaching model in the age of pandemics.

Exploring phase space with nested sampling

We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to the integration of partonic scattering cross sections and the generation of individual events distributed according to the corresponding squared matrix element. As a first concrete example we consider gluon scattering processes into 3-, 4- and 5-gluon final states and compare the performance with established sampling techniques. Starting from a flat prior distribution Nested Sampling outperforms the Vegas algorithm and achieves results comparable to a dedicated multi-channel importance sampler. We outline possible approaches to combine Nested Sampling with non-flat prior distributions to further reduce the variance of integral estimates and to increase unweighting efficiencies.

Structural damage detection via phase space based manifold learning under changing environmental and operational conditions

The feasibility and performance of existing vibration-based damage detection methods to real world civil engineering structures are inevitably affected by the varying environmental and operational conditions. Reliable damage detection methods with damage features that are sensitive to structural condition change but robust to environmental and loading effects are desirable for practical applications. This paper proposes a novel structural damage detection approach based on manifold learning for the effective condition assessment of real-world structures under environmental and operational conditions. The phase space representation of the vibration characteristics is reconstructed using the identified natural frequencies of structures. Then, the intrinsic nonlinear manifold between the environmental variables and natural frequencies in the high dimensional phase space is projected to a low-dimensional representation via manifold learning. The Gaussian process regression technique is introduced to extract reliable damage index from the learned manifold structure. The effectiveness and superiority of the proposed approach are demonstrated by two real-world engineering structures, that is, the Dowling Hall Footbridge and Z24 bridge. Damage detection results obtained from the proposed approach are compared with those from the current state-of-the-art Kernel PCA method, which is a representative nonlinear dimensionality reduction method to alleviate the environmental effects. The results demonstrate that the proposed approach is sensitive to structural damage but insensitive to changes in environmental and operational conditions. More importantly, the nonlinear environmental effects can be efficiently characterized by the proposed approach, using only partial datasets with environmental variations in the training datasets.

Long-term instability of the inner Solar system: numerical experiments

ABSTRACT Apart from being chaotic, the inner planets in the Solar system constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their high-dimensional phase space. Still, the probability of a dynamical instability is remarkably low over the next 5 billion years, a time-scale 1000 times longer than the Lyapunov time. The dynamical half-life of Mercury has indeed been estimated recently at 40 billion years. By means of the computer algebra system trip, we consider a set of dynamical models resulting from truncation of the forced secular dynamics recently proposed for the inner planets at different degrees in eccentricities and inclinations. Through ensembles of 103–105 numerical integrations spanning 5–100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilization is mainly due to terms of degree 6. This surprising result suggests an analogy to the Fermi–Pasta–Ulam–Tsingou problem, in which tangency to Toda Hamiltonian explains the very long time-scale of thermalization, which Fermi unsuccessfully looked for.

Novel high-dimensional phase space features for EEG emotion recognition

Novel high-dimensional phase space features for EEG emotion recognition

Construction of Multimedia Assisted Legal Classroom Teaching Model Based on Data Mining Algorithm

In order to quickly and accurately retrieve a required part from massive multimedia educational resources and improve the utilization of educational resources, a multimedia assisted legal classroom teaching model based on data mining algorithm is designed. Firstly, the attributes of multimedia assisted legal classroom teaching resources are judged, and the numerical resources are standardized and discretized. Then, the B+ tree is used to establish the model’s indexes and index library, and the corresponding retrieval algorithm is designed to complete the resource search, establish the data distribution structure model of the multimedia assisted legal classroom teaching system, mine the data, reconstruct the phase space of the fused data information flow, extract the high-order moment features of the specific data in the multimedia assisted legal classroom teaching system in the reconstructed high-dimensional phase space, and realize the accurate mining of the feature data. The experimental results show that the teaching effect of the designed model has more advantages and can promote the improvement of students’ performance.

Semi-implicit Hybrid Discrete $$\left( \text {H}^T_N\right) $$ Approximation of Thermal Radiative Transfer

The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing numerical solutions of the TRT equations accurately and efficiently is challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase space that includes the independent variables of time, space, and velocity. In order to reduce the dimensionality of the phase space, classical approaches such as the P\(_N\) (spherical harmonics) or the S\(_N\) (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H\(^T_N\)) approximation to the radiative thermal transfer equations. This approach acquires desirable properties of both P\(_N\) and S\(_N\), and indeed reduces to each of these approximations in various limits: H\(^1_N\) \(\equiv \) P\(_N\) and H\(^T_0\) \(\equiv \) S\(_T\). We prove that H\(^T_N\) results in a system of hyperbolic partial differential equations for all \(T\ge 1\) and \(N\ge 0\). Another challenge in solving the TRT system is the inherent stiffness due to the large timescale separation between propagation and collisions, especially in the diffusive (i.e., highly collisional) regime. This stiffness challenge can be partially overcome via implicit time integration, although fully implicit methods may become computationally expensive due to the strong nonlinearity and system size. On the other hand, explicit time-stepping schemes that are not also asymptotic-preserving in the highly collisional limit require resolving the mean-free path between collisions, making such schemes prohibitively expensive. In this work we develop an asymptotic-preserving numerical method that is based on a nodal discontinuous Galerkin discretization in space, coupled with a semi-implicit discretization in time. In particular, we make use of a second order explicit Runge–Kutta scheme for the streaming term and an implicit Euler scheme for the material coupling term. Furthermore, in order to solve the material energy equation implicitly after each predictor and corrector step, we linearize the temperature term using a Taylor expansion; this avoids the need for an iterative procedure, and therefore improves efficiency. In order to reduce unphysical oscillation, we apply a slope limiter after each time step. Finally, we conduct several numerical experiments to verify the accuracy, efficiency, and robustness of the H\(^T_N\) ansatz and the numerical discretizations.

A continuum approach for multipactor using Vlasov–Poisson analysis

Multipactor is studied based on the coupled Vlasov–Poisson equation set and applied to a parallel plate geometry. This approach can be considered complementary to the particle-in-cell (PIC) methods that have provided excellent insight into multipactor behavior. However, PIC methods have limitations in terms of ‘particle noise,’ which can affect electron energy distribution functions and create re-scaling issues under conditions of charge growth. Utilizing our continuum Vlasov–Poisson approach yields susceptibility curves that are in line with reports in the literature, Spark3D PIC simulations, and experimental data. Playing to the strength of the Vlasov–Poisson approach, the differences between various multipactor orders are elucidated as they are observed in phase-space, revealing electron density dynamics without requiring increased computational resources due to electron growth. The method presented is general and can be extended to multi-input excitations and higher-dimensional phase-space.

The weak Smale horseshoe and mean hyperbolicity

The paper concerns the mean hyperbolicity of the skew-product flows induced by the perturbation equations driven by varieties of non-periodic forcings. The weakly averaged horseshoe can be constructed as a mean hyperbolic invariant set in the Poincare section for high dimensional phase space. Due to the non-periodic property, the Poincare return map restricted to the weakly averaged horseshoe region can semi-conjugate to the full Bernoulli shift on infinite symbols, which implies the infinitely many independent choices on the length of return time. As a direct application of mean hyperbolicity, we extend the shadowing lemma due to Liao to the general nonautonomous dynamical systems.

Adaptive machine learning for time-varying systems: low dimensional latent space tuning

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.

Arnold web and dynamical tunneling in a four-site Bose–Hubbard model

We present the quantum and classical study of a four-well trapped Bose–Einstein condensate (BEC) modeled by the Bose–Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.

Visualizing the phase space of the HeI[formula omitted] van der Waals complex using Lagrangian descriptors

In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic maps. In order to illustrate its use, we apply it to a four-dimensional symplectic map model that is used in chemistry to explore the nonlinear dynamics of van der Waals complexes. The advantage of this technique is that it allows us to easily and effectively extract the invariant manifolds that determine the dynamics of the system under study by means of examining the intersections of the underlying phase space structures with low-dimensional slices. With this approach, one can perform a full computational phase space tomography from which three-dimensional representations of the higher-dimensional phase space can be systematically reconstructed. This analysis may be of much help for the visualization and understanding of the nonlinear dynamical mechanisms that take place in high-dimensional systems. In this context, we demonstrate how this tool can be used to detect whether the stable and unstable manifolds of the system intersect forming turnstile lobes that enclose a certain phase space volume, and the nature of their intersection.

Crisis-induced flow reversals in magnetoconvection.

We report the occurrence of flow reversals induced by the attractor-merging crisis in Rayleigh-Bénard convection of electrically conducting low-Prandtl-number fluids in the presence of a uniform external horizontal magnetic field. The simultaneous collision of two coexisting chaotic attractors with an unstable fixed point and its associated stable manifold takes place in the higher-dimensional phase space of the system, leading to a single merged chaotic attractor. The effect of strength of the magnetic field on the flow reversal phenomena is also explored in detail.

A new approach to measure the fractal dimension of a trajectory in the high-dimensional phase space

In this paper, we introduce a new approach, which measures the fractal dimension (FD) of a trajectory in the multi-dimensional phase space based on the self-similarity of the sub-trajectories. Actually, we first compute the length of the sub-trajectories extracted from zooming out the trajectory in the phase space and then estimate the average length of the sub-trajectories in these zooms. Finally, we also calculate the fractal dimension of the trajectory based on the exponent of the power-law between the average length and the zoom-out size. For validating this approach, we also use the Weierstrass cosine function, which can generate fractured (fractal) trajectories with different dimensions. A set of the EEG segments recorded under the eyes-open and eyes-closed resting conditions is also employed to validate this new method by the data of a natural system. Generally, the outcomes of this method represent that it can well follow variations create in the dimension of a fractal trajectory. Therefore, since this new dimension can be estimated in every high-dimensional phase space, it is a good choice for investigating the dimension and the behavior of the high-dimensional strange attractors.

Research on Non-structural Big Data Analysis Algorithm of Communication Network Based on Feature Fusion

Nowadays, Along with the fast development of information technology, the scale of data is increasing in an exponential way, and the worth of big data has been paid increasingly interested. At present, there are two key problems in the category of big data: how to delegate big data as a integrate model and what efficiently reduce dimensions of big data. Although the processing technology of various mold of data has been studied, the efficiency of parallel query has not been optimized deeply. Especially, it is more difficult to analyze the information of online users with widely dispersed information. A communication network non-structural big data analysis algorithm based on semantic relevance feature fusion is proposed, which reconstructs the high-dimensional phase space of the distributed information flow of cloud storage big data, extracts the semantic relevance dimension feature quantity of big data from the reconstructed phase space, and conducts adaptive learning training with the extracted feature quantity as the test set. Knowable from the simulation experiment that the algorithm effectively reduces the generation of redundant messages and improves the network running environment.

Automated classification of lung sound signals based on empirical mode decomposition

Chronic obstructive pulmonary disease (COPD) is a chronic non-reversible lung disease. Other acute respiratory illness due to infections are termed as non-chronic. In general, the pulmonologist carries preliminary screening by accessing lung sounds. In this paper, we propose a methodology to automatically classify lung sounds associated with non-chronic and chronic categories. To accomplish the task, at first, the empirical mode decomposition (EMD) is applied to lung sound signals to obtain intrinsic mode functions (IMFs). Considering the availability of IMFs in entire dataset and by using a hybrid strategy, first four IMFs have been selected for feature extraction purpose. The IMFs are then further processed to construct two-dimensional (2D) and higher-dimensional (HD) phase space representation (PSR). The feature space includes the 95% confidence ellipse area from 2D-PSR and interquartile range (IQR), mean, median, standard deviation, skewness and kurtosis of Euclidian distances computed from HD-PSR. The process is carried out for the first four IMFs corresponding to the non-chronic and chronic categories of the lung sounds. Neighborhood component analysis is used to select best performing features. The computed and selected features depict a significant ability to discriminate the two categories of lung sound signals. To perform classification, we use ensemble classifiers. Simulation outcomes on ICBHI 2017 lung sound dataset show the ability of the proposed method in effectively classifying non-chronic and chronic lung sound signals. Ensemble of Bagged tree provides the highest classification accuracy of 97.14% over feature space constituted by 10D-PSR of fourth IMF.