Sparseness-controlled non-negative tensor factorization and its application in machinery fault diagnosis

Aiming at the problems of bispectral analysis when applied to machinery fault diagnosis, a machinery fault feature extraction method based on sparseness-controlled non-negative tensor factorization （SNTF） is proposed. First, a non-negative tensor factorization（NTF） algorithm is improved by imposing sparseness constraints on it. Secondly, the bispectral images of mechanical signals are obtained and stacked to form a third-order tensor. Thirdly, the improved algorithm is used to extract features, which are represented by a series of basis images from this tensor. Finally, coefficients indicating these basis images＇ weights in constituting original bispectral images are calculated for fault classification. Experiments on fault diagnosis of gearboxes show that the extracted features can not only reveal some nonlinear characteristics of the system, but also have intuitive meanings with regard to fault characteristic frequencies. These features provide great convenience for the interpretation of the relationships between machinery faults and corresponding bispectra.

Local hierarchical non-negative tensor factorization and its application in machinery fault diagnosis

Aiming at the slow convergence and low accuracy problems of the traditional non-negative tensor factorization, a local hierarchical non-negative tensor factorization method is proposed by applying the local objective function theory to non- negative tensor factorization and combining the three semi-non- negative matrix factorization（NMF） model. The effectiveness of the method is verified by the facial feature extraction experiment. Through the decomposition of a series of an air compressor＇s vibration signals composed in the form of a bispectrum by this new method, the basis images representing the fault features and corresponding weight matrices are obtained. Then the relationships between characteristics and faults are analyzed and the fault types are classified by importing the weight matrices into the BP neural network. Experimental results show that the accuracy of fault diagnosis is improved by this new method compared with other feature extraction methods.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Solving sparse non-negative tensor equations： algorithms and applications

We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.

Prognostic model for prostate cancer based on glycolysis-related genes and non-negative matrix factorization analysis

Background:Establishing an appropriate prognostic model for PCa is essential for its effective treatment.Glycolysis is a vital energy-harvesting mechanism for tumors.Developing a prognostic model for PCa based on glycolysis-related genes is novel and has great potential.Methods:First,gene expression and clinical data of PCa patients were downloaded from The Cancer Genome Atlas(TCGA)and Gene Expression Omnibus(GEO),and glycolysis-related genes were obtained from the Molecular Signatures Database(MSigDB).Gene enrichment analysis was performed to verify that glycolysis functions were enriched in the genes we obtained,which were used in nonnegative matrix factorization(NMF)to identify clusters.The correlation between clusters and clinical features was discussed,and the differentially expressed genes(DEGs)between the two clusters were investigated.Based on the DEGs,we investigated the biological differences between clusters,including immune cell infiltration,mutation,tumor immune dysfunction and exclusion,immune function,and checkpoint genes.To establish the prognostic model,the genes were filtered based on univariable Cox regression,LASSO,and multivariable Cox regression.Kaplan–Meier analysis and receiver operating characteristic analysis validated the prognostic value of the model.A nomogram of the risk score calculated by the prognostic model and clinical characteristics was constructed to quantitatively estimate the survival probability for PCa patients in the clinical setting.Result:The genes obtained from MSigDB were enriched in glycolysis functions.Two clusters were identified by NMF analysis based on 272 glycolysis-related genes,and a prognostic model based on DEGs between the two clusters was finally established.The prognostic model consisted of LAMPS,SPRN,ATOH1,TANC1,ETV1,TDRD1,KLK14,MESP2,POSTN,CRIP2,NAT1,AKR7A3,PODXL,CARTPT,and PCDHGB2.All sample,training,and test cohorts from The Cancer Genome Atlas(TCGA)and the external validation cohort from GEO showed significant differences between the high-risk and low-risk groups.The area under the ROC curve showed great performance of this prognostic model.Conclusion:A prognostic model based on glycolysis-related genes was established,with great performance and potential significance to the clinical application.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances.The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers.The proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time convergence.Since all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability.Finally,simulation results validate the effectiveness of the proposed method.

Evaluating Partitioning Based Clustering Methods for Extended Non-negative Matrix Factorization (NMF)

Data is humongous today because of the extensive use of World WideWeb, Social Media and Intelligent Systems. This data can be very important anduseful if it is harnessed carefully and correctly. Useful information can beextracted from this massive data using the Data Mining process. The informationextracted can be used to make vital decisions in various industries. Clustering is avery popular Data Mining method which divides the data points into differentgroups such that all similar data points form a part of the same group. Clusteringmethods are of various types. Many parameters and indexes exist for the evaluationand comparison of these methods. In this paper, we have compared partitioningbased methods K-Means, Fuzzy C-Means (FCM), Partitioning AroundMedoids (PAM) and Clustering Large Application (CLARA) on secure perturbeddata. Comparison and identification has been done for the method which performsbetter for analyzing the data perturbed using Extended NMF on the basis of thevalues of various indexes like Dunn Index, Silhouette Index, Xie-Beni Indexand Davies-Bouldin Index.

三维稳态Q-tensor液晶流系统各向异性的Liouville型定理

考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<q<∞,则该稳态系统只有平凡解.这个结论推广了已有的结果.

Uniqueness and perturbation bounds for sparse non-negative tensor equations

We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the efficiency of the theoretical results.

Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions

In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.

Research on Tensor Multi-Clustering Distributed Incremental Updating Method for Big Data

The scale and complexity of big data are growing continuously,posing severe challenges to traditional data processing methods,especially in the field of clustering analysis.To address this issue,this paper introduces a new method named Big Data Tensor Multi-Cluster Distributed Incremental Update(BDTMCDIncreUpdate),which combines distributed computing,storage technology,and incremental update techniques to provide an efficient and effective means for clustering analysis.Firstly,the original dataset is divided into multiple subblocks,and distributed computing resources are utilized to process the sub-blocks in parallel,enhancing efficiency.Then,initial clustering is performed on each sub-block using tensor-based multi-clustering techniques to obtain preliminary results.When new data arrives,incremental update technology is employed to update the core tensor and factor matrix,ensuring that the clustering model can adapt to changes in data.Finally,by combining the updated core tensor and factor matrix with historical computational results,refined clustering results are obtained,achieving real-time adaptation to dynamic data.Through experimental simulation on the Aminer dataset,the BDTMCDIncreUpdate method has demonstrated outstanding performance in terms of accuracy(ACC)and normalized mutual information(NMI)metrics,achieving an accuracy rate of 90%and an NMI score of 0.85,which outperforms existing methods such as TClusInitUpdate and TKLClusUpdate in most scenarios.Therefore,the BDTMCDIncreUpdate method offers an innovative solution to the field of big data analysis,integrating distributed computing,incremental updates,and tensor-based multi-clustering techniques.It not only improves the efficiency and scalability in processing large-scale high-dimensional datasets but also has been validated for its effectiveness and accuracy through experiments.This method shows great potential in real-world applications where dynamic data growth is common,and it is of significant importance for advancing the development of data analysis technology.

Fault Diagnosis Scheme for Railway Switch Machine Using Multi-Sensor Fusion Tensor Machine

Railway switch machine is essential for maintaining the safety and punctuality of train operations.A data-driven fault diagnosis scheme for railway switch machine using tensor machine and multi-representation monitoring data is developed herein.Unlike existing methods,this approach takes into account the spatial information of the time series monitoring data,aligning with the domain expertise of on-site manual monitoring.Besides,a multi-sensor fusion tensor machine is designed to improve single signal data’s limitations in insufficient information.First,one-dimensional signal data is preprocessed and transformed into two-dimensional images.Afterward,the fusion feature tensor is created by utilizing the images of the three-phase current and employing the CANDE-COMP/PARAFAC(CP)decomposition method.Then,the tensor learning-based model is built using the extracted fusion feature tensor.The developed fault diagnosis scheme is valid with the field three-phase current dataset.The experiment indicates an enhanced performance of the developed fault diagnosis scheme over the current approach,particularly in terms of recall,precision,and F1-score.

Optimizing Recovery Following Mihata Superior Capsular Reconstruction Surgery with Tensor Fascia Lata Auto Graft: A Comprehensive Rehabilitation Protocol

Objective: Superior Capsular Reconstruction (SCR) using a Tensor Fascia Lata (TFL) autograft is an evolving technique for treating irreparable rotator cuff tears. The Mihata technique, initially developed in Japan, has shown promising long-term results. However, a standardized post-operative rehabilitation protocol for this procedure in the USA is lacking. Purpose: This study aims to evaluate the outcomes of a comprehensive rehabilitation protocol following SCR with TFL autograft in a cohort of nine patients. Participants and Methods: A prospective observational study was conducted at Concentra Urgent Care, San Francisco. Nine patients, aged 55 - 65 years, underwent SCR with TFL autograft performed by a specialized orthopedic surgeon. Post-operative rehabilitation was managed using a structured protocol, divided into three phases focusing on passive exercises, progressive range of motion, and strengthening. Outcomes were measured using the Visual Analogue Scale (VAS) for pain, forward flexion range of motion (FF-ROM), and Single Assessment Numeric Evaluation (SANE) scores over a six-month period. Results: Significant improvements were observed in pain reduction (mean VAS decrease of −3.67 points, p = 0.01), ROM (mean FF increase of 41.11 degrees, p = 0.014), and SANE scores (mean improvement of 42.11%, p = 0.009), indicating the efficacy of the rehabilitation protocol. Conclusion: The comprehensive rehabilitation protocol following SCR with TFL autograft significantly improved pain, range of motion, and shoulder function in patients, suggesting its potential utility in clinical practice.

Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Implementing and evaluating an automatic centroid moment tensor procedure for the Indonesia region and surrounding areas

The purpose of this research was to suggest an applicable procedure for computing the centroid moment tensor(CMT)automatically and in real time from earthquakes that occur in Indonesia and the surrounding areas.Gisola software was used to estimate the CMT solution by selecting the velocity model that best suited the local and regional geological conditions in Indonesia and the surrounding areas.The data used in this study were earthquakes with magnitudes of 5.4 to 8.0.High-quality,real-time broadband seismographic data were provided by the International Federation of Digital Seismograph Networks Web Services(FDSNWS)and the European Integrated Data Archive(EIDA)Federation in Indonesia and the surrounding areas.Furthermore,the inversion process and filter adjustment were carried out on the seismographic data to obtain good CMT solutions.The CMT solutions from Gisola provided good-quality solutions,in which all earthquake data had A-level quality(high quality,with good variant reduction).The Gisola CMT solution was justified with the Global CMT(GCMT)solution by using the Kagan angle value,with an average of approximately 11.2°.This result suggested that the CMT solution generated from Gisola was trustworthy and reliable.The Gisola CMT solution was typically available within approximately 15 minutes after an earthquake occurred.Once it met the quality requirement,it was automatically published on the internet.The catalog of local and regional earthquake records obtained through this technology holds great promise for improving the current understanding of regional seismic activity and ongoing tectonic processes.The accurate and real-time CMT solution generated by implementing the Gisola algorithm consisted of moment tensors and moment magnitudes,which provided invaluable insights into earthquakes occurring in Indonesia and the surrounding areas.

Prediction of(n,2n)reaction cross-sections of long-lived fission products based on tensor model

Interest has recently emerged in potential applications of(n,2n)reactions of unstable nuclei.Challenges have arisen because of the scarcity of experimental cross-sectional data.This study aims to predict the(n,2n)reaction cross-section of long-lived fission products based on a tensor model.This tensor model is an extension of the collaborative filtering algorithm used for nuclear data.It is based on tensor decomposition and completion to predict(n,2n)reaction cross-sections;the corresponding EXFOR data are applied as training data.The reliability of the proposed tensor model was validated by comparing the calculations with data from EXFOR and different databases.Predictions were made for long-lived fission products such as^(60)Co,^(79)Se,^(93)Zr,^(107)P,^(126)Sn,and^(137)Cs,which provide a predicted energy range to effectively transmute long-lived fission products into shorter-lived or less radioactive isotopes.This method could be a powerful tool for completing(n,2n)reaction cross-sectional data and shows the possibility of selective transmutation of nuclear waste.

A Novel Tensor Decomposition-Based Efficient Detector for Low-Altitude Aerial Objects With Knowledge Distillation Scheme

Unmanned aerial vehicles(UAVs) have gained significant attention in practical applications, especially the low-altitude aerial(LAA) object detection imposes stringent requirements on recognition accuracy and computational resources. In this paper, the LAA images-oriented tensor decomposition and knowledge distillation-based network(TDKD-Net) is proposed,where the TT-format TD(tensor decomposition) and equalweighted response-based KD(knowledge distillation) methods are designed to minimize redundant parameters while ensuring comparable performance. Moreover, some robust network structures are developed, including the small object detection head and the dual-domain attention mechanism, which enable the model to leverage the learned knowledge from small-scale targets and selectively focus on salient features. Considering the imbalance of bounding box regression samples and the inaccuracy of regression geometric factors, the focal and efficient IoU(intersection of union) loss with optimal transport assignment(F-EIoU-OTA)mechanism is proposed to improve the detection accuracy. The proposed TDKD-Net is comprehensively evaluated through extensive experiments, and the results have demonstrated the effectiveness and superiority of the developed methods in comparison to other advanced detection algorithms, which also present high generalization and strong robustness. As a resource-efficient precise network, the complex detection of small and occluded LAA objects is also well addressed by TDKD-Net, which provides useful insights on handling imbalanced issues and realizing domain adaptation.

Least Squares One-Class Support Tensor Machine

One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.

关于Focal Loss的Tensor Train多项式分类器

在模式分类领域,多项式分类器因其复杂决策边界能力而得到广泛研究。利用TensorTrain分解形式来表示多项式分类器,可有效克服维数灾难。针对多项式分类器在训练过程中遇到的训练集分布不平衡问题,文章使用FocalLoss重塑了标准交叉损失,以降低分配给易分类样本的损失的权重,并在被广泛使用的图像分类数据集MNIST上验证了分类器的有效性。