Tensor Transfer Learning for Intelligence Fault Diagnosis of Bearing with Semisupervised Partial Label Learning

A new tensor transfer approach is proposed for rotating machinery intelligent fault diagnosis with semisupervised partial label learning in this paper. Firstly, the vibration signals are constructed as a three-way tensor via trial, condition, and channel. Secondly, for adapting the source and target domains tensor representations directly, without vectorization, the domain adaptation (DA) approach named tensor-aligned invariant subspace learning (TAISL) is first proposed for tensor representation when testing and training data are drawn from different distribution. Then, semisupervised partial label learning (SSPLL) is first introduced for tackling a problem that it is hard to label a large number of instances and there exists much data left to be unlabeled. Ultimately, the proposed method is used to identify faults. The effectiveness and feasibility of the proposed method has been thoroughly validated by transfer fault experiments. The experimental results show that the presented technique can achieve better performance.

Thick branes in the scalar–tensor representation of f(R, T) gravity

Braneworld scenarios consider our observable universe as a brane embedded in a five-dimensional bulk. In this work, we consider thick braneworld systems in the recently proposed dynamically equivalent scalar–tensor representation of f(R, T) gravity, where R is the Ricci scalar and T the trace of the stress–energy tensor. In the general $$f\left( R,T\right) $$ f R , T case we consider two different models: a brane model without matter fields where the geometry is supported solely by the gravitational fields, and a second model where matter is described by a scalar field with a potential. The particular cases for which the function $$f\left( R,T\right) $$ f R , T is separable in the forms $$F\left( R\right) +T$$ F R + T and $$R+G\left( T\right) $$ R + G T , which give rise to scalar–tensor representations with a single auxiliary scalar field, are studied separately. The stability of the gravitational sector is investigated and the models are shown to be stable against small perturbations of the metric. Furthermore, we show that in the $$f\left( R,T\right) $$ f R , T model in the presence of an extra matter field, the shape of the graviton zero-mode develops internal structure under appropriate choices of the parameters of the model.

Adapting Neural Turing Machines for linguistic assessments aggregation in neural-symbolic decision support systems

Introduction: The construction of integrated neurosymbolic systems is an urgent and challenging task. Building neurosymbolic decision support systems requires new approaches to represent knowledge about a problem situation and to express symbolic reasoning at the subsymbolic level. Purpose: Development of neural network architectures and methods for effective distributed knowledge representation and subsymbolic reasoning in decision support systems in terms of algorithms for aggregation of fuzzy expert evaluations to select alternative solutions. Methods: Representation of fuzzy and uncertain estimators in a distributed form using tensor representations; construction of a trainable neural network architecture for subsymbolic aggregation of linguistic estimators. Results: The study proposes two new methods of representation of linguistic assessments in a distributed form. The first approach is based on the possibility of converting an arbitrary linguistic assessment into a numerical representation and consists in converting this numerical representation into a distributed one by converting the number itself into a bit string and further forming a matrix storing the distributed representation of the whole expression for aggregating the assessments. The second approach to translating linguistic assessments to a distributed representation is based on representing the linguistic assessment as a tree and coding this tree using the method of tensor representations, thus avoiding the step of translating the linguistic assessment into a numerical form and ensuring the transition between symbolic and subsymbolic representations of linguistic assessments without any loss of information. The structural elements of the linguistic assessment are treated as fillers with their respective positional roles. A new subsymbolic method of aggregation of linguistic assessments is proposed, which consists in creating a trainable neural network module in the form of a Neural Turing Machine. Practical relevance: The results of the study demonstrate how a symbolic algorithm for aggregation of linguistic evaluations can be implemented by connectionist (or subsymbolic) mechanisms, which is an essential requirement for building distributed neurosymbolic decision support systems.

BRAIN STROKE DETECTION USING TENSOR FACTORIZATION AND MACHINE LEARNING MODELS

Stroke is one of the foremost common disorders among the elderly. Early detection of stroke from Magnetic Resonance Imaging (MRI) is typically based on the representation method of these images. Representing MRI slices in two dimensional structures (matrices) implies ignoring the dependencies between these slices. Additionally, to combine all features exist in these slices requires more computations and time. However, this results in inexact diagnosis. In this paper, we propose a new tensor-based approach for stroke detection from MRI. The proposed methodology has two phases. In first phase, each patient’s MRI are represented as a tensor. Tensor representations are powerful because they capture the dependencies in high-dimensional data, MRI of patient, which gives more reliable and accurate results. Also, tensor factorization is used as a method for feature extraction and reduction, which improves the performance and accuracy of classifiers. In second phase, these extracted features are used to train support vector machine (SVM) and XGBoost classifiers to classify MRI images into normal and abnormal. The proposed method is assessed with MRI dataset, and the conducted experiments illustrate the efficiency of this approach. It achieves classification accuracy of 98%.

Another perspective on elastic and plastic anisotropy of textured metals

In textured metals, the elastic directionality reflects the crystallographic organization, while the plastic flow follows the preferential pathways of deformation beyond the elastic limit. In here, the elastic and plastic anisotropies are characterized by two observers. One of them is immersed into the material and, while there, is unaware of the texture-induced reorganizations, still, is in a position to detect elastic distortions. Another observer is located outside the material, monitors the elastic strain too and realizes that texture makes the elastic responses directional. The externally measured elastic strain will be called the texture strain. The key idea is to determine the transformation rules that correlate the elastic strains seen by the two observers. In what follows, the rules are derived by projecting the texture-distorted basis onto the basis of the external observations. It turns out that the rules reproduce directionality of elastic properties and include constraints that result from the limits imposed by the yield stress. The elastic anisotropy is linked to the strain that is free of the plasticity-induced constraints. By contrast, the constraints enable complete characterization of the plastic flow directionality. The concept is derived in the framework of tensor representations discussed in the electronic supplementary material.

The Laplacian on Cartesian products with mixed boundary conditions

A definition of the Laplacian on Cartesian products with mixed boundary conditions using quadratic forms is proposed. Its consistency with the standard definition for homogeneous and certain mixed boundary conditions is proved and, as a consequence, tensor representations of the corresponding Sobolev spaces of first order are derived. Moreover, a criterion for the domain to belong to the Sobolev space of second order is proved.

Relativistic symmetry

This chapter discusses relativistic symmetry, starting from the Lorentz transformations. Basic notions of group theory are introduced before a more detailed discussion of the Lorentz and Poincaré groups is given. Tensor representations and spinor representations of the Lorentz group are described, although full proofs of the theorems are not given. The chapter ends with the irreducible representations of the Poincaré group. This chapter provides all of the necessary notions for group theory, although it is not intended to replace a textbook on the subject.