Development of a Trainable Classifier of State of Rail Lines with Multiple Patterns of Image Recognition

Introduction. The necessity to classify the state of rail lines affected by significant damaging factors on the sensitive element of the information sensor providing the assurance of classification quality with the required length of the rail lines of the control section forms the task of creating a classifier with extended functionality. Extending the functionality is possible using multidimensional state images with a set of informative features and training procedures for classification models. Using the classical classification principle with a single model leads to an excessive complication of the classification algorithm with low accuracy due to inaccurate solution of the system of conditional equations with multidimensional approximation by Hermite polynomials. Materials and Methods. The principles of reducing the dimension of the features space, various procedures for trainable classifier of state of rail lines with multidimensional patterns, the selection of decisive classification rules with a hierarchical grouping of classes, and the formation of a set of models of varying degrees of complexity trained to solve an incompatible system of equations are considered to solve the problem. There were obtained various degrees of complexity used in the adaptive algorithm for classifying the rail lines states using Hermite polynomials as models. Results. The article presents the results of developing 57 classifier models using Hermite polynomials with features of 2, 3, 4, 5, 6 arguments. As an example, the procedure of developing models with 2–6 features is shown. The research results showed that with an increase in the number of features, the quality of classification improves, as when dividing the state space into several classes. Discussion and Conclusion. The results of the studies confirm the feasibility of the principle of classification of rail line states by a set of classification models, and an algorithm of recursively increasing the classification complexity using a model of increased complexity. The criterion for presenting a new, more complex model is the mismatch between the results of the class calculation by the i-th model and the real class in which the rail line is located at the moment in time.

Optimization of Abnormal Point Cloud Recognition in Robot Vision Grinding System Based on Multidimensional Improved Eigenvalue Method (MIEM)

To improve the accurate and sufficient recognition of abnormal points on the workpiece, a multidimensional anomaly point identification approach based on an improved eigenvalue method is proposed in this paper. Whether a point is normal or not depends on the angle between the two adjacent vectors which consisted of four adjacent points around the current focus. The comprehensive judgment is carried out by multidimensional approximation. The numerical simulation and actual experiment validate the efficiency of the proposed method to quickly and accurately identify the abnormal point cloud in the surface point cloud data.

Multidimensional spline–interpolation–extrapolation methods for approximating hydraulics of steering actuating units for rocket stages

The paper discusses development principles of multidimensional approximation methods for hydraulic properties of throttling windows in slide hydraulic valves of electrohydraulic amplifiers of steering actuator, that are based on cubic spline-interpolation-extrapolation (SIE) of functions. A distinctive feature of the methods that were developed consists in that math simulations do not require complex analytical dependences of the properties, but rather only tabular representation of experimental data is used for their approximation in the course of calculation. The high efficiency of cubic SIE-based multidimensional approximation methods presented in the paper has been proven and demonstrated in math models for static analysis of autonomous one-stage electrohydraulic steering actuators with two- and four-throttle electrohydraulic amplifiers. Thanks to these methods the calculations of static properties of steering actuators within wide ranges of working fluid temperatures and power supply voltages are at present accurate to within ±2%. Key words: multidimensional approximation method, cubic spline-interpolation-extrapolation, electrohydraulic steering actuator.

Tensor-Based Algorithms for Image Classification

Interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced multidimensional approximation of nonlinear dynamics (MANDy), the other an alternating ridge regression in the tensor train format. We apply both methods to the MNIST and fashion MNIST data set and show that the approaches are competitive with state-of-the-art neural network-based classifiers.

GEOMETRIC MEANING OF LEAST SQUARES METHOD

The geometric interpretation of the least squares method is presents. At the same time, one of its possible generalizations to multidimensional space is proposed. This approach makes it possible to expand the capabilities one of the key methods of multidimensional approximation and effectively use it for geometric modeling of multifactor processes and phenomena. The analytical description of the proposed method is performed using point equations. The geometric interpretation of the generalized least squares method, which consists in determining the linear surface of the minimum width between two hypersurfaces in the hyperspace of the General position, extends the tools of geometric modeling objects in multidimensional space and can be effectively used for geometric modeling of multifactor processes and phenomena’s, by presenting them in the form of geometric multiparameter objects passing through predetermined points. In this case, the approximation process is reduced to determining the coordinates of the nodal points of the geometric object of multidimensional space that satisfy the condition of minimizing the sum of the lengths of the segments between the nodal points and the given ones. Also, using the proposed approach, the generalization of the coefficient of determination on the multidimensional space as a tool for assessing the accuracy of the results of multidimensional approximation is performed. An example of using the proposed generalization for the geometric modeling of a three-parameter hypersurface of the response belonging to a four-dimensional space in relation to the determination of strength characteristics over the entire volume of a concrete column is given.

Multidimensional Approximation of Nonlinear Dynamical Systems

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.

Function Prediction at One Inaccessible Point Using Converging Lines

The focus of this paper is a strategy for making a prediction at a point where a function cannot be evaluated. The key idea is to take advantage of the fact that prediction is needed at one point and not in the entire domain. This paper explores the possibility of predicting a multidimensional function using multiple one-dimensional lines converging on the inaccessible point. The multidimensional approximation is thus transformed into several one-dimensional approximations, which provide multiple estimates at the inaccessible point. The Kriging model is adopted in this paper for the one-dimensional approximation, estimating not only the function value but also the uncertainty of the estimate at the inaccessible point. Bayesian inference is then used to combine multiple predictions along lines. We evaluated the numerical performance of the proposed approach using eight-dimensional and 100-dimensional functions in order to illustrate the usefulness of the method for mitigating the curse of dimensionality in surrogate-based predictions. Finally, we applied the method of converging lines to approximate a two-dimensional drag coefficient function. The method of converging lines proved to be more accurate, robust, and reliable than a multidimensional Kriging surrogate for single-point prediction.

High accuracy computational methods for behavioral modeling of thick-film resistors at cryogenic temperatures

The aim of this work was to elaborate two-dimensional behavioral modeling method of thick-film resistors working in low-temperature conditions. The investigated resistors (made from 5 various resistive inks: 10 resistor coupons, each with 36 resistors with various dimensions), were measured automatically in a cryostat system. The low temperature was achieved in a nitrogen-helium continuous-flow cryostat. For nitrogen used as a freezing liquid the minimal temperature possible to achieve was equal to −195.85 °C (77.3 K). Mathematical model in the form of a multiplication of two polynomials was elaborated based on the above mentioned measurements. The first polynomial approximated temperature behavior of the normalized resistance, while the second one described the dependence of resistance on planar resistors dimensions. Special computational procedures for multidimensional approximation purpose were elaborated. It was shown that proper approximation polynomials and sufficiently exact methods of calculations ensure acceptable modeling errors.