INERTIAL RELAXED TSENG METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACE

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the existing literature used are successfully weakened. The strong convergence of the proposed method to a minimum-norm solution of a variational inequality problem are established. Furthermore, we present an application and some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature.

Estimating efficiency of forecasting technical conditions of ship propulsion systems

The article considers an approach to assessing the effectiveness of the most common methods of predicting the technical conditions and failure with reference to the ship shafting. There have been analyzed the main factors in operation of the ship shaft line, which cause the change in its technical state. It has been found that a special feature of some loads acting on the propeller shaft is their stochastic or changing nature over time, which hampers predicting the technical state of the shafting and its units. The features of stochastic and extrapolation forecasting methods have been analyzed. The possibility of using statistical methods in conditions of mass standard production of shafting units with a relatively short regulated service life is estimated. An extrapolation method is proposed for predicting the maximum permissible clearance of stern tube bearings. The case of accumulating samples of measuring results of the propeller shaft sagging in the given time intervals is considered, the approximating functions are constructed. The criteria for the reliability of the results of extrapolation methods for predicting the wear of stern tube bearings are determined. There have been developed the proposals for adapting the causal method as an alternative to the extrapolation method. A schematic diagram of a system for the ship shafting failure predicting has been developed using the registration and analysis of vibration parameters, which serves as the basis for constructing a regression model of damage accumulation. The proposed forecasting system allows studying the actual operating conditions of the shafting, defining the actual external loads and the regularities of their occurrence, measuring deformations and stresses, and determining quantitative indicators of the reliability of the shafting during normal operation and special operating modes, for example, with vibration resonance. The theoretical basis of the algorithm for calculating and registering loads affecting the service life of shafts is proposed.

APPLICATION OF STATISTICAL TECHNIQUES IN THE PRACTICE OF BUILDING A DEFILIENCE SCALE

The main substantial features of the PD curve (default probability) formed in practical modeling are substantiated in the articles. It is proved that the main characteristics of the PD curve are that it is based on data on the actually restored default rate in each of the risk classes over a period of time and has a shape that approximate for coincides with the exposure function. It is shown that the best aspect that affects the calibration is the number of rating classes and ways to build them. It is determined that the slope of the curve demonstrates the classification model of efficiency. It is determined that the slope of the curve demonstrates the classification efficiency of the model. Models with high discriminant properties are characterized by a curve shape that has a slow increase in the rating classes of the upper part of the scale and a significant acceleration of growth in the last risk classes. Two main approaches to determining the number of risk classes are analyzed: the percentile-based approach and the equal score range approach. It is shown that when forming classes, it is necessary to take into account the total amount of sample observations, the proportion of «good» and «bad», and choose the number of classes so that it is not too large and not too small. Calibration practice shave been shown to be influenced by data, purpose, and study limitations. The application of the least squares method and the extrapolation method is considered on practical examples. The least squares method and in particular the derived extrapolation method allow to build a calibration curve on the basis of data on the relative frequency of defaults. It is determined that the mathematical apparatus of the family of nonlinear curves allows to model the process of exponential growth with different levels of intensity. The exponential curve and related functions may be useful in modeling more conservative PD estimates or for models with highly discriminatory properties, while the Weibull function, S-curve, and power function may be better adapted to moderate growth processes. The application of practical methods of constructing the PD scale is important for many domestic banking professionals who deal with internal models of credit risk. Keywords: Calibration, Default, Probability, Curves, Probability of default curve calibration, Least squares method, Extrapolation method. JEL Classіfіcatіon С44 Formulas: 21; fig.: 1; tabl.: 7; bibl.: 10.

Compilation of Load Spectrum for 5MN Metal Extruder Based on Long Short-Term Memory Network

As an important condition for fatigue analysis and life prediction, load spectrum is widely used in various engineering fields. The extrapolation of load samples is an important step in compiling load spectrum. It is of great significance to select an appropriate load extrapolation method. This paper proposes a load extrapolation method based on long short-term memory (LSTM) network, introduces the basic principle of the extrapolation method, and applies the method to the data set collected under the working state of 5MN metal extruder. The comparison between the extrapolated load data and the actual load shows that the trend of the extrapolated load data is basically consistent with the original tendency. In addition, this method is compared with the rain flow extrapolation method based on statistical distribution. Through the comparison of the short-term load spectrum compiled by the two extrapolation methods, it is found that the load spectrum extrapolation method based on LSTM network can better realize load prediction and optimize the compilation of load spectrum.