Global Optimization Method to Multiple Local Optimals with the Surface Approximation Methodology and Its Application for Industry Problems

Although generally speaking, a great number of functional evaluations may be required until convergence, it can be solved by using neural network effectively. Here, techniques to search the region of interest containing the global optimal design selected by random seeds is investigated. Also techniques for finding more accurate approximation using Holographic Neural Network (HNN) improved by using penalty function for generalized inverse matrix is investigated. Furthermore, the mapping method of extrapolation is proposed to make the technique available to general application in structural optimization. Application examples show that HNN may be expected as potential activate and feasible surface functions in response surface methodology than the polynomials in function approximations. Finally, the real design examples of a vehicle performance such as idling vibration, booming noise, vehicle component crash worthiness and combination problem between vehicle crashworthiness and restraint device performance at the head-on collision are used to show the effectiveness of the proposed method.

LU Decomposition method to solve bipolar fuzzy linear systems

The aim of this work is to solve the linear system of equations using LU decomposition method in bipolar fuzzy environment. We assume a special case when the coefficient matrix of the system is symmetric positive definite. We discuss this point in detail by giving some numerical examples. Moreover, we investigate m × n inconsistent bipolar fuzzy matrix equation and find the least square solution of the inconsistent bipolar fuzzy matrix using the generalized inverse matrix theory. The existence of the strong bipolar fuzzy least square solution of the inconsistent bipolar fuzzy matrix is discussed. In the end, a numerical example is presented to illustrate our proposed method.

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

This paper presents a new scheme for solving m-polar fuzzy system of linear equations (m-PFSLEs) by using LU decomposition method. We assume the coefficient matrix of the system is symmetric positive definite, and we discuss this point in detail with some numerical examples. Furthermore, we investigate the inconsistent m×nm-polar fuzzy matrix equation (m-PFME) and find the least square solution (LSS) of this system by using generalized inverse matrix theory. Moreover, we discuss the strong solution of m-polar fuzzy LSS of the inconsistent m-PFME. In the end, we present a numerical example to illustrate our approach.

The specificities of the research in the economics’ development of Sevastopol

A comprehensive study of regional processes implies a qualitative analysis of indicators over time, which is necessary not only to identify current trends, but also to make forecasts that are used in the development of regional development strategies and programs. In order to study the development of the city of Sevastopol on the basis of statistical data on the state of the economy in the Ukrainian and Russian periods, as well as determine the possibility of their use for making forecasts, it is necessary to solve the issue of homogeneity of the series of economic indicators. The existing criteria for verifying the homogeneity of data are not applicable to the solution of the issue of compatibility of multidimensional series belonging to different time intervals. The article proposes the use of exploratory factor analysis to solve this problem. However, the lack of statistical data leads to a degeneration of the matrix of pairwise correlations of economic indicators. To obtain estimates of the parameters of the factor model, a generalized inverse matrix is used, which is obtained as a result of a matrix iterative procedure. Exploratory factor models for the Ukrainian and Russian periods of Sevastopol have fundamental differences, and the corresponding multidimensional series cannot be combined for a holistic study of economic processes in the region.

Position-based impedance force controller with sensorless force estimation

Purpose This paper aims to purpose an improved sensorless position-based force controller in gravitational direction for applications including polishing, milling and deburring. Design/methodology/approach The first issue is the external force/torque estimation at end-effector. By using motor’s current information and Moore-Penrose generalized inverse matrix, it can be derived from the external torques of every joints for nonsingular cases. The second issue is the force control strategy which is based on position-based impedance control model. Two novel improvements were made to achieve a better performance. One is combination of impedance control and explicit force control. The other one is the real-time prediction of the surface’s shape allowing the controller adaptive to arbitrary surfaces. Findings The result of validation experiments indicates that the estimation of external force and prediction of surface’s shape are credible, and the position-based constant contact force controller in gravitational direction is functional. The accuracy of force tracking is adequate for targeted applications such as polishing, deburring and milling. Originality/value The value of this paper lies in three aspects which are sensorless external force estimation, the combination of impedance control and explicit force control and the independence of surface shape information achieved by real-time surface prediction.