SIMPLIFIED MODEL OF LINEAR INERTIAL MEASUREMENT SYSTEMS

Abstract

Problem. To increase the metrological reliability of measuring systems at technical objects, the number of sensors measuring the same process parameter is increased to several units and a model of a multi-channel measuring system is synthesized. This synthesis is usually based on the use of Markov's theory of linear filtering, but the presence of a connection between the input and output signals of the linear inertial system through the convolution integral significantly complicates the process of obtaining the optimal device. Goal. The aim of the article is to develop a method for approximating the integral equation of convolution, which describes a linear inertial system, and to estimate the limits of its application on the example of linear inertial sensors. Methodology. Instead of the output signal in the form of a convolution equation, the output signal, defined as the product of the input signal to an unknown time function is used. This function is represented by the Karhunen-Loev series. The distance in the functional space with a quadratic metric between these output signals is minimized by means of a genetic algorithm and the coefficients of the series and, therefore, the unknown function itself, are determined. Results. In the simulation, the relative difference between the output signals, which were calculated from exact and simplified expressions, was determined. Realizations of stationary signals were used as input signals, and the pulse characteristics of the linear inertial system varied over a wide range. The errors of approximation of the integral convolution equation by a simple model do not exceed a few percent. Origina-lity. The approximation of the convolution equation by a simplified model of the system is original and, although it cannot be applied in a wide range of conditions, it is acceptable for a separate class of stationary signals without restrictions. The accuracy of the approximation of the convolution equation is greatest if the width of the spectrum of the input signals is less than the bandwidth of the measuring system. Practical value. The obtained connection between input and output signals based on a simplified model allows to synthesize multi-channel measuring systems using advanced Markov filtering methods for a separate class of stationary input signals. To expand the application of the method in a wide range of conditions, a set of simplified models that are created in advance can be used.