Численный метод обработки результатов динамических измерений

Abstract

The problem of processing data obtained during dynamic measurements is one of the central problems in measuring technology. Purpose of the study. The article is devoted to the study of the stability of the method for solving the problem of processing the results of dynamic measurements with respect to the error in the initial data. Therefore, an urgent task is the development of algorithms for processing the results of dynamic measurements. Materials and methods. This article proposes an algorithm for processing the data obtained during dynamic measurements based on the finite-difference approach. The main prerequisites of the mathematical model of the problem of dynamic measurements associated with the processes of restoration of the input signal in conditions of incomplete and noisy initial data are as follows. Initially, the function of the noisy output signal is known. The restoration of the input signal is carried out using the transfer function of the sensor. The transfer function of the sensor is presented in the form of a differential equation. This equation describes the state of a dynamic system in real time. The proposed computational scheme of the method is based on finite-difference analogs of partial derivatives and the Tikhonov regularization method was used to construct a numerical model of the sensor. The problem of stability of the method for solving high-order differential equations is also one of the central problems of data processing in automatic control systems. Based on the approach of the generalized quasi-optimal choice of the regularization parameter in the Lavrent'ev method, the dependence of the regularization parameter, the parameters of the dynamic measuring system, the noise index and the required level of accuracy was found. Results. The main goal of the computational experiment was to construct a numerical solution to the problem under consideration. Standard test functions were considered as input signals. Test signals simulating various physical processes were used as an input signal. The function of the output signal was found using the proposed numerical method, the found function was noisy with an additive noise of 5 %. Conclusion. The input signal was restored from the noisy signal. The deviation of the reconstructed signal from the initial one in all experiments was no more than 0.05, which indicates the stability of this method with respect to noisy data.