Digital Analysis of the Vibration Signals Amplitude Spectrum Based on Fourier Processing of the Binary-Sign Analog-Stochastic Quantization Result

Abstract

The article is devoted to the problem of developing a digital algorithm for operational harmonic analysis of complex vibration signals. The basis for solving this problem was the generalized equation of statistical measurements, which defines the measurement procedure as the sequential execution of interrelated measurement and computational transformations. During the development of the algorithm, special attention is paid to analog-to-digital conversion because it directly affects the computational efficiency of digital procedures for obtaining the final result. As such a conversion, the use of binarysign analog-stochastic quantization is justified, which allows performing two-level quantization without systematic error regardless of the statistical properties of the analyzed signals. The discrete-event model of the binary-sign analog-stochastic quantization result allowed for the analytical calculation of integration operations in the transition to estimating the amplitude spectrum in digital form. As a result, the developed algorithm of harmonic analysis does not require performing digital multiplication operations typical for classical algorithms, which are based on the calculation of the direct discrete Fourier transform. The execution of the algorithm is reduced to the implementation of the addition and subtraction arithmetic operations of the cosine-function values in the time moments determined by the result of the binary-sign analogue-stochastic quantization. The exclusion of digital multiplication operations provided an increase in the computational efficiency of amplitude spectrum estimation. Laboratory studies of the developed algorithm were carried out using simulation modeling. The simulation results showed that the algorithm allows calculating estimates of the amplitude spectrum of complex signals with high accuracy and frequency resolution in the presence of additive noise. In real conditions, the testing of the developed algorithm was carried out during bench studies of the operational status of the MAZ-206067 bus, designed for the transportation of passengers on urban and suburban routes of average workload. Analysis of the results of experimental studies confirmed the possibility of using the algorithm as part of the diagnosability provision for operational monitoring of vibration signals in a complex noise environment.