Vibration measurement with nonlinear converter in the presence of noise

Abstract

Conventional vibration measurement methods use the linear properties of physical converters. These methods are strongly influenced by nonlinear distortions, because ideal linear converters are not available. Practically, any converter can be considered as a linear one, when an output signal is very small. However, the influence of noise increases significantly and signal-to-noise ratio decreases at lower signals. When the output signal is increasing, the nonlinear distortions are also augmenting. If the wide spectrum vibration is measured, conventional methods face a harmonic distortion as well as intermodulation effects. Purpose of this research is to develop a measurement method of wide spectrum vibration by using a converter described by a nonlinear function of type f(x), where x =x(t) denotes the dependence of coordinate x on time t due to the vibration. Parameter x(t) describing the vibration is expressed as Fourier series. The spectral components of the converter output f(x(t)) are determined by using Fourier transform. The obtained system of nonlinear equations is solved using the least squares technique that permits to find x(t) in the presence of noise. This method allows one to carry out the absolute or relative vibration measurements. High resistance to noise is typical for the absolute vibration measurement, but it is necessary to know the Taylor expansion coefficients of the function f(x). If the Taylor expansion is not known, the relative measurement of vibration parameters is also possible, but with lower resistance to noise. This method allows one to eliminate the influence of nonlinear distortions to the measurement results, and consequently to eliminate harmonic distortion and intermodulation effects. The use of nonlinear properties of the converter for measurement gives some advantages related to an increased frequency range of the output signal (consequently increasing the number of equations) that allows one to decrease the noise influence on the measurement results. The greater is the nonlinearity the lower is noise. This method enables the use of the converters that are normally not suitable due to the high nonlinearity.