Construction and investigation of a method for measuring the non-stationary pressure using a wavelet transform

Abstract

Automated control systems badly need measurements of fast-changing non-stationary physical quantities in real time, or close to that. In this area, there is a separate group of tasks on measuring the non-stationary pressure in liquids and gases. This paper demonstrates that measuring the non-stationary pressure in real time, or close to that, represents a problem on restoring an input signal, which, in terms of mathematics, belongs to the class of ill-posed problems (according to J. Hadamard). We have derived a solution to the inverse problem of measurement that is based on a mathematical model for measuring transformation enabled by a pressure sensor. Based on this solution, we have constructed a measuring method, which implies the wavelet processing of the sensor's output signal. In this case, we suggest that such basic functions of wavelet transformation should be selected that are the modification of the pulse transition function of the sensor. This paper reports an experimental study into the feasibility of the developed method, based on the measurement of the simulated pressure pulse. A pressure pulse is simulated by dropping a ball of the calibrated mass onto the sensor's membrane. We have proposed a measurement scheme for determining the duration of touch between the ball and the membrane. Testing the accuracy of the method implies comparing the actual mass of the ball with that derived from the sensor's output signal. The proposed method has demonstrated high accuracy because the maximum relative error in determining the mass of the falling ball was only 0.65 %. The proposed method for measuring the non-stationary pressure could be used in control systems that require the high-speed dynamic correction of a measurement error. Specifically, these include control system in aerospace engineering, testing complexes, military technology, scientific research