Mathematical Modeling of Ultrasonic Gas Flow Meter Based on Experimental Data in Three Steps

According to experimental data, the features of ultrasonic echo are studied, and a new mathematical model of ultrasonic gas flow meter is built so as to reflect the effects of the excitation signal and gas flow rate on ultrasonic echo. This mathematical model consists of three parts, and is established in three steps. An amplitude sub-model expressed as a polynomial is set up with the curve fitting method to express the non-linear relationship between the echo amplitude and the gas flow rate. A process sub-model described as an output-error model is established by the system identification method to reveal the influence of excitation on the echo shape. A delay time sub-model is built with piecewise fitting to obtain a relationship between the propagation time and the gas flow rate. These sub-models can quantitatively analyze the relationship between the excitation signals, gas flow rates, ultrasonic echo amplitudes, shapes, and propagation time.