Modelling of received ultrasonic signals based on variable frequency analysis

Abstract Modelling of received ultrasonic signals can provide basis for both signal analysis and process in various instrumentations based on ultrasonic measurement. At present, some empirical models where the resonance frequencies set to fixed values have been proposed for this purpose. However, significant errors can be found between the existing models and actual ultrasonic signals. This paper proposes a modelling method of received ultrasonic signal based on variable frequency analysis, which is then validated by application on ultrasonic gas flowmeter. In this method, the traditional exponential model is modified to contain a time-varying frequency parameter, whose value can be estimated by analyzing the sampled signal using the Teager Energy Operator (TEO). Other parameters in the model can be further determined by parameter estimation algorithms. In order to meet TEO's application conditions, a sinusoidal transformation of the received signal using Hilbert transform before the time-varying frequency estimation is proposed. Wavelet packet de-noising method, lag parameter and smoothing spline are introduced to improve the performance of the time-varying frequency acquisition in the presence of noise. A number of numerical tests are conducted on simulated signals with different time-varying frequencies and noise to confirm the effectiveness of the proposed method. The actual application significance is validated by analysis of the actual received signals on ultrasonic gas flowmeter.

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