Abstract:In the time delay estimation (TDE) of ultrasonic signals, the traditional fixed step size least mean square (LMS) algorithm struggles to balance convergence speed and steady-state accuracy. Moreover, existing variable step size algorithms often rely on instantaneous errors and fixed function models, leading to poor adaptability under non-stationary echo signals. To address these issues, a TDE method using a fuzzy variable step size LMS algorithm is proposed for ultrasonic thickness measurement in this paper. Based on the time-varying characteristics of ultrasonic echo signals, the conventional single-error feedback mechanism is discarded. Instead, the local correlation coefficient error between the output and desired signals, along with its variation, are extracted as the dual inputs for a fuzzy controller. A zero-order Sugeno fuzzy inference system is then designed to establish a nonlinear mapping rule between these input features and the step size, enabling adaptive dynamic adjustment of the step size. Numerical simulations are presented using simulated echo signals under different signal-to-noise ratios. The results demonstrate that the proposed method yields better overall performance compared to the fixed step size LMS, the hyperbolic tangent variable step size LMS, and the instantaneous error-based fuzzy variable step size LMS. It significantly reduces the steady-state misadjustment while ensuring fast convergence, thereby offering higher measurement accuracy and noise robustness. This is further verified using measurements made on standard gauge blocks with a laboratory ultrasonic thickness measurement platform. The experimental results show that the relative measurement errors of the proposed method for gauge blocks of varying thicknesses are consistently smaller than those of the other three LMS algorithms, with a maximum relative error of 0.710%. Ultimately, the fuzzy variable step size LMS method for TDE provides vital technical support for high-precision ultrasonic time-of-flight (TOF) calculations. It facilitates the development of ultrasonic non-destructive testing technologies and holds significant practical value in engineering applications.