Response Surface Methodology for Optimizing the Design Parameters of Ultrasonic Liquid-Level Measurement System

This study addresses the high-precision requirements for liquid-level detection of propellants in aerospace rockets and optimizes the design parameters of an ultrasonic liquid-level measurement system based on the response surface method (RSM). Meanwhile, a quantitative correlation model between multiple physical parameters and output voltage is established through theoretical derivation. Firstly, the effects of piezoelectric ceramic sheet diameter, ultrasonic frequency, excitation voltage and liquid temperature on the output voltage are investigated. The optimum conditions were obtained by one-way tests, where the output voltage reached its maximum when the diameter of the piezoelectric ceramic sheet was 15 mm and the frequency was 1 MHz. The excitation voltage was positively correlated with the output voltage. Elevated liquid temperature enhanced the echo amplitude. The influence of law remained consistent across different liquid levels. Subsequently, under the liquid level of 12 cm (half-full operating condition), a three-factor, three-level response surface methodology (RSM) analysis experiment was conducted, focusing on three factors that significantly affect energy transfer efficiency: piezoelectric ceramic sheet diameter (<i>D</i>), ultrasonic frequency (<i>f</i>), and liquid temperature (<i>T</i>). The best parameter combination was obtained through model optimization: <i>D</i> = 14.773 mm, <i>f</i> = 0.878 MHz, <i>T</i> = 33.661 °C. The predicted <i>U</i>-value was 8.976 V. The validation experiments demonstrated that the error rates between the measured average voltage values and the predicted values under different liquid levels were all <1%, and the coefficient of variation (CV) of the output signal was reduced to 0.9%. This not only meets the error requirements for aerospace liquid-level measurement but also verifies the reliability of the optimized model. This study significantly enhances the output signal stability and measurement accuracy, providing support for the liquid-level detection of aerospace propellants and high-precision liquid-level measurement in industrial applications.