Multi-Objective Optimization Study on the Separation Stability of the Falling Body in Absolute Gravimeters

The stability of absolute gravimeters during carriage-falling body separation is crucial for improving gravitational acceleration measurement accuracy. Transmission speed accuracy of the transmission system and system vibration are core factors determining this stability, while steel belt pre-tightening force, free-fall segment acceleration, and start-up segment displacement are key parameters influencing both. In-depth analysis of their coupling clarified their roles, and two objective function models (for speed accuracy and vibration) were established, with fitting accuracies R2 = 0.8976 and R2 = 0.8395, respectively. Since traditional single-objective optimization fails to balance “improving speed accuracy” and “suppressing vibration”, this study proposes a multi-objective optimization method: two Nondominated Sorting Genetic Algorithm II (NSGA-II) parameter sets were designed, Hypervolume (HV) index quantified solution set quality, and Wilcoxon signed-rank test was combined to determine the optimal parameter set; comparing the Global Criterion Method and Weighted Sum Method, the former was superior (no dimensional bias) and more suitable for this study, finally screening out the optimal parameter combination. Experimental results showed that the measured transmission speed accuracy was 0.09132 m/s (16.94% lower than the orthogonal experiment’s optimal level); the measured system vibration was 0.022 m/s2, falling within the orthogonal experiment’s optimal range. Consequently, separation moment stability was significantly enhanced, with its standard deviation reduced by 45% pre-optimization. This method achieves global balance in transmission system dynamic performance, providing an effective parameter optimization strategy for improving absolute gravimeter measurement accuracy.