GA-BP Stacking Temperature Compensation Method for Small Sample Ultrasonic Measurement

To address the impact of temperature variations on the measurement accuracy of ultrasonic water meters, this study proposes a stacking-based temperature compensation model optimized via a genetic algorithm (GA-BP Stacking), developed based on an analysis of data distribution characteristics. The model innovatively integrates classical machine learning models (Lasso regression, decision trees, and XGBoost) with a deep learning model (BP neural network) through an effective stacking strategy, fully leveraging their complementary strengths. A genetic algorithm is employed to perform global optimization of the stacking model’s hyperparameters, while an adaptive weighted mean squared error (MSE) loss function is designed to dynamically adjust error weights in critical areas such as low-flow and high-flow regions. Additionally, a customized data augmentation method based on temperature perturbations and random error adjustments is proposed, along with the construction of interaction features, to overcome limitations in generalization performance under small-sample conditions. Validation on datasets from two different operating conditions demonstrates that the GA-BP Stacking model significantly improves compensation accuracy across all flow regions, achieving a minimum MSE of 5.03 × 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−9</sup> and maintaining relative errors within ±1%. The results indicate that the proposed model substantially enhances measurement accuracy and robustness, offering valuable guidance for high-precision ultrasonic water meter applications.