Enhanced dynamic calibration in an instrumented cycling pedal: A gradient boosting approach

This study introduces an instrumented cycling pedal to measure three-dimensional pedal reaction forces and a novel calibration approach utilizing HistGradientBoostingRegressor (HGBR) of the Scikit-learn library in Python. This derivative of traditional gradient boosting machines, a type of machine learning algorithm based on decision trees, is optimized for ease of use, computational speed for large datasets, and robustness against overfitting. The HGBR is used to map the non-linear input-response relationship of the sensor that occurs under realistic, multiaxial, and dynamic loading conditions. Its accuracy is tested against the traditional linear calibration approach of a calibration matrix and a deep learning approach of a Multilayer Perceptron (MLP). Large datasets for HGBR and MLP training were generated in a custom test rig, ensuring coverage across a defined calibration space and cycling-specific conditions. The HGBR achieved notably lower error metrics (root mean squared error: RMSE; normalized RMSE: nRMSE) compared to both the matrix and the MLP approach, while being computationally reasonably demanding. Over the full calibration space, the HGBR model showed a combined RMSE of 1.96 N (nRMSE: 0.3%) and demonstrated even higher accuracies in cycling-specific scenarios (nRMSE: 0.04%). Further, Bland-Altman plots showed biases close to 0 and limits of agreement of less than ±4.04 N for all three loading directions, indicating an acceptably low systematic and random error for the HGBR-based calibration. This study underscores the potential of an HGBR-based calibration for advancing force sensor accuracy. The gradient boosting approach can outperform classical linear approaches and more complex deep learning models.