Data-driven multivariate nonlinear mathematical model of landing gear shock absorbers

To address the nonlinear dynamic characteristics of the oleo-pneumatic landing gear strut, this study establishes a multivariate nonlinear mathematical model with overload as the dependent variable, through a data-driven approach combined with theoretical analysis and drop-test data. The model comprehensively incorporates factors such as strut stroke, velocity, and acceleration, and is developed using the pseudo-linear least squares method. Through multiple iterative improvements, the model's fitting accuracy and predictive capability have been significantly enhanced. To resolve the time delay phenomenon observed between model predictions and experimental data, an acceleration term was introduced into the model. This adjustment reduced the root mean square error (RMSE) from 0.0447 to 0.0401 and increased the adjusted coefficient of determination from 0.968 to 0.974. A square-root acceleration term (acceleration increased to the power of 0.5) was added to the model in order to further address the fitting deviation problem during the first phase (stroke 0 mm to 50 mm). This refinement reduced the RMSE from 0.0401 to 0.0341 and increased the adjusted coefficient of determination from 0.974 to 0.981, significantly enhancing the model's ability to describe system dynamics and its predictive accuracy. The study demonstrates that the proposed model provides a more accurate method for describing the nonlinear dynamic characteristics of landing gear shock absorbers and offers a reliable theoretical foundation for the design and optimization of the overall automatic control system.