A Polynomial Recursive Nonlinear Least-Squares Algorithm for High-Accuracy Parameter Identification of Heavy-Haul Train Dynamics

To address the issues of low accuracy and poor adaptability in traditional dynamic parameter identification methods for heavy-haul trains, this article proposes a polynomial nonlinear recursive least-squares (PNRLS) algorithm. Conventional approaches, such as static quadratic empirical models, fail to effectively decouple multisource disturbances (e.g., wheel-rail wear and aerodynamic effects), while least-squares (LS)-based methods lack robustness in estimating time-varying parameters under noisy or incomplete data conditions. The PNRLS algorithm constructs a multidimensional linear dynamic model by expanding the dimensionality of the system equation through the Kronecker product, thereby integrating both low- and high-order variables. Simultaneously, by iteratively optimizing weight factors and recursively applying weighted LS (WLS) in high-dimensional space, it significantly enhances the accuracy and stability of parameter estimation, reduces reliance on historical data, and improves the utilization efficiency of high-order system information, effectively mitigating matrix ill-conditioning and reducing identification lag for time-varying parameters. Experimental validation using real traction force and velocity data from the HXD1 heavy-haul train demonstrates an average improvement of 13.62% in the estimation accuracy of basic resistance and rotational mass coefficients compared to LS, FF-RLS, and recursive maximum likelihood estimation (RMLE) methods, thereby significantly enhancing the accuracy and stability of parameter identification and confirming its superior performance under complex multisource disturbances and data noise conditions.