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<p>This paper addresses the requirement for high-precision and robust hydraulic pressure estimation in the electro-hydraulic brake systems of intelligent vehicles to meet functional safety redundancy standards. A novel pressure estimation approach integrating the Extended Kalman Filter (EKF) with the Backpropagation (BP) neural network is proposed. A simplified model of the decentralized electro-hydraulic brake actuator is developed, incorporating a permanent magnet synchronous motor, a ball screw mechanism, and a hydraulic execution unit. The cascaded estimation framework employs EKF for real-time state estimation of the nonlinear system, while the BP neural network provides dynamic compensation for EKF estimation residuals. This compensation mechanism effectively mitigates the impacts of system parameter uncertainties, nonlinear friction, and unmodeled dynamics on estimation accuracy. Simulation results show that under three typical braking conditions—step, sinusoidal, and trapezoidal—the proposed EKF-BP fusion method achieves significant improvements. Compared to the conventional quadratic fitting method, it achieves mean RMSE reductions of 90.3% (± 0.6%), 80.7% (± 5.4%), and 46.2% (± 7.6%) under step, sinusoidal, and trapezoidal conditions, respectively (mean ± standard deviation, N = 1000). Furthermore, the method consistently outperforms the standalone EKF approach, validating its effectiveness in a simulation-based proof-of-concept for enhancing estimation consistency, dynamic response capability, and system robustness.</p>

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Pressure Estimation Method for Electro-Hydraulic Brake Actuators on EKF-BP Neural Network Fusion

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Han Jiang Yi,
  • Sun Wang,
  • Chen Lin,
  • Lü De Yuan

摘要

This paper addresses the requirement for high-precision and robust hydraulic pressure estimation in the electro-hydraulic brake systems of intelligent vehicles to meet functional safety redundancy standards. A novel pressure estimation approach integrating the Extended Kalman Filter (EKF) with the Backpropagation (BP) neural network is proposed. A simplified model of the decentralized electro-hydraulic brake actuator is developed, incorporating a permanent magnet synchronous motor, a ball screw mechanism, and a hydraulic execution unit. The cascaded estimation framework employs EKF for real-time state estimation of the nonlinear system, while the BP neural network provides dynamic compensation for EKF estimation residuals. This compensation mechanism effectively mitigates the impacts of system parameter uncertainties, nonlinear friction, and unmodeled dynamics on estimation accuracy. Simulation results show that under three typical braking conditions—step, sinusoidal, and trapezoidal—the proposed EKF-BP fusion method achieves significant improvements. Compared to the conventional quadratic fitting method, it achieves mean RMSE reductions of 90.3% (± 0.6%), 80.7% (± 5.4%), and 46.2% (± 7.6%) under step, sinusoidal, and trapezoidal conditions, respectively (mean ± standard deviation, N = 1000). Furthermore, the method consistently outperforms the standalone EKF approach, validating its effectiveness in a simulation-based proof-of-concept for enhancing estimation consistency, dynamic response capability, and system robustness.