A Simplified Friction-Map Reconstruction Method for Electromechanical Actuators with a Load-Augmented Physics-Informed Neural Network

Friction monitoring is essential for the precision control and fault diagnosis of electromechanical actuators (EMAs). This paper presents a friction estimator that reconstructs friction under various loads and velocities solely from motor current signals. The estimator consists of a preprocessing stage and an extrapolation training stage using a physics-informed neural network (PINN). In the preprocessing stage, basic Stribeck parameters are estimated from no-load constant-speed measurements. In the extrapolation training stage, a load-augmented Stribeck law is embedded as a soft constraint within the PINN, and friction is distinguished from reflected load torque by its velocity-structured baseline. Because the load dependence is encoded in the physical law, the estimator extrapolates to loads absent from training, reconstructing the friction map from limited samples; a theoretical analysis derives the conditions for well-posed extrapolation. In dynamic simulations, the preprocessing stage estimates the base Stribeck parameters with a mean relative error of 0.87%. On graded load-extrapolation experiments, the constrained PINN keeps the mean relative error close to 1% at loads far beyond the maximum training load, about 90% lower than data-driven methods, and predicts friction in untrained dynamic processes with a mean relative error below 4.8%. Few quasi-static points thus suffice to reconstruct the full velocity–load friction map without force or torque sensors, and periodic re-estimation can track friction over the service life.