A novel performance prediction method for harmonic reducers based on the trend-enhanced Fisher’s discriminant ratio-Wiener process

Abstract Harmonic reducers, as core components of industrial robots, play a critical role in maintaining robot health. Performance degradation assessment and remaining useful life (RUL) prediction are essential for ensuring the operational reliability of such robots. To address the multistage characteristics and stochastic uncertainties in the performance degradation of harmonic reducers, a performance prediction method based on Fisher’s discriminant ratio and Wiener process is proposed. Firstly, the health indicator construction is defined as an optimization problem based on Fisher’s discriminant ratio and trend monotonicity constraints. By leveraging the sum of the multiplication of frequency amplitudes and optimized weights, precise segmentation of the multistage degradation process over the entire lifecycle is achieved. Notably, the optimized weights can automatically identify the resonance frequency bands caused by damage. Subsequently, a nonlinear Wiener process model with a drift coefficient in the form of a power function is established. The probability density function expression for RUL is derived based on the concept of first hit time. Additionally, a logarithmic likelihood function for the unknown parameters in the degradation model is constructed. The experimental results indicate that the proposed method surpasses the other two Wiener process models in terms of root mean square error, mean absolute percentage error, and cumulative relative accuracy. This provides robust support for preventive maintenance decision-making for harmonic reducers.