Variable Step-Size LMS Algorithm Based on Variational Versoria Function and Variational Gaussian Function

Abstract

Aiming at the noise interference problem in wing fatigue tests, this paper improves the traditional LMS algorithm using the variational Versoria function and the variational Gaussian function. Additionally, this paper proposes a variable step-size LMS (VSS-LMS) filtering algorithm based on the composite function (CVSS-LMS). The composite function combines the variational Versoria function and the variational Gaussian function to describe the nonlinear relationship between the iteration step size and the error. To adapt to environments with different signal-to-noise ratios, the algorithm replaces the fixed parameters with a combination of current and previous errors, thus enabling adaptive adjustment of the parameters. Moreover, a step-size dynamic constraint rule is proposed to further improve the stability of the algorithm. The algorithm is normalized using a combination of the cumulative sum of error squares, the mean square error (MSE), and the power of the input signal, which reduces the sensitivity to the input signal amplitude. The above parts finally constitute the adaptive CVSS-LMS (ACVSS-LMS) filtering algorithm. The convergence of the ACVSS-LMS algorithm is verified through theoretical derivation. The ACVSS-LMS algorithm is experimentally analyzed by using the simulation data generated by MATLAB and the actual data collected from the wing fatigue test, and the results show that the ACVSS-LMS algorithm proposed in this paper has a faster convergence speed and lower steady-state error compared to other algorithms.