Noise Reduction of pH Signal Based on Variable Step Size LMS Algorithm

Aiming at the noise reduction problem of pH time series in complex industrial environments, the ideas of normalization and feedback control are introduced to propose an adaptive filtering algorithm based on variable step size LMS (Least Mean Square) algorithm. The algorithm is firstly normalized to cancel signal noise gradient amplification problem and enhance the noise resistance of the system; secondly, the idea of variable step size factor is employed to establish a relationship between the coefficients of the step size and the error signals through the sigmoid function, which improves the stability of the LMS algorithm and the convergence speed. Simulation experiments and industrial field pH data indicate that the algorithm's signal-to-noise ratio has been enhanced by 51.811%, the mean-square error is 0.00285. Compared with the traditional LMS algorithm, wavelet noise reduction algorithm, SG noise reduction algorithm, its signal-to-noise ratio has improved by 40.295%, 21.691%, 30.498%; the mean-square error is reduced by 0.00613, 0.00191, 0.00314, the noise reduction effect is significantly improved, and when compared to the original algorithm, it demonstrates superior performance in both convergence speed and steady-state error.