Fig. 6 and Fig. 7 shows the soft sensor aluminum concentration as a function of the measured concentration. Ideally, all the values should lie on the y = x line. It can be seen that the red circle is closer to the straight line than the green circle, that is, the estimated alumina concentration obtained by MRF-based soft sensor tracks better the laboratory measurement than the estimated values obtained by BP neural network. In Fig. 8, the blue line and the red line 548 respectively indicate the relative error of the MRF-based soft sensor model and the BP neural network-based soft sensor estimated value. Fig. 8 shows that the relative error range of alumina concentration estimated by the soft sensor based on MRF is obviously smaller than that based on BP neural network. Therefore, the results show that the soft sensor method based on MRF can more effectively and accurately estimate the alumina concentration in the electrolyzer.