The modeling and control of pH neutralization processes is a difficult problem in the field of process control.A multi-modeling method using an improved k-means clustering based on a new validity function is proposed in this paper.There are some common problems

including the number of clusters assumed as a priori knowledge and initial cluster centers selected randomly for classical k-means clustering.The proposed algorithm is used to compute initial cluster centers and a new validity function is added to determine the appropriate number of clusters

then partial least squares (PLS) is used to construct the regression equation for each local cluster.Simulation results showed that multiple models using the proposed algorithm gave good performance

and the feasibility and validity of the proposed algorithm was verified.