Flotation process fault detection using output PDF of bubble size distribution

As an important indicator of flotation performance, bubble structure is believed to be related with the addition amount of chemical reagent. To differentiate film size calculated from surface froth image segmentation and underlying bubble size, post-segmentation analysis is carried out to archive the prediction of bubble size distribution from the known bubble film distribution. Based on the facts that the probability density distribution (PDF) of film size is found to be non-Gaussian and singular feature characterizing bubble structure becomes insufficient, a nonparametric kernel estimator is introduced to approximate the output PDF of bubble size distribution. Through transforming nonparametric description into dynamic kernel weight vectors, an output PDF based detection filter is designed, according to which LMIs are established to solve its stability condition by Lyapunov stability analysis on the estimated error system. Fault detection problem is then solved through a threshold criterion determined by the system stability condition. Simulation results show that desired fault detection for reagent addition in industrial froth flotation can be achieved using the proposed method.