Nonlinear modeling of the relationship between reagent dosage and flotation froth surface image by Hammerstein-Wiener model

Abstract

Due to the frequent and random disturbances to flotation banks, reagent dosages are frequently changed to stabilize the flotation process at a desired level to obtain an expected grade and recovery. It is widely accepted that the froth surface after a reagent change is the essential process output, corresponding to reagent dosages for a current chemical condition (that also can be characterized by the froth surface). Based on this causal relationship, the froth surface can be controlled to any expected stable state by changing reagent dosage. Therefore, a Hammerstein-Wiener based causal model that models bubble size distribution (the image feature used to characterize froth appearance) and reagent dosage as a nonlinear relationship was developed. Since existing watershed algorithms are ineffective in segmenting the highly reflective zinc bubble images, a novel illumination modeling-based marker watershed method was proposed. A log-normal distribution model was used to fit the bubble size distribution, and then a nonlinear model between bubble size distribution and reagent dosage was approximated by a wavelet-based Hammerstein-Wiener model. The proposed methods have been validated through comparative experiments for a lead–zinc flotation plant in China.