Grey-box Recursive Parameter Identification of a Nonlinear Dynamic Model for Mineral Flotation

TL;DR

This work tackles parameter drift in a nonlinear mineral flotation model by applying a grey-box recursive prediction error method to online estimate two key parameters, $n$ and $C$. Using a lab-scale, physics-based dynamic model, the method continuously updates parameters to counter varying disturbances, improving concentrate-grade predictions from nominal to near-ground-truth levels. The approach demonstrates efficient real-time adaptation through a Gauss-Newton update with a forgetting factor, validated under scenarios with changing air flow. The findings suggest significant implications for adaptive control of froth flotation and potential integration with closed-loop MPC for enhanced process performance.

Abstract

This study presents a grey-box recursive identification technique to estimate key parameters in a mineral flotation process across two scenarios. The method is applied to a nonlinear physics-based dynamic model validated at a laboratory scale, allowing real-time updates of two model parameters, n and C, in response to changing conditions. The proposed approach effectively adapts to process variability and allows for continuous adjustments based on operational fluctuations, resulting in a significantly improved estimation of concentrate grade - one key performance indicator. In Scenario 1, parameters n and C achieved fit metrics of 97.99 and 96.86, respectively, with concentrate grade estimations improving from 75.1 to 98.69 using recursive identification. In Scenario 2, the fit metrics for n and C were 96.27 and 95.48, respectively, with the concentrate grade estimations increasing from 96.27 to 99.45 with recursive identification. The results demonstrate the effectiveness of the proposed grey-box recursive identification method in accurately estimating parameters and predicting concentrate grade in a mineral flotation process.

Figures (7)

• Figure 1: Simplified P&ID of a froth flotation cell (adapted from Quintanilla2023EconomicModels) and the froth flotation phases (froth, interface and pulp). The inlet flow rates, feed ($Q_{feed}$) and air ($Q_{air}$), and outlet flow rates, concentrate ($Q_{conc}$) and tails ($Q_{tails}$) are also indicated. The controlled variable is pulp height ($h_p$), which is controlled by manipulating the tails flow rate.
• Figure 2: Scenario 1: Plots of the inputs $h_p$ and $Q_{air}$ between $600$ and $2400$ seconds.
• Figure 3: Scenario 2: Plots of the inputs $h_p$ and $Q_{air}$ between $600$ and $2400$ seconds.
• Figure 4: Scenario 1: Recursive estimation of parameters $n$ and $C$ from \ref{['eq: db-froth']} over time.
• Figure 5: Scenario 1: Real-time predicted concentration grade (blue), prediction using nominal parameters (grey), and true concentration grade (black line).