Froth flotation, a widely used mineral beneficiation technique, generates substantial volumes of data, offering the opportunity to extract valuable insights from these data for production line analysis. The quality of flotation data is critical to designing accurate prediction models and process optimisation. Unfortunately, industrial flotation data are often compromised by quality issues such as outliers that can produce misleading or erroneous analytical results. A general approach is to preprocess the data by replacing or imputing outliers with data values that have no connection with the real state of the process. However, this does not resolve the effect of outliers, especially those that deviate from normal trends. Outliers often occur across multiple variables, and their values may occur in normal observation ranges, making their detection challenging. An unresolved challenge in outlier detection is determining how far an observation must be to be considered an outlier. Existing methods rely on domain experts’ knowledge, which is difficult to apply when experts encounter large volumes of data with complex relationships. In this paper, we propose an approach to conduct outlier analysis on a flotation dataset and examine the efficacy of multiple machine learning (ML) algorithms—including k-Nearest Neighbour (kNN), Local Outlier Factor (LOF), and Isolation Forest (ISF)—in relation to the statistical $2\sigma$ rule for identifying outliers. We introduce the concept of “quasi-outliers” determined by the $2\sigma$ threshold as a benchmark for assessing the ML algorithms’ performance. The study also analyses the mutual coverage between quasi-outliers and outliers from the ML algorithms to identify the most effective outlier detection algorithm. We found that the outliers by kNN cover outliers of other methods. We use the experimental results to show that outliers affect model prediction accuracy, and excluding outliers from training data can reduce the average prediction errors.

In this work, the prediction and optimisation of copper flotation has been conducted in the rougher flotation circuit. The copper-recovery prediction involved the application of support vector machine (SVM), Gaussian process regression (GPR), multi-layer perceptron artificial neural network (ANN), linear regression (LR), and random forest (RF) algorithms on 15 rougher flotation variables at the BHP Olympic Dam. The predictive models’ performance was assessed using linear correlation ($r$), root mean square error (RMSE), mean absolute percentage error (MAPE), and variance accounted for (VAF). A simulated annealing (SA) optimisation algorithm, particle swarm optimisation (PSO) algorithm, surrogate optimisation (SO) algorithm, and genetic algorithm (GA) were investigated, using the GPR predictive function, to determine the optimal operating condition for maximising copper recovery. The predictive function of the best-performing model was extracted and used in optimising the flotation circuit. The results showed that the GPR model developed with the matern 3/2 kernel function makes the most precise copper-recovery prediction as compared to the other investigated predictive models, obtaining $r$ values $>$ 0.96, RMSE values $<$ 0.42, MAPE values $<$ 0.25%, and VAF values $>$ 94%. A hypothetical optimisation solution assessment showed that SA provides the best set of solutions for the maximisation of rougher copper recovery, obtaining a throughput of 638.02 t/h and a total net gain percentage of 14%–15.5% over the other optimisation algorithms with a maximum copper recovery of 94.76%. The operational benefits of implementing these algorithms have been highlighted.

Currently there are no available methods for in-line measurement of gas-liquid interfacial tension during the flotation process. Microfluidic devices have the potential to be deployed in such settings to allow for a rapid in-line determination of the interfacial tension, and hence provide information on frother concentration. This paper presents the development of a simple method for interfacial tension determination based on a microfluidic device with a flow-focusing geometry. The bubble generation frequency in such a microfluidic device is correlated with the concentration of two flotation frothers (characterized by very different adsorption kinetic behavior). The results are compared with the equilibrium interfacial tension values determined using classical profile analysis tensiometry.

Insight about the operation of froth flotation through modelling has been in existence since the early 1930s. Irrespective of the numerous industrial models that have been developed over the years, modelling of the metallurgical outputs of froth flotation often do not involve pulp chemistry variables. As such, this work investigated the influence of pulp chemistry variables (pH, Eh, dissolved oxygen and temperature) on the prediction performance of rougher copper recovery using a Gaussian process regression algorithm. Model performance assessed with linear correlation coefficient (r), root mean square error (RMSE), mean absolute percentage error (MAPE) and scatter index (SI) indicated that pulp chemistry variables are essential in predicting rougher copper recovery, and obtaining r values > 0.98, RMSE values < 0.32, MAPE values < 0.20 and SI values < 0.0034. RNCA feature weights reveal the pulp chemistry relevance in the order dissolved oxygen > pH > Eh > temperature.

Froth flotation, a widely used mineral beneficiation technique, generates substantial volumes of data, offering the opportunity to extract valuable insights from these data for production line analysis. The quality of flotation data is critical to designing accurate prediction models and process optimisation. Unfortunately, industrial flotation data are often compromised by quality issues such as outliers that can produce misleading or erroneous analytical results. A general approach is to preprocess the data by replacing or imputing outliers with data values that have no connection with the real state of the process. However, this does not resolve the effect of outliers, especially those that deviate from normal trends. Outliers often occur across multiple variables and their values may occur in normal observation ranges, making their detection challenging. An unresolved challenge in outlier detection is how far is far enough for an observation to be considered an outlier. Existing methods rely on domain experts’ knowledge which is difficult to apply when experts encounter large volumes of data with complex relationships. In this paper, we propose an approach to conduct outlier analysis on a flotation dataset. The approach uses a 2σ rule as the threshold to find quasi-outliers and multiple machine learning (ML) algorithms including k-Nearest Neighbour (kNN), Local Outlier Factor (LOF), and Isolation Forest (ISF) to identify true outliers. The approach then analyses the mutual coverage between quasi-outliers and outliers from the ML algorithms to identify the most effective outlier detection algorithm. We found that the outliers by kNN cover outliers of other methods. We use the experimental results to show that outliers affect model prediction accuracy and excluding outliers from training data can reduce the average prediction errors.