Predictive Insight into Tailings Flowability at Their Disposal Using Operating Data-Driven Artificial Neural Network (ANN) Technique

Abstract

This study investigates the application of artificial neural networks (ANNs) in predicting the flowability of mining tailings based on operational variables. As the mining industry seeks to enhance operations with complex ores, the constant improvement and optimization of mineral waste management are crucial. The flowability of tailings was investigated with data driven by properties such as particle-size distribution, water content, compaction capacity, and viscoelastic characteristics that can directly affect stacking, water recovery capabilities, and stability at disposal, influencing storage capacity, operational continuity, and work safety. There was a strong correlation between water content and tailings flowability, emphasising its importance in operational transport and deposition. Three ANN models were evaluated to predict tailings flowability across three and five categories, where a model based on thickening operational variables, including yield stress and turbidity, demonstrated the highest accuracy, achieving up to 94.4% in three categories and 88.9% in five categories. Key variables such as flocculant dosage, water content, yield stress, and solid concentration were identified as crucial for prediction accuracy The findings suggest that ANN models, even with limited datasets, can provide reliable flowability predictions, supporting tailings management and operational decision-making.

1. Introduction

The mining industry has shown a growing interest in addressing challenges related to the processing of low-grade sulphide ores; evidently, the major amount is waste material or tailings needing adequate management and disposal. A wide range of challenges may arise in the domains of tailings operations (e.g., inefficient management), structures (e.g., dam failures, unstable slopes, and seepage), and the environment (e.g., ecosystem disruption, acid mine drainage) [1,2]. Another challenge involves reusing water; for instance, a concentrator plant processing 100,000 tonnes of ore per day generates tailings with a solid concentration of 55%, which results in a daily loss of approximately 81,800 m³ of water during the disposal of the tailings [3]. Tailings characteristics such as mineralogy, particle-size distribution, water content, compaction capacity, and viscoelasticity have a direct impact on the day-to-day functioning of tailings storage facilities (TSFs), starting with the thickening stage and their water recovery performance, all the way to the final disposal [4]. TSFs’ capacity and geotechnical performance can be directly affected by these factors and changes in geotechnical conditions, leading to the risk of failure [5,6]. Such factors, together with unplanned disposal schedules, might result in safety problems, shorten the intended lifespan of the facility and disrupt water balance control during operation [7,8], and reveal how an increase in clay concentration in the tailings directly affects drainage in the tailings deposit. All the above prompt us to examine tailings behaviour, particularly the flowability of tailings during disposal. The flowability generated during this process can directly impact the long-term stability of the deposit, ensuring its operational continuity and permeability characteristics necessary for water recovery. In order to develop a thorough comprehension of tailings behaviour, it is necessary to ascertain the direct impact of the factors present in the various phases of tailings disposal.

Computer models have become indispensable instruments to optimise production in the mining industry [9,10,11,12]. Deep learning (a subfield of machine learning) utilises algorithms to discern intricate patterns from actual data, enabling them to comprehend the occurrence of interactions and generate predictions regarding future conduct [13]. These algorithms base their predictions on prior experiences that involve different information factors and utilise non-parametric statistical tools to facilitate pattern detection, forecasts, and decision-making using data [14,15]. In recent years, the mining industry has increasingly adopted deep learning techniques, particularly artificial neural networks (ANNs), to address challenges in various processes, where tailings disposal and their flowability predictability can be analysed. Traditional methods often lack certainty and comprehensive knowledge, which has prompted a shift towards deep learning. Deep learning offers enhanced pattern recognition, prediction, and decision-making capabilities, addressing the limitations of traditional methodologies. Studies conducted by researchers such as Bergh et al. [16], Correa Devés [14], Umucu et al. [17], and Leiva et al. [18] have explored the application of ANNs in tasks such as predicting surface quality in flotation and heap leaching processes and have compared the performance of Bayesian networks with ANNs. Salmani Nuri et al. [19] successfully employed ANNs to predict copper float rates under varying operational conditions, achieving a prediction quality of 93% during testing by analysing variables such as particle size, feed rate, and chemical reagent doses. Ai et al. [20] discussed the use of artificial intelligence models to predict flotation behaviour in coal processing, considering factors such as particle size and flotation time. Furthermore, the application of deep learning techniques extends to monitoring tailings operations. While approaches proposed by Ge et al. [21], Hui and Nrc [22], and Scaioni et al. [23] have been developed, there is a lack of established systems providing reliable data. Researchers such as Yu et al. [24], Hu and Liu [25], and Sun and Guo [26] have explored the possibility of establishing continuous monitoring systems for TSFs to manage their structural stability and overall safety. These systems often utilise diverse control technologies involving geosciences, mechanics, topography, and statistics, although their implementation can be costly. Moreover, multidisciplinary approaches, exemplified by Boente et al. [27], have applied techniques like Principal Component Analysis (PCA) to analyse element concentrations in different zones at site and evaluate their correlations under various operational conditions, aiming to understand the environmental impact of process reagents. Studies utilising smoothed particle hydrodynamics [28] have investigated mesh-free methods capable of identifying changes in a tailings dam, by considering complex dynamic moving structures interacting with the flow. Additionally, Li et al. [29] employed support vector regression (SVR) prediction to enhance dam monitoring by developing an early warning system for stability problems. While numerical and computational fluid dynamics (CFD) simulations, as discussed by Liu Beng [30], Trewhela et al. [31], and Vergara et al. [32], have shown promise in tailings management, they face limitations associated with uncertainties in the computed values and approximations made based on Navier–Stokes equations, as highlighted by McBride et al. [33]. Despite these challenges, the integration of deep learning techniques into tailings management holds considerable promise for improving operational efficiency and safety.

This work aims to develop a predictive model of tailings flowability at final disposal using deep learning techniques, which then can be used for control monitoring and to support decisions regarding storage capacity, operational support, and water strategy. The research evaluates the performance of standard predictive models and introduces a comprehensive comparison with other methods, such as decision tree (DT) and random forest (RF), to ascertain their efficacy. The use of a limited dataset perspective is also analysed, to determine the accuracy of flowability predictions using a representative dataset based on tailings operational variables and a flowability categorisation of the tailings. The objective is to reveal correlations and interdependency between the rheological and permeability properties of tailings and the operational variables (particle-size distribution, flocculation, viscosity, and moisture) identified by Adiguzel and Bascetin [34], Arancibia et al. [35], Balaniuk et al. [36], and Qi et al. [37]. Making informed decisions about the input variables to be used with a deep learning approach is possible to ensure relevance and accuracy in finding the behavioural patterns of tailings flowability. This dual approach improves the prediction accuracy and provides a framework for better tailings management, significantly contributing to sustainable mining practices and waste disposal strategies, even with limited data.

2. Methodology

In this study, an experimental design based on laboratory tests that allow a precise variable measurement for dataset creation and deep learning modelling processing is applied, to analyse the tailings flowability at disposal, considering their proven effectiveness in accurately predicting complex behaviours and their ability to handle datasets efficiently, as is presented in the approaches to mineral waste disposal operations investigated in Herrera et al. in [38,39]. The current strategy included the identification of variables relevant to tailings flowability, sampling, test development, results analysis, and data processing through ANN models. Figure 1 presents the systematic two-stage approach of this study, which involves laboratory tests and model generation. In the initial stage, the examination of the tailing sample included characterisation and laboratory tests focused on settling and flow behaviour under different operating conditions. This phase generates the data for the variables at each stage.

Subsequently, in the next stage, the output of the laboratory tests, i.e., the dataset, is prepared as the input for the ANN models. These prediction models are based on operational variables, where the flowability behaviour at final disposal is evaluated by flowability categories, as is presented in Section 3.2. These categories range from slow, indicating a minimal flow and higher resistance to movement, to high, indicating a maximum flow and lower resistance, representing a specific range of flow rates and associated characteristics relevant to disposal and tailings management.

2.1. Artificial Neural Network (ANN) Application

The methodology employed in this study follows an established approach previously described in Herrera et al. [39]. It entails the use of ANNs, which are composed of interconnected artificial neurons arranged in input, hidden, and output layers [40,41]. The workflow parallels a Gaussian Naïve Bayes classification method, using continuous variables that follow a Gaussian distribution. In the input layer, variables X_i with corresponding weights W_ij are processed using Gaussian basis functions (Equation (1)) [14]. These values are standardised in the input layer, and in the hidden layer, the contribution of each variable to the probability density function is calculated using an activation function g_ij (Equation (2)) [40,42,43]. The transfer function within the hidden layer of neurons ranges from −1 to 1 or 0 to 1 [44]. Each piece of training group data is represented in the summary layer (Equation (3)) [42,45,46]. The only adjustable parameter is the scaling parameter φ, which affect the decay rate of an observation influence. The model incorporates a misclassifying cost c_j and prior probability h_j to represent sample proportions, and a score is calculated for each output group (Equation (4)) [42,46]. Cross-validation is carried out using jackknifing re-sampling, and in the output layer, binary neurons activate based on the score comparison [47,48].

$$W=exp\left({\displaystyle \frac{{‖X-\mu ‖}^2}{{\sigma }^2}}\right)$$

(1)

$$g_{ij}=W\left({\displaystyle \frac{X-X_i}{\phi }}\right)$$

(2)

$$g_j(X)={\displaystyle \frac{1}{n_j}}\sum _{i=1}^n{g}_{ij}$$

(3)

$$Scor{e}_j=h_j{c}_j{g}_j\left(X\right)$$

(4)

where

i: input values;

j: output groups;

$X_i$: input variable in activation function;

$n_j$: number of observations belonging to output group j;

W: weight function (Gaussian basis or prob. density function);

φ: scaling parameter;

$h_j$: prior probability;

$c_j$: misclassification cost;

$g_j\left(X\right)$: probability density function.

Figure 2 illustrates the ANN application concept, focusing on tailing flowability at disposal. The input layer, pattern layer, and summary layer process the variables deemed most relevant, culminating in binary responses in the output layer. The model generates two predictions based on nearest neighbours [49]. Classification analysis using nearest neighbours relies on proximity to identify similar behavioural patterns [43,45]. This study used an ANN application with a supervised method to train the network. A total of 108 cases based on laboratory tests are used for dataset creation, with 90 cases used for training and 18 cases reserved for testing and validation. This approach ensures that the model is trained on a substantial portion of the data, while retaining enough cases to evaluate its performance effectively.

2.2. Tailing Sampling

The tailing sample used in this study was a product of a flotation process generated in the pilot plant of the Oulu Mining School (University of Oulu, Finland). The ore precedence is from the Pyhäsalmi mine, with over 70% sulphur in pyrite, chalcopyrite, sphalerite, and pyrrhotite form. The average concentration of the principal elements is 1.2% Cu, 2.2% Zn, and 38.4% S [50]. A total of 285 kg of tailing sample was used to carry out the laboratory tests. The sample was dried for 48 h at 80 °C, homogenised using riffle splitters, and reduce to subsamples of 2500 g and 500 g for flume and settling tests, respectively, with additional reductions according to the solid percentage required in the experimental design. A total of 100 g of subsamples was used for density, particle-size distribution, and chemical characterisation. The particle-size distribution (PSD) analysis (Figure 3) revealed a P₈₀ of 184 µm, with particles between 2 and 75 µm accounting for 46% and particles under 20 µm making up 18%. The tailing density was 3.34 g/mL, typical of a zinc–copper sulphide ore flotation. An XRF-based analysis showed a composition of 34.0% SO₃, 20.8% Fe₂O₃, and 17.3% SiO₂.

3. Experimental Design

3.1. Dataset

A test design was conducted to generate a dataset that would provide a comprehensive understanding of tailings behaviour in thickening and disposal operational conditions. This was achieved by focusing on two critical operational variables: solid percentage and flocculant dosage. As presented in Figure 4, settling tests were conducted to generate the data, with solid–liquid separation variables and flume tests to obtain the data from the tailings behaviour at their deposition. A total of 108 cases were completed using a variety of combinations of these variables, following the parameters specified in the design. The objective was to examine nonlinear behaviour and validate the predictive capabilities of artificial neural networks (ANNs) as demonstrated by Pasini [51], Condon [52], and Feng et al. [53] using a limited dataset. The initial step involved assessing the viability of causal relationships between variables related to tailings operations, followed by examining the relationship between these variables and the behaviour of the segregated tailings.

Figure 5 presents a summary of the 12 variables considered for generating the dataset. For test evaluation and volume estimations, the particle-size distribution, mineralogy, and density are determined.

In the settling test, key factors such as the sedimentation rate and equilibrium systems were examined, considering their direct dependence on particle size, minerology, and the type of flocculant [54,55]. The Kemira Superfloc A-130 flocculant was used for all the tests, prepared in a stock solution concentrated at 2 g/L and diluted to a working solution of 0.1 g/L. The measurements included water recovery, turbidity (using a Hanna HI 98703-02 turbidimeter), and yield stress, with rheological data measured using an Anton Paar RheolabQC rheometer. The yield stress was calculated to compare the evolution of this property in the tailings under different flocculant dosages, serving as a measure of the maximum stress that can be developed in a pulp without resulting in plastic deformation [56].

The second aspect of our investigation focused on dynamic changes in tailings drain flow through a flume test, using laboratory-scale acrylic equipment (200 cm long by 20 cm wide). We estimated the repose angle (qR) using Equation (5), based on measurements of the tailings heights (H₁ and H₂) and the length travelled by the material (L). In addition, the water recovered and final solid percentage were measured, using the methodologies presented by Clayton et al. [57], Kwak et al. [58], and Oliveira et al. [59]. Figure 6 offers a graphical representation of the experimental arrangement for the flume test.

$$qR=arctan\left({\displaystyle \frac{H_1-H_2}{L}}\right)$$

(5)

3.2. Flowability Categories

This research proposes the categorisation of tailings based on their flowability and behaviour shown at the moment they enter final deposition. Working with a soft computing tool such as ANN allows one to handle complex relationships between independent variables in the dataset, thanks to connections (synapses) between neurons within the network. The observed flowability of the tailings in the flume experiments were classified into five categories based on their run-out distance, e.g., the minimum observed (90 cm) and maximum observed (160 cm). Category 1 represented the driest tailing with less fluidity, whereas category 5 represented the wet tailings with complete fluidity. The description of these categories is presented in Figure 7.

3.3. Data Analysis

A correlation analysis is performed to gain insights into the dataset’s underlying structure and detect potential correlations between variables. This analysis helps to uncover trends and patterns that may influence/impact the performance of the model. This study includes an evaluation of soft computing methods such as decision trees, random forests, gradient-boosted trees, and support vector machines (SVM), in contrast to ANNs. Each technique possesses unique strengths and weaknesses, and their performance can vary based on the characteristics of the dataset. With this assessment, we can discern how effectively the method captures the underlying patterns and relationships in the dataset. The ANN approach employed in this study consisted of a pattern layer with 10 neurons. These neurons receive input data that correspond to the variables selected for each model. The input data are assigned a weight (Wi) and processed through several connections. The output of each neuron in the pattern layer is combined by five neurons in a summatory cell. This summatory cell computes the weighted sum of the inputs and applies an activation function. Finally, the output layer consists of 5 neurons, which correspond to the tailings flowability categories. These neurons determine the response of the network depending on the values calculated by the summatory cell. The selected variables were examined to develop several models using neural network analysis. Initially, a supervised method was employed to train the neural network and establish relationships between potential scenarios. Subsequently, with an unsupervised method, the network was prepared to provide predictions for the different categories of tailings flowability. This serves as corroboration data, with 3 and 5 responses as shown in Figure 8.

To create the predictive models, the software RAPIDMINER Studio Version 9.10 [60] was used. The process involved utilising a supervised method to train the neural network and analyse potential outcomes. Subsequently, an unsupervised method was employed to obtain the predictions from the network, followed by a verification stage for prediction checking. Initially, supervised training was conducted using six predictive variables associated with tailings operations (Figure 9) and selected from a correlation analysis associated with the tailings flowability categories. The combination of variables was extended based on the highest percentage of success in network training. The statistical information of these variables is also presented in

Table 1. Statistical summary of the variables used in the models.

Variable ID	Variable Name	Acronym	Average	Standard Deviation	Low Range	Medium Range	High Range
1	Initial solid percentage (%)	Cpi	22.0	5.6	15.0	20.0	30.0
2	Flocculation dosage (g/t)	Floc.	17.9	5.6	10.0	20.0	25.0
3	Sedimentation rate (cm/min)	SR	0.258	0.174	0.052	0.202	0.871
4	Yield stress (N/m)	φ	281.6	105.0	96.4	264.2	684.6
5	Viscosity (mPa.S)	μ	2356.2	4943.2	254.9	423.6	23,953.6
6	Turbidity (NTU)	Tn	44.1	56.0	3.5	19.5	231.2
7	Water recovered (sed. test) (mL)	Wsr	891.5	46.6	780.3	896.2	971.6
8	Water content (%)	Wc	27.1	4.9	10.5	28.2	34.9
9	Underflow solid percentage (%)	CPu	71.9	4.4	65.0	70.5	85.5
10	Repose angle (qr)	Qr	4.2	0.8	2.0	4.3	5.8
11	Water recovered (flume test) (mL)	Wfr	464.9	153.2	80.2	449.7	917.8
12	Run-out distance (cm)	Rod	133.2	17.8	74.8	132.6	179.8

.

The groups of variables chosen for Model 1 correspond to the variables that have the greatest impact on the tailings flow generated at the time of being deposited, including both the thickening and discharge operation [58,61,62]. Model 2 uses variables that can be monitored directly from the operation [2,63], including characteristics that can be analysed with portable instruments such as yield stress and turbidity. Model 3 considers a mixture of data, comprise those obtained in operation with real-time monitoring [64,65] and laboratory tests.

4. Results and Discussion

4.1. Correlation Matrix Analysis

The correlation matrix analysis reveals the complex nature of tailings process operations. Figure 10 shows density graphs on the major diagonal, highlighting the correlations among the dataset variables. A significant variability among the parameters indicates the necessity for meticulous monitoring and control to achieve the desired outcomes. Notably, the flocculant dosage correlates positively with sedimentation rate, yield stress, and repose angle. The solid concentration (%) significantly impacts water recovery, turbidity, moisture content, sedimentation rate, and yield stress. The positive correlation between water balance in the settling and flume tests and the final tailings water content underscores the intricate interactions within the system. High coefficients of variation (CVs) for turbidity (120.50%) and yield stress (40.02%) emphasise the variability in these measurements, due to factors like solids percentage and settling rate.

4.2. ANN Performance Comparison

Table 2. Performance of different soft computing method with variables groups.

	Model 1		Model 2		Model 3
	Correlation	RMSE	Correlation	RMSE	Correlation	RMSE
Generalised Linear Model	0.800	0.505	0.880	0.444	0.949	0.399
Artificial Neural Network	0.846	0.442	0.913	0.323	0.982	0.177
Decision Tree	0.739	0.494	0.873	0.381	0.964	0.324
Random Forest	0.816	0.460	0.888	0.429	0.957	0.348
Gradient-Boosted Trees	0.769	0.520	0.864	0.400	0.925	0.429
Support Vector Machine	0.779	0.569	0.846	0.431	0.935	0.336

presents a metric performance comparison between the ANN and other soft computing methods, where an artificial neural network outperforms the other soft computing methods in terms of correlations for the predictor variable groups. The RMSE (Root Mean Square Error) is a standard way to measure the error of a model in predicting quantitative data. The RMSE is particularly useful in our context, because it provides a single measure of prediction accuracy that accounts for the variability and scale of the data. The ANN presents the lowest RMSE values (Model 1: 0.442, Model 2: 0.323, Model 3: 0.177) and the smallest square error v alues (Model 1: 0.206, Model 2: 0.199, Model 3: 0.057) that have been effective in accurately predicting the tailings flowability. The decision tree (DT) and random forest (RF) models exhibit a reasonably good performance, although they have slightly lower correlation coefficients and a higher RMSE (Model 1: DT: 10.5%/RF: 3.9%, Model 2: DT: 15.2%/RF: 24.7%, and Model 3: DT: 45.4%/RF: 49.1%) compared to the ANN method, suggesting that the choice of ANN for this study was appropriate.

From a comparison analysis of prediction model reliability performance and computation time (Figure 11), the ANN stands out in performance, showcasing 20% lower RMSE values compared to the other methods, indicating its superior predictive accuracy. In computation time, the ANN exhibits low scoring times, with an average reduction of around 50% compared to the other methods. This efficiency underscores the ANN’s practical feasibility for real-time applications. Decision trees, while offering simplicity, display a mixed performance, with noticeable disparities in RMSE values. Random forests and gradient-boosted trees have a varying performance, with random forests showing a relatively stable performance, albeit with slightly higher computational requirements compared to the ANN. Gradient-boosted trees exhibits competitive RMSE values but with significantly higher scoring times, particularly evident with a five flowability categories scenario. Support vector machines (SVMs) demonstrate relatively high RMSE values, coupled with moderate to high scoring times. Generalised linear models consistently demonstrate a low RMSE at the three or five flowability categories.

4.3. Variable Weights Analysis

An analysis of the weights is conducted on the variable groups acquired from the tests (Figure 12), to determine the significance of the variables for the three variable groups (Figure 8) and examine their interactions. One important consideration is using a group of variables that are possible to measure at an industrial level (Model 2), and this type of method can be considered for obtaining data in the operational monitoring of tailings disposal. Based on the findings, the relative importance (weights) assigned to the input variables remains largely unchanged when the number of response categories is varied. For the predictive models, yield stress is a cross-sectional variable. For Models 1 and 2, variables like the amount of water in the tailings or the solid concentration at the thickenings exit are very important. This indicates that, from a sensitivity analysis perspective, these variables are both highly influential and critical to the accuracy and reliability of the model. Conversely, variables with lower weights and sensitivity, such as sedimentation rate and turbidity, were found to have a lesser impact on the model’s predictions. Model 3 presents variables with proportional weights between them, with the water recovered in the deposit from the tailings and the repose angle being the most relevant. These findings confirm that the key variables identified in the weights analysis are indeed the most significant contributors to the models’ performance.

4.4. ANN Model Training Stage

Table 3. Classification training results for Models 1, 2, and 3 for three flowability categories.

	Model 1 (3C)		Model 2 (3C)		Model 3 (3C)
Tailing Flowability Categories	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified
Solid	6	50.00	6	33.33	8	62.50
Intermediate	62	90.32	59	89.83	59	94.92
Liquid	22	72.73	25	72.00	23	65.22
Total	90	83.33	90	81.11	90	84.44

presents the training result for determining the process response (flowability category) based on six predictive variables for each model. The training process optimises the combination of variables used by the model to achieve the best possible performance. The training results for the three response categories (solid, intermediate, and liquid) are presented in Table 3, where model 3 obtained an 84.4% correct classification. For the intermediate category, all three models exhibited an overall higher accuracy of 91.69%. These results are expected, because variables such as the water content in tailings, yield stress, and repose angle are influential variables according to the bibliography [66,67] and the correlation analysis (jackknifing of 0.125).

The analysis of the data shows that including more examples of category 1 tailings behaviour would significantly improve the network’s ability to learn and classify new cases. The training results of model 2 are particularly relevant, since they provide the possibility of understanding performance using variables that are currently monitored in the industry and are possible to obtain from day-to-day operations. With a spacing parameter optimised during training by jackknifing of 0.0375, this model obtains a success rate of 81.1%.

Increasing to five response categories (solid, semi-solid, intermediate semi-liquid, and liquid) as presented in

Table 4. Classification training results for Models 1, 2, and 3 for five flowability categories.

	Model 1 (5C)		Model 2 (5C)		Model 3 (5C)
Tailing Flowability Categories	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified
Solid	2	100.00	2	100.00	2	100.00
Semi-solid	9	88.89	8	50.00	10	90.00
Intermediate	37	81.08	40	90.00	37	89.19
Semi-liquid	34	82.35	34	76.47	34	73.53
Liquid	8	50.00	6	50.00	7	71.43
Total	90	80.00	90	78.89	90	82.22

, the model 3 accuracy decreased by 2.22%. However, it remains a model with a better classification capacity compared to models 1 and 2. This close classification is also present in the three models, creating a correctly solid flowability category for the cases. In the intermediate category, all three models performed reasonably well, with accuracy rates ranging from 81.08% to 90.00%. Model 2 had the highest accuracy of 90.00% among the three models, correctly classifying 36 out of 40 cases. It is important to consider that the decrease in the correct classification has a dependence on the number of cases available to generate the prediction and the incorporation of two new categories.

As expressed by Alom et al. [68], the error can be minimised as more cases are used in the training, where the errors present mostly occur with neighbouring behaviours that the tailings present. This is relevant considering the number of cases available for this study. As time progresses, it is expected to update the database, including new results under different operating conditions. The categories with the least amount of data occur with intermediate categories and liquid behaviour. In this topic, as expressed by Albalasmeh et al. [69], minimising the error covers all the feasible options that may occur, adjusting the synaptic weights of the neurons, and modifying the outputs according to the error made in each learning step, until getting as close as possible to the desired output.

4.5. ANN Models Unsupervised Classification

To analyse the prediction level achieved by the models, an unsupervised classification method is applied with the remaining available data. This includes two probability classification levels of response: the first corresponding to the nearest neighbour (highest probability of being obtained), and the second corresponding to the second closest neighbour (second highest probability of coming out).

Table 5. Unsupervised classification results for Models 1, 2, and 3 for three categories.

	Model 1 (3C)		Model 2 (3C)		Model 3 (3C)
Tailing Flowability Categories	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified
Solid	2	50.00	2	100.00	1	100.00
Intermediate	9	88.89	13	92.31	12	91.67
Liquid	7	71.43	3	100.00	5	60.00
Total	18	77.78	18	94.44	18	83.33

shows that model 2 made 18 predictions, with 17 being correct (94.44% accuracy). In some cases, the predicted category is close to the boundary between two categories, leading to uncertainties and a misleadingly low certainty value. To address this, we consider the two predictions corresponding to the first and second highest probability for the tailings behaviour. This approach helps account for the uncertainty near category boundaries and provides a more nuanced view of the model’s predictions.

Model 2 was the most accurate at classifying, with a score of 94.44%, far surpassing Model 1 and Model 3, which were only 77.78% and 83.33% accurate, respectively. The prediction of Model 2 obtains 16.7% more success than in Model 1 because of flowability qualities in the solid and liquid categories, making Model 2 more drastic when making a decision in this category. By considering the first and second highest probability of a certain category occurring, Model 2’s predictions can identify the behaviour of tailings upon deposition using existing industrial measurements. Figure 13 shows a graphical comparison of the measured and predicted category values for three tailing flowability categories, where the high determination coefficient (0.837) for Model 2 indicates a strong correlation between the measured and predicted values. Incorporating data with intermediate solid concentrations in future tests could potentially reduce the model’s bias towards intermediate categories. This would also imply that its prediction would serve to establish strategies for incorporating it into the deposit in order to seek intermediate standardisation in the tailings.

Increasing to five response categories (

Table 6. Unsupervised classification results for Models 1, 2, and 3 for five categories.

	Model 1 (5C)		Model 2 (5C)		Model 3 (5C)
Tailing Flowability Categories	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified	Cases	Percentage Correctly Classified
Solid	1	0.00	1	100.00	0	0.00
Semi-solid	1	100.00	2	50.00	1	100.00
Intermediate	8	75.00	6	85.71	7	85.71
Semi-liquid	7	57.14	8	75.00	8	62.50
Liquid	1	0.00	1	100.00	2	50.00
Total	18	70.72	18	77.78	18	72.22

), the need to obtain new behaviour data in extreme categories continues to be shown. The performance of the three models can be considered similar across all categories. If we consider the joint use of models, Model 2 could benefit from improvements in correctly classifying intermediate and semi-liquid cases and Model 1 or 2 with semi-solid tailings behaviour. The use of variables such as the repose angle, which has a tendency towards normality, and water recovered in the deposit does not generate a significant impact compared to variables that are currently easier to obtain, as we used in Models 1 and 2.

Although there is a decrease of almost 17% when increasing to five categories, Model 2 continues to show an important capacity for classification, where the focus, as occurred with the previous analysis, is on the generation of new data that is close to the range ends of the semi-liquid and semi-solid categories to increase the hits obtained. Figure 14 expands the comparative analysis of the measured and predicted category evaluation with five categories. Here, Model 2 complement the 77.78% accuracy with a determination coefficient of 0.843, reflecting its robustness in managing more complex classifications. While Model 1’s accuracy dropped to 70.72% and Model 3 achieved a 72.22% accuracy, Model 2 continued to demonstrate a high performance, underscoring its ability to handle the additional classification complexity accurately. These findings highlight Model 2’s reliability and precision in predicting tailing flowability across different categorisation schemes.

As was mentioned, the errors produced in the models correspond to the responses given to the categories close to the true response, mostly in the intermediate behaviour and the semi-liquid classification. This leads to the point that from an operational perspective, the error is not considered serious, as it involves continuous behaviours where similar tailings discharge strategies are applied, without impacting the dump space disposal. These results demonstrate that the currently monitored variables and the ANN application can achieve a high degree of prediction, with the possibility of improving it by integrating new data related to tailings into the dataset. Analysing the weight given by the variables in the predictions, the flocculation doses are one of the variables that most influence the behaviour of tailings. As mentioned by López [4], when considering the solid percentage entering the thickening operation, it is important to consider physicochemical characteristics of the tailings. This ensures that the solid percentage at the thickener underflow is maximised without affecting the viscosity or yield stress, thereby avoiding any potential issue with tailings transport or disposal. Increasing the solid percentage generates greater compaction, which decreases the size of the pores and reduces their hydraulic conductivity, as established by Marchant [8], thereby preventing drainage in the deposit.

Figure 15 presents a summary of the unsupervised classification percentages of the ANN models categorised by stages and variations. Overall, the training stage achieved relatively high corroboration rates, ranging from 78% to 84.4% across the models. When considering only the highest probability prediction, the unsupervised classification rates varied, with Model 1 at five flowability categories achieving the lowest percentage of 65.4%, while Model 2 achieved the highest at 88.9%. When considering the top two highest probability predictions, the unsupervised classification rates improved for all models, with Model 2 achieving the highest rate of 94.4%. The possibility of using more than one model at a time and flexibility with variable associations open the opportunity, from plans generation to data generation, to increase prediction capability and consider direct operation monitoring to make predictions and apply models at the industrial level.

Figure 16 presents scatter diagrams for the three evaluated models, with respect to the base variables used in the experimental design and the most relevant input variable used for each model. The diagrams illustrate the spectrum of classified cases for three and five categories, demonstrating that in Model 1, the water content at the thickener discharge directly influences a pattern of flowability from low to high when flocculant doses exceed 15 g/t. Increasing the initial solid percentage in the thickening process feed also affects tailings fluidity. In Model 2, tailings stability increases with the final solid percentage, revealing a critical high flowability point when solids are below 70%. In Model 3, a higher repose angle directly impacts the tailings fluidity, indicating the importance of adjusting the flocculant and solid amounts during thickening. The scatter diagrams demonstrate that the ANN models’ classification percentages reflect the operating ranges of a copper tailings process. Using three or five categories effectively identifies the tailings flowability. Furthermore, the choice of variable groups at the start has a big effect on how well the models train and make predictions with smaller datasets, clearly showing the difference between flowability categories.

4.6. Flowability Behaviour and Tailing Water Content Relations

As it was established by Pieretti et al. [70], water content is a critical variable influencing tailings behaviour during transport and deposition. Analysing the water content percentage against flowability as shown in Figure 17, there is a clear relationship, where the water content increases for both cases independent of the number of categories selected. This relationship follows a logarithmical trend for both three and five categories, with correlation coefficients of 99.67% and 99.56%, respectively.

The use of water content as a key input variable is limited by the difficulty of reliably identifying and measuring it at the thickening process outlet. Systematic sampling of thickener discharge, followed by laboratory gravimetric characterisation and solid concentration identification, could enable continuous monitoring—a practice not currently implemented. Some online technologies, such as volumetric measurement sensors [71] and interferometer moisture analysers [72], have been studied for this purpose, but they exhibit deviations of 20% and 6.4%, respectively.

5. Conclusions

This study demonstrated that ANN models provide accurate predictions of tailings behaviour at the moment of disposal, achieving high accuracy prediction corroboration (94.4%). The use of three and five flowability categories was compared, showing that the five-category model provided finer distinctions in tailings behaviour but required more computation time. However, both models outperformed traditional methods in prediction accuracy and computational efficiency. Using a small dataset, competent prediction models for tailings flowability behaviour can be generated, considering a thoughtful design with a pre-studied operation condition representation.

The key findings reveal that the weight and relevance of yield stress, water content, and solid concentration are crucial for the ANN model predictions. The use of the solid concentration and flocculant dosage as critical factors for dataset creation was appropriate, with higher initial solid concentrations leading to an increased yield stress and slower sedimentation rates. Water content emerged as a crucial variable, affecting both the sedimentation rate and turbidity. The ANN models highlighted the importance of these variables, demonstrating that a precise optimisation can lead to substantial improvements in tailings management efficiency.

The practical implications for tailings operations are significant, with the possibility of optimising operational parameters, resulting in more efficient and environmentally friendly tailings disposal practices. Operators can predict and adjust variables such as the initial concentration and flocculant dosage using ANN models, to improve sedimentation rates, reduce turbidity, and improve overall tailings management.

Future research will focus on incorporating additional variables, such as mineralogical properties including clay presence, pH, or permeability, to refine the models and provide a more comprehensive understanding of tailings behaviour, offering greater insights for optimising tailings disposal processes.