A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks

Abstract

Multivariate analytical models are quite successful in explaining one or more response variables, based on one or more independent variables. However, they do not reflect the connections of conditional dependence between the variables that explain the model. Otherwise, due to their qualitative and quantitative nature, Bayesian networks allow us to easily visualize the probabilistic relationships between variables of interest, as well as make inferences as a prediction of specific evidence (partial or impartial), diagnosis and decision-making. The current work develops stochastic modeling of the leaching phase in piles by generating a Bayesian network that describes the ore recovery with independent variables, after analyzing the uncertainty of the response to the sensitization of the input variables. These models allow us to recognize the relations of dependence and causality between the sampled variables and can estimate the output against the lack of evidence. The network setting shows that the variables that have the most significant impact on recovery are the time, the heap height and the superficial velocity of the leaching flow, while the validation is given by the low measurements of the error statistics and the normality test of residuals. Finally, probabilistic networks are unique tools to determine and internalize the risk or uncertainty present in the input variables, due to their ability to generate estimates of recovery based upon partial knowledge of the operational variables.

Global sensitivity analyses of a neural networks model for a flotation circuit

“…The behavior of the stages (cells) and individual parameters was evaluated to understand which stages and/or operational parameters turn out to be the key to the fulfillment of the operational objectives. On the other hand, in future works, the dynamics of the system could be modeled using other machine learning techniques [52][53][54], and the developed models could be incorporated into a simulation framework [46] that quantifies the benefits associated with improving the efficiency of the process, which can lead to pilot tests and the implementation of this type of predictive models in production processes.…”

Copper Mineral Leaching Mathematical Models—A Review

“…To summarize, mineral leaching process modeling contributes to generating a better understanding of the process dynamic through an abstraction of its operation and expressing the mathematical functions that represent its behavior in an integral way. The different models developed in the literature have also contributed to identifying the impact of the variables and/or operational parameters on the copper minerals leaching, and new approaches, such as the application of machine learning techniques [ 137 , 138 ], could lead to significant improvements in the study of the inherent dynamics in mineral processing, or in the generation of systems that support the mineral leaching process [ 139 , 140 ].…”

Testing the Fit of Regression Models Estimated with Extremely Small Samples: Application in Pharmaceutical Stability Studies

“…Also, novel techniques such as machine learning or artificial intelligence may be used [33][34][35]. On the other hand, it would be of interest to incorporate stochastic modeling, in case of extending the analysis to a greater number of independent variables, in order to have a robust system that allows generating predictions of the response in front of partiality in the independent variables [36]. The results of the mentioned modeling techniques, would allow for redefinition of the allocation of the points and the number of the batches to be measured (in the pre-approval studies) that are defined by the ICH Q1A Guide [1], in order to increase the probability of the detection of model misspecification.…”