A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks
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 q...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-11-01
|
| Series: | Metals |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-4701/9/11/1198 |
| _version_ | 1818008945668653056 |
|---|---|
| author | Manuel Saldaña Javier González Ricardo I. Jeldres Ángelo Villegas Jonathan Castillo Gonzalo Quezada Norman Toro |
| author_facet | Manuel Saldaña Javier González Ricardo I. Jeldres Ángelo Villegas Jonathan Castillo Gonzalo Quezada Norman Toro |
| author_sort | Manuel Saldaña |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:35:46Z |
| format | Article |
| id | doaj.art-a0e7e1edf4554c608ade6111ff2eeff8 |
| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-04-14T05:35:46Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metals |
| spelling | doaj.art-a0e7e1edf4554c608ade6111ff2eeff82022-12-22T02:09:38ZengMDPI AGMetals2075-47012019-11-01911119810.3390/met9111198met9111198A Stochastic Model Approach for Copper Heap Leaching through Bayesian NetworksManuel Saldaña0Javier González1Ricardo I. Jeldres2Ángelo Villegas3Jonathan Castillo4Gonzalo Quezada5Norman Toro6Departamento de Ingeniería de Sistemas y Computación, Facultad de Ingeniería y Ciencias Geológicas, Universidad Católica del Norte, Antofagasta 1270709, ChileDepartamento de Ingeniería Metalúrgica y Minas, Facultad de Ingeniería y Ciencias Geológicas, Universidad Católica del Norte, Antofagasta 1270709, ChileDepartamento de Ingeniería Química y Procesos de Minerales, Facultad de Ingeniería, Universidad de Antofagasta, Antofagasta 1270300, ChileDepartamento de Ingeniería Metalúrgica y Minas, Facultad de Ingeniería y Ciencias Geológicas, Universidad Católica del Norte, Antofagasta 1270709, ChileDepartamento de Ingeniería en Metalurgia, Universidad de Atacama, Copiapó 1531772, ChileWater Research Center for Agriculture and Mining (CRHIAM), University of Concepción, Concepción 4030000, ChileDepartamento de Ingeniería Metalúrgica y Minas, Facultad de Ingeniería y Ciencias Geológicas, Universidad Católica del Norte, Antofagasta 1270709, ChileMultivariate 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.https://www.mdpi.com/2075-4701/9/11/1198bayesian networksuncertainty analysisstochastic process modellingheap leaching |
| spellingShingle | Manuel Saldaña Javier González Ricardo I. Jeldres Ángelo Villegas Jonathan Castillo Gonzalo Quezada Norman Toro A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks Metals bayesian networks uncertainty analysis stochastic process modelling heap leaching |
| title | A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks |
| title_full | A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks |
| title_fullStr | A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks |
| title_full_unstemmed | A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks |
| title_short | A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks |
| title_sort | stochastic model approach for copper heap leaching through bayesian networks |
| topic | bayesian networks uncertainty analysis stochastic process modelling heap leaching |
| url | https://www.mdpi.com/2075-4701/9/11/1198 |
| work_keys_str_mv | AT manuelsaldana astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT javiergonzalez astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT ricardoijeldres astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT angelovillegas astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT jonathancastillo astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT gonzaloquezada astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT normantoro astochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT manuelsaldana stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT javiergonzalez stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT ricardoijeldres stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT angelovillegas stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT jonathancastillo stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT gonzaloquezada stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks AT normantoro stochasticmodelapproachforcopperheapleachingthroughbayesiannetworks |