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. 2022 Feb 18;10(2):95.
doi: 10.3390/toxics10020095.

Neuro-Particle Swarm Optimization Based In-Situ Prediction Model for Heavy Metals Concentration in Groundwater and Surface Water

Kevin Lawrence M De Jesus  1   2   3 , Delia B Senoro  1   2   3   4 , Jennifer C Dela Cruz  1   5 , Eduardo B Chan  6
Affiliations

Neuro-Particle Swarm Optimization Based In-Situ Prediction Model for Heavy Metals Concentration in Groundwater and Surface Water

Kevin Lawrence M De Jesus et al. Toxics. .

Abstract

Limited monitoring activities to assess data on heavy metal (HM) concentration contribute to worldwide concern for the environmental quality and the degree of toxicants in areas where there are elevated metals concentrations. Hence, this study used in-situ physicochemical parameters to the limited data on HM concentration in SW and GW. The site of the study was Marinduque Island Province in the Philippines, which experienced two mining disasters. Prediction model results showed that the SW models during the dry and wet seasons recorded a mean squared error (MSE) ranging from 6 × 10-7 to 0.070276. The GW models recorded a range from 5 × 10-8 to 0.045373, all of which were approaching the ideal MSE value of 0. Kling-Gupta efficiency values of developed models were all greater than 0.95. The developed neural network-particle swarm optimization (NN-PSO) models for SW and GW were compared to linear and support vector machine (SVM) models and previously published deterministic and artificial intelligence (AI) models. The findings indicated that the developed NN-PSO models are superior to the developed linear and SVM models, up to 1.60 and 1.40 times greater than the best model observed created by linear and SVM models for SW and GW, respectively. The developed models were also on par with previously published deterministic and AI-based models considering their prediction capability. Sensitivity analysis using Olden's connection weights approach showed that pH influenced the concentration of HM significantly. Established on the research findings, it can be stated that the NN-PSO is an effective and practical approach in the prediction of HM concentration in water resources that contributes a solution to the limited HM concentration monitored data.

Keywords: groundwater; heavy metals; neural network; particle swarm optimization; surface water.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure A1
Figure A1
Spatial maps of temperature for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A2
Figure A2
Spatial maps of pH for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A3
Figure A3
Spatial maps of EC for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A4
Figure A4
Spatial maps of TDS for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A5
Figure A5
Spatial maps of Cr for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A6
Figure A6
Spatial maps of Cd for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A7
Figure A7
Spatial maps of Fe for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A8
Figure A8
Spatial maps of Mn for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A9
Figure A9
Spatial maps of Zn for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A10
Figure A10
Spatial maps of Ni for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A11
Figure A11
Spatial maps of Pb for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A12
Figure A12
Spatial maps of Cu for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A13
Figure A13
Correlation plots for NN-PSO simulations of Cr for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A14
Figure A14
Correlation plots for NN-PSO simulations of Cd for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A15
Figure A15
Correlation plots for NN-PSO simulations of Fe for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A15
Figure A15
Correlation plots for NN-PSO simulations of Fe for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A16
Figure A16
Correlation plots for NN-PSO simulations of Mn for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A17
Figure A17
Correlation plots for NN-PSO simulations of Zn for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A18
Figure A18
Correlation plots for NN-PSO simulations of Ni for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A19
Figure A19
Correlation plots for NN-PSO simulations of Pb for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A20
Figure A20
Correlation plots for NN-PSO simulations of Cu for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure A20
Figure A20
Correlation plots for NN-PSO simulations of Cu for (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the WS.
Figure 1
Figure 1
Major rivers and its tributaries in the province of Marinduque.
Figure 2
Figure 2
The architecture of the heavy metal prediction models.
Figure 3
Figure 3
The hN-PSO system.
Figure 4
Figure 4
Block diagram of ANN weights optimization using PSO.
Figure 5
Figure 5
Pearson’s correlation matrix plots for the surface water physicochemical parameters and HM concentrations during (a) DS; and (b) WS.
Figure 6
Figure 6
Pearson’s correlation matrix plots for the groundwater physicochemical parameters and HM concentrations during (a) DS; and (b) WS.
Figure 7
Figure 7
Effect of the hidden neurons on the heavy metal model performance measured using AIC: (a) surface water—dry season; (b) surface water—wet season; (c) groundwater—dry season; (d) groundwater—wet season.
Figure 7
Figure 7
Effect of the hidden neurons on the heavy metal model performance measured using AIC: (a) surface water—dry season; (b) surface water—wet season; (c) groundwater—dry season; (d) groundwater—wet season.
Figure 8
Figure 8
KGE values for SW and GW Models during the dry and wet season.
Figure 9
Figure 9
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu surface water models during the dry season.
Figure 9
Figure 9
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu surface water models during the dry season.
Figure 10
Figure 10
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu surface water models during the wet season.
Figure 10
Figure 10
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu surface water models during the wet season.
Figure 11
Figure 11
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu groundwater models during the dry season.
Figure 11
Figure 11
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu groundwater models during the dry season.
Figure 12
Figure 12
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu groundwater models during the wet season.
Figure 12
Figure 12
Radar graph showing the performance of the (a) Cr; (b) Cd; (c) Fe; (d) Mn; (e) Zn; (f) Ni; (g) Pb; (h) Cu groundwater models during the wet season.
Figure 13
Figure 13
The relative importance of the physicochemical parameters to the heavy metal concentration in (a) SW during the DS; (b) SW during the WS; (c) GW during the DS; (d) GW during the DS.
Figure 14
Figure 14
Comparison of the performance of the published models and the developed models for (a) DS surface water; (b) WS surface water; (c) DS groundwater; (d) WS groundwater.
Figure 14
Figure 14
Comparison of the performance of the published models and the developed models for (a) DS surface water; (b) WS surface water; (c) DS groundwater; (d) WS groundwater.
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