Comparative analysis of feed-forward neural network and second-order polynomial regression in textile wastewater treatment efficiency

Ali S. Alkorbi; Muhammad Tanveer; Humayoun Shahid; Muhammad Bilal Qadir; Fayyaz Ahmad; Zubair Khaliq; Mohammed Jalalah; Muhammad Irfan; Hassan Algadi; Farid A. Harraz; Ali S. Alkorbi; Muhammad Tanveer; Humayoun Shahid; Muhammad Bilal Qadir; Fayyaz Ahmad; Zubair Khaliq; Mohammed Jalalah; Muhammad Irfan; Hassan Algadi; Farid A. Harraz

doi:10.3934/math.2024536

AIMS Mathematics

2024, Volume 9, Issue 5: 10955-10976. doi: 10.3934/math.2024536

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Comparative analysis of feed-forward neural network and second-order polynomial regression in textile wastewater treatment efficiency

1.
Department of Chemistry, Faculty of Science and Arts at Sharurah, Najran University, Sharurah 68342, Saudi Arabia
2.
Department of Applied Sciences, National Textile University, Faisalabad, 37610, Pakistan
3.
Department of Textile Engineering, National Textile University, Faisalabad, 37610, Pakistan
4.
Department of Materials, National Textile University, Faisalabad, 37610, Pakistan
5.
Department of Electrical Engineering, College of Engineering, Najran University, Najran 11001, Saudi Arabia
6.
Advanced Materials and Nano-Research Centre (AMNRC), Najran University, Najran 11001, Saudi Arabia

Received: 12 December 2023 Revised: 20 February 2024 Accepted: 27 February 2024 Published: 20 March 2024
MSC : 65C20, 65D10, 65K99, 68T01

This study refines a single-layer Feed-Forward Neural Network (FFNN) for the treatment of textile dye wastewater, concentrating on percentage decolorization (%DEC) and percentage chemical oxygen demand (%COD) reduction. The optimized neural network configuration comprises four input and one output neuron, fine-tuned based on the mean squared error (MSE). The training phase demonstrates a consistent MSE decline, reaching its lowest at epoch 209 for %DEC and epoch 34 for %COD, with corresponding MSEs of $1.799 \times 10^{-5}$ and $ 1.4 \times 10^{-3} $, respectively. The maximum absolute errors for %DEC and %COD were found to be $ 4.0787 $ and $ 2.4486 $, while the mean absolute errors were $ 0.4821 $ and $ 0.7256 $, respectively. In contrast to second-degree polynomial regression, the FFNN model exhibits enhanced predictive accuracy, as indicated by higher $ R^2 $ values of $ 0.99363 $ for %DEC and $ 0.99716 $ for %COD, and reduced error metrics.
- feed-forward neural network,
- machine learning,
- multi-objective optimization,
- treatment of textile wastewater,
- decolorization,
- chemical oxygen demand,
- sustainable environment
Citation: Ali S. Alkorbi, Muhammad Tanveer, Humayoun Shahid, Muhammad Bilal Qadir, Fayyaz Ahmad, Zubair Khaliq, Mohammed Jalalah, Muhammad Irfan, Hassan Algadi, Farid A. Harraz. Comparative analysis of feed-forward neural network and second-order polynomial regression in textile wastewater treatment efficiency[J]. AIMS Mathematics, 2024, 9(5): 10955-10976. doi: 10.3934/math.2024536

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Abstract

This study refines a single-layer Feed-Forward Neural Network (FFNN) for the treatment of textile dye wastewater, concentrating on percentage decolorization (%DEC) and percentage chemical oxygen demand (%COD) reduction. The optimized neural network configuration comprises four input and one output neuron, fine-tuned based on the mean squared error (MSE). The training phase demonstrates a consistent MSE decline, reaching its lowest at epoch 209 for %DEC and epoch 34 for %COD, with corresponding MSEs of $1.799 \times 10^{-5}$ and $ 1.4 \times 10^{-3} $, respectively. The maximum absolute errors for %DEC and %COD were found to be $ 4.0787 $ and $ 2.4486 $, while the mean absolute errors were $ 0.4821 $ and $ 0.7256 $, respectively. In contrast to second-degree polynomial regression, the FFNN model exhibits enhanced predictive accuracy, as indicated by higher $ R^2 $ values of $ 0.99363 $ for %DEC and $ 0.99716 $ for %COD, and reduced error metrics.

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