Research Article
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Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study

Year 2025, Volume: 8 Issue: 2, 429 - 446, 30.06.2025

Recep Sinan Arslan , Murat Taşyürek , Bahatdin Daşbaşı , Teslima Daşbaşı

https://doi.org/10.35208/ert.1515094

Abstract

The discharge of urban wastewater represents a significant aspect to be considered in the development and design of water and wastewater treatment projects. In this study, the annual urban wastewater discharge was estimated using an artificial neural network (ANN) and differential equations. In order to achieve this, data pertaining to the recorded wastewater per capita amount for the Kayseri province (located in Turkey) over a 17-year period between 2003 and 2020, the city's population, capacity, number of WWTPs, the amount of daily wastewater discharged per person, and the wastewater treated in WWTPs (y(t)) were collated. As the initial data set was insufficient, it was augmented using the ARIMA model and then normalised. The augmented and normalised data was trained with ANN on two occasions, thus demonstrating the impact of other variables on the y(t) variable. Additionally, mathematical ANN activation functions in the form of a tangent hyperbolic function were proposed for this variable. Subsequently, the arbitrary parameters employed in a linear system comprising differential equations representing the aforementioned five variables were estimated utilising the normalised original data, thereby facilitating the formulation of an Ordinary Differential Equation (ODE) model. The performance of two ANN and ODE models was evaluated on normalized real data, and the results were compared. Consequently, the estimation of the quantity of wastewater with the lowest error rate of 0.00001 MSE among the models incorporating four time-dependent variables as inputs was conducted using the ODE model. The model exhibited an R² value of 0.9363 and a MAPE value of 0.0231. The promising estimation results obtained demonstrate the potential utility of this approach for the efficient management of wastewater demand and the protection of valuable water resources.

Keywords

Wastewater quantity ODE model ANN activation function parameter estimation MSE

Thanks

We would like to thank TUIK for providing information about wastewater data and the factors affecting this data.

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Year 2025, Volume: 8 Issue: 2, 429 - 446, 30.06.2025

Recep Sinan Arslan , Murat Taşyürek , Bahatdin Daşbaşı , Teslima Daşbaşı

https://doi.org/10.35208/ert.1515094

Abstract

References

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  • V. Novotny, “Diffuse pollution from agriculture — A worldwide outlook,” Water Science and Technology, vol. 39, no. 3, 1-13, 1999.
  • J. McLean, S. B. Cleveland, M. D. II, M. P. Lucas, R. J. Longman, T. W. Giambelluca ve G. A. Jacobs, “Building a portal for climate data—Mapping automation, visualization, and dissemination,” Concurrency and Computation: Practice and Experience, p. e6727, 2023.
  • M. Ahmadi, M. E. Lotfy, R. Shigenobu, A. M. Howlader ve T. Senjyu, “Optimal Sizing of Multiple Renewable Energy Resources and PV Inverter Reactive Power Control Encompassing Environmental, Technical, and Economic Issues,” IEEE Systems Journal, 3026--3037, 2019.
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  • G. Zhang, Y. Ge, Z. Ye ve M. Al-Bahrani, “Multi-objective planning of energy hub on economic aspects and resources with heat and power sources, energizable, electric vehicle and hydrogen storage system due to uncertainties and demand response,” Journal of Energy Storage, p. 106160, 2023.
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  • Y. Yang, K.-R. Kim, R. Kou, Y. Li, J. Fu, L. Zhao ve H. Liu, “Prediction of effluent quality in a wastewater treatment plant by dynamic neural network modeling,” Process Safety and Environmental Protection, 515-524, 2022.
  • H. Guo, K. Jeong, J. Lim, J. Jo, Y. M. Kim, J.-p. Park, J. H. Kim ve K. H. Cho, “Prediction of effluent concentration in a wastewater treatment plant using machine learning models”, Journal of Environmental Sciences, no. 32, 90-101, 2015.
  • S. Waqas, N. Y. Harun, N. S. Sambudi, U. Arshan, N. A. H. M. Nordin, M. R. Bilad, A. A. H. Saeed ve A. A. Malik, “SVM and ANN Modelling Approach for the Optimization of Membrane Permeability of a Membrane Rotating Biological Contactor for Wastewater Treatment”, Membranes, vol. 12, no. 9, 821, 2022.
  • K. Godini, G. Azarlan, A. Kimiaei, E. N. Dragoi ve S. Curteanu, “Modeling of a real industrial wastewater treatment plant based on aerated lagoon using a neuro-evolutive technique”, Process Safety and Environmental Protection, vol. 148, 114-124, 2021.
  • A. Tarun ve G. P. Reddy, “Artificial Neural Networks for Waste-water Treatment Plant Control”, Proceedings of International Conference on Industrial Instrumentation and Control , vol. 815, 409-419, 2022.
  • G. y. Zhao, H. Furumai ve M. Fujita, “Supporting data–enhanced hybrid ordinary differential equation model for phosphate dynamics in municipal wastewater treatment”, Bioresource Technology, vol. 409, 131217, 2024.
  • P. Veeresha, M. Yavuz ve C. Baishya, “A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators,” An International Journal of Optimization and Control: Theories & Applications, vol. 11, no. 3, 52-67, 2021.
  • P. A. Naik, Z. Eskandari, H. E. Shahkari ve K. M. Owolabi, “Bifurcation analysis of a discrete-time prey-predator model,” Bulletin of Biomathematics, vol. 1, no. 2, 111-123, 2023.
  • B. Ersoy, B. Daşbaşı ve E. Aslan, “Mathematical modelling of fiber optic cable with an electro-opticalcladding by incommensurate fractional-order differential equations,” An International Journal of Optimization and Control: Theories & Applications, vol. 14, no. 1, 50-61, 2024.
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  • E. K. Akgül, A. Akgül ve M. Yavuz, “New illustrative applications of integral transforms to financial models with different fractional derivatives,” Chaos, Solitons & Fractals, vol. 146, no. 110877, 2021.
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  • U. T. Mustapha, Y. U. Ahmad, A. Yusuf, S. Qureshi ve S. S. Musa, “Transmission dynamics of an age-structured Hepatitis-B infection with differential infectivity,” Bulletin of Biomathematics, vol. 1, no. 2, 124-152, 2023.
  • S. Diehl ve S. Farås, “Control of an ideal activated sludge process in wastewater treatment via an ODE–PDE model,” Journal of Process Control, vol. 23, no. 3, 359-381, 2013.
  • P. Zlateva ve N. Dimitrova, “Analysis of Some Properties of an Activated Sludge Wastewater Treatment Model,” %1 içinde The 6th International Conference on Energy and Environmental Science, 2022.
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  • A. Dishan, M. Barel, S. Hizlisoy, R. S. Arslan, H. Hizlisoy, D. A. Gundog, S. Al ve Z. Gonulalan, “The ARIMA model approach for the biofilm-forming capacity prediction of Listeria monocytogenes recovered from carcasses”, BMC Veterinary Research, vol. 20, no. 123, 1-13, 2024.
  • N. Minhaj, R. Ahmed, I. A. Khalique ve M. Imran, “A Comparative Research of Stock Price Prediction of Selected Stock Indexes and the Stock Market by Using Arima Model”, Global Economics Science, vol. 4, no. 1, 1-19, 2022.
  • S. Majumder, “Time Series Analysis — Stationarity Check using Statistical Test”, Analytics Vidhya, 02 05 2020. [Online]. Available: https://medium.com/analytics-vidhya/time-series-analysis-stationarity-check-using-statistical-test-f106e9045370#:~:text=If%20p%20%3E%200.05%2C%20then%20the,present%20data%20and%20past%20data.. [Access: 23 09 2024].
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  • R. Nau, ARIMA models for time series forecasting. Statistical Forecasting: Notes on Regression and Time Series Analysis, Durham: Duke University, 2017.
  • R. S. Arslan ve M. Tasyurek, “AMD-CNN: Android malware detection via feature graph and convolutional neural networks,” Concurrency and Computation: Practice and Experience, p. e7180, 2022.
  • M. Taşyürek, “Odrp: a new approach for spatial street sign detection from exif using deep learning-based object detection, distance estimation, rotation and projection system,” The Visual Computer, 2023.
  • M. Tasyurek ve R. S. Arslan, “RT-Droid: a novel approach for real-time android application analysis with transfer learning-based CNN models,” Journal of Real-Time Image Processing, 1-17, 2023.
  • Y.-c. Wu ve J.-w. Feng, “Development and application of artificial neural network,” Wireless Personal Communications, p. 1645–1656, 2018.
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There are 67 citations in total.

Details

Primary Language English
Subjects Water Quality and Water Pollution
Journal Section Research Articles
Authors

Recep Sinan Arslan 0000-0002-3028-0416

Murat Taşyürek 0000-0001-5623-8577

Bahatdin Daşbaşı 0000-0001-8201-7495

Teslima Daşbaşı 0000-0002-8546-612X

Publication Date June 30, 2025
Submission Date July 12, 2024
Acceptance Date October 5, 2024
Published in Issue Year 2025 Volume: 8 Issue: 2

Cite

APA Arslan, R. S., Taşyürek, M., Daşbaşı, B., Daşbaşı, T. (2025). Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study. Environmental Research and Technology, 8(2), 429-446. https://doi.org/10.35208/ert.1515094
AMA Arslan RS, Taşyürek M, Daşbaşı B, Daşbaşı T. Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study. ERT. June 2025;8(2):429-446. doi:10.35208/ert.1515094
Chicago Arslan, Recep Sinan, Murat Taşyürek, Bahatdin Daşbaşı, and Teslima Daşbaşı. “Predictive Analysis of Urban Wastewater Capacity Using ANN and ODE Model: A Case Study”. Environmental Research and Technology 8, no. 2 (June 2025): 429-46. https://doi.org/10.35208/ert.1515094.
EndNote Arslan RS, Taşyürek M, Daşbaşı B, Daşbaşı T (June 1, 2025) Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study. Environmental Research and Technology 8 2 429–446.
IEEE R. S. Arslan, M. Taşyürek, B. Daşbaşı, and T. Daşbaşı, “Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study”, ERT, vol. 8, no. 2, pp. 429–446, 2025, doi: 10.35208/ert.1515094.
ISNAD Arslan, Recep Sinan et al. “Predictive Analysis of Urban Wastewater Capacity Using ANN and ODE Model: A Case Study”. Environmental Research and Technology 8/2 (June 2025), 429-446. https://doi.org/10.35208/ert.1515094.
JAMA Arslan RS, Taşyürek M, Daşbaşı B, Daşbaşı T. Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study. ERT. 2025;8:429–446.
MLA Arslan, Recep Sinan et al. “Predictive Analysis of Urban Wastewater Capacity Using ANN and ODE Model: A Case Study”. Environmental Research and Technology, vol. 8, no. 2, 2025, pp. 429-46, doi:10.35208/ert.1515094.
Vancouver Arslan RS, Taşyürek M, Daşbaşı B, Daşbaşı T. Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study. ERT. 2025;8(2):429-46.
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