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Feasibility of a novel predictive model based on multilayer perceptron optimized with Harris hawk optimization for estimating of the longitudinal dispersion coefficient in rivers

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Abstract

Protecting water resources from pollution is one of the most important challenges facing water management researchers. The governing equation for river pollution is mostly the advection–dispersion equation, with considering the longitudinal dispersion coefficient as its most important effective parameter. The purpose of this paper is to develop a new framework for accurate prediction of the longitudinal dispersion coefficient of rivers based on artificial intelligence (AI) methods. To do this, we used a combination of multilayer perceptron (MLP), one of the most robust neural networks, and a novel metaheuristic algorithm, namely Harris hawk optimization (HHO). Besides, two optimized MLP models with particle swarm optimization (PSO) and imperialist competitive algorithm (ICA) were utilized to demonstrate the accuracy of the proposed model. To evaluate the developed models, 164 series of data collected from previous studies, including hydraulic and geometric parameters of rivers, were used. The indicated results proved the efficiency of the HHO to improve the optimum auto-selection of the AI models. Thus, the recorded results show very high accuracy of the newly developed model, MLP-HHO compared to others. Furthermore, to increase the prediction accuracy, a K-means clustering technique is coupled with MLP-HHO model during dividing the data to train and test categories. The proposed hybrid K-means-MLP-HHO model with coefficient of determination (R2) and root mean square error (RMSE), of 0.97 and 30.94 m2/s, respectively, significantly outperformed all existing and AI-based models. Furthermore, the sensitivity analysis showed that the flow width is the most influential factor in predicting the longitudinal dispersion coefficient.

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Data availability statement

The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. No Free Lunch.

References

  1. Alizadeh MJ, Shahheydari H, Kavianpour MR et al (2017) Prediction of longitudinal dispersion coefficient in natural rivers using a cluster-based Bayesian network. Environ Earth Sci 76:1–11. https://doi.org/10.1007/s12665-016-6379-6

    Article  Google Scholar 

  2. Hashemi Monfared SA, Mirbagheri SA, Sadrnejad SA (2014) A three-dimensional, integrated seasonal separate advection-diffusion model (ISSADM) to predict water quality patterns in the Chahnimeh reservoir. Environ Model Assess 19:71–83. https://doi.org/10.1007/s10666-013-9376-0

    Article  Google Scholar 

  3. Baghbanpour S, Kashefipour SM (2012) Numerical modeling of suspended sediment transport in rivers (case study: Karkheh River). J Sci Technol Agric Nat Resour 16:45–58

    Google Scholar 

  4. Boddula S, Eldho TI (2017) A moving least squares based meshless local petrov-galerkin method for the simulation of contaminant transport in porous media. Eng Anal Bound Elem 78:8–19. https://doi.org/10.1016/j.enganabound.2017.02.003

    Article  MathSciNet  MATH  Google Scholar 

  5. Noori R, Ghiasi B, Sheikhian H, Adamowski JF (2017) Estimation of the dispersion coefficient in natural rivers using a granular computing model. J Hydraul Eng 143:04017001. https://doi.org/10.1061/(asce)hy.1943-7900.0001276

    Article  Google Scholar 

  6. Alizadeh MJ, Ahmadyar D, Afghantoloee A (2017) Improvement on the existing equations for predicting longitudinal dispersion coefficient. Water Resour Manag 31:1777–1794. https://doi.org/10.1007/s11269-017-1611-z

    Article  Google Scholar 

  7. Taylor GI (1954) The dispersion of matter in turbulent flow through a pipe. Proc R Soc Lond Ser A Math Phys Sci 223:446–468. https://doi.org/10.1098/rspa.1954.0130

    Article  Google Scholar 

  8. Elder JW (1959) The dispersion of marked fluid in turbulent shear flow. J Fluid Mech 5:544–560. https://doi.org/10.1017/S0022112059000374

    Article  MathSciNet  MATH  Google Scholar 

  9. Sahay RR, Dutta S (2009) Prediction of longitudinal dispersion coefficients in natural rivers using genetic algorithm. Hydrol Res 40:544–552. https://doi.org/10.2166/nh.2009.014

    Article  Google Scholar 

  10. Fisher H (1968) Dispersion predictions in natural streams. J Sanit Eng Div 94:927–944

    Article  Google Scholar 

  11. Kashefipour S, Falconer RA (2002) Longitudinal dispersion coefficients in natural channels. Water Res 36:1596–1608. https://doi.org/10.1016/S0043-1354(01)00351-7

    Article  Google Scholar 

  12. Etemad-Shahidi A, Taghipour M (2012) Predicting longitudinal dispersion coefficient in natural streams using M5′ model tree. J Hydraul Eng 138:542–554. https://doi.org/10.1061/(asce)hy.1943-7900.0000550

    Article  Google Scholar 

  13. Li X, Liu H, Yin M (2013) Differential evolution for prediction of longitudinal dispersion coefficients in natural streams. Water Resour Manag 27:5245–5260. https://doi.org/10.1007/s11269-013-0465-2

    Article  Google Scholar 

  14. Sattar AMA, Gharabaghi B (2015) Gene expression models for prediction of longitudinal dispersion coefficient in streams. J Hydrol 524:587–596. https://doi.org/10.1016/j.jhydrol.2015.03.016

    Article  Google Scholar 

  15. Kargar K, Samadianfard S, Parsa J et al (2020) Estimating longitudinal dispersion coefficient in natural streams using empirical models and machine learning algorithms. Eng Appl Comput Fluid Mech 14:311–322. https://doi.org/10.1080/19942060.2020.1712260

    Article  Google Scholar 

  16. Memarzadeh R, Ghayoumi Zadeh H, Dehghani M et al (2020) A novel equation for longitudinal dispersion coefficient prediction based on the hybrid of SSMD and whale optimization algorithm. Sci Total Environ 716:137007. https://doi.org/10.1016/j.scitotenv.2020.137007

    Article  Google Scholar 

  17. Dehghani M, Zargar M, Riahi-Madvar H, Memarzadeh R (2020) A novel approach for longitudinal dispersion coefficient estimation via tri-variate archimedean copulas. J Hydrol 584:124662

    Article  Google Scholar 

  18. Jafari-Asl J, Ben Seghier MEA, Ohadi S, van Gelder P (2021) Efficient method using Whale Optimization Algorithm for reliability-based design optimization of labyrinth spillway. Appl Soft Comput 101:107036. https://doi.org/10.1016/j.asoc.2020.107036

    Article  Google Scholar 

  19. Julie MD, Kannan B (2012) Attribute reduction and missing value imputing with ANN: prediction of learning disabilities. Neural Comput Appl 21:1757–1763. https://doi.org/10.1007/s00521-011-0619-1

    Article  Google Scholar 

  20. Wróbel J, Kulawik A (2019) Calculations of the heat source parameters on the basis of temperature fields with the use of ANN. Neural Comput Appl 31:7583–7593. https://doi.org/10.1007/s00521-018-3594-y

    Article  Google Scholar 

  21. Shukla V, Bandyopadhyay M, Pandya V et al (2020) Artificial neural network based predictive negative hydrogen ion helicon plasma source for fusion grade large sized ion source. Eng Comput. https://doi.org/10.1007/s00366-020-01060-5

    Article  Google Scholar 

  22. Wang L, Von Laszewski G, Huang F et al (2011) Task scheduling with ANN-based temperature prediction in a data center: a simulation-based study. Eng Comput 27:381–391. https://doi.org/10.1007/s00366-011-0211-4

    Article  Google Scholar 

  23. Jalal M, Grasley Z, Gurganus C, Bullard JW (2020) A new nonlinear formulation-based prediction approach using artificial neural network (ANN) model for rubberized cement composite. Eng Comput. https://doi.org/10.1007/s00366-020-01054-3

    Article  Google Scholar 

  24. Koopialipoor M, Fahimifar A, Ghaleini EN et al (2020) Development of a new hybrid ANN for solving a geotechnical problem related to tunnel boring machine performance. Eng Comput 36:345–357. https://doi.org/10.1007/s00366-019-00701-8

    Article  Google Scholar 

  25. Mai SH, Ben Seghier MEA, Nguyen PL et al (2020) A hybrid model for predicting the axial compression capacity of square concrete-filled steel tubular columns. Eng Comput. https://doi.org/10.1007/s00366-020-01104-w

    Article  Google Scholar 

  26. Luat NV, Shin J, Lee K (2020) Hybrid BART-based models optimized by nature-inspired metaheuristics to predict ultimate axial capacity of CCFST columns. Eng Comput. https://doi.org/10.1007/s00366-020-01115-7

    Article  Google Scholar 

  27. Le LM, Ly HB, Pham BT et al (2019) Hybrid artificial intelligence approaches for predicting buckling damage of steel columns under axial compression. Materials (Basel) 12:1670. https://doi.org/10.3390/ma12101670

    Article  Google Scholar 

  28. Zounemat-Kermani M, Kisi O, Piri J, Mahdavi-Meymand A (2019) Assessment of artificial intelligence-based models and metaheuristic algorithms in modeling evaporation. J Hydrol Eng 24:04019033. https://doi.org/10.1061/(asce)he.1943-5584.0001835

    Article  Google Scholar 

  29. Jahandideh-Tehrani M, Jenkins G, Helfer F (2020) A comparison of particle swarm optimization and genetic algorithm for daily rainfall-runoff modelling: a case study for Southeast Queensland, Australia. Optim Eng. https://doi.org/10.1007/s11081-020-09538-3

    Article  MATH  Google Scholar 

  30. Ghorbani MA, Kazempour R, Chau KW et al (2018) Forecasting pan evaporation with an integrated artificial neural network quantum-behaved particle swarm optimization model: a case study in Talesh, Northern Iran. Eng Appl Comput Fluid Mech 12:724–737. https://doi.org/10.1080/19942060.2018.1517052

    Article  Google Scholar 

  31. Azad A, Farzin S, Kashi H et al (2018) Prediction of river flow using hybrid neuro-fuzzy models. Arab J Geosci 11:718. https://doi.org/10.1007/s12517-018-4079-0

    Article  Google Scholar 

  32. Najafzadeh M, Tafarojnoruz A (2016) Evaluation of neuro-fuzzy GMDH-based particle swarm optimization to predict longitudinal dispersion coefficient in rivers. Environ Earth Sci 75:157. https://doi.org/10.1007/s12665-015-4877-6

    Article  Google Scholar 

  33. Gholami A, Bonakdari H, Ebtehaj I et al (2018) Uncertainty analysis of intelligent model of hybrid genetic algorithm and particle swarm optimization with ANFIS to predict threshold bank profile shape based on digital laser approach sensing. Measurement 121:294–303. https://doi.org/10.1016/j.measurement.2018.02.070

    Article  Google Scholar 

  34. Jafari-Asl J, Azizyan G, Monfared SAH et al (2021) An enhanced binary dragonfly algorithm based on a V-shaped transfer function for optimization of pump scheduling program in water supply systems (case study of Iran). Eng Fail Anal 123:105323. https://doi.org/10.1016/j.engfailanal.2021.105323

    Article  Google Scholar 

  35. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  36. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  37. Te CV (1959) Open-channel hydraulics. McGraw-Hill, New York

    Google Scholar 

  38. Khandelwal M, Marto A, Fatemi SA et al (2018) Implementing an ANN model optimized by genetic algorithm for estimating cohesion of limestone samples. Eng Comput 34:307–317. https://doi.org/10.1007/s00366-017-0541-y

    Article  Google Scholar 

  39. Gao W, Guirao JLG, Basavanagoud B, Wu J (2018) Partial multi-dividing ontology learning algorithm. Inf Sci (NY) 467:35–58. https://doi.org/10.1016/j.ins.2018.07.049

    Article  MathSciNet  MATH  Google Scholar 

  40. Armaghani DJ, Momeni E, Abad SVANK, Khandelwal M (2015) Feasibility of ANFIS model for prediction of ground vibrations resulting from quarry blasting. Environ Earth Sci 74:2845–2860. https://doi.org/10.1007/s12665-015-4305-y

    Article  Google Scholar 

  41. Liu L, Moayedi H, Rashid ASA et al (2020) Optimizing an ANN model with genetic algorithm (GA) predicting load-settlement behaviours of eco-friendly raft-pile foundation (ERP) system. Eng Comput 36:421–433. https://doi.org/10.1007/s00366-019-00767-4

    Article  Google Scholar 

  42. Gao W, Raftari M, Rashid ASA et al (2020) A predictive model based on an optimized ANN combined with ICA for predicting the stability of slopes. Eng Comput 36:325–344. https://doi.org/10.1007/s00366-019-00702-7

    Article  Google Scholar 

  43. Moayedi H, Mehrabi M, Mosallanezhad M et al (2019) Modification of landslide susceptibility mapping using optimized PSO-ANN technique. Eng Comput 35:967–984. https://doi.org/10.1007/s00366-018-0644-0

    Article  Google Scholar 

  44. Dreyfus G (2005) Neural networks: methodology and applications. Springer Science & Business Media

  45. Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 65:386–408. https://doi.org/10.1037/h0042519

    Article  Google Scholar 

  46. Tukey JW (1962) The future of data analysis. Ann Math Stat 33:1–67

    Article  MathSciNet  MATH  Google Scholar 

  47. Montalvo I, Izquierdo J, Pérez R, Tung MM (2008) Particle swarm optimization applied to the design of water supply systems. Comput Math Appl 56:769–776. https://doi.org/10.1016/j.camwa.2008.02.006

    Article  MathSciNet  MATH  Google Scholar 

  48. Eberhart R, Kennedy J (1995) New optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39–43

  49. Jafari-Asl J, Sami Kashkooli B, Bahrami M (2020) Using particle swarm optimization algorithm to optimally locating and controlling of pressure reducing valves for leakage minimization in water distribution systems. Sustain Water Resour Manag 6:1–11. https://doi.org/10.1007/s40899-020-00426-3

    Article  Google Scholar 

  50. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks, pp 1942–1948

  51. Atashpaz Gargari E, Hashemzadeh F, Rajabioun R, Lucas C (2008) Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process. Int J Intell Comput Cybern. https://doi.org/10.1108/17563780810893446

    Article  MathSciNet  MATH  Google Scholar 

  52. Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

    Article  Google Scholar 

  53. Abbasi A, Firouzi B, Sendur P (2019) On the application of Harris hawks optimization (HHO) algorithm to the design of microchannel heat sinks. Eng Comput. https://doi.org/10.1007/s00366-019-00892-0

    Article  Google Scholar 

  54. Moayedi H, Abdullahi MM, Nguyen H, Rashid ASA (2019) Comparison of dragonfly algorithm and Harris hawks optimization evolutionary data mining techniques for the assessment of bearing capacity of footings over two-layer foundation soils. Eng Comput. https://doi.org/10.1007/s00366-019-00834-w

    Article  Google Scholar 

  55. Zhong C, Wang M, Dang C et al (2020) First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis. Struct Multidiscipl Optim 62:1951–1968. https://doi.org/10.1007/s00158-020-02587-3

    Article  MathSciNet  Google Scholar 

  56. Moayedi H, Osouli A, Nguyen H, Rashid ASA (2019) A novel Harris hawks’ optimization and k-fold cross-validation predicting slope stability. Eng Comput. https://doi.org/10.1007/s00366-019-00828-8

    Article  Google Scholar 

  57. Disley T, Gharabaghi B, Mahboubi AA, Mcbean EA (2015) Predictive equation for longitudinal dispersion coefficient. Hydrol Process 29:161–172. https://doi.org/10.1002/hyp.10139

    Article  Google Scholar 

  58. Ben Seghier MEA, Corriea JAFO, Jafari-Asl J et al (2021) On the modeling of the annual corrosion rate in main cables of suspension bridges using combined soft computing model and a novel nature-inspired algorithm. Neural Comput Appl 33:15969–15985. https://doi.org/10.1007/s00521-021-06199-w

    Article  Google Scholar 

  59. Seghier MEAB, Höche D, Zheludkevich M (2022) Prediction of the internal corrosion rate for oil and gas pipeline: Implementation of ensemble learning techniques. J Nat Gas Sci Eng 99:104425

  60. Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. https://doi.org/10.1029/2000JD900719

    Article  Google Scholar 

  61. Granata F, Gargano R, de Marinis G (2020) Artificial intelligence based approaches to evaluate actual evapotranspiration in wetlands. Sci Total Environ 703:135653. https://doi.org/10.1016/j.scitotenv.2019.135653

    Article  Google Scholar 

  62. Simão ML, Videiro PM, Silva PBA et al (2020) Application of Taylor diagram in the evaluation of joint environmental distributions’ performances. Mar Syst Ocean Technol 15:151–159. https://doi.org/10.1007/s40868-020-00081-5

    Article  Google Scholar 

  63. Seo IW, Cheong TS (1998) Predicting longitudinal dispersion coefficient in natural streams. J Hydraul Eng 124:25–32. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:1(25)

    Article  Google Scholar 

  64. Deng ZQ, Singh VP, Bengtsson L (2001) Longitudinal dispersion coefficient in straight rivers. J Hydraul Eng 127(11):919–927

    Article  Google Scholar 

  65. Zeng Y, Huai W (2014) Estimation of longitudinal dispersion coefficient in rivers. J Hydro Environ Res 8(1):2–8

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran

    Sima Ohadi, Seyed Arman Hashemi Monfared, Mehdi Azhdary Moghaddam & Mohammad Givehchi

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  1. Sima Ohadi
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  2. Seyed Arman Hashemi Monfared
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Ohadi, S., Hashemi Monfared, S., Azhdary Moghaddam, M. et al. Feasibility of a novel predictive model based on multilayer perceptron optimized with Harris hawk optimization for estimating of the longitudinal dispersion coefficient in rivers. Neural Comput & Applic 35, 7081–7105 (2023). https://doi.org/10.1007/s00521-022-08074-8

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