Development of Neural Network Model Based on Conjugate Gradient and Resilient Back-Propagation Training Function for Estimation of Longitudinal Dispersion Coefficient in Rivers

Subject Areas : Subjects

Roohollah Noori ¹ (Graduate Faculty of Environment, University of Tehran, No. 23, Ghods St., Enghelab Ave., Tehran, Iran, P.O.BOX: 14155-6135)
Behzad Ghiasi ² (دانشگاه تهران)
عبدالرضا کرباسی ³ (دانشگاه تهران)
امین سارنگ ⁴ (دانشگاه تهران)

Received: 2016-05-17 Accepted : 2019-08-26 Published : 2019-08-23

Keywords: Longitudinal Dispersion Coefficient, Water Pollutant, Intelligence Models, Training Algorithm,

Abstract :

Determining the longitudinal dispersion coefficient (LDC) for Advection-Diffusion equation is the first step in water quality modeling for one-dimensional water bodies such as rivers. In this research, an artificial neural network (ANN) model has been developed based on the standard numerical optimization algorithms and heuristic techniques to determine the LDC. In this regard, conjugate gradient (CG) training functions including Fletcher-Reeves, Polak-Ribiére, Powell-Beale and scaled conjugate gradient functions from the standard numerical optimization algorithms category and resilient back-propagation (Trainrp) training function from the heuristic algorithms, have been applied to optimizing ANN parameters. Then, the best model has been selected for each of the training functions according to indices that are used to evaluate results. Among the selected models, the ANN model with the Trainrp training function has been selected as the best model to predict the LDC due to DDR statistic. Finally, a comparison has been undertaken between the selected model and other suggested artificial intelligent methods by the researchers. According to the implemented comparisons, the Trainrp function acquired the best performance.

References:

1)       Akbarzadeh, A., Noori, R., Farokhnia, A., Khakpour, A., Sabahi, M. S. 2010. Accuracy and Uncertainty Analysis of Intelligent Techniques for Predicting the Longitudinal Dispersion Coefficient in Rivers. J. of Water and Wastewater. 21(3): 99-107. (In Persian)

2)       Adarsh, S. 2010. Prediction of longitudinal dispersion coefficient in natural channels using soft computing techniques. Scientia Iranica. Transaction A, Civil Engineering. 17(5): 363.

3)       Beale, E. M. L. 1972. A derivation of conjugate gradients In F A. Lootsma (Ed), Numerical methods/or nonlinear optimization. London: Academic Press.

4)       Brent, R. P. 1973. Algorithms for Minimization without Derivatives, Englewood Cliffs. NJ: Prentice-Hall.

5)       Charalambous, C. 1992. Conjugate gradient algorithm for efficient training of artificial neural networks. IEEE Proceedings. 139(3): 301–310.

6)       Chow, V. T. 1973. Open channel hydraulics. McGraw-Hill Company. pp.680.

7)       Coulibaly, P., Anctil, F., & Bobee, B. 2000. Daily reservoir inflow forecasting using artificial neural networks with stopped training approach. Journal of Hydrology. 230(3-4): 244-257.

8)       Deng, Z. Q., Singh, V. P., and Bengtsson, L. 2001. Longitudinal dispersion coefficient in straight rivers. Journal of hydraulic engineering. 127(11): 919-927.

9)       Etemad-Shahidi, A., and Taghipour, M. 2012. Predicting Longitudinal Dispersion Coefficient in Natural Streams Using M5′ Model Tree. Journal of hydraulic engineering. 138(6): 542–554.

10)   Fischer, H. B., List, J. E., Koh, C. R., Imberger, J., & Brooks, N. H. 1979. Mixing in inland and coastal waters. Elsevier. New York. 104–138.

11)   Fischer, H. B. 1975. Discussion of ‘Simple method for predicting dispersion in streams,’ by R. S. McQuivey and T. N. Keefer. Journal of the Environmental Engineering Division. 101(3): 453–455.

12)   Fletcher, R., and Reeves, C. M. 1964. Function minimization by conjugate gradients. Computer Journal. 7: 149–154.

13)   Hagan, M. T., Demuth, H. B., and Beale, M. H. 1996. Neural Network Design. Boston. MA: PWS Publishing, 1996.

14)   Ghiasi, B., Noori, R., Karbasi, A. R., Deng, Z. 2017. Estimating Longitudinal Dispersion Coefficient in rivers using non-linear regression model. Iranian Water Research Journal. 24(11): 97-108. (In Persian)

15)   Givehch, M., Maghrebi, M. F., Abrishami, J. 2008. Application of Depth-Averaged Velocity Profile for Estimation of Longitudinal Dispersion in Rivers. J. of Water and Wastewater. 20(4): 91-96. (In Persian)

16)   Haykin, S. 1994. Neural networks: a comprehensive foundation. Prentice Hall PTR.

17)   Hornik, K., Stinchcombe, M., White, H. 1989. Multilayer feedforward networks are universal approximators. Neural networks 2.5: 359-366.

18)   Huber, P. J. 1981. Robust statistics. John Wiley & Sons, Inc. New York.

19)   Jalili-Ghazizade, M., Noori, R. 2008. Prediction of Municipal Solid Waste Generation by Use of Artificial Neural Network: A Case Study of Mashhad. International Journal of Environmental Research. 2: 22-31.

20)   Kashefipour, M. S., and Falconer, R. A. 2002. Longitudinal dispersion coefficients in natural channels. Water Research. 36(6): 1596–1608.

21)   Kashefipour, M. 2007. Prediction of longitudinal dispersion coefficient in natural rivers using artificial neural networks. Iranian Journal of Hydraulic. 3: 15-25. (In Persian)

22)   Levenberg, K. 1944. A method for the solution of certain non-linear problems in least squares. Quarterly of applied mathematics. 2(2): 164-168.

23)   Marquardt, D. W. 1963. An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics. 11(2): 431–441.

24)   Maier, H. R., & Dandy, G. C. 2000. Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environmental modelling & software. 15(1): 101-124.

25)   Moller, M. F. 1993. A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks. 6: 525–533.

26)   Noori, R., Ghiasi, B., Sheikhian, H., Adamowski, J. F. 2017. Estimation of the Dispersion Coefficient in Natural Rivers Using a Granular Computing Model. Journal of Hydraulic Engineering 143(5): 04017001.

27)   Noori, R., Deng, Z., Kiaghadi, A., Kachoosangi, F. T. 2015. How reliable are ANN, ANFIS, and SVM techniques for predicting longitudinal dispersion coefficient in natural rivers? Journal of Hydraulic Engineering. 142(1): 04015039.

28)   Noori, R., Karbassi, A. R., Ashrafi, K., Ardestani, M., Mehrdadi, N. 2013. Development and application of reduced‐order neural network model based on proper orthogonal decomposition for BOD5 monitoring: Active and online prediction. Environmental progress & sustainable energy 32(1): 120-127.

29)   Noori, R., Khakpour, A., Omidvar, B., Farokhnia, A. 2010. Comparison of ANN and principal component analysis-multivariate linear regression models for predicting the river flow based on developed discrepancy ratio statistic. Expert Systems with Applications 37(8): 5856-5862.

30)   Noori, R., Karbassi, A., Farokhnia, A., & Dehghani, M. 2009 .Predicting the longitudinal dispersion coefficient using support vector machine and adaptive neuro-fuzzy inference system techniques. Environmental Engineering Science. 26(10): 1503-1510.

31)   Noori, R., Farokhnia, A., Morid, S., and Riahi Madvar, H. 2009. Effect of input variables preprocessing in artificial neural network on monthly flow prediction by PCA and wavelet transformation. Journal of Water and Wastewater. 69: 13-22. (In Persian)

32)   Noori, R., Abdoli, M. A., Ameri, A., and Jalili-Ghazizade, M. 2008. Prediction of municipal solid waste generation with combination of support vector machine and principal component analysis: A case study of Mashhad. Environmental Progress and Sustainable Energy. 28 (2): 249-258.

33)   Noori, R., Kerachian, R., Khodadadi, A., and Shakibinia, A. 2007. Assessment of importance of water quality monitoring stations using principal component and factor analysis: A case study of the Karoon River. Journal of Water and Wastewater. 63: 60-69. (In Persian)

34)   Parsaie, A. and Haghiabi, A. H. 2013. Evaluation of experimental provided equations and artificial intelligence models to compute the longitudinal dispersion of pollution in rivers. Journal of Environmental Management and Planing. 3(2): 57-71. (In Persian)

35)   Powell, M. J. D. 1977. Restart procedures for the conjugate gradient method. Mathematical Programming. 12: 241–254.

36)   Riahi-Madvar, H., Ayyoubzadeh, S. A., Khadangi, E., & Ebadzadeh, M. M. 2009. An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS. Expert Systems with Applications. 36(4): 8589-8596.

37)   Riahi-madvar, H., and Ayyaoubzadeh, S. A. 2008. Estimating longitudinal dispersion coefficient of pollutants using adaptive neuro-fuzzy inference system. Journal of Water and Wastewater. 67: 34-46. (In Persian)

38)   Rutherford, J. C. 1994. River mixing. John Wiley & Son Limited.

39)   Scales, L. E. 1985. Introduction to Non-Linear Optimization. New York: Springer-Verlag.

40)   Seo, I. W., Cheong, T. S. 1998. Predicting longitudinal dispersion coefficient in natural Streams. Journal of hydraulic engineering. 124(1): 25-32.

41)   Toprak, Z. F., Sen, Z., and Savci, M. E. 2004. Longitudinal dispersion coefficients in natural channels. Water Research. 38: 3193-3143.

42)   Tutmez, B., and Mehmet, Y. 2013. Regression Kriging Analysis for Longitudinal Dispersion Coefficient. Water resources management. 27(9): 3307-3318.

43)   Zeng, Y., and Wenxin, H. 2014. Estimation of longitudinal dispersion coefficient in rivers. Journal of Hydro-environment Research 8(1): 2-8.