Determinação do limite de deposição de sedimentos em galerias de drenagem utilizando redes neurais artificiais

Romero, Adhemar; Ota, José Junji

Adhemar Romero

Universidade Federal do Paraná, Curitiba, PR, Brasil

https://orcid.org/0000-0002-1001-7063

José Junji Ota

Universidade Federal do Paraná, Curitiba, PR, Brasil

https://orcid.org/0000-0001-9653-1495

E-mails: adhe.romero@gmail.com (AR), ota.dhs@ufpr.br (JJO)

Adhemar Romero: Contributed in literature review, data analysis, programming, development of ANN models, and writing.

José Junji Ota: Contributed in reviewing the theoretical basis of the sediment transport, supported in writing, data analysis, literature review and datasets collecting.

Editor-in-Chief: Adilson Pinheiro Associated Editor: Iran Eduardo Lima Neto

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Figure 1
Variation of the

ξ

with the relative depth inside the pipe.

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Figure 2
Representation of connections of one artificial neuron.

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Figure 3
Architecture of typical multilayer perceptron neural network.

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Figure 4
Comparison between the volumetric concentration at the limit of deposition obtained by the experimental data with the ANN-IV (best ANN model), ANN-XVI and ANN-XVII.

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Figure 5
Correlation between calculated and experimental volumetric concentrations at the limit of deposition for , , , and .

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Figure 6
Correlation between calculated and experimental volumetric concentrations at the limit of deposition for , , , and .

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Figure 7
MAPE calculated separately in the quartiles of the experimental dataset.

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Figure 8
MAE calculated separately in the quartiles of the experimental dataset.

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Figure 9
RMSE calculated separately in the quartiles of the experimental dataset.

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Figure 10
Comparison between the results obtained through the ANN analysis and .

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Table 1
Self-cleaning models used to determine the limit of deposition inside storm sewers.

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Table 2
Summary of numerical models evaluated in previous works regarding the definition of self-cleaning condition inside storm sewers.

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Table 3
Variation range of the main parameters of the experimental data set used.

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Table 4
Combinations of the input variables analyzed.

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Table 5
Topology of the best evaluated ANN model for each combination of input data with the related statistical measures.

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Table 6
Statistical quantities obtained comparing the results of the equations and the experimental data.

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Table 7
MAPE analyzed for each quartile of the experimental data.

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Table 8
MAE analyzed for each quartile of the experimental data.

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Table 9
RMSE analyzed for each quartile of the experimental data.

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Table 10
Summary of the statistical measures presented by the ANN-IV and using the entire dataset.

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Table 11
Summary of the statistical measures calculated for the ANN-IV and for the experimental data quartiles.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

Author	Model	Equation
Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 4.32 C_{v}^{0.23} {(\frac{d}{R_{h}})}^{- 0.68}$	(1)
Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$C_{v} = 0.03 {(\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}})}^{3.54} D_{g r}^{- 0.11} {(\frac{d_{50}}{R_{h}})}^{2.47} λ_{s}^{0.57}$	(2)
May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...	$C_{v} = 0.0303 (\frac{D^{2}}{A}) {(\frac{d_{50}}{D})}^{0.6} {(1 - \frac{V_{t}}{V})}^{4} {(\frac{V^{2}}{g D (S_{s} - 1)})}^{1.5}$	(5)
Ota (1999)Ota, J. J. (1999). Effect of particle size and gradation on sediment transport in storm sewers. Newcastle: University of Newcastle Upon Tyne.	$C_{v} = 2.9 ξ^{2.7} {(\frac{R_{h}}{d_{50}})}^{1.2} {(\frac{S}{(S_{s} - 1)})}^{2.2} \sqrt{\frac{λ_{0}}{8}} {(\frac{d_{50}}{k})}^{1.8}$	(11)
Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 4.31 C_{v}^{0.226} {(\frac{d_{50}}{R_{h}})}^{- 0.616}$	(12)
Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 4.49 C_{v}^{0.21} {(\frac{d_{50}}{R_{h}})}^{- 0.54}$	(13)
Najafzadeh et al. (2017)Najafzadeh, M., Laucelli, D. B., & Zahiri, A. (2017). Application of Model Tree and evolutionary polynomial regression for evaluation of sediment transport in pipes. KSCE Journal of Civil Engineering, 21(5), 1956-1963. http://dx.doi.org/10.1007/s12205-016-1784-7. http://dx.doi.org/10.1007/s12205-016-178...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 0.404 {(\frac{R_{h}}{d_{50}})}^{0.5} + 23.25 {(\frac{R_{h}}{d_{50}})}^{0.5} C_{v}^{0.5}$	(14)
Romero (2018)Romero, A. (2018). Determination of sediment deposition limit inside drainage pipes using artificial neural networks (Master degree dissertation). Universidade Federal do Paraná, Curitiba.	$C_{v} = 2,88 ξ^{2.6} {(\frac{R_{h}}{d_{50}})}^{1.1} {(\frac{S}{(S_{s} - 1)})}^{2.1} \sqrt{\frac{λ_{0}}{8}} {(\frac{d_{50}}{k})}^{1.732}$	(15)
Montes et al. (2020a)Montes, C., Vanegas, S., Kapelan, Z., Berardi, L., & Saldarriaga, J. (2020a). Non-deposition self-cleasing models for large sewer pipes. Water Science and Technology, 81(3), 606-621. PMid:32385214. http://dx.doi.org/10.2166/wst.2020.154. http://dx.doi.org/10.2166/wst.2020.154...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 4,79 λ_{0}^{0.058} C_{v}^{0.209} {(\frac{d_{50}}{R_{h}})}^{- 0.593}$	(16)
Tafarojnoruz & Sharafati (2020)Tafarojnoruz, A., & Sharafati, A. (2020). New formulations for prediction of velocity at limit of deposition in storm sewer based on a stochastic technique. Water Science and Technology, 81(12), 2634-2649. PMid:32857749. http://dx.doi.org/10.2166/wst.2020.321. http://dx.doi.org/10.2166/wst.2020.321...	$\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 3.39 C_{v}^{0.2} {(\frac{R_{h}}{d_{50}})}^{0.62}$	(17)

Author	Bed condition	Best model evaluated	Metrics used to evaluate the models	Dataset used	Parameters used	Equations evaluated
Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...	Clean bed (without deposit)	ANFIS	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
	Clean bed (without deposit)	ANFIS	RMSE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
Safari et al. (2013)Safari, M. J. S., Aksoy, H., & Mohammadi, M. (2013). Application of ANN for the analysis of sediment incipient deposition in rigid boundary channels. In Proceedings of the 16th International Conference Transport and Sedimentation of Solid Particles (pp. 53-62), Rostock, Germany.	Clean bed (without deposit)	ANN-MLP	R²	Loveless (1991)Loveless, J. H. (1991). Sediment transport in rigid boundary channels with particular reference to the condition of incipient deposition (PhD thesis). University of London, London.	$V$ = $f$ ( $Q$ , $C_{v}$ , $y$ , $S_{0}$ , $d_{50}$ , $R_{h}$ )	None
	Clean bed (without deposit)	ANN-MLP	MSE			None
Ebtehaj & Bonakdari (2013)Ebtehaj, I., & Bonakdari, H. (2013). Evaluation of sediment transport in sewer using artificial neural network. Engineering Applications of Computational Fluid Mechanics, 7(3), 382-392. http://dx.doi.org/10.1080/19942060.2013.11015479. http://dx.doi.org/10.1080/19942060.2013....	Clean bed (without deposit)	ANN	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Novak & Nalluri (1975)Novak, P., & Nalluri, C. (1975). Sediment transport in smooth fixed bed channels. Journal of the Hydraulics Division, 101(9), 1139-1154. http://dx.doi.org/10.1061/JYCEAJ.0004412. http://dx.doi.org/10.1061/JYCEAJ.0004412...
			RMSE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...
						Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
						May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
						Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
Ebtehaj & Bonakdari (2014a)Ebtehaj, I., & Bonakdari, H. (2014a). Performance evaluation of adaptative neural fuzzy inference system for sediment transport in sewers. Water Resources Management, 28(13), 4765-4779. http://dx.doi.org/10.1007/s11269-014-0774-0. http://dx.doi.org/10.1007/s11269-014-077...	Clean bed (without deposit)	ANFIS	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
			MRE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
			MARE			Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
			MSRE
			ME
			MAE
			RMSE
Ebtehaj & Bonakdari (2014b)Ebtehaj, I., & Bonakdari, H. (2014b). Comparison of genetic algorithm and imperialist competitive algorithms in predicting bed load transport in clean pipe. Water Science and Technology, 70(10), 1695-1701. PMid:25429460. http://dx.doi.org/10.2166/wst.2014.434. http://dx.doi.org/10.2166/wst.2014.434...	Clean bed (without deposit)	ICA	RMSE	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ , $D$ )	May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
	Clean bed (without deposit)	ICA	MAPE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
Ebtehaj & Bonakdari (2016)Ebtehaj, I., & Bonakdari, H. (2016). Assessment of evolutionary algorithms in predicting non-deposition sediment transport. Urban Water Journal, 13(5), 499-510. http://dx.doi.org/10.1080/1573062X.2014.994003. http://dx.doi.org/10.1080/1573062X.2014....	Clean bed (without deposit)	ICA	RMSE	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
	Clean bed (without deposit)	ICA	MAPE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
Ebtehaj & Bonakdari (2015)Ebtehaj, I., & Bonakdari, H. (2015). Bed load sediment transport estimation in a clean pipe using multilayer perceptron with different training algorithms. KSCE Journal of Civil Engineering, 20(2), 581-589. http://dx.doi.org/10.1007/s12205-015-0630-7. http://dx.doi.org/10.1007/s12205-015-063...	Clean bed (without deposit)	ANN-MLP-LM	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ , $D$ )	Novak & Nalluri (1975)Novak, P., & Nalluri, C. (1975). Sediment transport in smooth fixed bed channels. Journal of the Hydraulics Division, 101(9), 1139-1154. http://dx.doi.org/10.1061/JYCEAJ.0004412. http://dx.doi.org/10.1061/JYCEAJ.0004412...
			RMSE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
			MAPE			Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
						Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
Najafzadeh & Bonakdari (2017)Najafzadeh, M., & Bonakdari, H. (2017). Application of a neuro-fuzzy GMDH model for predicting the velocity at limit of deposition in storm sewers. Journal of Pipeline Systems Engineering and Practice, 8(1), 06016003. http://dx.doi.org/10.1061/(ASCE)PS.1949-1204.0000249. http://dx.doi.org/10.1061/(ASCE)PS.1949-...	Clean bed (without deposit)	Neuro-Fuzzy GMDH Model	R	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Novak & Nalluri (1975)Novak, P., & Nalluri, C. (1975). Sediment transport in smooth fixed bed channels. Journal of the Hydraulics Division, 101(9), 1139-1154. http://dx.doi.org/10.1061/JYCEAJ.0004412. http://dx.doi.org/10.1061/JYCEAJ.0004412...
			RMSE			Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...
			MAPE			Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
			SI			Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
			BIAS			Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
Ebtehaj et al. (2017a)Ebtehaj, I., Bonakdari, H., & Zaji, A. H. (2017a). A new hybrid decision tree method based on two artificial neural networks for predicting sediment transport in clean pipes. Alexandria Engineering Journal, 57(3), 1789-1795.	Clean bed (without deposit)	ANN-DT-MLP	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $D$ , $C_{v}$ )	Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
			RMSE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
			MARE	Ota & Nalluri (1999)Ota, J. J., & Nalluri, C. (1999). Graded sediment transport at limit of deposition in clean pipe channel. In 28th International Association for Hydro-environment Engineering and Research, Graz, Austria.		Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
			SI
			BIAS
Ebtehaj et al. (2017b)Ebtehaj, I., Bonakdari, H., Shamshirband, S., Ismail, Z., & Hashim, R. (2017b). New approach to estimate velocity at limit of deposition in storm sewers using vector machine coupled with firefly algorithm. Journal of Pipeline Systems Engineering and Practice, 8(2), 04016018. http://dx.doi.org/10.1061/(ASCE)PS.1949-1204.0000252. http://dx.doi.org/10.1061/(ASCE)PS.1949-...	Clean bed (without deposit)	SVM-FFA	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ , $D$ )	Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
			MAPE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
			RMSE	Ota & Nalluri (1999)Ota, J. J., & Nalluri, C. (1999). Graded sediment transport at limit of deposition in clean pipe channel. In 28th International Association for Hydro-environment Engineering and Research, Graz, Austria.		Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
			BIAS
			SI
Wan Mohtar et al. (2018)Wan Mohtar, W. H. M., Afan, H., El-Shafie, A., Bong, C. H. J., & Ghani, A. A. (2018). Influence of bed deposit in the prediction of incipient sediment motion in sewers using artificial neural networks. Urban Water Journal, 15(4), 296-302. http://dx.doi.org/10.1080/1573062X.2018.1455880. http://dx.doi.org/10.1080/1573062X.2018....	Deposited bed	ANN-MLP	R²	Yalin & Karahan (1979)Yalin, M. S., & Karahan, E. (1979). Inception of sediment transport. Journal of the Hydraulics Division, 105(11), 1433-1443. http://dx.doi.org/10.1061/JYCEAJ.0005306. http://dx.doi.org/10.1061/JYCEAJ.0005306...	$V$ = $f$ ( $W_{b}$ , $y$ , $d_{50}$ )	Novak & Nalluri (1975)Novak, P., & Nalluri, C. (1975). Sediment transport in smooth fixed bed channels. Journal of the Hydraulics Division, 101(9), 1139-1154. http://dx.doi.org/10.1061/JYCEAJ.0004412. http://dx.doi.org/10.1061/JYCEAJ.0004412...
			RMSE	Kuhnle (1993)Kuhnle, R. A. (1993). Incipient motion of sand-gravel sediment mixtures. Journal of Hydraulic Engineering, 119(12), 1400-1415. http://dx.doi.org/10.1061/(ASCE)0733-9429(1993)119:12(1400). http://dx.doi.org/10.1061/(ASCE)0733-942...		El-Zaemey (1991)El-Zaemey, A. K. S. (1991). Sediment transport over deposited bed sewers (Phd thesis). University of Newcastle, Newcastle upon Tyne, England.
			RE	Shvidchenko (2000)Shvidchenko, A. B. (2000). Incipient motion of streambeds (PhD thesis). University of Glasgow, Glasgow, United Kingdom.		Salem (1998)Salem, A. M. (1998). Incipient motion over loose deposited beds in a rigid rectangular channel (MSc thesis). University Sains Malaysia, Penang, Malasya.
				Salem (1998)Salem, A. M. (1998). Incipient motion over loose deposited beds in a rigid rectangular channel (MSc thesis). University Sains Malaysia, Penang, Malasya.		Bong (2013)Bong, C. H. J. (2013). Self-cleansing urban drain using sediment flushing gate based on incipient motion (Phd thesis). University Sans Malaysia, Penang, Malaysia.
				Bong (2013)Bong, C. H. J. (2013). Self-cleansing urban drain using sediment flushing gate based on incipient motion (Phd thesis). University Sans Malaysia, Penang, Malaysia.
Ebtehaj et al. (2019)Ebtehaj, I., Bonakdari, H., & Es-Haghi, M. S. (2019). Design of a hybrid ANFIS-PSO model to estimate sediment transport in open channels. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(4), 851-857.	Clean bed (without depositi)	ANFIS-PSO	R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $C_{v}$ , $D$ )	Azamathulla et al. (2012)Azamathulla, H. M., Ab Ghani, A., & Fei, S. Y. (2012). ANFIS-based approach for predicting sediment transport in clean sewer. Applied Soft Computing, 12(3), 1227-1230. http://dx.doi.org/10.1016/j.asoc.2011.12.003. http://dx.doi.org/10.1016/j.asoc.2011.12...
			RMSE	Ota & Nalluri (1999)Ota, J. J., & Nalluri, C. (1999). Graded sediment transport at limit of deposition in clean pipe channel. In 28th International Association for Hydro-environment Engineering and Research, Graz, Austria.		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
			MAPE	Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
			BIAS
			SI
Safari (2019)Safari, M. J. S. (2019). Decision tree (DT), generalized regression neural network (GR) and multivariate adaptive regression splines (MARS) models for sediment transport in sewer pipes. Water Science and Technology, 79(6), 1113-1122. PMid:31070591. http://dx.doi.org/10.2166/wst.2019.106. http://dx.doi.org/10.2166/wst.2019.106...	Clean bed (without deposit)	MARS	RMSE	Mayerle (1988)Mayerle, R. (1988). Sediment transport in rigid boundary channels (PhD thesis). Newcastle Upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...
			MAPE	May (1993)May, R. W. P. (1993). Sediment transport in pipes and sewers with deposited beds (Report SR 320). Wallingford: HR Wallingford.		Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
			CC	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.		Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
				Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
Kargar et al. (2019)Kargar, K., Safari, M. J. S., Mohammadi, M., & Samadianfard, S. (2019). Sediment transport modeling in open channels using neuro-fuzzy and gene expression programming techniques. Water Science and Technology, 79(12), 2318-2327. PMid:31411586. http://dx.doi.org/10.2166/wst.2019.229. http://dx.doi.org/10.2166/wst.2019.229...	Clean bed (without deposit)	NF	RMSE	Mayerle (1988)Mayerle, R. (1988). Sediment transport in rigid boundary channels (PhD thesis). Newcastle Upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...
			CC	May (1993)May, R. W. P. (1993). Sediment transport in pipes and sewers with deposited beds (Report SR 320). Wallingford: HR Wallingford.		Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
				Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.		Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
				Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
Mehr & Safari (2020)Mehr, A. D., & Safari, M. J. S. (2020). Application of soft computing techniques for particle Froude number estimation in sewers pipes. Journal of Pipeline Systems Engineering and Practice, 11(2), 04020002. http://dx.doi.org/10.1061/(ASCE)PS.1949-1204.0000449. http://dx.doi.org/10.1061/(ASCE)PS.1949-...	Deposited bed	MGGP	RMSE	El-Zaemey (1991)El-Zaemey, A. K. S. (1991). Sediment transport over deposited bed sewers (Phd thesis). University of Newcastle, Newcastle upon Tyne, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
			NSE	Perrusquia (1992Perrusquia, G. (1992). Sediment transport in pipe channels (Postdoctoral experiments studies). Chalmers University of Technology, Göteborg, Switzerland., 1993Perrusquia, G. (1993). An experimental study from flume to stream traction in pipe channels (Report). Göteborg, Switzerland: Chalmers University of Technology.)		Nalluri et al. (1997)Nalluri, C., El-Zaemey, A. K., & Chan, H. L. (1997). Sediment transport over fixed deposited beds in sewers: an appraisal of existing models. Water Science and Technology, 36(8-9), 123-128. http://dx.doi.org/10.2166/wst.1997.0654. http://dx.doi.org/10.2166/wst.1997.0654...
				May (1993)May, R. W. P. (1993). Sediment transport in pipes and sewers with deposited beds (Report SR 320). Wallingford: HR Wallingford.		Safari & Shirzad (2019)Safari, M. J. S., & Shirzad, A. (2019). Self-cleansing design of sewers: definition of the optimum deposited bed thickness. Water Environment Research, 91(5), 407-416. PMid:30731037. http://dx.doi.org/10.1002/wer.1037. http://dx.doi.org/10.1002/wer.1037...
				Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
Montes et al. (2020b)Montes, C., Berardi, L., Kapelan, Z., & Saldarriaga, J. (2020b). Predicting bedload sediment transport of non-cohesive material in sewer pipes using Evolutionary Polynomial Regression-Multi-Objective Genetic Algorithm strategy. Urban Water Journal, 17(2), 154-162. http://dx.doi.org/10.1080/1573062X.2020.1748210. http://dx.doi.org/10.1080/1573062X.2020....	Clean bed (without deposit)	EPR-MOGA	SSE	Mayerle (1988)Mayerle, R. (1988). Sediment transport in rigid boundary channels (PhD thesis). Newcastle Upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Craven (1953)Craven, J. (1953). The transportation of sand in pipes: I. Full-pipe flow. In Proceedings of the fifth hydraulics Conference (pp. 67-76), Iowa City, United States of America.
			R²	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.		Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498...
			AIC	Ota (1999)Ota, J. J. (1999). Effect of particle size and gradation on sediment transport in storm sewers. Newcastle: University of Newcastle Upon Tyne.		Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.
				Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
				Montes et al. (2020b)Montes, C., Berardi, L., Kapelan, Z., & Saldarriaga, J. (2020b). Predicting bedload sediment transport of non-cohesive material in sewer pipes using Evolutionary Polynomial Regression-Multi-Objective Genetic Algorithm strategy. Urban Water Journal, 17(2), 154-162. http://dx.doi.org/10.1080/1573062X.2020.1748210. http://dx.doi.org/10.1080/1573062X.2020....		Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...
						Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135...
						Najafzadeh et al. (2017)Najafzadeh, M., Laucelli, D. B., & Zahiri, A. (2017). Application of Model Tree and evolutionary polynomial regression for evaluation of sediment transport in pipes. KSCE Journal of Civil Engineering, 21(5), 1956-1963. http://dx.doi.org/10.1007/s12205-016-1784-7. http://dx.doi.org/10.1007/s12205-016-178...
						Safari et al. (2017)Safari, M., Aksoy, H., Unal, N., & Mohammadi, M. (2017). Non-deposition self-cleansing design criteria for drainage systems. Journal of Hydro-Enviroment Research., 14, 76-84. http://dx.doi.org/10.1016/j.jher.2016.11.002. http://dx.doi.org/10.1016/j.jher.2016.11...
Montes et al. (2021)Montes, C., Kapelan, Z., & Saldarriaga, J. (2021). Predicting non-deposition sediment transport in sewer pipes using Random Forest. Water Research, 189(1), 116639. PMid:33227613. http://dx.doi.org/10.1016/j.watres.2020.116639. http://dx.doi.org/10.1016/j.watres.2020....	Clean bed (without deposit)	RF	R²	Mayerle (1988)Mayerle, R. (1988). Sediment transport in rigid boundary channels (PhD thesis). Newcastle Upon Tyne, Newcastle, England.	$F_{r}$ = $f$ ( $d_{50}$ , $R_{h}$ , $λ_{0}$ , $D_{g r}$ , $C_{v}$ )	Montes et al. (2020b)Montes, C., Berardi, L., Kapelan, Z., & Saldarriaga, J. (2020b). Predicting bedload sediment transport of non-cohesive material in sewer pipes using Evolutionary Polynomial Regression-Multi-Objective Genetic Algorithm strategy. Urban Water Journal, 17(2), 154-162. http://dx.doi.org/10.1080/1573062X.2020.1748210. http://dx.doi.org/10.1080/1573062X.2020....
			RMSE	Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.		Kargar et al. (2019)Kargar, K., Safari, M. J. S., Mohammadi, M., & Samadianfard, S. (2019). Sediment transport modeling in open channels using neuro-fuzzy and gene expression programming techniques. Water Science and Technology, 79(12), 2318-2327. PMid:31411586. http://dx.doi.org/10.2166/wst.2019.229. http://dx.doi.org/10.2166/wst.2019.229...
			MAPE	Ota (1999)Ota, J. J. (1999). Effect of particle size and gradation on sediment transport in storm sewers. Newcastle: University of Newcastle Upon Tyne.		Safari (2019)Safari, M. J. S. (2019). Decision tree (DT), generalized regression neural network (GR) and multivariate adaptive regression splines (MARS) models for sediment transport in sewer pipes. Water Science and Technology, 79(6), 1113-1122. PMid:31070591. http://dx.doi.org/10.2166/wst.2019.106. http://dx.doi.org/10.2166/wst.2019.106...
				Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242...		May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210...
				Montes et al. (2020b)Montes, C., Berardi, L., Kapelan, Z., & Saldarriaga, J. (2020b). Predicting bedload sediment transport of non-cohesive material in sewer pipes using Evolutionary Polynomial Regression-Multi-Objective Genetic Algorithm strategy. Urban Water Journal, 17(2), 154-162. http://dx.doi.org/10.1080/1573062X.2020.1748210. http://dx.doi.org/10.1080/1573062X.2020....		Safari & Aksoy (2020)Safari, M. J., & Aksoy, H. (2020). Experimental analysis for self-cleansing open channel design. Journal of Hydraulic Research, 59(3), 500-511.
						Ebtehaj et al. (2019)Ebtehaj, I., Bonakdari, H., & Es-Haghi, M. S. (2019). Design of a hybrid ANFIS-PSO model to estimate sediment transport in open channels. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(4), 851-857.
						Ebtehaj et al. (2020) Ebtehaj, I., Bonakdari, H., Safari, M. J. S., Gharabaghi, B., Zaji, A. H., Madavar, H. R., Khozani, Z. S., Es-Haghi, M. S., Shishegaran, A., & Mehr, A. D. (2020). Combination of sensitivity and uncertainty analyses for sediment transport modeling in sewer pipes. International Journal of Sediment Research, 35(2), 157-170. http://dx.doi.org/10.1016/j.ijsrc.2019.08.005. http://dx.doi.org/10.1016/j.ijsrc.2019.0...

Author	Number of experiments	y (m)	k (m)	D (mm)	d₅₀ (mm)	V (m/s)	S (m/m)	Rh (m)	Cv (ppm)
May (1993) May, R. W. P. (1993). Sediment transport in pipes and sewers with deposited beds (Report SR 320). Wallingford: HR Wallingford.	97	0.058-0.299	0.00035-0.00070	76.7-299	0.57-7.9	0.429-1.498	0.0007-0.0237	0.019-0.090	0.31-2110
Mayerle (1988) Mayerle, R. (1988). Sediment transport in rigid boundary channels (PhD thesis). Newcastle Upon Tyne, Newcastle, England.	106	0.028-0.122	0.00035	152	0.5-8.74	0.374-1.104	0.0014-0.0056	0.017-0.046	20.4-1275
Ab Ghani (1993) Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England.	256	0.024-0.338	0.00035-0.001	154-450	0.46-8.3	0.24-1.216	0.0004-0.0056	0.0145-0.14	0.759-1450
Ota (1999) Ota, J. J. (1999). Effect of particle size and gradation on sediment transport in storm sewers. Newcastle: University of Newcastle Upon Tyne.	49	0.055-0.189	0.001	225-305	0.714-5.61	0.39-0.756	0.002	0.034–0.086	4.193–77.99
Montes et al. (2020a) Montes, C., Vanegas, S., Kapelan, Z., Berardi, L., & Saldarriaga, J. (2020a). Non-deposition self-cleasing models for large sewer pipes. Water Science and Technology, 81(3), 606-621. PMid:32385214. http://dx.doi.org/10.2166/wst.2020.154. http://dx.doi.org/10.2166/wst.2020.154...	36	0.003-0.218	0.00035	595	0.35-2.6	0.58-1.41	0.008-0.014	0.019–0.119	20-3410

ANN Model	Input layer parameters
ANN-I	$D$ , $y / D$ , $d_{50}$ , $k$ , $R_{h}$ , $S$ , 𝑉, $R e^{}$ , $ψ$ , $u^{}$ , $ξ$
ANN-II	$D$ , $y / D$ , $d_{50}$ , $k$ , $R_{h}$ , $V$ , $ψ$ , $u^{*}$ , $ξ$
ANN-III	$D$ , $y / D$ , $d_{50}$ , $k$ , $R_{h}$ , $V$ , $R e^{*}$ , $ψ$ , $ξ$
ANN-IV	$D$ , $y / D$ , $d_{50}$ , $k$ , $R_{h}$ , $S$ , $ψ$ , $R e^{*}$
ANN-V	$D$ , $y / D$ , $d_{50}$ , $k$ , $R_{h}$ , $S_{0}$ , $V$ , $ψ$ , $u^{*}$ , $ξ$
ANN-VI	$D$ , $y / D$ , $d_{50}$ , $k$ , $S_{0}$ , $V$ , $R e^{}$ , $ψ$ , $u^{}$ , $ξ$
ANN-VII	$D$ , $y / D$ , $d_{50}$ , $S$ , $R e^{}$ , $u^{}$
ANN-VIII	$D$ , $y / D$ , $d_{50}$ , $V$ , $S$ , $R e^{}$ , $u^{}$
ANN-IX	$D$ , $y / D$ , $d_{50}$ , $V$ , $S$ , $R e^{}$ , $u^{}$ , $ξ$
ANN-X	$D$ , $y / D$ , $d_{50}$ , $k$ , $S$ , $R e^{}$ , $u^{}$ , $ξ$
ANN-XI	$d_{50}$ , $R_{h}$ , $V$ , $D_{g r}$ , $λ_{0}$
ANN-XII	$D$ , $d_{50}$ , $R_{h}$ , $V$
ANN-XIII	$D$ , $d_{50}$ , $R_{h}$ , $V$ , $D_{g r}$ , $λ_{0}$
ANN-XIV	$D$ , $d_{50}$ , $R_{h}$ , $V, λ_{0}$
ANN-XV	$d_{50}$ , $R_{h}$ , $V$
ANN-XVI	$D$ , $d_{50}$ , $A$ , $V$ , $y$
ANN-XVII	$d_{50}$ , $k$ , $R_{h}$ , $S$ , $λ_{0}$ , $ξ$
ANN-XIII	$d_{50}$ , $R_{h}$ , $V$ , $λ_{0}$

		ANN model
		I	II	III	IV	V	VI	VII	VIII	IX	X	XI	XII	XIII	XIV	XV	XVI	XVII	XVIII
Neurons in first layer^* * Number of neurons which produced the best results for each combination of input variables.		5	11	9	18	15	7	22	23	23	15	8	14	22	21	17	21	16	10
Neurons in second layer*		12	5	7	8	5	9	5	5	7	5	9	10	6	6	10	11	9	12
Numbers of input variables		11	9	9	8	10	10	6	7	8	8	5	4	6	5	3	5	6	4
R2	Training dataset	0.78	0.88	0.88	0.92	0.86	0.88	0.72	0.80	0.80	0.85	0.73	0.82	0.76	0.82	0.74	0.81	0.91	0.76
	Evaluation dataset	0.70	0.76	0.57	0.90	0.65	0.85	0.77	0.77	0.70	0.90	0.45	0.60	0.41	0.50	0.42	0.42	0.89	0.35
	All data	0.78	0.88	0.89	0.92	0.86	0.87	0.72	0.80	0.80	0.86	0.73	0.82	0.76	0.81	0.74	0.81	0.90	0.75
MAPE	Training dataset	39.47	41.56	45.27	34.24	40.57	37.66	66.73	49.30	52.08	34.20	75.72	64.22	49.41	51.22	66.79	60.79	41.17	61.86
	Evaluation dataset	57.52	47.45	51.48	39.63	52.80	47.65	168.41	91.64	88.30	44.97	77.11	57.58	73.78	58.76	64.21	54.78	65.22	66.06
	All data	41.14	44.90	47.76	35.09	42.28	39.06	77.88	57.53	58.81	35.99	81.23	67.43	60.30	54.11	68.75	64.52	45.24	69.30
RMSE	Training dataset	175.25	176.26	222.97	143.73	171.55	148.22	182.74	164.61	170.56	152.19	353.27	224.25	217.99	233.40	353.72	231.94	253.26	349.14
	Evaluation dataset	238.11	218.29	305.84	167.11	225.04	180.77	218.32	218.65	227.00	187.43	462.04	303.92	301.40	317.52	463.95	323.74	330.70	456.39
	All data	184.84	183.35	231.38	146.32	180.99	153.16	190.90	172.71	179.89	159.61	374.41	230.61	224.59	240.70	376.19	240.96	277.42	370.01
MAE	Training dataset	70.40	71.29	83.11	57.18	70.15	60.76	83.91	70.40	74.40	62.66	134.79	94.20	90.41	94.87	137.92	92.53	92.58	135.64
	Evaluation dataset	112.23	101.43	140.23	73.85	106.40	86.40	111.46	107.69	111.83	89.97	205.34	143.17	146.19	150.62	208.69	150.17	133.98	205.72
	All data	77.44	76.51	89.94	59.84	76.34	64.89	90.16	76.09	80.94	68.54	146.91	98.82	96.11	100.83	150.14	98.48	104.05	147.91
MBE	Training dataset	39.70	33.25	47.68	13.61	36.78	23.00	43.00	32.60	30.52	32.30	97.76	37.47	47.13	51.00	102.99	48.42	52.91	100.00
	Evaluation dataset	95.89	86.89	131.27	49.91	88.72	63.69	61.75	82.54	83.51	66.05	193.22	126.25	134.21	135.29	194.97	142.91	104.68	190.74
	All data	50.12	43.09	57.98	20.47	46.62	31.87	49.79	41.10	39.31	41.58	110.95	46.40	55.80	59.51	116.67	58.17	66.87	112.43
SI	Training dataset	0.65	0.65	0.82	0.53	0.63	0.55	0.67	0.61	0.63	0.56	1.30	0.83	0.80	0.86	1.30	0.85	0.93	1.29
	Evaluation dataset	0.78	0.72	1.00	0.55	0.74	0.59	0.72	0.72	0.75	0.62	1.52	1.00	0.99	1.04	1.52	1.06	1.09	1.50
	All data	0.66	0.66	0.83	0.52	0.65	0.55	0.68	0.62	0.64	0.57	1.34	0.82	0.80	0.86	1.35	0.86	0.99	1.32
AIC	Training dataset	4238	4238	4430	4070	4218	4099	4262	4179	4210	4117	4798	4425	4406	4459	4795	4454	4528	4786
	Evaluation dataset	1511	1483	1575	1408	1493	1434	1477	1479	1492	1439	1679	1563	1565	1576	1676	1582	1590	1674
	All data	5701	5688	5941	5441	5676	5494	5726	5619	5665	5535	6457	5928	5903	5976	6458	5977	6133	6442

Author	R²	MAPE	RMSE	MAE	MBE	SI	AIC
Mayerle et al. (1991)Mayerle, R., Nalluri, C., & Novak, P. (1991). Sediment transport in rigid bed conveyances. Journal of Hydraulic Research, 29(4), 475-495. http://dx.doi.org/10.1080/00221689109498969. http://dx.doi.org/10.1080/00221689109498... ^* * Cv as dependent variable. – Equation 1	0.61	59.22	367.13	163.34	113.17	1.31	6435
Ab Ghani (1993)Ab Ghani, A. (1993). Sediment transport in sewers (PhD thesis). University of Newcastle upon Tyne, Newcastle, England. – Equation 2	0.83	79.71	352.43	144.50	-6.32	1.26	6395
May et al. (1996)May, R. W. P., Ackers, J. C., Butler, D., & John, S. (1996). Development of design methodology for self-cleaning sewers. Water Science and Technology, 33(9), 195-205. http://dx.doi.org/10.2166/wst.1996.0210. http://dx.doi.org/10.2166/wst.1996.0210... – Equation 5	0.84	56.53	342.28	133.42	66.95	1.22	6363
Ota (1999)Ota, J. J. (1999). Effect of particle size and gradation on sediment transport in storm sewers. Newcastle: University of Newcastle Upon Tyne. – Equation 11	0.88	53.69	328.38	130.75	14.11	1.17	6318
Vongvisessomjai et al. (2010)Vongvisessomjai, N., Tingsanchali, T., & Babel, M. S. (2010). Non-deposition design criteria for sewers with part-full flow. Urban Water Journal, 7(1), 61-77. http://dx.doi.org/10.1080/15730620903242824. http://dx.doi.org/10.1080/15730620903242... * – Equation 12	0.82	69.95	484.42	173.56	-32.03	1.73	6735
Ebtehaj et al. (2014)Ebtehaj, I., Bonakdari, H., & Sharifi, A. (2014). Design criteria for sediment transport in sewers based on self-cleaning concept. Journal of Zhejiang University., 15(11), 914-924. http://dx.doi.org/10.1631/jzus.A1300135. http://dx.doi.org/10.1631/jzus.A1300135... * – Equation 13	0.72	119.63	901.50	258.50	-158.30	3.22	7411
Najafzadeh et al. (2017)Najafzadeh, M., Laucelli, D. B., & Zahiri, A. (2017). Application of Model Tree and evolutionary polynomial regression for evaluation of sediment transport in pipes. KSCE Journal of Civil Engineering, 21(5), 1956-1963. http://dx.doi.org/10.1007/s12205-016-1784-7. http://dx.doi.org/10.1007/s12205-016-178... * – Equation 14	0.38	228.29	463.09	243.46	-175.08	1.66	6686
Romero (2018)Romero, A. (2018). Determination of sediment deposition limit inside drainage pipes using artificial neural networks (Master degree dissertation). Universidade Federal do Paraná, Curitiba. – Equation 15	0.86	73.16	352.44	151.24	-33.99	1.26	6395
Montes et al. (2020a)Montes, C., Vanegas, S., Kapelan, Z., Berardi, L., & Saldarriaga, J. (2020a). Non-deposition self-cleasing models for large sewer pipes. Water Science and Technology, 81(3), 606-621. PMid:32385214. http://dx.doi.org/10.2166/wst.2020.154. http://dx.doi.org/10.2166/wst.2020.154... * – Equation 16	0.80	84.01	727.45	220.22	-113.24	2.60	7181
Tafarojnoruz & Sharafati (2020)Tafarojnoruz, A., & Sharafati, A. (2020). New formulations for prediction of velocity at limit of deposition in storm sewer based on a stochastic technique. Water Science and Technology, 81(12), 2634-2649. PMid:32857749. http://dx.doi.org/10.2166/wst.2020.321. http://dx.doi.org/10.2166/wst.2020.321... * – Equation 17	0.78	75.73	804.04	231.52	-118.36	2.87	7286

Equation	First Quartile	Second Quartile	Third Quartile	Fourth Quartile
	(0.31 ppm – 28.82 ppm)	(29 ppm – 86.9 ppm)	(87.3 ppm – 320 ppm)	(290 ppm – 3,410 ppm)
(1)	71.84	53.48	55.45	56.09
(2)	162.00	51.74	54.94	50.18
(5)	99.25	40.51	45.39	40.97
(11)	90.68	39.10	40.44	44.52
(12)	102.39	48.78	65.92	62.69
(13)	168.77	100.28	118.84	90.62
(14)	383.57	269.10	187.72	72.75
(15)	132.51	52.10	54.30	53.75
(16)	105.44	62.12	86.77	81.70
(17)	87.16	51.22	77.47	87.05
ANN-IV	66.00	29.81	24.82	19.71

Equation	First Quartile	Second Quartile	Third Quartile	Fourth Quartile
	(0.31 ppm – 28.82 ppm)	(29 ppm – 86.9 ppm)	(87.3 ppm – 320 ppm)	(290 ppm – 3,410 ppm)
(1)	7.63	28.20	102.19	515.35
(2)	12.53	26.45	95.75	443.26
(5)	8.84	20.42	80.36	424.06
(11)	6.82	20.47	73.51	422.20
(12)	8.73	25.04	114.78	545.68
(13)	16.60	50.14	200.15	767.10
(14)	49.37	132.76	306.94	484.78
(15)	9.95	27.52	98.58	468.91
(16)	9.71	31.59	150.48	689.12
(17)	8.47	26.50	136.38	754.71
ANN-IV	6.93	15.44	43.84	173.16

Equation	First Quartile	Second Quartile	Third Quartile	Fourth Quartile
	(0.31 ppm – 28.82 ppm)	(29 ppm – 86.9 ppm)	(87.3 ppm – 320 ppm)	(290 ppm – 3,410 ppm)
(1)	9.54	31.70	125.70	722.66
(2)	22.34	35.38	154.94	686.34
(5)	15.76	29.06	111.01	674.70
(11)	10.06	33.16	111.57	646.29
(12)	14.85	36.16	176.54	951.82
(13)	31.12	90.74	329.58	1770.01
(14)	88.90	216.00	469.71	763.30
(15)	14.82	45.10	149.36	687.25
(16)	17.59	50.48	243.17	1433.44
(17)	12.90	36.31	227.00	1591.5
ANN-IV	9.84	22.50	60.60	285.25

Model	R2	MAPE	RMSE	MAE	MBE	SI	AIC
ANN-IV	0.92	35.09	146.32	59.84	20.47	0.52	5441
Equation 11	0.88	53.69	328.38	130.75	14.11	1.17	6318

Model	Variable	First Quartile	Second Quartile	Third Quartile	Fourth Quartile
ANN-IV	MAPE	66	29.81	24.82	19.71
	MAE	6.93	15.44	43.84	173.16
	RMSE	9.84	22.5	60.6	285.25
Equation 11	MAPE	90.68	39.1	40.44	44.52
	MAE	6.82	20.47	73.51	422.2
	RMSE	10.06	33.16	111.57	646.29

C_{v} = 0.03 {(\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}})}^{3.54} D_{g r}^{- 0.11} {(\frac{d_{50}}{R_{h}})}^{2.47} λ_{s}^{0.57}

\frac{V_{c}}{\sqrt{g d_{50} (S_{s} - 1)}} = 0.404 {(\frac{R_{h}}{d_{50}})}^{0.5} + 23.25 {(\frac{R_{h}}{d_{50}})}^{0.5} C_{v}^{0.5}

[1] E-mails: adhe.romero@gmail.com (AR), ota.dhs@ufpr.br (JJO)

Brasil

Brasil

Determinação do limite de deposição de sedimentos em galerias de drenagem utilizando redes neurais artificiais

RESUMO