Estimation of Discharge Coefficient of the Trapezoidal Broad Crested Weir Flow Using Support Vector Machines

Abstract

Weirs are the oldest and most practical structures used to control, regulate, and measure flow in rivers or open channels. The ratio of the actual discharge, smaller than the theoretical discharge due to the separation zone and boundary layer development, to the theoretically discharge is defined as the discharge coefficient (Cd). Cd values are depended on the hydraulic properties of the open channel flow and the type and geometric properties of the weir. In this study, a total of 88 weir head (H0) of the trapezoidal broad crested weir with different upstream and downstream slopes are experimentally measured and Cd values are calculated according to the weir characteristics. Calculated Cd values are estimated by using eight different input combinations with the dimensionless parameters. Three different kernel functions (Linear, Polynomial and Gaussian) of Support Vector Machines method are used. To determine the performance of the models, Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R2) values are employed. As a result of the study, the Gaussian kernel function is the most successful model and the input combination is H0/L (L as crest height), ɛ (H0/(H0+L)), upstream slope (α) and downstream slope (ꞵ) parameters are found to be most successful model to estimate Cd values.

Keywords

• Discharge coefficient
• trapezoidal broad crested weir
• support vector machine
• kernel function

Trapez Geniş Başlıklı Savakların Debi Katsayısının Destek Vektör Makineleri ile Tahmini

Öz

Savaklar, akarsularda veya açık kanallarda akımı kontrol etmek, düzenlemek ve akımın debisini ölçmek üzere kullanılan en eski ve pratik yapılardır. Akımda meydana gelen ayrılma bölgesi ve sınır tabası gelişiminden kaynaklı olarak teorik debiden daha küçük olan gerçek debinin, teorik olarak hesaplanan debiye oranı debi katsayısı (Cd) olarak tanımlanmaktadır. Cd debi katsayısı, açık kanal akımının hidrolik özelliklerine ve savak yapısının türüne ve geometrik özelliklerine bağlı olarak değişiklik göstermektedir. Bu çalışmada, farklı memba ve mansap eğimlerine sahip trapez geniş başlıklı savak akımına ait toplam 88 savak yükü değeri (H0) deneysel olarak ölçülmüş ve savak özelliklerine göre Cd değerleri hesaplanmıştır. Hesaplanan Cd değerleri, boyutsuz parametreler yardımıyla oluşturulan sekiz farklı girdi kombinasyonu ile Destek Vektör Makineleri yöntemindeki üç farklı çekirdek fonksiyonu (Lineer, Polinom ve Gaussian) kullanılarak tahmin edilmiştir. Oluşturulan modellerin performansını belirlemek için Karekök Ortalama Karesel Hata (KOKH) ve Ortalama Mutlak Yüzde Hata (OMYH), belirlilik katsayısı (R2) değerleri kullanılmıştır. Çalışma sonucunda, Gaussian çekirdek fonksiyonunun en başarılı model olduğu ve girdi kombinasyonu olarak savak yükü (H0) ve kret uzunluğu (L) olmak üzere, H0/L, ɛ (H0/(H0+L)), savak memba eğimi (α) ve savak mansap eğimi (ꞵ) parametrelerinin kullanıldığı kombinasyonun Cd değerini tahmin etmede başarılı model olduğu belirlenmiştir.

Anahtar Kelimeler

• Debi katsayısı
• trapez geniş başlıklı savak
• destek vektör makineleri
• çekirdek fonksiyon

References

1. Chanson H., Hydraulics of open channel flow. (2004):,Elsevier.
2. Mehboudi A., Attari J.,Hosseini S., Experimental study of discharge coefficient for trapezoidal piano key weirs, Flow Measurement and Instrumentation, 50 (2016) 65-72.
3. Li S., Yang J.,Ansell A., Discharge prediction for rectangular sharp-crested weirs by machine learning techniques, Flow Measurement and Instrumentation, 79 (2021) 101931.
4. Sargison J.E.,Percy A., Hydraulics of broad-crested weirs with varying side slopes, Journal of Irrigation and Drainage Engineering, 135 (2009) 115-118.
5. Emiroglu M.E., Agaccioglu H.,Kaya N., Discharging capacity of rectangular side weirs in straight open channels, Flow Measurement and Instrumentation, 22 (2011) 319-330.
6. Ameri M., Ahmadi A.,Dehghani A.A., Discharge coefficient of compound triangular–rectangular sharp-crested side weirs in subcritical flow conditions, Flow Measurement and Instrumentation, 45 (2015) 170-175.
7. Johnson M.C., Discharge coefficient analysis for flat-topped and sharp-crested weirs, Irrigation science, 19 (2000) 133-137.
8. Haghiabi A.H., Parsaie A.,Ememgholizadeh S., Prediction of discharge coefficient of triangular labyrinth weirs using adaptive neuro fuzzy inference system, Alexandria Engineering Journal, 57 (2018) 1773-1782.

9. Roushangar K., Alami M.T., Shiri J.,Asl M.M., Determining discharge coefficient of labyrinth and arced labyrinth weirs using support vector machine, Hydrology Research, 49 (2018) 924-938.
10. Parsaie A.,Haghiabi A.H., Improving modelling of discharge coefficient of triangular labyrinth lateral weirs using SVM, GMDH and MARS techniques, Irrigation and drainage, 66 (2017) 636-654.
11. Salmasi F., Yıldırım G., Masoodi A.,Parsamehr P., Predicting discharge coefficient of compound broad-crested weir by using genetic programming (GP) and artificial neural network (ANN) techniques, Arabian Journal of Geosciences, 6 (2013) 2709-2717.
12. Hoseini S.H.,Afshar H., Flow over a broad-crested weir in subcritical flow conditions, physical study, Journal of River Engineering, 2 (2014) 1005-1012.
13. Roushangar K., Akhgar S.,Salmasi F., Estimating discharge coefficient of stepped spillways under nappe and skimming flow regime using data driven approaches, Flow Measurement and Instrumentation, 59 (2018) 79-87.
14. Saffar S., Babarsad M.S., Shooshtari M.M.,Riazi R., Prediction of the discharge of side weir in the converge channels using artificial neural networks, Flow Measurement and Instrumentation, 78 (2021) 101889.
15. Hager W.H., Schwalt M., Broad-crested weir, Journal of Irrigation and Drainage Engineering, 120 (1994) 13-26.
16. Kabacoff R., R in action: data analysis and graphics with R, edited by: Kabacoff, R. (2015), Manning Publications Co., Shelter Island, New York.
17. Smola A.J.,Schölkopf B., A tutorial on support vector regression, Statistics and computing, 14 (2004) 199-222.
18. Magoulès F., Zhao H., Data mining and machine learning in building energy analysis. (2016): Wiley Online Library.
19. James G., Witten D., Hastie T.,Tibshirani R., An introduction to statistical learning. Vol. 112. (2013): Springer.
20. Yu-Wei C.D.C., Machine learning with R cookbook. (2015): Packt Publishing Ltd.
21. Kuhn M.,Johnson K., Applied predictive modeling. Vol. 26. (2013): Springer.
22. Vapnik V., The nature of statistical learning theory. (2013): Springer science & business media.
23. Awad M.,Khanna R., Efficient learning machines: theories, concepts, and applications for engineers and system designers. (2015): Springer nature.
24. Hornik K., Meyer D.,Karatzoglou A., Support vector machines in R, Journal of statistical software, 15 (2006).
25. Taylor K.E., Summarizing multiple aspects of model performance in a single diagram, Journal of Geophysical Research: Atmospheres, 106 (2001) 7183-7192.