پیش بینی مبتنی بر مدل برای استغراق بحرانی مصرف افقی در جریان های کانال باز با کف ترخیص کالا از گمرکهای متفاوت با استفاده از سبد خرید، ANN و روش رگرسیون خطی

This study presents the development of classification and regression tree (CART), artificial neural network (ANN) and linear regression approaches to predict the critical submergence in an open channel flow for different clearance bottoms. To use the models for application purposes and cover the wide range of inputs, the nondimensional parameters are employed to train and test. The testing results show that all three approaches satisfactorily estimate the critical submergence with margin differences. Also, committee models arithmetic mean-based for the testing results of the tree mentioned approaches are presented as the best models. A comparison between the present study and empirical approaches is carried out which indicates the proposed approaches outperform the empirical formulas expressed in the literature. In addition, committee models are presented as the more generalized approaches by AIC criterion. The results also indicate that the variations of the best approach (committee)-predicted and observed the normalized critical submergence with the intake pipe diameter versus the number of the testing data follow favorably a similar trend. Finally, a sensitivity analysis shows that the ratio of the velocity in an intake pipe to the velocity in a channel is the significant parameter in the estimation of the critical submergence.

Vertical and horizontal intakes are one of the most important parts of hydraulic sets such as a river for irrigation or a reservoir for power generation and industrial purposes. Insufficient water height above a pipe intake (submergence) can lead to vortex formation and air entry. These phenomena may cause the problems such as loss of hydraulic machinery performance or erosion and vibration in pipelines (Denny, 1956). Therefore, an accurate estimation of submergence depth above intakes in related hydraulic systems design has to be considered. The critical submergence of intakes has been extensively investigated in laboratory or experimentally. Denny (1956) carried out one of the first studies on the critical submergence and air-entraining vortices at pump sumps. He found that entry of 1% air volume to a vortex caused up to 15% reduction of pump performance. Several studies that yielded empirical expressions to predict the critical submergence of intakes have also been done (Kocabas and Yildrim, 2002, Odgaard, 1986, Reddy and Pickford, 1972 and Swaroop, 1973). Generally, presented relations to estimate the critical submergence were based on Froud number, Reynolds number, the critical height of intake, Weber number and circulation. Yildrim and Kocabas, 1998 and Yildrim and Kocabas, 2002, and Yildrim, Kocabas, and Gulcan (2000) determined the critical submergence for intakes from an open channel flow and still water reservoirs using potential theory and dimensional analysis. Furthermore, the critical submergence for a rectangular intake has been studied by Yildrim (2004). Recently, Ahmad, Rao, and Mittal (2008) proposed predictors for the critical submergence of horizontal intakes for the different bottom clearance (vertical distance of intake to bottom of tank) in open channel flows. It is very hard to find an exact relation between the effective parameters on the estimation of the critical submergence for a hydraulic system. Empirical formulas based on laboratory or experimentally data are used to predict the critical submergence. Also, due to complexity of the process, these conventional formulae based on regression approach may not be able to present complete relations in the process estimation. Hence, investigators have tried to estimate the critical submergence more accurate than empirical formulas. In the past few years, soft computing and data mining techniques such classification and regression tree (CART) and artificial neural networks (because of flexibility, ability to generalize and power to approximate nonlinear and complex system such as estimation of the critical submergence) have been widely used in many engineering problems. About CART applications in the sciences as a new model can mention to soil properties prediction in environmental science (Henderson, Bui, Moran, & Simon, 2005), risk management analysis in petroleum pipeline construction (Dey, 2002), prediction of significant wave height (Mahjoobi & Etemad-Shahidi, 2008) and estimation of wave-induced scour around a pile (Ayoubloo et al., 2008b and Ayoubloo et al., 2010). ANN models have been used to estimate scour around piles (Kambekar & Deo, 2003), below spillways (Azmathulla et al., 2005 and Azamathulla et al., 2008), downstream of grade-control structures (Guven & Gunel, 2008) and the critical submergence of a vertical intake (Kocabas, Unal, & Unal, 2008). Also, combinations of fuzzy inference system with ANN (ANFIS) have been employed to predict wave characteristics (Kazeminezkad et al., 2005 and Mahjoobi et al., 2008), water level in reservoir (Chang & Chang, 2005) and pile group scour (Bateni & Jeng, 2007). All aforementioned studies presented CART and ANN as the applicable and powerful tools compared with traditional regression schemes. This study aims to investigate the skills of CART and ANN methods in prediction of the critical submergence of horizontal intakes in open channel flows and to compare with those obtained from well known empirical formulas. As a conventional method, linear regression-based equations, predicting the critical submergence, are also developed. The two recently introduced soft computing techniques i.e. CART and ANN and linear regression are first briefly described. This is followed by a short discussion on the used experimental data set involving a total of 324 experimental data for the different bottom clearance. Afterwards, governing nondimensional parameters are discussed. Finally, the two developed data mining approaches and linear regression are applied to predict the scour depth to illustrate their efficiency and performance. The performance metrics of the employed methods for solving this problem are presented in forms of quantitative statistical measures and scatter plots and compared with those obtained from well known empirical formulae. The results show that the proposed methods are capable of predicting the critical submergence with an acceptable degree of accuracy. Furthermore, the excellent association between observed and committee model-yielded the critical submergence has proven the superior performance of this technique over all presented soft computing methods as well as commonplace empirical techniques.

CART, ANN and linear regression models were applied to predict the normalized critical submergence (Sc/di) for horizontal intakes in open channel flows for different clearance bottoms (0 and di/2). The models were trained and tested with the associated data. The models results showed that the critical submergence values could be the best predicted with ANN and linear regression approaches for c = 0 and c = di/2, respectively. Moreover, proposed methods (CART, ANN and linear regression) could improve the accuracy of the Sc/di prediction toward empirical formulas. Also, the committee model based on arithmetic mean of the output values of ANN, CART and linear regression outperformed the best empirical formula and predicted the Sc/di much more accurately. The capability to generalize of the proposed methods and empirical approaches was investigated and it was shown the committee model as the more generalized approach for c = 0 and c = di/2. The variation of Sc/di with respect to the testing data for the true and predicted (with committee models) values was investigated which showed the promising trend for the committee models toward the true values. Finally, a sensitivity analysis by CART, ANN and linear regression approaches was carried out and it was shown that Ui/U∞ is the most important parameter on the predicting of Sc/di. The present study demonstrates that proposed tools such as CART, ANN and linear regression are efficiently capable to model the highly complex and nonlinear process such as the critical submergence prediction smartly with no former knowledge about the process.