پيش‌بيني عمق آبشستگي در پائين‌دست سرريز جامي شكل توسط مدل ماشين آموزش نيرومند و روش اعتبار سنجي چند لايه

Prediction the Scour Depth At Downstream of Bucket Spillway Using the Extreme Learning Machine and K-Fold Cross Validation

در اين مطالعه، عمق آبشستگي در پائين‌دست سرريزهاي جامي با استفاده از مدل ماشين آموزش نيرومند شبيه‌سازي گرديد. ماشين آموزش نيرومند يك نوع شبكه عصبي تك لايه پيش‌خور است كه گره‌هاي محاسباتي را به‌صورت تصافي انتخاب كرده و وزن‌هاي خروجي را نيز به‌شكل تحليل تعيين مي‌نمايد. علاوه براين براي سنجش توانايي مدل‌هاي ماشين آموزش نيرومند از شبيه‌سازي‌هاي مونت كارلو استفاده مي‌شود. شبيه‌سازي مونت كارلو يك طبقه‌بندي گسترده از الگوريتم‌هاي محاسباتي است كه از نمونه‌گيري تصادفي براي محاسبه نتايج عددي استفاده مي‌كند. همچنين از روش اعتبار سنجي چند لايه براي بررسي توانايي مدل‌هاي عددي بهره گرفته مي‌شود. در روش اعتبار‌سنجي چند لايه اي، نمونه اصلي است به طور تصادفي به k نمونه هاي فرعي به اندازه مساوي تقسيم شود. مزيت اين روش، تكرار تصادفي نمونه هاي فرعي در روند آزمون و آموزش براي كليه مشاهدات است و هر مشاهده دقيقا يك‌بار براي اعتبار‌سنجي مورد استفاده قرار مي‌گيرد. در اين مطالعه مقدار k مساوي با 5 در نظر گرفته شد. سپس پارامترهاي تاثير گذار بر روي عمق آبشستگي شناسايي شد و شش مدل ماشين آموزش نيرومند تعريف گرديد. با انجام آناليز حساسيت موثرترين پارامتر كه شامل پارامتر بدون بعد دبي معرفي شد. همچنين با تجزيه و تحليل نتايج مدل‌هاي مختلف، مدل برتر معرفي گرديد. اين مدل مقادير آبشستگي را با دقت قابل قبولي پيش‌بيني كرد و تابعي از كليه پارامترهاي ورودي بود. به‌عنوان مثال مقادير ضريب تببين و شاخص پراكندگي به ترتيب مساوي 0/933 و 0/071 بدست آمد.

The ogee spillways are constructed to regulate the flow in reservoir of dams. When the excess waters overflow the ogee spillway, the velocity at toe of spillway is pretty high and the flow has a huge amount of energy. The bucket spillway is used in order to reduce the amount of such energy. Next, the trajectory flow combines with air and the flow loses its energy significantly. If the materials at downstream of spillway are erodible, the probability of the scour exist; as a result, the stability of spillway endangers. Therefore, the prediction of scour hole depth in this area is quite significant. In this study, the depth of scour at downstream of the bucket spillway simulated using the Extreme Learning Machine (ELM) model. One of the most popular methods based on the artificial intelligence is the feed-forward neural network (FFNN). The training speed of this algorithm is very low. It's due to the use of the gradient based algorithms such as the back propagation (BP) which has low speed and the adjustment of the parameters related to the network is iterative. The extreme learning machine (ELM) is a Single Layer Feed-Forward Neural Network (SLFFNN) which selects the number of nodes randomly and determines the output weights analytically. This algorithm is much faster than conventional neural networks and has a good generalization performance. The use of this method has had a good performance in different fields and its comparison with FFNN-BP has showed that this method in addition to reduce high computational costs has a higher accuracy. In current study, to evaluate the performance of ELM models, the Monte Carlo simulation (MCs) is applied. Monte Carlo simulation is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo simulation is mainly used in different problems such as optimization and numerical integration from a probability distribution. Also in this study, the k-fold Cross Validation (k-fold) is used for evaluating the models ability. In k-fold cross validation method, the original sample is randomly partitioned into k equal sized subsamples. In the k subsamples, a single subsample is retained as the validation data for testing the specific model, and the remaining k-1 subsamples are used as training data. The cross-validation process is then repeated k times (the folds), with each of the k subsamples used exactly once as the validation data. The k results from the folds can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling is that all observations are used for both training and validation, and each observation is used for validation exactly once. The k value was considered 5 in this study. In this study, to validate the results of numerical models, the Azmathullah et al. (2005) experimental measurements were used. They measured the scour depth at the downstream of bucket spillway. Next, the effective parameters on scour depth were identified and six ELM models defined. In other words, one model simulated the scour depth with combination of five input parameters including the discharge dimensionless parameter, the ratio of the total head to the tailwater depth(H/dw), the ratio of the bucket radius to the tailwater depth(R/dw), the ratio of the mean sediment size to the tailwater depth(d50/dw) and lip angle of bucket, and five models predicted the output variable using four input parameters. In addition, the sensitivity analysis was carried out in order to identify the effective factor. This sensitivity analysis showed that the discharge dimensionless parameter was the most effective factor. Also, the superior model was introduced by analyzing the results of all models. This model had reasonable accuracy and was the function of all input parameters. For example, the determination coefficient and scatter index were obtained 0.993 and 0.071, respectively. Also, The RMSE and MAPE for this model were obtained 0.240 and 8.891, respectively. Additionally, the maximum, minimum and average discrepancy ratios for the superior model were respectively calculated 1.567, 0.360 and 0.991.