Neural network for estimation of scour hole dimensions downstream of siphon spillway.
Spillways are hydraulic structures, which are provided in the dam to pass floodwater in excess of reservoir capacity and control of water flow downstream. Among several types of spillways, siphon can pass design discharge after slight increase in water level at upstream. No need for mechanical equipment is another benefit of this spillway. Water flow over the spillway and through the bottom outlets has a great potential in producing the scour on the bed at the tail water. Ski jump jet is used to energy dissipation through throwing water in to the air from bucket lip and then in the plunge pool formed at the point of impact on the tail water. The impact of the high velocity jet gives rise to the scour both upstream and downstream of the point of impingement. Such impact is transmitted through cracks and fissures of the rock by way of hydrodynamic pressure fluctuations causing hydraulic jacking action and by the transient pressure fluctuation caused due to air locking. This causes the rock mass to break into small pieces and to consequently get swept away in the downstream of the river. The erosion continues up to the point where the impinging jet energy is insufficient to exert breaking pressure on the rock or where the secondary current produced are less strong to remove the rock blocks. There are various hydraulic, morphologic, and geotechnical factors governing the scour hole dimensions which including (Referring to Figure (1))flow intensity (Q), bucket lip angle ([alpha]), sediment diameter ([d.sub.50]), water density ([[rho].sub.w]), sediment density ([[rho].sub.s]), tail water depth ([h.sub.t]). It is clear that the study of scour hole development is one of the challenging matters among the hydraulic structures designers. Numerous investigators [1, 2, 3, 4, 5, 6, 7]. in the past have explained the mechanics of scour on flip buckets including. A number of researchers in the past [2, 5, 8, 9] have developed empirical equations based mostly on laboratory measurements using regression technique in order to obtain the dimensions of scour hole downstream of a ski-jump spillway bucket.
Recently, Artificial Neural Network (ANN) has been widely applied in various areas of hydrology and water resources engineering, especially in the last 10 year. Among these, Grubert  used ANN to predict the flow conditions when interfacial mixing in stratified estuaries commences. The ANN results were compared to the semi-theoretical solution based on a combination of results in viscid from flow theory, turbulent flow theory, and interfacial friction experiments of the two solutions. Although neither of the two solutions was perfect in every respect, they were sufficiently close to one another. Kambekar and Deo carried out scour data analysis using ANN. Different networks were developed to predict the scour depth based on the input parameters of wave height, wave period, water depth, pile diameter, Reynolds number, maximum wave particle velocity, maximum shear velocity, Shields number, and Keulegan-Carpenter number. Their research showed that ANN is able to provide a better alternative to the statistical curve . Birikundavyi et al. investigated the performance of ANN as potential models capable of forecasting daily stream flow. They found that the results obtained with ANN were far superior to the ones obtained with classic models . Nagy et al. used ANN model to estimate the natural sediment discharge in rivers in terms of sediment concentration. The results indicated that an ANN approach estimates sediment concentration well compared to conventional models . The results of Coppola et al. about performance of ANN to predict transient water levels in a complex multilayered ground water system introduced ANN as a powerful tool for many types of ground water problems . Azmatullah et al. used ANN to predict some characteristics of scour hole downstream of free over fall spillway the results confirmed that ANN output has superior fitness with measured data . Azmatullah et al. used a combination of ANN and Adoptive Nero Fuzzy Inference System to improve the prediction of scour hole dimensions downstream of sky jump. Their results were satisfactory .
Despite analyzing a wide range of reliable prototype as well as model data the problem of scour prediction has remained inconclusive. It is felt that this is partly due to the complexity of the phenomenon involved and partly because of the limitation of the analytical tool commonly used by most of the earlier investigators, namely, statistical regression. It should be mentioned that most of these researches were focused on the scouring at the impact of jet from a bucket to the downstream and not a comprehensive study was done on submerged jets and it is rare in siphon spillway. The presentation of a new approach to predict scour whole dimensions using neural network is main object of this paper. Separate networks models were applied for physical model. Use of basic network architectures like Feed Forward Back Propagation (FFBP) and Cascade Forward Back Propagation (CFBP) were used. The ANN predictions have been compared with the regression and measured data. The studies incorporated use of the ANN tool box in MATLAB(2007).
MATERIALS AND METHODS
Experimental set up:
Determination of scour hole dimensions using ANN model was studied in this paper. Figure 1 shows the longitudinal section view of the experimental model. Experimental tests were conducted on a hydraulic model of a siphon spillway. A rectangular flume 1m width, 19m long and 0.8m high at the place of scouring and the place of siphon installation 1.6m high was used.
Based on Mason, [d.sub.50] was selected as the average diameter of the material in this research. The non-cohesive materials had [d.sub.50] equals to 1.4mm, 3.7mm, and 8.1mm. In the experiment procedure, three different bucket lip angle were investigated: 30[degrees], 45[degrees], and 60[degrees]. This model was studied under four different flow discharges equal to 0.039, 0.042, 0.045 and 0.05[m.sup.3].[s.sup.-1]. Tests were carried out for four tail water depths equal to 0.15, 0.20, 0.25, and 0.30m. scour hole data were recorded over a net of wire which was generated over the model to fix the points of measurements, namely 279 points in each test. A total of about 125 tests have been carried out. Referring to Figure 1, four characteristics of scour hole dimensions as following: equilibrium depth of scour hole ([d.sub.s]), measured from tail water surface, the distance of maximum scour depth from the siphon spillway bucket lip ([l.sub.max]), the distance of start point of scouring from the siphon spillway bucket lip ([l.sub.o]), the length of scouring ([l.sub.s]) were investigated in this research. They can be written as a function of flow discharge (Q), water density ([[rho].sub.w]), sediment density ([[rho].sub.s]), tail water depth ([h.sub.t]), flow dynamic viscosity ([mu]), mean sediment size ([d.sub.50]), acceleration due to gravity (g), and lip angle of bucket ([alpha]) as following:
[d.sub.s], [l.sub.max], [l.sub.o], [l.sub.s] = f (Q, [[rho].sub.w], [[rho].sub.s], [h.sub.t], [d.sub.50], g, [alpha]) (1)
Using the Buckingham [pi] theorem, the following non-dimensional equations can be developed:
[d.sub.s]/[h.sub.t], [l.sub.max]/[h.sub.t], [l.sub.o]/[h.sub.t], [l.sub.s]/[h.sub.t] = f([d.sub.50]/[h.sub.t], Q/[h.sup.2.sub.t][square root of (g([G.sub.s] - 1)[h.sub.t])], [alpha]) (2)
Which [G.sub.s] = [[rho].sub.s]/[[rho].sub.w] is the specific gravity of sediment particles. Non-linear and linear equations can be written for each characteristic as following:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Which x, y, z, p, x', y', z', and p' are the constants which should be evaluated.
RESULTS AND DISCUSSION
Based on non-linear and linear regression technique, 80% of the measurements selected randomly were used to evaluate the constants of equations (3) and (4), which are listed in table 1.
Validation of obtained equations was made with the help of the remaining 20% of observations, which were not involved in their derivation. Figures 2 to 5 shows measured versus calculated values of mentioned parameters at table 1 for linear predictors.
Figures 6 and 7 present corresponding values of measured and calculated values of parameter for non-linear predictors. As it is clear, there is good agreement between measured and calculated values for linear regression models.
Table 2 shows the comparison between measured and predicted values for non- linear and linear models, respectively. In this table, r is correlation coefficient between measured and calculated values, AE is average error (+ or -), d is the average absolute deviation, and RMSE is root mean square error.
As mentioned, Applications of ANN to solve problems in water resources have tremendously increased in the last 10 years. Therefore, using ANN has been applied to predict scour hole dimensions which is described at the following. ANN provides a random mapping in between an input and an output vector by mimicking the biological cognition process of our brain. Each typical ANN contains three layers of neuron including: input layer, hidden layer, and output layer. These neurons are interconnected, but independent computational unit (referring to Figure 8) which works as the following equation:
a = [w.sub.1,1][p.sub.1] + [w.sub.1,2][p.sub.2] + ... + [w.sub.1,R][p.sub.R] + b = [[summation].sup.R.sub.i=1][w.sub.1,i][p.sub.i] + b~f(wp + b) (5)
Which a is output of neuron, pi is input values, [w.sub.1,i] is connection weights that determines the strength of connection, b is bias value which increases the net input to the activation function and therefore accelerate the error convergence, f is transfer, activation or squashing function, which controls the output of neuron or squashes to a finite range like (0, 1) or (-1, 1) or (0.1, 0.9).
ANN derives their strength from a model free processing of data and a high degree of freedom associated with their architecture. Network training using available data is the first step to provide an ANN. Training comprises presentation of input and output pairs to the network and fixing the values of connection weights, bias or centers. The training may require many epochs (presentation of complete data sets once to the network). Generally, the network is presented with the input and output pairs until the training sum-square error reaches the error goal in order to give the desired network performance. Error back propagation is one type of training which has more application in engineering problems. The feed forward type of network has been considered in this paper. This network is trained both feed forward back propagation (FFBP) and cascade forward back propagation (CFBP). Therefore, two network were run to predict scour hole dimensions. Figure 9 shows the architecture of these two networks.
Both models employed the input of three dimensionless parameters namely [d.sub.50]/[h.sub.t], Q/[h.sup.2.sub.t][square root of (g([G.sub.s] - 1)[h.sub.t])] and [alpha] as well as output of relative dimension of scour hole namely [d.sub.s]/[h.sub.t], [l.sub.max]/[h.sub.t], [l.sub.o]/[h.sub.t] and [l.sub.s]/[h.sub.t] Out of the 125 input-output pairs, 80%, selected randomly were used for training and the rest, namely 20% of pairs, were used for model validation. All data were normalized within the range (0, 1). Logsigmoid and Tansigmoid activation function were selected for hidden and output layer of FFBP model, respectively. Tansigmoid and Purline activation function were selected for both hidden and output layer of CFBP model. Logsigmoid, Tansigmoid, and Purline activation functions have following expression, respectively:
a = 1/[1 + [e.sup.-n]] (6)
a = [[e.sup.n] + [e.sup.-n]]/[[e.sup.n] + [e.sup.-n]] (7)
It should be noted that this selection was done using trail-error process to gain best result. Table 3 presents the information on nodes numbers, and epochs numbers about FFBP and CFBP models.
The results of models performance are presented in figures 10 to 17 and table 2. Also, numerical analysis of models outputs are mentioned in table 2.
Scour hole which is a natural phenomena at downstream of the most hydraulic structure in alluvial system, has very serious role in their stability. According to the development of the artificial neural network in hydraulic, in this paper its application about scour hole dimensions prediction was studied. Measured value of physical modeling was used to verify neural network performance. As it clear from table 2, when scour hole depth is considered, FFBP model has the highest correlation coefficient (r = 0.9638), and the lowest error indices (AE = -2.44, d = 12.28, and RMSE = 0.086). When it comes to the distance of scour hole depth from bucket lip, there is no appropriate non-linear predictor. However, FFBP is the best performance, too. The regression coefficient is the highest (r = 0.9675) and error indices are the lowest (AE = 4.01, d = 9.96, RMSE = 0.1345). Analysis of table 2 for the case of start point of scour hole from bucket lip shows that there are considerable differences between accuracy indices between ANN and regression predictor groups. In this case, FFBP has appropriate performance, too (r = 0.9624, AE = -0.5471, d = 8.83, RMSE = 0.183). In the last case, scour hole length, there is no considerable difference between linear and CFBP predictors, but the indices of FFBP model is the best (r = 0.9513, AE = -0.9622, d = 6.205, RMSE = 0.451). The mentioned results show when it is acceptable accuracy of predicting scour hole dimensions (depth, length, start point and the distance of scour depth up to bucket lip), all error indices confirm that ANN predictors are in higher and better situation than regression predictors. Among FFBP and CPBF models, the first model is more appropriate because of highest correlation coefficient and lowest errors.
Received 14 September 2013
Received in revised form 21 November 2013
Accepted 25 November 2013
Available online 31 December 2013
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Mehdi Fuladipanah and Elham Sangi
Department of Civil Engineering, Ramhormoz Branch, IAU, Ramhormoz, Iran
Corresponding Author: Mehdi Fuladipanah, Department of Civil Engineering, Ramhormoz Branch, IAU, Ramhormoz, Iran Tel: +98-6912235520 Email: email@example.com
Table 1: Constants of non-linear and linear predictor equations. Parameter Non-linear predictor X y z P [d.sub.s]/ 0.748 -0.068 1.14 0.367 [h.sub.t] [l.sub.max]/ Non- appropriate model [h.sub.t] [l.sub.o]/ 1.784 -0.083 -0.095 2.58 [h.sub.t] [l.sub.s]/ Non-Appropriate model [h.sub.t] Parameter Linear predictor x' y z' P' [d.sub.s]/ 0.924 -1.589 0.097 -0.0808 [h.sub.t] [l.sub.max]/ -9.125 3.7 1.619 0.461 [h.sub.t] [l.sub.o]/ 4.25 0.0373 -0.421 -1.96 [h.sub.t] [l.sub.s]/ 7.809 -20.815 -3.627 3.935 [h.sub.t] Table 2: Comparison between measured and calculated scour hole relative dimensions. Parameter r AE d RMSE Linear model [d.sub.s]/[h.sub.t] 0.9076 -14.57 24.47 0.1279 [l.sub.max]/[h.sub.t] 0.871 -8.67 16.03 0.6955 [l.sub.a]/[h.sub.t] 0.8936 -1.47 15.21 0.346 [l.sub.s]/[h.sub.t] 0.9393 -5.52 13.7 0.867 Non-linear model [d.sub.s]/[h.sub.t] 0.9235 -7.79 22.26 0.1188 [l.sub.max]/[h.sub.t] -- -- -- -- [l.sub.a]/[h.sub.t] 0.7453 -20.00 28.62 0.3915 [l.sub.s]/[h.sub.t] -- -- -- -- FFBP [d.sub.s]/[h.sub.t] 0.9638 -2.44 12.82 0.086 [l.sub.max]/[h.sub.t] 0.9675 4.01 9.96 0.1345 [l.sub.a]/[h.sub.t] 0.9624 -0.5471 8.83 0.183 [l.sub.s]/[h.sub.t] 0.9513 -0.9622 6.205 0.451 CFBP [d.sub.s]/[h.sub.t] 0.9365 -3.78 15.1 0.102 [l.sub.max]/[h.sub.t] 0.9287 -1.28 12.58 0.1821 [l.sub.a]/[h.sub.t] 0.9461 -3.49 10.27 0.221 [l.sub.s]/[h.sub.t] 0.9316 -6.23 12.07 0.5533 Table 3: Network architectures. Algorithm Network configuration Epochs Input nodes Hidden nodes Output nodes Model 1 FFBP 3 10 4 97 Model 2 CFBP 3 10 4 252
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|Author:||Fuladipanah, Mehdi; Sangi, Elham|
|Publication:||Advances in Environmental Biology|
|Date:||Nov 1, 2013|
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