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Artificial Neural Networks and pattern recognition for air-water flow velocity estimation using a single-tip optical fibre probe
Journal of Hydro-environment Research 19 (2018) 150–159
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Research papers
Artificial Neural Networks and pattern recognition for air-water flow velocity estimation using a single-tip optical fibre probe
T
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D. Valeroa,b, , D.B. Bunga a b
Hydraulic Engineering Section (HES), FH Aachen University of Applied Sciences, Aachen, Germany Dept. of ArGEnCo, Research Group of Hydraulics in Environmental and Civil Engineering (HECE), University of Liege (ULg), Liège, Belgium
A R T I C L E I N F O
A B S T R A C T
Keywords: Air-water flow Feedforward network Interfacial velocity Stepped spillway Artificial intelligence Instrumentation
Interest in air-water flows has increased considerably for the last decades, being a common research field for different engineering applications ranging from nuclear engineering to large hydraulic structures or water quality treatments. Investigation of complex air-water flow behavior requires sophisticated instrumentation devices, with additional challenges when compared to single phase instrumentation. In this paper, a single-tip optical fibre probe has been used to record high-frequency samples (over 1 MHz). The main advantage of this instrumentation is that it allows direct computation of a velocity for each detected bubble or droplet, thus providing a detailed velocity time series. Fluid phase detection functions (i.e. the signal transition between two fluid phases) have been related to the interfacial velocities by means of Artificial Neural Networks (ANN). Information from previous measurements of a classical dual-tip conductivity probe (yielding time-averaged velocity data only) and theoretical velocity profiles have been used to train and test ANN. Special attention has been given to the input selection and the ANN dimensions, which allowed obtaining a robust methodology in order to non-linearly post-process the optical fibre signals and thus to estimate interfacial velocities. ANN have been found to be capable to recognize characteristic shapes in the fluid phase function and to provide a similar level of accuracy as classical dual-tip techniques. Finally, performance of the trained ANN has been evaluated by means of different accuracy parameters.
1. Introduction
2013; Bung and Valero, 2015, 2016a–c; Leandro et al., 2014), intrusive techniques are still the most widely used option (Boes and Hager, 2003; Chanson and Brattberg, 2002; Chanson and Toombes, 2002; Felder and Chanson, 2015; Wang and Chanson, 2015; Wang and Murzyn, 2016; Wang et al., 2014; Zhang and Chanson, 2016a). When the air fraction (C) exceeds 1–3%, accuracy of common instrumentation for single phase flow measurements is typically affected and conductivity or optical fibre probes become the best option (Felder and Chanson, 2015). Further discussion on single phase instrumentation applicability to slightly aerated flows can be found in Frizell (2000) and Matos et al. (2002). However, when using intrusive measurement techniques, some drawbacks and limitations can arise. Few attempts have been done to improve accuracy of such devices, testing different settings and signal post-processing techniques (Bung, 2012; Felder and Chanson, 2015). Given the considerable impact of scale effects (Chanson, 2009, 2013; Felder and Chanson, 2009; Murzyn and Chanson, 2008) and the increasing interest in the determination of air-water turbulence features (Bung and Valero, 2016c; Felder and Chanson, 2009; Wang and Murzyn, 2016), more demanding measurements in prototype and large
Air-water flows can be often found in large hydraulic structures, where self-aeration occurs as a complex and turbulent air-water compatibility phenomenon (Valero and Bung, 2016). When air entrainment occurs, flow bulking, friction reduction and turbulence modulation can be observed (Chanson, 2013), drastically changing the main flow properties and thereby complicating the flow behavior prediction. In spillway flows, recent research efforts have focused both on the aerated region (Boes and Hager, 2003; Bung, 2011; Chanson and Toombes, 2002; Felder and Chanson, 2009; Wilhelms and Gulliver, 2005; Zhang and Chanson, 2016a) and the non-aerated region (Amador et al., 2006; Castro-Orgaz, 2010; Meireles et al., 2012; Valero and Bung, 2016; Zhang and Chanson, 2016b). However, some key challenges remain unresolved (Chanson, 2013; Matos and Meireles, 2014). Similarly, airwater flow properties within hydraulic jumps have also attracted researchers’ interest (Chanson and Brattberg, 2002; Murzyn et al., 2005; Wang and Chanson, 2015; Wang and Murzyn, 2016; Wang et al., 2014). Although some new non-intrusive techniques are available (Bung,
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Corresponding author at: Hydraulic Engineering Section (HES), FH Aachen University of Applied Sciences, Aachen, Germany. E-mail address: [email protected] (D. Valero).
http://dx.doi.org/10.1016/j.jher.2017.08.004
Available online 26 August 2017 1570-6443/ © 2017 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
Journal of Hydro-environment Research 19 (2018) 150–159
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Fig. 1. Exemplary phase detection function for a bubble-tip impact event (note that tr can be directly extracted from the signal). Main parameters describing the phase detection function have been marked out (green for the finally selected inputs of the Artificial Neural Network). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
reports a relative error of around 10% both for air fraction estimation under laboratory conditions. Further discussion on the probe-bubble interaction and the effect upon the air fraction measurement accuracy can be found in the study of Vejražka et al. (2010). Errors are globally comparable for the single-tip and the dual-tip optical fibre techniques, but sensitivity to the flow regime can differ. For finely dispersed flows, single-tip optical probes are better suited while double-tip probe performance is better whenever large gas inclusions are present (Cartellier, 1998). Therefore, application of single-tip probes in highly turbulent aerated spillway flows becomes challenging. Also, their actual response is sensitive to small geometrical defects occurring at their tips as indicated by Cartellier and Barrau (1998a,b). Use of more complex data processing techniques than the rather simple rising time/velocity correlation provided by Eq. (2) can yield improved performance of the instrumentation. In this study, raw signals have been recorded with a single-tip optical fibre in a highly aerated flow on a moderately sloped stepped spillway; similar to the setup described in Bung and Valero (2015) and Bung (2011). These new signals have been processed evaluating the accuracy of the simple – yet physically based – approach of Eq. (2). At a second stage, they have been used to train and test an Artificial Neural Network (ANN). One of the main strengths of ANN is to allow detection of both simple and complex patterns in the input, which could remain indistinguishable to the researchers’ naked eye (it must be noted that different bubble/droplet impact events can generate different phase functions signatures). Different ANN configurations have been tested by means of the PyBrain open-source package (Schaul et al., 2010) and Python 2.7.
scale laboratory models may require from more exigent use of experimental techniques. Since the early study of Neal and Bankoff (1963), phase detection probes have become a common measuring technique in multiphase flow disciplines. The working principle of optical fibre probes is based upon the change of light refraction at air-water interfaces. Usually, these probes comprise two conical tips (dual-tip probes), being both tips intended to record two signals based on the same bubbly events. Similarly to conductivity probes (Chanson and Toombes, 2002), the most probable lag time (T ) can be obtained by cross-correlating both signals and consequently a mean interfacial velocity (v ) can be computed, given that the distance between both tips (Δx ) in flow direction is accurately known: (1)
v = Δx / T
Nonetheless, a second type of optical fibre is available based on a single-tip configuration. In such case, no cross-correlation can be performed since only a single signal is recorded. High sample rates help to record a more detailed signal (i.e.: phase detection function, see Fig. 1) and voltage gradients may be characterized with higher accuracy. Hence, single bubble/droplet velocities (vi ) can be approximated by: (2)
vi ≈ L/ tr
where tr is the so-called rising time, which represents the time that it takes to the voltage signal to pass from a lower threshold to an upper threshold (e.g. from 10% for the water level to 90% for the air level) and L is a characteristic length scale that the bubble/droplet travels through the probe, often referred to as latency length (Cartellier, 1998; Cartellier and Barrau, 1998a,b). Given a large number of velocities (vi ) obtained from the same number of bubble/droplet impacts, the mean velocity can be computed as an ensemble average:
1 v= N
2. Experimental setup All measurements have been conducted in a moderately sloped stepped spillway (1V:2H, chute slope ϕ = 26.6°, step height s = 6 cm) located at the Hydraulics Laboratory of FH Aachen, for three different flow rates q = 0.07, 0.09 and 0.11 m2/s. The total drop height is 1.74 m with a flume width of 0.50 m. Water is pumped from a lower basin into an open head tank from where it is conveyed into the stepped chute via an approaching channel of 1 m length. In order to complete a wide range of interfacial velocities, measurements have been conducted at downstream edges of step 13, 14, 18, 19 and 21 (see Fig. 2). Velocity in x -direction has been obtained perpendicularly to the pseudo-bottom with 2 mm spacing in the z -coordinate, resulting in 646 measurements. It must be noted that the air-water flow was found to be in the uniform flow region at step 21 for the highest discharge (see Figs. 2 and 3) according to Bung (2011).
N
∑ i=1
vi
(3)
with N the total number of samples (in this case the number of detected bubbles/droplets). A more robust approach to outliers would be considering the median value instead of the average, being the median the value which separates the ensemble in two equal parts (the 50% lower values from the upper 50%). To avoid a certain level of sensitivity to uncontrollable parameters (e.g. the angle of impact on the bubble interface), the probe geometry can differ from the commonly used dual-tip optical fibres. Thus, some more complex geometries, e.g. a cone + cylinder + cone geometry of the tip, could be used (Cartellier and Barrau, 1998b). Cartellier (1998) 151
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Fig. 2. Sketch of the experimental setup and flow regions on a stepped spillway.
The employed single-tip optical fibre probe (Fig. 3) corresponds to a simple cone geometry, which is more sensitive to uncontrolled parameters and manufacturing defects (Cartellier and Barrau, 1998a, 1998b). It has been placed at the centreline of the spillway and has been positioned by a CNC controlling system (isel) with an accuracy of ∼0.1 mm. The probe has been supplied by A2 Photonic Sensors, giving a relative error of 15% for the velocity estimation, including a signal recording software and the necessary electronic module. The probe provider recommends a velocity approximation based on Eq. (2) given by:
v = L·trb
High-frequency oscillations with small amplitudes may affect the analysis of the phase function, and more especially the accurate determination of the characteristic voltage levels sketched in Fig. 1. To remove these small oscillations, a central moving average filter with a moving window of 10 time steps has been applied. By removing sampled frequencies above a certain cutoff frequency, the moving average creates a smoothing effect upon the phase detection function, yielding a negligible effect when the averaging window is small enough. In order to make the signal independent from the adjusted voltage range, all the signals have been scaled to be comprised between 0 and 100%, thus resulting in a normalized voltage V ∗ (note that an absolute voltage range over 5 Volts has been always ensured during the data acquisition). To obtain a representative event for the ANN, a median signature (or median phase indicator function, similar to the one shown in Fig. 1) has been extracted from each recording. Different parameters defining this median phase indicator function have been selected, which can be segregated into (a) rising time parameters and (b) phase function shape parameters. As marked in Fig. 1, rising time related variables can be defined as: ti − j = t j−ti , which is the time difference between the dimensionless voltage V ∗ reaching the value j and i ; with i = 10, 25, 50 and 75, and j = 25, 50, 75 (in % of the range in the median phase indicator func∗ tion) and max corresponding to the maximum voltage (Vmax ) reached at ∗ each event. If Vmax remains below 75%, the entire event is rejected based on the impossibility to gather all the described parameters. The phase function shape descriptors have been marked in Fig. 1 as Vk∗, with k = max, 1, 2, 3, 4. These values have been taken at equal times between tmax and tend , being tend the time corresponding to V ∗ = 10% in the decreasing phase function region. Additionally, V1∗m ∗ and V2∗m are the normalized voltages measurements between Vmax and V1∗, V1∗ and V2∗ respectively. These additional voltages have been selected to better describe the exponentially decaying tail which has been ∗ commonly observed after Vmax .
(4)
where b is a parameter taking a value close to −1 (for the employed probe: b = −1.02 and L = 45.3 μm). However, it must be mentioned that Eq. (4) has been developed for less complex type of flow than the present highly-turbulent stepped spillway flow. In order to obtain a large number of information on the signal voltage gradients, the sampling rate has been set to 1 MHz, which is two orders of magnitude larger than the minimum sampling rate recommendations for such type of flows; see Felder and Chanson (2015) recommending a sample rate around 20–40 kHz. Sample time has been set to 30 s. It must be noted that the study of Felder and Chanson (2015) showed little effect upon velocity and turbulence estimations by incrementing the sample duration over 30 s. 3. Signal analysis For each of the 646 raw signals, 30 million data points have been taken into account to train and test the ANN; provided that the sample rate is 1 MHz and sample time of 30 s. Each signal displays a signature every time that a bubble/droplet impacts the probe tip (see Fig. 1) and, consequently, includes thousands of events (i.e. phase changes from water to air). Each signature can be divided into the bubble impact region (approximately during the rising time tr ) and a subsequently following plateau when the signal voltage stabilizes after the impact.
Fig. 3. Left: single-tip optical fibre probe, right: exemplary fully aerated flow at step 21 for q = 0.07 m2/s recorded with a high-speed camera (Bung and Valero, 2015).
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4. Artificial Neural Network
obtained for each event of the 646 conducted measurements. This has yielded thousands of values for each measurement. In order to get only one value per variable and signal the median value has been computed, hence summarizing a large quantity of data. Temporal variables have been inverted (t −1) which can be expected to be directly proportional to the velocity (see Eq. (2)). Shape parameters have been selected based on the previously observed fact that the bubble/droplet impacting the tip produces a characteristic signature (Cartellier, 1998; Cartellier and Barrau, 1998a,b). In order to make the shape parameters independent from the event duration (and consequently from the impacting bubble/ droplet size), the plateau of each event has been split in equal parts ranging from the maximum and the final voltages. For the temporal variables, a logarithmic distribution can be observed in the histograms. Consequently, logarithm of ti−−1j (i.e. log(ti−−1j )) has been considered to obtain a more homogeneous distribution of these parameters. Given a fixed number of training samples, the addition of redundant model inputs increases the ratio of the number of connection weights to the number of training samples, thus increasing the likelihood of overfitting, not providing any additional information to the model. Secondly, the inclusion of redundant model inputs introduces additional local minima in the error surface in weight space (Maier et al., 2010) which makes the training process more complicated. To detect redundancy between the described variables, correlation among them has been estimated (see Fig. 4) and highly correlated variables have been discarded before the training process. A strong correlation between the shape variables can be observed in ∗ the tail of the signature while Vmax , V1∗m and V 4∗ showed a lower correlation. Thus, the other shape variables have been omitted in the following analysis. Within the temporal variables, only t10 − 25 have been found to bear a high correlation with t25 − 50 . Given that t10 − 25 is more correlated to the remaining parameters than t25 − 50 , the former one has been neglected. Consequently, the selected variables for the ANN input vector (marked in green in Fig. 1) are the following:
4.1. General remarks Artificial Neural Networks (ANN), one of the earliest techniques of Artificial Intelligence (AI), have become a powerful tool for prediction and forecasting of water resources, mainly addressing hydrological and sediment problems. However, when it comes to hydraulic instrumentation prediction improvement, only a few attempts can be found in the literature. Carosone et al. (1995) and Chen et al. (1998) employed ANN altogether with Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV) techniques. Recently, Bung and Valero (2016a–c) have applied Artificial Intelligence techniques to turbulent flows obtaining, at least, as accurate velocity fields as classical cross-correlation based techniques, with a significant improvement for air-water flows. ANN models are composed of an input layer, where every input is represented by a single neuron, a given number of rows of hidden layers and an output layer which finally provides the desired variable by summarizing the information processed by the upstream neurons. The larger the number of hidden layers, the more complex patterns can be identified by the network. However, setting up a large number of hidden layers may result in an excessively large mathematical model. The herein employed network is composed of an input and an output layer and two hidden layers. The network is feedforward (i.e. with an acyclic topology) which can be used to approximate a nonlinear mapping between its inputs and outputs (Hu and Hwang, 2001). All ANN models, independently of the number of layers and neurons, take the basic form (Maier et al., 2010):
Y = f (X ,W ) + ε
(5)
where Y is the vector of model outputs, X is the vector of model input, W the vector of model parameters (or connection weights), f (·) is a functional relationship between model outputs, inputs and parameters; and ε is the vector of model errors. The functional relationship depends strongly on the ANN architecture. In this study, the model output is a single scalar (velocity v ), the vector of model input is discussed in Section 4.2 on the basis of the event-driven description of the recorded signal; the number of neurons is discussed in Section 4.3 and the vector of model errors is the result of the ANN training, discussed in Section 4.4. For the neuron activation functions, linear, sigmoid and hyperbolic tangents have been tested as they are available in the PyBrain package (Schaul et al., 2010), obtaining the best results with the combination shown in Table 1. For the net functions, linear summation has been employed (Hu and Hwang, 2001).
∗ X = [log(t25 − 50−1),log(t50 − 75−1),log(t75 − max −1 ),Vmax ,V1∗m,V 4∗]
Every element of the vector of model inputs is additionally normalized between -1 and 1 accelerating the training process. 4.3. ANN topology The ANN used in this study is a feedforward network with six input neurons, one output neuron and full connectivity. The dimensions of the input layer have been directly determined by the selected inputs (see Eq. (6)), the number of neurons in the output layer has been determined by the choice of the desired output or target (herein the interfacial velocity). Differently, the number of neurons in the hidden layers (n1 and n2 for hidden layers 1 and 2 respectively) has been chosen after an iterative process. While one hidden layer can identify simple patterns, two can guarantee recognition of more complex figures. Nonetheless, a large number of hidden layers considerably increases the number of parameters. In this study, two hidden layers have been set (as shown in Fig. 5) and the number of neurons has been carefully studied. It has been proven that with a sufficient number of hidden neurons, an ANN with as few as two hidden layers is capable of approximating an arbitrarily complex mapping within a finite support (Cybenko, 1989).
4.2. Input selection One of the most important steps in the ANN model development process is the determination of an appropriate set of inputs ( X ). As previously described, different parameters have been taken into account for each event (bubble or droplet detection) and their suitability as ANN input has been studied by using a correlation analysis of the proposed inputs, thus avoiding feeding the ANN with identical information more than once. The number of neurons in the hidden layers has been left variable and subject to analysis. Temporal and shape parameters, marked in Fig. 1, have been
4.4. ANN training As ANNs are prone to overfitting the calibration data, cross-validation is generally used. In this study, the calibration data has been divided into training and testing subsets (Maier et al., 2010). The entire available dataset (646 samples) has been divided in training and testing subsets with a proportion of 70% and 30% respectively (452 and 194 samples). The training algorithm adjusts the ANN parameters by reducing the
Table 1 Definition of neuron activation functions for each layer of the studied ANN. Activation functions as defined by Hu and Hwang (2001). Layer
Input
Hidden 1
Hidden 2
Output
Activation function
Linear
Sigmoid
Sigmoid
Linear
(6)
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Fig. 4. Correlation matrix for the variables marked in Fig. 1 obtained from all the recorded signals.
training. 5. Results 5.1. Mean air concentration Air concentrations have not been object of the ANN analysis. However, it is the basic parameter that an optical fibre probe must be able to provide. The accuracy of the interfacial velocity estimation will be constrained by the capacity of the instrumentation to properly detect the air concentration. Fig. 7 show the mean air concentration (C) obtained by using a simple threshold at 50% of the voltage range. The profiles are dimensionless by using the characteristic flow depth where air concentration C = 0.90 (h 90 ). Additionally, comparison with the conductivity probe results of Bung (2011) has been performed at the same steps and flow rates; showing that both experimental setups are alike. The greater discrepancy can be observed close to the step edges, with concentrations around or below 0.10. Data of Bung (2011) was obtained using a double threshold with gradient discrimination which may result on a bigger rejection of bubbles and, consequently, in lower concentration. Nonetheless, Felder and Pfister (2017) observed similar discrepancies when comparing optical fibre probes estimations to measurements conducted with conductivity probes. They concluded that concentrations at the region C < 0.10 obtained with the former can be up to 25% higher, suggesting that one of the probable causes is the difference in tip size – despite overall differences were negligible. Furthermore, the larger sampling rate of this study can result on a better detection of the smallest bubbles which are predominant in the lower region of the air
Fig. 5. Topology of the employed ANN: feedforward ANN with full connectivity, 6 input neurons, 2 hidden layers and 1 output layer. The number of neurons in the hidden layers are variable.
Mean Square Error (MSE, as defined by Bennett et al. (2013)) for the training subset while tracking the effect upon the testing subset. When the error in the testing subset stops decreasing, the training is stopped as well (see Fig. 6). Each iteration is commonly called epoch in the ANN literature. The employed training algorithm is RProp of Igel and Hüsken (2003) using all training samples with the same weight. The classic backpropagation algorithm has been also tested resulting on an inferior
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Fig. 6. Training with cross-validation for the ANN model. Mean Square Error (MSE) as defined by Bennett et al. (2013).
layer. Then, the marginal improvement in the accuracy drastically drops which might reveal that the ANN model cannot learn new relevant features from the data input in the training process. Moreover, Fig. 9 shows that ANNs with similar number of neurons in both hidden layers tend to produce better results at a lower parameter cost. In order to better illustrate the utility and strength of the ANN approach, results from Eq. (4) have been also shown in Fig. 10. The default parameters for Eq. (4) have failed to predict the highly turbulent aerated flow that can be observed in stepped spillways. Thus, parameters have been recalibrated reducing the MSE similarly to the ANN approach, obtaining L = 92.02 μm, when keeping b = −1.02 constant (i.e. the recommended value). It can be clearly appreciated that Eq. (4) alone has not been able to predict the large velocities observed in the stepped spillway. Different signatures might be expected from a bubble or a droplet impact which justifies the use of a more flexible approach. Fig. 11 shows where major dispersion of the predictions have occurred. For the sake of completeness, dual-tip conductivity probe (CP) measurements from Bung (2011) are also shown in Fig. 11, which show a similar dispersion to the herein presented ANN results. Eq. (4) with best fit parameters show different performance for the lower region (bubbles in water) than in the upper region (droplets in air), reinforcing the idea that a method capable of discerning differences in the signals can be better suited for the interfacial velocity prediction than the simple quasilinear approach. The histogram of all conducted measurements and the expected values are presented in Fig. 12. It can be observed that overall mapping of the velocity range has been achieved while a more peaked histogram
concentration profile. Diffusion air concentration profile of Chanson and Toombes (2002) has been also considered as it is known to properly reproduce air concentration profiles in stepped spillways.
5.2. ANN interfacial velocity estimation Alternatively to the MSE computed in the training process, the correlation coefficient (r ), as defined by Bennett et al. (2013), has been also computed to assess both Eq. (4) and ANN performances. The correlation coefficient is commonly used for model evaluation in environmental modelling (Bennett et al., 2013). In Fig. 8, r values are shown for ANN training and testing datasets for a total number of 13,068 trainings (108 trainings per combination of neurons in the hidden layer – n1 and n2 – combination, resulting from a sensitivity analysis). It is observed that all combinations provide an r value over 70% for both training and testing datasets for all studied n1 and n2 combinations; and a maximum value of 90.3% and 83.2% respectively. In Fig. 8, it can be also observed that a higher number of neurons in the hidden layers have improved the accuracy for the training datasets while it promptly has stabilized for the testing dataset. A smaller number of neurons for the same accuracy level is always preferable. Consequently, a combination of five neurons in the first hidden layer with five neurons in the second hidden layer (n1 = n2 = 5) has been finally selected for the ANN topology (as the learning rate has already stabilized, see Fig. 8). Fig. 9 shows the quick correlation coefficient growth from four connections (n1= n2 = 2 ) to 25 connections (n1= n2 = 5) in each hidden
Fig. 7. Mean air concentration at the edges of step 13 (left) and step 21 (right). Comparison with Bung (2011) and the diffusion air concentration profile of Chanson and Toombes (2002) for a mean air concentration of 0.35.
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Fig. 8. Best correlation coefficient (r ) for training (left), testing (center) and all datasets (right) after 108 trainings until convergence for different number of neurons in the hidden layers 1 and 2. Fig. 9. Best correlation coefficient obtained for testing after 108 trainings until convergence and different number of neurons in the hidden layers (and consequently different number of connections and parameters).
Fig. 10. Accuracy of the predicted interfacial velocity with the default and best fit of Eq. (4) (left) and the herein trained ANN (right). Empirically adjusted velocity profile of Bung (2011) is used in both cases as reference.
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Fig. 11. Dimensionless velocity profiles using the characteristic velocity (v 90 ) from Bung (2011). Conductivity probe (CP) data and the corresponding empirical profile of Bung (2011) for different spillway sections, comparison to CP data of Felder and Chanson (2017) for a similar setup and flow conditions.
Fig. 12. Interfacial velocities histograms for the dual-tip based empirical velocity profile of Bung (2011) and the ANN herein trained.
error may cause bias towards large values simultaneously avoiding cancellation between positive and negative errors. The Root Mean Square Error (RMSE) provides a result with same unit as the velocity. It represents the expected error for an ANN prediction. The Absolute Maximum Error (AME) records the maximum absolute error between both compared data series. Given the expected velocities of Bung (2011), these maximum error values correspond to 12.5% and 10.9% of the real velocity for both training and testing datasets, respectively. For all performance descriptors, ANN has been found to be superior to the quasilinear approach by reducing more than one order of magnitude MSE, MSRE, RMSE and AME. Additionally, on the basis of Fig. 11, improvement on Eq. (4) performance may be expected if distinction between flow regions is incorporated.
Table 2 ANN accuracy evaluation according to different parameters of performance, all defined by Bennett et al. (2013). Eq. (4) (best fit) has been added for completeness. Performance of:
MSE [m2/ s2]
r [–]
MSRE [m2/ s2]
RMSE [m/ s]
AME [m/s]
ANN Training ANN Testing Eq. (4) (best fit)
0.0221 0.0198 0.8734
0.7798 0.7823 0.5059
0.0019 0.0017 0.0715
0.1487 0.1406 0.9345
0.4471 0.3876 3.7015
has been obtained from the empirical velocities of the dual-tip measurements of Bung (2011). Minimum velocities have been worst reproduced by the ANN, which can be due to the lower amount of information used during the training process. Table 2 presents some performance descriptors of the analysed models, all of them as defined by Bennett et al. (2013), which might give a thorough insight on the employed ANN accuracy. For completeness, results of the Eq. (4) (best fit) have been also included. Mean Square Error (MSE) has been employed in the training process and consequently is the only parameter of Table 2 which has been directly minimized. The correlation of ANN prediction and expected values are shown by r . The Mean Square Relative Error (MSRE) computes the mean value of the relative squared error. In this parameter, squaring the
6. Conclusions In this study, a large number of measurements with a single-tip optical fibre probe have been performed in self-aerated stepped spillway flow. Measurements have been conducted at different steps for different discharges, obtaining a wide range of velocities at regions with different levels of aeration. After a correlation analysis, different parameters have been selected as input for a feedforward fully connected ANN with two hidden layers and one output neuron (for the 157
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velocity measurements: optimized sensing tips. Int. J. Multiph. Flow 24 (8), 1295–1315. http://dx.doi.org/10.1016/S0301-9322(98)00033-0. Cartellier, A., 1998. Measurement of gas phase characteristics using new monofiber optical probes and real-time signal processing. Nucl. Eng. Des. 184 (2–3), 393–408. http://dx.doi.org/10.1016/S0029-5493(98)00211-8. Castro-Orgaz, O., 2010. Velocity profile and flow resistance models for developing chute flow. J. Hydraul. Eng. 136 (7), 447–452. http://dx.doi.org/10.1061/(ASCE)HY.19437900.0000190. Chanson, H., Brattberg, T., 2002. Experimental study of the air–water shear flow in a hydraulic jump. Int. J. Multiph. Flow 26 (4), 583–607. http://dx.doi.org/10.1016/ S0301-9322(99)00016-6. Chanson, H., Toombes, L., 2002. Air–water flows down stepped chutes: turbulence and flow structure observations. Int. J. Multiph. Flow 28 (11), 1737–1761. http://dx.doi. org/10.1016/S0301-9322(02)00089-7. Chanson, H., 2009. Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environ. Fluid Mech. 9 (2), 125–142. http://dx.doi.org/10.1007/ s10652-008-9078-3. Chanson, H., 2013. Hydraulics of aerated flows: qui pro quo? J. Hydraul. Res. 51 (3), 223–243. http://dx.doi.org/10.1080/00221686.2013.795917. Chen, P.-H., Yen, J.-Y., Chen, J.-L., 1998. An artificial neural network for double exposure PIV image analysis. Exp. Fluids 24 (5), 373–374. http://dx.doi.org/10.1007/ s003480050185. Cybenko, G., 1989. Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2 (4), 303–314. http://dx.doi.org/10.1007/BF02551274. Felder, S., Chanson, H., 2009. Turbulence, dynamic similarity and scale effects in highvelocity free-surface flows above a stepped chute. Exp. Fluids 47 (1), 1–18. http://dx. doi.org/10.1007/s00348-009-0628-3. Felder, S., Chanson, H., 2015. Phase-detection probe measurements in high-velocity freesurface flows including a discussion of key sampling parameters. Exp. Thermal Fluid Sci. 61, 66–78. http://dx.doi.org/10.1016/j.expthermflusci.2014.10.009. Felder, S., Chanson, H., 2017. Scale effects in microscopic air-water flow properties in high-velocity free-surface flows. Exp. Thermal Fluid Sci. 83, 19–36. http://dx.doi. org/10.1016/j.expthermflusci.2016.12.009. Felder, S., Pfister, M., 2017. Comparative analyses of phase-detective intrusive probes in high-velocity air–water flows. Int. J. Multiph. Flow 90, 88–101. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2016.12.009. Frizell, K.W., 2000. Effects of aeration on the performance of an ADV. 2000 Joint Conf. on Water Resources Engineering and Water Resources Planning & Management, ASCE, Minneapolis, USA. Hu, Y.H., Hwang, J.-N., 2001. Handbook of Neural Network Signal Processing. CRC Press. Igel, C., Hüsken, M., 2003. Empirical evaluation of the improved Rprop learning algorithms. Neurocomputing 50, 105–123. http://dx.doi.org/10.1016/S0925-2312(01) 00700-7. Leandro, J., Bung, D.B., Carvalho, R., 2014. Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods. Exp. Fluids 55, 1732. http://dx.doi.org/10.1007/s00348-014-1732-6. Maier, H.R., Jain, A., Dandy, G.C., Sudheer, K.P., 2010. Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ. Model. Softw. 25 (8), 891–909. http://dx.doi.org/10.1016/j.envsoft.2010.02.003. Matos, J., Meireles, I.C., 2014. Hydraulics of stepped weirs and dam spillways: engineering challenges, labyrinths of research. In: Proc., 5th International Symposium on Hydraulic Structures: Hydraulic Structures and Society-Engineering Challenges and Extremes, Brisbane, Australia, 25–27 June 2014. Matos, J., Frizell, K.H., André, S., Frizell, K.W,. 2002. On the performance of velocity measurement techniques in air-water flows. In: Proceedings of the Hydraulic Measurements and Experimental Methods Conference, EWRI/ASCE & IAHR, Estes Park, USA. Meireles, I.C., Renna, F., Matos, J., Bombardelli, F.A., 2012. Skimming, nonaerated flow on stepped spillways over roller compacted concrete dams. J. Hydraul. Eng. 138 (10), 870–877. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000591. Murzyn, F., Chanson, H., 2008. Experimental assessment of scale effects affecting twophase flow properties in hydraulic jumps. Exp. Fluids 45 (3), 513–521. http://dx.doi. org/10.1007/s00348-008-0494-4. Murzyn, F., Mouaze, D., Chaplin, J.R., 2005. Optical fibre probe measurements of bubbly flow in hydraulic jumps. Int. J. Multiph. Flow 31 (1), 141–154. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2004.09.004. Neal, L.G., Bankoff, L.G., 1963. A high resolution resistivity probe for determination of local void properties in gas-liquid flow. AIChE J. 9 (4), 490–494. http://dx.doi.org/ 10.1002/aic.690090415. Schaul, T., Bayer, J., Wierstra, D., Sun, Y., Felder, M., Sehnke, F., Rückstieß, T., Schmidhuber, J., 2010. PyBrain. J. Mach. Learn. Res. 11, 743–746. Valero, D., Bung, D.B., 2016. Development of the interfacial air layer in the non-aerated region of high-velocity spillway flows. Instabilities growth, entrapped air and influence on the self-aeration onset. Int. J. Multiph. Flow 84, 66–74. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2016.04.012. Vejražka, J., Večeř, M., Orvalho, S., Sechet, P., Ruzicka, M.C., Cartellier, A., 2010. Measurement accuracy of a mono-fiber optical probe in a bubbly flow. Int. J. Multiph. Flow 36 (7), 533–548. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2010.03.007. Wang, H., Chanson, H., 2015. Air entrainment and turbulent fluctuations in hydraulic jumps. Urban Water J. 12 (6), 502–518. http://dx.doi.org/10.1080/1573062X.2013. 847464. Wang, H., Murzyn, F., 2016. Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface. Environ. Fluid Mech. 1–19. http://dx.doi.org/10.1007/s10652-016-9451-6. Wang, H., Felder, S., Chanson, H., 2014. An experimental study of turbulent two-phase
interfacial velocity, v ). The choice of these parameters has been based on previous studies found in the literature, which showed that rising times are related to the interfacial velocities and that signature shapes may depend on small geometrical defects occurring at the probes tips. The number of neurons in the hidden layers has been the result of an iterative process. A significant accuracy enhancement due to the use of an ANN model has been observed. The obtained level of accuracy in terms of timeaveraged velocities was found to be comparable to the experimental scatter of a dual-tip conductivity probe. However, the accuracy of the instantaneous velocities is still unknown. As the obtained velocity time series could provide a novel method to determine turbulence structures in air-water flows, this point needs to be further investigated in future. Accurate time series could allow for a reliable estimation of turbulence and thus improve the understanding of this type of flow in future. Another advantage of the presented method is given by the less intrusive single-tip probe compared to classical dual-tip probes without disturbances of the flow at a rear tip. The nonlinear nature of ANN, the ability to learn from their environments in both supervised and unsupervised ways, as well as the universal approximation property of neural networks make them highly suited for solving difficult problems. ANN can detect and profit some hidden patterns within the analyzed data which would remain unseen otherwise, yielding complex non-linear and robust methods when properly applied. Acknowledgments Authors thank A2 Photonic Sensors for providing the instrumentation and installation recommendations. The authors are also grateful for the valuable comments provided by the reviewers and the fruitful discussions with Prof. García-Bartual from Universitat Politècnica de València (UPV). References Amador, A., Sánchez-Juny, M., Dolz, J., 2006. Characterization of the non-aerated flow region in a stepped spillway by PIV. J. Fluids Eng. 128 (6), 1266–1273. http://dx.doi. org/10.1115/1.2354529. Bennett, N.D., Croke, B.F., Guariso, G., Guillaume, J.H., Hamilton, S.H., Jakeman, A.J., Marsili-Libelli, S., Newham, L.T., Norton, J.P., Perrin, C., Pierce, S.A., 2013. Characterising performance of environmental models. Environ. Model. Softw. 40, 1–20. http://dx.doi.org/10.1016/j.envsoft.2012.09.011. Boes, R., Hager, W.H., 2003. Two-phase flow characteristics of stepped spillways. J. Hydraul. Eng. 129 (9), 661–670. http://dx.doi.org/10.1061/(ASCE)07339429(2003) 129:9(661). Bung, D.B., Valero, D., 2015. Image Processing for Bubble Image Velocimetry in Selfaerated Flows. In: E-proceedings of the 36th IAHR World Congress, 28 June–3 July, 2015, The Hague, the Netherlands. ISBN: 978-90-824846-0-1. Bung, D.B., Valero, D., 2016a. Optical flow estimation in aerated flows. J. Hydraul. Res. 54 (5), 575–580. http://dx.doi.org/10.1080/00221686.2016.1173600. Bung, D.B., Valero, D., 2016b. Application of the Optical Flow Method to Velocity Determination in Hydraulic Structure Models. In: Proc., 6th International Symposium on Hydraulic Structures, Portland, Oregon, USA, 27–30 June 2016. http://dx.doi. org/10.15142/T3150628160853. Bung, D.B., Valero, D., 2016c. Image processing techniques for velocity estimation in highly aerated flows: bubble image velocimetry vs. optical flow. In: Erpicum (Ed.), Sustainable Hydraulics in the Era of Global Change. Taylor and Francis Group ISBN: 978-1-138-02977-4. Bung, D.B., 2011. Developing flow in skimming flow regime on embankment stepped spillways. J. Hydraul. Res. 49 (5), 639–648. http://dx.doi.org/10.1080/00221686. 2011.584372. Bung, D.B., 2012. Sensitivity of phase detection techniques in aerated chute flows to hydraulic design parameters. In: Proc., 2nd European IAHR congress, 27–29, June 2012, Munich. Bung, D.B., 2013. Non-intrusive detection of air–water surface roughness in self-aerated chute flows. J. Hydraul. Res. 51 (3), 322–329. http://dx.doi.org/10.1080/00221686. 2013.777373. Carosone, F., Cenedese, A., Querzoli, G., 1995. Recognition of partially overlapped particle images using the Kohonen neural network. Exp. Fluids 19 (4), 225–232. http:// dx.doi.org/10.1007/BF00196470. Cartellier, A., Barrau, E., 1998a. Monofiber optical probes for gas detection and gas velocity measurements: conical probes. Int. J. Multiph. Flow 24 (8), 1265–1294. http:// dx.doi.org/10.1016/S0301-9322(98)00032-9. Cartellier, A., Barrau, E., 1998b. Monofiber optical probes for gas detection and gas
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D. Valero, D.B. Bung flow in hydraulic jumps and application of a triple decomposition technique. Environ. Fluid Mech. 55, 1775. http://dx.doi.org/10.1007/s00348-014-1775-8. Wilhelms, S.C., Gulliver, J.S., 2005. Bubbles and waves description of self-aerated spillway flow. J. Hydraul. Res. 43 (5), 522–531. http://dx.doi.org/10.1080/ 00221680509500150. Zhang, G., Chanson, H., 2016a. Interaction between free-surface aeration and total
pressure on a stepped chute. Exp. Thermal Fluid Sci. 74, 368–381. http://dx.doi.org/ 10.1016/j.expthermflusci.2015.12.011. Zhang, G., Chanson, H., 2016b. Hydraulics of the developing flow region of stepped spillways. I: Physical modeling and boundary layer development. J. Hydraul. Eng. 04016015. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001138.
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Research papers
Artificial Neural Networks and pattern recognition for air-water flow velocity estimation using a single-tip optical fibre probe
T
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D. Valeroa,b, , D.B. Bunga a b
Hydraulic Engineering Section (HES), FH Aachen University of Applied Sciences, Aachen, Germany Dept. of ArGEnCo, Research Group of Hydraulics in Environmental and Civil Engineering (HECE), University of Liege (ULg), Liège, Belgium
A R T I C L E I N F O
A B S T R A C T
Keywords: Air-water flow Feedforward network Interfacial velocity Stepped spillway Artificial intelligence Instrumentation
Interest in air-water flows has increased considerably for the last decades, being a common research field for different engineering applications ranging from nuclear engineering to large hydraulic structures or water quality treatments. Investigation of complex air-water flow behavior requires sophisticated instrumentation devices, with additional challenges when compared to single phase instrumentation. In this paper, a single-tip optical fibre probe has been used to record high-frequency samples (over 1 MHz). The main advantage of this instrumentation is that it allows direct computation of a velocity for each detected bubble or droplet, thus providing a detailed velocity time series. Fluid phase detection functions (i.e. the signal transition between two fluid phases) have been related to the interfacial velocities by means of Artificial Neural Networks (ANN). Information from previous measurements of a classical dual-tip conductivity probe (yielding time-averaged velocity data only) and theoretical velocity profiles have been used to train and test ANN. Special attention has been given to the input selection and the ANN dimensions, which allowed obtaining a robust methodology in order to non-linearly post-process the optical fibre signals and thus to estimate interfacial velocities. ANN have been found to be capable to recognize characteristic shapes in the fluid phase function and to provide a similar level of accuracy as classical dual-tip techniques. Finally, performance of the trained ANN has been evaluated by means of different accuracy parameters.
1. Introduction
2013; Bung and Valero, 2015, 2016a–c; Leandro et al., 2014), intrusive techniques are still the most widely used option (Boes and Hager, 2003; Chanson and Brattberg, 2002; Chanson and Toombes, 2002; Felder and Chanson, 2015; Wang and Chanson, 2015; Wang and Murzyn, 2016; Wang et al., 2014; Zhang and Chanson, 2016a). When the air fraction (C) exceeds 1–3%, accuracy of common instrumentation for single phase flow measurements is typically affected and conductivity or optical fibre probes become the best option (Felder and Chanson, 2015). Further discussion on single phase instrumentation applicability to slightly aerated flows can be found in Frizell (2000) and Matos et al. (2002). However, when using intrusive measurement techniques, some drawbacks and limitations can arise. Few attempts have been done to improve accuracy of such devices, testing different settings and signal post-processing techniques (Bung, 2012; Felder and Chanson, 2015). Given the considerable impact of scale effects (Chanson, 2009, 2013; Felder and Chanson, 2009; Murzyn and Chanson, 2008) and the increasing interest in the determination of air-water turbulence features (Bung and Valero, 2016c; Felder and Chanson, 2009; Wang and Murzyn, 2016), more demanding measurements in prototype and large
Air-water flows can be often found in large hydraulic structures, where self-aeration occurs as a complex and turbulent air-water compatibility phenomenon (Valero and Bung, 2016). When air entrainment occurs, flow bulking, friction reduction and turbulence modulation can be observed (Chanson, 2013), drastically changing the main flow properties and thereby complicating the flow behavior prediction. In spillway flows, recent research efforts have focused both on the aerated region (Boes and Hager, 2003; Bung, 2011; Chanson and Toombes, 2002; Felder and Chanson, 2009; Wilhelms and Gulliver, 2005; Zhang and Chanson, 2016a) and the non-aerated region (Amador et al., 2006; Castro-Orgaz, 2010; Meireles et al., 2012; Valero and Bung, 2016; Zhang and Chanson, 2016b). However, some key challenges remain unresolved (Chanson, 2013; Matos and Meireles, 2014). Similarly, airwater flow properties within hydraulic jumps have also attracted researchers’ interest (Chanson and Brattberg, 2002; Murzyn et al., 2005; Wang and Chanson, 2015; Wang and Murzyn, 2016; Wang et al., 2014). Although some new non-intrusive techniques are available (Bung,
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Corresponding author at: Hydraulic Engineering Section (HES), FH Aachen University of Applied Sciences, Aachen, Germany. E-mail address: [email protected] (D. Valero).
http://dx.doi.org/10.1016/j.jher.2017.08.004
Available online 26 August 2017 1570-6443/ © 2017 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.
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Fig. 1. Exemplary phase detection function for a bubble-tip impact event (note that tr can be directly extracted from the signal). Main parameters describing the phase detection function have been marked out (green for the finally selected inputs of the Artificial Neural Network). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
reports a relative error of around 10% both for air fraction estimation under laboratory conditions. Further discussion on the probe-bubble interaction and the effect upon the air fraction measurement accuracy can be found in the study of Vejražka et al. (2010). Errors are globally comparable for the single-tip and the dual-tip optical fibre techniques, but sensitivity to the flow regime can differ. For finely dispersed flows, single-tip optical probes are better suited while double-tip probe performance is better whenever large gas inclusions are present (Cartellier, 1998). Therefore, application of single-tip probes in highly turbulent aerated spillway flows becomes challenging. Also, their actual response is sensitive to small geometrical defects occurring at their tips as indicated by Cartellier and Barrau (1998a,b). Use of more complex data processing techniques than the rather simple rising time/velocity correlation provided by Eq. (2) can yield improved performance of the instrumentation. In this study, raw signals have been recorded with a single-tip optical fibre in a highly aerated flow on a moderately sloped stepped spillway; similar to the setup described in Bung and Valero (2015) and Bung (2011). These new signals have been processed evaluating the accuracy of the simple – yet physically based – approach of Eq. (2). At a second stage, they have been used to train and test an Artificial Neural Network (ANN). One of the main strengths of ANN is to allow detection of both simple and complex patterns in the input, which could remain indistinguishable to the researchers’ naked eye (it must be noted that different bubble/droplet impact events can generate different phase functions signatures). Different ANN configurations have been tested by means of the PyBrain open-source package (Schaul et al., 2010) and Python 2.7.
scale laboratory models may require from more exigent use of experimental techniques. Since the early study of Neal and Bankoff (1963), phase detection probes have become a common measuring technique in multiphase flow disciplines. The working principle of optical fibre probes is based upon the change of light refraction at air-water interfaces. Usually, these probes comprise two conical tips (dual-tip probes), being both tips intended to record two signals based on the same bubbly events. Similarly to conductivity probes (Chanson and Toombes, 2002), the most probable lag time (T ) can be obtained by cross-correlating both signals and consequently a mean interfacial velocity (v ) can be computed, given that the distance between both tips (Δx ) in flow direction is accurately known: (1)
v = Δx / T
Nonetheless, a second type of optical fibre is available based on a single-tip configuration. In such case, no cross-correlation can be performed since only a single signal is recorded. High sample rates help to record a more detailed signal (i.e.: phase detection function, see Fig. 1) and voltage gradients may be characterized with higher accuracy. Hence, single bubble/droplet velocities (vi ) can be approximated by: (2)
vi ≈ L/ tr
where tr is the so-called rising time, which represents the time that it takes to the voltage signal to pass from a lower threshold to an upper threshold (e.g. from 10% for the water level to 90% for the air level) and L is a characteristic length scale that the bubble/droplet travels through the probe, often referred to as latency length (Cartellier, 1998; Cartellier and Barrau, 1998a,b). Given a large number of velocities (vi ) obtained from the same number of bubble/droplet impacts, the mean velocity can be computed as an ensemble average:
1 v= N
2. Experimental setup All measurements have been conducted in a moderately sloped stepped spillway (1V:2H, chute slope ϕ = 26.6°, step height s = 6 cm) located at the Hydraulics Laboratory of FH Aachen, for three different flow rates q = 0.07, 0.09 and 0.11 m2/s. The total drop height is 1.74 m with a flume width of 0.50 m. Water is pumped from a lower basin into an open head tank from where it is conveyed into the stepped chute via an approaching channel of 1 m length. In order to complete a wide range of interfacial velocities, measurements have been conducted at downstream edges of step 13, 14, 18, 19 and 21 (see Fig. 2). Velocity in x -direction has been obtained perpendicularly to the pseudo-bottom with 2 mm spacing in the z -coordinate, resulting in 646 measurements. It must be noted that the air-water flow was found to be in the uniform flow region at step 21 for the highest discharge (see Figs. 2 and 3) according to Bung (2011).
N
∑ i=1
vi
(3)
with N the total number of samples (in this case the number of detected bubbles/droplets). A more robust approach to outliers would be considering the median value instead of the average, being the median the value which separates the ensemble in two equal parts (the 50% lower values from the upper 50%). To avoid a certain level of sensitivity to uncontrollable parameters (e.g. the angle of impact on the bubble interface), the probe geometry can differ from the commonly used dual-tip optical fibres. Thus, some more complex geometries, e.g. a cone + cylinder + cone geometry of the tip, could be used (Cartellier and Barrau, 1998b). Cartellier (1998) 151
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Fig. 2. Sketch of the experimental setup and flow regions on a stepped spillway.
The employed single-tip optical fibre probe (Fig. 3) corresponds to a simple cone geometry, which is more sensitive to uncontrolled parameters and manufacturing defects (Cartellier and Barrau, 1998a, 1998b). It has been placed at the centreline of the spillway and has been positioned by a CNC controlling system (isel) with an accuracy of ∼0.1 mm. The probe has been supplied by A2 Photonic Sensors, giving a relative error of 15% for the velocity estimation, including a signal recording software and the necessary electronic module. The probe provider recommends a velocity approximation based on Eq. (2) given by:
v = L·trb
High-frequency oscillations with small amplitudes may affect the analysis of the phase function, and more especially the accurate determination of the characteristic voltage levels sketched in Fig. 1. To remove these small oscillations, a central moving average filter with a moving window of 10 time steps has been applied. By removing sampled frequencies above a certain cutoff frequency, the moving average creates a smoothing effect upon the phase detection function, yielding a negligible effect when the averaging window is small enough. In order to make the signal independent from the adjusted voltage range, all the signals have been scaled to be comprised between 0 and 100%, thus resulting in a normalized voltage V ∗ (note that an absolute voltage range over 5 Volts has been always ensured during the data acquisition). To obtain a representative event for the ANN, a median signature (or median phase indicator function, similar to the one shown in Fig. 1) has been extracted from each recording. Different parameters defining this median phase indicator function have been selected, which can be segregated into (a) rising time parameters and (b) phase function shape parameters. As marked in Fig. 1, rising time related variables can be defined as: ti − j = t j−ti , which is the time difference between the dimensionless voltage V ∗ reaching the value j and i ; with i = 10, 25, 50 and 75, and j = 25, 50, 75 (in % of the range in the median phase indicator func∗ tion) and max corresponding to the maximum voltage (Vmax ) reached at ∗ each event. If Vmax remains below 75%, the entire event is rejected based on the impossibility to gather all the described parameters. The phase function shape descriptors have been marked in Fig. 1 as Vk∗, with k = max, 1, 2, 3, 4. These values have been taken at equal times between tmax and tend , being tend the time corresponding to V ∗ = 10% in the decreasing phase function region. Additionally, V1∗m ∗ and V2∗m are the normalized voltages measurements between Vmax and V1∗, V1∗ and V2∗ respectively. These additional voltages have been selected to better describe the exponentially decaying tail which has been ∗ commonly observed after Vmax .
(4)
where b is a parameter taking a value close to −1 (for the employed probe: b = −1.02 and L = 45.3 μm). However, it must be mentioned that Eq. (4) has been developed for less complex type of flow than the present highly-turbulent stepped spillway flow. In order to obtain a large number of information on the signal voltage gradients, the sampling rate has been set to 1 MHz, which is two orders of magnitude larger than the minimum sampling rate recommendations for such type of flows; see Felder and Chanson (2015) recommending a sample rate around 20–40 kHz. Sample time has been set to 30 s. It must be noted that the study of Felder and Chanson (2015) showed little effect upon velocity and turbulence estimations by incrementing the sample duration over 30 s. 3. Signal analysis For each of the 646 raw signals, 30 million data points have been taken into account to train and test the ANN; provided that the sample rate is 1 MHz and sample time of 30 s. Each signal displays a signature every time that a bubble/droplet impacts the probe tip (see Fig. 1) and, consequently, includes thousands of events (i.e. phase changes from water to air). Each signature can be divided into the bubble impact region (approximately during the rising time tr ) and a subsequently following plateau when the signal voltage stabilizes after the impact.
Fig. 3. Left: single-tip optical fibre probe, right: exemplary fully aerated flow at step 21 for q = 0.07 m2/s recorded with a high-speed camera (Bung and Valero, 2015).
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4. Artificial Neural Network
obtained for each event of the 646 conducted measurements. This has yielded thousands of values for each measurement. In order to get only one value per variable and signal the median value has been computed, hence summarizing a large quantity of data. Temporal variables have been inverted (t −1) which can be expected to be directly proportional to the velocity (see Eq. (2)). Shape parameters have been selected based on the previously observed fact that the bubble/droplet impacting the tip produces a characteristic signature (Cartellier, 1998; Cartellier and Barrau, 1998a,b). In order to make the shape parameters independent from the event duration (and consequently from the impacting bubble/ droplet size), the plateau of each event has been split in equal parts ranging from the maximum and the final voltages. For the temporal variables, a logarithmic distribution can be observed in the histograms. Consequently, logarithm of ti−−1j (i.e. log(ti−−1j )) has been considered to obtain a more homogeneous distribution of these parameters. Given a fixed number of training samples, the addition of redundant model inputs increases the ratio of the number of connection weights to the number of training samples, thus increasing the likelihood of overfitting, not providing any additional information to the model. Secondly, the inclusion of redundant model inputs introduces additional local minima in the error surface in weight space (Maier et al., 2010) which makes the training process more complicated. To detect redundancy between the described variables, correlation among them has been estimated (see Fig. 4) and highly correlated variables have been discarded before the training process. A strong correlation between the shape variables can be observed in ∗ the tail of the signature while Vmax , V1∗m and V 4∗ showed a lower correlation. Thus, the other shape variables have been omitted in the following analysis. Within the temporal variables, only t10 − 25 have been found to bear a high correlation with t25 − 50 . Given that t10 − 25 is more correlated to the remaining parameters than t25 − 50 , the former one has been neglected. Consequently, the selected variables for the ANN input vector (marked in green in Fig. 1) are the following:
4.1. General remarks Artificial Neural Networks (ANN), one of the earliest techniques of Artificial Intelligence (AI), have become a powerful tool for prediction and forecasting of water resources, mainly addressing hydrological and sediment problems. However, when it comes to hydraulic instrumentation prediction improvement, only a few attempts can be found in the literature. Carosone et al. (1995) and Chen et al. (1998) employed ANN altogether with Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV) techniques. Recently, Bung and Valero (2016a–c) have applied Artificial Intelligence techniques to turbulent flows obtaining, at least, as accurate velocity fields as classical cross-correlation based techniques, with a significant improvement for air-water flows. ANN models are composed of an input layer, where every input is represented by a single neuron, a given number of rows of hidden layers and an output layer which finally provides the desired variable by summarizing the information processed by the upstream neurons. The larger the number of hidden layers, the more complex patterns can be identified by the network. However, setting up a large number of hidden layers may result in an excessively large mathematical model. The herein employed network is composed of an input and an output layer and two hidden layers. The network is feedforward (i.e. with an acyclic topology) which can be used to approximate a nonlinear mapping between its inputs and outputs (Hu and Hwang, 2001). All ANN models, independently of the number of layers and neurons, take the basic form (Maier et al., 2010):
Y = f (X ,W ) + ε
(5)
where Y is the vector of model outputs, X is the vector of model input, W the vector of model parameters (or connection weights), f (·) is a functional relationship between model outputs, inputs and parameters; and ε is the vector of model errors. The functional relationship depends strongly on the ANN architecture. In this study, the model output is a single scalar (velocity v ), the vector of model input is discussed in Section 4.2 on the basis of the event-driven description of the recorded signal; the number of neurons is discussed in Section 4.3 and the vector of model errors is the result of the ANN training, discussed in Section 4.4. For the neuron activation functions, linear, sigmoid and hyperbolic tangents have been tested as they are available in the PyBrain package (Schaul et al., 2010), obtaining the best results with the combination shown in Table 1. For the net functions, linear summation has been employed (Hu and Hwang, 2001).
∗ X = [log(t25 − 50−1),log(t50 − 75−1),log(t75 − max −1 ),Vmax ,V1∗m,V 4∗]
Every element of the vector of model inputs is additionally normalized between -1 and 1 accelerating the training process. 4.3. ANN topology The ANN used in this study is a feedforward network with six input neurons, one output neuron and full connectivity. The dimensions of the input layer have been directly determined by the selected inputs (see Eq. (6)), the number of neurons in the output layer has been determined by the choice of the desired output or target (herein the interfacial velocity). Differently, the number of neurons in the hidden layers (n1 and n2 for hidden layers 1 and 2 respectively) has been chosen after an iterative process. While one hidden layer can identify simple patterns, two can guarantee recognition of more complex figures. Nonetheless, a large number of hidden layers considerably increases the number of parameters. In this study, two hidden layers have been set (as shown in Fig. 5) and the number of neurons has been carefully studied. It has been proven that with a sufficient number of hidden neurons, an ANN with as few as two hidden layers is capable of approximating an arbitrarily complex mapping within a finite support (Cybenko, 1989).
4.2. Input selection One of the most important steps in the ANN model development process is the determination of an appropriate set of inputs ( X ). As previously described, different parameters have been taken into account for each event (bubble or droplet detection) and their suitability as ANN input has been studied by using a correlation analysis of the proposed inputs, thus avoiding feeding the ANN with identical information more than once. The number of neurons in the hidden layers has been left variable and subject to analysis. Temporal and shape parameters, marked in Fig. 1, have been
4.4. ANN training As ANNs are prone to overfitting the calibration data, cross-validation is generally used. In this study, the calibration data has been divided into training and testing subsets (Maier et al., 2010). The entire available dataset (646 samples) has been divided in training and testing subsets with a proportion of 70% and 30% respectively (452 and 194 samples). The training algorithm adjusts the ANN parameters by reducing the
Table 1 Definition of neuron activation functions for each layer of the studied ANN. Activation functions as defined by Hu and Hwang (2001). Layer
Input
Hidden 1
Hidden 2
Output
Activation function
Linear
Sigmoid
Sigmoid
Linear
(6)
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Fig. 4. Correlation matrix for the variables marked in Fig. 1 obtained from all the recorded signals.
training. 5. Results 5.1. Mean air concentration Air concentrations have not been object of the ANN analysis. However, it is the basic parameter that an optical fibre probe must be able to provide. The accuracy of the interfacial velocity estimation will be constrained by the capacity of the instrumentation to properly detect the air concentration. Fig. 7 show the mean air concentration (C) obtained by using a simple threshold at 50% of the voltage range. The profiles are dimensionless by using the characteristic flow depth where air concentration C = 0.90 (h 90 ). Additionally, comparison with the conductivity probe results of Bung (2011) has been performed at the same steps and flow rates; showing that both experimental setups are alike. The greater discrepancy can be observed close to the step edges, with concentrations around or below 0.10. Data of Bung (2011) was obtained using a double threshold with gradient discrimination which may result on a bigger rejection of bubbles and, consequently, in lower concentration. Nonetheless, Felder and Pfister (2017) observed similar discrepancies when comparing optical fibre probes estimations to measurements conducted with conductivity probes. They concluded that concentrations at the region C < 0.10 obtained with the former can be up to 25% higher, suggesting that one of the probable causes is the difference in tip size – despite overall differences were negligible. Furthermore, the larger sampling rate of this study can result on a better detection of the smallest bubbles which are predominant in the lower region of the air
Fig. 5. Topology of the employed ANN: feedforward ANN with full connectivity, 6 input neurons, 2 hidden layers and 1 output layer. The number of neurons in the hidden layers are variable.
Mean Square Error (MSE, as defined by Bennett et al. (2013)) for the training subset while tracking the effect upon the testing subset. When the error in the testing subset stops decreasing, the training is stopped as well (see Fig. 6). Each iteration is commonly called epoch in the ANN literature. The employed training algorithm is RProp of Igel and Hüsken (2003) using all training samples with the same weight. The classic backpropagation algorithm has been also tested resulting on an inferior
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Fig. 6. Training with cross-validation for the ANN model. Mean Square Error (MSE) as defined by Bennett et al. (2013).
layer. Then, the marginal improvement in the accuracy drastically drops which might reveal that the ANN model cannot learn new relevant features from the data input in the training process. Moreover, Fig. 9 shows that ANNs with similar number of neurons in both hidden layers tend to produce better results at a lower parameter cost. In order to better illustrate the utility and strength of the ANN approach, results from Eq. (4) have been also shown in Fig. 10. The default parameters for Eq. (4) have failed to predict the highly turbulent aerated flow that can be observed in stepped spillways. Thus, parameters have been recalibrated reducing the MSE similarly to the ANN approach, obtaining L = 92.02 μm, when keeping b = −1.02 constant (i.e. the recommended value). It can be clearly appreciated that Eq. (4) alone has not been able to predict the large velocities observed in the stepped spillway. Different signatures might be expected from a bubble or a droplet impact which justifies the use of a more flexible approach. Fig. 11 shows where major dispersion of the predictions have occurred. For the sake of completeness, dual-tip conductivity probe (CP) measurements from Bung (2011) are also shown in Fig. 11, which show a similar dispersion to the herein presented ANN results. Eq. (4) with best fit parameters show different performance for the lower region (bubbles in water) than in the upper region (droplets in air), reinforcing the idea that a method capable of discerning differences in the signals can be better suited for the interfacial velocity prediction than the simple quasilinear approach. The histogram of all conducted measurements and the expected values are presented in Fig. 12. It can be observed that overall mapping of the velocity range has been achieved while a more peaked histogram
concentration profile. Diffusion air concentration profile of Chanson and Toombes (2002) has been also considered as it is known to properly reproduce air concentration profiles in stepped spillways.
5.2. ANN interfacial velocity estimation Alternatively to the MSE computed in the training process, the correlation coefficient (r ), as defined by Bennett et al. (2013), has been also computed to assess both Eq. (4) and ANN performances. The correlation coefficient is commonly used for model evaluation in environmental modelling (Bennett et al., 2013). In Fig. 8, r values are shown for ANN training and testing datasets for a total number of 13,068 trainings (108 trainings per combination of neurons in the hidden layer – n1 and n2 – combination, resulting from a sensitivity analysis). It is observed that all combinations provide an r value over 70% for both training and testing datasets for all studied n1 and n2 combinations; and a maximum value of 90.3% and 83.2% respectively. In Fig. 8, it can be also observed that a higher number of neurons in the hidden layers have improved the accuracy for the training datasets while it promptly has stabilized for the testing dataset. A smaller number of neurons for the same accuracy level is always preferable. Consequently, a combination of five neurons in the first hidden layer with five neurons in the second hidden layer (n1 = n2 = 5) has been finally selected for the ANN topology (as the learning rate has already stabilized, see Fig. 8). Fig. 9 shows the quick correlation coefficient growth from four connections (n1= n2 = 2 ) to 25 connections (n1= n2 = 5) in each hidden
Fig. 7. Mean air concentration at the edges of step 13 (left) and step 21 (right). Comparison with Bung (2011) and the diffusion air concentration profile of Chanson and Toombes (2002) for a mean air concentration of 0.35.
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Fig. 8. Best correlation coefficient (r ) for training (left), testing (center) and all datasets (right) after 108 trainings until convergence for different number of neurons in the hidden layers 1 and 2. Fig. 9. Best correlation coefficient obtained for testing after 108 trainings until convergence and different number of neurons in the hidden layers (and consequently different number of connections and parameters).
Fig. 10. Accuracy of the predicted interfacial velocity with the default and best fit of Eq. (4) (left) and the herein trained ANN (right). Empirically adjusted velocity profile of Bung (2011) is used in both cases as reference.
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Fig. 11. Dimensionless velocity profiles using the characteristic velocity (v 90 ) from Bung (2011). Conductivity probe (CP) data and the corresponding empirical profile of Bung (2011) for different spillway sections, comparison to CP data of Felder and Chanson (2017) for a similar setup and flow conditions.
Fig. 12. Interfacial velocities histograms for the dual-tip based empirical velocity profile of Bung (2011) and the ANN herein trained.
error may cause bias towards large values simultaneously avoiding cancellation between positive and negative errors. The Root Mean Square Error (RMSE) provides a result with same unit as the velocity. It represents the expected error for an ANN prediction. The Absolute Maximum Error (AME) records the maximum absolute error between both compared data series. Given the expected velocities of Bung (2011), these maximum error values correspond to 12.5% and 10.9% of the real velocity for both training and testing datasets, respectively. For all performance descriptors, ANN has been found to be superior to the quasilinear approach by reducing more than one order of magnitude MSE, MSRE, RMSE and AME. Additionally, on the basis of Fig. 11, improvement on Eq. (4) performance may be expected if distinction between flow regions is incorporated.
Table 2 ANN accuracy evaluation according to different parameters of performance, all defined by Bennett et al. (2013). Eq. (4) (best fit) has been added for completeness. Performance of:
MSE [m2/ s2]
r [–]
MSRE [m2/ s2]
RMSE [m/ s]
AME [m/s]
ANN Training ANN Testing Eq. (4) (best fit)
0.0221 0.0198 0.8734
0.7798 0.7823 0.5059
0.0019 0.0017 0.0715
0.1487 0.1406 0.9345
0.4471 0.3876 3.7015
has been obtained from the empirical velocities of the dual-tip measurements of Bung (2011). Minimum velocities have been worst reproduced by the ANN, which can be due to the lower amount of information used during the training process. Table 2 presents some performance descriptors of the analysed models, all of them as defined by Bennett et al. (2013), which might give a thorough insight on the employed ANN accuracy. For completeness, results of the Eq. (4) (best fit) have been also included. Mean Square Error (MSE) has been employed in the training process and consequently is the only parameter of Table 2 which has been directly minimized. The correlation of ANN prediction and expected values are shown by r . The Mean Square Relative Error (MSRE) computes the mean value of the relative squared error. In this parameter, squaring the
6. Conclusions In this study, a large number of measurements with a single-tip optical fibre probe have been performed in self-aerated stepped spillway flow. Measurements have been conducted at different steps for different discharges, obtaining a wide range of velocities at regions with different levels of aeration. After a correlation analysis, different parameters have been selected as input for a feedforward fully connected ANN with two hidden layers and one output neuron (for the 157
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velocity measurements: optimized sensing tips. Int. J. Multiph. Flow 24 (8), 1295–1315. http://dx.doi.org/10.1016/S0301-9322(98)00033-0. Cartellier, A., 1998. Measurement of gas phase characteristics using new monofiber optical probes and real-time signal processing. Nucl. Eng. Des. 184 (2–3), 393–408. http://dx.doi.org/10.1016/S0029-5493(98)00211-8. Castro-Orgaz, O., 2010. Velocity profile and flow resistance models for developing chute flow. J. Hydraul. Eng. 136 (7), 447–452. http://dx.doi.org/10.1061/(ASCE)HY.19437900.0000190. Chanson, H., Brattberg, T., 2002. Experimental study of the air–water shear flow in a hydraulic jump. Int. J. Multiph. Flow 26 (4), 583–607. http://dx.doi.org/10.1016/ S0301-9322(99)00016-6. Chanson, H., Toombes, L., 2002. Air–water flows down stepped chutes: turbulence and flow structure observations. Int. J. Multiph. Flow 28 (11), 1737–1761. http://dx.doi. org/10.1016/S0301-9322(02)00089-7. Chanson, H., 2009. Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environ. Fluid Mech. 9 (2), 125–142. http://dx.doi.org/10.1007/ s10652-008-9078-3. Chanson, H., 2013. Hydraulics of aerated flows: qui pro quo? J. Hydraul. Res. 51 (3), 223–243. http://dx.doi.org/10.1080/00221686.2013.795917. Chen, P.-H., Yen, J.-Y., Chen, J.-L., 1998. An artificial neural network for double exposure PIV image analysis. Exp. Fluids 24 (5), 373–374. http://dx.doi.org/10.1007/ s003480050185. Cybenko, G., 1989. Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2 (4), 303–314. http://dx.doi.org/10.1007/BF02551274. Felder, S., Chanson, H., 2009. Turbulence, dynamic similarity and scale effects in highvelocity free-surface flows above a stepped chute. Exp. Fluids 47 (1), 1–18. http://dx. doi.org/10.1007/s00348-009-0628-3. Felder, S., Chanson, H., 2015. Phase-detection probe measurements in high-velocity freesurface flows including a discussion of key sampling parameters. Exp. Thermal Fluid Sci. 61, 66–78. http://dx.doi.org/10.1016/j.expthermflusci.2014.10.009. Felder, S., Chanson, H., 2017. Scale effects in microscopic air-water flow properties in high-velocity free-surface flows. Exp. Thermal Fluid Sci. 83, 19–36. http://dx.doi. org/10.1016/j.expthermflusci.2016.12.009. Felder, S., Pfister, M., 2017. Comparative analyses of phase-detective intrusive probes in high-velocity air–water flows. Int. J. Multiph. Flow 90, 88–101. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2016.12.009. Frizell, K.W., 2000. Effects of aeration on the performance of an ADV. 2000 Joint Conf. on Water Resources Engineering and Water Resources Planning & Management, ASCE, Minneapolis, USA. Hu, Y.H., Hwang, J.-N., 2001. Handbook of Neural Network Signal Processing. CRC Press. Igel, C., Hüsken, M., 2003. Empirical evaluation of the improved Rprop learning algorithms. Neurocomputing 50, 105–123. http://dx.doi.org/10.1016/S0925-2312(01) 00700-7. Leandro, J., Bung, D.B., Carvalho, R., 2014. Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods. Exp. Fluids 55, 1732. http://dx.doi.org/10.1007/s00348-014-1732-6. Maier, H.R., Jain, A., Dandy, G.C., Sudheer, K.P., 2010. Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ. Model. Softw. 25 (8), 891–909. http://dx.doi.org/10.1016/j.envsoft.2010.02.003. Matos, J., Meireles, I.C., 2014. Hydraulics of stepped weirs and dam spillways: engineering challenges, labyrinths of research. In: Proc., 5th International Symposium on Hydraulic Structures: Hydraulic Structures and Society-Engineering Challenges and Extremes, Brisbane, Australia, 25–27 June 2014. Matos, J., Frizell, K.H., André, S., Frizell, K.W,. 2002. On the performance of velocity measurement techniques in air-water flows. In: Proceedings of the Hydraulic Measurements and Experimental Methods Conference, EWRI/ASCE & IAHR, Estes Park, USA. Meireles, I.C., Renna, F., Matos, J., Bombardelli, F.A., 2012. Skimming, nonaerated flow on stepped spillways over roller compacted concrete dams. J. Hydraul. Eng. 138 (10), 870–877. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000591. Murzyn, F., Chanson, H., 2008. Experimental assessment of scale effects affecting twophase flow properties in hydraulic jumps. Exp. Fluids 45 (3), 513–521. http://dx.doi. org/10.1007/s00348-008-0494-4. Murzyn, F., Mouaze, D., Chaplin, J.R., 2005. Optical fibre probe measurements of bubbly flow in hydraulic jumps. Int. J. Multiph. Flow 31 (1), 141–154. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2004.09.004. Neal, L.G., Bankoff, L.G., 1963. A high resolution resistivity probe for determination of local void properties in gas-liquid flow. AIChE J. 9 (4), 490–494. http://dx.doi.org/ 10.1002/aic.690090415. Schaul, T., Bayer, J., Wierstra, D., Sun, Y., Felder, M., Sehnke, F., Rückstieß, T., Schmidhuber, J., 2010. PyBrain. J. Mach. Learn. Res. 11, 743–746. Valero, D., Bung, D.B., 2016. Development of the interfacial air layer in the non-aerated region of high-velocity spillway flows. Instabilities growth, entrapped air and influence on the self-aeration onset. Int. J. Multiph. Flow 84, 66–74. http://dx.doi.org/10. 1016/j.ijmultiphaseflow.2016.04.012. Vejražka, J., Večeř, M., Orvalho, S., Sechet, P., Ruzicka, M.C., Cartellier, A., 2010. Measurement accuracy of a mono-fiber optical probe in a bubbly flow. Int. J. Multiph. Flow 36 (7), 533–548. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2010.03.007. Wang, H., Chanson, H., 2015. Air entrainment and turbulent fluctuations in hydraulic jumps. Urban Water J. 12 (6), 502–518. http://dx.doi.org/10.1080/1573062X.2013. 847464. Wang, H., Murzyn, F., 2016. Experimental assessment of characteristic turbulent scales in two-phase flow of hydraulic jump: from bottom to free surface. Environ. Fluid Mech. 1–19. http://dx.doi.org/10.1007/s10652-016-9451-6. Wang, H., Felder, S., Chanson, H., 2014. An experimental study of turbulent two-phase
interfacial velocity, v ). The choice of these parameters has been based on previous studies found in the literature, which showed that rising times are related to the interfacial velocities and that signature shapes may depend on small geometrical defects occurring at the probes tips. The number of neurons in the hidden layers has been the result of an iterative process. A significant accuracy enhancement due to the use of an ANN model has been observed. The obtained level of accuracy in terms of timeaveraged velocities was found to be comparable to the experimental scatter of a dual-tip conductivity probe. However, the accuracy of the instantaneous velocities is still unknown. As the obtained velocity time series could provide a novel method to determine turbulence structures in air-water flows, this point needs to be further investigated in future. Accurate time series could allow for a reliable estimation of turbulence and thus improve the understanding of this type of flow in future. Another advantage of the presented method is given by the less intrusive single-tip probe compared to classical dual-tip probes without disturbances of the flow at a rear tip. The nonlinear nature of ANN, the ability to learn from their environments in both supervised and unsupervised ways, as well as the universal approximation property of neural networks make them highly suited for solving difficult problems. ANN can detect and profit some hidden patterns within the analyzed data which would remain unseen otherwise, yielding complex non-linear and robust methods when properly applied. Acknowledgments Authors thank A2 Photonic Sensors for providing the instrumentation and installation recommendations. The authors are also grateful for the valuable comments provided by the reviewers and the fruitful discussions with Prof. García-Bartual from Universitat Politècnica de València (UPV). References Amador, A., Sánchez-Juny, M., Dolz, J., 2006. Characterization of the non-aerated flow region in a stepped spillway by PIV. J. Fluids Eng. 128 (6), 1266–1273. http://dx.doi. org/10.1115/1.2354529. Bennett, N.D., Croke, B.F., Guariso, G., Guillaume, J.H., Hamilton, S.H., Jakeman, A.J., Marsili-Libelli, S., Newham, L.T., Norton, J.P., Perrin, C., Pierce, S.A., 2013. Characterising performance of environmental models. Environ. Model. Softw. 40, 1–20. http://dx.doi.org/10.1016/j.envsoft.2012.09.011. Boes, R., Hager, W.H., 2003. Two-phase flow characteristics of stepped spillways. J. Hydraul. Eng. 129 (9), 661–670. http://dx.doi.org/10.1061/(ASCE)07339429(2003) 129:9(661). Bung, D.B., Valero, D., 2015. Image Processing for Bubble Image Velocimetry in Selfaerated Flows. In: E-proceedings of the 36th IAHR World Congress, 28 June–3 July, 2015, The Hague, the Netherlands. ISBN: 978-90-824846-0-1. Bung, D.B., Valero, D., 2016a. Optical flow estimation in aerated flows. J. Hydraul. Res. 54 (5), 575–580. http://dx.doi.org/10.1080/00221686.2016.1173600. Bung, D.B., Valero, D., 2016b. Application of the Optical Flow Method to Velocity Determination in Hydraulic Structure Models. In: Proc., 6th International Symposium on Hydraulic Structures, Portland, Oregon, USA, 27–30 June 2016. http://dx.doi. org/10.15142/T3150628160853. Bung, D.B., Valero, D., 2016c. Image processing techniques for velocity estimation in highly aerated flows: bubble image velocimetry vs. optical flow. In: Erpicum (Ed.), Sustainable Hydraulics in the Era of Global Change. Taylor and Francis Group ISBN: 978-1-138-02977-4. Bung, D.B., 2011. Developing flow in skimming flow regime on embankment stepped spillways. J. Hydraul. Res. 49 (5), 639–648. http://dx.doi.org/10.1080/00221686. 2011.584372. Bung, D.B., 2012. Sensitivity of phase detection techniques in aerated chute flows to hydraulic design parameters. In: Proc., 2nd European IAHR congress, 27–29, June 2012, Munich. Bung, D.B., 2013. Non-intrusive detection of air–water surface roughness in self-aerated chute flows. J. Hydraul. Res. 51 (3), 322–329. http://dx.doi.org/10.1080/00221686. 2013.777373. Carosone, F., Cenedese, A., Querzoli, G., 1995. Recognition of partially overlapped particle images using the Kohonen neural network. Exp. Fluids 19 (4), 225–232. http:// dx.doi.org/10.1007/BF00196470. Cartellier, A., Barrau, E., 1998a. Monofiber optical probes for gas detection and gas velocity measurements: conical probes. Int. J. Multiph. Flow 24 (8), 1265–1294. http:// dx.doi.org/10.1016/S0301-9322(98)00032-9. Cartellier, A., Barrau, E., 1998b. Monofiber optical probes for gas detection and gas
158
Journal of Hydro-environment Research 19 (2018) 150–159
D. Valero, D.B. Bung flow in hydraulic jumps and application of a triple decomposition technique. Environ. Fluid Mech. 55, 1775. http://dx.doi.org/10.1007/s00348-014-1775-8. Wilhelms, S.C., Gulliver, J.S., 2005. Bubbles and waves description of self-aerated spillway flow. J. Hydraul. Res. 43 (5), 522–531. http://dx.doi.org/10.1080/ 00221680509500150. Zhang, G., Chanson, H., 2016a. Interaction between free-surface aeration and total
pressure on a stepped chute. Exp. Thermal Fluid Sci. 74, 368–381. http://dx.doi.org/ 10.1016/j.expthermflusci.2015.12.011. Zhang, G., Chanson, H., 2016b. Hydraulics of the developing flow region of stepped spillways. I: Physical modeling and boundary layer development. J. Hydraul. Eng. 04016015. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001138.
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