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Article

Using ANN and Combined Capacitive Sensors to Predict the Void Fraction for a Two-Phase Homogeneous Fluid Independent of the Liquid Phase Type

by
Tzu-Chia Chen
1,*,
Seyed Mehdi Alizadeh
2,
Abdullah K. Alanazi
3,
John William Grimaldo Guerrero
4,
Hala M. Abo-Dief
5,
Ehsan Eftekhari-Zadeh
6,* and
Farhad Fouladinia
7
1
College of Management and Design, Ming Chi University of Technology, New Taipei City 243303, Taiwan
2
Petroleum Engineering Department, Australian University, West Mishref 13015, Kuwait
3
Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
4
Department of Energy, Universidad de la Costa, Barranquilla 080001, Colombia
5
Department of Science and Technology, University College-Ranyah, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
6
Institute of Optics and Quantum Electronics, Abbe Center of Photonics, Friedrich Schiller University Jena, 07743 Jena, Germany
7
Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, Powstancow Warszawy 12, 35-959 Rzeszow, Poland
*
Authors to whom correspondence should be addressed.
Processes 2023, 11(3), 940; https://doi.org/10.3390/pr11030940
Submission received: 5 March 2023 / Revised: 14 March 2023 / Accepted: 17 March 2023 / Published: 20 March 2023
(This article belongs to the Special Issue Application of Artificial Intelligence (AI) in Chemical Science and Engineering)
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Versions Notes

Abstract

:
Measuring the void fraction of different multiphase flows in various fields such as gas, oil, chemical, and petrochemical industries is very important. Various methods exist for this purpose. Among these methods, the capacitive sensor has been widely used. The thing that affects the performance of capacitance sensors is fluid properties. For instance, density, pressure, and temperature can cause vast errors in the measurement of the void fraction. A routine calibration, which is very grueling, is one approach to tackling this issue. In the present investigation, an artificial neural network (ANN) was modeled to measure the gas percentage of a two-phase flow regardless of the liquid phase type and changes, without having to recalibrate. For this goal, a new combined capacitance-based sensor was designed. This combined sensor was simulated with COMSOL Multiphysics software. Five different liquids were simulated: oil, gasoil, gasoline, crude oil, and water. To estimate the gas percentage of a homogeneous two-phase fluid with a distinct type of liquid, data obtained from COMSOL Multiphysics were used as input to train a multilayer perceptron network (MLP). The proposed neural network was modeled in MATLAB software. Using the new and accurate metering system, the proposed MLP model could predict the void fraction with a mean absolute error (MAE) of 4.919.

1. Introduction

There are many different types of two-phase fluids in industries, for instance, oil–gas, oil–water, and water–air. These fluids can be found in a wide variety of industries such as chemical, petrochemical, oil, and gas [1]. Nowadays, one of the most remarkable issues in the mentioned fields is precisely predicting the void fraction through multi-phase fluids [2]. Some other things that flow metering of fluids is important to are also worth mentioning such as procedure control, financial metering, and repository management. Due to the inherent complexity of two-phase fluids, flow metering of this kind of fluid is an arduous task [3]. In order to measure the flow of each phase in pipelines through the common method, firstly, two mixed phases separate and then each one of them will be calculated. This method can cause a lot of problems, for example, it is time-consuming and, of course, expensive [4]. Therefore, designing and manufacturing flow meters can come with a multitude of benefits such as detecting the type of flow and measuring the void fraction, all of which can be done without any interruption to the process [5,6]. The void fraction in a two-phase air (or gas)–liquid fluid can be determined by dividing the portion of the pipe containing air by the entire cross-section of the pipe. Various non-destructive methods are available to calculate the void fraction [5,6,7,8,9,10,11]. Capacitive sensors are a suitable method for measuring the void fraction because they do not require interruption of the process or separation of phases. Electrodes are a crucial component of capacitive sensors and their configuration is remarkable for precise measurement. The type of liquid inside the pipe is directly related to the electrode configuration and concave, ring and helix are the most popular configurations. Choosing the electrode configuration for more accurate measurement depends on the type of liquid inside the pipe. Previous studies have focused on the three distinct flow regimes of stratified, annular, and homogeneous within a two-phase fluid in a pipe. For example, the concave electrode was recommended for a two-phase liquid–liquid conductive fluid [12,13,14,15,16,17]. Li et al. [18] studied the measurement error of capacitive sensors. They found that homogeneous sensitivity can reduce this error. Further research has been conducted to ameliorate a configuration that ensures homogeneous sensitivity and the helical electrode was found to have the highest level of homogeneous sensitivity [19,20,21]. Tollefsen and his colleagues [21] investigated a two-phase oil–water blend and found that capacitive sensors, utilizing direct plate surfaces, had a limitation in their reliance on regime and distribution and precise results could only be obtained if the components were thoroughly blended. If the size of the bubbles was smaller than the volume of the substance, the resulting mixture was roughly homogeneous. Jaworek et al. [22] analyzed two-phase water–air flow using five different structures (e.g., helix, concave, and double ring) and found that the concave configuration had the highest sensitivity. Furthermore, previous studies have examined the sensitivity of capacitance sensors in various two-phase flows. In [23], it was observed that the concave configuration had the highest sensitivity in a two-phase flow, while the double-ring structure had the lowest sensitivity. Kendoush and Sarkis [24] investigated air–solid two-phase flow. They tested various electrodes and found that the concave electrode has the highest sensitivity. Sami and Abouelwafa [25] conducted experiments on non-conductive liquid–gas two-phase flow using six different capacitors and found that the helical electrode was the most sensitive in oil–gas two-phase flow. They also discovered that the concave electrode offered the most accuracy for the annular pattern. In a study conducted by Ahmed [26], a capacitive sensor was utilized to detect the void fraction and identify the flow regime in a two-phase air–oil fluid through a horizontal pipe. The sensitivity of the capacitive sensor was evaluated using both concave and ring electrodes, with the latter indicating greater sensitivity. This study also highlighted the impact of the configuration type on the measured response as a limitation to accurately determining the void fraction. Roshani et al. [27] compared the performance of two well-known sensors in the multi-phase flow metering industry: gamma-ray attenuation-based and capacitance-based sensors. The sensors were tested in an annular air–oil two-phase flow. The momentary sensitivity of the sensors was obtained in different void fractions, in which the concave capacitance-based sensor had better performance in void fractions of 0.8–1. Wang et al. [28] used three different sensors in their investigation: concave, double ring, and array sensors. They researched the performance of the gas percentage of a two-phase fluid and using the obtained data, the type of regime was predicted. Krupa and his coworkers [29] used a type of capacitance-based sensor (such as concave) to measure the gas percentage in small channels with diameters of less than 10 mm. The frequency deviation of a high-frequency oscillator was implemented to calculate the gas percentage in two-phase flow after the capacitance sensor was coupled to a resonant circuit with an inductance in parallel. In [30], He and Chen used a multi-wire capacitance probe to measure the void fraction in stratified gas–liquid flow. This device was based on the single-wire capacitance probe and was able to measure the average and the local gas percentage by measuring the water level at various positions of the pipe. Artificial intelligence (AI) is one of the most common methods in the industrial sector [31]. ANN is a capable tool that has been widely utilized in various fields, such as electrical engineering and control engineering [32,33,34,35,36,37,38,39,40,41,42,43,44,45]. The things that affects the performance of capacitance sensors are fluid properties. For instance, density, pressure, and temperature can cause large errors in the measurement of the void fraction. One of the solutions to this issue is a periodic recalibration of the instrument, which can be grueling. With the help of the previous studies in this field, in this study, an attempt was made to present an accurate metering system to predict the amount of void fraction regardless of the type of liquid. For this purpose, a two-phase-flow homogenous regime in different void fractions was simulated using COMSOL Multiphysics software. By considering both capacitance-based sensors, concave and ring, on the two-phase flow and applying their outputs to an MLP neural network, it we tried to predict void percentages with high precision. In fact, improving the detecting system’s precision and the combination of two different capacitance-based sensors are the main contributions of the present research. The main aim of this paper was to present a technique based on ANN for intelligent estimating of the gas percentage in the two-phase flow regardless of the liquid phase changes. To train the ANN, a data set was created using COMSOL Multiphysics software. A combined capacitance-based sensor was modeled. This sensor was made from two widely used sensors, concave and ring, which were connected together in series. Simulations were done for a homogenous pattern of two-phase flow with five various liquid phases (crude oil, oil, gasoil, gasoline, and water) and the void fraction ranged from 0 to 1 with a step of 0.05. To predict the gas percentage of a homogeneous two-phase fluid with a distinct type of liquid, data obtained from the COMSOL Multiphysics were given as input to train a multilayer perceptron network (MLP) which was modeled in MATLAB software. Using the new and accurate metering system, the proposed MLP model could predict the void fraction with a low mean absolute error.

2. Validation and Simulations

Three distinct flow regimes are commonly observed in oil, chemical and petrochemical industries: annular, stratified, and homogeneous. These are illustrated in Figure 1. In this paper, a homogeneous regime for a two-phase air–liquid fluid was investigated. This type of regime happens when air and liquid inside the pipe are entirely blended. To benchmark the COMSOL Multiphysics software, based on the validated simulated data in the authors’ previous work [46], in which two widely used capacitance-based sensors, concave and ring, were designed and simulated, the results obtained from this software are valid. COMSOL Multiphysics is one of the most widely used software programs. This software utilizes the finite-element method (FEM) to provide a specific environment to simulate and analyze different branches such as chemical, electrical, and mechanical industries. During simulation, an air area is created because there are powerful electric fields that exist around the plates of the simulated capacitor. Since the electrical field depends on the inverse of distance cubically, the more the distance between electrodes increases, the more the electrical field decreases. This way, the surrounding electrical field which could grow indefinitely will be negligible, as variables that affect the electrical field are constant over time the stationary study is used. As mentioned previously, COMSOL Multiphysics software uses a finite-element method for simulating and producing the most precise results. There are several types of meshing and the mesh size was set to finer. COMSOL Multiphysics software utilizes a network of elements to simulate and solve the designed structure with the finite-element method. The finer mesh size results in decreasing the size of each element, so in this way, the software produces a more accurate result. The size of the different parts of the finer mesh size are given in Table 1. The maximum element size limits how big each mesh element can be, the minimum element size limits how small each mesh element can be, the maximum element growth rate limits the size difference of two contiguous mesh elements, and the curvature factor and the resolution of narrow areas limits how big a mesh element can be along a curved boundary and controls the number of layers of mesh elements in narrow regions. The computer that was used had an i7 4510U CPU and 6GB of RAM.

2.1. Designing and Simulation of a Concave Sensor in COMSOL Multiphysics

In this section, the concave sensor was simulated in the benchmarked software. Simulations were performed for a two-phase air–liquid homogeneous fluid and every simulation was repeated 21 times (void fraction 0 to 1 with a step of 0.05) for five different liquids such as crude oil, oil, gasoil, gasoline, and water. The parameter by which the electric field between the charges is reduced in comparison to the vacuum is called relative permittivity (εr). To model the homogeneous pattern in the software, the material inside the pipe was assigned different values of εr. To achieve this, a specific εr was supposed for the interior material for each void fraction, obtained using an averaging method. The values of εr for air, crude oil, oil, gasoil, gasoline, and water at room temperature were 1, 2, 2.2, 2.4, 2.7, and 81, respectively. For example, for oil, the εr of the homogenous flow inside the pipe was incrementally changed from 1 to 2.2 for every 5% decrease in void fraction. In all of the simulations, air content was defined due to the obvious fringing fields that could be recognized around the capacitor plates. These fields might rise to infinite, even though they decrease inversely proportional to the cube of the distance. To account for this, a 3D model of electrostatic physics was made, with variables related to the field set to remain constant over time in the stationary regime. In addition, as was mentioned, the mesh settings for simulation were set on “finer mode”. The simulated concave sensor with its dimensions is shown in Figure 2. A three-dimensional vision of the electrode schema, the meshed model of the capacitance-based sensor and the electrical potential (voltage) on the surf of the electrodes are illustrated in Figure 3. Moreover, fluid components were decomposed into 16429 3D fundamentals using FEM.

2.2. Designing and Simulation of a Ring Sensor in COMSOL Multiphysics

In this part, the ring sensor was simulated in the COMSOL Multiphysics software. All the mentioned things for the concave sensor were considered for this sensor as well. The simulated ring sensor is shown in Figure 4. In addition, as presented for the concave sensor, for the ring sensor, the three-dimensional vision of the electrode schema, the meshed model of the capacitance-based sensor and the electrical potential (voltage) on the surf of the electrodes are illustrated in Figure 5. Fluid components were decomposed into 16429 3D fundamentals using FEM. All of the results obtained from both sensors are presented in Table 2.
As is clear from Table 2, there are 21 rows per liquid to consider the void fraction from 0 to 1 with a step of 0.05. In addition, for every specific liquid for the specific void fraction, the capacitance amount of both sensors was measured and considered.

3. Artificial Neural Network

Artificial intelligence (AI) has many applications across various industries such as healthcare, finance, retail, transportation, and education. AI can be used to analyze medical images, diagnose diseases, and personalize treatment plans. For example, AI-powered systems can help radiologists detect abnormalities in medical images and provide more accurate diagnoses as well as predict disease progression and develop personalized treatment plans for patients. It can also be utilized to detect fraud, optimize investment portfolios, and automate trading. This tool can analyze large amounts of financial data to identify patterns and anomalies that indicate fraudulent activity and optimize investment portfolios by identifying the most promising stocks and making trades automatically based on market conditions. It can also be used to personalize shopping experiences, recommend products, and optimize supply chain operations. AI can assist customers with their purchases and provide personalized product recommendations based on their preferences and past behavior. This tool is useful in optimizing supply chain operations by predicting demand, managing inventory levels, and optimizing shipping routes. Moreover, it can be used to improve safety, optimize traffic flow, and automated driving. For example, AI-powered systems can analyze traffic data to identify areas with high accident rates and develop solutions to reduce the risk of accidents. It can be utilized to personalize learning experiences, identify areas where students need help, and develop personalized learning plans. For example, AI-powered systems can analyze student performance data to identify areas where students are struggling and provide personalized learning materials to help them improve [47,48,49,50,51]. One of the most accurate methods in mathematics is ANN which consists of neurons. The ANN is a reliable soft computing approach that can address convoluted issues [52]. Neurons are simple computing elements and can be produced as one or more layers [53]. Classification and prediction are two important parts of ANN and because of this, many types of ANNs exist and each with its own characteristics. One of the best ANNs with various applications is the multilayer perceptron (MLP). This makes it a good choice for researchers who need accurate results quickly [54]. This model has two sets of data, the training set and the testing set. A training set uses a finite amount of accurate data in order to train the network. A testing set consists of data that the network has never faced before and is defined with the aim of evaluating the network’s correctness [55]. To find the appropriate network with the lowest mean absolute error, several networks with different characteristics such as the number of neurons, number of epochs, number of hidden layers, and even different types of activation functions have been investigated and the best one was chosen. In fact, after investigating different parts of networks and changing them over and over, the proposed network was selected. The modeled MLP network which can be seen in Figure 6 had a single output and two inputs. The capacitance obtained from the concave sensor and ring sensor was used as the first and second inputs, respectively. Table 1 displays the data obtained from the combined sensors for various liquids, including crude oil (εr = 2), oil (εr = 2.2), gasoil (εr = 2.4), gasoline (εr = 2.7), and water (εr = 81). Using COMSOL Multiphysics software, 105 simulations were conducted for the mentioned liquids by altering the void fractions from 0 to 1 with a step of 0.05. Out of these simulations, 73 (70%) were used as the train data and 32 (30%) were reserved for the test data. After evaluating multiple networks with various numbers of neurons and layers, the optimum structure was acquired. The characteristics of the modeled network are presented in Table 3.

4. Results and Discussion

The diagram of predicting the void fraction using the proposed ANN is given in Figure 6. As mentioned previously, 105 sets of data were available from simulations and 70% and 30% of the data was used to train and to test, respectively. The data were divided randomly between the training and the testing sets. To opt for the best architecture many networks were investigated and the best one was chosen. There are two important factors in the results obtained from the presented ANN, real data and predicted data. Real data were produced by simulation and predicted data were provided by the proposed neural network; both are given in Figure 7. This figure shows that real and predicted data were close. By using Equation (1) the mean absolute error (MAE) of the proposed MLP model could be calculated. In this equation, N is the number of observations and X (Sim) and X (Pred) belong to simulated (COMSOL Multiphysics) and estimated (MLP) values, respectively. The regression diagrams of the training and testing data sets are shown in Figure 7a,b, respectively. Regression is a statistical technique that is used to evaluate the fortification of a relationship between two variables. MAE for the training and testing data sets were 4.621 and 4.919, respectively.
M A E = 1 N ∑ i = 1 z | x i ( S i m ) − x i ( P r e d ) |
Utilizing the accurate predicting system, the proposed MLP model can meter the void fraction with a low mean absolute error. This important point was achieved using an ANN and combined capacitive sensors. It is to be noted that the low MAE of the training and the testing sets show that the proposed ANN can give correct and accurate results. As can also be seen in Figure 7, underfitting or overfitting was not observed, which demonstrates the trustworthiness of the presented model. As mentioned previously, two different sorts of data are available for the ANN, training data and testing data. The network uses training data for training and creating the model and it contains information that is seen by the network. After training the modeled network is tested. At the end of calculating, the predicted values of training and testing data are compared with the real values of training and testing data. As can be seen, there is no over-fitting or under-fitting in the presented network.

5. Conclusions

The primary goal of this investigation was to predict the gas percentage of a two-phase fluid regardless of liquid phase changes. To achieve this aim, an MLP ANN was utilized. To supply data for the proposed ANN a new combined capacitance-based sensor was used. This sensor included a concave sensor and a ring sensor. Both of these sensors were designed and simulated in COMSOL Multiphysics software. Five different types of liquid were investigated: crude oil, oil, gasoil, gasoline, and water. Simulations were done 21 times (different void fractions ranging from 0 to 1 by a step of 0.05) for each liquid and this way 105 data sets were collected to train and test the modeled network. The presented ANN had two inputs (results obtained from the concave and ring sensors by simulating in COMSOL Multiphysics). This network also had one output which was the predicted void fraction. Applying the presented novel metering system, the gas percentage of any homogeneous two-phase flow with various liquid phases can be predicted accurately. In this regard, the functionality of an MLP ANN was investigated. The main aim was to predict the amount of void fraction precisely regardless of the type of liquid inside the pipe. To achieve this goal an MLP ANN and a combined capacitance-based sensor were used. Utilizing another type of ANN such as GMDH or RBF can be considered for future work. A combination of other shapes of sensors can also be considered.

Author Contributions

Methodology, T.-C.C., A.K.A., J.W.G.G., H.M.A.-D., F.F.; investigation, S.M.A., E.E.-Z., F.F. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Taif University Researchers Supporting Project grant number (TURSP- 2020/266), of Taif University, Taif, Saudi Arabia. We acknowledge support from the German Research Foundation Projekt-Nr. 512648189 and the Open Access Publication Fund of the Thueringer Universitaets- und Landesbibliothek Jena.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Processes 11 00940 g001 550
Figure 1. Distinct types of fluids. (a) Stratified, (b) annular, and (c) homogeneous.
Figure 1. Distinct types of fluids. (a) Stratified, (b) annular, and (c) homogeneous.
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Figure 2. The simulated concave sensor in COMSOL Multiphysics.
Figure 2. The simulated concave sensor in COMSOL Multiphysics.
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Figure 3. The simulated concave sensor. (a) Three-dimensional vision of the electrode schema, (b) meshed model, and (c) electrical potential (voltage) on the surf of the electrodes.
Figure 3. The simulated concave sensor. (a) Three-dimensional vision of the electrode schema, (b) meshed model, and (c) electrical potential (voltage) on the surf of the electrodes.
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Figure 4. The simulated ring sensor in COMSOL Multiphysics.
Figure 4. The simulated ring sensor in COMSOL Multiphysics.
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Figure 5. The simulated ring sensor. (a) Three-dimensional vision of the electrode schema, (b) meshed model, and (c) electrical potential (voltage) on the surf of the electrodes.
Figure 5. The simulated ring sensor. (a) Three-dimensional vision of the electrode schema, (b) meshed model, and (c) electrical potential (voltage) on the surf of the electrodes.
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Figure 6. Diagram of predicting the void fraction using the proposed ANN.
Figure 6. Diagram of predicting the void fraction using the proposed ANN.
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Figure 7. Regression diagrams of simulated and predicted results for (a) training set and (b) testing set.
Figure 7. Regression diagrams of simulated and predicted results for (a) training set and (b) testing set.
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Table
Table 1. Characteristics of the finer mesh size.
Table 1. Characteristics of the finer mesh size.
CharacteristicsAmount
The maximum element size0.7 cm
The minimum element size0.03 cm
The maximum element growth rate1.35
The curvature factor0.3
The resolution of narrow areas0.85
Table
Table 2. The results obtained from simulating both sensors.
Table 2. The results obtained from simulating both sensors.
Liquid Phase NameVoid FractionεrThe Simulated Results of the Concave Sensor (pF)The Simulated Results of the Ring Sensor (pF)
Crude oil0.001.0009.3375.979
Crude oil0.051.0509.4216.006
Crude oil0.101.1009.5046.033
Crude oil0.151.1509.5876.060
Crude oil0.201.2009.6696.086
Crude oil0.251.2509.7506.113
Crude oil0.301.3009.8306.139
Crude oil0.351.3509.9106.165
Crude oil0.401.4009.9896.191
Crude oil0.451.45010.0686.217
Crude oil0.501.50010.1456.243
Crude oil0.551.55010.2226.269
Crude oil0.601.60010.2996.294
Crude oil0.651.65010.3746.320
Crude oil0.701.70010.4506.345
Crude oil0.751.75010.5246.370
Crude oil0.801.80010.5986.395
Crude oil0.851.85010.6716.420
Crude oil0.901.90010.7446.445
Crude oil0.951.95010.8166.469
Crude oil1.002.00010.8886.494
Oil0.001.0009.3375.979
Oil0.051.0609.4386.011
Oil0.101.1209.5386.044
Oil0.151.1809.6366.076
Oil0.201.2409.7646.108
Oil0.251.3009.8306.139
Oil0.301.3609.9266.171
Oil0.351.42010.0216.202
Oil0.401.48010.1146.233
Oil0.451.54010.2076.264
Oil0.501.60010.2996.267
Oil0.551.66010.3906.325
Oil0.601.72010.4796.355
Oil0.651.78010.5696.385
Oil0.701.84010.6576.415
Oil0.751.90010.7446.445
Oil0.801.96010.8316.474
Oil0.852.02010.9166.503
Oil0.902.08011.0016.533
Oil0.952.14011.0866.562
Oil1.002.20011.1696.590
Gasoil0.001.0009.3375.979
Gasoil0.051.0709.4556.017
Gasoil0.101.1409.5706.054
Gasoil0.151.2109.6856.092
Gasoil0.201.2809.7986.129
Gasoil0.251.3509.9106.165
Gasoil0.301.42010.0216.202
Gasoil0.351.49010.1306.238
Gasoil0.401.56010.2386.274
Gasoil0.451.63010.3446.310
Gasoil0.501.70010.4506.345
Gasoil0.551.77010.5546.380
Gasoil0.601.84010.6576.415
Gasoil0.651.91010.7596.450
Gasoil0.701.98010.8596.484
Gasoil0.752.05010.9596.518
Gasoil0.802.12011.0586.552
Gasoil0.852.19011.1556.586
Gasoil0.902.26011.2526.619
Gasoil0.952.36011.3476.652
Gasoil1.002.40011.4416.685
Gasoline0.001.0009.3375.979
Gasoline0.051.0859.4806.025
Gasoline0.101.1709.6206.070
Gasoline0.151.2559.7586.115
Gasoline0.201.3409.8946.160
Gasoline0.251.42510.0296.204
Gasoline0.301.51010.1616.248
Gasoline0.351.59510.2916.292
Gasoline0.401.68010.4206.335
Gasoline0.451.76510.5466.378
Gasoline0.501.85010.6716.420
Gasoline0.551.93510.7956.462
Gasoline0.602.02010.9166.503
Gasoline0.652.10511.0376.545
Gasoline0.702.19011.1556.586
Gasoline0.752.27511.2726.626
Gasoline0.802.36011.3886.666
Gasoline0.852.44511.5026.706
Gasoline0.902.53011.6146.746
Gasoline0.952.61511.7266.785
Gasoline1.002.70011.8356.824
Water0.001.0009.3375.979
Water0.055.00014.3817.786
Water0.109.00017.4929.162
Water0.1513.00019.64310.308
Water0.2017.00021.22611.300
Water0.2521.00022.44412.181
Water0.3025.00023.41112.973
Water0.3529.00024.19713.694
Water0.4033.00024.84914.355
Water0.4537.00025.39914.964
Water0.5041.00025.86915.529
Water0.5545.00026.27616.054
Water0.6049.00026.63116.544
Water0.6553.00026.94317.002
Water0.7057.00027.22117.433
Water0.7561.00027.46917.837
Water0.8065.00027.69218.219
Water0.8569.00027.89318.580
Water0.9073.00028.07718.921
Water0.9577.00028.24419.244
Water1.0081.00028.39719.551
Table
Table 3. Configuration of the proposed ANN model.
Table 3. Configuration of the proposed ANN model.
Neural NetworkMLP
Neurons in the input layer2
Neurons in the hidden layer6
Neurons in the output layer1
Number of epochs400
Activation function of neurons in hidden layersTansig
Activation function of neurons in input and output layersPurelin
Method of trainingLevenberg–Marquardt [56,57]
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Chen, T.-C.; Alizadeh, S.M.; Alanazi, A.K.; Grimaldo Guerrero, J.W.; Abo-Dief, H.M.; Eftekhari-Zadeh, E.; Fouladinia, F. Using ANN and Combined Capacitive Sensors to Predict the Void Fraction for a Two-Phase Homogeneous Fluid Independent of the Liquid Phase Type. Processes 2023, 11, 940. https://doi.org/10.3390/pr11030940

AMA Style

Chen T-C, Alizadeh SM, Alanazi AK, Grimaldo Guerrero JW, Abo-Dief HM, Eftekhari-Zadeh E, Fouladinia F. Using ANN and Combined Capacitive Sensors to Predict the Void Fraction for a Two-Phase Homogeneous Fluid Independent of the Liquid Phase Type. Processes. 2023; 11(3):940. https://doi.org/10.3390/pr11030940

Chicago/Turabian Style

Chen, Tzu-Chia, Seyed Mehdi Alizadeh, Abdullah K. Alanazi, John William Grimaldo Guerrero, Hala M. Abo-Dief, Ehsan Eftekhari-Zadeh, and Farhad Fouladinia. 2023. "Using ANN and Combined Capacitive Sensors to Predict the Void Fraction for a Two-Phase Homogeneous Fluid Independent of the Liquid Phase Type" Processes 11, no. 3: 940. https://doi.org/10.3390/pr11030940

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