# Introducing the Effective Features Using the Particle Swarm Optimization Algorithm to Increase Accuracy in Determining the Volume Percentages of Three-Phase Flows

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## Abstract

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## 1. Introduction

- Extraction of frequency and wavelet properties for three-phase fluid volume percentages;
- Introducing effective features by means of the feature selection system based on the PSO algorithm;
- A notable improvement in accuracy in calculating volume percentages;
- Choosing the beneficial properties to use as the neural network’s inputs will reduce the number of computations that must be performed on the system.

## 2. Materials and Methods

#### 2.1. Radiation-Based System

#### 2.2. Feature Extraction

#### 2.2.1. Frequency Domain

#### 2.2.2. Wavelet

#### 2.3. Feature Selection

_{1}and c

_{2}(the cognitive and social parameters, respectively), and r

_{1}and r

_{2}are evenly distributed and lie between [0, 1]. Defining the cost function is one of the first steps in developing optimization systems. In this research, the mean square error (MSE) of a neural network consisting of one hidden layer and 10 neurons is used as the cost function of the PSO system. The first step involves feeding the network a non-sequential subset of the data’s characteristics. Then, the conventional optimization approach is used to progressively improve the inputs toward ideal values in an effort to minimize the cost function. The PSO system initially tries to foretell the target using a characteristic using an iterative process, then increases the number of inputs as needed and eventually implements the system for all modes with varying inputs.

#### 2.4. MLP Neural Network

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The signals recorded by the (

**a**) first and (

**b**) second detectors correspond to simulated flow regimes in different volume percentages.

**Figure 5.**Transmitted signals to the frequency domain of (

**a**) the first detector and (

**b**) the second detector.

**Figure 7.**The value of the cost function is calculated by the PSO algorithm in terms of the number of features.

**Figure 8.**The implemented neural network structure to determine the volumetric percentages of gas and water.

**Figure 9.**Regression diagram related to the prediction of water volume percentage for (

**a**) training, (

**b**) validation, and (

**c**) test data.

**Figure 10.**Regression diagram related to the prediction of gas volume percentage for (

**a**) training, (

**b**) validation, and (

**c**) test data.

Ref | Extracted Features | Feature Selection Method | Type of Neural Network | Maximum MSE | Maximum RMSE |
---|---|---|---|---|---|

[2] | No feature extraction | Lack of feature selection | MLP | 2.56 | 1.6 |

[3] | Time features | Lack of feature selection | GMDH | 1.24 | 1.11 |

[4] | Time features | Lack of feature selection | MLP | 0.21 | 0.46 |

[9] | Frequency features | Lack of feature selection | MLP | 0.67 | 0.82 |

[10] | Lack of feature extraction | Lack of feature selection | GMDH | 7.34 | 2.71 |

[11] | Full energy peak (transmission count), photon counts of Compton edge in the transmission detector, and total count in the scattering detector | Lack of feature selection | MLP | 1.08 | 1.04 |

[Current study] | Frequency and wavelet features | PSO-based feature selection | MLP | 0.13 | 0.36 |

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## Share and Cite

**MDPI and ACS Style**

Chen, T.-C.; Alizadeh, S.M.; Albahar, M.A.; Thanoon, M.; Alammari, A.; Guerrero, J.W.G.; Nazemi, E.; Eftekhari-Zadeh, E.
Introducing the Effective Features Using the Particle Swarm Optimization Algorithm to Increase Accuracy in Determining the Volume Percentages of Three-Phase Flows. *Processes* **2023**, *11*, 236.
https://doi.org/10.3390/pr11010236

**AMA Style**

Chen T-C, Alizadeh SM, Albahar MA, Thanoon M, Alammari A, Guerrero JWG, Nazemi E, Eftekhari-Zadeh E.
Introducing the Effective Features Using the Particle Swarm Optimization Algorithm to Increase Accuracy in Determining the Volume Percentages of Three-Phase Flows. *Processes*. 2023; 11(1):236.
https://doi.org/10.3390/pr11010236

**Chicago/Turabian Style**

Chen, Tzu-Chia, Seyed Mehdi Alizadeh, Marwan Ali Albahar, Mohammed Thanoon, Abdullah Alammari, John William Grimaldo Guerrero, Ehsan Nazemi, and Ehsan Eftekhari-Zadeh.
2023. "Introducing the Effective Features Using the Particle Swarm Optimization Algorithm to Increase Accuracy in Determining the Volume Percentages of Three-Phase Flows" *Processes* 11, no. 1: 236.
https://doi.org/10.3390/pr11010236