Application of the Fourier Transform to Improve the Accuracy of Gamma-Based Volume Percentage Detection System Independent of Scale Thickness
Abstract
:1. Introduction
- Enhancing the accuracy of the detecting mechanism.
- Conducting volumetric fraction measurements of a three-phase flow as it traveled through a scale-lined oil pipe.
- Analyzing the efficiency of the frequency characteristics in determining the volume percentages.
- Aggregating helpful characteristics to significantly reduce the computational load.
2. Materials and Methods
2.1. Simulation Setup
2.2. Feature Extraction
2.3. Radial Basis Function Neural Network
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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ANN | Gas Predictor | Oil Predictor | ||
---|---|---|---|---|
Neurons in the input layer | 4 | 4 | ||
Neurons in the hidden layer | 38 | 27 | ||
Neurons in the output layer | 1 | 1 | ||
RBF spread | 4 | 5 | ||
RMSE | Train set | Test set | Train set | Test set |
0.27 | 0.18 | 0.27 | 0.29 | |
MRE% | 0.9 | 1.1 | 1.0 | 1.2 |
Oil Percentage Predictor Network | Gas Percentage Predictor Network | |||||||
---|---|---|---|---|---|---|---|---|
Train | Test | Train | Test | |||||
Output | Target | Output | Target | Output | Target | Output | Target | |
1 | 40.0054 | 40 | 10.4679 | 10 | 29.7982 | 30 | 9.7902 | 10 |
2 | 60.2055 | 60 | 29.3219 | 30 | 49.5464 | 50 | 9.8175 | 10 |
3 | 29.7308 | 30 | 50.5092 | 50 | 20.0054 | 20 | 10.1537 | 10 |
4 | 29.4942 | 30 | 19.4093 | 20 | 10.2614 | 10 | 20.4569 | 20 |
5 | 79.9658 | 80 | 10.2367 | 10 | 70.1311 | 70 | 60.4357 | 60 |
6 | 59.8074 | 60 | 50.0003 | 50 | 79.5899 | 80 | 29.9579 | 30 |
7 | 10.4034 | 10 | 29.6052 | 30 | 9.5809 | 10 | 19.7405 | 20 |
8 | 20.3924 | 20 | 20.1003 | 20 | 50.2772 | 50 | 20.2639 | 20 |
9 | 30.2359 | 30 | 49.4711 | 50 | 50.4051 | 50 | 10.2593 | 10 |
10 | 39.4869 | 40 | 30.2396 | 30 | 10.0338 | 10 | 60.2406 | 60 |
11 | 39.3302 | 40 | 40.1394 | 40 | 39.6092 | 40 | 30.2437 | 30 |
12 | 40.0838 | 40 | 9.3784 | 10 | 30.3258 | 30 | 29.6059 | 30 |
13 | 39.7211 | 40 | 9.3789 | 10 | 59.8381 | 60 | 10.1816 | 10 |
14 | 70.6152 | 70 | 59.5135 | 60 | 29.7940 | 30 | 19.9633 | 20 |
15 | 10.6733 | 10 | 49.3275 | 50 | 30.2463 | 30 | 49.7122 | 50 |
16 | 29.7013 | 30 | 9.9092 | 10 | 9.5103 | 10 | 29.5985 | 30 |
17 | 60.4211 | 60 | 60.4651 | 60 | 9.5484 | 10 | 60.3236 | 60 |
18 | 10.5546 | 10 | 10.1643 | 10 | 10.1679 | 10 | 19.6750 | 20 |
19 | 30.1365 | 30 | 20.0282 | 20 | 10.1035 | 10 | 49.6636 | 50 |
20 | 10.5376 | 10 | 10.5094 | 10 | 30.0261 | 30 | 10.1660 | 10 |
21 | 20.6212 | 20 | 39.4368 | 40 | 50.2297 | 50 | 10.3944 | 10 |
22 | 40.0688 | 40 | 40.5713 | 40 | 10.2073 | 10 | 40.0166 | 40 |
23 | 10.3197 | 10 | 9.4512 | 10 | 30.2814 | 30 | 40.2027 | 40 |
24 | 30.1075 | 30 | 10.0238 | 10 | 19.7880 | 20 | 9.6536 | 10 |
25 | 49.3362 | 50 | 29.5004 | 30 | 10.1925 | 10 | 30.4535 | 30 |
26 | 19.9251 | 20 | 80.0831 | 80 | 20.0567 | 20 | 50.0409 | 50 |
27 | 50.2048 | 50 | 39.3064 | 40 | 39.8965 | 40 | 10.1797 | 10 |
28 | 10.0297 | 10 | 40.3734 | 40 | 39.5616 | 40 | 29.5366 | 30 |
29 | 39.8212 | 40 | 30.4882 | 30 | 60.2802 | 60 | 10.3092 | 10 |
30 | 50.6120 | 50 | 30.5835 | 30 | 69.8376 | 70 | 40.2486 | 40 |
31 | 20.4613 | 20 | 70.6818 | 70 | 20.1079 | 20 | 19.6202 | 20 |
32 | 60.4887 | 60 | 30.0072 | 30 | 50.2413 | 50 | 60.0250 | 60 |
33 | 39.8215 | 40 | 69.6800 | 70 | 19.6048 | 20 | 39.8258 | 40 |
34 | 30.1305 | 30 | 9.4411 | 10 | 29.6279 | 30 | 10.0464 | 10 |
35 | 20.5216 | 20 | 40.0110 | 40 | 10.0495 | 10 | 9.8989 | 10 |
36 | 50.6069 | 50 | 30.1199 | 30 | 49.9852 | 50 | 9.9151 | 10 |
37 | 70.2358 | 70 | 30.3680 | 30 | 70.3905 | 70 | 79.6807 | 80 |
38 | 69.5895 | 70 | 29.4161 | 30 | 40.2990 | 40 | 39.7554 | 40 |
39 | 70.2154 | 70 | 50.2262 | 50 | 30.2343 | 30 | 69.5205 | 70 |
40 | 79.4009 | 80 | 10.0238 | 10 | 49.5513 | 50 | 30.4237 | 30 |
41 | 59.8694 | 60 | 49.5395 | 50 | 49.5729 | 50 | 20.1537 | 20 |
42 | 50.2337 | 50 | 40.6140 | 40 | 29.5885 | 30 | 20.4326 | 20 |
43 | 30.6072 | 30 | 20.1267 | 20 | 20.2984 | 20 | 9.6635 | 10 |
44 | 30.4353 | 30 | 19.9169 | 20 | 20.4430 | 20 | 30.4211 | 30 |
45 | 59.9784 | 60 | 10.6187 | 10 | 80.1837 | 80 | 40.2947 | 40 |
46 | 10.3594 | 10 | 10.2183 | 10 | 9.6321 | 10 | 10.0774 | 10 |
47 | 69.8839 | 70 | 59.9327 | 60 | 20.2227 | 20 | 9.9400 | 10 |
48 | 30.6605 | 30 | 10.4756 | 10 | 59.6104 | 60 | 9.7576 | 10 |
49 | 40.6832 | 40 | 20.0457 | 20 | 9.6175 | 10 | 60.2519 | 60 |
50 | 50.5098 | 50 | 20.0754 | 20 | 50.1407 | 50 | 19.7287 | 20 |
51 | 39.8444 | 40 | 20.2521 | 20 | 9.8288 | 10 | 19.5642 | 20 |
52 | 29.9366 | 30 | 19.8141 | 20 | 10.1538 | 10 | 60.2673 | 60 |
53 | 29.6454 | 30 | 19.6350 | 20 | 40.2491 | 40 | 10.1712 | 10 |
54 | 10.3982 | 10 | 40.1105 | 40 | 60.0832 | 60 | 40.2152 | 40 |
55 | 10.5360 | 10 | 10.5136 | 10 | 40.2400 | 40 | 60.1421 | 60 |
56 | 20.5792 | 20 | 19.8695 | 20 | 9.7348 | 10 | 79.9190 | 80 |
57 | 10.0816 | 10 | 49.4577 | 50 | 20.2350 | 20 | 29.8908 | 30 |
58 | 70.1384 | 70 | 69.9214 | 70 | 50.4706 | 50 | 60.3161 | 60 |
59 | 9.5084 | 10 | 69.7203 | 70 | 10.3669 | 10 | 9.8174 | 10 |
60 | 20.5596 | 20 | 39.8619 | 40 | 19.5862 | 20 | 10.3145 | 10 |
61 | 9.9306 | 10 | 40.4667 | 40 | 9.8664 | 10 | 20.2891 | 20 |
62 | 49.5879 | 50 | 19.8651 | 20 | 29.8692 | 30 | 10.3523 | 10 |
63 | 10.5595 | 10 | 59.8462 | 60 | 70.1850 | 70 | 10.0056 | 10 |
64 | 20.3676 | 20 | 39.8046 | 40 | 20.0979 | 20 | 30.1357 | 30 |
65 | 10.5355 | 10 | 39.4964 | 40 | 50.2894 | 50 | 20.4509 | 20 |
66 | 9.6989 | 10 | 9.6642 | 10 | 39.8677 | 40 | 19.9440 | 20 |
67 | 20.2425 | 20 | 19.4215 | 20 | 49.7060 | 50 | 29.5600 | 30 |
68 | 40.2300 | 40 | 9.9012 | 10 | 39.5867 | 40 | 30.3667 | 30 |
69 | 39.4719 | 40 | 39.6602 | 40 | 20.2719 | 20 | 10.1312 | 10 |
70 | 19.8702 | 20 | 9.7166 | 10 | 69.7057 | 70 | 9.8551 | 10 |
71 | 49.6854 | 50 | 19.8948 | 20 | 29.8883 | 30 | 20.4970 | 20 |
72 | 30.3033 | 30 | 69.4669 | 70 | 40.0518 | 40 | 39.7242 | 40 |
73 | 9.6967 | 10 | 19.9931 | 20 | 39.7290 | 40 | 10.1525 | 10 |
74 | 60.5547 | 60 | 20.2890 | 20 | 20.1419 | 20 | 40.1050 | 40 |
75 | 50.4572 | 50 | 59.6410 | 60 | 69.9845 | 70 | 29.8872 | 30 |
76 | 19.8460 | 20 | 40.3991 | 40 | 9.6518 | 10 | 39.6422 | 40 |
77 | 79.9971 | 80 | - | - | 30.2819 | 30 | - | - |
78 | 30.2727 | 30 | - | - | 19.6006 | 20 | - | - |
79 | 50.4681 | 50 | - | - | 29.7941 | 30 | - | - |
80 | 60.1535 | 60 | - | - | 19.7374 | 20 | - | - |
81 | 80.1046 | 80 | - | - | 40.0309 | 40 | - | - |
82 | 29.7565 | 30 | - | - | 9.5915 | 10 | - | - |
83 | 19.9390 | 20 | - | - | 59.9053 | 60 | - | - |
84 | 60.2993 | 60 | - | - | 29.6048 | 30 | - | - |
85 | 10.5382 | 10 | - | - | 29.6123 | 30 | - | - |
86 | 60.3092 | 60 | - | - | 20.2844 | 20 | - | - |
87 | 29.3261 | 30 | - | - | 9.7916 | 10 | - | - |
88 | 50.2447 | 50 | - | - | 40.1035 | 40 | - | - |
89 | 39.9139 | 40 | - | - | 50.4644 | 50 | - | - |
90 | 59.9129 | 60 | - | - | 9.9325 | 10 | - | - |
91 | 19.4639 | 20 | - | - | 40.1948 | 40 | - | - |
92 | 50.4406 | 50 | - | - | 20.2581 | 20 | - | - |
93 | 39.7548 | 40 | - | - | 19.9326 | 20 | - | - |
94 | 19.6447 | 20 | - | - | 30.1555 | 30 | - | - |
95 | 29.7798 | 30 | - | - | 39.6098 | 40 | - | - |
96 | 19.8260 | 20 | - | - | 30.4338 | 30 | - | - |
97 | 50.0652 | 50 | - | - | 29.6875 | 30 | - | - |
98 | 20.0867 | 20 | - | - | 29.7662 | 30 | - | - |
99 | 39.8542 | 40 | - | - | 40.2978 | 40 | - | - |
100 | 19.8574 | 20 | - | - | 49.9876 | 50 | - | - |
101 | 10.0215 | 10 | - | - | 60.2690 | 60 | - | - |
102 | 10.2205 | 10 | - | - | 19.8960 | 20 | - | - |
103 | 20.6313 | 20 | - | - | 19.7729 | 20 | - | - |
104 | 80.3113 | 80 | - | - | 19.5372 | 20 | - | - |
105 | 59.8601 | 60 | - | - | 60.1733 | 60 | - | - |
106 | 40.4646 | 40 | - | - | 29.9296 | 30 | - | - |
107 | 69.4881 | 70 | - | - | 9.9517 | 10 | - | - |
108 | 9.3847 | 10 | - | - | 20.1099 | 20 | - | - |
109 | 19.4179 | 20 | - | - | 39.5594 | 40 | - | - |
110 | 49.5295 | 50 | - | - | 69.8158 | 70 | - | - |
111 | 79.7539 | 80 | - | - | 80.2727 | 80 | - | - |
112 | 9.7224 | 10 | - | - | 40.1964 | 40 | - | - |
113 | 9.3164 | 10 | - | - | 49.6253 | 50 | - | - |
114 | 10.0559 | 10 | - | - | 29.6302 | 30 | - | - |
115 | 19.4335 | 20 | - | - | 9.5924 | 10 | - | - |
116 | 19.5051 | 20 | - | - | 29.5078 | 30 | - | - |
117 | 20.1836 | 20 | - | - | 49.9231 | 50 | - | - |
118 | 10.5030 | 10 | - | - | 20.1556 | 20 | - | - |
119 | 30.6639 | 30 | - | - | 50.2229 | 50 | - | - |
120 | 20.0992 | 20 | - | - | 20.0312 | 20 | - | - |
121 | 30.6956 | 30 | - | - | 49.6088 | 50 | - | - |
122 | 30.0750 | 30 | - | - | 20.1318 | 20 | - | - |
123 | 20.0216 | 20 | - | - | 19.6265 | 20 | - | - |
124 | 9.7630 | 10 | - | - | 59.6343 | 60 | - | - |
125 | 19.9020 | 20 | - | - | 9.5986 | 10 | - | - |
126 | 29.9885 | 30 | - | - | 49.6420 | 50 | - | - |
127 | 49.3995 | 50 | - | - | 49.6683 | 50 | - | - |
128 | 30.5428 | 30 | - | - | 19.6962 | 20 | - | - |
129 | 29.3905 | 30 | - | - | 39.8175 | 40 | - | - |
130 | 29.9107 | 30 | - | - | 49.8164 | 50 | - | - |
131 | 40.4573 | 40 | - | - | 9.7176 | 10 | - | - |
132 | 49.8523 | 50 | - | - | 39.7510 | 40 | - | - |
133 | 30.1589 | 30 | - | - | 30.3929 | 30 | - | - |
134 | 20.4461 | 20 | - | - | 30.2032 | 30 | - | - |
135 | 10.5407 | 10 | - | - | 10.0557 | 10 | - | - |
136 | 30.6036 | 30 | - | - | 39.6844 | 40 | - | - |
137 | 39.5671 | 40 | - | - | 69.7120 | 70 | - | - |
138 | 49.6620 | 50 | - | - | 29.5773 | 30 | - | - |
139 | 30.5570 | 30 | - | - | 80.4138 | 80 | - | - |
140 | 40.1307 | 40 | - | - | 20.2067 | 20 | - | - |
141 | 60.0054 | 60 | - | - | 10.0578 | 10 | - | - |
142 | 10.1579 | 10 | - | - | 69.8134 | 70 | - | - |
143 | 70.4472 | 70 | - | - | 29.6662 | 30 | - | - |
144 | 50.0446 | 50 | - | - | 20.1225 | 20 | - | - |
145 | 9.5829 | 10 | - | - | 50.4879 | 50 | - | - |
146 | 9.9355 | 10 | - | - | 69.6704 | 70 | - | - |
147 | 9.8991 | 10 | - | - | 39.7578 | 40 | - | - |
148 | 10.6525 | 10 | - | - | 29.8968 | 30 | - | - |
149 | 10.1681 | 10 | - | - | 69.5740 | 70 | - | - |
150 | 20.2735 | 20 | - | - | 10.1841 | 10 | - | - |
151 | 60.3082 | 60 | - | - | 49.9024 | 50 | - | - |
152 | 39.7857 | 40 | - | - | 30.4828 | 30 | - | - |
153 | 10.0238 | 10 | - | - | 19.9022 | 20 | - | - |
154 | 60.0794 | 60 | - | - | 30.1207 | 30 | - | - |
155 | 39.5191 | 40 | - | - | 69.6544 | 70 | - | - |
156 | 30.0869 | 30 | - | - | 19.8813 | 20 | - | - |
157 | 20.2727 | 20 | - | - | 19.6611 | 20 | - | - |
158 | 9.8970 | 10 | - | - | 20.2581 | 20 | - | - |
159 | 20.4708 | 20 | - | - | 20.3711 | 20 | - | - |
160 | 30.3239 | 30 | - | - | 59.8508 | 60 | - | - |
161 | 49.8040 | 50 | - | - | 60.1855 | 60 | - | - |
162 | 9.9359 | 10 | - | - | 39.7941 | 40 | - | - |
163 | 29.8409 | 30 | - | - | 60.0306 | 60 | - | - |
164 | 30.3858 | 30 | - | - | 60.3324 | 60 | - | - |
165 | 10.3280 | 10 | - | - | 50.0975 | 50 | - | - |
166 | 49.9024 | 50 | - | - | 39.8353 | 40 | - | - |
167 | 20.2713 | 20 | - | - | 79.7992 | 80 | - | - |
168 | 50.6233 | 50 | - | - | 59.9526 | 60 | - | - |
169 | 20.3979 | 20 | - | - | 69.9226 | 70 | - | - |
170 | 20.2878 | 20 | - | - | 19.8596 | 20 | - | - |
171 | 29.4531 | 30 | - | - | 40.0583 | 40 | - | - |
172 | 9.8459 | 10 | - | - | 10.2425 | 10 | - | - |
173 | 60.1273 | 60 | - | - | 9.9243 | 10 | - | - |
174 | 9.9431 | 10 | - | - | 9.9294 | 10 | - | - |
175 | 69.3705 | 70 | - | - | 39.6249 | 40 | - | - |
176 | 19.6202 | 20 | - | - | 49.5244 | 50 | - | - |
Ref. | Maximum MSE | Maximum RMSE | Extracted Features | Type of Neural Network |
---|---|---|---|---|
[5] | 0.21 | 0.46 | Time features | MLP |
[27] | 7.34 | 2.71 | No feature extraction | GMDH |
[28] | 1.24 | 1.11 | Time features | GMDH |
[29] | 0.67 | 0.82 | Frequency features | MLP |
[30] | 2.56 | 1.6 | No feature extraction | MLP |
[31] | 1.08 | 1.04 | No feature extraction | MLP |
[32] | 0.19 | 0.44 | Wavelet features | GMDH |
[current study] | 0.07 | 0.27 | Frequency features | RBF |
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Mayet, A.M.; Guerrero, J.W.G.; Ijyas, T.; Bhutto, J.K.; Shukla, N.K.; Eftekhari-Zadeh, E.; Alhashim, H.H. Application of the Fourier Transform to Improve the Accuracy of Gamma-Based Volume Percentage Detection System Independent of Scale Thickness. Separations 2023, 10, 534. https://doi.org/10.3390/separations10100534
Mayet AM, Guerrero JWG, Ijyas T, Bhutto JK, Shukla NK, Eftekhari-Zadeh E, Alhashim HH. Application of the Fourier Transform to Improve the Accuracy of Gamma-Based Volume Percentage Detection System Independent of Scale Thickness. Separations. 2023; 10(10):534. https://doi.org/10.3390/separations10100534
Chicago/Turabian StyleMayet, Abdulilah Mohammad, John William Grimaldo Guerrero, Thafasal Ijyas, Javed Khan Bhutto, Neeraj Kumar Shukla, Ehsan Eftekhari-Zadeh, and Hala H. Alhashim. 2023. "Application of the Fourier Transform to Improve the Accuracy of Gamma-Based Volume Percentage Detection System Independent of Scale Thickness" Separations 10, no. 10: 534. https://doi.org/10.3390/separations10100534