Thermal–Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning
Abstract
:1. Introduction
2. Research Methods and Contents
2.1. The Research Process for Thermal–Mechanical Coupling Evaluation of Prefabricated Cabin-Type Substation Panel Performance
2.2. Thermal–Mechanical Coupling Evaluation Model of the Panel Performance Based on BP Neural Networks
2.2.1. Establishment of Evaluation Factors
- The geometric parameters of the panel include length, width, and height.
- The fire resistance performance parameters of the panel include the heating time, average furnace temperature, average temperature of the backfire surface, and pressure parameters.
- The mechanical performance parameters of the panel include time and bending load.
2.2.2. Construction of BP Neural Network
3. Case Application Analysis
3.1. Substation Panel
3.1.1. Fire Resistance Test of Panel
3.1.2. The Stress Test of the Panel
3.2. Thermal–Mechanical Coupling Evaluation of Panel Performance
- Initialize the BP neural network. We randomly selected 100 sets of data from Table A1 as the input node data of the training sample, and the remaining 84 sets of data in Table A1 were used as prediction samples. Then, the weights and offsets of the neural network were initialized. Finally, the sample data were normalized.
- Train the BP neural network. The BP neural network was used to train 100 sets of training sample data until the calculations at the end of the network training. The thermal–mechanical coupling evaluation model of the panel performance based on the BP neural network was obtained when the BP neural network converged after learning and training.
- Predict the BP neural network. The randomly selected 84 sets of test sample data were predicted through the trained BP neural network to finally obtain the prediction result output. The graph is drawn as shown in Figure 8.
3.3. Numerical Simulation
3.4. The Functional Relationship between Fire Resistance and Stress Resistance
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Sample | Heating Time (min) | Average Furnace Temperature (°C) | Average Temperature of Backfire Surface (°C) | Pressure (Pa) | Time (s) | Bending Load (KN) |
---|---|---|---|---|---|---|
1 | 0 | 0 | 0 | 0 | 0.000 | 0 |
2 | 1 | 79.84 | 3.29 | 3.0577 | 1.798 | 0.0152 |
3 | 2 | 173.4 | 3.06 | 4.349 | 3.596 | 0.0619 |
4 | 3 | 267.91 | 3.12 | 5.4032 | 5.394 | 0.0949 |
5 | 4 | 360.6 | 4.9 | 5.8117 | 7.192 | 0.1097 |
6 | 5 | 433.88 | 2.36 | 5.1342 | 8.991 | 0.1888 |
7 | 6 | 468.52 | 3 | 11.858 | 10.789 | 0.287 |
8 | 7 | 504.38 | 2.5 | 6.7311 | 12.587 | 0.3562 |
9 | 8 | 535.65 | 1.09 | 8.499 | 14.385 | 0.4535 |
10 | 9 | 577.35 | 3.45 | 7.9913 | 16.183 | 0.5464 |
11 | 10 | 625 | 2.94 | 10.133 | 17.981 | 0.6664 |
12 | 11 | 634.44 | 2.04 | 11.221 | 19.779 | 0.8527 |
13 | 12 | 643.43 | 1.94 | 9.6595 | 21.577 | 0.9194 |
14 | 13 | 664.89 | 1.28 | 11.8 | 23.375 | 1.0552 |
15 | 14 | 690.58 | 1.9 | 9.017 | 25.173 | 1.1762 |
16 | 15 | 705.34 | 3.27 | 11.87 | 26.972 | 1.2974 |
17 | 16 | 721.01 | 3.77 | 9.6982 | 28.770 | 1.4346 |
18 | 17 | 734.37 | 3.24 | 8.1376 | 30.568 | 1.5541 |
19 | 18 | 742.72 | 2.88 | 11.704 | 32.366 | 1.7039 |
20 | 19 | 750.87 | 2.65 | 12.759 | 34.164 | 1.8248 |
21 | 20 | 757.59 | 3.6 | 10.145 | 35.962 | 1.9602 |
22 | 21 | 763.69 | 3.13 | 12.014 | 37.760 | 2.114 |
23 | 22 | 773 | 2.27 | 13.136 | 39.558 | 2.3759 |
24 | 23 | 780.88 | 2.33 | 15.751 | 41.356 | 2.5796 |
25 | 24 | 794.49 | 3.52 | 12.086 | 43.154 | 2.7826 |
26 | 25 | 802.42 | 2.67 | 14.159 | 44.953 | 2.9971 |
27 | 26 | 809.7 | 2.96 | 16.672 | 46.751 | 3.2553 |
28 | 27 | 817.29 | 2.32 | 13.244 | 48.549 | 3.4676 |
29 | 28 | 828.68 | 1.68 | 11.989 | 50.347 | 3.659 |
30 | 29 | 840.37 | 4.26 | 11.958 | 52.145 | 3.8044 |
31 | 30 | 844.53 | 3.45 | 14.878 | 53.943 | 4.0017 |
32 | 31 | 851.16 | 3.73 | 17.732 | 55.741 | 4.3081 |
33 | 32 | 857.39 | 4.34 | 15.323 | 57.539 | 4.5063 |
34 | 33 | 854.14 | 5.18 | 13.932 | 59.337 | 4.6692 |
35 | 34 | 861.78 | 6.84 | 13.22 | 61.135 | 4.9182 |
36 | 35 | 867.05 | 3.7 | 12.95 | 62.934 | 5.1096 |
37 | 36 | 871.16 | 6.4 | 14.14 | 64.732 | 5.3131 |
38 | 37 | 876.67 | 5.2 | 18.894 | 66.530 | 5.4892 |
39 | 38 | 881.12 | 5.24 | 15.398 | 68.328 | 5.7004 |
40 | 39 | 884.83 | 4.83 | 14.108 | 70.126 | 5.8432 |
41 | 40 | 887.87 | 4.21 | 13.907 | 71.924 | 5.9585 |
42 | 41 | 889.97 | 2.81 | 13.67 | 73.722 | 6.0633 |
43 | 42 | 893 | 1.73 | 12.992 | 75.520 | 6.4429 |
44 | 43 | 898.57 | 1.2 | 12.621 | 77.318 | 6.692 |
45 | 44 | 900.57 | 1.55 | 13.437 | 79.116 | 6.9692 |
46 | 45 | 905.35 | 1.64 | 14.015 | 80.915 | 7.1593 |
47 | 46 | 908.14 | 3.61 | 13.948 | 82.713 | 7.3998 |
48 | 47 | 910.72 | 2.79 | 13.949 | 84.511 | 7.6056 |
49 | 48 | 914.22 | 2.12 | 13.951 | 86.309 | 7.9198 |
50 | 49 | 914.51 | 4.92 | 13.954 | 88.107 | 8.1175 |
51 | 50 | 919.4 | 3.94 | 13.989 | 89.905 | 8.3583 |
52 | 51 | 922.69 | 6.19 | 14.364 | 91.703 | 8.634 |
53 | 52 | 925.51 | 6.38 | 14.84 | 93.501 | 8.8009 |
54 | 53 | 929.22 | 6.44 | 14.399 | 95.299 | 9.002 |
55 | 54 | 933.64 | 7.51 | 14.027 | 97.097 | 9.2243 |
56 | 55 | 938.97 | 9.24 | 14.843 | 98.896 | 9.3998 |
57 | 56 | 942.03 | 11.24 | 16.543 | 100.694 | 9.5576 |
58 | 57 | 944.37 | 12.45 | 18.004 | 102.492 | 9.7716 |
59 | 58 | 947.88 | 14.54 | 16.851 | 104.290 | 9.937 |
60 | 59 | 944.27 | 17.79 | 13.966 | 106.088 | 10.116 |
61 | 60 | 947.25 | 15.6 | 13.934 | 107.886 | 10.237 |
62 | 61 | 949.48 | 13.49 | 14.342 | 109.684 | 10.439 |
63 | 62 | 952.08 | 13.32 | 15.022 | 111.482 | 10.679 |
64 | 63 | 954.15 | 16.91 | 16.586 | 113.280 | 10.9 |
65 | 64 | 955.83 | 19.37 | 17.402 | 115.078 | 11.103 |
66 | 65 | 958.84 | 18.06 | 18.863 | 116.877 | 11.379 |
67 | 66 | 962.18 | 21.68 | 15.877 | 118.675 | 11.6 |
68 | 67 | 966.24 | 20.39 | 14.384 | 120.473 | 11.794 |
69 | 68 | 969.58 | 20.66 | 13.91 | 122.271 | 12.07 |
70 | 69 | 967.65 | 21.86 | 14.387 | 124.069 | 12.231 |
71 | 70 | 970.98 | 19.67 | 16.629 | 125.867 | 12.374 |
72 | 71 | 973.61 | 23.63 | 16.834 | 127.665 | 12.742 |
73 | 72 | 976.41 | 24.6 | 16.088 | 129.463 | 12.884 |
74 | 73 | 978.48 | 26.5 | 14.731 | 131.261 | 13.016 |
75 | 74 | 978.69 | 28.38 | 14.053 | 133.059 | 13.21 |
76 | 75 | 981.34 | 29.56 | 16.432 | 134.858 | 13.381 |
77 | 76 | 982.55 | 31.64 | 18.029 | 136.656 | 13.548 |
78 | 77 | 983.33 | 31.82 | 18.777 | 138.454 | 13.693 |
79 | 78 | 986 | 32.33 | 17.387 | 140.252 | 13.835 |
80 | 79 | 985.67 | 37.18 | 13.891 | 142.050 | 13.985 |
81 | 80 | 986.19 | 34.77 | 15.217 | 143.848 | 14.102 |
82 | 81 | 987.83 | 37.34 | 16.949 | 145.646 | 14.218 |
83 | 82 | 989.37 | 38.31 | 17.731 | 147.444 | 14.448 |
84 | 83 | 992.76 | 40.21 | 14.677 | 149.242 | 14.555 |
85 | 84 | 997.82 | 43.91 | 13.965 | 151.040 | 14.666 |
86 | 85 | 999.42 | 42.37 | 15.563 | 152.839 | 14.86 |
87 | 86 | 1001.8 | 47.47 | 16.311 | 154.637 | 15.123 |
88 | 87 | 1004 | 47.86 | 17.738 | 156.435 | 15.303 |
89 | 88 | 1005.8 | 50.86 | 16.551 | 158.233 | 15.469 |
90 | 89 | 1009.2 | 52.06 | 14.923 | 160.031 | 15.585 |
91 | 90 | 1006.1 | 45.67 | 16.52 | 161.829 | 15.71 |
92 | 91 | 1007.6 | 46.3 | 17.301 | 163.627 | 15.968 |
93 | 92 | 1008.8 | 48.17 | 16.862 | 165.425 | 16.002 |
94 | 93 | 1011.3 | 50.79 | 16.047 | 167.223 | 16.039 |
95 | 94 | 1013 | 55.77 | 15.029 | 169.021 | 16.167 |
96 | 95 | 1014.3 | 55.85 | 14.896 | 170.820 | 16.339 |
97 | 96 | 1016.1 | 57.01 | 15.814 | 172.618 | 16.428 |
98 | 97 | 1017.8 | 58.17 | 14.865 | 174.416 | 16.512 |
99 | 98 | 1020.6 | 56.41 | 14.865 | 176.214 | 16.596 |
100 | 99 | 1020.3 | 56.48 | 14.935 | 178.012 | 16.681 |
101 | 100 | 1022.5 | 58.42 | 16.329 | 179.810 | 16.74 |
102 | 101 | 1025.1 | 53.55 | 17.756 | 181.608 | 16.865 |
103 | 102 | 1026.3 | 56.35 | 15.992 | 183.406 | 16.986 |
104 | 103 | 1028.8 | 58.47 | 15.757 | 185.204 | 17.071 |
105 | 104 | 1029.3 | 61.61 | 17.863 | 187.002 | 17.123 |
106 | 105 | 1031.7 | 58.83 | 15.589 | 188.801 | 17.229 |
107 | 106 | 1031.5 | 60.25 | 14.911 | 190.599 | 17.369 |
108 | 107 | 1034.3 | 60.88 | 16.814 | 192.397 | 17.487 |
109 | 108 | 1036.5 | 60.93 | 14.881 | 194.195 | 17.605 |
110 | 109 | 1035.1 | 64.07 | 14.881 | 195.993 | 17.577 |
111 | 110 | 1037.6 | 65.42 | 16.92 | 197.791 | 17.662 |
112 | 111 | 1037.8 | 60 | 15.529 | 199.589 | 17.877 |
113 | 112 | 1038.9 | 58.92 | 14.885 | 201.387 | 17.853 |
114 | 113 | 1040.1 | 58.82 | 17.807 | 203.185 | 17.876 |
115 | 114 | 1042.2 | 58.58 | 15.499 | 204.983 | 17.968 |
116 | 115 | 1042.9 | 60.23 | 14.923 | 206.782 | 18.081 |
117 | 116 | 1043.3 | 59.86 | 16.86 | 208.580 | 18.181 |
118 | 117 | 1045.1 | 59.06 | 14.858 | 210.378 | 18.182 |
119 | 118 | 1046.5 | 58.54 | 16.83 | 212.176 | 18.27 |
120 | 119 | 1045.9 | 60.74 | 16.83 | 213.974 | 18.366 |
121 | 120 | 1047.3 | 64.13 | 16.83 | 215.772 | 18.392 |
122 | 121 | 1048.9 | 58.24 | 14.897 | 217.570 | 18.488 |
123 | 122 | 1051 | 58.63 | 17.819 | 219.368 | 18.58 |
124 | 123 | 1052.8 | 59.49 | 15.749 | 221.166 | 18.639 |
125 | 124 | 1054.6 | 59.2 | 14.052 | 222.964 | 18.655 |
126 | 125 | 1055.7 | 60.53 | 14.97 | 224.763 | 18.733 |
127 | 126 | 1057.5 | 60.28 | 15.006 | 226.561 | 18.916 |
128 | 127 | 1058.9 | 58.28 | 19.863 | 228.359 | 18.961 |
129 | 128 | 1060.6 | 57.76 | 15.857 | 230.157 | 18.998 |
130 | 129 | 1060.7 | 57 | 16.98 | 231.955 | 19.101 |
131 | 130 | 1063.2 | 57.95 | 16.98 | 233.753 | 19.139 |
132 | 131 | 1064.8 | 58.31 | 15.963 | 235.551 | 19.271 |
133 | 132 | 1066.1 | 57.56 | 17.866 | 237.349 | 19.345 |
134 | 133 | 1068.7 | 58.53 | 15.933 | 239.147 | 19.469 |
135 | 134 | 1066.8 | 58.26 | 18.854 | 240.945 | 19.456 |
136 | 135 | 1069.3 | 58.71 | 16.037 | 242.744 | 19.544 |
137 | 136 | 1070.3 | 58.68 | 16.853 | 244.542 | 19.677 |
138 | 137 | 1070.7 | 58.49 | 17.941 | 246.340 | 19.674 |
139 | 138 | 1072 | 58.11 | 15.973 | 248.138 | 19.672 |
140 | 139 | 1071.6 | 58.5 | 16.891 | 249.936 | 19.815 |
141 | 140 | 1073.3 | 59.79 | 15.738 | 251.734 | 19.827 |
142 | 141 | 1074 | 60.42 | 14.925 | 253.532 | 19.85 |
143 | 142 | 1077.2 | 59.75 | 15.367 | 255.330 | 19.961 |
144 | 143 | 1075.3 | 58.78 | 16.999 | 257.128 | 20.132 |
145 | 144 | 1077.2 | 59.56 | 16.185 | 258.926 | 20.111 |
146 | 145 | 1077.1 | 59.34 | 15.405 | 260.725 | 20.281 |
147 | 146 | 1077.6 | 60.26 | 14.863 | 262.523 | 20.4 |
148 | 147 | 1078 | 58.89 | 16.935 | 264.321 | 20.36 |
149 | 148 | 1077.2 | 60.51 | 15.918 | 266.119 | 20.547 |
150 | 149 | 1079.2 | 63.73 | 17.923 | 267.917 | 20.555 |
151 | 150 | 1081.2 | 61.49 | 15.921 | 269.715 | 20.593 |
152 | 151 | 1083.1 | 58.71 | 17.925 | 271.513 | 20.787 |
153 | 152 | 1086 | 58.99 | 15.991 | 273.311 | 20.758 |
154 | 153 | 1085.5 | 59.37 | 17.962 | 275.109 | 20.805 |
155 | 154 | 1087.8 | 59.31 | 15.892 | 276.907 | 20.912 |
156 | 155 | 1090 | 59.96 | 15.895 | 278.706 | 21.004 |
157 | 156 | 1090.9 | 59.23 | 15.895 | 280.504 | 21.061 |
158 | 157 | 1092.7 | 58.71 | 15.895 | 282.302 | 21.038 |
159 | 158 | 1089.6 | 58.42 | 15.93 | 284.100 | 21.135 |
160 | 159 | 1093.5 | 58.03 | 15.933 | 285.898 | 21.264 |
161 | 160 | 1095.2 | 60.64 | 15.933 | 287.696 | 21.275 |
162 | 161 | 1096.7 | 58.66 | 16.818 | 289.494 | 21.257 |
163 | 162 | 1098.2 | 58.48 | 15.868 | 291.292 | 21.402 |
164 | 163 | 1096 | 57.96 | 15.868 | 293.090 | 21.405 |
165 | 164 | 1098.5 | 58.82 | 15.868 | 294.888 | 21.443 |
166 | 165 | 1099.2 | 60.62 | 15.868 | 296.687 | 20.986 |
167 | 166 | 1099.9 | 59.08 | 15.943 | 298.485 | 20.603 |
168 | 167 | 1101.3 | 58.55 | 15.946 | 300.283 | 20.502 |
169 | 168 | 1099 | 59.65 | 15.946 | 302.081 | 20.263 |
170 | 169 | 1101 | 58.56 | 15.946 | 303.879 | 19.9 |
171 | 170 | 1101.8 | 61.27 | 17.916 | 305.677 | 19.858 |
172 | 171 | 1102.2 | 57.09 | 15.982 | 307.475 | 19.903 |
173 | 172 | 1102.4 | 56.92 | 19.039 | 309.273 | 19.868 |
174 | 173 | 1102.4 | 57.55 | 17.783 | 311.071 | 19.913 |
175 | 174 | 1104.5 | 58.75 | 15.985 | 312.869 | 19.827 |
176 | 175 | 1105 | 58.93 | 15.037 | 314.668 | 19.665 |
177 | 176 | 1106.2 | 60.01 | 16.871 | 316.466 | 19.445 |
178 | 177 | 1107 | 60.76 | 16.975 | 318.264 | 19.301 |
179 | 178 | 1107.5 | 60.35 | 18.946 | 320.062 | 19.131 |
180 | 179 | 1107.9 | 61.09 | 16.06 | 321.860 | 18.953 |
181 | 180 | 1108.2 | 61.39 | 19.016 | 323.658 | 18.834 |
182 | 181 | 1089.3 | 61.3 | 16.809 | 325.456 | 18.664 |
183 | 182 | 1089.2 | 61.44 | 10.868 | 327.254 | 16.174 |
184 | 183 | 1010.7 | 61.69 | 10.19 | 329.052 | 12.114 |
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Test Items | Standard Clause | Judgment Criteria | |
---|---|---|---|
Fire resistance | Completeness | GB/T 9978.8-2008 Article 10 GB/T 9978.1-2008 Article 10.2.2 Article 8.4 | The duration of the test specimen’s continuous fire resistance performance in the fire test. Any one of the following limited conditions of the test specimen shall be considered as a loss of integrity: (a) A cotton pad test is conducted, and the cotton pad is ignited. (b) A gap probe of 6 mm penetrates the specimen into the furnace and moves 150 mm along the length of the crack; a gap probe of 25 mm penetrates the specimen into the furnace. (c) A flame appears on the backfire surface and lasts for more than 10 s. |
Thermal insulation | GB/T 9978.8-2008 Article 10 GB/T 9978.1-2008 Article 10.2.3 | If the duration of the fire resistance and heat insulation performance of the test specimen in the fire test as well as the temperature rise of the backfire surface of the test specimen exceeds any of the following limits, it is considered to have lost the heat insulation: (a) The average temperature rise exceeds the initial average temperature of 140 °C. (b) The temperature rise at any point exceeds the initial temperature (including the moving thermocouple) by 180 °C (the initial temperature should be the initial average temperature of the back surface at the beginning of the test). | |
GB/T 9978.1-2008 Article 12.2.2 | If the “integrity” of the test specimen does not meet the requirements, it is considered that the “heat insulation” of the test specimen does not meet the requirements. |
Time | Observation Record |
---|---|
0 | Test start. |
30 | No significant change from the previous stage. |
60 | No significant change from the previous stage. |
90 | No significant change from the previous stage. |
120 | Concave deformation. |
150 | No significant change from the previous stage. |
181 | Integrity and thermal insulation are undamaged; test is stopped. |
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Lei, X.; Ouyang, J.; Wang, Y.; Wang, X.; Zhang, X.; Chen, F.; Xia, C.; Liu, Z.; Zhou, C. Thermal–Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning. Fire 2021, 4, 93. https://doi.org/10.3390/fire4040093
Lei X, Ouyang J, Wang Y, Wang X, Zhang X, Chen F, Xia C, Liu Z, Zhou C. Thermal–Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning. Fire. 2021; 4(4):93. https://doi.org/10.3390/fire4040093
Chicago/Turabian StyleLei, Xiangsheng, Jinwu Ouyang, Yanfeng Wang, Xinghua Wang, Xiaofeng Zhang, Feng Chen, Chang Xia, Zhen Liu, and Cuiying Zhou. 2021. "Thermal–Mechanical Coupling Evaluation of the Panel Performance of a Prefabricated Cabin-Type Substation Based on Machine Learning" Fire 4, no. 4: 93. https://doi.org/10.3390/fire4040093