# American Institute of Mathematical Sciences

## Mathematical model of energy conservation evaluation of passive building based on fuzzy clustering algorithm

 1 School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China 2 School of Management, Henan University of Urban Construction, Pingdingshan 467000, China 3 School of Energy and Environmental Engineering, Hebei University of Technology Tianjin 300401, China

* Corresponding author: Lichao Jiao

Received  March 2019 Revised  May 2019 Published  December 2019

When evaluating the energy conservation effect of passive buildings, the traditional gray comprehensive evaluation model cannot comprehensively analyze the building's own factors, which leads to lower accuracy of analysis. Mathematical model of energy conservation evaluation of passive building based on fuzzy clustering algorithm is designed, which uses the analytic hierarchy process to determine the weight of the energy conservation evaluation index of passive building. The system of energy conservation indicators for passive buildings is constructed to calculate fuzzy similarities between different evaluation indicators and to calculate them. Through the clustering of the calculation results, the energy conservation evaluation results of the passive building are obtained. The experimental results show that the designed model can effectively evaluate the energy conservation effect of passive buildings, and its generalization ability is better. The average accuracy of the evaluation is as high as 98%, and the evaluation rate is as high as 96%. The average time-consuming value of the eight passive buildings is only 540.54 s. It has the advantage of high evaluation accuracy and high efficiency.

Citation: Xian Rong, Lichao Jiao, Xiangfei Kong, Guangpu Yuan. Mathematical model of energy conservation evaluation of passive building based on fuzzy clustering algorithm. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020203
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Evaluation results of this model
evaluation speed growth rate comparison chart
A-B judgement matrix
 A B 1 B 2 B 3 B 4 B 1 1 2 5 4 B 2 1/2 1 3 5 B 3 1/5 1/3 1 2 b 4 1/4 1/5 1/2 1
 A B 1 B 2 B 3 B 4 B 1 1 2 5 4 B 2 1/2 1 3 5 B 3 1/5 1/3 1 2 b 4 1/4 1/5 1/2 1
Building energy efficiency passive building energy efficiency evaluation system
 Total target layer $A$ Subtarget layer $B_i$ Weight $WB_i$ Index layer Weight $C_i$ Comprehensive evaluation of building energy efficiency Economic indicators $B_1$ 0.486 Unit cost of energy saving transformationC11 0.495 Investment cost of building energy efficiency projectsC12 0.311 Energy cost of building operationC13 0.133 Building energy efficiency gainsC14 0.061 Technical indicators $B_2$ 0.319 Building (layout, shape, type) energy saving technologyC21 0.444 Building envelopeC22 0.444 Refrigeration heating lighting technologyC23 0.111 Environmental indicators $B_3$ 0.117 Greening rateC31 0.451 Hardened pavement and shading technologyC32 0.171 Living environmentC34 0.305 Living healthy environmentC35 0.073 Area coefficientC41 0.141 Functional indicators $B_4$ 0.077 Structural safetyC42 0.454 Sound insulationC43 0.263 Envelope energyC44 0.141
 Total target layer $A$ Subtarget layer $B_i$ Weight $WB_i$ Index layer Weight $C_i$ Comprehensive evaluation of building energy efficiency Economic indicators $B_1$ 0.486 Unit cost of energy saving transformationC11 0.495 Investment cost of building energy efficiency projectsC12 0.311 Energy cost of building operationC13 0.133 Building energy efficiency gainsC14 0.061 Technical indicators $B_2$ 0.319 Building (layout, shape, type) energy saving technologyC21 0.444 Building envelopeC22 0.444 Refrigeration heating lighting technologyC23 0.111 Environmental indicators $B_3$ 0.117 Greening rateC31 0.451 Hardened pavement and shading technologyC32 0.171 Living environmentC34 0.305 Living healthy environmentC35 0.073 Area coefficientC41 0.141 Functional indicators $B_4$ 0.077 Structural safetyC42 0.454 Sound insulationC43 0.263 Envelope energyC44 0.141
Evaluation results of this model
 Serial number The model evaluation results are presented in this paper Actual energy consumption grade 1 Ⅲ Ⅲ 2 Ⅱ partial Ⅲ Ⅱ partial Ⅲ 3 Ⅲ Ⅲ 4 Ⅲ partial Ⅱ Ⅲ partial Ⅱ 5 Ⅳ partial Ⅲ Ⅳ partial Ⅲ 6 Ⅲ Ⅲ 7 Ⅲ partial Ⅱ Ⅳ Ⅲ partial Ⅱ Ⅳ 8 Ⅳ Ⅳ
 Serial number The model evaluation results are presented in this paper Actual energy consumption grade 1 Ⅲ Ⅲ 2 Ⅱ partial Ⅲ Ⅱ partial Ⅲ 3 Ⅲ Ⅲ 4 Ⅲ partial Ⅱ Ⅲ partial Ⅱ 5 Ⅳ partial Ⅲ Ⅳ partial Ⅲ 6 Ⅲ Ⅲ 7 Ⅲ partial Ⅱ Ⅳ Ⅲ partial Ⅱ Ⅳ 8 Ⅳ Ⅳ
Results of evaluation accuracy of this model
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 Passive building 1 95 97 97 96 97 98 98 98 97 Passive building 2 96 95 97 97 97 98 98 99 97 Passive building 3 99 99 98 96 98 99 95 96 98 Passive building 4 95 97 96 98 99 99 98 98 98 Passive building 5 99 99 95 97 98 99 97 95 97 Passive building 6 98 98 99 98 98 99 95 95 98 Passive building 7 97 98 98 98 98 98 98 98 98 Passive building 8 99 95 98 99 95 98 99 95 97
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 Passive building 1 95 97 97 96 97 98 98 98 97 Passive building 2 96 95 97 97 97 98 98 99 97 Passive building 3 99 99 98 96 98 99 95 96 98 Passive building 4 95 97 96 98 99 99 98 98 98 Passive building 5 99 99 95 97 98 99 97 95 97 Passive building 6 98 98 99 98 98 99 95 95 98 Passive building 7 97 98 98 98 98 98 98 98 98 Passive building 8 99 95 98 99 95 98 99 95 97
Grey comprehensive evaluation model accuracy rate results
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 1 85 87 87 86 87 88 88 88 87 Passive building 2 86 85 87 87 87 88 88 88 87 Passive building 3 88 88 88 86 88 88 85 86 87 Passive building 4 85 87 86 88 88 88 88 88 87 Passive building 5 88 88 85 87 88 88 87 85 87 Passive building 6 88 88 88 88 88 88 85 85 87 Passive building 7 87 88 88 88 88 88 88 88 88 Passive building 8 88 85 88 88 85 88 88 85 87
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 1 85 87 87 86 87 88 88 88 87 Passive building 2 86 85 87 87 87 88 88 88 87 Passive building 3 88 88 88 86 88 88 85 86 87 Passive building 4 85 87 86 88 88 88 88 88 87 Passive building 5 88 88 85 87 88 88 87 85 87 Passive building 6 88 88 88 88 88 88 85 85 87 Passive building 7 87 88 88 88 88 88 88 88 88 Passive building 8 88 85 88 88 85 88 88 85 87
Energy management risk assessment model accuracy rate results
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 Passive building 1 65 61 64 61 61 62 59 64 62 Passive building 2 65 62 64 65 63 63 64 56 63 Passive building 3 58 58 61 62 58 61 59 56 59 Passive building 4 55 55 56 58 58 58 58 58 57 Passive building 5 58 57 57 57 58 58 57 55 57 Passive building 6 58 58 49 54 58 57 56 55 56 Passive building 7 67 58 56 71 46 58 58 58 59 Passive building 8 88 45 54 51 47 48 48 67 56
 Experimental object Number of times/times (%) Mean value (%) 1 2 3 4 5 6 7 8 Passive building 1 65 61 64 61 61 62 59 64 62 Passive building 2 65 62 64 65 63 63 64 56 63 Passive building 3 58 58 61 62 58 61 59 56 59 Passive building 4 55 55 56 58 58 58 58 58 57 Passive building 5 58 57 57 57 58 58 57 55 57 Passive building 6 58 58 49 54 58 57 56 55 56 Passive building 7 67 58 56 71 46 58 58 58 59 Passive building 8 88 45 54 51 47 48 48 67 56
Grey comprehensive evaluation model evaluation time consuming
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Mean value 1 168 168 167.5 167.4 167.73 2 336 336 335 334.8 335.45 3 504 504 502.5 502.2 503.18 4 672 672 670 669.6 670.9 5 840 840 837.5 837 838.63 6 1008 1008 1005 1004.4 1006.35 7 1176 1176 1172.5 1171.8 1174.08 8 1344 1344 1340 1339.2 1341.8 Mean value 756 756 753.75 753.3 754.765
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Mean value 1 168 168 167.5 167.4 167.73 2 336 336 335 334.8 335.45 3 504 504 502.5 502.2 503.18 4 672 672 670 669.6 670.9 5 840 840 837.5 837 838.63 6 1008 1008 1005 1004.4 1006.35 7 1176 1176 1172.5 1171.8 1174.08 8 1344 1344 1340 1339.2 1341.8 Mean value 756 756 753.75 753.3 754.765
Time consuming of model evaluation in this paper
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Time per request 1 120 120 120 120.5 120.13 2 240 240 240 241 240.25 3 360 360 360 361.5 360.13 4 480 480 480 482 480.5 5 600 600 600 602.5 600.63 6 720 720 720 723 720.75 7 840 840 840 843.5 840.88 8 960 960 960 964 961 Mean value 540 540 540 542.25 540.54
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Time per request 1 120 120 120 120.5 120.13 2 240 240 240 241 240.25 3 360 360 360 361.5 360.13 4 480 480 480 482 480.5 5 600 600 600 602.5 600.63 6 720 720 720 723 720.75 7 840 840 840 843.5 840.88 8 960 960 960 964 961 Mean value 540 540 540 542.25 540.54
Energy management risk assessment model evaluation time consuming
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Time per request 1 144 144.5 144.5 1144.5 144.38 2 288 289 289 289 288.75 3 432 433.5 433.5 433.5 433.13 4 576 578 578 578 577.5 5 720 722.5 722.5 722.5 721.88 6 864 867 867 867 866.25 7 1008 1011.5 1011.5 1011.5 1010.63 8 1152 1156 1156 1156 1155 Mean value 648 650.25 650.25 775.25 649.69
 Passive building quantity/individual Time consuming /s First times Second times Third times Fourth times Time per request 1 144 144.5 144.5 1144.5 144.38 2 288 289 289 289 288.75 3 432 433.5 433.5 433.5 433.13 4 576 578 578 578 577.5 5 720 722.5 722.5 722.5 721.88 6 864 867 867 867 866.25 7 1008 1011.5 1011.5 1011.5 1010.63 8 1152 1156 1156 1156 1155 Mean value 648 650.25 650.25 775.25 649.69
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