Novel Method for Measuring the Heat Collection Rate and Heat Loss Coefficient of Water-in-Glass Evacuated Tube Solar Water Heaters Based on Artificial Neural Networks and Support Vector Machine
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental
Parameters | Portable Test instruments | Accuracy | Picture |
---|---|---|---|
Final temperate of water | Digital thermoelectric thermometer | ±0.5% | |
Hot water mass in tank | Electric platform scale | ±1.0% | |
Diameter, tube center distance, tube length, collector area | Taper ZSH-3 | ±0.5% |
Item | Tube Length (mm) | Number of Tubes | TCD (mm) | Tank Volume (kg) | Collector Area (m2) | Angle (°) | Final Temp. (°C) | HCR (MJ/m2) | HLC (W/(m3K)) |
---|---|---|---|---|---|---|---|---|---|
Maximum | 2200 | 64 | 151 | 403 | 8.24 | 85 | 62 | 11.3 | 13 |
Minimum | 1600 | 5 | 60 | 70 | 1.27 | 30 | 46 | 6.7 | 8 |
Range | 600 | 59 | 91 | 333 | 6.97 | 55 | 16 | 4.6 | 5 |
Average | 1811 | 21 | 76.2 | 172 | 2.69 | 46 | 53 | 8.9 | 10 |
Standard deviation | 87.8 | 5.8 | 5.11 | 47.0 | 0.73 | 3.89 | 2.0 | 0.48 | 0.77 |
2.2. Artificial Neural Networks (ANNs)
2.2.1. Multilayer Feed-Forward Neural Networks (MLFNs)
2.2.2. General Regression Neural Network (GRNN)
2.3. Support Vector Machine (SVM)
3. Results and Discussion
3.1. Model Development
Model Type | Mean RMS Error in Testing | Mean Training Time | Mean Prediction Accuracy (30% tolerance) | Mean Prediction Accuracy (20% tolerance) | Mean Prediction Accuracy (10% tolerance) |
---|---|---|---|---|---|
SVM | 0.29 | 0:00:10 | 100% | 99.85% | 95.11% |
GRNN | 0.33 | 0:00:14 | 100% | 99.82% | 94.42% |
MLFN (2 Nodes) | 0.17 | 0:05:57 | 100% | 99.96% | 97.08% |
MLFN (3 Nodes) | 0.15 | 0:07:12 | 100% | 100% | 98.33% |
MLFN (4 Nodes) | 0.15 | 0:08:35 | 100% | 100% | 97.21% |
MLFN (5 Nodes) | 0.17 | 0:10:03 | 100% | 99.96% | 97.03% |
MLFN (6 Nodes) | 0.17 | 0:11:23 | 100% | 99.96% | 96.89% |
MLFN (7 Nodes) | 0.15 | 0:13:39 | 100% | 100% | 97.31% |
MLFN (8 Nodes) | 0.19 | 0:14:35 | 100% | 99.89% | 96.54% |
MLFN (9 Nodes) | 0.15 | 0:15:45 | 100% | 100% | 97.18% |
MLFN (10 Nodes) | 0.15 | 0:17:56 | 100% | 100% | 97.62% |
MLFN (11 Nodes) | 0.15 | 0:19:10 | 100% | 100% | 97.19% |
MLFN (12 Nodes) | 0.14 | 0:20:47 | 100% | 100% | 98.57% |
MLFN (13 Nodes) | 0.16 | 0:21:51 | 100% | 99.96% | 97.01% |
MLFN (14 Nodes) | 0.15 | 0:23:12 | 100% | 100% | 97.31% |
MLFN (15 Nodes) | 0.17 | 0:24:19 | 100% | 99.96% | 96.92% |
MLFN (16 Nodes) | 0.19 | 0:26:05 | 100% | 99.89% | 96.43% |
MLFN (17 Nodes) | 0.16 | 0:29:05 | 100% | 100% | 95.72% |
MLFN (18 Nodes) | 0.23 | 0:28:50 | 100% | 99.82% | 96.33% |
MLFN (19 Nodes) | 0.19 | 0:30:20 | 100% | 99.89% | 96.57% |
MLFN (20 Nodes) | 0.2 | 0:32:26 | 100% | 99.89% | 95.92% |
... | ... | ... | ... | ... | ... |
MLFN (39 Nodes) | 0.22 | 1:07:44 | 100% | 99.85% | 95.41% |
Model Type | Mean RMS Error in Testing | Mean Training Time | Mean Prediction Accuracy (30% tolerance) | Mean Prediction Accuracy (20% tolerance) | Mean Prediction Accuracy (10% tolerance) |
---|---|---|---|---|---|
SVM | 0.73 | 0:00:10 | 100% | 98.81% | 82.31% |
GRNN | 0.71 | 0:00:08 | 100% | 99.38% | 83.14% |
MLFN (2 Nodes) | 0.75 | 0:05:47 | 100% | 98.44% | 81.43% |
MLFN (3 Nodes) | 0.74 | 0:06:46 | 100% | 98.51% | 81.97% |
MLFN (4 Nodes) | 0.78 | 0:08:22 | 100% | 98.17% | 80.69% |
MLFN (5 Nodes) | 0.74 | 0:09:44 | 100% | 98.61% | 82.54% |
MLFN (6 Nodes) | 0.73 | 0:10:56 | 100% | 98.76% | 82.63% |
MLFN (7 Nodes) | 0.77 | 0:12:30 | 100% | 98.13% | 81.03% |
MLFN (8 Nodes) | 0.76 | 0:14:07 | 100% | 98.44% | 81.64% |
MLFN (9 Nodes) | 0.75 | 0:15:33 | 100% | 98.65% | 81.86% |
MLFN (10 Nodes) | 0.76 | 0:17:02 | 100% | 98.43% | 81.55% |
MLFN (11 Nodes) | 0.79 | 0:18:21 | 100% | 97.97% | 80.74% |
MLFN (12 Nodes) | 0.9 | 0:19:37 | 100% | 93.32% | 75.14% |
MLFN (13 Nodes) | 0.75 | 0:21:05 | 100% | 98.66% | 81.43% |
MLFN (14 Nodes) | 0.78 | 0:22:38 | 100% | 98.04% | 81.03% |
MLFN (15 Nodes) | 0.8 | 0:24:27 | 100% | 97.36% | 80.78% |
MLFN (16 Nodes) | 0.73 | 0:25:31 | 100% | 98.35% | 82.22% |
MLFN (17 Nodes) | 0.88 | 0:26:59 | 100% | 93.93% | 76.23% |
MLFN (18 Nodes) | 0.8 | 0:28:30 | 100% | 96.41% | 80.67% |
MLFN (19 Nodes) | 0.79 | 0:30:06 | 100% | 97.43% | 80.93% |
MLFN (20 Nodes) | 0.88 | 0:31:25 | 100% | 93.86% | 76.61% |
... | ... | ... | ... | ... | ... |
MLFN (39 Nodes) | 1.05 | 1:04:57 | 100% | 89.61% | 71.52% |
3.2. Model Analysis
3.2.1. The MLFN-3 for Heat Collection Rate
3.2.2. The GRNN for Heat Loss Coefficient
3.3. Robustness Analysis
3.4. Comparison with Conventional Methods
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
H | the amount of solar radiation, MJ/m2 |
ta | the ambient temperature, °C |
ti | the initial temperature of water in tank, °C |
S | the area of tubes, m2 |
USL | the heat loss coefficient according to GB/T 19141, W/(m3K) |
US | the heat loss coefficient to ISO 9459-2, W/K |
ρw | the water density, kg/m3 |
Cp,w | the specific heat of water, kJ/(kg °C) |
Vs | the heat water mass in tank, kg |
tis | the initial temperature of water, °C |
tfs | the final temperature of water, °C |
tas(av) | the ambient average temperature, °C |
V | the volume of water, m3 |
∆τ | the duration time of heat loss coefficient experiments, s |
qs | the heat collection rate, MJ/m2 |
the predicted value, MJ/m2 or W/(m3K) | |
the actual value, MJ/m2 or W/(m3K) | |
the number of tested samples, no unit | |
the number of tested samples, no unit | |
a1, a2, a3 | the regression coefficients, no unit |
SWH | solar water heater |
ANNs | artificial neural networks |
SVM | support vector machine |
MLFN | multilayer feed-forward neural network |
GRNN | general regression neural network |
RMS | root mean square |
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Liu, Z.; Li, H.; Zhang, X.; Jin, G.; Cheng, K. Novel Method for Measuring the Heat Collection Rate and Heat Loss Coefficient of Water-in-Glass Evacuated Tube Solar Water Heaters Based on Artificial Neural Networks and Support Vector Machine. Energies 2015, 8, 8814-8834. https://doi.org/10.3390/en8088814
Liu Z, Li H, Zhang X, Jin G, Cheng K. Novel Method for Measuring the Heat Collection Rate and Heat Loss Coefficient of Water-in-Glass Evacuated Tube Solar Water Heaters Based on Artificial Neural Networks and Support Vector Machine. Energies. 2015; 8(8):8814-8834. https://doi.org/10.3390/en8088814
Chicago/Turabian StyleLiu, Zhijian, Hao Li, Xinyu Zhang, Guangya Jin, and Kewei Cheng. 2015. "Novel Method for Measuring the Heat Collection Rate and Heat Loss Coefficient of Water-in-Glass Evacuated Tube Solar Water Heaters Based on Artificial Neural Networks and Support Vector Machine" Energies 8, no. 8: 8814-8834. https://doi.org/10.3390/en8088814