Prediction and Analysis of Dew Point Indirect Evaporative Cooler Performance by Artificial Neural Network Method
Abstract
:1. Introduction
2. Preparing for BP ANN
2.1. Cooler Overview
2.2. Sample Data Collection
2.3. Processing of Sample Data
2.4. Design of BP ANN
2.5. Analysis of the Influencing Degree of Input Variables on the Output Variables
3. BP ANN for Performance Prediction
3.1. Analysis of BP ANN Training Results
3.2. Analysis of the Predicted Results of BP ANN
4. PSO-BP ANN for Performance Prediction
4.1. Predicted Results of PSO-BP ANN Model
4.2. Comparative Analysis of BP and PSO-BP ANN Models
5. Conclusions
- (1)
- The BP ANN results of evaporation efficiency are basically consistent with the measured values. The RMSE of the evaporation efficiency of the BP ANN is 3.1367, and the r2 is 0.9659. However, the relative error of sample 7 is close to 10% which is a little bit large.
- (2)
- A PSO-BP ANN was established to improve the accuracy of the BP ANN. The relative error of the PSO-BP model is generally smaller than that of the BP ANN. For sample 7, the relative error of the PSO-BP ANN is 2.21% with an improvement of 7.39% when compared with the BP ANN.
- (3)
- The influencing degrees of seven input parameters on evaporation efficiency were discussed, among which the secondary/primary air volume ratio has the biggest impact.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Nomenclature | |
b | threshold scalar |
c1, c2 | learning factors |
D | dimension of particles |
k | ith time |
l | number of neurons in the output layer |
m | number of neurons in the input layer |
n | number of neurons in the hidden layer |
N | size of particle swarm |
Pg | optimal position of the particles swarm |
pi | optimal position of the particles |
r1, r2 | random numbers between 0 and 1 |
r2 | square of the correlation coefficient |
ri | correlation degree |
vid | velocity vector of D-dimensional component of the ith particle |
W | weight matrix |
x | normalized input value |
xi | original input value |
xid | position vector of D-dimensional component of the ith particle |
xmax | maximum value of original input |
xmin | minimum value of original input |
y | normalized target value |
yi | original value Target value |
ymax | maximum value of original target |
ymin | minimum value of original target |
YP(k) | predicted evaporation efficiency at the current time |
YT(k) | actual evaporation efficiency at the current time |
Greek symbols | |
ζ | correlation coefficient |
ω | inertia weight |
η | relative error |
Abbreviations | |
AAE | average absolute error |
ABE | average biased error |
ANFIS | adaptive neuro-fuzzy inference system |
ANN | artificial neural network |
BP | back propagation |
DPIE | Dew point indirect evaporative |
FIS | fuzzy inference system |
FNN | feedforward neural network |
GA | genetic algorithms |
GRA | grey relational analysis |
HVAC | heating, ventilation, and air conditioning |
MSE | mean square error |
PSO | particle swarm optimization |
R&D | research and development |
RMS | root mean square |
RMSE | root mean square error |
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Description | Operating Parameters and Environmental Parameters |
---|---|
Yulin City, Shaanxi Province, China (moderate humidity) | 1. Unit Type, AJL120-MFH200A 2. Air volume, 20,000 m3/h 3. Actual air supply volume, 11,403 m3/h 4. Exhaust air volume, 6620 m3/h 5. Secondary/primary air volume ratio, 0.58 6. Outdoor environment: temperature, 28.1~29.1 °C relative humidity, 27.8~28.4% |
Automatic recorder (Testo 174H) | Range, 0~100 °C/%; Sensor accuracy, ±0.5 °C/±3% |
Infrared Detector (Testo 869) | Range, −20~280 °C; Sensor accuracy, <0.12 °C |
Anemometer (Testo 410-1) | Range, 0.4~20.0 m/s; Sensor accuracy, ±(0.2 m/s + 2%) |
Number of Nodes | r2 | RMSE | Relative Error η (%) |
---|---|---|---|
10 | 0.9567 | 4.7312 | 3.0357 |
11 | 0.9552 | 4.8981 | 3.1943 |
12 | 0.9537 | 5.0528 | 3.5273 |
13 | 0.9561 | 4.7929 | 3.2475 |
14 | 0.9581 | 4.6170 | 2.9422 |
15 | 0.9474 | 5.7428 | 3.8813 |
16 | 0.9480 | 5.6769 | 3.9655 |
17 | 0.9412 | 4.9289 | 4.0346 |
18 | 0.9542 | 5.0018 | 3.7074 |
Number | Air Inlet Dry Bulb Temperature/°C | Relative Humidity/% | Total Air Volume/m3/h | Head Wind Speed/m/s | Primary Air Volume/m3/h | Secondary Air Volume/m3/h | Secondary/Primary Air Volume Ratio |
---|---|---|---|---|---|---|---|
1 | 0.8068 | 0.4895 | 0.8459 | 0.9495 | 0.6706 | 0.6778 | 0.8755 |
2 | 0.7238 | 0.5706 | 0.7086 | 0.8519 | 0.5814 | 0.5867 | 0.7293 |
3 | 0.6675 | 0.6581 | 0.6193 | 0.7260 | 0.5198 | 0.5241 | 0.6350 |
4 | 0.8403 | 0.6471 | 0.7216 | 0.8708 | 0.5901 | 0.5956 | 0.7431 |
5 | 0.9230 | 0.5838 | 0.9479 | 0.8471 | 0.7332 | 0.7417 | 0.9853 |
6 | 0.8589 | 0.5958 | 0.9714 | 0.8293 | 0.7471 | 0.7560 | 0.9915 |
7 | 0.9783 | 0.7253 | 0.7946 | 0.9793 | 0.6380 | 0.6444 | 0.8207 |
8 | 0.8666 | 0.7140 | 0.8459 | 0.9495 | 0.6706 | 0.6778 | 0.8755 |
9 | 0.8355 | 0.6907 | 0.8840 | 0.9057 | 0.6943 | 0.7020 | 0.9164 |
10 | 0.9505 | 0.7263 | 0.7788 | 0.9555 | 0.6278 | 0.6340 | 0.8039 |
Type | Air Inlet Dry Bulb Temperature/°C | Relative Humidity/% | Total Air Volume/m3/h | Head Wind Speed/m/s | Primary Air Volume/m3/h | Secondary Air Volume/m3/h | Secondary/Primary Air Volume Ratio |
---|---|---|---|---|---|---|---|
r | 0.7687 | 0.5885 | 0.6879 | 0.7717 | 0.5605 | 0.5657 | 0.8258 |
Sample Number | Test Moment/h | Measured Values/% | Value of BP/% | Value of PSO-BP/% | AAE of BP/% | ABE of BP/% | AAE of PSO-BP/% | ABE of PSO-BP/% |
---|---|---|---|---|---|---|---|---|
1 | 9:00 | 90.53 | 89.68 | 90.13 | 3.21 | −0.61 | 1.13 | −0.23 |
2 | 10:00 | 115.63 | 111.34 | 113.8 | ||||
3 | 11:00 | 120 | 114.89 | 117.03 | ||||
4 | 12:00 | 114.29 | 112.03 | 114.95 | ||||
5 | 13:00 | 85.71 | 83.97 | 84.97 | ||||
6 | 14:00 | 82.46 | 78.99 | 81.64 | ||||
7 | 15:00 | 102.04 | 111.84 | 104.3 | ||||
8 | 16:00 | 112.33 | 110.15 | 112.01 | ||||
9 | 17:00 | 113.04 | 116.39 | 114.97 | ||||
10 | 18:00 | 91.4 | 91.79 | 91.28 |
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Sun, T.; Huang, X.; Liang, C.; Liu, R.; Huang, X. Prediction and Analysis of Dew Point Indirect Evaporative Cooler Performance by Artificial Neural Network Method. Energies 2022, 15, 4673. https://doi.org/10.3390/en15134673
Sun T, Huang X, Liang C, Liu R, Huang X. Prediction and Analysis of Dew Point Indirect Evaporative Cooler Performance by Artificial Neural Network Method. Energies. 2022; 15(13):4673. https://doi.org/10.3390/en15134673
Chicago/Turabian StyleSun, Tiezhu, Xiaojun Huang, Caihang Liang, Riming Liu, and Xiang Huang. 2022. "Prediction and Analysis of Dew Point Indirect Evaporative Cooler Performance by Artificial Neural Network Method" Energies 15, no. 13: 4673. https://doi.org/10.3390/en15134673