Time Series Prediction and Modeling of Visibility Range with Artificial Neural Network and Hybrid Adaptive Neuro-Fuzzy Inference System
Abstract
1. Introduction
2. Prediction of Visibility Using ANN and ANFIS
2.1. ANN Architecture Description and Its Applications
2.2. Adaptive Neuro-Fuzzy Inference System
2.2.1. ANFIS Architecture
- 1.
- Layer 1: Membership Function or Fuzzy layer
- 2.
- Layer 2: Rules Layer
- 3.
- Layer 3: Normalized Firing Strength (NFS)
- 4.
- Layer 4: Defuzzification
- 5.
- Layer 5: Addition Layer
2.2.2. Hybrid Learning Algorithm
3. Site, Data, and Methods
3.1. Site Study and Meteorological Data
3.2. ANN Approach to Predict Visibility Range
3.2.1. Feed-Forward Neural Network
3.2.2. Selection of ANN Model Parameters
3.3. Accuracy Measurement Methods
4. Results and Discussion
4.1. Standard Statistical Techniques
4.2. Artificial Neural Network Simulation and Results
4.2.1. ANN Simulation Procedure
4.2.2. ANN Prediction Results
City | Input Cases | Input Variables | Approx. 95% CI for Mean R2 | p-Value | |||
---|---|---|---|---|---|---|---|
DBN | Case—A | RH | 0.4771 | 0.5291 | 0.5156 | [0.5063, 0.5249] | <0.001 |
Case—B | RH, WS | 0.5794 | 0.6122 | 0.6065 | [0.6006, 0.6124] | <0.001 | |
Case—C | RH, T, P | 0.5797 | 0.6301 | 0.6219 | [0.6129, 0.6309] | <0.001 | |
Case—D | RH, WS, P | 0.5988 | 0.6644 | 0.6450 | [0.6333, 0.6567] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6388 | 0.6725 | 0.6701 | [0.6641, 0.6761] | <0.001 | |
CPT | Case—A | RH | 0.4911 | 0.5401 | 0.5368 | [0.5280, 0.5456] | <0.001 |
Case—B | RH, WS | 0.6042 | 0.6498 | 0.6335 | [0.6254, 0.6416] | <0.001 | |
Case—C | RH, T, P | 0.6155 | 0.6734 | 0.6573 | [0.6469, 0.6677] | <0.001 | |
Case—D | RH, WS, P | 0.6213 | 0.6811 | 0.6760 | [0.6653, 0.6867] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6702 | 0.7185 | 0.7002 | [0.6916, 0.7089] | <0.001 | |
MTA | Case—A | RH | 0.4772 | 0.5297 | 0.5191 | [0.5097, 0.5285] | <0.001 |
Case—B | RH, WS | 0.5599 | 0.6033 | 0.5964 | [0.5886, 0.6042] | <0.001 | |
Case—C | RH, T, P | 0.5719 | 0.6288 | 0.6178 | [0.6076, 0.6280] | <0.001 | |
Case—D | RH, WS, P | 0.6077 | 0.6512 | 0.6384 | [0.6306, 0.6462] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6279 | 0.6853 | 0.6612 | [0.6509, 0.6715] | <0.001 | |
BFT | Case—A | RH | 0.4588 | 0.5096 | 0.4955 | [0.4864, 0.5046] | <0.001 |
Case—B | RH, WS | 0.5589 | 0.5974 | 0.5792 | [0.5723, 0.5861] | <0.001 | |
Case—C | RH, T, P | 0.5612 | 0.6060 | 0.5912 | [0.5832, 0.5992] | <0.001 | |
Case—D | RH, WS, P | 0.5677 | 0.6195 | 0.6001 | [0.5908, 0.6094] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6023 | 0.6541 | 0.6322 | [0.6229, 0.6415] | <0.001 | |
JHB | Case—A | RH | 0.4711 | 0.5189 | 0.5073 | [0.4988, 0.5158] | <0.001 |
Case—B | RH, WS | 0.5587 | 0.6001 | 0.5899 | [0.5825, 0.5973] | <0.001 | |
Case—C | RH, T, P | 0.5701 | 0.6216 | 0.6132 | [0.6040, 0.6224] | <0.001 | |
Case—D | RH, WS, P | 0.6165 | 0.6412 | 0.6221 | [0.6177, 0.6265] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6275 | 0.6813 | 0.6658 | [0.6562, 0.6754] | <0.001 | |
MHK | Case—A | RH | 0.4485 | 0.4911 | 0.4798 | [0.4722, 0.4874] | <0.001 |
Case—B | RH, WS | 0.5556 | 0.5945 | 0.5714 | [0.5645, 0.5783] | <0.001 | |
Case—C | RH, T, P | 0.5683 | 0.6101 | 0.5955 | [0.5881, 0.6029] | <0.001 | |
Case—D | RH, WS, P | 0.5703 | 0.6235 | 0.6011 | [0.5916, 0.6106] | <0.001 | |
Case—E | RH, T, P, WS (All Variables) | 0.6102 | 0.6583 | 0.6235 | [0.6149, 0.6321] | <0.001 |
4.3. ANFIS Simulation and Results
4.3.1. ANFIS Simulation Procedure and Analysis
4.3.2. ANFIS Prediction Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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ANN Model Properties | Functions and Values |
---|---|
Neural Network (NN) Type | Feed-forward Back Propagation Neural Network |
Network Training Method | Gauss–Newton-based Levenberg–Marquardt algorithm |
Adaptive Learning Function | LEARNGDM |
Network Training Function | TRAINLM |
Network Transfer Function | TANSIG |
Number of Neurons | 15 |
Number of hidden Layers | 2 |
Input Variable | Durban | Cape Town | Mthatha | Bloemfontein | Johannesburg | Mahikeng |
---|---|---|---|---|---|---|
RH | 0.3018 | 0.3619 | 0.3476 | 0.2514 | 0.3073 | 0.2566 |
T | 0.1169 | 0.1516 | 0.1214 | 0.1306 | 0.1219 | 0.1309 |
P | 0.0357 | 0.0235 | 0.0575 | 0.0349 | 0.0489 | 0.0659 |
WS | 0.1092 | 0.1509 | 0.0938 | 0.1787 | 0.1123 | 0.1392 |
DBN | ||||
---|---|---|---|---|
Input Cases | Input Variables | Mean RMSE (%) | Mean MBE (%) | |
Case—A | RH | 0.5156 | 38.560 ± 0.251 | −0.320 ± 0.111 |
Case—B | RH, WS | 0.6065 | 35.481 ± 0.243 | −0.352 ± 0.100 |
Case—C | RH, T, P | 0.6219 | 33.822 ± 0.451 | −0.501 ± 0.352 |
Case—D | RH, WS, P | 0.6450 | 33.011 ± 0.683 | −0.203 ± 0.300 |
Case—E | RH, T, P, WS (All Variables) | 0.6701 | 31.972 ± 0.882 | −0.221 ± 0.121 |
CPT | ||||
Input Cases | Input Variables | Mean | Mean RMSE (%) | Mean MBE (%) |
Case—A | RH | 0.5368 | 36.623 ± 0.154 | −0.252 ± 0.120 |
Case—B | RH, WS | 0.6335 | 33.592 ± 0.222 | −0.101 ± 0.252 |
Case—C | RH, T, P | 0.6573 | 32.761 ± 0.550 | −0.342 ± 0.300 |
Case—D | RH, WS, P | 0.6760 | 31.453 ± 0.761 | −0.200 ± 0.131 |
Case—E | RH, T, P, WS (All Variables) | 0.7002 | 29.421 ± 0.923 | −0.152 ± 0.103 |
MTA | ||||
Input Cases | Input Variables | Mean | Mean RMSE (%) | Mean MBE (%) |
Case—A | RH | 0.5191 | 39.713 ± 0.172 | −0.344 ± 0.222 |
Case—B | RH, WS | 0.5964 | 37.020 ± 0.281 | −0.202 ± 0.100 |
Case—C | RH, T, P | 0.6178 | 35.771 ± 0.430 | −0.412 ± 0.324 |
Case—D | RH, WS, P | 0.6384 | 34.324 ± 0.654 | −0.551 ± 0.252 |
Case—E | RH, T, P, WS (All Variables) | 0.6612 | 32.553 ± 0.753 | −0.254 ± 0.251 |
BFT | ||||
Input Cases | Input Variables | Mean | Mean RMSE (%) | Mean MBE (%) |
Case—A | RH | 0.4955 | 40.050 ± 0.273 | −0.201 ± 0.330 |
Case—B | RH, WS | 0.5792 | 37.884 ± 0.340 | −0.440 ± 0.294 |
Case—C | RH, T, P | 0.5912 | 36.853 ± 0.392 | −0.561 ± 0.302 |
Case—D | RH, WS, P | 0.6001 | 36.010 ± 0.583 | −0.252 ± 0.310 |
Case—E | RH, T, P, WS (All Variables) | 0.6322 | 34.132 ± 0.761 | −0.304 ± 0.351 |
JHB | ||||
Input Cases | Input Variables | Mean | Mean RMSE (%) | Mean MBE (%) |
Case—A | RH | 0.5073 | 39.111 ± 0.142 | −0.321 ± 0.264 |
Case—B | RH, WS | 0.5899 | 36.893 ± 0.330 | −0.484 ± 0.300 |
Case—C | RH, T, P | 0.6132 | 35.662 ± 0.421 | −0.503 ± 0.323 |
Case—D | RH, WS, P | 0.6221 | 35.132 ± 0.564 | −0.241 ± 0.100 |
Case—E | RH, T, P, WS (All Variables) | 0.6658 | 32.924 ± 0.693 | −0.350 ± 0.253 |
MHK | ||||
Input Cases | Input Variables | Mean | Mean RMSE (%) | Mean MBE (%) |
Case—A | RH | 0.4798 | 41.091 ± 0.292 | −0.461 ± 0.200 |
Case—B | RH, WS | 0.5714 | 39.682 ± 0.323 | −0.334 ± 0.234 |
Case—C | RH, T, P | 0.5955 | 37.033 ± 0.481 | −0.402 ± 0.152 |
Case—D | RH, WS, P | 0.6011 | 36.230 ± 0.640 | −0.340 ± 0.300 |
Case—E | RH, T, P, WS (All Variables) | 0.6235 | 35.672 ± 0.834 | −0.323 ± 0.262 |
Location | ||
---|---|---|
DBN | ||
CPT | ||
MTA | ||
BFT | ||
JHB | ||
MHK |
Place | Input MF Type | Epoch | Inputs | Output | Function | Obtained Error |
---|---|---|---|---|---|---|
Durban | Linear MF | 30 | Temperature, Relative Humidity, Pressure and Wind Speed | Visibility | gaussmf | 0.0262 |
Cape Town | Linear MF | 30 | gaussmf | 0.0132 | ||
Mthatha | Linear MF | 30 | gaussmf | 0.0139 | ||
Bloemfontein | Linear MF | 30 | gaussmf | 0.0097 | ||
Johannesburg | Linear MF | 30 | gaussmf | 0.0182 | ||
Mahikeng | Linear MF | 30 | gaussmf | 0.0068 |
ANN | ANFIS | Enhancement (%) | |||||||
---|---|---|---|---|---|---|---|---|---|
Place | Inputs | Output | |||||||
Training | Testing | Validation | Training | Testing | Training | Testing | |||
Durban | Temperature, Relative Humidity, Pressure and Wind Speed | Visibility | 0.6844 | 0.5799 | 0.6411 | 0.9998 | 0.8958 | 31.54 | 31.59 |
Cape Town | 0.7323 | 0.6012 | 0.6689 | 0.9999 | 0.9282 | 26.76 | 32.70 | ||
Mthatha | 0.6966 | 0.6081 | 0.6287 | 0.9999 | 0.9134 | 30.33 | 30.53 | ||
Bloemfontein | 0.6456 | 0.6398 | 0.6499 | 0.9999 | 0.9293 | 35.43 | 28.95 | ||
Johannesburg | 0.6941 | 0.5811 | 0.6185 | 0.9998 | 0.8993 | 30.57 | 31.82 | ||
Mahikeng | 0.6332 | 0.7067 | 0.6601 | 0.9999 | 0.9301 | 36.67 | 22.34 |
Place | ANN | ANFIS |
---|---|---|
Durban | 1.4051 | 0.1172 |
Cape Town | 2.4012 | 0.2185 |
Mthatha | 1.2885 | 0.1133 |
Bloemfontein | 0.8659 | 0.0681 |
Johannesburg | 1.1075 | 0.1007 |
Mahikeng | 1.1547 | 0.0730 |
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Share and Cite
Layioye, O.A.; Owolawi, P.A.; Ojo, J.S. Time Series Prediction and Modeling of Visibility Range with Artificial Neural Network and Hybrid Adaptive Neuro-Fuzzy Inference System. Atmosphere 2025, 16, 928. https://doi.org/10.3390/atmos16080928
Layioye OA, Owolawi PA, Ojo JS. Time Series Prediction and Modeling of Visibility Range with Artificial Neural Network and Hybrid Adaptive Neuro-Fuzzy Inference System. Atmosphere. 2025; 16(8):928. https://doi.org/10.3390/atmos16080928
Chicago/Turabian StyleLayioye, Okikiade Adewale, Pius Adewale Owolawi, and Joseph Sunday Ojo. 2025. "Time Series Prediction and Modeling of Visibility Range with Artificial Neural Network and Hybrid Adaptive Neuro-Fuzzy Inference System" Atmosphere 16, no. 8: 928. https://doi.org/10.3390/atmos16080928
APA StyleLayioye, O. A., Owolawi, P. A., & Ojo, J. S. (2025). Time Series Prediction and Modeling of Visibility Range with Artificial Neural Network and Hybrid Adaptive Neuro-Fuzzy Inference System. Atmosphere, 16(8), 928. https://doi.org/10.3390/atmos16080928