An Interval Forecasting Model Based on Phase Space Reconstruction and Weighted Least Squares Support Vector Machine for Time Series of Dissolved Gas Content in Transformer Oil
Abstract
:1. Introduction
2. Related Work
3. Fundamentals of bootstrap and PSR-CRO-WLSSVM Model
3.1. Phase Space Reconstruction
3.2. Weighted Least Squares Support Vector Machine
3.2.1. Least Squares Support Vector Machine
3.2.2. Weighted LSSVM
- Step 1:
- Given training data set find the optimal parameters (through the following chemical reaction optimization algorithm).For the optimal parameter, is calculated by Equation (20).
- Step 2:
- The robust estimate is calculated based on the distribution of error
- Step 3:
- According to Equation (21), the corresponding weight value is determined by .
- Step 4:
- According to Equation (21), a* and b* are solved, and the final nonlinear prediction model is given as Equation (23):
3.3. Chemical Reaction Optimization
- Step 1:
- Initializes the chemical reaction optimization algorithm. It is necessary to determine the number of initial molecules in the container (PopSize), the upper limit (KELossRate) of the percentage of KE loss in the wall-hitting reaction, the determinants of molecular reaction type (MoleColl), the determinants of monomolecular reaction type (α), the determinants of multi-molecular reaction type (β), the maximum iteration times (Iteration), etc.
- Step 2:
- Calculate the initial potential energy of each molecule, and take the molecular KE initial value as the initial kinetic energy.
- Step 3:
- Iteratively optimize the molecules in the container through four basic reaction operators. Only one basic reaction operator is executed in each iteration. The optimization process of each iteration consists of three judgment processes, which are reaction type, monomolecular reaction type, and intermolecular reaction type.
- Step 4:
- Set the objective function. If the molecule meets the stop condition of the algorithm, the optimization calculation will be terminated. The smallest PE molecule is the global optimal solution, and the corresponding solution is the initial kernel width and penalty coefficient of the optimized WLSSVM, which can be assigned to WLSSVM to obtain the forecasting model of dissolved gas content.
3.4. Bootstrap
- Step 1:
- Assume that the original sample is the original sample is divided into partially overlapping blocks which can be expressed as , where the length of the block is , and the generated block set can be expressed as .
- Step 2:
- Extract R blocks from with replacement, and construct a sample , where .
- Step 3:
- Define the newly generated subsample as , where the length of the subsample is .
- Step 4:
- Repeat steps 1 to 3 M times to construct M subsamples in sequence.
4. Transformer Forecasting Model Based on bootstrap and PSR-CRO-WLSSVM
4.1. Parameter Selection
4.2. Evaluation Index
4.3. Modeling Process of bootstrap and PSR-CRO-WLSSVM
5. Experimental study
5.1. Forecasting Examples
5.2. Comparison Results of Different Models
6. Conclusions
- (1)
- WLSSVM is used as a forecasting model to predict small samples, and PSR method is introduced into the forecasting of oil-dissolved gas of transformer. The PSR method based on chaos theory considers the autocorrelation of gas time, fully excavates the inherent laws and characteristics contained in historical data, and realizes the preprocessing and feature extraction of gas data. Meanwhile, the global search advantage of CRO is used to optimize the forecasting model. The results show that the above method can effectively help the WLSSVM model to improve the forecasting accuracy of dissolved gas in oil.
- (2)
- By combining the bootstrap method with the PSR-CRO-WLLSVM, a model for both point forecasting and interval forecasting was constructed. This method considers the data noise error and model error, which can describe the accuracy of the forecasting and the uncertainty of the forecasting. Compared with BPNN and LSSVM in the aspect of point forecasting and interval forecasting, the model presented in this paper has the best performance in five indexes such as MASE, CWC, etc.
- (3)
- The actual case analysis proves that by combining the results of point forecasting and interval forecasting, the model in this paper can closely follow the change trend of dissolved gas, and discover potential risks through the change of uncertainty of interval. At the same time, the output result of the model can be used as the input parameter of fault diagnosis method for real-time fault forecasting, which provides more comprehensive decision support for the development trend, hidden risks, and fault analysis of dissolved gas.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Gas | Index | Delay time (τ) | |||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 20 | ||
H2 | S1 | 0.403 | 0.338 | 0.290 | 0.248 | 0.223 | 0.201 | 0.173 | 0.147 | 0.136 | 0.112 | 0.074 | 0.079 | 0.012 | |
S2 | 0.178 | 0.165 | 0.150 | 0.131 | 0.121 | 0.112 | 0.097 | 0.081 | 0.079 | 0.065 | 0.043 | 0.046 | 0.012 | ||
S3 | 0.225 | 0.173 | 0.140 | 0.116 | 0.102 | 0.089 | 0.076 | 0.066 | 0.056 | 0.046 | 0.031 | 0.033 | 0.000 | ||
C2H2 | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 65 | ||
S1 | 0.451 | 0.433 | 0.420 | 0.412 | 0.405 | 0.404 | 0.398 | 0.401 | 0.399 | 0.399 | 0.398 | 0.394 | 0.304 | ||
S2 | 0.136 | 0.132 | 0.128 | 0.126 | 0.124 | 0.126 | 0.119 | 0.126 | 0.125 | 0.125 | 0.129 | 0.126 | 0.198 | ||
S3 | 0.315 | 0.300 | 0.292 | 0.285 | 0.281 | 0.279 | 0.278 | 0.275 | 0.274 | 0.273 | 0.269 | 0.268 | 0.106 | ||
C2H6 | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 37 | ||
S1 | 0.439 | 0.392 | 0.355 | 0.333 | 0.315 | 0.297 | 0.293 | 0.288 | 0.273 | 0.266 | 0.252 | 0.255 | 0.159 | ||
S2 | 0.193 | 0.192 | 0.182 | 0.178 | 0.170 | 0.161 | 0.162 | 0.162 | 0.151 | 0.151 | 0.140 | 0.144 | 0.103 | ||
S3 | 0.246 | 0.200 | 0.172 | 0.155 | 0.145 | 0.136 | 0.131 | 0.126 | 0.121 | 0.115 | 0.112 | 0.110 | 0.056 | ||
CH4 | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 59 | ||
S1 | 0.434 | 0.396 | 0.376 | 0.368 | 0.357 | 0.359 | 0.341 | 0.344 | 0.332 | 0.335 | 0.342 | 0.329 | 0.098 | ||
S2 | 0.180 | 0.182 | 0.185 | 0.188 | 0.188 | 0.193 | 0.183 | 0.188 | 0.180 | 0.185 | 0.193 | 0.184 | 0.068 | ||
S3 | 0.254 | 0.214 | 0.191 | 0.179 | 0.169 | 0.166 | 0.158 | 0.156 | 0.153 | 0.150 | 0.149 | 0.144 | 0.031 | ||
CO2 | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 32 | ||
S1 | 0.415 | 0.361 | 0.310 | 0.272 | 0.252 | 0.224 | 0.223 | 0.218 | 0.194 | 0.178 | 0.176 | 0.154 | 0.052 | ||
S2 | 0.160 | 0.151 | 0.135 | 0.123 | 0.119 | 0.108 | 0.110 | 0.110 | 0.096 | 0.092 | 0.091 | 0.082 | 0.031 | ||
S3 | 0.255 | 0.210 | 0.174 | 0.149 | 0.134 | 0.116 | 0.112 | 0.108 | 0.098 | 0.086 | 0.085 | 0.072 | 0.021 | ||
CO | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 34 | ||
S1 | 0.428 | 0.376 | 0.337 | 0.316 | 0.291 | 0.273 | 0.257 | 0.238 | 0.227 | 0.209 | 0.204 | 0.195 | 0.024 | ||
S2 | 0.184 | 0.177 | 0.166 | 0.161 | 0.150 | 0.143 | 0.135 | 0.125 | 0.122 | 0.110 | 0.108 | 0.101 | 0.021 | ||
S3 | 0.244 | 0.199 | 0.171 | 0.155 | 0.141 | 0.131 | 0.122 | 0.113 | 0.106 | 0.099 | 0.096 | 0.093 | −0.002 | ||
O2 | Delay time (τ) | ||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | … | 37 | ||
S1 | 0.391 | 0.321 | 0.271 | 0.229 | 0.207 | 0.172 | 0.147 | 0.140 | 0.116 | 0.163 | 0.101 | 0.128 | 0.071 | ||
S2 | 0.143 | 0.125 | 0.113 | 0.100 | 0.088 | 0.086 | 0.075 | 0.062 | 0.055 | 0.078 | 0.048 | 0.066 | 0.069 | ||
S3 | 0.248 | 0.196 | 0.158 | 0.128 | 0.119 | 0.086 | 0.072 | 0.078 | 0.061 | 0.085 | 0.053 | 0.062 | 0.002 |
Gases | |||
---|---|---|---|
H2 | 11 | 20 | 3 |
C2H2 | 5 | 65 | 12 |
C2H6 | 6 | 37 | 8 |
CH4 | 5 | 59 | 13 |
CO2 | 6 | 32 | 7 |
CO | 12 | 34 | 4 |
O2 | 9 | 37 | 6 |
Key Parameters | Value |
---|---|
τ | 11 |
m | 3 |
Penalty coefficient γ | 0.1–100 |
Kernel width σ | 0.01–30 |
Kernel function | RBF |
Epochs | 4000 |
Initial number of molecules | 80 |
Upper limit of KE loss | 0.3 |
MoleColl | 0.3 |
α | 500 |
β | 15 |
k fold cross validation | 5 |
Iteration | 5000 |
Parameters | D1 | D2 |
---|---|---|
γ | 50.848 | 16.876 |
σ | 0.0945 | 0.0313 |
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Yuan, F.; Guo, J.; Xiao, Z.; Zeng, B.; Zhu, W.; Huang, S. An Interval Forecasting Model Based on Phase Space Reconstruction and Weighted Least Squares Support Vector Machine for Time Series of Dissolved Gas Content in Transformer Oil. Energies 2020, 13, 1687. https://doi.org/10.3390/en13071687
Yuan F, Guo J, Xiao Z, Zeng B, Zhu W, Huang S. An Interval Forecasting Model Based on Phase Space Reconstruction and Weighted Least Squares Support Vector Machine for Time Series of Dissolved Gas Content in Transformer Oil. Energies. 2020; 13(7):1687. https://doi.org/10.3390/en13071687
Chicago/Turabian StyleYuan, Fang, Jiang Guo, Zhihuai Xiao, Bing Zeng, Wenqiang Zhu, and Sixu Huang. 2020. "An Interval Forecasting Model Based on Phase Space Reconstruction and Weighted Least Squares Support Vector Machine for Time Series of Dissolved Gas Content in Transformer Oil" Energies 13, no. 7: 1687. https://doi.org/10.3390/en13071687