A Hybrid Method for Prediction of Ash Fouling on Heat Transfer Surfaces
Abstract
:1. Introduction
- By employing the EMD, the denoised cleanliness factor data is decomposed into several intrinsic mode functions (IMFs) and a residual sequence;
- The SVR model is utilized to fit the residual signal, which can capture the long-term cleanliness factor degeneration. Meanwhile, the Gaussian process regression (GPR) model is applied to fit the IMFs separately, which can capture the local fluctuations;
- The predictive property of several machine learning models are investigated, and the results prove that the combined SVR + GPR model outperforms other models;
- For both the one-step- and multistep-ahead cleanliness factor predictions, the proposed hybrid method has high precision and good extrapolating performance.
2. Problem Statement and Data Description
3. Techniques
3.1. Empirical Mode Decomposition
- In the total dataset, the number of extrema and the number of zero-crossings must be equal, or at most, different by one;
- At any dot, the envelopes that are defined by the local extrema must produce a zero mean.
- Step 1:
- According to the upper and lower extreme points of the original signal, the upper and lower envelope lines are drawn respectively.
- Step 2:
- Take the mean of the upper and lower envelope and plot the mean envelope.
- Step 3:
- Subtracting the mean envelope from the original signal gives the intermediate signal.
- Step 4:
- Judge whether the intermediate signal meets the above two conditions. If so, the signal is an IMF component. If not, perform step 1 to step 4 analysis again based on this signal. Obtaining IMF components usually requires several iterations.
- Step 5:
- Each time you get an IMF, subtract it from the original signal and repeat the above steps, all the way to the end where the signal is just a monotone sequence or a constant sequence.
3.2. Support Vector Regression
3.3. Gaussian Process Regression
3.4. Overall Structure
- Step 1:
- For data preprocessing, the original cleanliness factor degradation data is denoised by using the wavelet threshold denoising theory. Then, the EMD technique is utilized to decouple the data into several IMFs and a residual. For the model part, the suitable kernel functions are chosen for SVR and GPR, respectively. Initialize the parameters for both the SVR and GPR models.
- Step 2:
- For the residual sequence, train the SVR model to fit the residual signal. For the IMFs, train the GPR models to fit the IMFs separately.
- Step 3:
- Apply the well-trained SVR model to forecast the future residual value, and use the well-trained GPR models to predict the values of each IMF. Combine these results to obtain the predicted cleanliness factor value.
4. Results and Discussions
4.1. Preprocessing
4.2. Accuracy Indicators
- Root mean square error (RMSE):
- Mean absolute percentage error (MAPE):
- Mean absolute error (MAE):
4.3. Performance Comparison of Multifarious Models
4.4. Prediction Results
4.4.1. One-Step Prediction
4.4.2. Multistep Prediction
4.5. Discussions
5. Conclusions
- The long-term cleanliness factor degeneration was exactly captured by the SVR, while the local undulations were well expressed by means of GPR, further leading to advanced predicted results;
- Compared with the sole SVR, sole GPR, SVR + EMD and GPR + EMD models, our proposed SVR + GPR model is better than other models;
- In both the one-step- and multistep-ahead cleanliness factor forecasts, the combined SVR + GPR model obtained satisfactory extrapolation capability.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Methods | SVR | GPR | SVR + EMD | GPR + EMD | SVR + GPR |
---|---|---|---|---|---|
RMSE | 0.00163 | 0.00092 | 0.00015 | 0.00020 | 0.00006 |
MAPE | 0.02503 | 0.02537 | 0.00019 | 0.00022 | 0.00008 |
MAE | 0.00117 | 0.00067 | 0.00012 | 0.00014 | 0.00005 |
Devices | Reheater | LTS | HTS |
---|---|---|---|
RMSE | 0.00004 | 0.00006 | 0.00002 |
MAPE | 0.00006 | 0.00009 | 0.00002 |
MAE | 0.00003 | 0.00005 | 0.00001 |
Steps | Three-Step | Six-Step | Nine-Step |
---|---|---|---|
RMSE | 0.00074 | 0.00174 | 0.00273 |
MAPE | 0.00067 | 0.00167 | 0.00258 |
MAE | 0.00044 | 0.00109 | 0.00169 |
Steps | Three-Step | Six-Step | Nine-Step |
---|---|---|---|
RMSE | 0.00043 | 0.00085 | 0.00123 |
MAPE | 0.00048 | 0.00099 | 0.00146 |
MAE | 0.00028 | 0.00058 | 0.00086 |
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Cui, F.; Qin, S.; Zhang, J.; Li, M.; Shi, Y. A Hybrid Method for Prediction of Ash Fouling on Heat Transfer Surfaces. Energies 2022, 15, 4658. https://doi.org/10.3390/en15134658
Cui F, Qin S, Zhang J, Li M, Shi Y. A Hybrid Method for Prediction of Ash Fouling on Heat Transfer Surfaces. Energies. 2022; 15(13):4658. https://doi.org/10.3390/en15134658
Chicago/Turabian StyleCui, Fangshu, Sheng Qin, Jing Zhang, Mengwei Li, and Yuanhao Shi. 2022. "A Hybrid Method for Prediction of Ash Fouling on Heat Transfer Surfaces" Energies 15, no. 13: 4658. https://doi.org/10.3390/en15134658