An Online Hybrid Model for Temperature Prediction of Wind Turbine Gearbox Components
<p>The overall framework of the proposed model.</p> "> Figure 2
<p>The construction process of modeling data for temperature prediction model.</p> "> Figure 3
<p>The basic structure of long short term memory (LSTM) network.</p> "> Figure 4
<p>The decomposition results of different wind speed series by the empirical mode decomposition (EMD) algorithm: (<b>a</b>) wind speed series 1; (<b>b</b>) wind speed series 2.</p> "> Figure 5
<p>The decomposition results of different wind speed series by variational mode decomposition (VMD) algorithm: (<b>a</b>) wind speed series 1; (<b>b</b>) wind speed series 2.</p> "> Figure 6
<p>The comparison of different models for gearbox oil temperature prediction in #1.</p> "> Figure 7
<p>The comparison of different models for gearbox oil temperature prediction in wind #2.</p> "> Figure 8
<p>The comparison of different models for gearbox oil temperature prediction in #3.</p> "> Figure 9
<p>The comparison of different models for gearbox input shaft temperature prediction in #1.</p> "> Figure 10
<p>The comparison of different models for gearbox input shaft temperature prediction in #2.</p> "> Figure 11
<p>The comparison of different models for gearbox input shaft temperature prediction in #3.</p> "> Figure 12
<p>The comparison of different models for gearbox output shaft temperature prediction in #1.</p> "> Figure 13
<p>The comparison of different models for gearbox output shaft temperature prediction in #2.</p> "> Figure 14
<p>The comparison of different models for gearbox output shaft temperature prediction in #3.</p> ">
Abstract
:1. Introduction
2. Methodology
2.1. The Overall Framework of the Proposed Model
- The original temperature series was predicted by the LSTM model to generate preliminary prediction results. Meanwhile, error series was generated by comparing predicted values with actual values.
- Faced with the non-stationary, high-frequency and chaotic characteristics of error series, the VMD decomposition algorithm was employed to decompose it into sub-sequences of different frequencies. In order to apply the model to the online prediction process, as shown in Figure 2, a rolling data decomposition process was developed. In Figure 2, , and represent the original temperature series, the error series of the preliminary prediction and the frequency component of error series decomposed by the VMD algorithm respectively, where i is a time label and j stands for the labels of different frequency components.
- The prediction model of each frequency component was established by the error prediction model, and the final error prediction results were reconstructed based on the adaptive error correction algorithm.
- The final forecasting results were obtained by adding the error prediction results with the preliminary temperature prediction results. When the predicted temperature exceeds a certain threshold, a high-temperature warning should be carried out.
2.2. Preliminary Prediction Model
2.3. Adaptive Error Correction Model
2.3.1. The VMD Algorithm
2.3.2. Adaptive Error Correction Algorithm
Algorithm 1 The adaptive error correction algorithm. |
|
2.4. Model Performance Evaluation
3. Case Study and Contrast Analysis
3.1. Data Description
3.2. Simulation Result
3.2.1. The Case of Decompose Algorithm
3.2.2. The Case of Gearbox Components Temperature Prediction
- (a)
- By comparing the predictive performance of LSTM, ELM, and BP, the forecasting accuracy of the LSTM model was higher than other prediction models under the same conditions. Take the prediction results of wind turbine one gearbox oil temperature as an example in Table 2, promoting of the MSE of the BP and ELM model by the LSTM model are 0.7129 and 0.4046, respectively. Thus, it can be seen that the LSTM model can learn more about the non-stationary and non-linear characteristics of temperature data to a certain extent.
- (b)
- The prediction model with error correction has higher accuracy than the single prediction model in general. There are some prediction results, such as ELM and ELM-EC prediction results of the gearbox input shaft temperature in Table 3, which can prove this point. However, there are some special cases with opposite results, which contains three LSTM and LSTM-EC prediction results of the gearbox output shaft temperature and so on in Table 4. Therefore, it can be seen that some residual series will lead to worsening correction results.
- (c)
- Whether with ELM or LSTM, the accuracy of the prediction model with adaptive error correction can be improved. For example, in the prediction results of gearbox oil temperature in Table 2, promoting of the MSE of the LSTM model by the LSTM-AEC model are 0.2317, 0.0654 and 0.0819, respectively.
- (d)
- In all the prediction models involved, the proposed hybrid model has the best forecasting performance than other comparative models. From Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, it can be seen that the predicted value of the proposed hybrid model in the high-temperature part is very accurate, which provides a guarantee for high-temperature warning of gearbox components. As shown in Figure 12 and Figure 14, the temperature of the gearbox output shaft exceeds the high-temperature warning threshold at several points in #1 and #3 respectively, such as the high-temperature series starting from time points 45, 218, 629 and 938 in #1.
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
LSTM | Long short term memory neural network |
VMD | Variational mode decomposition |
LSTM-EC | Combination of long short term memory neural network and Error correction |
LSTM-AEC | Combination of long short term memory neural network and Adaptive error correction |
SCADA | Supervisory control and data acquisition |
PCA | Principal component analysis |
DBN | Deep belief network |
ARIMA | Autoregressive integrated moving average |
ARIMA-ARCH | Combination of autoregressive integrated moving Average and autoregressive conditional heteroskedasticity |
ANN | Artificial neural network |
SVM | Support vector machine |
ELM | Extreme learning machine |
WT | Wavelet transform |
AR | Autoregressive |
WPD | Wavelet packet decomposition |
FEEMD | Fast ensemble empirical mode decomposition |
WD | Wavelet decomposition |
EMD | Empirical mode decomposition |
EEMD | Ensemble empirical mode decomposition |
CEEMDAN | Complete ensemble empirical mode decomposition |
EWT | Empirical wavelet transform |
RNN | Recurrent neural network |
ADMM | Alternate direction method |
IMF | Intrinsic mode function |
MAPE | Mean absolute percentage error |
MAE | Mean absolute error |
MSE | Mean square error |
BP | Back Propagation |
ELM-EC | Combination of extreme learning machine and error correction |
ELM-AEC | Combination of extreme learning machine and adaptive error correction |
GA | Genetic algorithm |
RBF | Radial basis function |
ICEEMDAN | Improved complementary ensemble empirical mode decomposition with adaptive noise |
Variables | Parameters |
Input vectors of LSTM neural network | |
Output of LSTM neural network | |
The output results of LSTM input gate | |
The output results of LSTM forget gate | |
The output results of LSTM output gate | |
The activation state of each cell | |
The output results of memory unit | |
, , , | The corresponding weight vectors |
, , , | The corresponding weight vectors |
, , , | The corresponding bias vectors |
, , , | Vectors of all 1 corresponding to , , , |
Transposition operation | |
Dirac distribution | |
Intrinsic mode function | |
Center frequencies of corresponding modes | |
K | Total number of modal components |
f | The decomposed original signal |
Quadratic multiplication factor | |
Lagrangian multipliers | |
The -norm symbol | |
n | The number of iterations |
The frequency form of the corresponding signal | |
Sign function | |
Update coefficient of | |
d | Result of error prediction |
m | Error series after correction |
c | Error series before correction |
The absolute value symbol | |
g | Difference between and |
, , | Threshold of Algorithm 1 |
The original temperature series | |
The error series of the preliminary prediction | |
The frequency component decomposed by the VMD algorithm | |
wind tubine one, wind turbine two and wind turbine three |
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Methods | Article | Data | Model | |
---|---|---|---|---|
prediction methods | statistical methods | Masseran et al. [15] | single-variable | ARIMA-ARCH |
Poggi et al. [16] | single-variable | AR | ||
conventional machine learning methods | Huang et al. [12] | multi-variable | PCA, NARX | |
Li et al. [17] | single-variable | ANN, RBF | ||
Abdoos et al. [18] | single-variable | ELM | ||
deep learning methods | Wang et al. [13] | multi-variable | DBN | |
Wang et al. [19] | single-variable | DBN | ||
Wang et al. [20] | single-variable | CNN | ||
optimization methods | signal processing techniques | Liu et al. [22] | single-variable | WPD, FEEMD |
Mi et al. [23] | single-variable | WPD, EMD | ||
Naik et al. [24] | single-variable | VMD | ||
parameter optimization techniques | Meng et al. [25] | single-variable | crisscross optimization | |
Liu et al. [26] | multi-variable | GA | ||
error correction techniques | Wang et al. [27] | single-variable | Markov | |
Wang et al. [28] | single-variable | ICEEMDAN-ARIMA |
Model | Wind Turbine One | Wind Turbine Two | Wind Turbine Three | ||||||
---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MAPE | MSE | MAE | MAPE | MSE | MAE | MAPE | |
BP | 1.5008 | 0.9053 | 1.6086 | 1.5409 | 0.9932 | 1.8618 | 1.7483 | 1.0916 | 1.7954 |
ELM | 1.1925 | 0.8580 | 1.4192 | 0.7639 | 0.6582 | 1.2515 | 1.8713 | 1.1128 | 1.7849 |
LSTM | 0.7879 | 0.6476 | 1.0912 | 0.7425 | 0.6000 | 1.1564 | 0.7419 | 0.6194 | 1.0679 |
ELM-EC | 0.8974 | 0.5929 | 1.0725 | 0.9790 | 0.6494 | 1.2663 | 0.9749 | 0.6270 | 1.1342 |
LSTM-EC | 0.7373 | 0.5228 | 0.9471 | 0.8368 | 0.5815 | 1.1278 | 0.8096 | 0.5618 | 1.0225 |
ELM-AEC | 0.6858 | 0.5438 | 0.9686 | 0.7066 | 0.5819 | 1.1310 | 0.7355 | 0.5911 | 1.0601 |
LSTM-AEC | 0.5562 | 0.4902 | 0.8728 | 0.6771 | 0.5343 | 1.0401 | 0.6600 | 0.5426 | 0.9691 |
Model | Wind Turbine One | Wind Turbine Two | Wind Turbine Three | ||||||
---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MAPE | MSE | MAE | MAPE | MSE | MAE | MAPE | |
BP | 2.5913 | 1.0706 | 1.8015 | 1.9533 | 0.9144 | 1.6179 | 2.6841 | 1.0255 | 1.6514 |
ELM | 1.6284 | 1.0104 | 1.5815 | 1.3447 | 0.7964 | 1.3750 | 2.3209 | 1.1940 | 1.8400 |
LSTM | 1.1318 | 0.7194 | 1.2076 | 1.1029 | 0.5708 | 1.0103 | 1.6469 | 0.7458 | 1.1956 |
ELM-EC | 1.4474 | 0.7071 | 1.1817 | 1.4839 | 0.7152 | 1.2518 | 2.3193 | 0.8454 | 1.3877 |
LSTM-EC | 1.2412 | 0.6557 | 1.0925 | 1.2526 | 0.6527 | 1.1379 | 1.9056 | 0.7704 | 1.2582 |
ELM-AEC | 1.1376 | 0.6430 | 1.0502 | 1.2871 | 0.6593 | 1.1627 | 1.6162 | 0.7207 | 1.1668 |
LSTM-AEC | 1.0052 | 0.5630 | 0.9349 | 1.0691 | 0.5704 | 0.9981 | 1.5309 | 0.6614 | 1.0809 |
Model | Wind Turbine One | Wind Turbine Two | Wind Turbine Three | ||||||
---|---|---|---|---|---|---|---|---|---|
MSE | MAE | MAPE | MSE | MAE | MAPE | MSE | MAE | MAPE | |
BP | 3.9916 | 1.2172 | 2.0092 | 3.1086 | 1.1294 | 1.9873 | 3.5203 | 1.2143 | 1.9511 |
ELM | 3.1493 | 1.3990 | 2.1770 | 2.0997 | 0.9992 | 1.7154 | 3.4253 | 1.4656 | 2.2725 |
LSTM | 2.2322 | 0.9961 | 1.7227 | 1.7538 | 0.8150 | 1.4096 | 2.3699 | 0.9408 | 1.5193 |
ELM-EC | 3.1834 | 1.0349 | 1.7282 | 2.4298 | 0.9219 | 1.5838 | 3.4413 | 1.0565 | 1.7332 |
LSTM-EC | 2.7991 | 0.9691 | 1.6238 | 2.1177 | 0.8580 | 1.4753 | 3.0108 | 0.9840 | 1.6220 |
ELM-AEC | 2.2232 | 0.8794 | 1.4491 | 2.0220 | 0.8294 | 1.4387 | 2.4348 | 0.9101 | 1.4894 |
LSTM-AEC | 2.0654 | 0.8140 | 1.3872 | 1.6990 | 0.7347 | 1.2785 | 2.2739 | 0.8257 | 1.3676 |
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Share and Cite
Zhao, Q.; Bao, K.; Wang, J.; Han, Y.; Wang, J. An Online Hybrid Model for Temperature Prediction of Wind Turbine Gearbox Components. Energies 2019, 12, 3920. https://doi.org/10.3390/en12203920
Zhao Q, Bao K, Wang J, Han Y, Wang J. An Online Hybrid Model for Temperature Prediction of Wind Turbine Gearbox Components. Energies. 2019; 12(20):3920. https://doi.org/10.3390/en12203920
Chicago/Turabian StyleZhao, Qiang, Kunkun Bao, Jia Wang, Yinghua Han, and Jinkuan Wang. 2019. "An Online Hybrid Model for Temperature Prediction of Wind Turbine Gearbox Components" Energies 12, no. 20: 3920. https://doi.org/10.3390/en12203920