# Early Fault Detection of Wind Turbines Based on Operational Condition Clustering and Optimized Deep Belief Network Modeling

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- A general multioperation condition partition scheme is proposed to partition normal state data into several different clusters. Then, normal behaviors are built under different condition clusters. This divide-and-conquer strategy can help reduce false alarms caused by methods that only consider a single operating condition.
- (2)
- An optimized DBN (ODBN) model with CSO is designed to capture the normal behavior in each cluster, which reduces the complexity of parameter selection of DBNs. To the best of our knowledge, it is the first time DBN is applied to deal with complex SCADA data from wind turbines for the purpose of fault detection.
- (3)
- A real case from wind turbine main bearing fault was used to evaluate the performance of the proposed health monitoring approach using the SCADA data of multiple wind turbines from a real wind farm, and comparative studies were conducted.

## 2. Problem Description

## 3. Proposed Health Monitoring Framework

- (1)
- Collect normal SCADA data from multiple wind turbines on a wind farm.
- (2)
- Choose operation parameters that characterize the complex operating conditions of wind turbines and segment the operation parameter data into K clusters using the k-means method and silhouette index. The obtained K clusters represent the corresponding K operating conditions, i.e., $[{C}_{1},{C}_{2},\cdots ,{C}_{K}]$. Then, divide the normal state data into corresponding K parts based on the partitioned operating conditions.
- (3)
- Select appropriate modeling variables for each operating condition by combining three variable selection techniques, and the final selected variables for different operating clusters can be represented as $[{V}_{1},{V}_{2},\cdots ,{V}_{K}]$.
- (4)
- Build a normal behavior model under each operating condition using ODBNs to explore the sophisticated nonlinear characteristics among modeling variables, resulting in multiple DBN models, denoted as ${[\mathrm{DBN}}_{1},{\mathrm{DBN}}_{2},\cdots ,{\mathrm{DBN}}_{K}]$ for K operating clusters.
- (5)
- Calculate the threshold for abnormal detection under different operating conditions using the Mahalanobis distance (MD) measure to automatically identify the anomalies that occur in the operation of the wind turbines, i.e., $[{\mathrm{MD}}_{1},{\mathrm{MD}}_{2},\cdots ,{\mathrm{MD}}_{K}]$.
- (6)
- For the new incoming SCADA data, first recognize the operating condition ${C}_{i}$ that it belongs to, then select the corresponding modeling input variable ${V}_{i}$ and predict the output using the constructed DBN
_{i}. Next, compute the MD value and compare it with the threshold MD_{i}under condition ${C}_{i}$, and then output the real-time online health monitoring results.

#### 3.1. Data Preprocessing

#### 3.2. Operation Condition Partition Using K-Means Clustering

#### 3.3. Variable Selection

#### 3.4. Proposed ODBN Method

#### 3.4.1. DBN Architecture

#### 3.4.2. ODBN Method

- (1)
- Initialize the parameters, including number of chickens, dimensions of individual positions, maximum iteration number, updated frequency of chicken swarm, and proportions of roosters, hens, and mother hens.
- (2)
- Randomly produce an initial population of chickens. Train the DBN and compute the fitness values, and determine the optimal individual and global fitness values and corresponding positions. Here, the root mean square error (RMSE) of the validation set is considered as the fitness function.
- (3)
- In the next iteration, first determine the relationship between the roosters, hens, and chicks in a group, and then update their positions according to Equations (9)–(14) and calculate their fitness values. Next, update the optimal individual and global fitness values and their corresponding positions.

#### 3.5. Anomaly Detection Approach

## 4. Case Study and Discussion

#### 4.1. Data Description

#### 4.2. Model Development

#### 4.2.1. Operation Condition Partition

**C**

_{1}) and condition 2 (

**C**

_{2}).

**C**

_{1}, the range is 186.73 to 359, whereas in

**C**

_{2}, the range is 0.38 to 186.73. In terms of wind speed, ambient temperature, generator speed, and generator torque, there is little difference in the ranges under the two conditions. One can see from the comparison results that the wind turbine operating conditions are clearly partitioned according to this operation parameter, i.e., wind direction, and thus this parameter can be used for subsequent real-time condition recognition purposes. However, it is well known that wind direction ranges from 0° to 360°, so here, if the wind direction is between 359°–360° and 0°–0.38°, they will be automatically categorized as

**C**

_{1}and

**C**

_{2}separately. It should be noted that there is no theoretical (i.e., no mechanical or electrical basis) reasoning for the choice of wind direction as the partitioning parameter here and that this based purely on the analysis of the clustering data.

**C**

_{1}and

**C**

_{2}are 154,089 and 199,042, respectively.

#### 4.2.2. Parameter Selection for Each Condition Cluster

**C**

_{1}, nine state variables are regarded as

**V**

_{1}to construct the prediction model: hub temperature, generator front bearing temperature, gearbox rear bearing temperature, nacelle temperature, ambient temperature, gearbox inlet oil temperature, gearbox oil temperature, converter ambient temperature, and generator rear bearing temperature. As can be seen in Figure 8b, in addition to the nine input variables under

**C**

_{1}, blade 1 and 3 motor temperatures also meet the set threshold requirements, so 11 variables are considered to be

**V**

_{2}to develop the regression model under

**C**

_{2}. Moreover, it is not difficult to see in Figure 8 that although the Kendall technique produces relatively small values under these two conditions, a similar ordering is generated compared to the first two approaches.

#### 4.2.3. Performance Evaluation and Comparison

**C**

_{1}and

**C**

_{2}. The architecture of DBN

_{1}and DBN

_{2}is determined as 9-39-82-1 and 11-56-21-1, respectively.

^{2}), are adopted, which are defined as follows [43]:

**C**

_{1}and

**C**

_{2}are displayed in Table 5.

**C**

_{1}for the training set, validation set, and testing set, DBN

_{1}is better than the SHL-BP

_{1}, DHL-BP

_{1}, and SVM

_{1}models, as it offers the lowest RMSE, MAE, and MAPE and highest R

^{2}values. In terms of the prediction results in

**C**

_{2}, DBN

_{2}produces the lowest RMSE and MAE values and the highest R

^{2}values in the three datasets, whereas MAPE is slightly higher than the other three models. As indicated from quantitative evaluation results, the ODBNs generally get a higher modeling accuracy than the three traditional methods. The main reason is that the SHL-BP network is based on the principle of empirical minimization, which is prone to fall into local minima during the training process and thus produces poor results. At the same time, because it is difficult to train the depth structure effectively with the BP algorithm, the prediction accuracy of the DHL-BP model is not much different from that of SHL-BP model. The SVM algorithm also obtains poor prediction results because it is not suitable for large-scale training samples, whereas ODBNs can deeply learn and uncover the sophisticated nonlinear relationships among modeling variables by establishing a depth model, which results in better prediction accuracy. Hence, the proposed ODBN approach is used for real-time health monitoring of main bearings under varying operating conditions.

^{2}values. As the results indicate, the ODBNs achieve the best prediction performance compared to the other three conventional models, illustrating the predominance of DBN method in modeling. Thus, it is deemed to be the more appropriate model for monitoring the main bearing temperature.

#### 4.3. Health Monitoring Results

#### 4.3.1. Testing Normal Wind Turbine Behavior

^{2}values for the two turbines than the model without this characteristic, which illustrates the superiority of the operating condition partition. In view of the better prediction performance of the proposed method, the loss of computational cost is acceptable. The condition monitoring results are displayed in Figure 10 and Figure 11.

_{1}and MD

_{2}are 4.122 and 4.127, respectively. Since the two values in this study are not much different, they are approximated as straight in Figure 10a and Figure 11a.

#### 4.3.2. Detecting Abnormal Main Bearing Behavior

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Global Wind Statistics 2017; Global Wind Energy Council (GWEC): Brussels, Belgium, 2018.
- Takoutsing, P.; Wamkeue, R.; Ouhrouche, M.; Slaoui-Hasnaoui, F.; Tameghe, T.A.; Ekemb, G. Wind turbine condition monitoring: State-of-the-art review, new trends, and future challenges. Energies
**2014**, 7, 2595–2630. [Google Scholar] - Jiang, G.Q.; He, H.B.; Xie, P.; Tang, Y.F. Stacked multilevel-denoising autoencoders: A new representation learning approach for wind turbine gearbox fault diagnosis. IEEE. Trans. Instrum. Meas.
**2017**, 66, 2391–2402. [Google Scholar] [CrossRef] - Antoniadou, I.; Manson, G.; Staszewski, W.J.; Barszcz, T.; Worden, K. A time–frequency analysis approach for condition monitoring of a wind turbine gearbox under varying load conditions. Mech. Syst. Signal Process.
**2015**, 64, 188–216. [Google Scholar] [CrossRef] - Zhu, J.D.; Yoon, J.M.; He, D.; Bechhoefer, E. Online particle-contaminated lubrication oil condition monitoring and remaining useful life prediction for wind turbines. Wind Energy
**2015**, 18, 1131–1149. [Google Scholar] [CrossRef] - Sanchez, P.; Mendizabal, D.; Gonzalez, K.; Zamarreno, C.R.; Hernaez, M.; Matias, I.R.; Arregui, F.J. Wind turbines lubricant gearbox degradation detection by means of a lossy mode resonance based optical fiber refractometer. Microsyst. Technol.
**2016**, 22, 1619–1625. [Google Scholar] [CrossRef] - Yang, W.X.; Court, R.; Jiang, J.S. Wind turbine condition monitoring by the approach of SCADA data analysis. Renew. Energy
**2013**, 53, 365–376. [Google Scholar] [CrossRef] - Kusiak, A. Break through with big data. Ind. Eng.
**2015**, 47, 38–42. [Google Scholar] - Zaher, A.; McArthur, S.D.J.; Infield, D.J.; Patel, Y. Online wind turbine fault detection through automated SCADA data analysis. Wind Energy
**2009**, 12, 574–593. [Google Scholar] [CrossRef] - Guo, P.; Infield, D.; Yang, X.Y. Wind turbine generator condition-monitoring using temperature trend analysis. IEEE Trans. Sustain. Energy
**2012**, 3, 124–133. [Google Scholar] [CrossRef] - Kusiak, A.; Verma, A. Analyzing bearing faults in wind turbines: A data-mining approach. Renew. Energy
**2012**, 48, 110–116. [Google Scholar] [CrossRef] - Schlechtingen, M.; Santos, I.F.; Achiche, S. Wind turbine condition monitoring based on SCADA data using normal behavior models. Part 1: System description. Appl. Soft Comput.
**2013**, 13, 259–270. [Google Scholar] [CrossRef] - Schlechtingen, M.; Santos, I.F. Wind turbine condition monitoring based on SCADA data using normal behavior models. Part 2: Application examples. Appl. Soft Comput.
**2014**, 14, 447–460. [Google Scholar] [CrossRef] - Bangalore, P.; Tjernberg, L.B. An artificial neural network approach for early fault detection of gearbox bearings. IEEE Trans. Smart Grid
**2015**, 6, 980–987. [Google Scholar] [CrossRef] - Bangalore, P.; Letzgus, S.; Karlsson, D.; Patriksson, M. An artificial neural network-based condition monitoring method for wind turbines, with application to the monitoring of the gearbox. Wind Energy
**2017**, 20, 1421–1438. [Google Scholar] [CrossRef] - Bi, R.; Zhou, C.K.; Hepburn, D.M. Detection and classification of faults in pitch-regulated wind turbine generators using normal behaviour models based on performance curves. Renew. Energy
**2017**, 105, 674–688. [Google Scholar] [CrossRef] - Zhan, S.; Tao, Q.Q.; Li, X.H. Face detection using representation learning. Neurocomputing
**2016**, 187, 19–26. [Google Scholar] [CrossRef] - Wang, Y.; Wang, X.G.; Liu, W.Y. Unsupervised local deep feature for image recognition. Inf. Sci.
**2016**, 351, 67–75. [Google Scholar] [CrossRef] - Jiang, G.Q.; Xie, P.; He, H.B.; Yan, J. Wind turbine fault detection using a denoising autoencoder with temporal information. IEEE ASME Trans. Mechatron.
**2018**, 23, 89–100. [Google Scholar] [CrossRef] - Yang, Z.X.; Wang, X.B.; Zhong, J.H. Representational learning for fault diagnosis of wind turbine equipment: A multi-layered extreme learning machines approach. Energies
**2016**, 9, 379. [Google Scholar] [CrossRef] - Hinton, G.E.; Osindero, S.; Teh, Y.W. A fast learning algorithm for deep belief nets. Neural Comput.
**2006**, 18, 1527–1554. [Google Scholar] [CrossRef] - Chen, H.Z.; Wang, J.X.; Tang, B.P.; Xiao, K.; Li, J.Y. An integrated approach to planetary gearbox fault diagnosis using deep belief networks. Meas. Sci. Technol.
**2017**, 28, 025010. [Google Scholar] [CrossRef] - Wan, J.; Liu, J.F.; Ren, G.R.; Guo, Y.F.; Yu, D.R.; Hu, Q.H. Day-ahead prediction of wind speed with deep feature learning. Int. J. Pattern Recognit. Artif. Intell.
**2016**, 30, 1650011. [Google Scholar] [CrossRef] - Chen, Z.Y.; Li, W.H. Multisensor feature fusion for bearing fault diagnosis using sparse autoencoder and deep belief network. IEEE Trans. Instrum. Meas.
**2017**, 66, 1693–1702. [Google Scholar] [CrossRef] - Ren, H.; Chai, Y.; Qu, J.F.; Ye, X.; Tang, Q. A novel adaptive fault detection methodology for complex system using deep belief networks and multiple models: A case study on cryogenic propellant loading system. Neurocomputing
**2018**, 275, 2111–2125. [Google Scholar] [CrossRef] - Shao, H.D.; Jiang, H.K.; Zhang, X.; Niu, M.G. Rolling bearing fault diagnosis using an optimization deep belief network. Meas. Sci. Technol.
**2015**, 26, 115002. [Google Scholar] [CrossRef] - Unal, M.; Onat, M.; Demetgul, M.; Kucuk, H. Fault diagnosis of rolling bearings using a genetic algorithm optimized neural network. Measurement
**2014**, 58, 187–196. [Google Scholar] [CrossRef] - Qiao, W.; Lu, D.G. A survey on wind turbine condition monitoring and fault diagnosis-Part I: Components and subsystems. IEEE Trans. Ind. Electron.
**2015**, 62, 6536–6545. [Google Scholar] [CrossRef] - Kusiak, A.; Li, W.Y. The prediction and diagnosis of wind turbine faults. Renew. Energy
**2011**, 36, 16–23. [Google Scholar] [CrossRef] - Lapira, E.; Brisset, D.; Davari Ardakani, H.; Siegel, D.; Lee, J. Wind turbine performance assessment using multi-regime modeling approach. Renew. Energy
**2012**, 45, 86–95. [Google Scholar] [CrossRef] - Yang, H.H.; Huang, M.L.; Lai, C.M.; Jin, J.R. An approach combining data mining and control charts-based model for fault detection in wind turbines. Renew. Energy
**2018**, 115, 808–816. [Google Scholar] [CrossRef] - Macqueen, J. Some methods for classification and analysis of multivariate observations. In Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA, 21 June–18 July 1965; pp. 281–297. [Google Scholar]
- Jain, A.K. Data clustering: 50 years beyond k-means. Pattern Recognit. Lett.
**2010**, 31, 651–666. [Google Scholar] [CrossRef] - Rousseeuw, P. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math.
**1986**, 20, 53–65. [Google Scholar] [CrossRef] - Mazidi, P.; Bertling Tjernberg, L.; Sanz Bobi, M.A. Wind turbine prognostics and maintenance management based on a hybrid approach of neural networks and a proportional hazards model. Proc. Inst. Mech. Eng. Part O J. Risk Reliab.
**2017**, 231, 121–129. [Google Scholar] [CrossRef] - Fisher, R.A. Statistical methods for research workers. Int. J. Plant Sci.
**1954**, 21, 340–341. [Google Scholar] - Best, D.J.; Roberts, D.E. Algorithm AS 89: The upper tail probabilities of Spearman’s rho. J. R. Stat. Soc.
**1975**, 24, 377–379. [Google Scholar] [CrossRef] - Taylor, J.M.G. Kendall and Spearman correlation-coefficients in the presence of a blocking variable. Biometrics
**1987**, 43, 409–416. [Google Scholar] [CrossRef] [PubMed] - Hinton, G.E. Training products of experts by minimizing contrastive divergence. Neural Comput.
**2002**, 14, 1771–1800. [Google Scholar] [CrossRef] [PubMed] - Hinton, G.E. A practical guide to training restricted boltzmann machines. In Neural Networks: Tricks of the Trade; Springer: Berlin, Germany, 2012; Volume 7700, pp. 599–619. [Google Scholar]
- Meng, X.B.; Liu, Y.; Gao, X.Z.; Zhang, H.Z. A new bio-inspired algorithm: Chicken swarm optimization. In Swarm Intelligence; Springer International Publishing: Berlin, Germany, 2014; Volume 8794, pp. 86–94. [Google Scholar]
- Niu, G.; Singh, S.; Holland, S.W.; Pecht, M. Health monitoring of electronic products based on Mahalanobis distance and Weibull decision metrics. Microelectron. Reliab.
**2011**, 51, 279–284. [Google Scholar] [CrossRef] - Bai, Y.; Sun, Z.Z.; Zeng, B.; Deng, J.; Li, C. A multi-pattern deep fusion model for short-term bus passenger flow forecasting. Appl. Soft Comput.
**2017**, 58, 669–680. [Google Scholar] [CrossRef]

**Figure 2.**Flowchart of the proposed health monitoring framework. SCADA, supervisory control and data acquisition; DBN, deep belief network; MD, Mahalanobis distance.

**Figure 8.**Correlation coefficients with different variable selection methods for (

**a**)

**C**

_{1}and (

**b**)

**C**

_{2}.

Continuous Parameter | |||
---|---|---|---|

Gearbox oil temperature | Wind direction | Current phase C | Absolute wind direction |

Gearbox front bearing temperature | Generator speed | Converter side speed | Blade 1 motor current |

Gearbox inlet oil temperature | Gearbox speed 1 | Converter side torque | Blade 2 motor current |

Generator front bearing temperature | Wind speed 1 | Wind speed 1 s average | Blade 3 motor current |

Generator rear bearing temperature | Wind speed 2 | Wind speed 1 min average | Blade 1 motor temperature |

Generator stator winding temperature | Active power | Wind speed 10 min average | Blade 2 motor temperature |

Converter ambient temperature | Reactive power | Ambient temperature | Blade 3 motor temperature |

Gearbox rear bearing temperature | Wind speed | Main bearing temperature | Hub temperature |

Wind direction 1 s average | Voltage phase A | Nacelle temperature | Cable winding angle |

Wind direction 1 min average | Voltage phase B | Active power 1 s average | Generator torque |

Wind direction 10 min average | Voltage phase C | Active power 1 min average | |

Gearbox oil pump pressure | Current phase A | Active power 10 min average | |

Gearbox inlet oil pressure | Current phase B | Hydraulic system pressure |

Dataset | Time Stamps | Turbines Considered |
---|---|---|

Modeling | 1/7/2014–31/8/2014 | 6, 17, 24, 33–34, 37, 49, 53, 88 |

Testing normal behavior | 30/7/2014–2/8/2014 | 20 |

14/8/2014–17/8/2014 | 46 | |

Testing abnormal behavior | 10/9/2014–14/9/2014 | 42 |

2/7/2014–4/7/2014 | 13 |

Distribution | C_{1} | C_{2} |
---|---|---|

Wind speed (m/s) | 0.3–29.28 | 0.3–25.33 |

Wind direction ($\xb0$) | 186.73–359 | 0.38–186.73 |

Ambient temperature ($\xb0\mathrm{C}$) | 4.97–37.33 | 4.96–37.58 |

Generator speed (rpm) | 0.17–1852.8 | 0.17–1859.2 |

Generator torque ($\mathrm{N}\cdot \mathrm{m}$) | −970–8600 | −970–8600 |

Description | Parameter Setting |
---|---|

DBN pretraining phase | size of batch training 100, training iterations 10, learning rate 1, momentum 0 |

DBN fine-tuning phase | size of batch training 10, training iterations 20 |

CSO for optimization | max iterations 20, dimension 2, population size 20, range of each dimension [1, 100], updated frequency of chicken swarm 10, proportions of roosters, hens, and mother hens 0.15, 0.7, 0.5 |

**Table 5.**Comparison of prediction results. SHL-BP, back-propagation network with single hidden layer; DHL-BP, back-propagation network with double hidden layers; SVM, support vector machine; RMSE, root mean square error; MAE, mean absolute error; MAPE, mean absolute percentage error.

Dataset | Criteria | C_{1} | C_{2} | ||||||
---|---|---|---|---|---|---|---|---|---|

SHL-BP_{1} | DHL-BP_{1} | SVM_{1} | DBN_{1} | SHL-BP_{2} | DHL-BP_{2} | SVM_{2} | DBN_{2} | ||

Training | RMSE | 1.9274 | 1.8044 | 1.8846 | 1.1463 | 1.8365 | 1.8325 | 1.9066 | 1.0858 |

MAE | 1.5034 | 1.4665 | 1.5361 | 0.8815 | 1.4444 | 1.4880 | 1.5696 | 0.8392 | |

MAPE (%) | 0.6370 | 1.4872 | 0.7092 | 0.4393 | 0.3451 | 0.3097 | 0.9101 | 1.0432 | |

R^{2} | 0.7095 | 0.7454 | 0.7223 | 0.8973 | 0.7345 | 0.7356 | 0.7138 | 0.9072 | |

Validation | RMSE | 1.8908 | 1.8014 | 1.8898 | 1.1448 | 1.8333 | 1.8191 | 1.9108 | 1.0859 |

MAE | 1.4865 | 1.4627 | 1.5467 | 0.8822 | 1.4428 | 1.4731 | 1.5731 | 0.8329 | |

MAPE (%) | 0.6054 | 1.4638 | 0.7382 | 0.3806 | 0.2916 | 0.3384 | 0.9469 | 0.9889 | |

R^{2} | 0.7219 | 0.7476 | 0.7222 | 0.8980 | 0.7348 | 0.7388 | 0.7119 | 0.9069 | |

Testing | RMSE | 1.9255 | 1.7982 | 1.8869 | 1.1607 | 1.8188 | 1.8198 | 1.9095 | 1.0790 |

MAE | 1.4941 | 1.4625 | 1.5390 | 0.8836 | 1.4319 | 1.4787 | 1.5694 | 0.8335 | |

MAPE (%) | 0.6141 | 1.5531 | 0.7079 | 0.4485 | 0.3051 | 0.3315 | 0.9274 | 0.9726 | |

R^{2} | 0.7118 | 0.7486 | 0.7232 | 0.8953 | 0.7394 | 0.7391 | 0.7127 | 0.9083 |

Dataset | Evaluation Criteria | Model | |||
---|---|---|---|---|---|

SHL-BP | DHL-BP | SVM | DBNs | ||

Training | RMSE | 1.9784 | 1.8538 | 1.8929 | 0.9615 |

MAE | 1.5959 | 1.4438 | 1.5574 | 0.7310 | |

MAPE (%) | 0.0717 | 0.3721 | 0.7373 | 0.2933 | |

R^{2} | 0.6930 | 0.7305 | 0.7190 | 0.9275 | |

Validation | RMSE | 1.9737 | 1.8477 | 1.8879 | 0.9509 |

MAE | 1.5910 | 1.4397 | 1.5518 | 0.7242 | |

MAPE (%) | 0.0907 | 0.3959 | 0.7543 | 0.2984 | |

R^{2} | 0.6941 | 0.7319 | 0.7201 | 0.9290 | |

Testing | RMSE | 1.9680 | 1.8470 | 1.8857 | 0.9536 |

MAE | 1.5852 | 1.4366 | 1.5518 | 0.7251 | |

MAPE (%) | 0.0917 | 0.4039 | 0.7468 | 0.3066 | |

R^{2} | 0.6955 | 0.7318 | 0.7205 | 0.9285 |

Turbine | Model | Evaluation Criteria | Time (s) | |||
---|---|---|---|---|---|---|

RMSE | MAE | MAPE (%) | R^{2} | |||

20 | K-means based ODBNs | 0.8125 | 0.6621 | 0.3725 | 0.9067 | 126.541 |

ODBNs | 0.8566 | 0.7021 | 0.7172 | 0.8963 | 4.308 | |

46 | K-means based ODBNs | 1.5225 | 1.3038 | 4.1577 | 0.6272 | 124.126 |

ODBNs | 1.8409 | 1.5830 | 5.3136 | 0.4550 | 4.622 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, H.; Wang, H.; Jiang, G.; Li, J.; Wang, Y.
Early Fault Detection of Wind Turbines Based on Operational Condition Clustering and Optimized Deep Belief Network Modeling. *Energies* **2019**, *12*, 984.
https://doi.org/10.3390/en12060984

**AMA Style**

Wang H, Wang H, Jiang G, Li J, Wang Y.
Early Fault Detection of Wind Turbines Based on Operational Condition Clustering and Optimized Deep Belief Network Modeling. *Energies*. 2019; 12(6):984.
https://doi.org/10.3390/en12060984

**Chicago/Turabian Style**

Wang, Hong, Hongbin Wang, Guoqian Jiang, Jimeng Li, and Yueling Wang.
2019. "Early Fault Detection of Wind Turbines Based on Operational Condition Clustering and Optimized Deep Belief Network Modeling" *Energies* 12, no. 6: 984.
https://doi.org/10.3390/en12060984