# Data–Driven Fault Diagnosis of a Wind Farm Benchmark Model

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## Abstract

**:**

## 1. Introduction

## 2. Wind Farm Benchmark Model

#### 2.1. Wind Farm Fault Scenario and Model Parameters

## 3. Data-Driven Fault Diagnosis Strategies

#### 3.1. Fault Diagnosis Scheme

#### 3.2. Fault Sensitivity Analysis for the Wind Farm System

#### 3.3. Fuzzy System Modelling

- the data matrix $\mathbf{Z}$ of Equation (13) is defined;
- the so-called fuzzy partition matrix $\mathbf{U}=\left[{\mu}_{ik}\right]$ is defined, which contains the values of the membership function for the couple i-th measurement/k-th cluster;
- the vector $\mathbf{V}=[{\mathbf{v}}_{1},\phantom{\rule{0.166667em}{0ex}}\dots ,\phantom{\rule{0.166667em}{0ex}}{\mathbf{v}}_{{n}_{C}}]$ containing the cluster prototypes is defined; they have to be determined and represent the centres from which the distance of each measurement is computed.

#### 3.3.1. Fuzzy Model Parameter Estimation

#### 3.4. Neural Network Modelling

#### 3.4.1. Fault Diagnosis Design Procedure

## 4. Model-Based Fault Diagnosis Method

## 5. Simulation Results

#### 5.1. Fuzzy Estimator Results

#### 5.2. Neural Network Estimator Results

#### 5.3. Fault Diagnosis NLGA Simulations

#### 5.4. Validation and Comparative Analysis

**False Alarm Rate**(FAR): the ratio between the number of wrongly detected faults and the number of simulated faults;**Missed Fault Rate**(MFR): the ratio between the total number of missed faults (detection/isolation) and the number of simulated faults;**True Fault diagnosis Rate**(TFR): the ratio between the number of correctly detected/isolated faults and the number of simulated faults (complementary to MFR);**Mean Fault diagnosis Delay**(MFD): the delay time between the fault occurrence and the fault detection/isolation.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Sample Availability: The software simulation codes for the proposed control strategies and the simulated wind farm benchmark are available from the authors in the MATLAB and Simulink environments. |

**Figure 4.**The general estimator scheme for the reconstruction of the equivalent input or output faults, ${f}_{u}$ or ${f}_{y}$.

**Figure 5.**The nonlinear autoregressive neural network with exogenus input topology (NN–NARX) used to reconstruct of the general fault signal ${\widehat{f}}_{i}\left(k\right)$.

**Figure 6.**Neural networks and fuzzy model similarity in the general design procedure. NN: neural network; TS: Takagi–Sugeno.

**Figure 8.**Fault 1 estimator residual ${r}_{1}\left(k\right)$ (continuous lines) and its threshold level (dotted line).

**Figure 9.**Fault 2 estimator residual ${r}_{2}\left(k\right)$ (continuous lines) and its threshold level (dotted line).

**Figure 10.**Fault 3 estimator residual ${r}_{3}\left(k\right)$ (continuous lines) and its threshold level (dotted line).

Fault # | Fault Cause | Description | Fault Effect |
---|---|---|---|

1 | Blade surface debris build-up | Scaling factor (aerodyn. model) | Reduced generated power |

2 | Blade misalignment | Sensor offset | Measured pitch angle offset |

3 | Drive-train wear and tear | Drive-train model params. | Generator speed oscillation |

Variable Name | Parameter Value |
---|---|

R | 57.5 m |

${\tau}_{p}$ | 1.2 rad/s |

${\gamma}_{p}$ | 1000 W |

${\sigma}_{p}$ | 10 Hz |

${\tau}_{\beta}$ | 1.6 rad/s |

${\omega}_{g,max}$ | 158 rad/s |

Residual/Fault | ${\mathit{f}}_{1}$ | ${\mathit{f}}_{2}$ | … | ${\mathit{f}}_{\mathit{r}}$ | ${\mathit{f}}_{\mathit{r}+1}$ | ${\mathit{f}}_{\mathit{r}+2}$ | … | ${\mathit{f}}_{\mathit{r}+\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|

${r}_{1}$ | 1 | 0 | … | 0 | 0 | 0 | … | 0 |

${r}_{2}$ | 0 | 1 | … | 0 | 0 | 0 | … | 0 |

⋮ | ⋱ | … | ⋮ | |||||

${r}_{r}$ | 0 | 0 | … | 1 | 0 | 0 | … | 0 |

${r}_{r+1}$ | 0 | 0 | … | 0 | 1 | 0 | … | 0 |

${r}_{r+2}$ | 0 | 0 | … | 0 | 0 | 1 | … | 0 |

⋮ | … | ⋱ | ⋮ | |||||

${r}_{r+m}$ | 0 | 0 | … | 0 | 0 | 0 | … | 1 |

Fault Case ${\mathit{f}}_{\mathit{i}}\left(\mathit{k}\right)$ | Most Sensitive Measurements ${\mathit{u}}_{\mathit{j}}\left(\mathit{k}\right)$ and ${\mathit{y}}_{\mathit{l}}\left(\mathit{k}\right)$ |
---|---|

1 | ${\beta}_{2}$, ${P}_{g,2}$, ${\beta}_{7}$, ${P}_{g,7}$, ${v}_{w,m}$ |

2 | ${\beta}_{1}$, ${\omega}_{g,1}$, ${\beta}_{5}$, ${\omega}_{g,5}$, ${v}_{w,m}$ |

3 | ${\beta}_{6}$, ${P}_{g,6}$, ${\beta}_{8}$, ${\omega}_{g,8}$, ${v}_{w,m}$ |

Fault | # Affected Turbine: (i, j) | Time (s) |
---|---|---|

1 | # 7: (3, 1) | 1000–1100 |

# 2: (1, 2) | 3000–3100 | |

2 | # 1: (1, 1) | 1300–1400 |

# 5: (2, 2) | 3300–3400 | |

3 | # 6: (2, 3) | 1600–1700 |

# 8: (3, 2) | 3600–3700 |

2*Data Set | RMSE (%) | ||
---|---|---|---|

Fault 1 Estimator | Fault 2 Estimator | Fault 3 Estimator | |

Estimation | 0.0090 | 0.0087 | 0.0092 |

Validation | 0.0103 | 0.0101 | 0.0105 |

Test | 0.0108 | 0.0103 | 0.0109 |

Fault Estimator # | 1 | 2 | 3 |
---|---|---|---|

RMSE % (training set) | 0.0089 | 0.0091 | 0.0092 |

RMSE % (validation set) | 0.0091 | 0.0093 | 0.0095 |

RMSE % (test set) | 0.0106 | 0.0104 | 0.0123 |

**Table 8.**The optimal values of the parameter $\delta $ used for fault diagnosis purposes by the designed residual generators.

Residual ${\mathit{r}}_{\mathit{i}}\left(\mathit{k}\right)={\widehat{\mathit{f}}}_{\mathit{i}}\left(\mathit{k}\right)$ | $\mathit{\delta}$ for the Fuzzy Estimators | $\mathit{\delta}$ for the Neural Network Estimators |
---|---|---|

1 | 2.15 | 2.34 |

2 | 2.23 | 2.45 |

3 | 2.34 | 2.89 |

**Table 9.**RMSE of the nonlinear differential geometric approach (NLGA) fault estimator with disturbance decoupling.

Fault Case | Fault 1 Estimator | Fault 2 Estimator | Fault 3 Estimator |
---|---|---|---|

RMSE (%) | 0.0007 | 0.0008 | 0.0009 |

Parameter | Nominal Value | Error Value |
---|---|---|

$\rho $ | 1.225 kg/m${}^{3}$ | $\pm 20\%$ |

J | 7.794 × 10${}^{6}$ kg/m${}^{3}$ | $\pm 30\%$ |

${C}_{p}$ | ${C}_{p0}$ | $\pm 50\%$ |

**Table 11.**Comparison of the fault diagnosis results with the different fault diagnosis strategies. FF: fuzzy filter; IPE: interval parity equation; NLGA-AF: NLGA adaptive filter; NNF: neural network filter; CBD: CUSUM–based detection.

Fault Case | Index | FF | NNF | NLGA-AF | CBD | IPE |
---|---|---|---|---|---|---|

1 | FAR | 0.0010 | 0.0010 | 0.0006 | 0.0013 | 0.0024 |

MFR | 0.0010 | 0.0010 | 0.0007 | 0.0000 | 0.0005 | |

TFR | 0.9990 | 0.9990 | 0.9994 | 0.9999 | 0.9995 | |

MFD (s) | 0.02 | 0.01 | 0.007 | 4.7 | 1.1 | |

2 | FAR | 0.0010 | 0.2280 | 0.0004 | 0.0111 | 0.0015 |

MFR | 0.0030 | 0.0010 | 0.0005 | 0.0015 | 0.0005 | |

TFR | 0.9970 | 0.9990 | 0.9996 | 0.9985 | 0.9995 | |

MFD (s) | 0.08 | 0.08 | 0.008 | ND | 12.4 | |

3 | FAR | 0.0030 | 0.0010 | 0.0005 | 0.0055 | 0.0007 |

MFR | 0.0080 | 0.0010 | 0.0006 | 0.0000 | 0.0010 | |

TFR | 0.9920 | 0.9990 | 0.9995 | 0.9999 | 0.9990 | |

MFD (s) | 0.02 | 0.01 | 0.006 | 13.1 | 15.2 |

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**MDPI and ACS Style**

Simani, S.; Castaldi, P.; Farsoni, S.
Data–Driven Fault Diagnosis of a Wind Farm Benchmark Model. *Energies* **2017**, *10*, 866.
https://doi.org/10.3390/en10070866

**AMA Style**

Simani S, Castaldi P, Farsoni S.
Data–Driven Fault Diagnosis of a Wind Farm Benchmark Model. *Energies*. 2017; 10(7):866.
https://doi.org/10.3390/en10070866

**Chicago/Turabian Style**

Simani, Silvio, Paolo Castaldi, and Saverio Farsoni.
2017. "Data–Driven Fault Diagnosis of a Wind Farm Benchmark Model" *Energies* 10, no. 7: 866.
https://doi.org/10.3390/en10070866