4. Simulation results

This section summarises the simulations performed with the considered wind turbine benchmark, and the performances of the proposed fault diagnosis solutions. Due to the presence of the uncertainty and disturbance effects included in the benchmark, the robustness features of the developed fault diagnosis techniques are also verified in simulation.

With reference to the wind turbine benchmark of Section 2, all simulations are driven by the same wind mean speed sequence. It was acquired from a real measurement of wind speed, which represents a good coverage of typical operating conditions, as it ranges from 5 to 20 m/s, with a few spikes at 25 m/s, see Odgaard et al. [12]. The simulations last for 4400 s, with single fault occurrences. The discrete-time simulator runs at a sampling frequency of 100 Hz, so that N = 440,000 samples are acquired during each simulation. With reference to the different fault cases reported in Section 2.2, Table 4 shows the shape and the timing of the fault modes affecting the process. They model input (actuator) or output (sensor) additive faults, which are used for sensitivity analysis of Section 3.3.

As an example, in order to highlight the actual fault effect on the wind turbine measurements, Figure 5 shows the fault sensitivity test. In particular, the cases of the faults 1, 2, 3 and 8 in fault-free and faulty conditions are depicted.


approach is different from the one presented in Simani et al. [21], where the fuzzy

tified for each cluster by following the procedure of Section 3.1. The TS models of Eq. (13) were thus implemented and nine fault estimators were designed, built and organised into the estimator scheme in order to accomplish the fault diagnosis task,

The effectiveness of the fuzzy TS fault estimators used was assessed in terms of root mean squared error (RMSE), which is computed as the difference between the

In this case, these estimated signals ^<sup>f</sup> <sup>i</sup> are directly exploited as diagnostic resid-

Note that, in general, each of the nine fuzzy fault estimators described by the relations of Eqs. (13) and (14) has three inputs (see Table 3), with a number of delays n ¼ 3 and nC ¼ 4 clusters. Therefore, the number of estimated parameters

ð Þ� 3 þ 1 n ¼ 12. Moreover, for each fault estimator, the estimation of the fuzzy

In the following, the main simulation results are summarised. Two actuator faults fu and two sensor fault fy are considered, namely the fault cases 1, 4, 8 and 9 of

Fault estimator ^fi <sup>12345</sup> RMSE 0.016 0.023 0.021 0.020 0.019

Residual rið Þ k 123456 789 δ 3.8 4.3 4.2 4.5 3.7 4.4 4.3 3.5 3.9

According to Table 3, these faults caused the alteration of the monitored input and output signal <sup>u</sup>, <sup>y</sup> affecting the residual <sup>r</sup><sup>1</sup> <sup>¼</sup> ^<sup>f</sup> <sup>1</sup>, <sup>r</sup><sup>4</sup> <sup>¼</sup> ^<sup>f</sup> <sup>4</sup>, <sup>r</sup><sup>8</sup> <sup>¼</sup> ^<sup>f</sup> <sup>8</sup> and <sup>r</sup><sup>9</sup> <sup>¼</sup> ^<sup>f</sup> <sup>9</sup> generated by the fuzzy fault estimators. These faults ^<sup>f</sup> <sup>i</sup> depicted in Figure 6 demonstrate

with i ¼ 1, …, 9. Table 5 summarises the achieved performance of the nine fault

uals ri, as remarked by Eq. (8). They can be compared with the thresholds of Eq. (9), optimally selected in order to achieve the optimisation of the overall fault diagnosis performance indices, in terms of missed fault and the false alarm rates, see Ding [22]. In particular, Table 6 summarises the values of the parameter δ of

for each fuzzy MISO model (three inputs and one output) is equal to

membership functions λið Þ� of Eq. (13) with i ¼ 1, …, nC was required.

Fault estimator ^fi <sup>6789</sup> RMSE 0.021 0.017 0.021 0.019

Section 3.1 suggested to exploit the fuzzy c-means clustering algorithm. When applied to the data of the wind turbine simulator, a number nC ¼ 4 of clusters and o ¼ 3 delays on input and output regressors were determined. The tool also generated the membership function points that are fitted through Gaussian membership

<sup>j</sup> and δ

ð Þi

ð Þk signals for each of the fuzzy estimators,

<sup>j</sup> of Eq. (15) were iden-

models were used as output predictors.

Fault Diagnosis Techniques for a Wind Turbine System DOI: http://dx.doi.org/10.5772/intechopen.83810

as sketched in Figure 3.

estimators of Figure 3.

Eq. (9) for each fault estimator i.

the scenarios recalled in Section 2.2.

Fuzzy fault estimator capabilities with RMSE.

The parameter δ for the threshold selection.

predicted ^<sup>f</sup> <sup>i</sup>

Table 5.

Table 6.

59

functions. After data clustering, the regressands αð Þ<sup>i</sup>

ð Þk and the actual fault fi

#### Table 4.

Wind turbine simulator fault conditions.

Figure 5. Example of fault-free (grey line) and faulty (black line) signals.

#### 4.1 Fuzzy estimators for fault diagnosis

The problem of the fault diagnosis of the wind turbine simulator is solved in this work by designing fuzzy prototypes as fault reconstructors. The considered

approach is different from the one presented in Simani et al. [21], where the fuzzy models were used as output predictors.

Section 3.1 suggested to exploit the fuzzy c-means clustering algorithm. When applied to the data of the wind turbine simulator, a number nC ¼ 4 of clusters and o ¼ 3 delays on input and output regressors were determined. The tool also generated the membership function points that are fitted through Gaussian membership functions. After data clustering, the regressands αð Þ<sup>i</sup> <sup>j</sup> and δ ð Þi <sup>j</sup> of Eq. (15) were identified for each cluster by following the procedure of Section 3.1. The TS models of Eq. (13) were thus implemented and nine fault estimators were designed, built and organised into the estimator scheme in order to accomplish the fault diagnosis task, as sketched in Figure 3.

The effectiveness of the fuzzy TS fault estimators used was assessed in terms of root mean squared error (RMSE), which is computed as the difference between the predicted ^<sup>f</sup> <sup>i</sup> ð Þk and the actual fault fi ð Þk signals for each of the fuzzy estimators, with i ¼ 1, …, 9. Table 5 summarises the achieved performance of the nine fault estimators of Figure 3.

In this case, these estimated signals ^<sup>f</sup> <sup>i</sup> are directly exploited as diagnostic residuals ri, as remarked by Eq. (8). They can be compared with the thresholds of Eq. (9), optimally selected in order to achieve the optimisation of the overall fault diagnosis performance indices, in terms of missed fault and the false alarm rates, see Ding [22]. In particular, Table 6 summarises the values of the parameter δ of Eq. (9) for each fault estimator i.

Note that, in general, each of the nine fuzzy fault estimators described by the relations of Eqs. (13) and (14) has three inputs (see Table 3), with a number of delays n ¼ 3 and nC ¼ 4 clusters. Therefore, the number of estimated parameters for each fuzzy MISO model (three inputs and one output) is equal to ð Þ� 3 þ 1 n ¼ 12. Moreover, for each fault estimator, the estimation of the fuzzy membership functions λið Þ� of Eq. (13) with i ¼ 1, …, nC was required.

In the following, the main simulation results are summarised. Two actuator faults fu and two sensor fault fy are considered, namely the fault cases 1, 4, 8 and 9 of the scenarios recalled in Section 2.2.

According to Table 3, these faults caused the alteration of the monitored input and output signal <sup>u</sup>, <sup>y</sup> affecting the residual <sup>r</sup><sup>1</sup> <sup>¼</sup> ^<sup>f</sup> <sup>1</sup>, <sup>r</sup><sup>4</sup> <sup>¼</sup> ^<sup>f</sup> <sup>4</sup>, <sup>r</sup><sup>8</sup> <sup>¼</sup> ^<sup>f</sup> <sup>8</sup> and <sup>r</sup><sup>9</sup> <sup>¼</sup> ^<sup>f</sup> <sup>9</sup> generated by the fuzzy fault estimators. These faults ^<sup>f</sup> <sup>i</sup> depicted in Figure 6 demonstrate


#### Table 5.

Fuzzy fault estimator capabilities with RMSE.


#### Table 6.

4.1 Fuzzy estimators for fault diagnosis

Example of fault-free (grey line) and faulty (black line) signals.

Table 4.

Figure 5.

58

Wind turbine simulator fault conditions.

Fault Detection, Diagnosis and Prognosis

The problem of the fault diagnosis of the wind turbine simulator is solved in this

Fault case Fault type Fault shape Occurrence (s) Actuator Step 2000–2100 Actuator Step 2300–2400 Actuator Step 2600–2700 Actuator Step 1500–1600 Actuator Step 1000–1100 Sensor Step 2900–3000 Sensor Trapezoidal 3500–3600 Sensor Step 3800–3900 Sensor Step 4100–4300

work by designing fuzzy prototypes as fault reconstructors. The considered

The parameter δ for the threshold selection.

Fault estimate ^fið Þ <sup>k</sup> 1 2 345 RMSE 0.009 0.009 0.009 0.012 0.011

ð Þ <sup>k</sup> <sup>6789</sup>

rið Þ k 1 2 345 6 7 89 δ 4.2 4.9 4.7 5.1 4.2 4.6 4.8 4.1 4.3

ð Þk and thresholds (dashed line) for cases 1, 2, 3 and 4.

RMSE 0.011 0.009 0.009 0.014

Fault Diagnosis Techniques for a Wind Turbine System DOI: http://dx.doi.org/10.5772/intechopen.83810

Fault estimate ^fi

Neural network performances.

δ values for the threshold selector.

Table 7.

Table 8.

Figure 7.

61

Estimated faults (continuous line) ^<sup>f</sup> <sup>i</sup>

Figure 6. Fault-free (grey line) and faulty (black continuous line) residuals with faults 1, 4, 8 and 9.

the achievement of the fault diagnosis task, as they exceed the threshold levels only when the relative fault is active, as recalled in Table 4.

Figure 6 depicts the reconstructed fault functions ^<sup>f</sup> <sup>i</sup> ð Þk generated by the fuzzy estimators in faulty conditions (black continuous line) with respect to the fault-free residuals (grey line). The fixed thresholds are depicted with dotted lines. The considered residuals refer to the fault cases 1, 4, 8 and 9. It is worth noting that in fault-free conditions, the estimated fault functions ^<sup>f</sup> <sup>i</sup> ð Þk are not zero due to both the model-reality mismatch. Figure 6 also highlights the robustness and reliability features of the developed fuzzy estimators.

#### 4.2 Neural networks for fault diagnosis

As for the fuzzy systems, nine NARX neural networks described in Section 3.2 were designed to estimate the nine faults affecting the acquired measurements, according to the scheme of Figure 3. The neural networks selected for fault diagnosis purpose consist of 3 layers, with 3 neurons in the input layer, 16 in the hidden one, and 1 neuron in the output layer. A number of du ¼ dy ¼ 4 delays were selected in the relation of Eq. (16). Both the input and the hidden layers used sigmoidal activation functions, while the output layer exploits the linear one. According to Table 3 and Figure 4, each of the nine neural networks was driven by three inputs.

As for the fuzzy models, the prediction efficacy of the designed neural networks was verified in terms of RMSE. The achieved results are summarised in Table 7, which were obtained by comparing the estimated faults with respect to the simulated ones.

### Fault Diagnosis Techniques for a Wind Turbine System DOI: http://dx.doi.org/10.5772/intechopen.83810


#### Table 7.

Neural network performances.


#### Table 8.

the achievement of the fault diagnosis task, as they exceed the threshold levels only

Fault-free (grey line) and faulty (black continuous line) residuals with faults 1, 4, 8 and 9.

estimators in faulty conditions (black continuous line) with respect to the fault-free residuals (grey line). The fixed thresholds are depicted with dotted lines. The considered residuals refer to the fault cases 1, 4, 8 and 9. It is worth noting that in

As for the fuzzy systems, nine NARX neural networks described in Section 3.2 were designed to estimate the nine faults affecting the acquired measurements, according to the scheme of Figure 3. The neural networks selected for fault diagnosis purpose consist of 3 layers, with 3 neurons in the input layer, 16 in the hidden one, and 1 neuron in the output layer. A number of du ¼ dy ¼ 4 delays were selected in the relation of Eq. (16). Both the input and the hidden layers used sigmoidal activation functions, while the output layer exploits the linear one. According to Table 3 and Figure 4, each of the nine neural networks was driven by three inputs. As for the fuzzy models, the prediction efficacy of the designed neural networks was verified in terms of RMSE. The achieved results are summarised in Table 7, which were obtained by comparing the estimated faults with respect to the

model-reality mismatch. Figure 6 also highlights the robustness and reliability

ð Þk generated by the fuzzy

ð Þk are not zero due to both the

when the relative fault is active, as recalled in Table 4. Figure 6 depicts the reconstructed fault functions ^<sup>f</sup> <sup>i</sup>

fault-free conditions, the estimated fault functions ^<sup>f</sup> <sup>i</sup>

features of the developed fuzzy estimators.

Fault Detection, Diagnosis and Prognosis

4.2 Neural networks for fault diagnosis

simulated ones.

60

Figure 6.

δ values for the threshold selector.

The fault diagnosis task is thus achieved by comparing the residuals ri <sup>¼</sup> ^<sup>f</sup> <sup>i</sup> ð Þk of Eq. (8) with fixed optimised thresholds, as described by Eq. (9). As for the fuzzy estimators, the values of the parameter δ of Eq. (9) for each fault estimator i is summarised in Table 8.

References

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On the other hand, Figure 7 shows an example of residual signals for the fault cases 1, 2, 3 and 4, together with the selected thresholds.

In particular, Figure 6 depicts the residuals ^<sup>f</sup> <sup>i</sup> ð Þk generated in faulty conditions by the neural network estimators (continuous line) compared with the fixed thresholds (dashed line). The considered residuals refer to the faults f <sup>1</sup>ð Þk , f <sup>2</sup>ð Þk , f <sup>3</sup>ð Þk and f <sup>4</sup>ð Þk of Table 4.

The achieved results show the effectiveness of the proposed fault diagnosis solutions, also with respect to disturbance and uncertainty effects on the wind turbine simulator, thus highlighting their potential application to real wind turbine systems.

### 5. Conclusion

The chapter studied data-driven tools for solving the problem of the fault diagnosis and prognosis of a wind turbine process. The design of this fault detector is based on the estimate of the fault itself, achieved by means of artificial intelligence methods. They were considered since these viable tools demonstrated to be able to cope with poor information on the process dynamics, in the presence of errors, model-reality mismatch and disturbance effects. In particular, these methodologies rely on fuzzy and neural network structures used to determine the non-linear dynamic links between measurements and fault signals. The selected structures belong to the non-linear autoregressive with exogenous input architectures, since they may model any non-linear dynamic relationship with arbitrary degree of accuracy. The fault diagnosis and prognosis strategies were validated via a high-fidelity simulator of a wind turbine process. The achieved performances in terms of reliability and robustness were thus tested by considering the presence of uncertainty and disturbance effects modelled by this wind turbine simulator. Further works will verify the features of the same fault diagnosis schemes when applied to real plants.
