Table 3.

The design parameters are represented by the number of neurons and the number of delays of the network inputs and outputs, while the value of the weights of each neuron are derived from the network training from the data acquired from the

The design of the fault diagnosis schemes proposed for the application example considered in this chapter have been summarised in Section 4. However, the tool addressed in this chapter enhances the design of the banks of these fault estimators

This tool consists of a fault sensitivity analysis that has to be performed on the wind turbine simulator. It is aimed at defining the most sensitive measurements

practice, the considered fault signals have been injected into the wind turbine simulator, assuming that only a single fault may occur. Then, the relative mean square errors (RMSE) between the fault-free and faulty measured signals are eval-

selected. The results of the fault sensitivity analysis are summarised in Table 2 for

Nx <sup>¼</sup> Sx S∗ x

Sx <sup>¼</sup> xfð Þ� <sup>k</sup> xnð Þ<sup>k</sup> 

k k xnð Þk <sup>2</sup>

xfð Þ� <sup>k</sup> xnð Þ<sup>k</sup> 

The value of Nx indicates the effect of the considered fault case with respect to

the general measured signal x kð Þ, with k ¼ 1, 2, …, N. The subscripts 'f' and 'n'

Fault fi 12345 Measurements uj, yl β1,m<sup>1</sup> β2,m<sup>2</sup> β3,m<sup>1</sup> ωr,m<sup>1</sup> ωr,m<sup>1</sup> RMSE 11.29 0.98 2.48 1.44 1.45

indicate the faulty and the fault-free case, respectively. Therefore, the

Fault fi 6789 Measurements uj or yl β2,m<sup>1</sup> β3,m<sup>2</sup> τg,m ωg,m<sup>1</sup> RMSE 0.80 0.73 0.84 0.77

ð Þk .

ð Þk with respect ujð Þk and yl

k k xnð Þk <sup>2</sup>

 2

> 2

In particular, the fault sensitivity analysis is conducted on the basis of a selection algorithm that is performed by introducing the normalised sensitivity function Nx,

ð Þk considered in Section 2.2. In

ð Þk can be

(17)

(18)

(19)

ð Þk with respect to the fault conditions fi

uated, so that, for each fault, the most sensitive signal ujð Þk and yl

S∗ <sup>x</sup> ¼ max

system under diagnosis, see Hunt et al. [20].

3.3 Fault sensitivity analysis

Fault Detection, Diagnosis and Prognosis

depicted in Figure 3.

the wind turbine system.

defined in Eq. 17:

with

and

Table 2. Fault sensitivity fi

56

ujð Þk and yl

Fault sensitivity test.

measurements that are most affected by the considered fault lead to a value of Nx equal to 1. Otherwise, a smaller value of Nx, that is, close to zero, represents a signal x kð Þ not affected by the fault. Those signals characterised by high value of Nx are thus selected as the most sensitive measurements, and they will be considered in the design of the fault diagnosis modules of the bank sketched in Figure 3.

The complete results of the fault sensitivity analysis are summarised in Table 3. For each fault case, the selected signals of the wind turbine benchmark are marked as inputs or outputs.

This method represents a key feature of the proposed approach to fault diagnosis. In fact, the fault estimators of the bank of Figure 3 can be designed by exploiting a reduced number of signals, thus leading to a noteworthy simplification of the overall complexity, and a decrease in the computational cost of the training and identification phases.
