**4.2.2 Failure of spike**

624 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

The use of the mathematical model makes it easier to test the wavelet-based fault detection system, but the characteristic of the datasets may not reflect the real flight environment and the actual actuator failures. On the other hand, real autonomous flight experiments with an injected sensor failure can be potentially dangerous for the helicopter because it can take the RUAV out of control and RUAV may crash. Thus, we planned to inject the sensor failure while the absence of the security problems of the RUAV with its manual mode. As is shown in the figure 9, the pilot controls the helicopter using radio controller. The onboard

To demonstrate the effectiveness of the fault detection scheme, the failure scenario of abrupt

A "db2" ("db" is define in Matlab) wavelet with a vanishing moment 2 is applied to these abrupt faults of sensor. Figure 10 and 11 show their wavelet transforms in scale-D1 to scale-S3 including the original data signals. In figure 10, scale-D1 to scale-D3 denote the details of the wavelet transform of the signals on scales 1 to 3, respectively, while the scale-S3

<sup>0</sup> <sup>2000</sup> <sup>4000</sup> <sup>6000</sup> <sup>8000</sup> <sup>10000</sup> <sup>12000</sup> <sup>14000</sup> -10

<sup>0</sup> <sup>2000</sup> <sup>4000</sup> <sup>6000</sup> <sup>8000</sup> <sup>10000</sup> <sup>12000</sup> <sup>14000</sup> -10

<sup>0</sup> <sup>2000</sup> <sup>4000</sup> <sup>6000</sup> <sup>8000</sup> <sup>10000</sup> <sup>12000</sup> <sup>14000</sup> -5

<sup>0</sup> <sup>2000</sup> <sup>4000</sup> <sup>6000</sup> <sup>8000</sup> <sup>10000</sup> <sup>12000</sup> <sup>14000</sup> -5

<sup>0</sup> <sup>2000</sup> <sup>4000</sup> <sup>6000</sup> <sup>8000</sup> <sup>10000</sup> <sup>12000</sup> <sup>14000</sup> -5

t/0.02s

In figure 10, an example sensor failure experiment is presented. At the point of 7000, the

abrupt failure detection, we are only interested in the local maxima of <sup>1</sup> | ( , )| *W f s t* . When detecting the local maxima of <sup>1</sup> | ( , )| *W f s t* , we call also keep the value of the wavelet

. For

The local maxima of the first derivative are sharp variation points of [ ( )] ( ) *<sup>s</sup> f xt t*

original signal

computer online detects the fault with wavelet-based algorithm (Qi & Han, 2007).

bias and spike in compass roll channel is assumed.

represents the approximation of them on scale 3.

0 10

0 10 scale-S3

> 0 5 scale-D3

> 0 5 scale-D2

> 0 5 scale-D1

compass roll channel gets bias of 5 degree.

transform at the corresponding location.

**4.2.1 Failure of bias** 

Fig. 10. Bias failure and its wavelet transform(t=0.02s)

Amplitude (deg)

We also made a spike failure injection to RUAV system in manual mode to test the performance of the wavelet-based fault detection system. At the point of 7000, the compass roll channel gets spike which the signal return to zero.

Similar to the bias failure experiment, the location of fault agree with the maximum values of the wavelet transform on different scales.

From the results, it can be conclude that the proposed method is effective for detection the abrupt faults of the RUAV sensor system. Fault point could be also being described accurately at some certain resolution. Local characteristics of wavelet are represented well in time and frequency-domains.
