Simulated Aircraft Model FDD

To show the diagnostic characteristics brought by the application of the proposed PM and NLGA-AF FDD schemes to a general aviation PIPER PA30 aircraft, some simulation results obtained in the Matlab^R and Simulink^R environments are

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Fig. 3.3 Behaviour of the residual r - Fault-free situation (left) / OFC (right)

reported in this Section which also considers briefly the important features of the performance evaluation of the diagnosis schemes, i.e. their robustness and reliabil-ity with respect to the uncertainty and disturbance acting on the system by means of a Monte-Carlo analysis.

The mathematical simulation model of the aircraft used in this Section is based on the classical nonlinear 6 Degrees of Freedom (6 DoF) rigid body formulation [85], whose motion occurs as a consequence of applied forces and moments (aero-dynamic, thrust and gravitational). A set of local approximations for these forces has been computed and scheduled depending on the values assumed by True Air Speed (TAS), flap, altitude, curvature radius and flight path angle. In this way, it is also possible to obtain a simplified mathematical model for each flight condition that is suitable for a state-space representation, as it can be made explicit. The param-eters in the analytic representation of the aerodynamic actions have been obtained from wind tunnel experimental data. It should be observed that aerodynamic forces and moments are not implemented by the classical linearised expressions (stability derivatives).

Static aerodynamic actions (e.g. lift and drag characteristics), are implemented by means of cubic splines approximating nonlinear experimental curves. More de-tails can be found in the related paper [86]. The linear aircraft model used by the proposed PM described in Section 3.2.1 embeds the linearisation both of the 6 DoF model and of the propulsion system. On the other hand, the NLGA-AF FDD scheme described in Section 3.2.7 requires a nonlinear input affine system [27], but the adopted simulation model of the aircraft does not fulfil this requirement. For this reason, a simplified aircraft model has been considered, as reported in [45].

The PM residual generator filters are fed by the 4 component input vector c(t) and the 9 component output vector y(t) acquired from the nonlinear simulation aircraft model [87, 46]. Each filter of the PM bank is independent of one of the 4 input signals and then is also insensitive to the corresponding fault signals. Clearly, the residual generator bank has been designed to be decoupled from the disturbance signals, i.e. the wind gust signals, which represent disturbance terms acting on the aircraft system.

Samples (sec.) Samples (sec.)

Samples (sec.) Samples (sec.)

Elevator sensor residuals Aileron sensor residuals

Rudder sensor residuals Throttle sensor residuals 0 50 100 150 200 250 300

Fig. 3.4 PM residuals for the elevator sensor fault diagnosis.

In order to assess the diagnosis technique, different fault sizes have been simu-lated on each sensor. As an example, the 4 residual functions rc_i(t) generated by the filter bank for input sensor fault isolation, under both fault-free and faulty conditions are shown in fig. 3.4.

Continuous lines represent the fault-free residual functions, while the dashed lines depict the faulty residual signals. The dotted lines correspond to the settled thresholds. The fault considered in Fig 3.4 has been generated on the elevator sen-sor of the considered aircraft, starting at time t= 150 s. The first residual function of fig. 3.4 also provides the isolation of the input sensor fault under consideration.

Regarding the new NLGA-AF FDD scheme, in order to assess its effectiveness in estimating the faults affecting the input sensors, the same flight condition (a coordi-nated turn at constant altitude) previously described for the PM evaluation has been considered. A bank of 4 adaptive filters has been used in order to perform the diag-nosis, the isolation, and the estimation of the elevator, aileron, rudder and throttle actuator fault magnitudes. It is important to note that each filter is structurally de-coupled from the vertical and lateral wind disturbance components and is sensitive to a single input sensor fault.

In fig. 3.5, the simulation results referring to a particular case are reported, where a small fault with a size of 2^o starting at time t = 150 s is added to the elevator actuator.

With reference to the results obtained, the proposed FDD strategies appear to be promising for diagnostic application to commercial aircraft. Advantages and draw-backs of the PM and the new NLGA-AF FDD methods developed in this Section can be summarised as follows. Both PM filters and NLGA-AF perform lowpass filtering of input/output measurements. For the particular aircraft application, the computational burden of polynomial filters is lower than that of NLGA adaptive filters, so that they are suitable for low-cost implementations. On the other hand, NLGA-AF can obtain smaller detection time, compared with PM filters, thanks to

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Fig. 3.5 Adaptive filters via the nonlinear geometric approach for elevator sensor fault diag-nosis and size estimation.

the fact that they directly take into account nonlinear terms [45]. It is worth not-ing that the results of the Monte-Carlo analysis applied to the PM and NLGA-AF FDD scheme show how the proper design and optimisation of the dynamic filters allows the achievement of low false and missed alarm rates, with high detection and isolation rates, and with minimal detection and isolation delay times, as described in [45].

As for the NLGA-NF, the NLGA Particle Filter (NLGA-PF) has been designed as described in [82, 46]). The NLGA-PF filter is implemented via the algorithm summarised in Section 3.2.2 with a number M= 200 of particles and it uses 20000 data samplesδthkand n_ek, acquired from the continuous-time aircraft model.

As an example, the residual functions generated by the NLGA-NF and NLGA-PF filters for the throttle actuator FDI, under both fault-free and faulty conditions, are shown in fig. 3.6. The continuous lines represent the fault-free residual functions, whilst the dotted lines depict the faulty residual signals. As illustrated in fig. 3.6, the fault has been generated on the throttle actuator of the aircraft, starting at time t= 100s.