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Several procedures for sensor fault detection and isolation (FDI) applied to a simulated model of a commercial aircraft are presented. The main contributions of the paper are related to the design and the optimisation of two FDI schemes based on a linear polynomial method (PM) and the nonlinear geometric approach (NLGA). The FDI strategies are applied to the aircraft model, characterised by tight-coupled longitudinal and lateral dynamics. The robustness and the reliability properties of the residual generators related to the considered FDI techniques are investigated and verified by simulating a general aircraft reference trajectory. Extensive simulations exploiting the Monte Carlo analysis tool are also used for assessing the overall performance capabilities of the developed FDI schemes, in the presence of turbulence, measurement, and model errors. Comparisons with other disturbance-decoupling methods for FDI based on neural networks (NNs) and unknown input kalman filter (UIKF) are finally reported.

Increasing demands on reliability for safety critical systems such as aircraft or spacecraft require robust control and fault diagnosis capabilities as these systems are potentially subjected to unexpected anomalies and faults in actuators, input-output sensors, components, or subsystems. Consequently, fault diagnosis capabilities and requirements
for aerospace applications have recently been receiving a great deal of
attention in the research community [

The first part of this work deals with the residual generator design for the FDI of input-output sensors of a general aviation aircraft subject to turbulence, wind gust disturbances, and measurement noises.
The developed PM scheme belongs to the parity space approach [

This section recalls briefly the description of the monitored aircraft whose main parameters and variables are reported in Table

Nomenclature.

Angle of attack | |

Angle of sideslip | |

Roll rate | |

Pitch rate | |

Yaw rate | |

Bank angle | |

Elevation angle | |

Heading angle | |

Engine shaft angular rate | |

Inertia moment matrix | |

True airspeed (TAS) | |

Elevator deflection angle | |

Aileron deflection angle | |

rudder deflection angle | |

Throttle aperture percentage | |

Altitude | |

Flight path angle | |

Airplane mass | |

Wind gust components |

The considered aircraft simulation model consists of a PIPER PA-30, based on the classical nonlinear

The linear model used by the proposed PM FDI approach described in Section

On the other hand, regarding the NLGA FDI scheme described in Section

Let us consider the input-output representation of a continuous-time, time-invariant linear dynamic system affected by faults and
disturbances in the form

Models of type (

An important aspect of the residual generator design concerns the decoupling properties of the disturbance

If the matrix

This work is focused on the problem of detecting and isolating additive faults acting on the input and output sensors of the monitored system. If the input-output measurements are modelled by the relations of (

The residual generator described by (

The diagnostic capabilities of the residual generator of (

In the following, the freedom design in the selection of the rows of the polynomial matrix

If

Given the vector

The solution to the problem described by Proposition

From (

Let us indicate

The matrix

The same solution can be found by maximising the function

The problem described by Proposition

Section

When

The previous consideration leads to introduce the polynomial

The degree

In Section

As

Let us suppose that

In order to understand the proposed solution, the following points should be considered.

The choice of

When

Even if the
system admits solutions, the inverse of the matrix

The use of a polynomial vector

This section is focused on the design of residual generators on the basis of a given reference function with disturbance-decoupling and fault sensitivity maximisation properties. The pole location influences the transient dynamics of the designed residual filters, while the steady-state properties depend on the PM residual design, as it maximises the residual steady-state values with respect to step faults affecting input and output sensors. The poles of the residual functions
could be optimised with respect to both fault and disturbance terms, as shown, for example, in a work by the same authors [

This section addresses the design problem of residual generator banks for the isolation of faults affecting the input and the output sensors. This design is performed by using the disturbance-decoupling method suggested in Section

To univocally isolate a fault concerning one of the

In presence of a fault on the

In these conditions, the system of (

Let us indicate

From the comparison between (

In more detail, as shown in Section

It is worth noting that the similar design technique can be used for

The problem requirements determine the selection of the specific fault with respect to which the design depends. Most often in practice, it is important to obtain

The considered NLGA to the FDI problem is suggested in
[

More precisely, the approach considers a nonlinear system model in the form

Therefore, if

If

In the new (local) coordinate defined previously, the system of (

As already described in Section

Under these assumptions, by means of computations detailed in [

It is worth observing that each residual generator is affected by a single input sensor fault and is decoupled from the wind components and the faults affecting the remaining input sensors. This feature
can be obtained by defining a different

The proposed NLGA-based scheme consists of two design steps:

the structural decoupling of critical disturbances (wind gust and turbulence) and critical modelling errors can be obtained as described in Section

the nonlinear residual generators robustness is improved by minimising the effects of both noncritical disturbances and modelling errors, whilst maximising the fault effects on the residual signals.

It can be noted that the tuning of the residual generator gains, in the framework of the

The following system, which is referred to as

The following definition will be used throughout the section.

The norms

Given two scalars

For all

From the definition (

The set

By means of Proposition

If

From the definition (

Given

The proof of the theorem is not reported, as it is straightforward from Propositions

Let us consider the following performance index to maximise

In fact, from

Finally, from (

(1) Choose

(2) Compute

(3) Choose

(4) Apply the chosen gain

To show the diagnostic characteristics brought by the application of the proposed FDI schemes to general aviation aircrafts, some numerical results obtained in the Matlab and Simulink environments are reported. The final performances that are achieved with the developed FDI schemes are finally reported. These performances are evaluated by means of extensive simulations applied to the aircraft simulation model. This section presents also some comparisons of the developed PM and NLGA FDI strategies with NN and UIKF FDI schemes.

The designed PM residual generator filters are fed by the

It is worth noting that the aircraft reference trajectories are typically made up of a sequence of steady-state flight conditions, each
one described by the associated input state output set point and the linearised model of (

the true
airspeed is

the curvature
radius is

the
flight-path angle is

the altitude is

the flap
deflection is

Regarding the PM, the detection properties of the filters in terms of fault sensitivity and disturbance rejection can be achieved according to Section

In this paper, the threshold test for FDI is performed with the logic described by (

Thus, in this case, a suitable value of

PM FDI technique: minimal

Variable | Fault size | Delay time | |
---|---|---|---|

Elevator | |||

Aileron | |||

Rudder | |||

Throttle aperture % |

On the other hand, the minimal detectable ramp faults
are reported in Table

PM FDI technique: minimal

Variable | Fault size | Delay time | |
---|---|---|---|

Elevator | |||

Aileron | |||

Rudder | |||

Throttle aperture % |

Concerning the NLGA, the synthesis of the residual generators has been performed by using filter gains that optimise the fault sensitivity and reduce as much as possible the occurrence of false alarms due to model uncertainties and to disturbances not completely decoupled. This robustness requirement has been fulfilled by designing the residual gains
according to the Procedure

In order to assess the NLGA diagnosis technique, single step and ramp faults have been used. Moreover, also in this case the threshold values have been chosen in simulation according to (

NLGA FDI technique: minimal

Variable | Fault size | Delay time | |
---|---|---|---|

Elevator | |||

Aileron | |||

Rudder | |||

Throttle aperture % |

On the other hand, the minimal detectable input sensor ramp faults are reported in Table

NLGA FDI technique: minimal

Variable | Fault size | Delay time | |
---|---|---|---|

Elevator | |||

Aileron | |||

Rudder | |||

Throttle aperture % |

The minimal detectable step fault values in Tables

As an example, Figure

PM residuals for the 1st input sensor ramp fault

The horizontal lines represent the levels of the fault-free thresholds that are settled according to test (

The second example of Figure

NLGA residuals for the 1st input sensor fault isolation with

In this section, the robustness characteristics of the proposed PM and NLGA FDI schemes have been evaluated and compared also with respect to the UIKF scheme [

In the following of this section, the performances of the different FDI schemes have been evaluated by considering a more complex aircraft
trajectory. This has been obtained by means of the
guidance and control functions of a standard autopilot which stabilises the aircraft motion towards the reference trajectory as depicted in Figure

Aircraft complete trajectory example.

The reference turn flight condition is used to design the PM and the NLGA filters. The achieved results are reported in Tables

As an example, the fault-free and faulty residuals generated by the designed NN and UIKF banks are shown in Figures

NN residuals with

UIKF residuals with

Table

Performances of the FDI schemes for a complete aircraft trajectory.

Variable | PM | NLGA | UIKF | NN |
---|---|---|---|---|

Mean detection delay |

The choice of

It is worth noting that the NLGA has a theoretical advantage by taking into account the nonlinear dynamics of the aircraft. However, the behaviour of the related nonlinear residual generators is quite sensitive to the model uncertainties due to variation of the flight condition. In fact, the NLGA FDI scheme requires high values of

The simulation model applied to the complete trajectory is an effective way to test the performances of the proposed FDI methods with respect to modelling mismatch and measurement errors. The obtained results demonstrate the reliability of the PM-, NLGA-, UIKF-, and NN-based FDI schemes as long as proper design procedures are adopted.

In this section, further experiment results have been reported. They regard the performance evaluation of the developed FDI scheme with respect to uncertainty acting on the system. Hence, the simulation of different fault-free and faulty data sequences was performed by exploiting the aircraft Matlab-Simulink simulator and a

For robustness and reliability experimental analysis of the FDI schemes, some performance indices have been used. The performances of the FDI method are then evaluated on a number of Monte Carlo runs equal to

These indices are hence computed for the number of Monte Carlo simulations and for each fault case. Table

PM Monte Carlo analysis with

Faulty sensor | ||||
---|---|---|---|---|

The same analysis can be applied again to the residual generated by means of the NLGA, NN, and UIKF FDI schemes. The results are summarised in Tables

NLGA Monte Carlo analysis with

Faulty sensor | ||||
---|---|---|---|---|

NN Monte Carlo analysis with

Faulty sensor | ||||
---|---|---|---|---|

UIKF Monte Carlo analysis with

Faulty sensor | ||||
---|---|---|---|---|

Tables

The paper provided the development and application of two FDI techniques based on a PM scheme and on an NLGA method, respectively. The PM procedure led to residual generators optimising the tradeoff between disturbance-decoupling and fault sensitivity. Moreover, the application of the PM FDI scheme resulted robust with respect to
model uncertainties. On the other hand, the NLGA relies on a novel design
scheme based on the structural decoupling of disturbances and modelling errors, Thus, the mixed