Airplane Crew Support Implementation Basing on Ellipsoidal Model of the Closed “ Pilot-Airplane ” Ergatic System

The paper discusses the problem of closed-loop ergatic “pilot airplane” system monitoring for the purposes of flight safety. The new approach is proposed, based on the confidential ellipsoidal model, which parameters are estimated by flight data processing. The ellipsoidal model of ergatic “pilot airplane” system enables to detect system emergency operation mode and to identify the source of such emergency mode. The operability of the proposed approach is confirmed by the experimental data processing.


Introduction
Analysis of aviation accidents shows, that they are mainly caused by the following factors: -on-board failures of the airplane and its equipment (22% of aviation accidents); -pilot's misunderstanding of the current flight situation and resulting pilot's inadequate response (20% of aviation accidents); -pilot's control errors, that is the manipulating the control levers in unfit mode ( 18% aviation accidents).
All the above mentioned factors refer to the general ergatic "pilot-airplane" system, that is the closed-loop system which includes pilot, plane, engines, control system, cockpit's indication etc.It is clear that these factors are crucial from the viewpoint of flight safety, so the mathematic model of this ergatic system may be of a great value.The paper proposes a new model for onitoring the state of the closed-loop ergatic system "pilot-airplane" based on the concept of multidimensional confidence ellipsoids.This ellipsoidal model of ergatic system is a intellectual kernel of the suggested approach.This model provides an opportunity to predict flight safety threat.The parameters of the ellipsoidal model of ergatic "pilot-airplane" system are estimated using the flight data.

Ellipsoidal model of closed ergatic "pilot-airplane" system and its use for flight safety threat identification
Let us assume, that ergatic system "pilot-airplane" state vector in every time instant t has a block structure , where vector Х(t) includes parameters of the aircraft motion, and vector U(t) includes pilot's generated controls such as pitch control stick, throttle lever, pedals, etc.All the components of these vectors are measured and saved by the on-board system of flight data measurement and registration.
Let's consider a typical flight task, for example, the landing of the aircraft.Let us assume, that in the multidimensional space, corresponding to the state vector , there is a subspace E(t) which principal property is the following: If in any instant of time t ergatic system state vector (t) Z belongs to a subspace E(t) the considered flight task may be completed successfully with great probability E, which is close to 1. Let us denote this subspace E(t) as accessibility subspace [1][2][3][4][5].
We can also use the approximation of this accessibility subspace in the multidimensional space in the form of parallelepiped as well as sphere or correlation ellipsoid with a given probability measure [4].
Let us consider the approximation of accessibility subspace E(t) as the correlation ellipsoid E E (t) with given probability measure E: Where m z (t) is mathematical expectation of "pilotairplane" system state vector at instant t for all the flight paths corresponding to successful flight task completion; K Z (t) is covariation matrix of "pilot-airplane" system state vector at instant t for all the flight paths corresponding to successful flight task completion; R Z (E) is specific dimension of correlation ellipsoid, which correspond to confidential probability E.
Let us further refer the E E (t) (1) as a confidential ellipsoid.
The above defined confidential ellipsoid E E (t), approximates the accessibility subspace E(t) and enables to consider statistical relation between airplane flight parameters and pilot's control signals.It would make possible to carry out the identification of flight safety threats.Algorithms for estimating confidential ellipsoid E E (t) parameters using the flight data are detailed in [5].
The confidential ellipsoid E E (t) being formed , it is possible for every instant t of the flight path to estimate the process of piloting from the viewpoint of the flight safety.For this purpose let's assume that measurement errors of vector Z(t) components are negligible and may be used instead of this vector Z(t) .If this assumption is not valid it's always possible to use Kalman filtering or any other statistical estimators [2].For systematic errors methods like [6] schould be applied.So, the flight safety analysis of ergatic "pilot-airplane" system is reduced to checking the condition: ( If for an an arbitrary time instant t flight data meets the condition (2), the ergatic "pilot-airplane" system is operating normally, i.e. any threats to flight safety are absent with guaranteeing probabilityE .In the opposite, the break of the condition (2) should be treated as an indication of emergency operation mode in the closedlooped "pilot-airplane" contour.So, the condition (2) is integral indicator of "pilot-airplane" mode of operation.However, condition (2) does not enable to identify the cause of emergency situation.
As it was said above, these causes may be divided into three groups: on-board failures of the airplane and its equipment; -pilot's misunderstanding of the current flight situation; -pilot's control errors, i.e. the insufficient pilot's control activities coordination.
To generate formal criteria for emergency causes identification, it's necessary to consider the formulas (1) and (2) in a detailed way.First we are to note that the correlation ellipsoid (1) and the condition (2) are equivalent to the following inequation: Considering block structure of the vector Z(t), the correlation matrix K Z (t) may also be presented in blocks: Let's designate the inverse matrix Using evident relation where E is the unit matrix, we can write analytic expressions for elements of inverse matrix -1 K Z : The inequation (3) may be represented in the following form:

Conclusion
Thus, the processing of the experimental results confirm that the proposed ellipsoidal model of ergatic "pilotairplane" system provides the detection of emergency modes of operation and also the identification of flight safety threats.

Fig. 4 .
Fig. 4. Relations UU ( ) R l , UU ( ) R l D relations for landing modes, breaking the landing accuracy requirements