2.

Formalization

To study the problem of assessing the quality of

flight crew operations when using the simulator, the following objectives are

solved in the work:

– the definition of formalization elements that

would allow the implementation of evaluation logic;

– development of automated assessment methods;

– development of automated assessment system

software components-prototypes with the purpose of working capacity experimental

approbation of the proposed automated assessment method.

The problem of fully automatic assessment of the

crew’s activities at the moment cannot be solved, because there are no

exhaustive formal criteria and strict methodology for crew activities in the

industry. A key determinant of the assessment system is an expert instructor,

who forms integral assessments,

based on his experience. Therefore, the main objectives of the work are limited

to the automated generation of generalized data (partial estimates), which

simplify the process of forming integral final evaluations done by the

instructor.

The developed methodology includes the following set

of basic sequential actions of the system: receiving and recording of flight

data, the formation of certain particular assessments of pilot actions tied to

flight phases, the recording and visualization of the pilot’s actions

assessment results. Recording of the pilot’s actions assessment results will

not be covered in this work. In general, the developed methodology does not

depend on the type of aircraft, although to formalize particular estimates for

a particular aircraft, it is necessary to define the evaluation elements, since

they depend on aircraft design and operation characteristics.

The recorded flight data from the simulators will

serve as the input data for the assessment, that will include both instrument

readings and information from aircraft systems. According to paragraph 4 of

section 1, this data will be sufficient to determine the main crew control

activities. The remaining data, which can not be formalized and subsequently

automatically identified, will need to be identified and assessed by the

instructor. It should be noted that, perhaps, this technique can be used to

assess the actions of the crew in real flight on the basis of flight parameters

from onboard flight data recorder. In this case, it will be possible to assess

the actions of the crew after the actual flight.

According to paragraph 3 section 1, aircraft flight

is divided into phases, and each phase will have different assessment criteria.

For example, the normal speed of the aircraft at the cruise phase of flight and

landing phase is significantly different. Also, based on the aircraft flight

operation manuals, at some phases of the flight, some aircraft systems must be

turned off, for example, on an L-410 aircraft it is necessary to turn off the

central electronic limiter (CEBO) during landing and take-off to ensure that

the engines power will reach the maximum operating mode. This objective will be

solved by method at the stage of recognition of the flight phase.

The

assessment of the crew actions is done by the instructor through comparing the

actions of the aircraft crew members in each section of the flight and in

emergency situations with criteria that are described in the flight manuals and

the general international rules to check if crew sustains proper operations and

permissible flight parameters.

To solve the problem of determining the formalization of

evaluation elements, the situational calculus and event calculus are used in

the work. Situational calculus allows to form sequences of transitions of

flight situations, based on a certain initial situation and transitions to

subsequent situations depending on the actions of pilots. This makes it

possible to identify the classified situations in which the crew may be in

flight, and which are selected in terms of the impact on the assessment of the

crew’s actions.

2.1.

Situation

calculus

2.1.1.

Situation

calculus description

The situation calculus is a logic formalism

designed for representing and reasoning about dynamical domains.

The

situation calculus represents changing scenarios as a set of first-order

logic formulae. The basic elements of the calculus are:

·

The actions that can be performed in

the world

·

The fluents that describe

the state of the world

·

The situations

A domain is

formalized by a number of formulae, namely:

·

Action precondition axioms, one for

each action

·

Successor state axioms, one for each

fluent

·

Axioms describing the world in

various situations

·

The foundational axioms of the

situation calculus

The main elements of the situation

calculus are the actions, fluents and the situations. A number of objects are

also typically involved in the description of the world. The situation calculus

is based on a sorted domain with three sorts: actions, situations, and objects,

where the objects include everything that is not an action or a situation.

Variables of each sort can be used. While actions, situations, and objects are

elements of the domain, the fluents are modeled as either predicates or

functions. The actions form a sort of the domain. Variables of sort action can

be used. Actions can be quantified. In the situation calculus, a dynamic world

is modeled as progressing through a series of situations as a result of various

actions being performed within the world. A situation represents a history of

action occurrences. Statements whose truth value may change are

modeled by relational fluents, predicates which take a situation as their

final argument. Also possible are functional fluents, functions which take

a situation as their final argument and return a situation-dependent value.

Fluents may be thought of as “properties of the world”‘.

Situation calculus language Lsitcalc is a second order language with

equality. It has three disjoint sorts: action

for actions, situation for

situations, and a catch-all sort object

for everything else depending on the domain of application. Apart from the

standard alphabet of logical symbols there is ?, ¬ and ?, with the usual definitions of a

full set of connectives and quantifiers —

Lsitcalc has the

following alphabet:

·

Countably

infinitely many individual variable symbols of each sort. We shall use s and a, with subscripts and superscripts, for variables of sort situation and action, respectively. We normally use lower case roman letters

other than a; s, with subscripts and superscripts for variables of sort object. In addition, because Lsitcalc is second order, its alphabet includes countably infinitely

many predicate variables of all arities.

·

Two

function symbols of sort situation:

1. A constant symbol S0,

denoting the initial situation.

2. A binary function symbol do

: action × situation ® situation. The

intended interpretation is that do(a, s) denotes the successor situation

resulting from performing action a in

situation s.

·

A

binary predicate symbol ?: situation × situation, defining an ordering relation

on situations. The intended interpretation of situations is as action

histories, in which case s ? s’ means that s is a proper subhistory of s’.

·

A

binary predicate symbol Poss : action × situation. The intended interpretation of Poss(a, s) is that it is

possible to perform the action a in

situation s.

·

For

each n ? 0, countably infinitely many predicate symbols with arity n, and sorts (action ? object)n. These

are used to denote situation independent relations.

·

For

each n ? 0, countably infinitely many function symbols of sort (action ? object)n ® object. These are used to denote

situation independent functions.

·

For

each n ? 0, a finite or countably infinite number of function symbols of sort (action ? object)n

® action. These are called action

functions, and are used to denote actions. In most applications, there will be

just finitely many action functions, but we allow the possibility of an

infinite number of them.

·

·

For

each n ? 0, a finite or countably infinite number of predicate symbols with

arity n + 1, and sorts (action ? object)n × situation.

These predicate symbols are called relational fluents. In most applications,

there will be just finitely many relational fluents, but we do not preclude the

possibility of an infinite number of them. These are used to denote situation

dependent relations. Notice that relational fluents take just one argument of

sort situation and this is always its last argument.

·

For

each n ? 0, a finite or countably infinite number of function symbols of sort (action ? object)n × situation ® action ? object. These function symbols are called functional fluents. In

most applications, there will be just finitely many functional fluents, but we

do not preclude the possibility of an infinite number of them. These are used

to denote situation dependent functions. Notice that functional fluents take

just one argument of sort situation and this is always its last argument.

Notice

that only two functions symbols of Lsitcalc

— S0

and do —

are permitted to take values in sort situation.

Thus, the situational calculus allows us to identify the

current situation on the basis of the previous situation and the pilot’s

actions. For example, during take-off, when the aircraft speeds up on runway,

the pilot uses brakes, which causes the rejected takeoff:

do(useBrakes, takeoffRun) ®

rejectedTakeoff

In this case useBrakes is the action of the pilot, namely the use of brakes, takeoffRun – the current situation,

namely the takeoff and rejectedTakeoff

– the next situation, namely the rejected takeoff:

2.1.2.

Limitations

of situation calculus

Situational calculus fully justifies itself if there is a

single agent performing instant, discrete actions and if an action occurs

before or after another within a situation.

There is no way of expressing that an action occurs at a particular time, or

that two or more actions occur concurrently. Moreover, the definition of the

state of the external world in the situational calculus is closed on the agent

who performs the actions, and therefore external influences or effects created

not by the agent are not taken into account.

The above limitations make it

impossible to determine such situations as, for example, during takeoff when

the airplane speeds up on runway, the pilot briefly uses brakes, the airplane

does not stop and continues to take off. Similarly, if in this case the pilot,

in parallel with the use of brakes, switches on the reverse, it will be

impossible to determine the parallel use of these systems.

To solve the problem of identifying the pilot’s

actions leading to a situation change, let’s try to apply an event calculus

that takes into account the time intervals of actions.

2.2.

Event

calculus

2.2.1.

Event

calculus description

The event calculus is a formalism for reasoning

about action and change. Like the situation calculus, the event calculus has

actions, which are called events, and time-varying properties or fluents. In

the situation calculus, performing an action in a situation gives rise to a

successor situation. Situation calculus actions are hypothetical, and time is

tree-like. In the event calculus, there is a single time line on which actual

events occur.

A narrative is a possibly incomplete specification

of a set of actual event occurrences, i.e. a time structure which is

independent of any action occurrences is established or assumed, and then

statements about when various actions occur within this structure are

incorporated in the description of the domain under consideration. The event

calculus is narrative-based, unlike the standard situation calculus in which an

exact sequence of hypothetical actions is represented.

Like the situation calculus, the event calculus

supports context-sensitive effects of events, indirect effects, action

preconditions, and the commonsense law of inertia. Certain phenomena are

addressed more naturally in the event calculus, including concurrent events,

continuous time, continuous change, events with duration, nondeterministic

effects, partially ordered events, and triggered events.

Informally, the basic idea of the Event Calculus is

to state that fluents (time-varying properties of the world) are true at

particular time-points if they have been initiated by an action occurrence at

some earlier time-point, and not terminated by another action occurrence in the

meantime. Similarly, a fluent is false at a particular time-point if it has

been previously terminated and not initiated in the meantime. Domain dependent

axioms are provided to describe which actions initiate and terminate which

fluents under various circumstances, and to state which actions occur when. In

the context of the Event Calculus, individual action occurrences are often

referred to as “events”, so that “actions” are “event types”.

The

Event Calculus given here is written in a sorted predicate calculus with

equality, with a sort A for actions

(variables a, a1, a2,…),

a sort F for fluents (variables f, f1, f2, …), a

sort T for timepoints (here either

real numbers or integers, variables t, t1,

t2, …) and a sort X

for domain objects (variables x, x1,

x2, …). To describe a very basic calculus we need five

predicates (other than equality); Happens

?

A×T ,

HoldsAt ?

F ×T ,

Initiates ?

A× F× T ,

Terminates ?

A× F× T and