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Modeling Supervisory Pilot Behavior with General Systems Theory Formalisms
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MODELING SUPERVISORY PILOT BEHA VIOR WITH GENERAL SYSTEMS THEORY FORMALISMS B. Doring Foncilllllpinlfifllf /fir ,4I1filruj}(Jf"rilllik, D-5JO/ \\'{J(ilflil'lg-\\'l'Ifhil{)"I'II , F[?(;
Abstract. In a simulation study, conducted to determine information flow at a pilotcoclZpClt- -interface during an automated landing approach, a mathematical model of pilot's supervisory control tasks was developed. For modeling those tasks and their network combination, production systems were used and described with general systems theory formalisms. For that the pilot was considered as a sequential input/output system and described with input, output, internal, and memory variables. While performing a task, only subsets of all variables and of their value sets are required. For describing the pilot's selection behavior, selection functions were introduced which specify task relevant variables and their values. From task relevant variables, behavior relevant variables are derived. Then the task performance behavior of the pilot can be described with binary relations among all value sets of behavior relevant variables which are task specific and invariant during the duration of a task. Each relation element represents an ordered pair of coordinates of which the first describes the left situation side of a production rule and the second its right action side. The resulting model guides the required task analysis and supports the development of a simulation program. Keywords. Man-machine systems; Models; Ergonomics; Artificial intelligence; Simulation.
INTRODUCTION
System theory;
System
analysis;
MODELING THE PILOT'S BEHAVIOR
In highly automated man-machine systems, such as ships, aircraft, and nuclear power plants, operators are increasingly involved with monitoring and supervisory control tasks in addition to, or instead of, continuous control tasks. In modeling the human supervisor, different approaches have been applied. They include applications of control theory, queuing theory, fuzzy set theory, network techniques, and production systems (Pew and col leguages, 1977; Rouse, 1980). This presentation reports a model which was developed for simulating the information flow between a pilot and his cockpit environment during a highly automated landing approach. During such an approach the pilot has to perform a number of distinct supervisory control tasks. According to the predecessor/successor relations between those tasks a network technique was applied for mode ling the situation-dependent branching between tasks. Production systems were used for each task to model pilot's information processing in detail. The basic structure of that model and its utilization in a simulation study was already described by Daring and Knauper (1983). Here it will be shown how the model was described mathematically with formalisms of the general systems theory of Klir (1969). A detailed presentation of that model description is given by Daring (1983).
During an automated landing approach the pilot has to perform various supervisory tasks. To determine those tasks they were considered to be normative, i.e., what the pilot should do during the landing approach (Sheridan, 1976). Those tasks were categorized into five types, viz, adjusting, activating, monitoring, checking, and special tasks. By considering the course of events during the approach, predecessor/successor relations among the identified tasks were determined so that the tasks could be arranged in a task network (Seifert and Daring, 1981). In order for the pilot to perform his tasks, he has to perceive input information from his cockpit environment. He then has to process this information for generating outputs to affect that environment. Each task can be analyzed into basic functions which represent the constituents of pilot activities. Those functions are sensing (information receiving), information processing and decision, action (physical control or communication), and information storage (McCormick, 1976) (Fig. 1). Here it is assumed that the task relevant information can be determined through a task analysis. The flow of information through the basic functions is not considered in detail but only the time duration
InformatIon storage /
Sensing (information receivIng)
J
+ I
Information processing and decision
Fig. I. Types of basic operator functions.
117
""
Action functions ( physical cant rol 0 r communication)
148
B. Diiring output variables, internal variables, and memory variables. The mathematical formalisms used for all variables to describe the pilot behavior are explained below in detail only for the input variables. For the other variables formalisms are explained in detail only in part.
which the pilot needs for performing a task, i.e. from beginning of sensing to completion of his action. Furthermore it is assumed that the input information is only received at the beginning of a task and not during the task performance. Production systems were used in modeling pilot tasks. The major elements of a production system are a database, a set of productions, and a control system (Barr and Feigenbaum, 1981; Davis and King, 1977; Nilsson, 1980). The productions operate on the database. Rouse (1980) defines a production as situation-action pair where the situation side is a list of things to watch for and the action side is a list to do. The actions resulting from one production change the database. The control system chooses which applicable production should be applied.
According to the stated assumptions and the selected degree of detail a task is the smallest behavioral element which is represented in the model by its onset time, t e , and by its completion time, te+l> with te,te+! ER++, R++=R+U {O} (U = union), and R+ the set of all positive real numbers. It is assumed that the completion of a task coincides with the start of its successor task. Therefore, each time characterizes the end of a task as well as the start of another. The only exeptions are the very first task onset time te=O at which no predecessor task exists, and the completion time of the last task at which no successor task follows.
Applying the production scheme to a pilot task, the situation side represents the actual values of that information variables which the pilot has to perceive from his environment or to retrieve from his memory. The action side describes the actual values of the variables which he has to generate when performing a task. Each pilot task is described by a subset of productions which can be considered as part of a production subsystem (Winston, 1977). Accordingly,the large amount of knowledge required by the pilot during the landing approach could be partitioned and arranged to correspond with subsets of productions. The production control system selects the appropriate production subset which has to be applied according to the actual approach situation. The control strategy used in each subset was to follow a preset order of productions which were ranked according to their mission importance. The production database represents the interface between the pilot and his cockpit environment. The state of the database was changed by pilot actions as well as by events in his environment (Fig. 2).
r----------, :
Some pilot tasks are, e.g., "Adjust Heading Marker Position" (AD HMP), "Activate Autopilot Lateral Mode" (AC LM), "Monitor Heading" (MO HD), "Check Indicated Air Speed" (CH IAS). The intervals between te and te+l are determined by durations of such tasks. For instance, the duration of the task (MO HD) can be described by a normal distribution with a mean value of 2.5 sec and a standard deviation of 0.5 sec. Let A be the set of all tasks ak then to each ak can be assigned a mean value d{ak) of duration. With those durations the set T of all observation times can be defined: d: A ->R+
(I)
T = { t : (t=t e v t=t e +!) Ate+! =te+d(ak) A
, - - -· - - - - - - - - - - - l I
I
I I
I
I
I I
Oatabase
Envtfon-
mental Processes
VakEA31rER+: d{ak)=r
I
I I I I
I I I
The input of the pilot can be specified by those input variables which he has to perceive in his cockpit environment for a successful landing. Such variables are, e.g., indicated air speed, heading, course, altitude, and vertical speed. Let X be the set of all possible input variables Xi required by the pilot during the approach, Xi the set of all possible values of the input variable Xi' and xi{t) a value of the input variable Xi at time t ET. Therefore with the index set Ix: X (2)
I I
I I r- --- ~
___ _ _ .L~t~_...J
Fig. 2. Modeling the Pilot with Production Systems. MATHEMATICAL MODEL DESCRIPTION For the mathematical task description the pilot is regarded as a "sequential controlled system" (Klir, 1969). Generally, a controlled system is an open system which maintains relations to its environment by receiving input information from and giving output information to it. Pichler (1975) even calls it input/output system. By the term "sequential" is meant that the output at a distinct time depends not only from the input at that time but also from the cumulative history implicit in the present system state (Kammerer, 1974). To describe the behavior of a sequential input/output system Klir (1969) uses four different variables: input variables,
Here it is assumed that values xi(t) of the input variable Xi as well as values of the other variables are discrete in nature. This is permitted because the appropriate resolution level of values can be selected during the task analysis. While performing a distinct task the pilot requires only a task relevant subset of input variables, assembled in X. That subset he has to select from those variables available in the set X. To describe this selection process mathematically a relation RAX c AxX is introduced which relates the task set A to the set X of all input variables Xi' Then an element akRAXxi of the relation means that the pilot needs input variable Xi for performing task ak' Usually more than one input variable is required at a task. For describing the selection process unequivocally an variable selection function SX is introduced at which A is the domain and P{X) is the range, where P{X) is the power set of X (Fig. 3):
(3)
149
A
SX
P(X)
Let XX(ak) be the set of all value sets SXi(ak) of required input variables xi E SX(ak) for task ak" Therefore:
As an example, for task a3 the task relevant value set SHDA(a3) of the actual heading hda E SX(a3) comprises values from 0 to 360 degrees, expressed by the symbol R(O,360). The value set SHDVA(a3) of the actual heading variation hdvaESX(a3) comprises values from 0 to 4 deg/sec. It then follows: XX(a3) = {SHDA(a3),SHDVA(a3)}={R(O,360),R(O,4) } .(6)
Fig. 3. Exemplified selection function SX of task relevant input variables.
An essential attribute of a task is the output with which the pilot affects the aircraft state which in turn is reflected on his cockpit displays. Some output variables are, e.g., heading marker position, course arrow position, autopilot mode, throt-
For instance, with task a3 "Monitor Heading" the pilot has to make time estimates and predictions to determine when to again change the position of the heading marker. During this task he has to (I) evaluate whether the actual heading is in its tolerance range between 185 deg and 263 deg, (2) evaluate whether the actual heading variation is in its tolerance range between 2.5 deg/sec and 3.5 deg/sec, (3) compare the actual value of the heading with its desired value of 190 deg, and (4) estimate the time available until reaching 190 deg. Input variables which the pilot has to read from his instruments are the actual heading hda and the actual heading variation hdva. Therefore, the set of task relevant input variables is SX(a3) = {hda,hdva} • At a task ak only a subset of the value set Xi belonging to the input variable xi E SX(ak) is required. This subset again has to be selected by the pilot for each task. To describe this selection process mathematically another relation RAX i c AxXi is introduced which relates the set A to the set Xi so that an element akRAXixi(t) characterizes that the pilot needs the value xi(t) of the input variable xi for performing task ak. Because more than one value xi(t) may be of relevance with task ak a value selection function SX i is used with A as domain and P(X i ) as range, where P(X i ) is the power set of Xi (Fig. 4):
tle position, and vertical speed. For specifying the output mathematically, let Yi be the value set of the output variable Yi' Y the set of all output variables Yi necessary during the landing approach . For specifying task relevant output variables and their task relevant values, output selection functions SY and SY i are defined: SY : A -+P(Y) : V ak E A 3 1 y* E P(Y) SY i : A-+ P(Y i ) : VakEA:!1 Yi*EP(Y i ) Let YY(ak) be the set of all value sets SYi(ak) of required output variables Yi E SY(ak) for task ak. Therefore:
For instance, with task a3 there is no output because it is a monitoring task. Therefore, SY(a3)=~. But with task al "Adjust Heading Marker Position" the set SY(al) of task relevant output variables contains the heading marker position hdmp as an element. This task appears during the approach at distinct points of time at which distinct actions, Le., the values 90, 170, 190 deg of hdmp, have to be entered into the autopilot. Therefore, the set SHDMP(al) which represents the task relevant values of the variable hdmp contains those values as elements. That means: {{90,170,190}} •
A
(9)
P(Xj)
Internal Variables It is assumed that during task performance the pilot generates temporary information which is used for generating the task relevant output and for selecting the successor task. Because those information variables do not appear externally they are called internal variables. By considering them it is possible to describe mathematically the function between input and ouput . Let Wi be the value set of the internal variable wi and W the set of all internal variables wi. Then selection functions SV and SV i are defined for specifying task relevant internal variables and their values: SW : A-+P(W) :VakE A3 1 W*Ep(W) : SW(ak)=W*,
(IO)
SW i : A-+P(W i ) :VakEA31Wi*EP(Wi): SWi(ak)=W i *· Fig. 4. Exemplified selection function SX i of task relevant values of the input variable xi.
ADE-F
Let WW(ak) be the set of all value sets SWi(ak) of internal variables vi ESW(ak) which are relevant to
l:jO
B. [)iirillg
task ak then WW(ak) is given by:
iable vi which has to be store d, and V the set all vi' It then follows:
V= X UY UW For instance, with task a3 "Monitor Heading" the pilot has to make time estimate s and predictions to determine when to again change the position of the heading marker. The result of his decisions can be described by the internal decision variable dvhr of the heading range, dvvr of heading variation range, dvhd of the difference between actual and desired heading, dvt10 and dvt25 of 10 sec respectively 25 sec available time until reaching the desired heading of 190 deg. Because these variables are Boolean in nature the ir value sets contain the elements 0 and L. Depending on his decision the pilot has to perform successor task ai' a3' a28' or a37' For describing the selection of successor tasks an internal variable, called st, is used. Then, the set SW(a3) contains those mentioned internal variables. The sets SDVHR(a3)' SDVVR(a3), SDVHD(a3)' SDVT10(a3)' and SDVT25(a3) take the values 0 and L, and SST(a3)= ( al,a3,a28,a37 ) ' Therefore: {dvhr,dvvr,dvhd,dvt10,dvt25,st} (SDVHR(a3),SDVVR(a3),SDVHD(a3)' SDVTIO(a3),SDVT25(a3),SST(a3))
(12)
{{O,L ),{o,d, {O,L),{O,L}, {O,L}, ( al,a3,a28,a37 } )
For performing a task the pilot has to rely on resources which he has stored previously in his long term memory during his training or during the performance of previous tasks. The variables which describe those resources are called memory variables. They may be previously stored input, output, or internal variables. F~r describing them formally let Ui be the set of values of such a memory variable ui and U the set of all ui' From these variables and their values the pilot selects task relevant subsets for task performance. Selection functions SU and SUi are introduced for describing the selection process mathematically: SU : A-+P(U) : VakE A 3 1 U* EP(U) : SU(ak)=U*,
(13)
SUi: A-+ P(U i ) : V akEA3 1 Ui*EP(U i ) : SUi(ak)=U i *, Let UU(ak) be the set of all value sets SUi(ak) of memory variables ui ESU(ak) for task ak' Therefore:
For instance, for accomplishing task a3 "Monitor Heading" which was described previously in detail the pilot needs the desired heading hdd, the desired heading variation hdvd, and the ranges hdr and hdvr of both heading and heading variation in which the actual heading and the actual heading variation have to be located. Because for task a3 he has to retrieve values of these variables from his memory they are task relevant memory variables. Respective value sets are SHDD(a3)= { 190} , SHDVD(a3)= ( 3 ) , SHDR(a3)=R(185,263), and SHDVR(a3)=R(2.5,3.5). Therefore: ( hdd,hdvd,hdr,hdvr ) ,
(15)
and
of (16)
During task performance only subsets of V and Vi will be stored. This can be described mathematically by storage s e lection functions SV and SV i :
(17)
With the set VV(ak) of all value sets SVi(ak) of variables Vi E SV(ak) which the pilot must store during task ak follows:
For instance, with task a3 "Monitor Heading" the pilot estimates the time until reaching the desired heading of 190 deg. If this time is greater then 25 sec, then after accomplishing the monitor task, he continues with a cross-check of relevant flight variables. If this check is completed without detection of a failure he then can be idle for a while because the difference between actual and desired heading is still large enough. To decide to be idle after the cross check he has to have in mind that the time estimate was greater then 25 sec. This is the case if the internal decision variable dvt25 takes the value dvt25(t)=L. Therefore the pilot has to store that value during task a3: ( dvt25 ) c SW(a3) , (19)
Because a task ak is represented only by its onset time te and completion time t e +1=t e +d(ak) it is assumed that variables Xi and ui are selected at te and variables Yi' Vi' and wi are generated at t e + 1 • Therefore, for mathematically describing pilot behavior for a task, the variables cannot be related directly. Rather, new behavior relevant variables p and q have to be derived from task relevant variables. For describing that transformation, a time identi f i e r A is applied which has the values -d(ak) and O. The relationship between task relevant and behavior relevant variabl e s is specified with oneto-one correspondences (Klir, 1969). Using te+l as time reference point, behavior relevant variables Pm' Pn' q., and qs can be specified, with te= te+l-d(akJ and te,t e + l E T, xh(t +l-d(ak))E SXh(ak)' ui(t e + 1-d(ak))ESU i (ak)' Yj(t e +1)ESY j (ak)' wl(t e +1)E SW(ak) as follows (Fig. 5): Pm( te+l)
xh(te+l-d(ak))
(h,-d(ak)<->m,
Pn (te+l)
ui (te+l-d(ak))
(i, -d (ak) )<-> n,
qr(t e +1)
y j(t e +1)
(j ,O)<->r,
qs(te+l)
wl (te+l)
(1,0)<-> s.
(20)
Let Pm' Pn , Qr' and Qs be the value sets of Pm' Pn qr' and qs then follows:
{{ 190}, {3}, R(185, 263), R( 2.5,3.5)} Variables related to a spe c ial type of memory,i.e., short term memory, are those which have to be stored temporarily by the pilot when performing a task. Those variables are used later when performing a successor task. The y may be task r e levant input, output, or internal variabl e s. Let Vi be the set of values vi(t) of suc h short term memory var-
Let C(ak) be the set of all Pm' Pn , Qr' and Qs which are specified for ak' then C(ak) is given by:
1,,1
!\Jodelling Supenisol'Y Pi lol Beha,-ior
ti me
x
le =(te+1-d(a k))
,....-
-
u
y w
xh(t e ) Uj
t e+1
-- --
(te)
-
- --
-- --- -
Yj(te+ll
---
-
----
= («hda(t),*,*,*,R(185,263),*,*,*,*,*,*),L) hda(t) E R(185,263), «hda(t),*,*,*,R( 185,263),*,*,*,*,*,*),O) : hda(t) ~ R(l85,263)}.
te+ 1 Pn(te+ll
p
I---- -
---
q
Fig. 5. Transf o rmation x,
u,
and
Pm (te+ll _._---
+--
Qs(te+1) - - - - - -1--- - Qr! t e+ 1)
of task r eleva nt
w variables p and q. y,
into behavior
( 25)
(5HDA(a3) x SHDVA(a3) x SHDD(a3) x 5HDVD(a3) x 5HDR(a3) x SHDVR(a3) x 5DVVR(a3) x 5DVHD(a3) x 5DVT10(a3) x 5DVT25(a3) x 5ST(a3» x 5DVHR(a3)'
1-- - - -
WI(te+1)
time
(XQ1, Ql ) = (X SDVHR(a3)' 5DVHR(a3»
--
variables relevant
The pilot behavior for a task ak is represented by a set RQ(ak) of relations which temporarily exist between all sets Pi and Q- during the time d(ak) and which are invariant during that time. With differences Qr=C(ak) - {Qr}and Qs=C(ak)- {Qshhis ca n be expressed mathematically by binary relations ~Qr a~d RQ s which exist between Cartesian produc ts XQ., XQ s and the sets Qr' Qs respectivel~ (Klir, 1969) . Th~n the binary relations RQr c (XQr,Qr) and RQ s c (XQs,Qs) are given by:
El ements of the rel a tion RQl are tupels the co-ordinat es of which are the values of the task r e l e vant variables. Th e symbol * i nd ica t e s that the corresponding variables hdva, hdd, hdvd, hdvr, dvvr, dvhd, dvtl0, dvt25, and st do not influence the decision variable dvhr of the heading range . The symbol represents all values of those vari a bles . The decision variable dvhr t akes the value L if the val ue hda(t) of the actual head ing hda takes values between 185 deg and 263 deg, otherwise dvhr(t)=O . The relation RQ6 c (XQ6,Q6) specifies the branc hing from th e task a3 to the successor tasks:
Q6
55T(a3) = C(a3)-{Q6} = C(a3)- {S5T(a3) } ( 5HDA(a3),SHDVA(a3),5HDD(a3),5HDVD(a3)' 5HDR(a3)' 5HDVR(a3),5DVHR(a3),5DVVR(a3)' 5DVHD(a3) ,5DVTIO(a3) ,5DVT25(a3) } , (26) (SHDA(a3) x 5HDVA(a3) x 5HDD(a3) x 5HDVD(a3) x 5HDR(a3) x 5HDVR(a3) x SDVHR(a3) x 5DVVR(a3) x 5DVHD(a3) x 5DVT10(a3) x 5DVT25(a3» x 55T(a3)'
RQ6 c (X 55T(a3)' 55T(a3» Applying the specified equations to variables which are relevant to task a3 "Monitor Heading", as an example, behavior relevant value sets P and Q which are elements of the set C(a3) can be deriv ed fo r t hat task: {P 1 ,P 2 }
(SHDA(a3),SHDVA(a3)} {P3,P4,P 5 ,P6} , (SHDD(a3),5HDVD(a3),SHDR(a3),5HDVR(a3) }
fJ ,
(24)
{ Q1 ' Q2 ,Q3 ,Q4 ,Q5' Q6 } ( 5DVHR( a3 ),SDVVR(a3),5DVHD(a3)' SDVT10(a3),SDVT25(a3),55T(a3) } , (SHDA(a3),5HDVA(a3),5HDD(a3),SHDVD(a3)' 5HDR(a3),SHDVR(a3),5DVHR(a3),SDVVR(a3)' 5DVHD(a3),5DVT10(a3),5DVT25(a3),5ST(a3) } • For describin g th e pilot behavior which are required with t~ks a3 the differen ces Ql' Q2' Q3' Q4' Q5' and Q6 are generated and the relations RQ[, RQ2' RQ3' RQ4' RQS' RQ6 are estab~ished. As an exam~e, only relations RQl c (XQ1,Ql) and RQ6 c (XQ6,Q6) are r ega rded in the f ollowing:
{ «*,*,*,*,*,*,O,*,*,*,*),a37)' «*,*,*,*,*,*,L,Q,*,*, * ),a37)' «*,*,*,*,*,*,L,L,O,*,*), aO l)' «*,*,*,*,*,*,L,L,L,O,*),a03)' «*,*,*,*,*,*,L,L,L,L,*),a28) } Again, the symbol * characterizes variables like hda, hdva, hdd, hdvd, hdr, hdvr, and dvt25 which do not direc tl y influence the selection of the s uccessor task . The value 0 of the decision variable dvhr of the heading range indicates that the heading is out of its situation specific t o l e rance. The n the s ucc esso r task a37 "Perform Failure Procedure" has to be accomp l ished by the pilot . Th e same is true if the decision variable dvvr of the heading varia tion range takes the value o. If both variables take the value L the n branching depends on the val ue of decis ion variable dvhd of the diff e rence between actual and desired heading . dvhd(t)=O indi cates that the actual headi ng has re ached the des ired heading. Then the successor ta s k al "Adjust Heading Marker Position" has to be pe r formed. If there is any difference between both he adings then the decision variable dvtl0 specifies whether the available time until reaching the desired headi ng is g r ea t e r or le ss then 10 sec.dvtl 0(t)=L indi ca t es that there are more than 10 sec available, i . e., that there is enough time to pe rform a cross - check which starts with task a28 "Check Indicat e d Air Speed". In the case of dvtlO(t)=O a3 is the s ucc es sor task, i.e., the pilot continues to monitor the headi ng . Expressing these decisio n s ituations with productions, the fol l owing rul es ca n be established:
B. OiirillgIF dvhr(t)=O, THEN perform st a37 "Failure Procedure". IF dvhr(t)=L and dvvr(t)=O, THEN perform st a 37 "Failure Procedure". IF dvhr(t)=L and dvvr(t)=L and dvhd(t)=O, THEN perform st a l "Adjust Heading Marker
Position" .
IF
dvhr(t)=L and dvvr(t)=L and dvhd(t)=L and dvtIO(t)=O, THEN perform st a3 "Monitor Heading". IF
dvhr(t)=L and dvvr(t)=L and dvhd(t)=L and dvtIO(t)=L, THEN perform st a 28 "Check Indicated Air Speed". Comparing generally an element (qi(te+I),qi(t e + I » of a relation RQ i with a production it then becomes obviously that ~i(te+l) specifies the left situation side of a production and qi(t e + l ) the right action side. Some elements describe the selection of the successor task, e.g ., the elements of relation RQ with the t ask "Monitor Heading". There6 fore, tney represent productions which can be regarded as components of a decentralized control system. Consequently, RQ(a k ) represents the set of all productions which describe the pilot behavior required for perfoming a task a k and for selecting the successor task depending on the situation. CONCLUSION All possible sequences of pilot tasks which are considered as elements of his supervisory behavior can be represented in a complex network. With the formalisms of Klir's general system theory, this network and detailed information processing task aspects can be modeled. Each task is described by a set of binary relations among behavior relevant va ri ables which are task specific and invariant during task duration. Relation elements specify mathematically that production subsystem which models the task. By means of one-to-one correspondences behavior relevant variables are derived from task relevant input, output, internal, and memory variables. The pilot selects those task relevant variables and their corresponding task relevant values from available variables and their possible values. The required selection process was described by selection functions. By means of a task analysis , elements of selection functions can be determined. They are the basis for establis hing the binary relations and consequently for developing the mathematical behavior model of the pilot. The requirements of that model advantageously guide the suppo rting tasks analysis. The resulting model effectively combines the features of network techniques and production systems for simulating pilot's supervisory behavior. With a network technique different types of pilot tasks a nd their mission-dependent predecessor/successor relations can be modeled. Production systems were used for modeling tasks in detail. Advantages of production systems include, e . g., the modular structure of productions used for the detailed description of each ta sk, and their uniform information presentation with condition-a ction pairs. Therefore, the resulting model suppo rts and simplifies the development of a simulation program.
REFERENCES Barr, A., E.A. Feigenbaum (Ed.)(1981). The Handbook of Artificial Intelligence, Vol.I . HeurisTech Press, Stanford, CAL, William Kaufmann, Inc., Los Altos, CAL.
Davis, R., J. King (1977). An overview of production systems. In Elcock, E.W., D. Michie (Ed.), Machine Intelligence 8. Halsted Press/John Wiley&Sons Inc., New York, London, 300-332 . Daring, B. (1983). Analyse des Arbeitsprozesses bei der Fahrzeugfuhrung am Beispiel eines Landeanflugs; Eine systemergonomische Simulationsstudie. Forschungsinstitut fur Anthropotechnik, Wachtberg-Werthhoven, Bericht Nr.59. Daring, B., A. Knauper (1983). A simulation study with a combined network and production system model of pilot behavior on an ILS-approach. In Automatica, Vol.19, No.6, 741-747. Kammerer, W. (1974). Einfuhrung in mathematische Methoden der Kybernetik, 2.Auflage. Akademie Verlag, Berlin. Klir, G.J. (1969). An Approach to General Systems Theory. Van Nostrand Reinhold Comp., New York, London. McCormick, E.J. (1976). Human Factors in Engineering and Design. McGraw-Hill Book Comp., New York, London. Nilsson, N.J. (1980). Principles of Artificial Intelligence. Tioga Publishing Comp., Palo Alto, CAL. Pew, R.W., S. Baron, C.E. Fehrer, D.C. Miller (1977) . Critical review and analysis of performance models applicable to man machine systems evaluation. Bolt, Beranek and Newman Inc., Cambridge, MA, BBN Report No . 3446. Pichler, F. (1975). Mathematische Systemtheorie; Dynamische Konstruktionen. W.de Gr uyter Verlag, Berlin, New York . Rouse, W.B. (1980). Systems Engineering Models of Human-Machine-Interaction. North-Holland, Oxford, New York. Seifert, D.J., B. Daring (1981). SAINT - Ein Verfahren zur Modelliering, Simulation und Analyse von Mensch-Maschine-Systemen. In Angewandte Systemanalyse, Vo1.2, 3, 127-135. Sheridan, T.B. (1976). Preview of models of the human monitor and supervisor. In T.B. Sheridan, G. Johannsen (Ed.) Monitoring Behavior and Supervisory Control. Plenum Press, New York, 175-180. Winston, D.H. (1977) . Artificial Intelligence. Addison-Weslex, London.
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MODELING SUPERVISORY PILOT BEHA VIOR WITH GENERAL SYSTEMS THEORY FORMALISMS B. Doring Foncilllllpinlfifllf /fir ,4I1filruj}(Jf"rilllik, D-5JO/ \\'{J(ilflil'lg-\\'l'Ifhil{)"I'II , F[?(;
Abstract. In a simulation study, conducted to determine information flow at a pilotcoclZpClt- -interface during an automated landing approach, a mathematical model of pilot's supervisory control tasks was developed. For modeling those tasks and their network combination, production systems were used and described with general systems theory formalisms. For that the pilot was considered as a sequential input/output system and described with input, output, internal, and memory variables. While performing a task, only subsets of all variables and of their value sets are required. For describing the pilot's selection behavior, selection functions were introduced which specify task relevant variables and their values. From task relevant variables, behavior relevant variables are derived. Then the task performance behavior of the pilot can be described with binary relations among all value sets of behavior relevant variables which are task specific and invariant during the duration of a task. Each relation element represents an ordered pair of coordinates of which the first describes the left situation side of a production rule and the second its right action side. The resulting model guides the required task analysis and supports the development of a simulation program. Keywords. Man-machine systems; Models; Ergonomics; Artificial intelligence; Simulation.
INTRODUCTION
System theory;
System
analysis;
MODELING THE PILOT'S BEHAVIOR
In highly automated man-machine systems, such as ships, aircraft, and nuclear power plants, operators are increasingly involved with monitoring and supervisory control tasks in addition to, or instead of, continuous control tasks. In modeling the human supervisor, different approaches have been applied. They include applications of control theory, queuing theory, fuzzy set theory, network techniques, and production systems (Pew and col leguages, 1977; Rouse, 1980). This presentation reports a model which was developed for simulating the information flow between a pilot and his cockpit environment during a highly automated landing approach. During such an approach the pilot has to perform a number of distinct supervisory control tasks. According to the predecessor/successor relations between those tasks a network technique was applied for mode ling the situation-dependent branching between tasks. Production systems were used for each task to model pilot's information processing in detail. The basic structure of that model and its utilization in a simulation study was already described by Daring and Knauper (1983). Here it will be shown how the model was described mathematically with formalisms of the general systems theory of Klir (1969). A detailed presentation of that model description is given by Daring (1983).
During an automated landing approach the pilot has to perform various supervisory tasks. To determine those tasks they were considered to be normative, i.e., what the pilot should do during the landing approach (Sheridan, 1976). Those tasks were categorized into five types, viz, adjusting, activating, monitoring, checking, and special tasks. By considering the course of events during the approach, predecessor/successor relations among the identified tasks were determined so that the tasks could be arranged in a task network (Seifert and Daring, 1981). In order for the pilot to perform his tasks, he has to perceive input information from his cockpit environment. He then has to process this information for generating outputs to affect that environment. Each task can be analyzed into basic functions which represent the constituents of pilot activities. Those functions are sensing (information receiving), information processing and decision, action (physical control or communication), and information storage (McCormick, 1976) (Fig. 1). Here it is assumed that the task relevant information can be determined through a task analysis. The flow of information through the basic functions is not considered in detail but only the time duration
InformatIon storage /
Sensing (information receivIng)
J
+ I
Information processing and decision
Fig. I. Types of basic operator functions.
117
""
Action functions ( physical cant rol 0 r communication)
148
B. Diiring output variables, internal variables, and memory variables. The mathematical formalisms used for all variables to describe the pilot behavior are explained below in detail only for the input variables. For the other variables formalisms are explained in detail only in part.
which the pilot needs for performing a task, i.e. from beginning of sensing to completion of his action. Furthermore it is assumed that the input information is only received at the beginning of a task and not during the task performance. Production systems were used in modeling pilot tasks. The major elements of a production system are a database, a set of productions, and a control system (Barr and Feigenbaum, 1981; Davis and King, 1977; Nilsson, 1980). The productions operate on the database. Rouse (1980) defines a production as situation-action pair where the situation side is a list of things to watch for and the action side is a list to do. The actions resulting from one production change the database. The control system chooses which applicable production should be applied.
According to the stated assumptions and the selected degree of detail a task is the smallest behavioral element which is represented in the model by its onset time, t e , and by its completion time, te+l> with te,te+! ER++, R++=R+U {O} (U = union), and R+ the set of all positive real numbers. It is assumed that the completion of a task coincides with the start of its successor task. Therefore, each time characterizes the end of a task as well as the start of another. The only exeptions are the very first task onset time te=O at which no predecessor task exists, and the completion time of the last task at which no successor task follows.
Applying the production scheme to a pilot task, the situation side represents the actual values of that information variables which the pilot has to perceive from his environment or to retrieve from his memory. The action side describes the actual values of the variables which he has to generate when performing a task. Each pilot task is described by a subset of productions which can be considered as part of a production subsystem (Winston, 1977). Accordingly,the large amount of knowledge required by the pilot during the landing approach could be partitioned and arranged to correspond with subsets of productions. The production control system selects the appropriate production subset which has to be applied according to the actual approach situation. The control strategy used in each subset was to follow a preset order of productions which were ranked according to their mission importance. The production database represents the interface between the pilot and his cockpit environment. The state of the database was changed by pilot actions as well as by events in his environment (Fig. 2).
r----------, :
Some pilot tasks are, e.g., "Adjust Heading Marker Position" (AD HMP), "Activate Autopilot Lateral Mode" (AC LM), "Monitor Heading" (MO HD), "Check Indicated Air Speed" (CH IAS). The intervals between te and te+l are determined by durations of such tasks. For instance, the duration of the task (MO HD) can be described by a normal distribution with a mean value of 2.5 sec and a standard deviation of 0.5 sec. Let A be the set of all tasks ak then to each ak can be assigned a mean value d{ak) of duration. With those durations the set T of all observation times can be defined: d: A ->R+
(I)
T = { t : (t=t e v t=t e +!) Ate+! =te+d(ak) A
, - - -· - - - - - - - - - - - l I
I
I I
I
I
I I
Oatabase
Envtfon-
mental Processes
VakEA31rER+: d{ak)=r
I
I I I I
I I I
The input of the pilot can be specified by those input variables which he has to perceive in his cockpit environment for a successful landing. Such variables are, e.g., indicated air speed, heading, course, altitude, and vertical speed. Let X be the set of all possible input variables Xi required by the pilot during the approach, Xi the set of all possible values of the input variable Xi' and xi{t) a value of the input variable Xi at time t ET. Therefore with the index set Ix: X (2)
I I
I I r- --- ~
___ _ _ .L~t~_...J
Fig. 2. Modeling the Pilot with Production Systems. MATHEMATICAL MODEL DESCRIPTION For the mathematical task description the pilot is regarded as a "sequential controlled system" (Klir, 1969). Generally, a controlled system is an open system which maintains relations to its environment by receiving input information from and giving output information to it. Pichler (1975) even calls it input/output system. By the term "sequential" is meant that the output at a distinct time depends not only from the input at that time but also from the cumulative history implicit in the present system state (Kammerer, 1974). To describe the behavior of a sequential input/output system Klir (1969) uses four different variables: input variables,
Here it is assumed that values xi(t) of the input variable Xi as well as values of the other variables are discrete in nature. This is permitted because the appropriate resolution level of values can be selected during the task analysis. While performing a distinct task the pilot requires only a task relevant subset of input variables, assembled in X. That subset he has to select from those variables available in the set X. To describe this selection process mathematically a relation RAX c AxX is introduced which relates the task set A to the set X of all input variables Xi' Then an element akRAXxi of the relation means that the pilot needs input variable Xi for performing task ak' Usually more than one input variable is required at a task. For describing the selection process unequivocally an variable selection function SX is introduced at which A is the domain and P{X) is the range, where P{X) is the power set of X (Fig. 3):
(3)
149
A
SX
P(X)
Let XX(ak) be the set of all value sets SXi(ak) of required input variables xi E SX(ak) for task ak" Therefore:
As an example, for task a3 the task relevant value set SHDA(a3) of the actual heading hda E SX(a3) comprises values from 0 to 360 degrees, expressed by the symbol R(O,360). The value set SHDVA(a3) of the actual heading variation hdvaESX(a3) comprises values from 0 to 4 deg/sec. It then follows: XX(a3) = {SHDA(a3),SHDVA(a3)}={R(O,360),R(O,4) } .(6)
Fig. 3. Exemplified selection function SX of task relevant input variables.
An essential attribute of a task is the output with which the pilot affects the aircraft state which in turn is reflected on his cockpit displays. Some output variables are, e.g., heading marker position, course arrow position, autopilot mode, throt-
For instance, with task a3 "Monitor Heading" the pilot has to make time estimates and predictions to determine when to again change the position of the heading marker. During this task he has to (I) evaluate whether the actual heading is in its tolerance range between 185 deg and 263 deg, (2) evaluate whether the actual heading variation is in its tolerance range between 2.5 deg/sec and 3.5 deg/sec, (3) compare the actual value of the heading with its desired value of 190 deg, and (4) estimate the time available until reaching 190 deg. Input variables which the pilot has to read from his instruments are the actual heading hda and the actual heading variation hdva. Therefore, the set of task relevant input variables is SX(a3) = {hda,hdva} • At a task ak only a subset of the value set Xi belonging to the input variable xi E SX(ak) is required. This subset again has to be selected by the pilot for each task. To describe this selection process mathematically another relation RAX i c AxXi is introduced which relates the set A to the set Xi so that an element akRAXixi(t) characterizes that the pilot needs the value xi(t) of the input variable xi for performing task ak. Because more than one value xi(t) may be of relevance with task ak a value selection function SX i is used with A as domain and P(X i ) as range, where P(X i ) is the power set of Xi (Fig. 4):
tle position, and vertical speed. For specifying the output mathematically, let Yi be the value set of the output variable Yi' Y the set of all output variables Yi necessary during the landing approach . For specifying task relevant output variables and their task relevant values, output selection functions SY and SY i are defined: SY : A -+P(Y) : V ak E A 3 1 y* E P(Y) SY i : A-+ P(Y i ) : VakEA:!1 Yi*EP(Y i ) Let YY(ak) be the set of all value sets SYi(ak) of required output variables Yi E SY(ak) for task ak. Therefore:
For instance, with task a3 there is no output because it is a monitoring task. Therefore, SY(a3)=~. But with task al "Adjust Heading Marker Position" the set SY(al) of task relevant output variables contains the heading marker position hdmp as an element. This task appears during the approach at distinct points of time at which distinct actions, Le., the values 90, 170, 190 deg of hdmp, have to be entered into the autopilot. Therefore, the set SHDMP(al) which represents the task relevant values of the variable hdmp contains those values as elements. That means: {{90,170,190}} •
A
(9)
P(Xj)
Internal Variables It is assumed that during task performance the pilot generates temporary information which is used for generating the task relevant output and for selecting the successor task. Because those information variables do not appear externally they are called internal variables. By considering them it is possible to describe mathematically the function between input and ouput . Let Wi be the value set of the internal variable wi and W the set of all internal variables wi. Then selection functions SV and SV i are defined for specifying task relevant internal variables and their values: SW : A-+P(W) :VakE A3 1 W*Ep(W) : SW(ak)=W*,
(IO)
SW i : A-+P(W i ) :VakEA31Wi*EP(Wi): SWi(ak)=W i *· Fig. 4. Exemplified selection function SX i of task relevant values of the input variable xi.
ADE-F
Let WW(ak) be the set of all value sets SWi(ak) of internal variables vi ESW(ak) which are relevant to
l:jO
B. [)iirillg
task ak then WW(ak) is given by:
iable vi which has to be store d, and V the set all vi' It then follows:
V= X UY UW For instance, with task a3 "Monitor Heading" the pilot has to make time estimate s and predictions to determine when to again change the position of the heading marker. The result of his decisions can be described by the internal decision variable dvhr of the heading range, dvvr of heading variation range, dvhd of the difference between actual and desired heading, dvt10 and dvt25 of 10 sec respectively 25 sec available time until reaching the desired heading of 190 deg. Because these variables are Boolean in nature the ir value sets contain the elements 0 and L. Depending on his decision the pilot has to perform successor task ai' a3' a28' or a37' For describing the selection of successor tasks an internal variable, called st, is used. Then, the set SW(a3) contains those mentioned internal variables. The sets SDVHR(a3)' SDVVR(a3), SDVHD(a3)' SDVT10(a3)' and SDVT25(a3) take the values 0 and L, and SST(a3)= ( al,a3,a28,a37 ) ' Therefore: {dvhr,dvvr,dvhd,dvt10,dvt25,st} (SDVHR(a3),SDVVR(a3),SDVHD(a3)' SDVTIO(a3),SDVT25(a3),SST(a3))
(12)
{{O,L ),{o,d, {O,L),{O,L}, {O,L}, ( al,a3,a28,a37 } )
For performing a task the pilot has to rely on resources which he has stored previously in his long term memory during his training or during the performance of previous tasks. The variables which describe those resources are called memory variables. They may be previously stored input, output, or internal variables. F~r describing them formally let Ui be the set of values of such a memory variable ui and U the set of all ui' From these variables and their values the pilot selects task relevant subsets for task performance. Selection functions SU and SUi are introduced for describing the selection process mathematically: SU : A-+P(U) : VakE A 3 1 U* EP(U) : SU(ak)=U*,
(13)
SUi: A-+ P(U i ) : V akEA3 1 Ui*EP(U i ) : SUi(ak)=U i *, Let UU(ak) be the set of all value sets SUi(ak) of memory variables ui ESU(ak) for task ak' Therefore:
For instance, for accomplishing task a3 "Monitor Heading" which was described previously in detail the pilot needs the desired heading hdd, the desired heading variation hdvd, and the ranges hdr and hdvr of both heading and heading variation in which the actual heading and the actual heading variation have to be located. Because for task a3 he has to retrieve values of these variables from his memory they are task relevant memory variables. Respective value sets are SHDD(a3)= { 190} , SHDVD(a3)= ( 3 ) , SHDR(a3)=R(185,263), and SHDVR(a3)=R(2.5,3.5). Therefore: ( hdd,hdvd,hdr,hdvr ) ,
(15)
and
of (16)
During task performance only subsets of V and Vi will be stored. This can be described mathematically by storage s e lection functions SV and SV i :
(17)
With the set VV(ak) of all value sets SVi(ak) of variables Vi E SV(ak) which the pilot must store during task ak follows:
For instance, with task a3 "Monitor Heading" the pilot estimates the time until reaching the desired heading of 190 deg. If this time is greater then 25 sec, then after accomplishing the monitor task, he continues with a cross-check of relevant flight variables. If this check is completed without detection of a failure he then can be idle for a while because the difference between actual and desired heading is still large enough. To decide to be idle after the cross check he has to have in mind that the time estimate was greater then 25 sec. This is the case if the internal decision variable dvt25 takes the value dvt25(t)=L. Therefore the pilot has to store that value during task a3: ( dvt25 ) c SW(a3) , (19)
Because a task ak is represented only by its onset time te and completion time t e +1=t e +d(ak) it is assumed that variables Xi and ui are selected at te and variables Yi' Vi' and wi are generated at t e + 1 • Therefore, for mathematically describing pilot behavior for a task, the variables cannot be related directly. Rather, new behavior relevant variables p and q have to be derived from task relevant variables. For describing that transformation, a time identi f i e r A is applied which has the values -d(ak) and O. The relationship between task relevant and behavior relevant variabl e s is specified with oneto-one correspondences (Klir, 1969). Using te+l as time reference point, behavior relevant variables Pm' Pn' q., and qs can be specified, with te= te+l-d(akJ and te,t e + l E T, xh(t +l-d(ak))E SXh(ak)' ui(t e + 1-d(ak))ESU i (ak)' Yj(t e +1)ESY j (ak)' wl(t e +1)E SW(ak) as follows (Fig. 5): Pm( te+l)
xh(te+l-d(ak))
(h,-d(ak)<->m,
Pn (te+l)
ui (te+l-d(ak))
(i, -d (ak) )<-> n,
qr(t e +1)
y j(t e +1)
(j ,O)<->r,
qs(te+l)
wl (te+l)
(1,0)<-> s.
(20)
Let Pm' Pn , Qr' and Qs be the value sets of Pm' Pn qr' and qs then follows:
{{ 190}, {3}, R(185, 263), R( 2.5,3.5)} Variables related to a spe c ial type of memory,i.e., short term memory, are those which have to be stored temporarily by the pilot when performing a task. Those variables are used later when performing a successor task. The y may be task r e levant input, output, or internal variabl e s. Let Vi be the set of values vi(t) of suc h short term memory var-
Let C(ak) be the set of all Pm' Pn , Qr' and Qs which are specified for ak' then C(ak) is given by:
1,,1
!\Jodelling Supenisol'Y Pi lol Beha,-ior
ti me
x
le =(te+1-d(a k))
,....-
-
u
y w
xh(t e ) Uj
t e+1
-- --
(te)
-
- --
-- --- -
Yj(te+ll
---
-
----
= («hda(t),*,*,*,R(185,263),*,*,*,*,*,*),L) hda(t) E R(185,263), «hda(t),*,*,*,R( 185,263),*,*,*,*,*,*),O) : hda(t) ~ R(l85,263)}.
te+ 1 Pn(te+ll
p
I---- -
---
q
Fig. 5. Transf o rmation x,
u,
and
Pm (te+ll _._---
+--
Qs(te+1) - - - - - -1--- - Qr! t e+ 1)
of task r eleva nt
w variables p and q. y,
into behavior
( 25)
(5HDA(a3) x SHDVA(a3) x SHDD(a3) x 5HDVD(a3) x 5HDR(a3) x SHDVR(a3) x 5DVVR(a3) x 5DVHD(a3) x 5DVT10(a3) x 5DVT25(a3) x 5ST(a3» x 5DVHR(a3)'
1-- - - -
WI(te+1)
time
(XQ1, Ql ) = (X SDVHR(a3)' 5DVHR(a3»
--
variables relevant
The pilot behavior for a task ak is represented by a set RQ(ak) of relations which temporarily exist between all sets Pi and Q- during the time d(ak) and which are invariant during that time. With differences Qr=C(ak) - {Qr}and Qs=C(ak)- {Qshhis ca n be expressed mathematically by binary relations ~Qr a~d RQ s which exist between Cartesian produc ts XQ., XQ s and the sets Qr' Qs respectivel~ (Klir, 1969) . Th~n the binary relations RQr c (XQr,Qr) and RQ s c (XQs,Qs) are given by:
El ements of the rel a tion RQl are tupels the co-ordinat es of which are the values of the task r e l e vant variables. Th e symbol * i nd ica t e s that the corresponding variables hdva, hdd, hdvd, hdvr, dvvr, dvhd, dvtl0, dvt25, and st do not influence the decision variable dvhr of the heading range . The symbol represents all values of those vari a bles . The decision variable dvhr t akes the value L if the val ue hda(t) of the actual head ing hda takes values between 185 deg and 263 deg, otherwise dvhr(t)=O . The relation RQ6 c (XQ6,Q6) specifies the branc hing from th e task a3 to the successor tasks:
Q6
55T(a3) = C(a3)-{Q6} = C(a3)- {S5T(a3) } ( 5HDA(a3),SHDVA(a3),5HDD(a3),5HDVD(a3)' 5HDR(a3)' 5HDVR(a3),5DVHR(a3),5DVVR(a3)' 5DVHD(a3) ,5DVTIO(a3) ,5DVT25(a3) } , (26) (SHDA(a3) x 5HDVA(a3) x 5HDD(a3) x 5HDVD(a3) x 5HDR(a3) x 5HDVR(a3) x SDVHR(a3) x 5DVVR(a3) x 5DVHD(a3) x 5DVT10(a3) x 5DVT25(a3» x 55T(a3)'
RQ6 c (X 55T(a3)' 55T(a3» Applying the specified equations to variables which are relevant to task a3 "Monitor Heading", as an example, behavior relevant value sets P and Q which are elements of the set C(a3) can be deriv ed fo r t hat task: {P 1 ,P 2 }
(SHDA(a3),SHDVA(a3)} {P3,P4,P 5 ,P6} , (SHDD(a3),5HDVD(a3),SHDR(a3),5HDVR(a3) }
fJ ,
(24)
{ Q1 ' Q2 ,Q3 ,Q4 ,Q5' Q6 } ( 5DVHR( a3 ),SDVVR(a3),5DVHD(a3)' SDVT10(a3),SDVT25(a3),55T(a3) } , (SHDA(a3),5HDVA(a3),5HDD(a3),SHDVD(a3)' 5HDR(a3),SHDVR(a3),5DVHR(a3),SDVVR(a3)' 5DVHD(a3),5DVT10(a3),5DVT25(a3),5ST(a3) } • For describin g th e pilot behavior which are required with t~ks a3 the differen ces Ql' Q2' Q3' Q4' Q5' and Q6 are generated and the relations RQ[, RQ2' RQ3' RQ4' RQS' RQ6 are estab~ished. As an exam~e, only relations RQl c (XQ1,Ql) and RQ6 c (XQ6,Q6) are r ega rded in the f ollowing:
{ «*,*,*,*,*,*,O,*,*,*,*),a37)' «*,*,*,*,*,*,L,Q,*,*, * ),a37)' «*,*,*,*,*,*,L,L,O,*,*), aO l)' «*,*,*,*,*,*,L,L,L,O,*),a03)' «*,*,*,*,*,*,L,L,L,L,*),a28) } Again, the symbol * characterizes variables like hda, hdva, hdd, hdvd, hdr, hdvr, and dvt25 which do not direc tl y influence the selection of the s uccessor task . The value 0 of the decision variable dvhr of the heading range indicates that the heading is out of its situation specific t o l e rance. The n the s ucc esso r task a37 "Perform Failure Procedure" has to be accomp l ished by the pilot . Th e same is true if the decision variable dvvr of the heading varia tion range takes the value o. If both variables take the value L the n branching depends on the val ue of decis ion variable dvhd of the diff e rence between actual and desired heading . dvhd(t)=O indi cates that the actual headi ng has re ached the des ired heading. Then the successor ta s k al "Adjust Heading Marker Position" has to be pe r formed. If there is any difference between both he adings then the decision variable dvtl0 specifies whether the available time until reaching the desired headi ng is g r ea t e r or le ss then 10 sec.dvtl 0(t)=L indi ca t es that there are more than 10 sec available, i . e., that there is enough time to pe rform a cross - check which starts with task a28 "Check Indicat e d Air Speed". In the case of dvtlO(t)=O a3 is the s ucc es sor task, i.e., the pilot continues to monitor the headi ng . Expressing these decisio n s ituations with productions, the fol l owing rul es ca n be established:
B. OiirillgIF dvhr(t)=O, THEN perform st a37 "Failure Procedure". IF dvhr(t)=L and dvvr(t)=O, THEN perform st a 37 "Failure Procedure". IF dvhr(t)=L and dvvr(t)=L and dvhd(t)=O, THEN perform st a l "Adjust Heading Marker
Position" .
IF
dvhr(t)=L and dvvr(t)=L and dvhd(t)=L and dvtIO(t)=O, THEN perform st a3 "Monitor Heading". IF
dvhr(t)=L and dvvr(t)=L and dvhd(t)=L and dvtIO(t)=L, THEN perform st a 28 "Check Indicated Air Speed". Comparing generally an element (qi(te+I),qi(t e + I » of a relation RQ i with a production it then becomes obviously that ~i(te+l) specifies the left situation side of a production and qi(t e + l ) the right action side. Some elements describe the selection of the successor task, e.g ., the elements of relation RQ with the t ask "Monitor Heading". There6 fore, tney represent productions which can be regarded as components of a decentralized control system. Consequently, RQ(a k ) represents the set of all productions which describe the pilot behavior required for perfoming a task a k and for selecting the successor task depending on the situation. CONCLUSION All possible sequences of pilot tasks which are considered as elements of his supervisory behavior can be represented in a complex network. With the formalisms of Klir's general system theory, this network and detailed information processing task aspects can be modeled. Each task is described by a set of binary relations among behavior relevant va ri ables which are task specific and invariant during task duration. Relation elements specify mathematically that production subsystem which models the task. By means of one-to-one correspondences behavior relevant variables are derived from task relevant input, output, internal, and memory variables. The pilot selects those task relevant variables and their corresponding task relevant values from available variables and their possible values. The required selection process was described by selection functions. By means of a task analysis , elements of selection functions can be determined. They are the basis for establis hing the binary relations and consequently for developing the mathematical behavior model of the pilot. The requirements of that model advantageously guide the suppo rting tasks analysis. The resulting model effectively combines the features of network techniques and production systems for simulating pilot's supervisory behavior. With a network technique different types of pilot tasks a nd their mission-dependent predecessor/successor relations can be modeled. Production systems were used for modeling tasks in detail. Advantages of production systems include, e . g., the modular structure of productions used for the detailed description of each ta sk, and their uniform information presentation with condition-a ction pairs. Therefore, the resulting model suppo rts and simplifies the development of a simulation program.
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