- Email: [email protected]
The method of the knowledge representation in an expert system for metal cutting engineering
stic decision seque
ease the effectiveness
ate facts and inference rules, which can be recorded in elements of this base, that leads to cr
approximate inference rules, make the approximate interpretation of knowledge of an expert system. This approximation, called also the un nty, is defined as lack of suitable hile making a decision on application information to make a decision under considerations to fix the methods to determine the of approximate knowledge representation, uncertainty of statements-and inference rules. any methods are known, the review of which one can find in [23. In this paper, the notation of approximate know1 ge representation is applied by means of grades of necessity and possibility. The notion of necessity and possibility can be used to extend the idea of sharp decision tables. We need to change some properties of the sharp tables. In the result, we receive a modti decision table. 09’24-0135/97/$17.00 8 1997 Elsevier Scim
PII 0924-0136 (96) 025824
S.A. Ail I$+
mewed
320
A. Paszek, R Knosala /Journal of Materials Processing Technology 64 (1997) 319-326
2. GRADE OF NECESSITY A
ITY
In [3], there is a description of grade ofpossibility notion. We assume, that variable V takes value x from set X specified in the finite space U. Let A be a fuzzy subset. In accordance with Zadeh, the statement of wriable vczlueV is a j3.q~ element of set A has grade of necessity II defined within the set X. Generally, for each x E X the possibility, that x is a value of V, is defined by function II(x), where: II(x) =A(x)
(1)
The function A(x) determines the grade of attachment of value x to the set A. The difference between II(x) and A(x) consists only in various interpretation of these functions. Affiliation function A(x) determines the x-th value of a variable, and function II(x) determines the possibility of assuming the x-th fuzzy value The work [4] containsthe definitionof grade of necessity notion. For given statement from set A, this definition may be presented in form of the following formula: N(A) = 1 - II(l A) where N(A) describes the grade of necessity of statement A by means of grade of possibility lack of statement 1 A. One can prove, that for each statement from set A C U we have the relationships [!5]: N(A f~1 A) = min[N(A),N(l A)] = 0 U(A n 1 A) = max[fI(A),II(l A)] = 1 N(A) > 0 + N(1 A) = 0 + U(A) = 1 If(A) < 1 + II(l A) = 1 + N(A) = 0
(3) (4 (3 (6)
3. DESCRIPTION OF APPROX The expert system described with approximate knowledge representation is used to aid the decision making in engineering process design of piston rod elements and glands of hydraulic servo-motors. The scope of system operation includes the procedures as follows: - semi-product selection, - determination of engineering operations necessary to make the given element, - assignment of machine tools or other operation stands for separate engineering operations, - selection of engineering tools (machine cutting tools, measurement gauges etc.), - selection of machining conditions (machining speed and rate of feed, etc.). Construction of approximate knowledge representation was started from definition of rules of engineering process formation of selected elements of hydraulic servo-motors. Input data for this stage were as follows: - geometric characteristics and production plans of elements of hydraulic servo-motor, - engineering characteristics of the system which is responsible for manufacturing process, - general engineering knowledge including theoretical rules of designing. The above mentioned rules are created on the basis of reference examinations of design problems of engineering processes as well as consultation with production engineer experts.
ISEs>
then
remises of a rule have t
deals with selection of c of their applicability
with extension of
The basic structure of modal decision tables is composed of rows and columns. Rows contain descriptions and premises values (conditions) as well as conclusions (operations) of inkrence rules. Besides, in one of last rows the output logic values are contained obtained s are inserted in columns after examination carrid out on the given decision table. De to decision table consists of separate inference rule. Realization of inference operations in examination of rules as sequence of their notation in columns, until the rule is met, for which all conditions indicated in it are fulfilled. Now, operations assigned to operation rule are carried out (also in accordance with sequence of notation). Identification of decision table elements is possible due to assignment to these elements the proper symbols.
322
A. Pas&, R Knosala / Journal qf Materials Processing‘I’echnology63 (I 997) 319-326
Not&m od approximate inference rules is performed in accordance with the assumptions as follows 163: - examination of conditions is performed on the basis of the dialogue with a user, and pairs of digits are values of these conditions interpreted as grades of necessity and possibility, respectively, of recognizing the condition as true (fulfiled), - fields of columns of right side part of table within the area of conditions contain p digits , which restrict the expected range of grades of necessity and possibilit the condition. This denotes, that the condition under examination will be considerd as when:
a< =N< =II< =b
(g)
To simplify the processes of dialogue with users of decision tables in MAS system, the linguistic constants of condition fulfilment were introduced, to which the assigned in form of pairs < NJ> . A set of such constants is as follows: - Certainly TRUE - Almost TRUE - Rather TRUE 7 1 Rather FALSE - Almost FALSE - Certainly FALSE
= = = = = = =
cl.0 l.O> co.7 l.O> <0.4 l.O> co.0 l.O> co.0 o.o>
(9) (10) (11) (12) (13) (14) (1%
Decision tables have been proposed as a special tool for writing rules and can be used directly to model knowledge bases for expert systems with forward chaining [7]. After slight modifications of exists, i.e. assuming that each table ought to return a value (e.g. YES or NO) we can speak about such tables as about special casas of conditions. Return value have to be assigned to all columns on the right-hand side of the table. Moreover, a default value ought to be assigned to the whole table in the case of incomplete sets of rules. The table returning a value can be used as a condition in another table. It is very useful to write such a table as a special case of a frame. The entries of the table ought to be written as frames, too. Such modific&ions allow to simulate some kinds of backward chaining, and allow to write the rules dealing with the knowledge (about the object) and with the meta-knowledge (about the reasoning process) in a similar, uniform way. Knowledge base contains the network of decision tables. Interconnection of tables is performed by means of table output values. A value obtained from one table has been recorded as a value of condition in another one. Due to this, it was possible to elaborate the tables characterized by small dimensions, that simplified the process of recording of tables, and their modification as well.
4. AN EXAMPLE OF MODAL DECISION TABLE Decision table presented in Table 1 has been used in selection procedure of machine tools used for roughing and profiling of hydraulic servo-motor piston rod. Rows CO1+CO3 describe conditions of inference rules. Grades of necessity and possibility of conditions have
323
ia ........ 1
repeatable k&s. .,......... __r ._C.~__r____~.,~~-~_ I . . _. ...-...... - “..“..........” .._...* wiil the production of small number d pieces prowded m lots ; Pr
. Ask
io io
0
;v
0.4 ! 0.4 ; 0.7 .i_........ _..: .:.. y
j
:.
........ y ;
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i i ; : : .:..... ...i.... ...i i i i i
.;.<
.;
.;.
.i.................. ; i : : : .. __.Ii .i._ __:;
iN ;
of small repeatabiiy?
I
.....“....‘... ..‘... .. ..:. .(. pece productton of pston rod selected?
J..
.:.
Ask
i Pr
_s!@!EL._ .. . . ___..___.._ In small lot production - make ;Y using a standard engine lathe ,..................~....,.............~...............................~.......: Indarsi;‘iai’ . .g.;. . :.~~nti .<... ..;. ... . In large-series production - turn the m&arraPUSI lathes equipped with CNC control or use multi-tad blhe We / canusealsotracerlathe:.~ _,,_,,,_,_,,,,,,__,_,.,.,,,,., ,_,,__,._,,. .._............ . .,.....i Tun roughly and shape both parts of material using one ; PI Concl operation by means of engine lathe.
.._-._.._._ _...“.._.:
: ; Pr
,
In mass production . rnak&&$%n~ &&efficient indusbial lathes. One should take into consideration ,;. ~~~ca.tjono~~~~~~!!~!~~~.nd.e.~~~~~~ Due to market demand this type of production of piston rods i Pr of hydraulic servo-motors is most frequently used.
___.._._. __.______.n
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Approximate inference rules have been recorded in columns Rl tR8. conditional portion of these rules includes row CO1, the uncertainty elements to these rules. The uncertain premise is the statement on production rate of piston rod. On the basis of examinations it was found, that repeatable lot production is most frequently used one. However, departure from these rules exist and, to ensure the full range of system utilization, record of different types of production rate were applied as ambigu one. Grades of necessity and possibility were assigned to separate types of namely: - repeatable lot production - < 0.6 1> , - small lot production and large-lot production - ~0.3 ‘I> as well as
ease the effectiveness
ate facts and inference rules, which can be recorded in elements of this base, that leads to cr
approximate inference rules, make the approximate interpretation of knowledge of an expert system. This approximation, called also the un nty, is defined as lack of suitable hile making a decision on application information to make a decision under considerations to fix the methods to determine the of approximate knowledge representation, uncertainty of statements-and inference rules. any methods are known, the review of which one can find in [23. In this paper, the notation of approximate know1 ge representation is applied by means of grades of necessity and possibility. The notion of necessity and possibility can be used to extend the idea of sharp decision tables. We need to change some properties of the sharp tables. In the result, we receive a modti decision table. 09’24-0135/97/$17.00 8 1997 Elsevier Scim
PII 0924-0136 (96) 025824
S.A. Ail I$+
mewed
320
A. Paszek, R Knosala /Journal of Materials Processing Technology 64 (1997) 319-326
2. GRADE OF NECESSITY A
ITY
In [3], there is a description of grade ofpossibility notion. We assume, that variable V takes value x from set X specified in the finite space U. Let A be a fuzzy subset. In accordance with Zadeh, the statement of wriable vczlueV is a j3.q~ element of set A has grade of necessity II defined within the set X. Generally, for each x E X the possibility, that x is a value of V, is defined by function II(x), where: II(x) =A(x)
(1)
The function A(x) determines the grade of attachment of value x to the set A. The difference between II(x) and A(x) consists only in various interpretation of these functions. Affiliation function A(x) determines the x-th value of a variable, and function II(x) determines the possibility of assuming the x-th fuzzy value The work [4] containsthe definitionof grade of necessity notion. For given statement from set A, this definition may be presented in form of the following formula: N(A) = 1 - II(l A) where N(A) describes the grade of necessity of statement A by means of grade of possibility lack of statement 1 A. One can prove, that for each statement from set A C U we have the relationships [!5]: N(A f~1 A) = min[N(A),N(l A)] = 0 U(A n 1 A) = max[fI(A),II(l A)] = 1 N(A) > 0 + N(1 A) = 0 + U(A) = 1 If(A) < 1 + II(l A) = 1 + N(A) = 0
(3) (4 (3 (6)
3. DESCRIPTION OF APPROX The expert system described with approximate knowledge representation is used to aid the decision making in engineering process design of piston rod elements and glands of hydraulic servo-motors. The scope of system operation includes the procedures as follows: - semi-product selection, - determination of engineering operations necessary to make the given element, - assignment of machine tools or other operation stands for separate engineering operations, - selection of engineering tools (machine cutting tools, measurement gauges etc.), - selection of machining conditions (machining speed and rate of feed, etc.). Construction of approximate knowledge representation was started from definition of rules of engineering process formation of selected elements of hydraulic servo-motors. Input data for this stage were as follows: - geometric characteristics and production plans of elements of hydraulic servo-motor, - engineering characteristics of the system which is responsible for manufacturing process, - general engineering knowledge including theoretical rules of designing. The above mentioned rules are created on the basis of reference examinations of design problems of engineering processes as well as consultation with production engineer experts.
ISEs>
then
remises of a rule have t
deals with selection of c of their applicability
with extension of
The basic structure of modal decision tables is composed of rows and columns. Rows contain descriptions and premises values (conditions) as well as conclusions (operations) of inkrence rules. Besides, in one of last rows the output logic values are contained obtained s are inserted in columns after examination carrid out on the given decision table. De to decision table consists of separate inference rule. Realization of inference operations in examination of rules as sequence of their notation in columns, until the rule is met, for which all conditions indicated in it are fulfilled. Now, operations assigned to operation rule are carried out (also in accordance with sequence of notation). Identification of decision table elements is possible due to assignment to these elements the proper symbols.
322
A. Pas&, R Knosala / Journal qf Materials Processing‘I’echnology63 (I 997) 319-326
Not&m od approximate inference rules is performed in accordance with the assumptions as follows 163: - examination of conditions is performed on the basis of the dialogue with a user, and pairs of digits
a< =N< =II< =b
(g)
To simplify the processes of dialogue with users of decision tables in MAS system, the linguistic constants of condition fulfilment were introduced, to which the assigned in form of pairs < NJ> . A set of such constants is as follows: - Certainly TRUE - Almost TRUE - Rather TRUE 7 1 Rather FALSE - Almost FALSE - Certainly FALSE
= = = = = = =
cl.0 l.O> co.7 l.O> <0.4 l.O> co.0 l.O>
(9) (10) (11) (12) (13) (14) (1%
Decision tables have been proposed as a special tool for writing rules and can be used directly to model knowledge bases for expert systems with forward chaining [7]. After slight modifications of exists, i.e. assuming that each table ought to return a value (e.g. YES or NO) we can speak about such tables as about special casas of conditions. Return value have to be assigned to all columns on the right-hand side of the table. Moreover, a default value ought to be assigned to the whole table in the case of incomplete sets of rules. The table returning a value can be used as a condition in another table. It is very useful to write such a table as a special case of a frame. The entries of the table ought to be written as frames, too. Such modific&ions allow to simulate some kinds of backward chaining, and allow to write the rules dealing with the knowledge (about the object) and with the meta-knowledge (about the reasoning process) in a similar, uniform way. Knowledge base contains the network of decision tables. Interconnection of tables is performed by means of table output values. A value obtained from one table has been recorded as a value of condition in another one. Due to this, it was possible to elaborate the tables characterized by small dimensions, that simplified the process of recording of tables, and their modification as well.
4. AN EXAMPLE OF MODAL DECISION TABLE Decision table presented in Table 1 has been used in selection procedure of machine tools used for roughing and profiling of hydraulic servo-motor piston rod. Rows CO1+CO3 describe conditions of inference rules. Grades of necessity and possibility of conditions have
323
ia ........ 1
repeatable k&s. .,......... __r ._C.~__r____~.,~~-~_ I . . _. ...-...... - “..“..........” .._...* wiil the production of small number d pieces prowded m lots ; Pr
. Ask
io io
0
;v
0.4 ! 0.4 ; 0.7 .i_........ _..: .:.. y
j
:.
........ y ;
.i.
i i ; : : .:..... ...i.... ...i i i i i
.;.<
.;
.;.
.i.................. ; i : : : .. __.Ii .i._ __:;
iN ;
of small repeatabiiy?
I
.....“....‘... ..‘... .. ..:. .(. pece productton of pston rod selected?
J..
.:.
Ask
i Pr
_s!@!EL._ .. . . ___..___.._ In small lot production - make ;Y using a standard engine lathe ,..................~....,.............~...............................~.......: Indarsi;‘iai’ . .g.;. . :.~~nti .<... ..;. ... . In large-series production - turn the m&arraPUSI lathes equipped with CNC control or use multi-tad blhe We / canusealsotracerlathe:.~ _,,_,,,_,_,,,,,,__,_,.,.,,,,., ,_,,__,._,,. .._............ . .,.....i Tun roughly and shape both parts of material using one ; PI Concl operation by means of engine lathe.
.._-._.._._ _...“.._.:
: ; Pr
,
In mass production . rnak&&$%n~ &&efficient indusbial lathes. One should take into consideration ,;. ~~~ca.tjono~~~~~~!!~!~~~.nd.e.~~~~~~ Due to market demand this type of production of piston rods i Pr of hydraulic servo-motors is most frequently used.
___.._._. __.______.n
_...........
_..._._.._
. . . .
_..__
.,_..,............................
i
.
‘1’
....
. _..+
.
.
‘.’
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:
;.
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.
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: : i
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______.
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i
j
Cond
: : i
i
i.
Cond
.:. Nj
.f. .._... I
L AL
..,
‘N
.
A..
.;.
.:.
i_
Approximate inference rules have been recorded in columns Rl tR8. conditional portion of these rules includes row CO1, the uncertainty elements to these rules. The uncertain premise is the statement on production rate of piston rod. On the basis of examinations it was found, that repeatable lot production is most frequently used one. However, departure from these rules exist and, to ensure the full range of system utilization, record of different types of production rate were applied as ambigu one. Grades of necessity and possibility were assigned to separate types of namely: - repeatable lot production - < 0.6 1> , - small lot production and large-lot production - ~0.3 ‘I> as well as
,
A. Paszek?R. Knasala~‘JouwtaiofMatedaIsProcessing Technolo@ 64 (1997) 319-326
324
piece and mass production - C 0 0.7 > . Values of these stage were recorded in the first row of the table, relationships (5) and (6).
-
A USE
5. AN EXAMPLE OF DIALOGUE WI
The dialogue presented here relates to the above described decision table. Questions ask a user relate to examination of conditional part of approximate inference rules. On the basis of responses provided by a user the values of separate conditions will be assumed; this leads to application of the given inference rule. The first question generated on computer screen is shown in Figure 1. The question relates to determination of grade of truth of statement. Besides, the dialogue with the system includes: - asking the questions Why?, where the response for this question contains d~sc~~tio~ of t reason of statement formation, - utilization Help, which contains the descriptio n of led notions within the range of the problem being solved.
rile
Edit
Search
Run
Uiew
Tools
MAS Options
The sentence is I’”. ..... ... ............ I...... ..I ......) iCertainly TRUE! i.............................._.............
Please, check if one may assume the following assumption:
0 Almost TRUE batches, which contain the defined number of products; they will be mostly
0
Rather TRUE
O? 0
Rather FALSE
I
0 Almost FALSE 0
Certainly FALSE
Figure 1. An example of dialogue with expert system with possibility to give the uncertain responses
aw
5
2
lathe
30
e ore
transverse
tsae second
side
hohi?s
c 7
Make shot bPasting
Figure 2. The fragment of basic description of engineering process of piston rod
In the expert system described the approximate knowledge representation was used. It was possible due to proper structure of inference rules, in which the premises contain uncertainty elements. Values of grades of necessity and possibility of separate statements are determined subjectively, that may cause some difficulties in their proper assignment to the set of
326
A. Pasrek, R Knosala /Journal of Materials Processing Technology 64 (1997) 319-3%
linguistic constantsincluded in MAS system. Decision tables network enabled the division of e decision problems into stages, being solved by single decision tables. Due to this modification. modular achitecture of knowledge base was obtained, an easy one for Application of the expert system shell improved construction of base of engi~~~ng knowledge and enabled the effective processing of this knowledge. The expert syst presented serves as database of existing engineering processes as well as makes possible aid in making the decisions while designing new engineering processes of machine elements which are alike from point of view of engineering process.
1. R. Maus and J. Keyes, Handbook of expert systems in manufacturing, McGrawNew York, 1991. 2. W. Cholewa, Approximate statements in expert systems, III-rd International Conference “Achievements in the mech‘anicaland material engineering”, Gliwice, 1994, pp. 49-62, (Polish). 3. R. Yager and D. Filev, Essential of fuzzy modelling and control, John Inc., New York, 1994, pp. 24-25. 4. D. Dubois and H. Prade, Fuzzy Sets and Systems. Academic Press, New York, 1980. 5. W. Cholewa and W. Pedrycz, Expert systems, Handbook nr 1447, Silesian Technical University, Gliwice, 1987, pp. 76-83 (Polish). 6. W. Cholewa, MAS - shell expert system - User’s Guide, Chair of Fundamen Machine Design, Silesian Technical University, Gliwice, 1993, (Polish). 7. W. Cholewa and W. Moczulski, Knowledge acquisition in shell expert system International Conference on CIM, Gliwice, 1994, pp. 109-122. 8. A. Paszek and R. Knosala, Approximate reasoning in the expert system for engineering processes design, XIII-th Conference “Polioptimization and CA Kolobrzeg, 1995, pp. 163-170, (Polish).