FUZZY HUMAN/MACHINE RELIABILITY USING VHDL

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1 FUZZY HUMN/MCHINE RELIBILITY USING VHDL Carlos. Graciós M. 1, lejandro Díaz S. 2, Efrén Gorroiea H. 3 (1) Insiuo Tecnológico de Puebla v. Tecnológico 420. Col. Maravillas, C. P , Puebla, Pue. México (2) Insiuo Nacional de srofísica, Ópica y Elecrónica (INOE) Luis Enrique Erro No. 1, Tonanzinla, Pue. México (3) Insiuo Tecnológico de Queréaro v. Tecnológico S/N Esq. M. Escobedo, Col. Cenro, C. P , Qro. México (1) cgracios@ipuebla.edu.mx, (2) adiazsan@inaoep.mx, (3) efren.hurado@usa.ne BSTRCT novel algorihm o generae Human/Machine model is proposed. generalised scheme is applied using Dynamic Sysems (FDS) arihmeic. To deermine he rihmeic Srucures, a NETLIST is developed o ranslae he Graph informaion in a VHDL descripion. The rihmeic is coded using VHDL for he implemenaion of he scheme obained in a Programmable Device for validaion. 1. INTRODUCTION The modelling and simulaion of Dynamic Sysems have ineresed in he las 30 years o academic and indusrial communiies [1]. Due he complexiy o model and simulae FDS, several soluions have been proposed in his focus [2, 3]. One of he mos acual problems found in indusrial applicaion is o improve he ineracion of Humans wih sofware and Hardware in an Open and Dynamic Srucure scheme for he new Inelligen Manufacuring Sysems (IMS) [4]. Several conribuions on he applicaion of approach o solve hese ypes of problems can be found in recen lieraure. Zadeh and Gupa sars wih his ype of proposiion where Gupa, Pedrycz, Sugeno and Yasukawa ake heirs conribuion basis [8]. Yager and Filev address heir suggesions o inroduce Linguisic models (LM) for FDS. Mandani-Type (Consrucive) and Logical-Type (Desrucive) are he wo principal ypes of LM for is applicaions in modelling and conrol of several ype of process. However, Terano [3] and his colleagues, propose new applicaions in he indusrial area. I is due he mos plan and ranspor breakdowns happen because of some form of human error. I can be considered has he acual problemaic in erms of creae improved manufacured sysems where human aciviies are modelled by Schemes. The presen work begins wih he fundamenal conceps of FDS where a Finie auomaon is proposed o generalise he ypical descripion of FDS. fer ha, he new scheme o describe srucure and behaviour of his sysems are defined as a generalised algorihm o generae he VHDL core descripion. The relaionship beween FDS model and VHDL algorihm descripion is expressed o demonsrae heir similariies. Finally, an example of modelling and simulaion of a FDS is described. 2. FUNDMENTL CONCEPTS ll By definiion [7], a finie auomaon is a dynamic sysem operaing in discree ime ha ransform sequences of oupu saes (responses) produced a he oupu of he sysem. each discree ime, he response of he sysem is deermined because of he received simulus and he inernal sae of he sysem. I response is used o obain he new acual sae. If he finie saes of an auomaon are defined by fuzzy ses, and each discree sae and fuzzy relaion expresses is response, hen a Finie fuzzy auomaon (FF) is obained (See figure 1), i.e.: 1

2 Relaions B R and S Sorage C = E -1 Inpu Sysem R Oupu Figure 2. Sysem wih Inpu and Oupu In his ype of scheme, wo paricular problems can be considered: B Figure 1. Generalised Dynamic Sysem. ={X, Y, Z, R, S} (1) where: X is a nonempy finie se of inpu saes (Simuli), Y is a nonempy finie se of oupu saes (responses), Z is a nonempy finie se of inernal saes, R is a fuzzy relaion on Z x Y, and S is a fuzzy relaion on X x Z x Z. dding a his definiion, o observe he evoluion of any FF i is necessary calculaing his se of equaions. This se of equaion are sufficien for handling any sequence 1, 2, r of r fuzzy inpu saes applied o a given iniial fuzzy sae C 1. ( ) ( i j) = ( k) ( k i j) S z, z max min k N n x, S x, z, z K(2) E = C os K(3) B C R = o K(4) This definiion can be exended o obain a Dynamic Sysem (FDS) where X, Y and Z ses have same definiion for a FF. However, T and U ses are included o analyse he evoluion in he discree ime for he saes defined of he sysem. If we can observe as he fuzzy inpu, B as he fuzzy oupu, and R as he fuzzy sysems, he FDS can be considered as any fuzzy process where a any inpu responses a B oupu in erms of he parameric elemens defined for he R and S inernal relaions. The values of he fuzzy parameers could represen he adjusmens of movemens in a ypical human aciviy as is showed by Terano. The scheme in figure 2, express his concepion. a) Given and R, find B (Oupu resuls). b) Given, and B, find R (The parameers of he fuzzy sysems) Now, Relaions equaions are applied o solve he second problem, hen we can consider, for any a, b [0,1], le 1; a b (5) a α b = b ; a > b wih his new definiion, R can be obained. To calculae he values in he fuzzy model, a fas programmable device is required o sample in efficien ime he aciviies in each resource of he sysem. 3. GENERLISED LGORITHM In his par, he wo paricular problems in he FDS definiion are solved; proposing an algorihm o ranslae he graph-marix expressions described in par 2 a a VHDL code. I is due, VHDL is an acual ool o model, simulae and conrol of discree even sysems (DES) [5]. If we consider any sequence of aciviies has non-deerminisic, and ake in accoun he resuls obained by Salapura & Hamman [6], hen VHDL represens an adequae ool for he rapid prooyping of FDS o model or conrol he behaviour of acual sysems[5]. library IEEE; use IEEE.STD_LOGIC_1164.LL; use IEEE.STD_LOGIC_RITH.LL; use IEEE.STD_LOGIC_UNSIGNED.LL; use WORK.FUZZYEVL:LL; eniy FDS is Por ( : in sd_logic_vecor(7 downo 0); C1 : in sd_logic_vecor(15 downo 0); B: ou sd_logic_vecor(11 downo 0)); end FDS; Figure 3. Srucural descripion of a FDS in VHDL 2

3 a) Given and R B. Using he iniial definiion for he srucural par of he FDS,, C1 will be inpu por for he FDS and B he oupu, hen a LM is proposed in figure 3. I shows he Generic eniy descripion for a FDS, where he descripion library used he IEEE sandard for digial circui descripion. Noe ha FUZZYEVL library is proposed o evaluae he operaion for he evoluion of he FDS. This library is used for behavioural descripion. Now, o obain he behaviour of he sysem, he calculaion of S is basic. nalysing he fuzzy operaions needed o obain he nex sae in he FDS from equaion (2) a generalised algorihm can be described. 1) Define Xdim, Ydim, Zdim; 2) Define R(Ydim,Zdim), SX1(Zdim,Zdim), SX2(Zdim,Zdim), C(Zdim), (Xdim) 3) For m=1:zdim, for n=1:zdim 4) For i=1:xdim 5) Sa(m,n)=max{min[((i),SX1(m,n)], min[(i),sx2(m,n)]} 6) E(m)=max{min[Sa(n,m),C(n)]} 7) end i; end n ; end m ; 8) For m=1 :Ydim, for n=1 :Zdim 9) B=max{min[R(n,m),C(n)]} 10) end n; end m; Figure 4. lgorihm for case a) In he algorihm showed in figure 4, wo specific fuzzy operaions can be disinguished: 1) Marix manipulaion 2) muliplicaion. Then, VHDL definiion should include hese wo paricular operaions in behavioural descripion. In a firs approach, C1,, fuzzy inpu vecor is applied by exernal connecion, defining hem as oupu por. value Binary value Table 1. Code for FDS evoluion las, a paricular binary code conversion for he fuzzy values in marix definiions is proposed in Table 1, o obain he Generic VHDL descripion in figure 5. This descripion is based on he scheme suggesed by Salapura and Hamman [6], where a generic scheme is developed using VHDL. They propose novel calculaion archiecure for is descripion. However, in his case a paricular library is defined o make calculaions for Dynamic Sysems evoluion efficienly. rchiecure behaviour of FDS is consan Xdim, Ydim, Zdim; consan R(Ydim,Zdim), SX1(Zdim,Zdim), SX2(Zdim,Zdim); process(, C1) variable S; for m in 1 o Zdim loop for n in 1 o Zdim loop for I in 1 o Xdim loop Sa(m,n)=max(min(((i),SX1(m,n)), min((i),sx2(m,n))); E(m)=max(min(Sa(n,m),C(n))) for m in 1 o Ydim loop for n in 1 o Zdim loop B=max(min(R(n,m),C(n))); end process end behaviour; Figure 5. Behavioural descripion of a FDS in VHDL b) Given and B R The marix manipulaions and max-min operaions have been made more efficien because he locaing and evaluaing processes have been changed from complex digial srucure o pariy comparaive srucure. I is due, he scaling srucure given a he binary relaion beween all possible fuzzy values obained in a FDS and heir mean in he evoluion of FMS. In his paricular case, he VHDL code, require he calculaions using equaion (5) o obain he inernal srucure of he Sysem. 1) Define Xdim, Ydim, Zdim; 2) Define R(Ydim,Zdim), SX1(Zdim,Zdim), SX2(Zdim,Zdim), B(Zdim), (Xdim) 3) For m=1:zdim, for n=1:zdim 4) For i=1:xdim 5) Compare (, B) R 6) end i; end n ; end m ; 7) For m=1 :Ydim, for n=1 :Zdim 8) C=max{min[R(n,m),C(n)]} 9) end n; end m; Fig. 6 lgorihm for case b) 3

4 4. EXMPLES OF PPLICTION To observe he benefis of he modelling and simulaing procedure, consider he nex FDS where and R is known. If he sysem is modelled using he mehod proposed by Klir and Folger [8], hen a Fuzy Dynamic model is obained as follows: R ( YxZ) = L(6) S( XxZxZ) = L(7) where X={x 1, x 2 }, Y={y 1, y 2, y 3 } and Z={z 1, z 2, z 3, z 4 }. In his case, values on S represen probabiliy of occurrence for asks in a manufacuring process. Using algorihm obained and inpu his sysem and he VHDL CORE generaed, a simulaion for his paricular sysem, a ool for analyse he evoluion of he sysem is obained. Figure 7 shows he simulaion for a shor fuzzy sae sequence. Hexadecimal code is used as a ranslaion beween fuzzy sae value and is binary value. X and Y can address a possible sequence of values in erms of measures o obain a Relaion R, which can indicae he fuzzy sequence of aciviies for he painer. Consider X= [ ] and Y= [ ]. If equaion 5 is applied in he conex for case b), hen a 3 x 3 marix is obained. M = L(8) For his example, represen he increasing facor of abiliy for he painer; however Y consider he reducion in he force o develop he aciviy. The marix obained can be considering a symmeric expression in he evoluion of he aciviies for he painer. This descripion was applied in he descripion of fuzzy aciviies by Graciós, Vargas and Díaz [7]. By Terano e al, he experimens wih human reliabiliy le obain model for he case of several people cooperaing o accomplish one ask. Using FDS, i is possible o obain a Sequence model o rain a robo manipulaor in erms of make more close he behaviour of he robo a he human movemens. I is wished in indusrial or aresian process where he finesses of he movemens are required o emulae he same characerisics of he human. 5. CONCLUSIONS ND FUTURE WORK Fig. 7 Simulaion for he sysem proposed. Now, for he nex case, consider a fuzzy modelling sraegy o analyse he behaviour of he movemens for a human making he paining procedure for an auomoive fascia. For his case, X represens inpu parameers for he posiions in he sequences of paining, Y is he oupu force vecor in he paining procedure. The resuls of he applicaion of he Human Reliabiliy model show improvemens in modelling and simulaion simpliciy, and a beer performance when a Human/Machine behaviour is modelled and simulaed in is non-deerminisic schemes. The alernaive archiecure o calculae he fuzzy evoluion of he FDS allows o he sysem more realisic descripion. Therefore, he suggesion offers a safey way o represen he srucure and behaviour of real Human or machine aciviies and he inclusion of fuure inelligen conrol schemes. The projec goals have been fulfilled, and he complee environmen is now been used o analyse and conrol a new FMS proposed for he Research Laboraory in he Insiuo Tecnológico de Puebla, where he inelligen conrol sysem applied shows an improved performance for he programmed aciviies. 4

5 The proposed mehod demonsraes he feasibiliy of he applicaion of novel analyse and conrol sraegies, which can be resriced by he use of discree even models of process using discree sae variables for he elemens and devices. 6. REFERENCES [1] Klir-Yuang, ses and fuzzy logic.-theory and pplicaions, PTR Prenice Hall, [2] R. Yager and D. Filev, Essenials of Modelling and Conrol, John Wiley and Sons, [3] T. Terano, K. sai, M. Sugeno, Sysems Theory and Is applicaions, cademia Pres, INC [4] Shen W., Norrie D. H. Shen, W. and Norrie, D.H. gen-based Sysems for Inelligen Manufacuring: Sae-of-he-r Survey. Knowledge and Informaion Sysems, an Inernaional Journal, 1(2), , 1999 [5] Gupa P., Hardware-Sofware codesign, IEEE Poenials, December 2001/2002. [6] Salapura V., Hamann V., Implemening Conrol Sysems using VHDL and Saechars, Technische Universia Wien,usria, 2001 [7] C.. Graciós Marín, E. Vargas Soo,. Díaz Sánchez, Model and Simulaion of IMS using FNRTPN and VHDL.-a new C..D. mehod., [8] Klir & Folger, Ses, Uncerainy, and Informaion, Prenice Hall, PTR,