Effectiveness evaluation of electronic warfare command and control system based on grey AHP method

Transcription

1 Avalable onlne Jounal of hemcal and Phamaceutcal Reseach, 014, 6(7): Reseach Atcle ISSN : ODEN(USA) : JPR5 Effectveness evaluaton of electonc wafae command and contol system based on gey AHP method QI Zong-feng 1 and Wang Guo-sheng * 1 The State Key Laboatoy of omplex Electomagnetc Envonment Effects on Electoncs and Infomaton System (EMEE), Luoyang, hna Depatment of ontol Engneeng, Academy of Amoed Foces Engneeng, Bejng, hna ABSTRAT The gey AHP effectveness evaluaton poblem of electonc wafae command and contol system (EWS) unde complex electomagnetc envonment s nvestgated. Fst, the evaluaton heachy stuctues of EWS unde complex electomagnetc envonment ae put fowad and can be classfed nto taget heachy, ule heachy and scheme heachy. Then, the gey AHP Algothm s gven as a pelmnay knowledge to evaluate the effectveness evaluaton of EWS unde complex electomagnetc envonment. Fnally, an effectveness evaluaton example of thee EW systems unde complex electomagnetc envonment s consdeed by usng the gey analytc heachy pocess (AHP) Algothm, and the gey compehensve evaluatons fo the thee EW systems unde complex electomagnetc envonment and the gades of the gey compehensve evaluaton ae poposed. Key wods: Electonc wafae command and contol system; complex electomagnetc envonment; gey AHP; compehensve effectveness evaluaton INTRODUTION The electonc wafae equpments ae moe and moe mpotant n moden nfomaton battles. Wth the development of the new compute technology, the electonc wafae equpments become moe and moe complex, pegnable and damageable such that t s dffcult to evaluate the pefomance and effectveness of the electonc wafae equpments. a et al establsh the ant-jammng effcency evaluaton model of the tactcal communcaton net and evaluate the ant-jammng effcency of the tactcal communcaton net by GEM and GAHP n [1]. u et al detemne the dffeent gey fuzzy weghts fo dffeent factos by usng analytcal heachy pocess, and constuct gey fuzzy elaton matx by gey fuzzy weght, membeshp, pont gey n []. In ode to solve the dsadvantages fo the effcency evaluaton of the undewate acoustc countemeasue,esultng fom the undewate nfomaton fuzzy and data scacty, Tang et al popose the gay analytc heachy evaluaton method n [3]. Yn et al ntoduce a new gey heachy evaluaton method,used fo evaluatng of EW pefomance n multple abone platfom system, establsh the complete pefomance evaluaton ndex system EW pefomance n multple abone platfoms system,and gve the defnton and calculaton fomula of each ndex n [4]. Sh et al study the Fuzzy-AHP n evaluaton of EM command effectveness to calculate the nfluence degee of each ngedent and evaluate the EM command effectveness n [5]. Accodng to ts chaactestcs of nsuffcent nfomaton and uncetanty, Yu et al evaluate the EW system opeaton effectveness by usng the method of gey heachy evaluaton n [6]. hen et al calculate the effectveness of nstucted EW system by usng analytc heachy pocess, the weghted coeffcent of each gudelne s defned, and the effectveness of nstucted EW system s calculated n [7]. Lu et al buld an effectveness evaluaton ndex system of abone EM system whch 535

2 can eflect the abone EM system capacty geneally and mpesonally n [8]. As one of mpotant electonc wafae equpments, an electonc wafae system unde complex electomagnetc envonment plays an mpotant ole n the moden nfomaton battle. Theefoe, the effectveness evaluaton poblem of electonc wafae command and contol system (EWS) unde complex electomagnetc envonment has become a popula topc n the nvestgaton of moden battle theoy. Thus n ths pape we wll nvestgate the effectveness evaluaton of electonc wafae command and contol system unde complex electomagnetc envonment by usng the gey AHP method. Fst, the evaluaton heachy stuctues of EWS unde complex electomagnetc envonment ae poposed. Then, the detal gey AHP algothm s put fowad as pelmnaes fo the effectveness evaluaton of EWS unde complex electomagnetc envonment. And then, the effectveness evaluaton example of thee EW systems unde complex electomagnetc envonment s desgned by usng AHP and the smulaton esult shows that the gey AHP method s effectve and smple fo effectveness evaluaton of EWS unde complex electomagnetc envonment. EVALUATION HIERARHY STRUTURES OF EWS Accodng to the featues of EWS unde complex electomagnetc envonment, many factos whch ae elated wth the pefomances of EWS unde complex electomagnetc envonment can be found out and can be classfed nto the taget heachy, the ule heachy and the scheme heachy. The taget heachy o the fst heachy fo effectveness evaluaton of EWS unde complex electomagnetc envonment can be denoted by A. The ule heachy of EWS unde complex electomagnetc envonment ncludes scoutng and detectng ablty 1, command and contol ablty, communcatng and safeguadng ablty 3, and battlefeld electomagnetsm envonment 4. Fo smplcty, we only select two scheme specfcatons fo evey component n the ule heachy of EWS unde complex electomagnetc envonment. The scheme heachy of scoutng and detectng ablty 1 ncludes scoutng and detectng method 11 and scoutng and detectng ange 1. The scheme heachy of command and contol ablty nclude ablty of auxlay decson 1 and decson delay. The scheme heachy of communcatng and safeguadng ablty 3 nclude coveng ange 31 and communcatng capacty 3. The scheme stuctue of battlefeld electomagnetsm envonment 4 ncludes qualty of electomagnetsm adant pont 41 and densty of electomagnetsm sgnal 4. Based on the above analyss of EWS unde complex electomagnetc envonment, we can gve the heachy stuctue wth the taget heachy, the ule heachy and the scheme heachy n Fg. 1. Fg. 1 : The heachy stuctue of EWS unde complex electomagnetc envonment GREY AHP METHOD AHP s a decson makng suppot tool developed n the 1970s by Thomas Saaty, a mathematcs lectue fom the Unvesty of Pttsbugh, US. The pocess eques the establshment of a heachy of ctea whch s mpotant to acheve the goal of the decson poblem. AHP povdes a atonal famewok fo decson makng by beakng down the pocess nto components wth espect to an oveall goal. Based on the classc AHP method, many genealzed AHP methods and the applcatons ae studed. As one of genealzed AHP methods, Evangelos et al and Ke et al nvestgate the detal algothm of gey AHP n [9] and [10]. Based on the above efeences, we can lst the Gey 536

3 AHP method as follows: Step 1. Establsh the heachy stuctue of the effectveness evaluaton system. The effectveness evaluaton system s usually decomposed nto dffeent heaches, such as the goal o taget heachy, the ule heachy and the scheme heachy, whch ae denoted by the ladde stuctue. Step. Establsh the pa-wse judgment matx. ompang the dffeent factos n the same heachy wth one of ules n the above heachy, we can obtan the mpotant degees and the coespondng judgment matces. The values of the pa-wse compasons n the AHP ae detemned accodng to the scale ntoduced by Saaty. Accodng to ths scale, the avalable values fo the pa-wse compasons ae membes of the set: {9, 8, 7, 6, 5, 4, 3,, 1, 1/, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9}. Step 3. Extact the elatve mpotance mpled by the pevous pa wse compasons. alculate the coespondng maxmum left egenvecto of the judgment matx s appoxmated by usng the geometc mean of each ow and the numbes ae nomalzed by dvdng them wth the sum. Step 4. Test the consstency of the elatve mpotance. In the AHP, the pa wse compasons n a judgment matx ae consdeed to be adequately consstent f the coespondng consstency ato (.R.) s less than 10%. The. R. coeffcent s calculated as follows: 1) The consstency ndex (.I.) needs to be estmated. Ths s done by addng the columns n the judgment matx and multply the esultng vecto by the vecto of potes (.e., the appoxmated egenvecto) obtaned eale. Ths yelds an appoxmaton of the maxmum egenvalue, denoted by λ. ) The. I. value s calculated by usng the fomula:.i. = ( λmax -n)/(n-1). Next the consstency ato R s obtaned by dvdng the. I. value by the Random onsstency ndex (R. I.) as gven n Table 1. max Table 1: R.I. values fo dffeent values of n n R.I Step 5. alculate the elatve weght of the compaed components to the heachy, and calculate the elatve weght w of the components n the ule heachy and the elatve weght w of the components n the scheme heachy to the goal heachy. Step 6. Detemne the evaluated swatch matces fo the specfcatons n the scheme heachy. Assume that the numbe of the evaluated systems s p and the numbe of the specfcatons unde the ule heachy s k, thus the evaluated swatch matx can be wtten by d11 d 1 L d 1 p d1 d d p D L = M M L M dk1 dk L dkp (1) Step 7. Assume that thee ae fou evaluated gey speces, and the evaluated gades ae excellent, good, common and bad, whch ae denoted by e = 1,,3, 4, espectvely. Accodng to the analyss of the evaluated system, the gey numbe ( = 1,,3,4 ) and the whtenzed weght functon f ( x) ( = 1,,3,4 ) of the gey speces as follows 1 = [ 0.7, 0.9, 1.0] x 0.7, x [ 0.7, 0.9 ] 0., when e = 1 () f1( x) = 1 x, x [ 0.9, 1.0] 0, x [ 0.7, 1.0 ] 537

4 [ 0.5, 0.7, 0.9] = x 0.5, x 0.5, x f( x) =, x 0.7, , x 0.5, 0.9 [ 0.3, 0.5, 0.7] 3 = x 0.3, x 0.3, x f3( x) =, x 0.5, , x 0.3, 0.7 [ 0, 0.3, 0.5] 4 = x, x [ 0, 0.3 ] x f4 ( x) =, x 0.3, , x [ 0, 0.5], when e = (3), when e = 3 (4), when e = 4 (5) whee the gey numbe stands fo the gade assocated wth the specfcaton x, the value of the gey numbe stands fo the nteval of the scoe, the mddle value stands fo the best scong value. Step 8. Detemne the evaluated weght matces. Denote the gey evaluated weght assocated wth the e -th gey spece by je, whch can be obtan by system specfcaton, and j c je je =, whee cj p c = f ( d ) s the gey evaluated coeffcent of the je e jt t = 1 4 j = cje s the total gey evaluated coeffcent. Thus the gey evaluated weght e= 1 c vecto whch s composed of evey gey evaluated weght je fo j can be wtten by =,,, (6) j j1 j j3 j 4 Theefoe, the gey evaluated matx specfcaton j whch belongs to Based on the weght vecto the specfcaton j whch belongs to R can be obtaned fom the gey evaluated weght vecto j fo the as follows w of the specfcaton 1 R = M k can be gven by whch belongs to j (7), the compehensve evaluaton fo B = w R (8) Fom (8), we can obtan the gey evaluated matx fo the total specfcaton A as 538

5 B1 B B = M B k (9) Step 9. Detemne the gey compehensve evaluaton. The value fo the gey compehensve evaluaton s E = wb (10) whee = [ ] T stands fo the vecto that conssts of the scoe value coespondng to the gey evaluated speces. A NUMERIAL EXAMPLE Based on the Evaluaton heachy stuctue of EWS unde complex electomagnetc envonment n Fg. 1, the AHP algothm and the gey algothm, we wll calculate the effectveness evaluaton of EWS unde complex electomagnetc envonment. Assume that the expets gve the elatve mpotance of the ctea n the pa-wse judgment matces of the EWS unde complex electomagnetc envonment. The coespondng pa-wse judgment matx among complex electomagnetc envonment nclude scoutng and detectng ablty 1, command and contol ablty, communcatng and safeguadng ablty 3, and battlefeld electomagnetsm envonment 4 can be gven by the followng table. And the weght vecto of 1,, 3 and 4 s [ ] T,. R. = < 0.1 shows that the elatve mpotance of the pa-wse judgment matx s consstent. Table : The pa-wse judgment matx among 1,, 3 and 4 A w λ max = R = < I = The coespondng pa-wse judgment matx between scoutng and detectng method 11, and scoutng and detectng ange 1 n scoutng and detectng ablty 1 can be gven by Table 3. And the weght vecto of 11 and 1 s [ ] T,. R. = 0 < 0.1 shows that the elatve mpotance of the pa-wse judgment matx s consstent. Table 3: The pa-wse judgment matx among 11 and w The coespondng pa-wse judgment matx between ablty of auxlay decson 1, and decson delay n command and contol ablty can be gven by can be gven by Table 4. And the weght vecto of 1 and s [ ] T,. R. = 0 < 0.1 shows that the elatve mpotance of the pa-wse judgment matx s consstent. Table 4: The pa-wse judgment matx among 1 and 1 w The coespondng pa-wse judgment matx between coveng ange 31 and communcatng capacty 3 n communcatng and safeguadng ablty 3 can be gven by Table 5. And the weght vecto of 31 and 3 s [ ] T,. R. = 0 < 0.1 shows that the elatve mpotance of the pa-wse judgment matx s consstent. 539

6 Table 5: The pa-wse judgment matx among 31 and w The coespondng pa-wse judgment matx between qualty of electomagnetsm adant pont 41 and densty of electomagnetsm sgnal 4 n battlefeld electomagnetsm envonment 4 can be gven by Table 6. And the weght vecto of 41 and 4 s[ ] T,. R. = 0 < 0.1 shows that the elatve mpotance of the pa-wse judgment matx s consstent. Table 6: The pa-wse judgment matx among 41 and w Fom Table 3, we can know that the weght vecto of 1,, 3 and 4 w = [ ] T can be shown by Fg.. Fom Fg., we can dectly fnd that the sot ode of the elatve mpotance among 1,, 3 and 4 s 1»3»»4, whee» mples that the fome s moe mpotant than the late. 0.7 the weght of the second degee cteon Fg. : The elatve mpotance among 1,, 3 and 4 Fom the esult fo the elatve mpotance among 1,, 3 and 4, we can know that the mpotance of scoutng and detectng ablty 1 s Thus we can know that n ode to mpove the effectveness of EW systems unde complex electomagnetc envonment, the scoutng and detectng ablty 1 s fst consdeed, and the othe pefomances ae smultaneously consdeed. In the scoutng and detectng ablty 1, the elatve mpotance of scoutng and detectng ange 1 s Based on the above esults of AHP algothm, we contnue to consde the effectveness evaluaton of thee EW systems unde complex electomagnetc envonment by usng the gey algothm. Assume that the scoes of the above specfcatons fo thee EW systems unde complex electomagnetc envonment S1, S, and S3, ae gven n Table 7 and the scoes afte undmensonalzed by the maxmum value ae gven n Table 8. Table 7: The scoes of specfcatons n the scheme hechacy S S S Table 8: The scoes afte undmensonalzed by the maxmum value S S S Fom Table 8, we can establsh the evaluated swatch matces fo S1, S and S3 as 540

7 D1 = , D = D3 = , D4 = Fo 11 of S1, fom ()-(5) we can obtan the whtenzed weght value of the gey speces as e = 1, c = f (0.778) = 0.39, e =, c = f 11 (0.778) = 0.61 e = 3, c = f (0.778) = 0, e = 4, c = f (0.778) = Thus the total gey evaluatng weght vecto fo 11 s 11 = Fo 1 of S1, fom ()-(5) we can obtan the whtenzed weght value of the gey speces as e = 1, c = f 11 1 (0.7471) = 0.355, e =, c = f 1 (0.7471) = , e = 3, c = f (0.7471) = 0, e = 4, c = f (0.7471) = Thus fom (6) we can obtan the total gey evaluatng weght vecto fo 1 of S1 as 1 = [ ] Thus fom (7) we can obtan the gey evaluatng matx fo 1 of S1 as R1 = Smlaly, we can obtan the gey evaluatng matces R, R 3 and R 4 fo, 3, and 4 of S1, espectvely, as follows R = , R3 = , R4 = Fom (8), we can obtan the compehensve evaluaton fo the specfcaton 1,, 3 and 4 of S1, espectvely, as B 1 = [ ], B = [ ], B 3 = [ ], B 4 = [ ] Fom (9), we can obtan the gey evaluated matx fo the total specfcaton A of S1 as B = Fnally, fom (10) we can obtan the value fo the gey compehensve evaluaton of S1 as E 1 = Smlaly, we can obtan the values fo the gey compehensve evaluaton of S and S3, espectvely, as E = , E =. Fom the above values fo the gey compehensve evaluaton of S1, S and S3, we can know that the EW system unde complex electomagnetc envonment S1 s common, the EW system unde complex electomagnetc envonment S s good, and the EW system unde complex electomagnetc envonment S3 s bad. The evaluatng esults of the EW systems unde complex electomagnetc envonment S1, S and S3 by usng the gey AHP method can be shown n Table

8 Table 9: The compehensve evaluaton esults by the gey AHP method Paametes Thee EW systems S1 S S3 Value fo the gey compehensve evaluaton Gade fo the gey compehensve evaluaton common good bad ONLUSION In ths pape we consde the gey AHP effectveness evaluaton poblem of EWS unde complex electomagnetc envonment s nvestgated. By usng the gey AHP method, an effectveness evaluaton example of thee EW systems unde complex electomagnetc envonment s consdeed, and the gey compehensve evaluatons and the gades of the gey compehensve evaluaton ae poposed. In the next eseach, we wll nvestgate gey synthetcally assocated analyss method to evaluate the effectveness evaluaton poblem of EWS wth nsuffcent nfomaton. Acknowledgments Ths wok was fnancally suppoted by the Open Poject Foundaton of the State Key Laboatoy of EMEE (EMEE014K0305B). REFERENES [1] a Y. J., Fe ontol & ommand ontol, vol. 37, pp , 01. [] u J. G., Fu K. Y., hen X.., QI Y. W., Jang L. Y., Acta Aeonautca et Astonautca Snca, vol. 34, pp. 1-9, 013. [3] Tang Z.,Sun.,Lu Z. W., Meng D., Acta Amamenta, vol. 33, pp , 01. [4] Yn H. T.,Wang X. Y.,Gu X. J.,Wu J. B., Jounal of Nothwesten Polytechncal Unvesty, vol. 30, pp , 01. [5] Sh R., Han. J.,Huang J., ommand ontol & Smulaton, vol. 8, pp , 006. [6] Yu H., Lu G. X., hen Y., Zhou L., Rado Engneeng, vol. 39, pp , 009. [7] hen G. Z., Xue Y. F., Electonc Wafae, vol. 106, pp. 6-34, 006. [8] Lu Z. Y., Png D. F., Wang L., Shp Electonc Engneeng, vol. 3, pp , 01. [9] Evangelos T., Stuat H. M., Intenatonal Jounal of Industal Engneeng, Applcatons and Pactce, vol., pp , [10] Ke H., Ke K., Mathematc n Pactce and Theoy, vol. 41, pp ,