Multicriteria Choice of the NVG Optoelectronic Channel Elements

Transcription

1 БЪЛГАРСКА АКАДЕМИЯ НА НАУКИТЕ BULGARIAN ACADEMY O SCIENCES ПРОБЛЕМИ НА ТЕХНИЧЕСКАТА КИБЕРНЕТИКА И РОБОТИКАТА 56 PROBLEMS O ENGINEERING CYBERNETICS AND ROBOTICS 56 София 2006 Sofia Multicriteria Choice of the NVG Optoelectroic Chael Elemets Daiela Borissova Istitute of Iformatio Techologies 1113 Sofia dabor@iit.bas.bg 1. Itroductio The ight visio goggles (NVG) are gettig cheaper ad are spreadig widely i differet applicatio areas recetly. That is a cosequece of techological developmet ad mass productio. The process of the NVG desig ivolves choice of optoelectroic chael elemets (jectives image itesifier tubes IIT oculars) amog their subsets. The chose elemets must fulfill specific requiremets of the NVG optoelectroic chael ad it has to meet user's expectatios. As a result a eed for the developmet of some relevat optimizatio models exists. A sigle-criteria optimizatio model has bee developed ad tested showig good practical workability [1]. The defied jective fuctio icludes the most commo practically demaded compoets such as price weight workig rage field of view etc. To be more precise i real live modelig it should be metioed that some of the criterio compoets are icompatible ad coflictig. Usig optimizatio for more adequate describig real egieerig prlems it is atural to look for multi-criteria optimizatio prlems defiitio [2 3]. Cosiderig each criterio compoet of the formulated sigle-criterio prlem [1] as uique criterio the sigle-criterio prlem ca be trasformed to a multicriteria prlem as described i the curret paper. 2. ormulatio of quality criteria of NVG The parameters of the NVG optoelectroic chael are crucial for the quality of NVG itself. The practical expertise shows that the most importat of them are [1]: Q 1 = R the workig rage Q 2 = W the field of view Q 3 = (1/ ) the jective -umber 6 1

2 Q 4 = the jective focus rage Q 5 = AD ab jective (distortio) Q 6 = ER the eye relief Q 7 = L the weight of NVG optoelectroic chael Q 8 = P the price of NVG optoelectroic chael A multi-criteria optimizatio model of the NVG optoelectroic chael could be formulated as follows: (1) max {Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8 } subject to costraits describig the specifics of the NVG optoelectroic chael [1]: (2) y j j (3) 6 2 k 1 l z l y jw j zk k 1 k oc k oc k equality of the jective ad ocular focal legth for NVG magificatio 1? W jective field of view ocular field of view d d (4) R 0.07 a EKА ' KIITK detectio rage for a stadig ma [4] (5) (6) IIT m K x ik i 1 K y j K IIT i j IIT quality parameter jective quality parameter (7) AD y j AD j jective distortio (8) 1 y j 1 (9) y j j W l ER z k k 1 l j (10) y j W j (11) ER (12) Woc y k W k k 1 k oc jective -umber jective focus rage jective field of view eye relief ocular field of view (13) L LIIT L Lоc optoelectroic tract weight (14) P PIIT P Pоc optoelectroic tract price where x y z {0 1} are biary iteger variables for choice of the relevat elemets of the NVG optoelectroic chael [1]. The ambiet light coditio ad the target area are costats with kow umerical values:

3 a = 0.7 atmosphere trasmittace E = 0.01 lx ambiet light illumiatio K = 0.2 cotrast betwee the surveillace target ad backgroud A = 0.7 m 2 target area for a stadig ma [4] The multicriteria prlem solutio depeds o the optimizatio strategy [3]. The defied i the curret paper determiistic multicriteria oliear optimizatio model has bee solved usig two approaches by e-costraits approach ad by weighted sum approach [5 6 7]. 3. Results of usig e-costraits approach As source data for prlem formulatig the parameters of five jectives five IITs of differet geeratios ad five oculars show i tables 1 2 ad 3 were used. Table 1. IITs parameters S No IIT A/lm lp/mm M L IIT P IIT g $ 1 Ge II SHD XD XR MX-10160B Table 2. Objectives parameters No Objective W AD L P mm o deg % сm g $ 1 NVG Prilep AN/PVS-5C AN/PVS-5A NVG D-2V Table 3. Oculars parameters No Ocular oc W oc ER L оc P оc mm deg mm g $ 1 NVG Prilep NVG M M M The e-costraits approach requires oe jective to be selected for optimizatio ad the other jectives to be reformulated as costraits creatig i this way scalar subprlems to be solved as sigle-criterio prlems [5 6 7]. 6 3

4 Scalar subprlem D(R) for detectio rage: (15) max R d subject to (2)-(14) with values from Tables ad the additioal costraits for the rest of criteria from (1): (16) 35 W (17) 1 (1/ ) (18) 30 (19) AD 9 (20) 20 ER (21) L 300 (22) P The decisio of the D(R) will be a costrait for R d for all other scalar subprlems. Scalar subprlem D(W ) for jective field of view: (23) max W subject to (2)-(14) with values from Tables costraits (17)-(22) for the rest of criteria from (1) ad the additioal costrait: (24) 400 R d The D(W ) decisio will be a costrait for W for other scalar subprlems. Scalar subprlem D(1/k) for jective -umber: (25) max 1/ subject to (2)-(14) with values from Tables costraits (18)-(22) (24) for the rest of criteria from (1) ad the additioal costrait: (26) 40 W The D(1/ ) decisio will be a costrait for 1/ for other scalar subprlems. Scalar subprlem D() for jective focus rage: (27) mi subject to (2)-(14) with values from Tables costraits (19)-(22) (24) (26) for the rest of criteria from (1) ad the additioal costrait: (28) 1 (1/ ) The D() decisio will be a costrait for for other scalar subprlems. Scalar subprlem D(AD ) for jective distortio: (29) mi AD subject to (2)-(14) with values from Tables costraits (20)-(22) (24) (26) (28) for the rest of criteria from (1) ad the additioal costrait: (30) 30. The D(AD ) decisio will be a costrait for AD for other scalar subprlems. 6 4

5 Scalar subprlem D(ER) for eye relief: (31) max ER subject to (2)-(14) with values from Tables costraits (21) (22) (24) (26) (28) (30) for the rest of criteria from (1) ad the additioal costrait: (32) AD 7. The D(ER) decisio will be a costrait for ER for other scalar subprlems. Scalar subprlem D(L) for NVG optoelectroic chael weight: (33) mi L subject to (2)-(14) with values from Tables costraits (22) (24) (26) (28) (30) (32) for the rest of criteria from (1) ad the additioal costrait: (34) 10 ER. The D(L) decisio will be a costrait for L for other scalar subprlems. Scalar subprlem D(P) for NVG optoelectroic chael price: (35) mi P subject to (2)-(14) with values from Tables costraits (24) (26) (28) (30) (32) (34) for the rest of criteria from (1) ad the additioal costrait: (36) L 250. The results from the decisios of the scalar subprlems D(R) D(W ) D(1/ ) D() D(AD ) D(ER) D(L) D(P) are show i Table 4. Table 4. The results from scalar subprlems ad sigle-criterio optimizatio prlem D1 decisios Tasks D1 D(R) D(W ) D(1/ ) D() D(AD ) D(ER) D(L) D(P) Criteria all 1st 2d 3th 4th 5th 6th 7th 8th Chose IIT (from Table 1) Chose jective (from Table 2) Chose ocular (from Table 3) Detectig rage m ield of view deg umber Objective focus rage сm Distortio % Eye relief mm Weight g Price $ A sigle-criterio optimizatio oliear prlem defied as D1 [1]: (37) max Q = (R + W + (1/ ) AD + ER L P) subject to (2)-(14) with values from Tables ad the same boudaries (16)-(22) (24) as i a multicriteria prlem is solved ad the results of its decisio are show 5 Prlems of Egieerig Cyberetics ad Rotics

6 also i Table 4. The results for optoelectroic chael parameters from the decisios of D1 ad the last scalar subprlem D(P) are equal. The graphical presetatio of the taied detectio rage values ad the optoelectroic chael price by the decisios of the scalar subprlems D(R) D(W ) D(1/ ) D() D(AD ) D(ER) D(L) D(P) ad by decisio of the sigle-criterio prlem D1 are show i ig. 1 ad ig. 2 respectively. 700 PrlemD1 Detectig rage m Criteria ig. 1. Detectio rage values from the scalar subprlems ( ad D1 ( ) decisios 7000 Prlem D Price $ Criteria ig. 2. Price values from the scalar subprlems ( ) ad D1 ( ) decisios 4. Results of usig weighted sum approach Oe of the widely used for the multicriteria prlems solvig is the weighted sum approach. The prefereces of the decisio-maker are take ito accout by choosig differet weights for the differet jectives [5 6 7]. Usually the jective fuctios are of differet magitudes ad should be ormalized first. The ormalizatio is doe solvig maximizatio ad miimizatio siglecriterio prlems for each of the criteria discardig the rest of the criteria. The taied maximum ad miimum values for each criterio of the formulated i the curret paper multicriteria prlem are show i Table

7 Table 5. The maximum ad miimum values for each criterio R W Criterio 1/ AD ER L P m deg cm % cm g $ Max / Mi / The values from the Table 5 are used to defie a ormalized sigle-jective fuctio: R Rmi (38) max{k 1 Rmax Rmi W W + k 2 max W W mi mi (1/ ) (1/ ) mi + k 3 (1/ ) max (1/ ) mi + max max AD AD ER ER mi + k 4 + k max 5 max mi + k 6 mi AD AD ERmax ERmi Pmax P + k 8 }. Pmax Pmi L L max +k 7 Lmax Lmi The weighted sum approach trasforms multiple criteria to a sigle-criterio defied as a sum of ormalized criteria with proper weight coefficiets k i where k 1. our sets of the weight coefficiets k i have bee chose for usig i i weighted sum approach as show i Table 6. Table 6. The sets of the weight coefficiets Set k 1 k 2 k 3 k 4 k 5 k 6 k 7 k 8 (1) (2) (3) (4) The decisios of the correspodig trasformed sigle-criterio prlems for each set of weighted coefficiets are show i table 7. Table 7. The results of the multicriteria prlem usig four sets of weighted coefficiets Parameter D(1) D(2) D(3) D(4) Chose IIT from Table Chose jective from Table Chose ocular from Table Detectig rage m ield of view deg umber ocus rage cm Distortio % Eye relief mm Weight g Price $

8 5. Coclusio Modelig of the NVG optoelectroic chael for the goal of the optimal choice of its elemets could be doe usig sigle-criterio ad multicriteria optimizatio models. Multicriteria models are closer to the practical requiremets for NVG but are more difficult to solve. The result taied by usig the e-costraits approach suggests that a equivalet sigle-criterio trasformed prlem where a sum of the multiple criteria forms a sigle criterio could be used for solvig the origial multicriteria prlem i this particular specific case. Usig the weighted sum approach demads good kowledge about the specifics of the prlems ad multiple tries for adjustig of the weighted coefficiets to get acceptable results. R e f e r e c e s 1. B o r i s s o v a D. I. M o u s t a k e r o v. A Optimal Choice Method of the Elemets for NVG s Optoelectroics Tract. IIT/WP-214B B a l a z s M. E. G. T. P a r k s P. J. C l a r k s o. Optimizatio i Idustry What Does Idustry Really Need?. Optimizatio i Idustry 2002 No A d e r s s o J. Multijective Optimizatio i Egieerig Desig. Likopig Studies i Sciece ad Techology. Dissertatios. No p B o r i s s o v a D. Aalytical Calculatio of Night Visio Goggles Workig Rage. Cyberetics ad Iformatio Techologies Vol No K l a m r o t h K. J. T i d S. Z u s t. Iteger Programmig Duality i Multiple Objective Programmig. Joural of Glal Optimizatio A d e r s s o J. A Survey of Multijective Optimizatio i Egieerig Desig. Techical Report LiTH-IKP-R Departmet of Mechaical Egieerig Likopig Uiversity Likopig Swede 2000 p V a s s i l e v a M. Classificatio-Orieted Iteractive Methods Algorithms ad a System for Solvig of Liear ad Iteger Prlems of the Multi-Criteria Optimizatio. Post-Doctoral Thesis. Istitute of Iformatio Techologies Bulgaria Academy of Scieces Многокритериальный выбор элементов для оптико-электронного канала очков ночного видения Даниела Борисова Институт информационных технологий 1113 София dabor@iit.bas.bg (Р е з ю м е) Описана многокритериальная оптимизационная модель для выбора элементов оптико-электронного канала очков ночного видения. Показаны решения соответствующих многокритериальных задач через методов е-ограничения и тегловых сум и сделаны выводы для практического применения. 6 8