I., 1 Wright-Patterson Air Force Base, Ohio DTIC OFP S AP119D AIR FORCE INSTITUTE OF TECHNOLOGY ELECTE

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1 OFP CI THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA VOLUME II THESIS Michael Grant Captain, USAF AFIT/G OR/ENY/ ENS /90M-8 DTIC ELECTE DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY S AP119D AIR FORCE INSTITUTE OF TECHNOLOGY I., 1 Wright-Patterson Air Force Base, Ohio B

2 SECURITY CLASSIFICATION OF THIS PAGE REPORT DOCUMENTATION PAGE Form OMF Approved No. 0p04r018e la. REPORT SECURI1,Y CLASSIFICATION lb. RESTRICTIVE MARKINGS UNCLASSIFIED "za. SECURITY CLASSIFICATIUN AUTHORITY 3 DISTRIBUTION/AVAILABILITY OF REPORT Approved for pu-ilic release: 2b. DECLASSIFICATION/DOWNGRADING SCHEDULE distribution unlimited 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5 MONITORING ORGANIZATION REPORT NUMBER(S) AFIT/GOR/ENY/ENS/9OM-8 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME-aF MONITORING ORGANIZATION School of Engineering A I Pfl fcfl') 6c. ADDRESS (City, State, and ZIPCode) / 7b. ADDRESS (City, State, and ZIP Code) 8a. NAME OF FUNDING /SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) AAMRL HEG 8c. ADDRESS (City, State, and ZIP Code) '0. SOURCE OF FUNDING NUMBERS AAMPL/HEG PROGRA.M PROJECT TASK WORK UNIT ELEMENT NO. NO. NO. ACCESSION NO. WPAFB, OH TITLE (Include Security Classification) THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA 12 PERSONAL AUTHOR(S) Michael Grant, B.S., M.S., Capt, USAF 13a. TYPE OF REPORT 113b. T:ME COVERED 114. DATE OF REPORT (Year, Month, Day) 15. PAGE COUNT MS Thesis FROM TO SUPPLEMENTARY NOTATION 17..Z COSATI CODES 18.-3UBJECT TERMS (Continue on reverse if necessary and identify by block number) -FIELD GROUP SU'BGROUP ->Kriging." Bayesian Statistics- Morphometricz' Geostatistics' Multivariate Analysis_,-) I ' 19. ABSTRACT (Continue on reverse if necessary and identify by block numberl Thesis Advisors: David G. Robinson Assistant Professor Department of Aeronautics and Astronautics Kenneth W. Bauer Assistant Professor Department of Operational Sciences 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION S UNCLASSIFIED/UNLIMITED 0 SAME AS RPT El DTiC USERS UNCLASSIFIED 22a. NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) 122C. OFFICE SYMBOL David G. Robinson, Asst. Professor (513) AFIT/ENY DD Form 1473, JUN 86 Previous editions ate obsolete. SECURITY CLASSIFICATION C'( THIS PAGE

3 --- UNCLASSIFIED Quality flight equipment is essential to flight crew safety and performance. Oxygen masks, night-vision goggles, and other apparatus must fit crew members comfortably and with complete functional precision. A problem currently facing the Air Force is the inconsistent quality of flight equipment. As new equipment is developed to improve crew members' performance, the requirement for design engineers-to accurately account for the shape arid variability of facial features becomes more critical. This thesis develops the application of kriging in the statistical analysis of anthropometric data to support improvements in the design of flight equipment. Specifically, the geostatistical estimation technique of kriging is used to estimate the facial surfaces which influence the designs of flight apparatus. These surfaces account for the shape of the facial features and minimize the variance between individuals. A Kalman filter is developed to update and aggregate the kriged surfaces. As a proof of concept study, the techniques are demonstrated using data to support the design of the night-vision goggles currently under development. To further enhance the surface estimates, a multivariate analysis is performed to identify the factors which account for the majority of the variability between faces and to group the faces into homogenous clusters. ;- / r._- 7, /7

4 AFIT/GOR/ENY/ENS/90M-8 THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA VOLUME II THESIS Presented to the Faculty of the School of Engineering of the Air Force Institute of Technology Air University In Partial Fulfi!lment of the Requirements for the Degree of Master of Science in Operations Research LAOOO9SODlon DTIC T.AB0 w M ichael Grant, B.S., M.S. Uni.ounOd 0 Captain, USAF March 1990 By... - Dit tr ibut ion/l AvallabilitY Codes Avail and/or Approved for public release; distribution unlimited

5 Appendix A. Subjects This appendix provides a graphical representation of the facial data used for this research effort. The first 25 subjects were included in the trend analysis and the final variogram analysis. The next five subjects were used in the kriging and updating analysis. Following these subjects are a group of five faces which were used only in the trend analysis. The last two faces were considered for the analysis but discarded because of inherent shortfalls in the data. A-1

6 *~~0 Subject 09 A-2

7 20o 1go b, M Subject 10 A-3

8 5O Subject 60 A-4

9 too 50 Subject 68 A-5

10 200 i5o 50 0 Subject 114 A-6

11 Subject 116 A-7

12 2000 oo 150 go- Subject 118 A-8

13 100 f50 Subject 122 A-9

14 g O Subject 130 A-10

15 Subject 133 A-11

16 200 10o t50. Subject 136 A-12

17 oo 150 O0! Subject 140 A-13

18 200 too- 50 Subject 142 A-1.4

19 00 f50 10 Subject 153 A-15

20 200 z5o 50O Subject 154 A-16

21 f5o *~, 0 Subject 155 A-17

22 ~~ 0 Subject 159 A-18

23 2Oo 150, SfO0 50 Subject 160 A-19

24 goo 15o too Subject 161 A-20

25 z0' O Subject 167 A-21

26 100 O0 Subject 171 A-22

27 200 16O g~o Subject 173 A-23

28 too 150 Subject 176 A-24

29 "20o go0 100 go- Subject 183 A-25

30 ZOO= 160 f~o 0 Subject 185 A-26

31 200 15o 50 Subject 112 A-27

32 Subject 141 A-28

33 '00. go. 600 Subject 152 A-29

34 20o 50 Subject 156 A-30

35 Ooo.50 Subject 199 A-31

36 $00 t5o too- 50 Subject 01 A-32

37 Subject 07 A-33

38 too Subject 12 A-34

39 ] Subject 89 A-35

40 200. Subject 150 A-36

41 160,r 400 Subject 33 A-37

42 Subject 151 A-38

43 Append c B. Residual Plots This appendix includes the residual plots obtained by differencing the subject data with the trend data. The first 25 residual data sets where used to determine the overall variogram and were used in the kriging and updating analysis. The next five data sets were excluded from the overall variogram analysis, the kriging analysis, and the updating analysis because the variograms were not consistent with the set of 25. These five data sets were included in the trend. The final seven data sets were considered for the kriging and updating procedures. However, only the first five sets followed the standard variogram pattern and were used for kriging and updating the surface estimates. B-1

44 20 io ~0 0) Subject 09 Residuals B-2

45 90' f 0 -to Subject 10 Residuals B-3

46 ,jo 10 0 to Subject 60 Residuals B-4

47 ý ( 0o Subject 68 Residuals B-5

48 g0 0) Subject 114 Residuals B-6

49 20-10 Subject 116 Residuals B-7

50 20, Subject 118 Residuals B-8

51 2 0 ~0 10 Uo...0 Subject 122 Residuals B-9

52 20 10 /0 lip Subject 130 Residuals B-10

53 20-10 Subject 133 Residuals B-11

54 c "10 -~0 Subject 136 Residuals B-12

55 Subject 140 Residuals B-13

56 20 20 d ~o Subject 142 Residuals B-14

57 U, 0 o) /10 Subject 153 Residuals B-15

58 ili Subject 154 Residuals B- 16

59 f. m 20 Cm to co 100 Subject 155 Residuals B-17

60 go 10 ~0 go Subject 159 Residuals

61 10 ~0,-.g Subject 160 Residuals B-19

62 Subject 161 Residuals B-20

63 20 t0 Subject 167 Residuals

64 o0 t0, I Subject 171 Residuals

65 go 80 0 Subject 173 Residuals B-23

66 20 10 Subject 176 Residuals B-24

67 '_ 0 20 CO ~0 '70_ :S h Subject 183 Residuals B-25

68 20 1o -.10 r 00 Subject 185 Residuals B-26

69 20.1ý0 Subject 01 Residuals B-27

70 10 co 110 Subject 07 Residuals B-28

71 20 'fo 0).. lip Subject 12 Residuals B-29

72 t0 go '90O Subject 89 Residuals B-30

73 20- ~0 U, 0 Subject 150 Residuals B-31

74 20 10 S10 Subject 112 Residuals B-32

75 1*o 20 PP Subject 141 Residuals B-33

76 go- Subject 152 Residuals B-34

77 go -- 10" 0.10 Subject 156 Residuals B-35

78 g Subject 199 Residuals B-36

79 20 'go 400 Subject 33 Residuals B-37

80 to,, Subject 151 Residuals B-38

81 Appendix C. Variograms This appendix provides the variograms corresponding to each of the residual data sets in the previous appendix. Each plot displays a set of four variograrns (one for each direction for the individual) and the overall variogram. C-1

82 10'-I Subject 09 -Esf,.mated "., h (disto.?,ce) Subject 09 Variograms 6r Subject 10 -Estimated _ 6 h (distance) Subject 10 variogrrms C-2

83 to -0u j.ct Estimatied i, h (distance) Subject 60 Variograms -,Subject 68 -Estimated h (distance) Subject 68 Variograms C-3

84 10 Subject Estimated h (distance) Subject 114 Variograms Subject stima Ztd h (distance) Subject 116 Variograms 6 8 C-4

85 10. 8 O-Subject 118 -Estimated h (distance) Subject 118 Variograms 10-8 ""-[ Subject Estimated 6 4 S h (distance) Svtbject 122 Variograms C-5

86 W0 $ubject Es~imated h (distance) Subject 130 Variograms 10. Eabject 133 SEstimaryted L h (dilstance) Subject 133 Variograrns C-6

87 10, 10 Subject Estimated h (distance) Subject 136 Variograms 10[.' $ubject EsUmnAted "-- - r h (distance) Subject 140 Variograms C-7

88 S- ubject Estimated , h (distance) Subject 142 Variograms 10 -" " " ' " SI ubject 15? Estimated h (distance) Subject 153 Variograms C-8

89 10 Subject 154 8Estimated h (distance) Subject 154 Variograms "S'- Subject 165 E- stimated h (distance) Subject 155 Variograms C-9

90 10 -Ubject Estimated h (distance) Subject 159 Variograms 10.! - 5-' Subject 160 b 8 Estir,v't, d 4 2 0, I, h (distance) Subject 160 Variograms C-10

91 10 _uuject 161 a' Estimated 8 A-mGU h (distance) Subject 161 Variograms i 0 8 Subject 167 SEstimated a h (distance) Subject 167 Variograms C-11

92 10. 8 Subject Estimated h (distance) Subject 171 Variograms 10. I I. S--': ubject Estimated h (distance) Subject 173 Variograms C-12

93 10, bject u 176 Esftmated " /',...".% ~ h (distance) Subject 176 Variograms 10 ] 8 ' Estimated ,' ' -. 4 // o.'" 2 /,,/ h (distance) Subject 183 Variograrns C-13

94 Subject E- Estimated h (distance) Subject 185 Variograms 20. Subject 01 Estimated h (distance) Subject 01 Variograms C- 14

95 2 0 :subject 0?7_ 75 -EsiatemLd oo....o 10 "'"" """ -" h (distance) Subject 07 Variograms 2 0 i ' ' " " ' ' " ' ' ' '.. -Subject 12 Estimnced ''" I, 10" 5 9./ ft (cdis (mce) C-1 Subject 12 Va~riograms C-15

96 S'uh'jec, t 89 -Es~rtimted ~10~ 5 -,- o h, (distance) Subject 89 Variograms 20 - Subject 150 SEstimated ;... 0 ~ h (distance) Subject 150 Variograms C-16

97 10~ 10.Subject Estimated i h (distance) Subject 112 Variograms 10. 1;*,ubjuct Estimated h (distance) Subject 141 Variograms C-17

98 Subject Estimated 6-, h (distanmce) Subject 152 Variograms 4f 8- [ Subject 156 Estimated h (distance) Subject 156 Variograms G-18

99 10 Subject f99 Estimated h (&dstance) Subject 199 Variograms Subject 33 - Estimated h (distance) Subject 33 Variograms C-19

100 20 "-Subject 157 -Estimated 15,% h (distance) Subject 151 Variograms C-20

101 Appeadix D. Kriging Analysis Figures Kriged Residual Plots This section includes the kriged residual plots for the 30 data sets used in kriging and updating procedures. D-1

102 0o 10 'to Sb00 Subject 09 Kriged Residuals

103 10 b I I Subject 10 Kriged Residuals D-3

104 10 8t0 Subject 60 Kriged Residuals D-4

105 go /0 40 Subject 68 Kriged Residuals D-5

106 20 ~0.10 Subject 114 Kriged Residuals D-6

107 0 10 '20 Subject 116 Kriged Residuals D-7

108 I, /101 Subject 118 Kriged Residuals D-8

109 10 ~0 Subject 122 Kriged Residuals D-9

110 Subject 130 Kriged Residuals D-10

111 290 ~0 Q~Q Subject 133 Kriged Residuals D-11

112 Subject 1.36 Kriged Residuals D-12

113 20 b10 Subject 140 Kriged Residuals D-13

114 .,90 10,1 0 Subject 142 Kriged Residuals D-14

115 20 t0.0 Subject 153 Kriged Residuals D.15

116 20 10 Subject 154 Kriged Residuals i! i I i-i6

117 ýo 10 U Subject 155 Kriged Residuals D-17

118 20 joý i0 'I,1 -I-- ý-i Subject 159 Kriged Residuals D-18

119 20 10,10..0 Subject 160 Kriged Residuals D-19

120 ,00 C,0 10 Subject 161 Kriged Residuals D-20

121 20 10 tf0 nps Subject 167 Kriged Residuals D-21

122 to t0) Subject 171 Kriged Residuals D-22

123 fo Subject 173 Kriged Residuals D-23

124 10 20 C,1 d.o Subject 176 Kriged Residuals D-24

125 10 ~0 re "10 Subject 183 Kriged Residuals D-25

126 20 co 10" Subject 185 Kriged Residuals D-26

127 ~0 Subject 112 Kriged Residuals D-27

128 10 ioi 101 0, Subject 141 Kriged Residuals D-28

129 20 ~0 CIO 1 0 0) 100 Subject 152 Kriged Residuals D-29

130 20 t0 Jo,10... N0 Subject 156 Kriged Residuals D-30

131 20 10 I~bp Subject 199 Kriged Residuals D-31

132 Kriged Facial Surfaces This section provides the kriged facial surfaces for the 30 data sets. The kriged facial surfaces were obtained by combining the kriged residuals with the trend. D-32

133 O, Subject 09 Kriged Surface D-33

134 o. Subject 10 Kriged Surface D-34

135 IO0 Subject 60 Kriged Surface D-35

136 200 5o0 SfO0 5o 0 Subject 68 Kriged Surface D-36

137 200r Subject 114 Kriged Surface D-37

138 ' l o.l _ 50 Subject 116 Kriged Surface D-38

139 20o 150 O00 go. Subject 118 Kriged Surface D-39

140 Ooo '900. fo 100 i Subject 122 Kriged Surface D-40

141 '60, Subject 130 Kriged Surface D-41

142 2000 ~5O too 50 0 Subject 133 Kriged Surface D-42

143 Subject 136 Kriged Surface D-43

144 ZO0 F 150. Subject 140 Kriged Siirface D-44

145 ,go Subject 142 Kriged Surface D-45

146 Subject 153 Kriged Surface D-46

147 Subject 154 Kriged Surface D-47

148 200 15o- 6 0o 0 Subject 155 Kriged Surface D-48

149 a Subject 159 Kriged Surface D-49

150 200 06o Subject 160 Kriged Surface D-50

151 200 f go t oo- 50 Subject 161 Kriged Surface D-51

152 200,go 100 l oo go Subject 167 Kriged Surface D-52

153 D-- Subject 171 Kriged Surface D-53

154 Subject 173 Kriged Surface D-54

155 ZOo Subject 176 Kriged Surface D-55

156 ZOO 15o. 55O Jill 4r D-56

157 Subject 185 Kriged Surface D-57

158 O Subject 112 Kriged Surface D-58

159 ,700 g0o. Subject 141 Kriged Surface D-59

160 o, SJe 2i r).qp

161 ' 50 Su;. l5k. Kriged Surface

162 goo 150, 50. Siihiprt. I(YA Rriored Siirfai-p

163 Facial Surface Estimation Variances This section provides the kriging variances corresponding to the figures displayed in the previous sections. D-63

164 6m 1O 2! 0 Estimation Variances for Subject 09 D-64

165 fo 6.~4 c0 Estimation Variances for Subject 10 D-65

166 ?4 Estimation Variances for Subject 60 D-66

167 fof Estimation Variances for Subjezt 68 D-67

168 10,I 6 Estimation Variances for Subject 114 D-68

169 10 6 Estimation Variances for Subject 116 D-69

170 to- 6.~4 2 lip Estimation Variances for Subject 118 D-70

171 10 6 0) Estimation Variances for Subject 122 D-71

172 Ito, a 6. ~4. Estimation Variances for Subject 130 D-.72

173 Sm 6, lip. 4 0 Estimation Variances for Subject 133 D-73

174 t Estimation Variances for Subject 136 D-74

175 to 8 V 6 4 Estimation Variances for Subject 140 D-75

176 to Estimation Variances for Subject 142 D-76

177 6 4 0 Estimation Variances for Subject 153 D-77

178 10L 8. 6 S4 Estimation Varia.nces for Subject 154 D-78

179 to- 0 1 Estimation Variances for Subject 155 D-79

180

181 6 4, 00 Estimation Variances for Subject 160 D-81

182 Estimation Variances for Subject 161 D-82

183 10 6 CC3 Estimation Variances for Subject 167 D-83

184 10 B Estimation Varihnces for Subject 171 D-84

185 i0 U fd 6 QP Estimation Variances for Subject 173 D-85

186 10 6 ~4-0,, Estimation Variances for Subject 176 D-86

187 to Estimation Variance; for Subject 183 D-87

188 Estimation Variances for Subject 185 D-88

189 to S Estimation Variances for Subject 112 D-89

190 6 4-0, Estimation Variances for Subject 141 D-90

191 6, 0- Estimation Variances for Subject 152 D-91

192 10 6.~4 Estimation Variances for Subject 156 D-92

193 8 0, Estimation Variances for Subject 199 D-93

194 Appendix E. Updated Surface Plots This appendix includes the updated surfaces and variances obtained by the updating procedure. The surfaces were produced sequentially beginning with the lowest numbered subject. Each surface represents the aggregate smr-i;ce or all the subjects up to and including the most recent update. Updated Facial Surfaces This section includes the surface estimates. E-1

195 Updated Surface After Subject 09 E-2

196 200, 150 Updated Surface After Subject 10 E-3

197 500 0 Updated Surface After Subject 60 E-4

198 Updated Surface After Subject 68 E-5

199 io0 50O Updated Surface After Subject 114 E-6

200 "200 r ~50 0o 50 Updated Surface After Subject 116 E-7

201 d 50 Updated Surface After Subject 118 E-8

202 o 1o00 d 50 Updated Surface After Subject 122 E-9

203 Updated Surface After Subject 130 E-10

204 Updated Surface After Subject 133 E-11

205 Updated Surface After Subject 136 E-12

206 Updated Surface After Subject 140 E-13

207 15o.o io 200-5o- Updated Surface After Subject 142 E-14

208 Updated Surface After Subject 153 E- 15

209 Updated Surface After Subject 154 E-16

210 0oo 150 Stoo- 50 * 0O Updated Surface After Subject 155 E-17

211 Updated Surface After Subject 159 E-18

212 200.6O. t0o Updated Surface After Subject 160 E-19

213 200, o 0 Updated Surface After Subject 161 E-20

214 Updated Surface After Subject 167 E-21

215 foo 50, Updated Surface After 3ubject 171 E-22

216 Updated Surface After Subject 173 E-23

217 Updated Surface After Subject 176 E-24

218 2o0 150 o0 Updated Surface After Subject 183 E-25

219 20O 150 Updated Surface After Subject 185 E-26

220 15o. 200' 50 Updated Surface After Subject 112 E-27

221 200 15o. i * Updated Surface After Subject 141 E-28

222 200 50o 10 Updated Surface After Subject 152 E-29

223 00. too 60o Updated Surface After Subject 156 E-30

224 200 50' SO0 p~np Updated Surface After Subject 199 E-31

225 Updated Estimation Variances This section includes the plots of the variances. E-32

226 3 Updated Variances After Subject 09 E-33

227 41 3-0f Updated Variances After Subject 10 E-34

228 4 IB Updated Variances After Subject 60 E-35

229 3.. Z, ot.. Updated Variances After Subject 68 E-36

230 o ,g 04 0 Updated Variances After Siibject 114 E-37

231 f " o*, Updated Variances After Subject 116 E-38

232 1.0 0',6 0.6 "0 0. Updated Variances After Subject 118 E-39

233 t Updated Variances After Subject 122 E-40

234 ' Updated Variances After Subject 130 E-41

235 ' " Updated Variances After Subject 133 E-42

236 1.0O Updated Variances After Subject 136 E-43

237 f Updated Variances After Subject 140 E-44

238 I.e ,. 1.p Updated Variances After Subject 142 E-45

239 " 'o,. Updated Variances After Subject 153 E-46

240 Updated Variances After Subject 154 E-47

241 o S0.1o 0.05 Updated Variances After Subject 155 E-48

242 Updated Variances After Subject 159 E-49

243 0.20 O.fg b Updated Variances After Subject 160 E-50

244 O.2o O.05 Updated Variances After Subject 161 E-51

245 ole- Updated Variances After Subject 167 E-52

246 0.20 O Updatk.d Variances After Subject 171 E-53

247 I V o - 0., Updated Variances After Subject 173 E-54

248 o Updated Variances After Subject 176 E-55

249 0.20 ~a Updated Variances After Subject 183 E-56

250 0.Z0 0.1f5 0.05' S0.10 Updated Variances After Subject 18.5 E-57

251 f n I I I E-58

252 Updated Variances After Subject 141 E-.59

253 "0.9 0.: Updated Variances After Subject 152 E-60

254 0.20 S Updated Variances After Subject 156 E-e 1

255 IO Updated Variances After Subject 199 E-62

OF NAVAL RESEARCH. Technical Report No. 87. Prepared for Publication. in the.. v.. il and/or -- c Spocial Journal of Elactroanalytical Chemistry it

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