脳波モデルを用いたReal-time集中状態判別器の実演と現状の稼働アルゴリズムの紹介

ྟচੜମϥϘதؒใࠂձ 5VFTEBZ ೴೾൝%͏͑͸Β͚ΜΏ͏ɹ ,FZXPSETΧΦεɼ&&( %VGpOHํఔࣜɼٯ໰୊ɼαϙʔτϕΫλʔϚγϯ 47. ʻ໨࣍ʼ ɹ̍ɽ࣮ԋɹɹɹɹɹɿ3FBMUJNFͰूதঢ়ଶΛ൑ผ͢ΔσϞ
ɹ̎ɽݚڀഎܠͱ໨తɿ%VGpOHํఔࣜʹΑΔ೴೾ϞσϧͱՄೳੑ ɹ̏ɽղੳख๏ɹɹɹɿٯ໰୊Λղ͖ɼ/POMJOFBS47.Ͱ෼ྨ ɹ̐ɽ݁Ռͱߟ࡯ɹɹɿׂҎ্ͷ൑ผਖ਼ղ཰ͷ࣮ݱɼࠔ೉ͳέʔε΋ ୊໨ͱ໨࣍ ೴೾ϞσϧΛ༻͍ͨ3FBMUJNFूதঢ়ଶ൑ผثͷ࣮ԋͱ ݱঢ়ͷՔಇΞϧΰϦζϜͷ঺հ

࣮ԋɿ3FBMUJNFͰूதঢ়ଶΛ൑ผ͢ΔσϞ ೴೾Λ༻͍ͨ3FBMUJNFूதঢ়ଶ൑ผͷ࣮ԋ ύʔιφϥΠζͨ͠ ൑ผث࡞੒ ϦΞϧλΠϜ ूதঢ়ଶ൑ผ ೴೾औಘ ҆੩ूத ೴೾ͷ਺஋Խ  Ϟσϧύϥϝʔλಉఆ
҆੩ूதͷ൑ผث࡞੒ ඇઢܗ47. ʮ҆੩ूதͷ൑ผثʯ ඇઢܗ47. ೴೾औಘ ೴೾ͷ਺஋Խ  Ϟσϧύϥϝʔλಉఆ ूதঢ়ଶΛϞχλ ιϑτ΢ΤΞͷྲྀΕ #FOFTTFͷλΠϐϯάࢼݧΛ΍Γ·͢ ҆੩ ෼ λΠϐϯάࢼݧ ෼ ϕωοη͕ग़͍ͯ͠Δ  ݕఆͷλΠϐϯάαΠτ ࣮ݧ৚݅

਺ࣜͰ͔͚Δܾఆ࿦తϞσϧͰ͋Δ ॳظ஋ͷͪΐͬͱͨ͠ҧ͍ʹΑͬͯڍಈ͕ඇपظతʹͳΔ ݚڀഎܠɿ%VGpOHํఔࣜʹΑΔ೴೾ϞσϧͱՄೳੑ ΧΦεɾɾɾॏৼΓࢠ͸ΧΦεతڍಈͱ͍͏ྫ (m1 + m2 )l2 1 ··
θ1 + m2 l1 l2 cos(θ1 − θ2 ) ·· θ2 + m2 l1 l2 sin(θ1 − θ2 ) · θ2 2 + g(m1 + m2 )l1 sin θ1 = 0 m2 l2 2 ·· θ2 + m2 l1 l2 cos(θ1 − θ2 ) ·· θ1 − m2 l1 l2 sin(θ1 − θ2 ) · θ2 1 + gm2 l2 sin θ2 = 0 IUUQTKBXJLJQFEJBPSH XJLJೋମ໰୊ IUUQTKBXJLJQFEJBPSHXJLJ ΞϯϦɾϙΞϯΧϨ ̏ମ໰୊ ղ͚ͳ͍Α  ͩͬͯΧΦεͩ΋Μ IUUQTKBXJLJQFEJBPSHXJLJ ΞΠβοΫɾχϡʔτϯ ଠཅɼ஍ٿɼ݄ɼ͜ ͷମͷఱମͷيಓ ͸ղੳతʹղ͚ͳ͍

神経インパルス ʮ೴೾ʯ΋ʮΧΦεʯ͕ೝΊΒΕ͍ͯΔ ೥೴ͷجຊߏ੒ཁૉͰ͋Δχϡʔϩϯ͕ΧΦεԠ౴Λࣔ͢͜ͱ͕໌Β͔ʹ͞Εͨ<> <>%FHO ) )PMEFO "7BOE0MTFO -' $IBPTJO#JPMPHJDBM4ZTUFNT 1MFOVN1SFTT
/: <>௡ాҰ࿠ɼz਺ֶͱҩֶ೴೾ͱ຺೾ͷΧΦεղੳΛΊ͙ͬͯzɼ਺ֶɼ7PM /P QQ ೴೾ &&(&MFDUSP&ODFQIBMP(SBN ೴಺ͷిؾత΍ΓͱΓΛ಄ൽ্Ͱܭଌͨ͠৴߸ ೴೾ͷৼΔ෣͍΋ΧΦεతͰ͋Δ<> ΧΦε౓߹͍ΛଌΔ୅දతͳํ๏ ɾϦΞϓ ϊϑࢦ਺ ɾ૬ؔ࣍ݩ ೾ܗͦͷ΋ͷΛॲཧͯ͠਺஋Խ͢Δ  Ͳͷ͘Β͍೾ܗ͕ΧΦεͳͷ͔ʁ ݚڀഎܠɿ%VGpOHํఔࣜʹΑΔ೴೾ϞσϧͱՄೳੑ લճͷதؒ ͰऔΓ্͛ͨ

ΧΦεͷಛੑɾɾɾܾఆ࿦త ਺ࣜͰ͔͚Δ΋ͷ Ͱ͋Γɼॳظ஋Ӷහੑ͕͋Δ ·· x + A· x + Bx
+ Cx3 = P cos(ωt + ϕ) %VGpOHํఔࣜ t → ∞Ͱશ͘ҟͳΔڍಈ x0 = 0.0 x0 = 0.001 x Ұ֊ৗඍ෼ํఔࣜʹඇઢܗ߲͕ ೖͬͨγϯϓϧͳࣜ ΧΦεΛৼΔ෣͏͜ͱͰ ༗໊ͳඇઢܗͳӡಈํఔࣜ ʮ೴೾ͷৼΔ෣͍ʯΛ ʮϞσϦϯάʯͰ͖ΔͷͰ͸ʁ ݚڀഎܠɿ%VGpOHํఔࣜʹΑΔ೴೾ϞσϧͱՄೳੑ

໨తɿඇઢܗํఔࣜʹΑΔ೴೾ϞσϧΛୡ੒͢ΔͨΊʹ͸ʁ ʻνϟϨϯδϯάͳ͜ͱͱ޻෉఺ʼ ೴೾ˠΧΦεͱ͍͏ੑ࣭ˠ਺ࣜͰ͔͚Δܾఆ࿦ˠॳظ஋Ӷහੑˠ௕ظ༧ଌ͕ࠔ೉ %VGpOHํఔ͕ࣜɼ೴೾ͱಉ༷ͳৼΔ෣͍ Λࣔ͢͜ͱ͕Ͱ͖Δͷ͔ʁ %VGpOHํఔࣜΛ༻͍ͨ೴೾ղੳϞσϧͷߏங ˠՄೳͰ͋Δ ͕ɽɽɽ ɾγϛϡϨʔγϣϯϞσϧ ॱ໰୊
ʹؔ͠ ɹͯ͸ࠔ೉Ͱ͋Δɽ ɾ্ͷ੍໿Λ্ख͘ߟྀͨ͠ٯ໰୊ͱ͍͏ ɹख๏Λ༻͍Δͱɼ࣌ࣄࠁʑͱมಈ͢Δ೴ ɹ೾ͷఆྔԽ͕ՄೳͰ͋Δɽ ղੳ̍ɽ೴೾ͷ࣮ଌ஋Λਖ਼ղ஋ͱͨ͠%VGpOHํఔࣜͷϑΟοςΟϯά݁Ռ<> ղੳ̎ɽ3FBMUJNFঢ়ଶ൑ผثͱͯ͠ػೳͤ͞Δॲཧํ๏<> <>,FOZV6 5BLBTIJ4 &YQFSJNFOUBM*EFOUJpDBUJPOPG.PEFM1BSBNFUFSTBOEUIF4UBUJTUJDBM1SPDFTTJOH6TJOHB/POMJOFBS0TDJMMBUPS"QQMJFEUP&&("OBMZTJT 1SPDFFEJOHTPGUIF"4.&*OUFSOBUJPOBM.FDIBOJDBM&OHJOFFSJOH$POHSFTTBOE&YQPTJUJPO *.&$& 75" <>্ݪݡ༞ɼᴡ౻ढ़ɼzूதঢ়ଶΛ൑ผ͢ΔγεςϜ΁ͷ࣮༻Λ໨ࢦͨ͠Ϟσϧϕʔευͳ೴೾৴߸ղੳʹ͍ͭͯͷݚڀzɼୈճ೔ຊੜମҩ޻ֶձେձɼ10#

ݚղੳख๏ɿ࠷খೋ৐๏Ͱٯ໰୊Λղ͖ɼ/POMJOFBS47.Ͱ෼ྨ A B C 'SFRVFODZ )[ 5JN F
T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF ೴೾ܭଌ͸ඵؒ αϯϓϦϯάप೾਺ )[ $PODFOUSBUJPO ࣮ݧσʔλ 3FMBY ɾඃݧऀ໊ ɾ՝୊ ΩʔϘʔυλΠϐϯάɼϚεܭࢉɼεϚϗΞϓϦήʔϜ ɾ՝୊͸ඵ͔Βඵ·Ͱͷؒ ɾܭଌՕॴ͸ޙ಄෦0 ࠃࡍج४๏ ɾ೴೾ܭ1PMZNBUF** ʻ࣮ݧʹؔ͢Δॾઃఆʼ ຊ࣮ݧ͸ຊֶػց޻ֶՊਓؒ޻ֶ ࣮ࢪલνΣοΫ ҕһձͷ৹ࠪʹΑΓɼ ྙཧతʹ໰୊͕ͳ͍͜ͱ͕ೝΊΒΕ࣮ͨݧͰ͋Δ -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO

ղੳख๏ɿ࠷খೋ৐๏Ͱٯ໰୊Λղ͖ɼ/POMJOFBS47.Ͱ෼ྨ A B C 'SFRVFODZ )[ 5JN F
T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO &&(ͷ࣌ؒˠप೾਺ʹؔ͢Δ৘ใ΁ɿҙຯͷ͋Δ৘ใͷநग़ ඵ N=2048 Δf = fs N = 500 2048 = 0.244 サンプリング周波数 fs 500 Hz (0.002 sec) 0.244 0.488 0.732 0.976 0.244 ʢ෼ղೳʣͷഒ਺ (Hz) ɾɾɾ प೾਺஋ͷ ִؒͷ͓࿩ ͳΔ΂͘प೾਺෼ղೳΛ্͍͛ͨʂ /ˠେ ͚Ͳɼ࣌ؒత෼ղೳ΋͍͋͛ͨʂ /ˠখ Α͠ʂΦʔόʔϥοϓͩʂ /ΛॏͶΔ 4 - 30 Hz प೾਺෼ղೳ ͸ ม͑Εͳ͍ ͬͪ͜͸  ม͑ΕΔ ଳҬ੍ݶ  όϯυύεϑΟϧλ ੜཧֶతಛ௃͕  ؔ࿈͍ͯ͠Δ ''5ʹΑΔप೾਺όϯυύεϑΟϧλϦϯάˠ*''5ʹΑΔ࣌ؒԽ

T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO &&(ͷ࣌ؒˠप೾਺ʹؔ͢Δ৘ใ΁ɿҙຯͷ͋Δ৘ใͷநग़ ඵ N=2048 Δf = fs N = 500 2048 = 0.244 サンプリング周波数 fs 500 Hz (0.002 sec) 0.244 0.488 0.732 0.976 0.244 ʢ෼ղೳʣͷഒ਺ (Hz) ɾɾɾ प೾਺஋ͷ ִؒͷ͓࿩ ͳΔ΂͘प೾਺෼ղೳΛ্͍͛ͨʂ /ˠେ ͚Ͳɼ࣌ؒత෼ղೳ΋͍͋͛ͨʂ /ˠখ Α͠ʂΦʔόʔϥοϓͩʂ /ΛॏͶΔ 4 - 30 Hz प೾਺෼ղೳ ͸ ม͑Εͳ͍ ͬͪ͜͸  ม͑ΕΔ ଳҬ੍ݶ  όϯυύεϑΟϧλ ੜཧֶతಛ௃͕  ؔ࿈͍ͯ͠Δ ''5ʹΑΔप೾਺όϯυύεϑΟϧλϦϯάˠ*''5ʹΑΔ࣌ؒԽ

T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO ''5ʹΑΔप೾਺όϯυύεϑΟϧλϦϯάˠ*''5ʹΑΔ࣌ؒԽ &&(ͷ࣌ؒˠप೾਺ʹؔ͢Δ৘ใ΁ɿҙຯͷ͋Δ৘ใͷநग़ ඵ N=2048 Δf = fs N = 500 2048 = 0.244 サンプリング周波数 fs 500 Hz (0.002 sec) 0.244 0.488 0.732 0.976 0.244 ʢ෼ղೳʣͷഒ਺ (Hz) ɾɾɾ प೾਺஋ͷ ִؒͷ͓࿩ ͳΔ΂͘प೾਺෼ղೳΛ্͍͛ͨʂ /ˠେ ͚Ͳɼ࣌ؒత෼ղೳ΋͍͋͛ͨʂ /ˠখ Α͠ʂΦʔόʔϥοϓͩʂ /ΛॏͶΔ 4 - 30 Hz प೾਺෼ղೳ ͸ ม͑Εͳ͍ ͬͪ͜͸  ม͑ΕΔ ɾɾɾ ɾɾɾ ඵຖͷ೾ܗʹରͯ͠ɼ࠷খೋ৐๏Ͱύϥϝλಉఆ ଳҬ੍ݶ  όϯυύεϑΟϧλ ੜཧֶతಛ௃͕  ؔ࿈͍ͯ͠Δ ɾɾɾ

T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO ໿ඵຖʹ࠷খೋ৐๏ -4. ʹΑΔύϥϝʔλಉఆ %VGpOHํఔࣜ min N ∑ i=1 (ϵi )2 ϵi = ·· xi + A · xi + Bxi + Cx3 i − D ϵi ࢒ࠩ xi ·· x + A · x + Bx + Cx3 = D ∂∑N i=1 ϵ2 i ∂A = 0 ∂∑N i=1 ϵ2 i ∂B = 0 ∂∑N i=1 ϵ2 i ∂C = 0 ∂∑N i=1 ϵ2 i ∂D = 0 ࠷খԽͷҰ֊৚݅ͭͷύϥϝλɼͭͷํఔࣜ ֤ม਺ͷภඍ෼Λ ඵຖʹղ͍͍ͯ͘ ೴೾σʔλ˔ ͸཭ࢄ৴߸ ಉఆ͞ΕͨϞσϧύϥϝλͷ஋ʹඇઢܗ47.Λద༻ͯ͠  ҆੩ूதͷ෼ྨثΛ࡞Δ

T A B C D ɾɾɾ ɾɾɾ 5JNF T 5JNF T 5JNF T "OBMZTJT8JOEPX T Y ·· x + A · x + Bx + cx3 = D .BQQJOHPG  .PEFM1BSBNFUFST  ˔3FMBY ˔$PODFOUSBUJPO 130$&44 3FMBY $PODFOUSBUJPO #PVOEBSZTVSGBDF -4.  1BSBNFUFS *EFOUJpDBUJPO &YQFSJNFOUBM EBUB ''5  'SFRVFODZ #1'JMUFSJOH *''5  'SFRVFODZUP 5JNF /POMJOFBS47.  $MBTTJpDBUJPO ඇઢܗ47.ͷ࣮૷ A-BΛྫʹ͢Δ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ˔҆੩ɹ ˔ूத ूத࣌ɼ͹Β͖ͭ͸ݟΒΕΔ΋ͷͷɼ෼෍ܗঢ়͸ಉ༷ͳ܏޲͕ݟΒΕΔʜ ඇઢܗ47.Ͱ҆੩࣌ͱूத࣌ͷڥքઢΛఆΊ͍ͨ Ϛʔδϯ࠷େԽ max{ ˜ L(α) = n ∑ i=1 αi − 1 2 n ∑ i=1 n ∑ i=j αi αj ti tj ϕ(x)T i ϕ(x)j} ϕ(x)T i ϕ(x)j ಛ௃ྔ ಛ௃ྔ αϙʔτϕΫτϧ αϙʔτϕΫτϧ Ϛʔδϯ࠷େԽ ໼ҹ෦ͷ௕͞ K2 K1 wT x + b = 0 w αɿϥάϥϯδϡ৐਺ ϥάϥϯδϡؔ਺Λ࠷େʹ͢ΔΑ͏ʹڥքઢΛܾΊΔ ઢܗͷ֓೦ ڭࢣ ςετ ڭࢣ ςετ 3FMBY $PODFOUSBUJPO αϙʔτϕΫλʔϚγϯʹΑΔඇઢܗ෼཭ ɹɾಛ௃ྔ͸ಉఆͨ͠ύϥϝʔλͷ͏ͪͭ "# "$ #$ ɽ ɹɾ࣍ͷଟ߲ࣜΧʔωϧΛ༻͍ͨࣸ૾ɽ ɹɾճͷަࠩݕূޙɼਖ਼ղ཰ͷฏۉ஋Λ༻͍ͯධՁɽ

ݚڀ݁ՌͷҰྫɿ"#ͷ47. ճͷަࠩݕূͷ͏ͪɼҰྫ ࠨଆɿڭࢣσʔλ  ӈଆɿςετσʔλ ɾڭࢣσʔλ͸ڥքΛҾͨ͘Ίͷ΋ͷ ɾςετͰڥքΛҾ͍ͨ΋ͷͷਖ਼ղ཰Λࢉग़
ɹશମత ࢀߟࢿྉ ʹਖ਼ղ཰Λݟͯ΋ɼׂҎ্Ͱ ूதঢ়ଶͷ൑ผ͕ՄೳͰ͋Δɽ ɹ͔͠͠ɼඃݧऀE /P ͷΑ͏ʹڥքΛҾ͘ͷ ͕ඇৗʹࠔ೉ͳέʔε΋͋ͬͨɽ  ɹଟ߲ࣜΧʔωϧͷࣸ૾࣍਺Λ૿΍ͨ͠Γ͕ͨ͠ɼ  ਖ਼ղ཰্͕͕Δ͜ͱ͸ͳ͔ͬͨɽ ɹͦ͏͍ͬͨ৔߹͸ɼ࠶౓՝୊Λ΍Γ௚ͯ͠ɼ൑ผ ثΛ࠶ߏங͢Δ͜ͱͰରԠ͢Δɽ

݁ݴɿࠓճͷൃදͰߦͳͬͨ͜ͱ ˔3FBMUJNFͰػೳ͢Δूதঢ়ଶ൑ผثͷσϞΛެ։ͨ͠ɽ ˔Ϟσϧύϥϝλͷ෺ཧతͳҙຯ߹͍Ͱ͸ͳ͘ɼ൑ผΞϧΰϦζϜʹ͍ͭͯൃදͨ͠ɽ ˔ΧΦεΛ༗͢Δ೴೾ͷϞσϧͱͯ͠ɼ%VGpOHํఔࣜΛ࢖༻͢Δཧ༝Λઆ໌ͨ͠ɽ ˔47.ͳͲͷٕज़ͷઆ໌͸͠ͳ͔͕ͬͨɼͬ͘͟Γͱͨ͠ॲཧͷϓϩηεΛ঺հͨ͠ɽ ˔ׂҎ্ͷਖ਼ղ཰Ͱूதঢ়ଶΛ൑ผͰ͖Δ͜ͱΛ͔֬Ίͨɽ ೴೾ϞσϧΛ༻͍ͨ3FBMUJNFूதঢ়ଶ൑ผثͷ࣮ԋͱ ݱঢ়ͷՔಇΞϧΰϦζϜͷ঺հ ൃද಺༰ͷ૯ׅ ˓Ϟσϧύϥϝλͷ෺ཧతҙຯ߹͍ͷ͋ΔϚοϓΛ࡞Δɽ
ɹˠଞͷঢ়ଶͷ࣮ݧΛ͢Δඞཁ͕͋Δ ɹˠ47.ͷ಺ଆͷΞϧΰϦζϜͷࡉ͔͍ઃఆΛ͢Δ

ऴΘΓ ͓ΘΓ

ࢀߟࢿྉ ʻࢀߟࢿྉʼ ɹɾ%VGpOHํఔࣜͷϑΟοςΟϯάʹؔͯ͠ ɹɾ%VGpOHํఔࣜͷετϨϯδΞτϥΫλ ɹɾ࣮ݧσʔλͷ೴೾ͷੜσʔλ ɹɾϞσϧύϥϝʔλಉఆ݁Ռ ɹɾ૭෯ͷݕ౼ ઢܗ47.ͷ࣌୅ ɹɾ''5ͷप೾਺৘ใʹؔͯ͠
प೾਺ؚ༗ྔͱप೾਺ϐʔΫͷҰྫ ɹɾओ੒෼෼ੳʹΑΔ௿࣍ݩԽ ɹɾઢܗ47.ɼۣܗ૭ɼϋχϯά૭ɼಛ௃ྔͷݕ౼ ɹɾύϥϝλಉఆͷ݁Ռ ಈը෇͖ ɹɾઢܗ47.ͷ݁Ռ ɹɾඇઢܗ47.ͷ݁Ռ ɹɾଟ߲ࣜࣸ૾ͷ޻෉ ɹɾ೴೾ͷ৽ͨͳ৘ใఏࣔʹ޲͚ͨऔΓ૊Έ ɹɾ֎෦ࢀߟϦϯΫ 47.ͱ͸ʁɼલճͷதؒใࠂͷࢿྉ

ղੳɿ%VGpOHํఔࣜͷϑΟοςΟϯάํ๏ʹ͍ͭͯ ·· xsim + A · xsim + Bxsim +
C(xsim)3 = P(t) ઢܗ߲ ඇઢܗ߲ ֎෦ೖྗ߲ ࣮ଌͨ͠೴೾࣌ܥྻσʔλ ϞσϧʹΑΔγϛϡϨʔγϣϯ஋ ඵؒ ࣮ଌ஋ͷॳظ஋ʢx0, v0 ʣΛϞσϧʹ༩͑Δ Error(A, B, C, P(t)) ධՁؔ਺ ཧ૝ Ϟσϧͷܭࢉ݁Ռ͸ ɹɹ࣮ݧ஋ͱಉ༷ʹ͍ͨ͠ = 1 N N ∑ i=1 (xexp i − xsim i )2 A B C P(t) xexp xsim xexp ܾఆ஋ Λຬ଍͢ΔϞσϧ ύϥϝʔλΛಉఆ xsim → xexp ࠷దԽख๏ͷ࣮਺ܕ("ʢҨ఻తΞϧΰ ϦζϜʣΛ࢖༻ͯ͠࠷খ஋໰୊Λܭࢉ ධՁؔ਺͕࠷খʹͳΔ ύϥϝλͷ૊Έ߹Θͤ

C(xsim)3 = P(t) ઢܗ߲ ඇઢܗ߲ ֎෦ೖྗ߲ ࣮ଌͨ͠೴೾࣌ܥྻσʔλ ϞσϧʹΑΔγϛϡϨʔγϣϯ஋ ࣮ଌ஋ͷॳظ஋ʢx0, v0 ʣΛϞσϧʹ༩͑Δ Error(A, B, C, P(t)) ධՁؔ਺ = 1 N N ∑ i=1 (xexp i − xsim i )2 A B C P(t) xexp xsim xexp ܾఆ஋ Λຬ଍͢ΔϞσϧ ύϥϝʔλΛಉఆ xsim → xexp ࠷దԽख๏ͷ࣮਺ܕ("ʢҨ఻తΞϧΰ ϦζϜʣΛ࢖༻ͯ͠࠷খ஋໰୊Λܭࢉ ධՁؔ਺͕࠷খʹͳΔ ύϥϝλͷ૊Έ߹Θͤ ඵؒ ཧ૝ Ϟσϧͷܭࢉ݁Ռ͸ ɹɹ࣮ݧ஋ͱಉ༷ʹ͍ͨ͠

C(xsim)3 = P(t) ઢܗ߲ ඇઢܗ߲ ֎෦ೖྗ߲ ࣮ଌͨ͠೴೾࣌ܥྻσʔλ ϞσϧʹΑΔγϛϡϨʔγϣϯ஋ ࣮ଌ஋ͷॳظ஋ʢx0, v0 ʣΛϞσϧʹ༩͑Δ Error(A, B, C, P(t)) ධՁؔ਺ = 1 N N ∑ i=1 (xexp i − xsim i )2 xexp xsim xexp ܾఆ஋ Λຬ଍͢ΔϞσϧ ύϥϝʔλΛಉఆ xsim → xexp ࠷దԽख๏ͷ࣮਺ܕ("ʢҨ఻తΞϧΰ ϦζϜʣΛ࢖༻ͯ͠࠷খ஋໰୊Λܭࢉ ඵؒ ཧ૝ Ϟσϧͷܭࢉ݁Ռ͸ ɹɹ࣮ݧ஋ͱಉ༷ʹ͍ͨ͠ A B C P(t) ධՁؔ਺͕࠷খʹͳΔ ύϥϝλͷ૊Έ߹Θͤ

C(xsim)3 = P(t) ઢܗ߲ ඇઢܗ߲ ֎෦ೖྗ߲ ࣮ଌͨ͠೴೾࣌ܥྻσʔλ ϞσϧʹΑΔγϛϡϨʔγϣϯ஋ ࣮ଌ஋ͷॳظ஋ʢx0, v0 ʣΛϞσϧʹ༩͑Δ Error(A, B, C, P(t)) ධՁؔ਺ = 1 N N ∑ i=1 (xexp i − xsim i )2 xexp xsim xexp ܾఆ஋ Λຬ଍͢ΔϞσϧ ύϥϝʔλΛಉఆ xsim → xexp ࠷దԽख๏ͷ࣮਺ܕ("ʢҨ఻తΞϧΰ ϦζϜʣΛ࢖༻ͯ͠࠷খ஋໰୊Λܭࢉ ඵؒ ඵؒ ඵؒ ඵؒ A B C P(t) ධՁؔ਺͕࠷খʹͳΔ ύϥϝλͷ૊Έ߹Θͤ ೴೾ͷ࣮ଌ஋ͷৼΔ෣͍ͱಉ༷ͳγϛϡϨʔγϣϯ೾ܗΛಘΔ͜ͱ͕Ͱ͖Ε ͹ɼ࣌ࣄࠁʑͱมಈ͢Δ೴೾ࣗମͷఆྔԽ͕ՄೳͰ͋Δ

ղੳɿ%VGpOHํఔࣜͷϑΟοςΟϯάํ๏ʹ͍ͭͯ ϦϥοΫε74ετϨε೴೾ͷݕ౼ ɾΞϧϑΝ೾<)[> ɾϦϥοΫε೴೾TFD ɾετϨε೴೾TFD Ϛεܭࢉ ɾޙ಄෦ ࢹ֮໺0
ɾ4BNQMJOHTFD ɾղੳ૭ඵؒTBNQMF ώτͷঢ়ଶΛਪఆ ·· x + A · x + Bx + Cx3 = P1 cosωt + P2 sinωt ฏۉޡࠩ ฏۉޡࠩ ϦϥοΫε ετϨε ˔%VGpOHํఔࣜͰɼ೴೾ͷෳࡶͳৼΔ෣͍ΛϞσ ɹϧԽ͢Δ͜ͱ͕ՄೳͰ͋Δ ˔ಉఆ͞ΕͨϞσϧύϥϝʔλͰώτͷঢ়ଶਪఆ͕ ɹՄೳͰ͋Δ ϦϥοΫεɼετϨε೴೾ͱ΋ʹɼ࣮ଌ஋ ͷৼΔ෣͍ʹҰக͍ͯ͠Δ͜ͱ͕෼͔Δ

·· x + A · x + Bx + Cx3
= P cos(ωt + ϕ) ϙΞϯΧϨ੾அ໘ ϙΞϯΧϨࣸ૾ ࿈ଓతͳӡಈΛ͋ΔҰఆपظͰ ཭ࢄԽ͢Δهड़ํ๏ حົͳղू߹͕ݱΕΔ ࢀߟࢿྉɿ%VGpOHํఔࣜͷΞτϥΫλͷ঺հ ڧ੍%VGpOHܥͷΧΦεͷಛ௃ɿδϟύχʔζΞτϥΫλ <>্ాⅼ྄ɼzΧΦεݱ৅࿦zɼίϩφࣾʻݱ୅ඇઢܗՊֶγϦʔζʼɼ*4#/

ࢀߟࢿྉɿղੳʹ࢖༻࣮ͨ͠ݧσʔλ ूத࣌ʢλΠϐϯάʣ ҆੩ ҆੩ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ूத࣌ʢεϚϗΞϓϦʣ ҆੩
҆੩ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ूத࣌ʢϚεܭࢉʣ ҆੩ ҆੩ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀਓ෼ͷੜσʔλ ɾඃݧऀ໊ ɾ՝୊ λΠϐϯάɼϚεܭࢉɼεϚϗήʔϜ ɾ՝୊͸ඵ͔Βඵ·Ͱͷؒ ɾܭଌՕॴ͸ޙ಄෦0 ࠃࡍج४๏ ɾ೴೾ܭ1PMZNBUF** ຊ࣮ݧ͸ຊֶػց޻ֶՊਓؒ޻ֶ ࣮ࢪલνΣοΫ ҕһձͷ৹ࠪʹΑΓɼ ྙཧతʹ໰୊͕ͳ͍͜ͱ͕ೝΊΒΕ࣮ͨݧͰ͋Δ ॎ࣠ͷେ͖͞ଗ͑ͯͳ͍Ͱ͢

ࢀߟࢿྉɿϞσϧύϥϝʔλ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ˔҆੩ɹ ˔ूத Ϟσϧύϥϝλಉఆ݁Ռ )[ଳҬͷ ೴೾σʔλΛ༻͍ͨ
ύϥϝλಉఆͷ݁Ռ  ·· x + A· x + Bx + Cx3 = D ࣌ؒΛແࢹͨ͠ %ϓϩοτ ඃݧऀ͝ͱʹ ύϥϝʔλ෼෍ܗঢ়ʹ ͹Β͖ͭ͸͋Δ΋ͷͷ ҆੩ͱूதͷ۠ผ͕ ग़དྷͦ͏

ࢀߟࢿྉɿϞσϧύϥϝʔλ A-B ͷΈ ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ඃݧऀ/P ˔҆੩ɹ ˔ूத Ϟσϧύϥϝλಉఆ݁Ռ
A-B ·· x + A· x + Bx + Cx3 = D ूத࣌͸ɼࠨ্ʹ޲͔͏ ܏޲͕ݟΒΕΔ #ˠ૿Ճ   "ˠݮগ ඃݧऀ/P͸  ͦͷ܏޲͕ݦஶ ҆੩ͱूதͷ෼཭ڥքΛ Ҿͨ͘Ίʹ47.Λࢼ͢

ࢀߟࢿྉɿղੳ૭ʹؔ͢Δௐࠪ प೾਺ղੳͷղੳ૭ʹؔͯ͠ͷௐࠪ ɾ೴೾ͷΧΦεੑͳͲΛ൓өͨ͠Ϟ ɹσϧύϥϝλͷ֫ಘͷͨΊɽ ɾ47.ͷ෼ྨਫ਼౓͕࠷΋ྑ͘ͳΔ৚ ɹ݅ͷࠜؾ୳ࡧͷͨΊɽ ͜Εͱ͸ผʹ૭ؔ਺ͷௐࠪ΋࣮ࢪ ɾۣܗ૭ ɾϋχϯά૭
ɾϋϛϯά૭ ɾ*''5࣌ͷϋχϯά૭ͷׂ௚͠ͳͲ ࠓ͸ʮᶆʯͱʮۣܗ૭ʯΛ ϦΞϧλΠϜঢ়ଶ൑ผʹ࢖༻

ʔɹϕʔλ ʔɹΞϧϑΝ ʔɹγʔλ ᶃ ᶄ ᶅ ᶆ ετϨεঢ়ଶ ϦϥοΫεঢ়ଶ ඃݧऀͷϚεܭࢉͷඵؒͷͭͷप೾਺ϐʔΫ
C ϦϥοΫε࣌ T D ετϨε࣌ T B ͭͷϐʔΫͷ࣌ؒతมಈ ౓਺ ౓਺ ᶃ ᶄ ᶅ ᶆ ʔɹୈϐʔΫ૯਺ 0WFSMBQΛ૿΍͢ͱɼετϨε࣌ʹ ଟ͘ग़ͯཉ͍͠ϕʔλଳҬͷϐʔΫ͕ݮΔ ᶃͱᶆΛ ൺ΂Δͱݦஶ ଟ͍ গͳ͍ ˡΦʔόʔϥοϓʴ θϩύσΟϯάʴˠ ඃݧऀͷϚεܭࢉͷप೾਺ؚ༗཰ͷ࣌ؒతਪҠ प೾਺ͷ৘ใΛαϙʔτϕΫλʔϚγϯͷಛ௃ྔͱͯ͠׆༻͢ΔͨΊௐࠪ ɾ0WFSMBQΛ૿΍͢ͱ ᶆͱ͔ ɼप೾਺ؚ༗཰ͷׂ߹͕҆ఆ͢Δ ྑ͍͜ͱ ɾ0WFSMBQΛ૿΍͢ͱ ᶆͱ͔ ɼߴप೾ͷϐʔΫ஋͕ݮΔ ݏͳ͜ͱˠ͜Ε͕ਖ਼͍͠΋ͷͰ͋Δͷ͕ͩ ૭෯ ࢀߟࢿྉɿप೾਺ͷ৘ใʹؔͯ͠ Ұྫ

ඃݧऀ ඃݧऀ ඃݧऀ ඃݧऀ "d$ प೾਺ ϐʔΫ ओ੒෼෼ੳʹΑΔ ௿࣍ݩԽ ࢀߟࢿྉɿओ੒෼෼ੳʹΑΔ௿࣍ݩԽ࣍ݩˠ࣍ݩ
ϞσϧύϥϝλͷΈͰ΋ ෼཭͕Ͱ͖Δ͕ɼ ग़དྷͳ͍σʔλ΋͋Δ  ஫ҙɿ ͜ͷ࣌ͷύϥϝλಉఆ͸ɼ  #1ϑΟϧλແ͠ͷશप೾਺ଳҬ  ͷ೴೾σʔλͰ͋Δ ͜ͷ࣌ͷप೾਺ϐʔΫ͸ ʮᶃʯ ඵ૭ ̌QBEEJOHඵ ࣠͸)[ ϐʔΫͷ৘ใΛೖΕͯɼ ओ੒෼෼ੳΛ͢Δ΋ɼ  ઢܗ47.ͷ෼ྨਫ਼౓͸ ͕͋Βͳ͍͜ͱΛ֬ೝ ඃݧऀ

''5ʹ༻͍Δ૭ؔ਺ͷݕ౼ɿۣܗ૭ͷ෯Λௐ΂Δ ઢܗ47.ʹΑΔ෼ྨධՁ ɾશͯͷඃݧऀ͓ΑͼશͯͷλεΫΛௐ΂ͨ ɾᶃdᶆͷ৚݅ͷ૭෯ʹରͯ͠ɼಛ௃ྔΛύλʔϯݕ౼ͨ͠ ɾಛ௃ྔͷύλʔϯ͸ ಛ௃ྔ " # $ ɼಛ௃ྔ
ಛ௃ྔ % ɼಛ௃ྔ ಛ௃ྔ ૭಺ͷप೾਺ͭ ɾΦʔόʔϥοϓແ͠ͷํ͕෼ྨثͱͯ͠ͷੑೳ͕ྑ͍ ɾظ଴ͱ͸ٯͷ܏޲ʹͳͬͨͷͰಾ ͨͩ͜͠Ε͸ઢܗ47.ͷ࿩ Φʔόϥοϓແ͠Ͱ΋શવ͋Γʂ ࢀߟࢿྉɿ47.ɼۣܗ૭ɼಛ௃ྔͷݕ౼

''5ʹ༻͍Δ૭ؔ਺ͷݕ౼ɿ)BOOJOH૭ͷ෯Λௐ΂Δ ઢܗ47.ʹΑΔ෼ྨධՁ ɾશͯͷඃݧऀ͓ΑͼશͯͷλεΫΛௐ΂ͨ ɾᶃdᶆͷ৚݅ͷ૭෯ʹରͯ͠ɼಛ௃ྔΛύλʔϯݕ౼ͨ͠ ɾಛ௃ྔͷύλʔϯ͸ ಛ௃ྔ " # $ ɼಛ௃ྔ
ಛ௃ྔ % ɼಛ௃ྔ ಛ௃ྔ ૭಺ͷप೾਺ͭ ɾ̓ಛ௃ྔΛೖΕͯ΋෼ྨਫ਼౓͕͕͋Βͳ͍͜ͱ͕֬ೝͰ͖Δ ɾ૭෯Λ௕ͯ͘͠΋෼ྨਫ਼౓͕͕͋Βͳ͍͜ͱ͕֬ೝ͞ΕΔ ಛ௃ྔͰ΋શવ͋Γʂ ࢀߟࢿྉɿ47.ɼϋχϯά૭ɼಛ௃ྔͷݕ౼

ϋχϯά૭ ۣܗ૭ ϋϛϯά૭  ૭ؔ਺ͰׂΓ௚ͨ͠ ϋχϯάʹ௥Ճͯ͠ʮϋϛϯάʯͱʮۣܗʯΛௐࠪ ઌߦݚڀ<> ඵ ඵ ඵ ύϥϝλಉఆ
ࢀߟࢿྉɿ''5ͷ૭ؔ਺ͷݕ౼ ύϥϝλͷ૬ؔΛΈΔ ύϥϝλಉఆʹ࢖༻͢Δ࣌ؒσʔλͷͨΊͷɼ''5ʹ࢖༻͢Δ૭ؔ਺ͷௐࠪ ελʔτͷඵ͸QBEEJOH QBSBNFUFS#"VFIBSBXPSE@IBN 3FMBY 4USFTT 3FMBY QBSBNFUFS$"VFIBSBXPSE@IBN 3FMBY 4USFTT 3FMBY QBSBNFUFS#$VFIBSBXPSE@IBN 3FMBY 4USFTT 3FMBY QBSBNFUFS#"VFIBSBXPSE@SFD 3FMBY 4USFTT 3FMBY QBSBNFUFS$"VFIBSBXPSE@SFD 3FMBY 4USFTT 3FMBY QBSBNFUFS#$VFIBSBXPSE@SFD 3FMBY 4USFTT 3FMBY QBSBNFUFS#"VFIBSBXPSE@IBO 3FMBY 4USFTT 3FMBY QBSBNFUFS$"VFIBSBXPSE@IBO 3FMBY 4USFTT 3FMBY QBSBNFUFS#$VFIBSBXPSE@IBO 3FMBY 4USFTT 3FMBY ϋχϯά૭ ϋϛϯά૭ ۣܗ૭ W(n) = 0.5 − 0.5 cos( 2πn N ) W(n) = 0.54 − 0.46 cos( 2πn N ) W(n) ૭ؔ਺ W(n) = 1 ૭ؔ਺ͷҧ͍ʹΑͬͯɼಉఆ͞Εͨύϥϝʔλʹେ͖ͳҧ͍͕ ੜ͡ͳ͍͜ͱΛ͔֬Ίͨɽ ӈͷਤ͸ɼϞσϧύϥϝʔλͷ૬ؔΛࣔ͢ɽ ʢঢ়ଶ͸ɼϦϥοΫεˠετϨεˠϦϥοΫεͷਪҠͰ͋Δʣ

ࢀߟࢿྉɿ''5ͷ૭ؔ਺ɼύϥϝλಉఆɼϋχϯάͷ۩ମྫ ϋχϯά૭ͷ*''5ͷྫ ελʔτͷඵ͸QBEEJOH ղੳ૭ΛΦʔόʔϥοϓΛ͔͚͍ͯΔͷͰɼσʔλ௕͸ഒʹͳΔ͕ɼॲཧͷ࣮࣌ؒ͸ॏͶΔͷͰζϨͳ͍ ύϥϝλಉఆ  ඵ෼ Time (s) EEG
(micro V) ॳΊͷඵ͸7Λ Ճ͍͑ͯΔ ॳΊͷඵ͸7Λ Ճ͍͑ͯΔ ύϥϝλಉఆ  ඵ෼ Time (s) EEG (micro V) ɾϋϛϯά૭ͷ৔߹ɼ*''5ͷ࣌ؒ೾ܗ͕྆୺Ͱ7ʹͳΔ͕ɼۣܗ૭Ͱ͸ͦΕ͕ͳ͍ ɾϞσϧύϥϝλಉఆͱ͍͏࢓૊Έ্ɼ྆୺Ͱ೾ܗͷϘϦϡʔϜ͕མͪΔͷ͸ݏɽ ɾϞσϧύϥϝλͷӨڹʹ͓͍ͯɼ૭ؔ਺ͷӨڹ͕ͳ͍͜ͱΛ͖ͪΜͱௐ΂ͨ ઌߦݚڀͱͷണ཭๷ࢭ ɽ

ύϥϝλಉఆʹ࢖༻͢Δ࣌ؒσʔλͷͨΊͷɼ''5ʹ࢖༻͢Δ૭ؔ਺ͷௐࠪ ελʔτͷඵ͸QBEEJOH ࢀߟࢿྉɿ''5ͷ૭ؔ਺ͷݕ౼ ύϥϝλͷ૬ؔΛΈΔ ϋχϯά૭ ϋϛϯά૭ ۣܗ૭ प೾਺ ϐʔΫ
A B C *''5 &&( D Time(s) ɾղੳ૭͸ɼඵ෯Λ༻͍͍ͯΔ ɾΦʔόʔϥοϓ ɾ࠷ޙͷඵΛύϥϝλಉఆ ύϥϝλͷ܏޲͸Ͳͷ૭ؔ਺Ͱ΋ಉ༷Ͱ͋Δ ۣܗ૭ͷ࠾༻ ूத࣌೴೾

ࢀߟࢿྉɿϋχϯάɼϋϛϯά૭ύϥϝʔλಉఆ ಈը ඃݧऀ/P $ ͷύϥϝλಉఆ݁Ռɼ૭ؔ਺ͷҧ͍Λ֬ೝ ϋχϯά૭ प೾਺ ϐʔΫ ϋϛϯά૭
A B C *''5 &&( D Time(s) प೾਺ ϐʔΫ A B C *''5 &&( D Time(s)

ࢀߟࢿྉɿۣܗ૭ύϥϝʔλಉఆ ಈը ඃݧऀ/P $ ͷύϥϝλಉఆ݁Ռɼ૭ؔ਺ͷҧ͍Λ֬ೝ ۣܗ૭ प೾਺ ϐʔΫ A
B C *''5 &&( D Time(s)

ςετ ࢀߟࢿྉɿઢܗαϙʔτϕΫλʔϚγϯͷ෼ྨੑೳ TFD TFD ूத ҆੩ TFD ڭࢣσʔλඵ ςετσʔλඵ
ςετσʔλͰ࢖͏ඵؒͷ৔ॴΛม͑ͯ ߹ܭճ෼Ͱ47.Λ͢Δ ݕূ 3FMBYڭࢣ 3FMBYςετ 4USFTTڭࢣ 4USFTTςετ d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d ڭࢣ ςετ 3FMBY $PODFOUSBUJPO ڭࢣ αϙʔτϕΫλʔϚγϯ͸ɼڭࢣσʔλ ςετσʔλ ͷ஋͕ภΔ৔߹͕͋ΔͷͰɼަࠩݕূΛ͢Δ ۩ମతͳ਺஋ͷ֬ೝ ڭࢣσʔλͱςετσʔλΛೖΕସ͑ͯɼ σʔλࣗମͷภΓ͕ͳ͍͔֬ೝ͢Δ ɾ࣮ݧσʔλΛڭࢣͱςετʹ෼͚Δ ɾςετͷྔ͸ڭࢣͷ ɾύϥϝλ͸"#Λ༻͍Δ

ࢀߟࢿྉɿઢܗ47.ͷ෼ྨௐࠪ݁Ռ 8PSEݕূaඃݧऀ " # $ %
ฏۉ λΠϐϯά Nݕূaඃݧऀ " # $ % ฏۉ Ϛεܭࢉ (BNFݕূaඃݧऀ " # $ % ฏۉ ΞϓϦ ֤՝୊ʹ͓͚ΔαϙʔτϕΫλʔϚγϯͷ෼ྨ݁Ռ ަࠩݕূͷฏۉ஋Λݟͯʂ ɾઢܗ47.Ͱ΋ͦͦ͜͜෼ྨͰ͖Δɽ ɾඃݧऀ$͸෼ྨਫ਼౓͕ߴ͍͕ɼͦ͏Ͱͳ͍ਓ΋͍Δɽ ɾ஋෼ྨ ׂ͕࠷௿ ͳͷͰɼඃݧऀʹΑΒͣɼׂҎ্ͷਖ਼ղ཰Λ໨ࢦ͢ΞϧΰϦζϜʹ͍ͨ͠ɽ

ࢀߟࢿྉɿඇઢܗ47.ͷ݁Ռ A-BͱA-CɼλΠϐϯά ඇઢܗαϙʔτϕΫλʔϚγϯͷ෼ྨ݁Ռ A-B A-C ·· x + A·
x + Bx + Cx3 = D ໌Β͔ʹࣦഊ΋͋Δ ೴೾σʔλΛऔΓ௚͢ ࠨଆ͕ڭࢣσʔλͰɼ෼཭ڥքઢΛҾ͍ͯΔ΋ͷɽӈଆ͕ςετσʔλͰɼ෼ྨثͷධՁΛ͍ͯ͠Δ΋ͷ

ࢀߟࢿྉɿඇઢܗ47.ͷ݁Ռ B-CɼλΠϐϯά ඇઢܗαϙʔτϕΫλʔϚγϯͷ෼ྨ݁Ռ ·· x + A· x +
Bx + Cx3 = D ࠨଆ͕ڭࢣσʔλͰɼ෼཭ڥքઢΛҾ͍ͯΔ΋ͷɽӈଆ͕ςετσʔλͰɼ෼ྨثͷධՁΛ͍ͯ͠Δ΋ͷ B-C

ࢀߟࢿྉɿඇઢܗ47.ͷ݁Ռ ަࠩݕূ A B C ҆੩ ूத ҆੩ूத࣌ͷσʔλΛ̑౳෼ͯ͠ɼ ͦͷ͏ͪͭΛςετσʔλʹ͢Δ
ڭࢣ ڭࢣ ςετ ςετ ճ෼ަࠩݕূͷ֤ඃݧऀͷ෼෍ ඇઢܗαϙʔτϕΫλʔϚγϯͷ෼ྨ݁Ռ ·· x + A· x + Bx + Cx3 = D ɾઢܗ47.Ͱ͸શͯͷඃݧऀͰୡ੒ग़དྷͳׂ͔ͬͨͷਖ਼ղ཰͕ɼඇઢܗ47.Ͱ͸ୡ੒͢Δ͜ͱ͕Ͱ͖ͨ

ࢀߟࢿྉɿඇઢܗ47.ͷ݁Ռ ަࠩݕূ ඇઢܗαϙʔτϕΫλʔϚγϯͷ෼ྨ݁Ռ ·· x + A· x +
Bx + Cx3 = D ɾͭͷಛ௃ྔɼͭ·ΓɼA - B, A - C, B - Cͷͭͷ৔߹ΛऔΓ্͛ɼͦΕͧΕʹ47.Λద༻ͯ҆͠੩ঢ়ଶͱूதঢ়ଶͷ൑ผʹ༻͍ͨ ɾͲͪΒͷ৔߹͍ʹ͓͍ͯ΋ɼ҆੩ঢ়ଶͱूதঢ়ଶͷ൑ผʹࡍཱͬͯ༏ҐͳϞσϧύϥϝʔλͷ૊Έ߹Θͤ͸ͳ͔ͬͨ ɾ͔͠͠Ͳͷ৔߹ʹ͓͍ͯ΋ɼͭͷλεΫʹ͓͚Δूதঢ়ଶͷ൑ผ͕΄ͱΜͲҎ্ͷਖ਼ղ཰Ͱ൑ผ͕ՄೳͰ͋Δ͜ͱ͕Θ͔ͬͨ

ࢀߟࢿྉɿඃݧऀ/Pͷଟ߲ࣜΧʔωϧͷ޻෉ ࣍Ҏ্ͷଟ߲ࣜࣸ૾ Λࢼ͕ͨ͠ɼಛ௃্ۭؒͰͷ෼཭௒ฏ໘͕ෳࡶʹͳΔ͚ͩɽ
ɾଟ߲ࣜΧʔωϧ K(xi , xj ) = (xT i xj + 1)d xi , xj xT i xj

ࢀߟࢿྉɿඇઢܗ47.ͷ޻෉ Verification of a system to determine concentration state
Running window Band Pass in sub-bands between 4 - 30 Hz IFFT Parameter identification ɾɾɾ Standardization Tree-dimensional polynomial mapping Train/Cross Validate SVM Classifier Standardization Tree-dimensional polynomial mapping Tree-dimensional polynomial mapping Tree-dimensional polynomial mapping Xstd = X − ¯ X σ Standardization ෼෍ฏۉ ඪ४ภࠩ (A, B) ɹ↓ ( 1, A, B, A2, AB, B2, A3, A2B, AB2, B3) Tree-dimensional polynomial mapping ɾଟ߲ࣜΧʔωϧ K(xi , xj ) = (xT i xj + 1)3 xi , xj xT i xj A B A B ࣍ݩ֦ு ࣸ ૾ ͷ ֓ ೦ ฏۉ஋෼ࢄͷσʔλ܊ʹଗ͑Δˠࣸ૾ ඪ४Խͱ࣍ݩͷଟ߲ࣜࣸ૾

ࢀߟࢿྉɿඇઢܗ47.ʹΑΔूத൑ผ 3FBMUJNFूதঢ়ଶ൑ผςετ ܭଌऴྃޙͷը૾ ҆੩ ෼ λΠϐϯάࢼݧ ෼ ϕωοη͕ग़͍ͯ͠Δ  ݕఆͷλΠϐϯάαΠτ
ന͍นΛ௚ࢹ ࢼݧલετϨον ௒ͥͭ҆Β͙ঢ়ଶ ࣮ݧ৚݅ ೴೾ܭ͸&NPUJW&10$ ɼTBNQMJOHप೾਺)[ɼऔಘϲॴ͸0

ಈը൛ 3FBMUJNFूதঢ়ଶ൑ผςετಈը൛ ࢀߟࢿྉɿඇઢܗ47.ʹΑΔूத൑ผ ूதঢ়ଶ͔Ͳ͏͔Λ ൑ผ͢Δάϥϑ ύϥϝλϚοϓ ͋Β͔͡ΊύʔιφϥΠζ͞Εͨ΋ ͷΛ࡞੒͓ͯ͘͠ඞཁ͕͋Δ ࣮ݧ͝ͱʹઃఆͨ͠ঢ়ଶΛݩʹ
ͦͷਓ͕Ͳͷ͘Β͍ूதͰ͖͍ͯ ͔ͨΛ࠷ޙʹฦ͢

ࢀߟࢿྉɿ೴೾ͷ৽ͨͳ৘ใఏࣔʹ޲͚ͨऔΓ૊Έ ೴೾Λ࢖ͬͨ৽͍͠πʔϧͷ։ൃʹ޲͚ͯ ·· x + A · x +
Bx + Cx3 = P cos(ωt + ϕ) ϦϥοΫε ूத ϦϥοΫε ＜Modeling＞ Modeling of EEG, 1DOF, no random term ूத ϦϥοΫε ɾਓؒঢ়ଶΛՄࢹԽͰ͖Δ  ɾݸਓͷಘҙෆಘҙ͕Θ͔Δ  ɾ࣬ױͷ਍அࢧԉ͕Ͱ͖Δ  ɾΞϓϦέʔγϣϯͷ૑ग़  ɾࣾձ͕ଟ༷ʹͳͬͯ໘ന͘ͳΔ ଞͷੜཧ ਫ਼ਆ ׆ಈʹ  ؔ࿈͕͋Δ͔΋ ڥքΛ෼͚ΔͨΊͷ࢓૊Έ ਓ ෼ ͷ   ώ τ ೴ ೾ ͩ Α ಈըϑΝΠϧ Necomimi, Neurowear, Japan, Oﬃcial video Τϯλϝͷಓ۩ͱͯ͠ ೴೾͕࢖ΘΕ͍ͯΔ ಈըϑΝΠϧ

֎෦ϦϯΫɿ4MJEF4IBSFʹஔ͍ͯ·͢ αϙʔτϕΫλʔϚγϯʹؔ͢Δৄ͍͠આ໌͸ҎԼ IUUQTXXXTMJEFTIBSFOFUTTVTFSGTWN αϙʔτϕΫλʔϚγϯ 47. ͷ਺ֶΛΈΜͳʹઆ໌͍͚ͨͩ͠ͷձ ΫϦοΫͰඈ΂·͢ લճͷதؒใࠂͷࢿྉ IUUQTXXXTMJEFTIBSFOFUTTVTFSGFFHBOBMZTJTOPOMJOFBS ΫϦοΫͰඈ΂·͢
ώτͷঢ়ଶਪఆΛ͢ΔͨΊʹ೴೾ͷ࣌ܥྻσʔλΛ೗ԿʹϞσϦϯά͢Δ͔ʁ

脳波モデルを用いたReal-time集中状態判別器の実演と現状の稼働アルゴリズムの紹介

脳波モデルを用いたReal-time集中状態判別器の実演と現状の稼働アルゴリズムの紹介

More Decks by kenyu

Other Decks in Education

Featured

Transcript