St u dy on Developm en t of Tr a ck Condit ion Mon it or in g Syst em Usin g In -ser vice Ra ilwa y Veh icles

営業列車を活用した

軌道状態監視システムの構築に関する研究

森 裕 貴

1 1

1.1 . . . 1

1.1.1 . . . 1

1.1.2 . . . 3

1.1.3 . . . 5

1.2 . . . 7

1.2.1 . . . 7

1.2.2 . . . 8

1.2.3 . . . 10

1.2.4 . . . 13

1.2.5 . . . 16

1.2.6 . . . 17

1.3 . . . 21

1.3.1 . . . 21

1.3.2 . . . 22

1.4 . . . 25

1.4.1 . . . 25

1.4.2 . . . 26

1.5 . . . 28

1.6 . . . 30

1.7 . . . 32

2 34 2.1 . . . 34

2.2 . . . 35

2.2.1 RMS . . . 35

2.2.2 . . . 36

2.3.1 . . . 38

2.3.2 . . . 38

2.4 . . . 42

2.4.1 . . . 42

2.4.2 . . . 42

2.4.3 . . . 43

2.5 . . . 49

2.5.1 . . . 49

2.5.2 . . . 58

2.5.3 . . . 64

2.6 . . . 70

2.6.1 RMS . . . 70

2.6.2 . . . 73

2.7 . . . 75

3 77 3.1 . . . 77

3.2 . . . 77

3.2.1 . . . 77

3.2.2 . . . 80

3.2.3 . . . 82

3.2.4 . . . 86

3.2.5 . . . 88

3.3 . . . 89

3.3.1 . . . 89

3.3.2 . . . 93

3.3.3 . . . 94

3.3.4 . . . 94

3.3.5 . . . 94

3.4 . . . 95

3.4.1 . . . 95

4 105

4.1 . . . 105

4.2 . . . 105

4.3 . . . 107

4.3.1 . . . 108

4.3.2 . . . 114

4.3.3 . . . 122

4.4 . . . 124

4.4.1 RMS . . . 125

4.4.2 . . . 134

4.5 . . . 139

4.5.1 . . . 140

4.5.2 . . . 145

4.6 . . . 149

5 151

155 160

St u dy on Developm en t of Tr a ck Condit ion Mon it or in g Syst em Usin g In -ser vice Ra ilwa y Veh icles

H ir ot a ka Mor i

Con dit ion m on it or in g of r a ilwa y t r a ck s a r e essen t ia l in en su r in g t h e sa fet y of r a ilwa ys.

In -ser vice veh icles equ ipped wit h sen sor s a n d GP S syst em s ca n a ct a s pr obes t o det ect a n d a n a lyze veh icle vibr a t ion . Th ey m a y a lso dr a m a t ica lly ch a n ge t h e cu r r en t st yle of r a il m a in t en a n ce, t h u s con t r ibu t in g t o t h e est a blish m en t of sa fer t r a n spor t syst em s. Su ch t r a in s a r e kn own a s pr obe veh icles. Th e pr obe veh icle ca n ch a n ge t h e cu r r en t m a in t en a n ce st yle t o a focu s on loca t ion s r ega r ded a s essen t ia l m a in t en a n ce a r ea s, u t ilizin g da t a a cqu ir ed by h igh fr equ en cy m on it or in g of a ct u a l vibr a t ion t oget h er wit h posit ion a l in for m a t ion obt a in ed by GP S. F or t h is pu r pose, con dit ion m on it or in g syst em of r a ilwa y t r a ck u sin g in -ser vice r a ilwa y veh icles h a s developed. Mon it or in g ba sed on in for m a t ion obt a in ed by developed syst em m a y en a ble t h e det ect ion of t r a ck fa u lt s a t a n ea r ly st a ge, t h u s con t r ibu t in g t o t h e r evit a liza t ion of loca l r a ilwa ys by m a kin g m a in t en a n ce t a sk s m or e efficien t .

In t h is pa per, t h e developm en t of t r a ck con dit ion m on it or in g syst em u sin g in -ser vice r a ilwa y veh icles fr om ca r -body vibr a t ion is descr ibed. Th is pa per a lso in t r odu ces ou r lon g t er m exper ien ce in J a pa n ese r a ilwa y t r a ck con dit ion m on it or in g u sin g in -ser vice r a ilwa y veh icles.

Ch a pt er 1 descr ibes pr oblem s of t r a ck m a in t en a n ce a n d t h e ba ckgr ou n d of t h e con dit ion m on it or in g of r a ilwa y t r a cks.

Ch a pt er 2 descr ibes det ect ion m et h ods of t r a ck fa u lt s fr om ca r-body a cceler a t ion u sin g r oot m ea n squ a r e (RMS) va lu e a n d wa velet t r a n sfor m . It is sh own t h a t t h e RMS va lu e of t h e ca r-body a cceler a t ion a n d r oll r a t e a r e u sefu l for t h e det ect ion of t r a ck fa u lt s. Th e wa velet t r a n sfor m t h a t ch a n ges t im e-fr equ en cy win dow size a u t om a t ica lly is em ployed for obt a in in g det a il in for m a t ion of t h e t r a ck fa u lt s. An in ver se a n a lysis is a lso pr oposed t o est im a t e t r a ck ir r egu la r it y fr om ca r-body a cceler a t ion .

1

1.1

1.1.1

[1]

1.1.1 [2] 1993

227 2002

2014 236

1.1.1: [2]

2011 3 11

10

BRT bus rapid transit

.

1.1.2

,

.

2014 CO₂

1.1.2[3]

CO2

1.1.2: [3]

1.1.3

1.1.3 [4]

1.1.4 26

97.4

10 10

15 .

.

. .

1.1.3: [4]

1.2

1.2.1

1.2.2

1.2.1

[5]

1.2.1:

[6]

9

1.2.3

[7]

1. Longitudinal level irregularity 10m

2. Alignment irregularity 10m

1500mm

4. Gauge irregularity

5. Twist irregularity

2.5m 5.0m

[7]

1.2.2:

1.2.3:

1.2.4:

1.2.5:

1.2.4

5

10m

10m [7]

3 [8]

2 1.13

3

10m [9, 10, 11]

1.14 270km/h

East.i 1.15 275km/h

[12]

5m 5m

1.2.7: 10m

2.5m 17.5m

1.2.8:

1.2.9:

1.2.10: East.i

1.2.5

. .

.

20 30km/h

.

1.2.6

JR

[13]

1.2 24

1.18 4

2 2 3

1.2.1:

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

኱㒔ᕷ㧗㏿㕲㐨ィ ࠺ࡕᆅୗ㕲 ㊰㠃㟁㌴ィ ᆅ᪉᪑ᐈ㕲㐨ィ

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୍⯡⟶⌮㈝

ཌ⏕⚟฼᪋タ㈝

᱌ෆᐉఏ㈝

㍺㏦⟶⌮㈝

ಖᏲ⟶⌮㈝

㐠㍺㈝

㐠㌿㈝

㌴୧ಖᏑ㈝

㟁㊰ಖᏑ㈝

⥺㊰ಖᏑ㈝

ᖹᡂ䠎䠐ᖺᗘ㕲㐨⤫ィᖺሗ

ฟᒎ䠖ᖹᡂ24ᖺᗘ㕲㐨⤫ィᖺሗ

1.2.11:

᪋タಖ᭷࡟

ಀࡿ⤒㈝

㍺㏦࡟┤᥋ ᚲせ࡞⤒㈝

ࡑࡢ௚⤒㈝

ᖹᡂ䠎䠐ᖺᗘ㕲㐨⤫ィᖺሗ

ฟᒎ䠖ᖹᡂ24ᖺᗘ㕲㐨⤫ィᖺሗ

᪋タಖ᭷䛻ಀ䜛⤒㈝

䠄⥺㊰ಖᏑ㈝䠈㟁㊰ಖᏑ㈝䠈

㌴୧ಖᏑ㈝䠈ಖᏲ⟶⌮㈝䠈ῶ౯ൾ༷㈝䠅

㍺㏦䛻┤᥋ᚲせ䛺⤒㈝

䠄㐠㌿㈝䠈㐠㍺㈝䠈㍺㏦⟶⌮㈝䠅 䛭䛾௚䛾⤒㈝

䠄᱌ෆᐉఏ㈝䠈ཌ⏕⚟฼ཌ⏕㈝䠈

୍⯡⟶⌮㈝䠈ㅖ⛯䠅

1.2.12:

.

70 7

[14]

1.19 45

[15]

.

7 9

.

1.3

1.3.1

Schenkendorf [25]

PHM Population Health Management

1.3.1

1.3.1:

1.3.2

[17, 18]

Waston [19, 20, 21]

[22, 23] .

.

1.2.6

1.3.2

•

•

1.3.2:

1.4

1.4.1

[26]

Probe

ABS GPS

•

•

•

• ABS

GPS

1.4.2

GPS

1.4.1 [27, 29]

[28] [30]

.

- 2

1.4.1:

1.5

.

.

.

.

1.6

1.6.1

.

1.6.1:

1.7

5 1.7.1

. 1

. 2

. (RMS Root Mean

Square

. .

3

4 2 3

5

1.7.1:

2

2.1

2.2

RMS

2.2.1

2.2.1:

2.2.1 RMS

p-p peak to peak 3.5m/s² p-p 2.5m/s²

p-p RMS

p-p

RMS RMS

p-p RMS

2.2.2

RMS [33]

2 [33]

2.2.3

RMS

mm mm

[34]

2.3 RMS

2.3.1

RMS

x(τ) RMS 2.3.1

RM S(t) =

!"

"

# 1 N

t+N$−1 τ=1

x(τ)² (2.3.1)

RMS

t 0.0012s RMS

N = 26 0.0318s N

2.3.2

2.3.1

50km/h 300m Table.2.3.1

m_t

m_t I_t θ_t2 Z_t2 I_t θ_t1

k_p c_p k_p c_p k_p c_p k_p c_p

k_s c_s k_s c_s

m_b

2l_b

I_b θ_b Z_b

2l_t

Z_t1 ν

2.3.1: 6

2.3.1: 6

Symbol Description Unit Value

m_b Car-body mass kg 14600

mt Truck mass kg 2400

Ib Car-body inertia kgm² 500452

It Truck pitch inertia kgm² 2773.5

2lb Car-body base m 14.1

2lt Wheel base m 2.15

kp Primary suspension vertical stiffness kN/m 1090 ks Secondary suspension vertical stiffness kN/m 329 cp Primary suspension vertical damping kNs/m 19.6 cs Secondary suspension vertical damping kNs/m 27.2

v Vehicle speed km/h 50

2.3.2

[35] A₁ = 3 10⁻⁵ ₁ = 6.7 V = 13.9m/s

1 2.3.2

40m 60m

2 145m 155m 10m

1mm 175Hz

0.08m 250m 2mm

2.3.3

G(s) = 2π√ A1V s+ 1

(2.3.2)

0 50 100 150 200 250 300

-40 -20 0 20 40

Track irregularity [mm]

Distance [m]

irregularity 2.3.2:

Track irregularity [mm]

Distance [m]

0 50 100 150 200 250 300

-40 -20 0 20 40

Track irregularity Corrugation Step

2.3.3:

2.3.1 820[Hz]

2.3.4 1×10⁻³m/s²

0 50 100 150 200 250 300

-3 0 3

Car-body vertical acceleration [m/s2]

Distance [m]

2.3.4:

RMS

2.3.5 2.3.1

RMS 2.3.5 50m

50m RMS

2.3.5: RMS

2.4

2.4.1

x(t) ψ(t)

2.4.1

(Wψx)(a, b) =

% _∞

−∞

√1 aψ

&

t−b a

'

x(t)dt (2.4.1)

a b

ψ(x) b

1/a (Wψf)(b, a) b

1/a

2.4.2

2.4.1 a b 2.4.2

Dm,n =

% _∞

−∞

x(t)ψm,n(t)dt (2.4.2)

ψm,n(t) = 2^−m/2ψ(2^−mt−n) (2.4.3)

x(t) =

$∞ n=−∞

Am0,nφm0,n(t) +

m0

$

m=−∞

$∞ n=−∞

Dm,nψm,n(t) (2.4.4) φm,n(t)

φ_m,n(t) = 2^−m/2φ(2^−mt−n) (2.4.5)

Am,n =

% _∞

−∞

x(t)φm,n(t)dt (2.4.6)

m dm(t) =

$∞ n=−∞

Dm,nψm,n(t) (2.4.7)

x(t)

x(t) = x_m0(t) +

m0

$

m=−∞

d_m(t) (2.4.8)

2.4.3

RMS

2.3.1 2.3.2

2.3.4

2.4.1

0.08m 50km/h 174Hz

2.4.1(b) 250m

2.4.1(c)

1Hz [36] 50m

Distance [m]

333.1 256.3 208.2 175.3 151.4

Frequency[Hz]

0 50 100 150 200 250 300

0.1

0 0.05

Distance [m]

44.42 0.3

Frequency[Hz] (a)Signal plane(333-151[Hz])

44.42 33.31 26.65 22.21 19.04

0.3

0 0.15

0 50 100 150 200 250 300

Distance [m]

Frequency[Hz]

3.331 24

Frequency[Hz] (b)Signal plane(44.4-19[Hz])

3.331 2.082 1.514 1.19 0.98

0 50 100 150 200 250 300

Distance [m]

24

0 12

Frequency[Hz]

(c)Signal plane(3.33-0.98[Hz]) 2.4.1:

2.4.2

Daubechies 8

[37] m0 = 6

2.4.2

d1 d2 d3

d4 a6

2.4.3 2.4.3(a) 150m

d3 d4 2.4.3(b)

250m

d3 2.4.3(c) 50m

2 2.4.3(a)(b)

RMS

-0.05 0 0.05 d2:(205- 103Hz)

0 50 100 150 200 250 300

-0.05 0 0.05 d3:(103- 51.3Hz)

0 50 100 150 200 250 300

-0.2 0 0.2 d5:(25.6- 12.8Hz)

0 50 100 150 200 250 300

-1 0 1 d6:(12.8- 6.41Hz)

0 50 100 150 200 250 300

Distance [m]

Distance [m]

Distance [m]

Distance [m]

-0.1 0 0.1 d4:(51.3- 25.6Hz)

0 50 100 150 200 250 300

Distance [m]

-2 0 2 a6: (6.41Hz-)

0 50 100 150 200 250 300

Distance [m]

-0.02 0 0.02 d1: (410- 205Hz)

0 50 100 150 200 250 300

Distance [m]

Car-body vertical acceleration [m/s2]

0 2

-20 50 100 150 200 250 300

Distance [m]

ᡂᙧ䝣䜱 䝹䝍౑⏝

෌ᵓᡂᡂศ Ἴ≧ᦶ⪖䢪䣦䢳䢭䣦䢴凛

෌ᵓᡂᡂศ ẁᕪ䢪䣦䢵䢭䣦䢶凛

෌ᵓᡂᡂศ 㧗ప≬傪䢪䣣䢸凛

෌ᵓᡂᡂศ 㧗ప≬傪䢪䣣䢸䢭䣦䢸凛

෌ᵓᡂᡂศ 㧗ప≬傪䢪䣆䢸䢭䣣䢸䢭䣆䢷䢫෌ᵓᡂᡂศ Ἴ≧ᦶ⪖䢪䣆䢳䢭䣆䢴凛

෌ᵓᡂᡂศ ẁᕪ

䢪䣆䢵䢭䣆䢶䢫

2.4.2:

(a)Reconstructed signal (d1+d2: 410Hz - 103Hz)

(b)Reconstructed signal(d3+d4: 51.3Hz - 25.6Hz)

(c)Reconstructed signal((a6: 6.4Hz - ) 2.4.3:

2.5

2.5.1

2.5.1 1

2 2

6 1 Zc Zt1

Zt2 θc θt1

θt2 r1a r1b r2a r2b

2.5.1: 6

Z¨c

Z¨_t1 Z¨t2

Z˙c

Z˙_t1 Z˙t2

Zc

Z_t1 Zt2

θ¨c

θ¨_t1 θ¨t2

θ˙c

θ˙_t1 θ˙t2

θc

θ_t1 θt2

r1a 1

r1b 2

r2a 3

r2b 4

Ic

It

mc

mt

lc

lt

ks

c

Z¨c = _m¹_c(

csZ˙t1+csZ˙t2−2csZ˙c+ksZt1+ksZt2−2ksZc

)

(2.5.1)

θ¨c = 1 I_c

(−cslcZ˙t1+cslcZ˙t2−2csl²_cθ˙c −kslcZt1 +kslcZt2−2ksl²_cθc

)

(2.5.2)

Z¨t1 = _m¹_t{(−cs−2cp) ˙Zt1+csZ˙c+cslcθ˙c+ (−ks−2kp)Zt1

+ksZc +kslcθc+cpr˙1a+cpr˙1b+kpr1a+kpr1b (2.5.3)

θ¨_t1 = 1 It

(−c_pl_tr˙_1a+c_pl_tr˙_1b−2c_pl²_tθ˙_t1−k_pl_tr_1a+k_pl_tr_1b−2k_pl²_tθ_t1) (2.5.4)

Z¨t2 = 1

mt{(−cs−2cp) ˙Zt2+csZ˙c −cslcθ˙c + (−ks−2kp)Zt2

+ksZc−kslcθc +cpr˙2a+cpr˙2b+kpr2a+kpr2b (2.5.5)

θ¨t2 = 1 It

(−cpltr˙2a+cpltr˙2b−2cpl²_tθ˙t2−kpltr2a+kpltr2b−2kpl²_tθt2

)

(2.5.6)

(2.5.1)∼ (2.5.6) MCK (2.5.7)

MZ(t) +¨ CZ(t) +˙ KZ(t) =Dr˙(t) +Er(t) (2.5.7)

M C K Z¨ Z˙

Z r r˙

M = diag*

m_c I_c/l²_c m_t I_t/l_t² m_t I_t/l_t²+

(2.5.8)

C =

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎣

2cs 0 −cs 0 −cs 0

0 2cs −cs 0 cs 0

−cs −cs 2cp+cs 0 0 0

0 0 0 2cp 0 0

−cs cs 0 0 2cp+cs 0

0 0 0 0 0 2cp

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎦

(2.5.9)

K =

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎣

2ks 0 −ks 0 −ks 0

0 2k_s −k_s 0 k_s 0

−ks −ks 2kp +ks 0 0 0

0 0 0 2kp 0 0

−k_s k_s 0 0 2k_p+k_s 0

0 0 0 0 0 2kp

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎦

(2.5.10)

D =

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎣

0 0 0 0

0 0 0 0

cp cp 0 0

c_p −c_p 0 0 0 0 cp cp

0 0 cp −cp

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎦

(2.5.11)

E =

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎢

0 0 0 0

0 0 0 0

k_p k_p 0 0

kp −kp 0 0

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎥

(2.5.12)

1

MCK 2

Newmark β [38][39] Newmark β

2 Newmark β

2.5.2 y h

k+ 1

MZ¨k+1+CZ˙k+1+KZk+1 =Dr˙k+1+Erk+1 (2.5.13)

2.5.2 tk tk+1

2.5.3(a) τ Z¨τ

Z¨τ =Z¨k+τ h

4Z¨k+1−Z¨k

5 (2.5.14)

Z˙τ Zτ τ Z˙_τ =Z˙_k+Z¨_kτ + 1

2h

4Z¨_k+1−Z¨_k5

τ² (2.5.15)

Zτ =Zk+Z˙kτ +1

2Z¨kτ²+ 1 6h

4Z¨k+1−Z¨k

5

τ³ (2.5.16) τ = h Z¨τ = Z¨k+1 Z˙τ = Z˙k+1 Zτ = Zk+1

Z˙k+1 =Z˙k+1 2h4

Z¨k+Z¨k+1

5

(2.5.17)

˙ 1 ₂¨ 1 ₂¨

Newmark β β

t_k+1 Z˙_k+1 Z_k+1

Z˙k+1 = Z˙k+ 1 2h4

Z¨k+Z¨k+1

5

Zk+1 =Zk+hZ˙k+

&

1 2 −β

'

h²Z¨k+βh²Z¨k+1 (2.5.19)

(2.5.17) (2.5.19) (2.5.13) Z¨_k+1

Z¨k+1=

&

M +1

2hC+βh²K '₋1

6

Dr˙_k+1+Er_k+1−C

&

Z˙_k+1 2hZ¨_k

'

−K 7

Zk+hZ˙k+

&

1 2 −β

' h²Z¨k

89

(2.5.20)

(2.5.20) tk

tk+1

(2.5.7) Newmark β γ = 1/2 β = 1/6 h

xk = F xk−1 + Guk−1+wk−1 (2.5.21)

yk = Hxk + vk (2.5.22)

xk uk yk

wk vk F

A =

⎡

⎢⎣

I O −βh²I O I −0.5hI K C M

⎤

⎥⎦ (2.5.23)

B =

⎡

⎢⎣

I h (0.5−β)h²I

O I 0.5hI

O O O

⎤

⎥⎦ (2.5.24)

C =

⎡

⎢⎣

O O O O E D

⎤

⎥⎦ (2.5.25)

t

t

y

k 1

y

State

Time

h

2.5.2:

tk t_k1

Zk

k1

Z

h W

Acceleration

Time

(a) Acceleration

tk t_k1

Zk

k1

Z

h W

Velocity

Time

(b) Velocity

tk t_k1

Zk

k1

Z

Time

h W

Displacement

(c) Displacement

2.5.3: Newmark β β = 1/6

2.5.2

2.5.21 F G 2.5.22

H

⎡

⎢⎢

⎢⎢

⎢⎢

⎣ xk

x_k−1 ... ...

xk−L+1

⎤

⎥⎥

⎥⎥

⎥⎥

⎦ : ;< =

xk

=

⎡

⎢⎢

⎢⎢

⎢⎢

⎢⎣

0 · · · 0 1 . .. ... ... ...

0 . .. ... ... ...

... . .. ... ... ...

0 · · · 0 1 0

⎤

⎥⎥

⎥⎥

⎥⎥

⎥⎦

: ;< =

F

⎡

⎢⎢

⎢⎢

⎢⎢

⎣ xk−1

x_k−2 ... ...

xk−L

⎤

⎥⎥

⎥⎥

⎥⎥

⎦ : ;< =

xk−1

+

⎡

⎢⎢

⎢⎢

⎢⎢

⎣ 1 0 ... ... 0

⎤

⎥⎥

⎥⎥

⎥⎥

⎦ : ;< =

G

(uk−1+wk−1) : ;< =

uk−1

(2.5.26)

⎡

⎢⎢

⎢⎢

⎢⎢

⎣ yk

yk−1

...

... y_k−L+1

⎤

⎥⎥

⎥⎥

⎥⎥

⎦ : ;< =

y_k

=2

h(0) h(1) · · · h(L) 3

: ;< =

H

⎡

⎢⎢

⎢⎢

⎢⎢

⎣ xk

xk−1

...

... x_k−L+1

⎤

⎥⎥

⎥⎥

⎥⎥

⎦ : ;< =

x_k

+v_k (2.5.27)

xk yk vk

uk

(2.5.26)

uk wk

(2.5.27)

2.5.4 [40]

2.5.4:

FIR Finite Impulse Response

g(τ) (2.5.27)

[41] g(τ)

x(t)

x(t) y(t)

y(t) =

% t 0

g(τ)x(t−τ)dτ (2.5.28)

= g(t)∗x(t) (2.5.29)

(2.5.29) (2.5.28) 2.5.5

60km/h 2.5.6

[42]

2.5.5:

2.5.6: (60km/h)

xk|k−1 =F xk−1|k−1 + Gu_k−1 (2.5.30)

P_k|k−1 =F P_k−1|k−1F^T +GQG^T (2.5.31)

Kk =Pk|k−1H^T *

HPk|k−1H^T +R+−1

(2.5.32)

xk|k = xk|k−1+Kk

*yk−Hxˆk|k−1

+ (2.5.33)

Q R

xk

10m

[43][44] 10m

a(x) =b(x)− b(x+ 5 ) +b(x−5 )

2 (2.5.35)

a(x) 10m b(x)

2.5.3

2.5.7

(I) 2

(II) 6.00m

(III) (II) (I)

(IV) (III)

(II)

(V) (II) (IV) 10m

2.5.7:

2.5.8 2.5.9

6.00m 1

2.5.8:

2.5.9:

2.5.10

2.5.10:

2.5.1:

Symbol Description Unit Value

mc Car-body mass kg 25000

m_t Truck mass kg 3100

Ic Car-body pitch inertia kgm² 856940

I_t Truck pitch inertia kgm² 3417.8

2lc Car-body base m 14.1

2lt Wheel base m 2.1

kp Primary suspension vertical stiffness kN/m 2120 ks Secondary suspension vertical stiffness kN/m 400 cp Primary suspension vertical damping kNs/m 39.2 cs Secondary suspension vertical damping kNs/m 96

2.5.11 w_n

vn σ_w² = 1.00×10⁻¹m² σ_v² = 5.00×10⁻³(m/s²)² 2.5.11

10m 2.00mm

2.5.11:

2.6

GUI(Graphical User Interface) GUI MATLAB(MathWorks)

RMS RMS

2.6.1 RMS

2.6.1

(2.3.1) RMS

2.6.1 RMS

2.6.2 RMS

RMS

㽢㽢 㽢 㽢

䕿

䕿

䕿

㊥㞳

㉮⾜᪥᫬

2.6.1:

㽢

㽢 㽢 㽢

䕿

䕿

㊥㞳

2.6.2: RMS

2.6.3

2.0m/s² RMS

RMS

5260m 2.6.3

RMS

2012 9 2013 2 RMS

2.6.2 2.6.3)

㽢 + + 㽢 㽢 㽢

+ +

䕿

䕿

䕿

㊥㞳 [m]

20120921 20130201 20130531

㉮⾜᪥᫬

2.6.3: RMS

2.6.2

2.6.4 RMS

2.6.4:

2.6.5

m0

2.6.5:

2.7

(1)RMS Root Mean Square (2)

(3)

(1) RMS

RMS

(2) (1)

RMS

(3)

10m 2mm

Graphical User Interface RMS

3

3.1

.

3.2

[45, 46, 47]

[48] .

. .

.

3.2.1

3.2.1

GPS ,

GPS GPS

GPS

.

3.2.1:

3.2.2

[49]

. GPS GPS

GPS

3.2 GPS

GPS 1 v(t)

t=t_G GPS x_G

t=τ x(τ)

x(τ) =xG+

% τ tG

v(t)dt (t ≤τ) (3.2.1)

v(t) GPS

1

a(t) GPS 2

t =t GPS v

3.2.2:

3.2.3

3.2.3 3.2.4 GPS 3.2.5

3.2.3:

3.2.5:

RMS 3.2.6 RMS GPS

RMS .

RMS ( 3.2.6 )

3.2.7 3.2.8

RMS

. RMS

.

3.2.6: RMS

3.2.7:

3.2.8:

3.2.4

.

(1)

(2)

(3)

(4)

2.5V

.

(1)

.

. (3)

.

.

3.2.5

(1)

(2)

(3)

(4) .

(1)

. (3)

.

3.3

3.3.1

3.3.1:

3.3.2:

CPU

3.3.3:

3.3.2

MEMS Micro Electro Mechanical Systems

3.3.1 6

GPS

I/F

3.3.2 GPS

3.3.1: ADIS16362

ACCELEROMETERS GYROSCOPES

Dynamic Range 1.7 G 75

Offset error 0.003 G 0.114

Gain error model 0.009 G 0.375

Sampling frequency 0.4Hz 820Hz 0.4Hz 820Hz

3.3.2: GPS FV25RS

GPS receiver Receiving sensitivity -149dBm

Sampling frequency 4Hz 1Hz

3.3.3

DC12V

6 AC 100V 200V

.

3.3.4

SSD

microSD .

microSD

3.3.5

LED

GPS

LED 3.3.4

3.3.4: LED

3.4

3.4.1

1 8MB

1 200GB

3.4.2

( )

820Hz 82Hz

3.5

3.5.1

3.5.1 3.5.2

3.5.3 .

40 A4

.

180mm 72mm

.

3.5.4 6

. 3.5.5

. microSD

.

3.5.1:

3.5.2:

3.5.3:

3.5.4:

3.5.5:

3.5.2

3.5.6

3.5.6:

3.5.7:

y

z 50mm 0.7Hz

3.5.8 3.5.9

0.7Hz

3.5.8:

3.5.9:

3.6

(1)

(2)

(3) microSD

4

4.1

2 3

4.2

3

2

4.2.1

4.2.1:

4.3

2015 2 21 3

24 1

4.3.1 8

.

4.3.1:

4.3.1

2 22 3 8 3 21 4.3.2

RMS 4.3.3

RMS RMS

RMS

RMS

RMS

4070m 4220m

4.3.2:

4.3.3: RMS

2 22 3

8 3 21 4.3.4 RMS

4.3.5 RMS

RMS

RMS 9300m

9600m 9700m

50m

RMS 3

9330m

4.3.4:

4.3.5: RMS

4.3.2

RMS RMS

4

4.3.6 A O

4.3.6

4.3.7 2 22

3 8 3 21 RMS

4.3.8

4.3.8 RMS 1.0m/s²

C-D G-H N-O

3

䠉2015/02/22 3down 䠉2015/02/22 5down 䠉2015/02/22 7down 䠉2015/02/22 8down

A B C D E F G H I J K L M N O

0 1 2 3 4 5 6 7 8 9 10

2 1 0 -1 Car-body vertical 2acceleration [m/s] -2

Distance [km]

䠉 䠉 䠉

䠉2015/02/22 3down 䠉2015/03/08 2down 䠉2015/03/21 4down

body vertical acceleration [m/s] 4.3.6: A-O

䠉 䠉 䠉 䠉

䠉 䠉 䠉

body ]

A B C D E F G H I J K L M N O

䠉2015/02/22 3down 䠉2015/03/08 2down 䠉2015/03/21 4down

0 1 2 3 4 5 6 7 8 9 10

2 1 0 -1 Car-body vertical 2acceleration [m/s] -2

Distance [km]

4.3.7: A-O

4.3.8: RMS A-O

C-D G-H N-O RMS

4.3.9 4.3.10 4.3.11

C-D 4.3.9 (b) RMS C-D

1.7km D

150m 4.3.9 (c)

.

. 4.3.8

RMS

4.3.10 RMS G-H

4.4km 4.3.10 (c)

H 200m

.

.

N-O

RMS 4.3.11 (b) RMS 9.4km

9.5km 2 4.3.10 (c)

C-D .

RMS

GPS RMS

RMS .

䠉2015/02/22 3down 䠉2015/03/08 2down 䠉2015/03/21 4down

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

2 0

Car-body vertical 2acceleration [m/s] -2

Distance [km]

D C

䠉 䠉 䠉

body [m/s]

(a)Car-body vertical acceleration

(b)RMS of car-body vertical acceleration

100m 50m D

150mCrossing

(c)Aerial photograph 4.3.9: C-D

䠉2015/02/22 3down 䠉2015/03/08 2down 䠉2015/03/21 4down

3.9 4 4.1 4.2 4.3 4.4 4.5 4.6

2 0

Car-body vertical 2acceleration [m/s] -2

Distance [km]

H G

䠉 䠉 䠉

body [m/s]

(a)Car-body vertical acceleration

(b)RMS of car-body vertical acceleration

100m H 200m

(c)Aerial photograph 4.3.10: G-H

䠉2015/02/22 3down 䠉2015/03/08 2down 䠉2015/03/21 4down

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

2 0

Car-body vertical 2acceleration [m/s] -2

Distance [km]

O N

䠉 䠉 䠉

body ]

(a)Car-body vertical acceleration

(b)RMS of car-body vertical acceleration

N 100m 200m 300m

(c)Aerial photograph 4.3.11: N-O

4.3.12

m₀ = 6 9.4km 9.5km 9.4km

d2 d3 9.5km d1, d2, d3, d4

d2 d3

1Hz 9.4km

9.5km d1

2 .

9.4km 4.3.11 (c)

.

9.4km RMS

9.5km RMS

. d1

.

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 -2

0 2

Vertical car body acceleration [m/s2]

Distance [km]

-0.2 0 0.2 d1: (10.3-5.13 Hz)

Distance [km]

-0.5 0 0.5 d2: (5.13-2.56 Hz)

Distance [km]

d3: (2.56-1.28 Hz) -2

0 2

Distance [km]

d4: (1.28-0.640 Hz) -0.5

0 0.5

Distance [km]

d5: (0.640-0.320 Hz) -0.2

0 0.2

Distance [km]

a5: (0.320 Hz-) -0.1

0 0.1

Distance [km]

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

䠉2015/02/22 3down

4.3.12: N-O

4.3.3

C-D G-H N-O

1 RMS 4.3.13

. . RMS

1.3m/s² .

.

0 0.5 1 1.5

2/21 2/23 2/25 2/27 3/1 3/3 3/5 3/7 3/9 3/11 3/13 3/15 3/17 3/19 3/21 3/23 3/25 3/27 Average of max RMS for a day [m/s2]

Date

for a day [m/s] (a)C-D section

0 0.5 1 1.5

2/21 2/23 2/25 2/27 3/1 3/3 3/5 3/7 3/9 3/11 3/13 3/15 3/17 3/19 3/21 3/23 3/25 3/27 Average of max RMS for a day [m/s2]

Date

max for a day [m/s] (b)G-H section

0 0.5 1 1.5

2/21 2/23 2/25 2/27 3/1 3/3 3/5 3/7 3/9 3/11 3/13 3/15 3/17 3/19 3/21 3/23 3/25 3/27 Average of max RMS for a day [m/s2]

Date

(c)N-O section

4.3.13: G-H RMS

4.4

. 2015

2015 5 6 .

5 .

4.4.1 .

86.3

97.3 .

.

4.4.1:

4.4.1 RMS

2015 5 12 5

RMS .

4.4.2 .

4.4.3 A-Q .

.

RMS .

.

. .

2.0m/s² RMS

D-E L-M .

2015 12 27 2.0m/s² RMS

G-H

.

4.4.2:

㉥‮ ༡㝧 ᕷᙺ ᡤ ᐑ

ෆ 厬叫 叐叀 ᲍

㒓 す኱ ሯ ௒

Ἠ ᫬

ᗞ ༡㛗

஭㛗

஭ 厤句 叢බ ᅬ

⩚๓ ᡂ⏣ ⓑ

ඡ ⺋

᱓ 㩗

㈅ ᅄᏘ 叏㒓 Ⲩ

◒

Velocity km/h]

0 20 40 60 80

0 5 10 15 20 25 30

Distance [km]

AB C D E F G H I JK L M N OP Q

䠉2015/05/08 䠉2015/06/19 䠉2015/07/30 䠉2015/11/06 䠉2015/12/27

䠉 䠉 䠉 䠉 䠉

body vertical [m/s] ^{䠉 䠉 䠉 䠉 䠉}(a)Traveling speed

㉥‮ ༡㝧 ᕷᙺ ᡤ ᐑ

ෆ 厬叫 叐叀 ᲍

㒓 す኱ ሯ ௒

Ἠ ᫬

ᗞ ༡㛗

஭㛗

஭ 厤句 叢බ ᅬ

⩚๓ ᡂ⏣ ⓑ

ඡ ⺋

᱓ 㩗

㈅ ᅄᏘ 叏㒓 Ⲩ

◒

䠉 䠉 䠉 䠉 䠉

RMS of vertical

䠉 䠉 䠉 䠉 䠉

Car-body vertical acceleration [m/s2]

-4 -2 0 2 4

0 5 10 15 20 25 30

Distance [km]

AB C D E F G H I JK L M N OP Q

䠉2015/05/08 䠉2015/06/19 䠉2015/07/30 䠉2015/11/06 䠉2015/12/27

(b)Car-body acceleration

(c)RMS Car-body acceleration 4.4.3:

D-E 2015 5 8 6 19 4.4.4

.4500 6000 RMS

1 RMS

. 4530 4650 6030

5

. RMS

RMS

.

RMS 2.0m/s²

RMS 1.6m/s² 1.8m/s² p-p 3.5 m/s² 4.0m/s²

1.5m/s² .

5500 2.5m/s² RMS

6 19 7 30 4.4.5 . 6

RMS 5500

5550 5580 7 30

RMS 1.0m/s² 4.4.5 4500

RMS 2.0m/s² RMS

.

RMS .

. .

RMS

.

4.4.4: 2015 5 D-E

4.4.5: 2015 6 D-E

L-M 5

4.4.6 . 21300 21700 22000

22100 23110 5

RMS .

22600 22700 2.3m/s² RMS

.L-M

RMS .

.

2.0m/s² RMS

G-H 4.4.7 .

. 14220

14550 RMS

.

4.4.6: 2015 5 L-M

ὀ┠༊㛫䛤䛸䛻デ᩿䠄௒Ἠ䞊᫬ᗞ䠅

Velocity km/h]

0 20 40 60 80

12.5 13 13.5 14 14.5

Distance [km]

䠉2015/05/08 䠉2015/06/19 䠉2015/07/30 䠉2015/11/06 䠉2015/12/27 H G

䠉 䠉 䠉 䠉 䠉

body vertical acceleration [m/s2] 䠉2015/05/08 䠉2015/06/19 䠉2015/07/30 䠉2015/11/06 䠉2015/12/27

(a)Traveling speed

ὀ┠༊㛫䛤䛸䛻デ᩿䠄௒Ἠ䞊᫬ᗞ䠅

Distance [km]

䠉 䠉 䠉 䠉 䠉

RMS of vertical

䠉 䠉 䠉 䠉 䠉

Car-body vertical acceleration [m/s2]

-4 -2 0 2 4

12.5 13 13.5 14 14.5

Distance [km]

䠉2015/05/08 䠉2015/06/19 䠉2015/07/30 䠉2015/11/06 䠉2015/12/27 H G

(b)Car-body acceleration

(c)RMS of car-body acceleration

4.4.7: G-H

4.4.2

2 .

1.

2.

10m

6m

3. 2. 1.

4. 1. 3.

5. 3. 4.

4.4.8 4.4.1

4.4.1:

Symbol Description Unit Value

mc Car-body mass kg 24900

mt Truck mass kg 2800

Ic Car-body pitch inertia kgm² 567520

It Truck pitch inertia kgm² 2268

2lc Car-body base m 13.0

2lt Wheel base m 1.8

kp Primary suspension vertical stiffness kN/m 16960 ks Secondary suspension vertical stiffness kN/m 600 cp Primary suspension vertical damping kNs/m 39.2 cs Secondary suspension vertical damping kNs/m 12

4.4.9 4.4.10 500m

4.4.11

4.4.11(a) 4.4.11(b)

10m

w_n v_n σ_w² = 1.00× 10⁻¹m²

σ²_v = 5.00×10⁻³(m/s²)²

JR 4 1

22mm[50]

4.4.10

4.4.9:

4.4.10:

(a) Estimated track irregularity

(b) Measured track irregularity 4.4.11:

4.5

.

.

4.5.1:

4.5.1

4.5.1 .

2013 2 1 4.5.2

. 2.0m/s² RMS

RMS . RMS 2.0m/s²

4.5.3 4.5.6 . 4.5.3

. 4.5.4

4.5.5

.

.

4.5.3:

4.5.4:

4.5.5:

4.5.6:

4.5.7 .

[51].

RMS

. 4.5.2 ,

4.5.8 .

4.0km RMS 2.0m/s²

RMS .

RMS

.

.

RMS .

4.5.7:

4.5.8: RMS

4.5.2

4.4 .

4.5.9 .

2 .

RMS RMS

1100 1200 1100

1200

RMS .

1100 1200

( ) .

4.5.10 . .

. [52, 53, 54].

.

.

4.5.9:

4.5.10:

4.5.11:

4.6

2 3 GPS

1. 3 2

2. RMS

3.

4.

mm

2

4.6.1 4.6.1

4.6.1:

5

3

2

RMS Root Mean Square

(1) RMS

RMS

(2)

RMS

(3)

10m 2mm

Graphical User Interface RMS

3

(1) (2)

(3) microSD

(1)

(2) RMS

RMS RMS

(3)

(4)

(1)

3

(2)

GPS

GPS

(3)

[1] (1997)

[2] http://www.mlit.go.jp/k-

toukei/tetsuyu/tetsuyu.html [3]

http://www.mlit.go.jp/sogoseisaku/environment/index.html

[4] http://www.mlit.go.jp/statistics/file000004.html

[5] RRR Vol 68 No 4 pp 18-21

(2011)

[6] RRR Vol 65 No

11 pp 10-13 (2008) [7]

(1997)

[8] RRR (2011)

[9] JR EAST

Technical Review-No 2 pp 7-10 (2003) [10]

Vol.94 No.6 pp 41-45 (2012)

[11] RRR Vol.70 No.5 pp. 28-31 (2013)

[12]