K. Nakano Lab
独立成分分析法（ICA）の車両振動計測への適用
Applications for Measuring Vehicle Vibration by Independent Component Analysis
Support: IMV corp.
Fund: Grant-in-Aid for Scientific Research
English Version
自動車モデルでの実験
独立成分分析 Independent component analysis
Observed signal x(t)
x1 x2
・・・
xn
Automobile model experiment
 x1 (t ) 
 s1 (t ) 
 x (t )
 s (t ) 
 2   A 2 
  
  




 xn (t )
 sn (t )
s2
z2r
c2r
Measured
signal
k2f
x1r
c2f
z 2f
x1f
s1,s2 … sn
 s1 (t ) 
 x1 (t ) 




s
(
t
)
x
(
t
)
2
2

 W

  
  
学際情報学府，機械工学専攻




 sn (t )
 xn (t )
θ
x2
k2r
s1
x0r
x0f
k1f
k1r
Source to be
estimated
Direction
Source
(a)
0.1
Front
0
Front
4
-0.1
2
4
2
2
kurt( s)=E ( s )-3[ E ( s )]
0.1
+
4
5
6
7
8
2
0
(b)
-2
Input force (N)
Input force (A)
観測信号xから尖度(Kurtosis)を最大にするWを繰り返し
計算で求める．この時のsは推定する信号源の候補．
3
0
-0.1
2
3
0.1
4
+
5
6
7
-4
2
3
 s1 ( s)  W11 ( s)
 s ( s) 

 2 
   

 
 sn ( s )  
  x1 ( s) 
  x ( s)
 2 
  


  xn ( s ) 
 s11 (t )  W 1111 W 1211 W1113
 2   21
22
23
s
(
t
)
W
W
W
11
11
 1   11
 s 31 (t )  W 3111 W 3211 W 3311


   
 s 2 n (t ) 
 3
 
 s n (t )  
  x1 (t ) 
  x (t ) 

 1
   x1 (t ) dt 





  xn (t ) 


   xn (t ) dt 
5
6
7
8
6
7
8
Rear
4
2
8
0
(c)
-2
-4
2
力学系への応用 Applications for dynamics
4
0
3
4
5
Time (s)
Rear
-0.1
2
3
4
5
Time (s)
6
7
8
Rectangle
Estimated source
10
0
-10
2
5
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
Time (s)
6
7
8
0
-5
2
1
0
-1
-2
-3
2
10
伝達関数から線形方程式を立てる．ここでのsはラプラス演算子．
鉄道台車への入力推定
2.5Hz
sinusoidal
wave
0
-10
2
Input estimation on rail vehicle bogie
Accelerometer
Measured acceleration
実車での推定
Estimation on real vehicle
Direction of travel
Estimated source
f 10mm
f 8mm
f 12mm
Measured acceleration
Trunk
Publications
5
0
-5
28
20
0
-20
28
5
0
-5
28
20
0
-20
28
(a)
20
0
29
30
(b)
Sprung mass at right rear
31
32
-20
28
20
29
30
31
32
33
34
29
30
31
32
33
34
29
30
31
32
33
34
29
30
31
32
33
34
29
30
31
32
33
34
0
29
30
Unsprung mass at right(c)
rear
29
30
(d)
Sprung mass at front rear
31
31
32
32
Amplitude [-]
Accelerations [m/s2]
5
0
-5
28
Estimated source
-20
28
10
0
-10
28
5
0
29
30
unsprung mass at front(e)
rear
31
32
-5
28
5
0
29
30
Time [s]
31
32
-5
28
Time [s]
Bolts
中村弘毅，中野公彦，内山康宏， 柿原正治，2013，路面状態推定のための独立成分分析の応用，日本機械学会論文集(C
編)，2013年9月，79巻805号，pp．3002－3013, DOI: http://doi.org/10.1299/kikaic.79.3002
中村弘毅，中野公彦，2010，独立成分分析を用いた車両振動の解析，日本機械学会論文集(C編)，76巻765号，2010年5月，
pp．1163－1170．
H. Nakamura, K. Nakano, 2009, Estimation of gauge irregularity using independent component analysis, Proc. of International
Symposium on Speed-up, Safety and Service Technology for Railway and Maglev Systems, Niigata Japan.
Institute of Industrial Science, the University of Tokyo

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