音響信号に対する異常音検知技術と応用

https://sites.google.com/site/yumakoizumiweb/
https://www.slideshare.net/yumakoizumi75/

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complexity of the mode shapes increases with higher frequencies. The analysis of mode shapes of
all modes observed in this frequency range indicates that the deformation of the eggshell during
ARTICLE IN PRESS
Fig. 8. The lab-scale test arrangement for eggshell breakage inspection, with egg support by diabolo-shaped rollers (1),
the impacting rod (2) and the microphone (3), located at 90
from the impactor.
P. Coucke et al. / Journal of Sound and Vibration 266 (2003) 711–721720
P. Coucke, B. De Ketelaere, and J. De Baerdemaeker, ”Experimental analysis of the dynamic, mechanical
behaviour of a chicken egg,” Journal of Sound and Vibration , pp.711–721, 2003.
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Y. Koizumi, S. Saito, N. Harada, H. Uematsu, and K. Imoto, “ToyADMOS: A Dataset of Miniature-Machine Operating
Sounds for Anomalous Sound Detection,” in Proc. of WASPA, 2019.
GitHub: https://github.com/YumaKoizumi/ToyADMOS-dataset/

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https://github.com/YumaKoizumi/ToyADMOS-dataset/

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Figure 3: Anomaly scores of RE (green dotted), SNP (blue dashed),
and BU (red solid). Yellow areas denote anomalous areas.
Table 1: KLD between oracle PDFs and estimated PDFs.
D(pa(x)kpb(x)) denotes the KLD between pa(x) and pb(x).
Cost-function D(p(x)kq✓(x)) D(U(x)kq✓(x))
J RE
✓ 1.395 0.913
J SNP
✓ 0.222 0.333
J BU
✓ 0.403 0.083
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…
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SKlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexitlatexit sha1_base64=GzfaadDxjRPvyCYjDtW0PJ/gUUk=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/latexit
Overlooked anomaly
8 4

h g e i
CE✓k
S
=
NX
n=1
ln S(x(u)
n , mk, ✓k
S) +
MX
m=1
ln
⇣
1 S(x(a)
m , mk, ✓k
S)
⌘
latexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=8Uw8OAhobVq+70jx3VwKfg8mvYg=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/latexitlatexit sha1_base64=WRNf3Vjt8Jc0+Njj0ZYNTHsY4YQ=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/latexitlatexit sha1_base64=WRNf3Vjt8Jc0+Njj0ZYNTHsY4YQ=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/latexitlatexit sha1_base64=G1Mn+w7JJHtE1ncIFQy7+e8cpcE=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexitlatexit sha1_base64=nnlG8CCsWXafrehKba6QIaka6aw=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/latexit
g lF h g l
- i PN
h : =
a
( F 5 8
h g F
)N
- --

0
✓K
S argmin✓K
S
FPR(✓K
S , ) s.t. K-TPR(✓K
S , ) = 1
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1 , +0 6 9 A 6 8 :A9 6 6 A 6 :A:C A6
2- :E : , 11
I E I F 0

0 E 0 F
min
h
score(x(K)
m , ✓)
iM
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⇡
1
N
NX
n=1
sigmoid
h
score(x(u)
n , ✓)
i
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✓K
S argmin✓K
S
FPR(✓K
S , ) s.t. K-TPR(✓K
S , ) = 1
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S I N E
N P S S E NR
{xK
m}M
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p(x|y = K)latexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexitlatexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexitlatexit sha1_base64=RCIJYcli5PRopg4zqef5Xc9ua0Q=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/latexit
N [ N R S P KI
K-TPR(✓K
S , ) =
Z
H [score(x, ✓) ] p(x|y = K)dx
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1 , +0 7 9 A 8 :A9 A :A:C A
2- :E : , 11

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p(x|y = 0)latexit sha1_base64=LvyHXGLluvq5A0bF05TSav9VeC8=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 sha1_base64=LvyHXGLluvq5A0bF05TSav9VeC8=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
mklatexit sha1_base64=FhONU9fzMgK/Vp4v+PQrD+g8VsQ=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 sha1_base64=FhONU9fzMgK/Vp4v+PQrD+g8VsQ=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

1
Overlooked
anomaly
Normal
training data
VAE
DV
latexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=AAACj3ichVHNLkNBFP56/VX9VW0kNo2GWDWnIlEW0mDBrkWRUHLvNbjp/XPvtEk1XsALWNioxEI8gAew8QIWHkEsSWwsnN7eRBCcycx88835zsyXo7mm4Uuix4jS1t7R2RXtjvX09vUPxAcT675T8XRR1B3T8TY11RemYYuiNKQpNl1PqJZmig2tvNC836gKzzcce03WXFGy1APb2Dd0VTJV2rZUeairZn3xZGd9N56iNAWR/AkyIUghjLwTv8U29uBARwUWBGxIxiZU+Dy2kAHBZa6EOnMeIyO4FzhBjLUVzhKcoTJb5vWAT1sha/O5WdMP1Dq/YvL0WJnEGD3QNb3QPd3QE73/Wqse1Gj+pca71tIKd3fgdHj17V+VxbvE4afqD4XG2X97kthHNvBisDc3YJou9Vb96vHZy+rsylh9nC7pmf016JHu2KFdfdWvCmLlHDFuUOZ7O36C4mR6Jk2FqVRuPuxUFCMYxQS3Yxo5LCGPIj97hDNcoKEklKwyp+RaqUok1AzhSyjLH/xflOg=/latexitlatexit sha1_base64=fxoBzb4iaar9HERD/tFhQpDsnl4=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/latexit
mKlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=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/latexitlatexit sha1_base64=oBXTwvTOs4zrBcjekBN6earN7c4=AAACinichVHNLgNRGD3GfynFRmLTaCpWzVcklI1gIbGpUm3SNs3MuJiYv8xMm1TTF7C0sWBDYiEewAPYeAELjyCWJDYWvk4nERr1Tebec8/9zjdzchRb11yP6LlL6u7p7esfGAwNDYdHRiNj43uuVXFUkVUt3XLyiuwKXTNF1tM8XeRtR8iGoouccrzevM9VheNqlrnr1WxRMuRDUzvQVNljKl9UjLrRKG+VIzFKkF/RdpAMQAxBpa3IPYrYhwUVFRgQMOEx1iHD5aeAJAg2cyXUmXMYaf69QAMh1la4S3CHzOwxr4d8KgSsyefmTNdXq/wVnV+HlVHE6Ylu6Y0e6Y5e6PPPWXV/RvNfarwrLa2wy6Onkzsf/6oM3j0cfas6KBTu7uzJwwGWfC8ae7N9pulSbc2vnpy/7Sxn4vUZuqZX9ndFz/TADs3qu3qzLTIXCHFAyd9xtIPsXCKVoO2F2OpakNQApjCNWY5jEavYRBpZP4YzXOBSCkvzUkpaabVKXYFmAj9K2vgCGPOSyg==/latexit
x(K)
nlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexitlatexit sha1_base64=zY0AEOc1xdLNfIm3265U8VjiOPs=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/latexit
EV
latexit sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=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 sha1_base64=yEomzIlRoTOyYTFl9alCYM21zMg=AAACj3ichVHNLkNBFP56/VX9VW0kNo2GWDWnIlEW0hAJuxZFQsm91+Cm98+90ybVeAEvYGGjEgvxAB7AxgtYeASxJLGxcHp7E0FwJjPzzTfnOzNfjuaahi+JHiNKW3tHZ1e0O9bT29c/EB9MrPtOxdNFUXdMx9vUVF+Yhi2K0pCm2HQ9oVqaKTa08kLzfqMqPN9w7DVZc0XJUg9sY9/QVclUadtS5aGumvXFk5313XiK0hRE8ifIhCCFMPJO/Bbb2IMDHRVYELAhGZtQ4fPYQgYEl7kS6sx5jIzgXuAEMdZWOEtwhspsmdcDPm2FrM3nZk0/UOv8isnTY2USY/RA1/RC93RDT/T+a616UKP5lxrvWksr3N2B0+HVt39VFu8Sh5+qPxQaZ//tSWIf2cCLwd7cgGm61Fv1q8dnL6uzK2P1cbqkZ/bXoEe6Y4d29VW/KoiVc8S4QZnv7fgJipPpmTQVplK5+bBTUYxgFBPcjmnksIQ8ivzsEc5wgYaSULLKnJJrpSqRUDOEL6EsfwD+gZTp/latexit
p(x|y = K) VAE(mK)
{x(K)
n }N
n=1 ⇠ p(x|y = K)latexit sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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 sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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 sha1_base64=OeOFWFhG3xUrP+2/9X8ac+szoeU=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

2
Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Other registered parameters
✓K
Slatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=AAACjnichVG7SgNBFD2u7/hIoo1gI4aIVbgRwQeIok3ARo1RwWjYXSfJ4mZ32Z0EYsgP+AFaWPgAC/ED/AAbf8DCTxDLCDYW3mwWREW9w8ycOXPPnTlczTENTxI9tSntHZ1d3T29ob7+gcFwJDq05dllVxcZ3TZtd0dTPWEalshIQ5pix3GFWtJMsa0drjTvtyvC9Qzb2pRVR+yV1IJl5A1dlUxls7IopJqrpev7q7lIjBLkx9hPkAxADEGs2ZE7ZHEAGzrKKEHAgmRsQoXHYxdJEBzm9lBjzmVk+PcCdYRYW+YswRkqs4e8Fvi0G7AWn5s1PV+t8ysmT5eVY4jTI91Qgx7olp7p/ddaNb9G8y9V3rWWVji58PFI+u1fVYl3ieKn6g+Fxtl/e5LIY9b3YrA3x2eaLvVW/crRaSM9vxGvTdAVvbC/S3qie3ZoVV7163WxcYYQNyj5vR0/QWYqMZeg9enY0nLQqR6MYhyT3I4ZLCGFNWT4WQcnOMeFElVmlAVlsZWqtAWaYXwJJfUBBJ2UfQ==/latexitlatexit sha1_base64=u9Cobn9VzxVrpzEDF1ZWps/uZds=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/latexit
{✓1
S, ..., ✓K 1
S }latexit sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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 sha1_base64=wyy4JFHwMwxMOC2z1ZT3V4m73hI=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
DV
x(u)
nlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexitlatexit sha1_base64=2Nq7mZbUqbWxVfmh3wGCPXbUhIw=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/latexit
Elatexit sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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 sha1_base64=cwXENOa1muv1/eInYtZ+l0K0cZk=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
x(K)
EV
Dlatexit sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=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 sha1_base64=Pkuk8LFsaH5+wIAmpapWSh3/ONA=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

Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Threshold
calc.
✓K
{✓1
S, ..., ✓K 1
DV
x(u)
x(K)
EV
min
h
score(x(K)
m , ✓)
iM
m=1latexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=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/latexitlatexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=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/latexitlatexit sha1_base64=oGgGXwkVf9iTriMTDHFakC3vG1Y=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/latexit

Overlooked
anomaly
Normal
training data
VAE
Normal model
Anomaly
score
calc.
Threshold
calc.
SNIPER
Iterative training
Update
✓K
{✓1
S, ..., ✓K 1
DV
x(u)
x(K)
EV
✓K
S argmin✓K
S
1
N
NX
n=1
sigmoid
h
score(x(u)
n , ✓)
i
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音響信号に対する異常音検知技術と応用

音響信号に対する異常音検知技術と応用

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音響信号に対する異常音検知技術と応用