DAGA '06 - Braunschweig
Lo ca liza tio n o f Bra k e Sq uea l
Nile sh Mad h u †, R aine r Martin†,
He inz -W e rne r R e h n‡ and And re as Fisch e r ‡
†Institute of C ommunication A coustics (IK A ), Ruhr-U niv ersität Bochum
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‡V olk sw agen A G , W olfsburg
{firstname}.{lastname}@ v olk sw agen.de
F ourier tra nsform (D F T) on overla p p ing fra m es in ea ch
seg m ent. Note tha t the fi nite sp ectra l resolution of the
d iscrete F ourier tra nsform , coup led w ith the frequency
jitter of the sources sm ea rs ea ch na rrow ba nd a coustic
event a cross m ore tha n one frequency bin. The a ccretion of such a d ja cent frequency bins build s w ha t w e sha ll
d enote a s frequency ban ds, w here ea ch a ctive ba nd cha ra cteriz es a n a coustic event. C onsequently, the a na lysis is
on a ban d-by-ban d ba sis. W e a lso a ssum e tha t it is not
necessa ry for ea ch a rra y to ha ve a Line of S ig ht (LoS )
to ea ch source. The a lg orithm p roceed s in tw o step s:
in the fi rst step the a ctive frequency ba nd s a re d etected
using na rrow ba nd noise estim a tes a nd then the squea levents a re a ssig ned to the a ctive bra ke(s) using a coherence w eig hted cost function. The a p p roa ch ha s been
verifi ed by exp erim ents ca rried out on a m oving vehicle.
Intro ductio n
This contribution investig a tes the use of m icrop hone a rra ys for the d etection a nd loca liz a tion of bra ke squea l of
a m oving vehicle. The a d va nta g es of using m icrop hone
a rra ys over other a p p roa ches (such a s those using vibra tion sensors, etc.) a re: d ep loym ent need not be in the
im m ed ia te vicinity of the bra ke d iscs, robustness a g a inst
ind ivid ua l sensor fa ilures a nd vehicle-structure ind ep end ency, to m ention a few . B ra ke squea l occurs a s a result
of the resona nce betw een the bra ke d isc a nd the bra ke
shoe, m a king the a coustic source a d istributed one. The
squea l is na rrow -ba nd in na ture, w ith squea l frequencies
typ ica lly ra ng ing from 1 kHz to 16 kHz . Also, the squea l
frequencies cha ng e from event to event a nd from w heel
to w heel. F urtherm ore, the a coustic environm ent und ernea th a n a uto g ives rise to m ultip a th p rop a g a tion a nd
sta nd ing w a ves. Ad d itiona lly, the loca liz a tion a lg orithm
ha s to cop e w ith the follow ing :
Arra y 1
8 1
• m ore tha n once source ca n contribute to a squea l
event.
25 32
D irection of m otion
Arra y 4
9
16
• the p ow er of the sp ectra l ha rm onics of the sources
a re unknow n a nd , further, va ry from event to event,
a nd , fi na lly,
Arra y 2
• the sources em it jittered na rrow ba nd sig na ls (a nd ,
in som e ca ses, one or tw o hig her ha rm onics),
Arra y 3
17
Und er these circum sta nces d etecting a nd releg a ting a
squea l event to the corresp ond ing w heels is a very d em a nd ing ta sk.
24
Figu re 1: A rray positions and microphone indices. T he
numbers indicate the global channel indices of the first and
the last microphone of the respectiv e array .
S ta nd a rd source loca liz a tion a lg orithm s (G C C [1] etc.)
fa il in this context beca use of the na rrow -ba nd na ture
of the bra ke squea l a nd the com p lex a coustic environm ent. C onsequently, this p a p er p resents a n a p p roa ch for
solving this p roblem using a w eig hted cost function, sim ila r in som e resp ects to the steered -resp onse-p ow er a p p roa ch [2 ], on a tw o-d im ensiona l sea rch fi eld . The setup
com p rises four a rra ys, w ith a tota l of 3 2 cha nnels for sig na l inp ut (F ig ure 1). The a rra ys a re linea rly confi g ured ,
w ith log a rithm ic sp a cing betw een the elem ents to ta ke
into a ccount the w id e ra ng e of the squea l sig na l frequencies.
Lo ca liza tio n
As the squea l events a re concentra ted in the reg ion
a round the resp ective w heels, the va lid source loca tions
a re restricted to the reg ion a round the w heels. F urtherm ore, ea ch a rra y only com p utes the loca liz a tion estim a tes for those bra ke d iscs it ha s a d irect line of sig ht to.
The sea rch sp a ces for a rra y 3 a re illustra ted in F ig ure 2 .
Also, d ue to the d istributed na ture of the sources, w e d o
not seek the op tim a l source loca tion vector rs,opt ; ra ther,
w e look for the op tim a l reg ion. This im p lies a sp a tia l a vera g ing of the cost function over the sea rch reg ions. The
sp ectra l sp rea d d ue to jitter a nd fi nite tim e-frequency resolution requires tha t the tim e-a vera g ed estim a te be further a vera g ed over ea ch frequency ba nd , w here the ba nd s
F urther, the d etection a nd loca liz a tion of the squea l
events m ust be a ccom p lished in rea l-tim e, w ith low la tency. F or this rea son the inp ut sig na ls a re a na lyz ed in
seg m ents of 2 0 0 m s d ura tion, using a w ind ow ed d iscrete
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DAGA '06 - Braunschweig
1
16000
14000
Analysis frame o f 20 0 ms
12000
Frequency
10000
4
2
8000
6000
4000
2000
3
0
Figu re 2: Valid source re gions (in gre e n). Each array only
calculate s the cost function for re gions around w he e ls it has
a dire ct Line of Sight (LoS) to.
0
0.5
1
1.5
2
Time
2.5
3
3.5
4
4.5
4
4.5
(a ) Sp e c tro g ra m o f sing le bra k e e v e nt
16000
14000
a re fo rm e d b y c lu ste rin g th e c lo se st a c tive b in s. F u rth e r
ro b u stn e ss o f th e a lg o rith m c o m e s fro m a ve ra g in g o ve r
tim e a n d o ve r fre qu e n c y b a n d s.
12000
L o calize d e v e nt (fro nt rig h t)
Frequency [Hz]
10000
Detectio n
8000
6000
T h e b a n d -b a se d lo c a liz a tio n is ro o te d o n th e im p lic it a ssu m p tio n th a t th e b a n d in c o n c e rn c o n ta in s a squ e a l
e ve n t. O rd e r sta tistic (O S ) [4] a p p ro a ch e s c a n b e u se d to
m a ke a ro b u st d e te c tio n o f su ch a c tive fre qu e n c y b a n d s.
S u ch a p p ro a ch e s a lso , im p lic itly, c o n fi rm th e p re se n c e
o r a b se n c e o f a squ e a l e ve n t. Ho w e ve r, th e se m e th o d s
c o m e w ith a la rg e c o m p u ta tio n a l c o st. As b ra ke squ e a l
e ve n ts o c c u r in te rm itte n tly, th e syste m is a c c e le ra te d b y
d e te c tin g th e p re se n c e o f b ra ke -squ e a l in a sig n a l se g m e n t
u sin g c o m p u ta tio n a lly le ss in te n sive m e a su re s, re se rvin g
th e O S a p p ro a ch e s o n se g m e n ts w h e re b ra ke -squ e a l is d e te c te d – fo r a c tive fre qu e n c y e stim a tio n . As b ra ke -squ e a l
e ve n ts a re n a rro w b a n d , w ith m o st o f th e sp e c tra l e n e rg y
b e in g c o n c e n tra te d in th e squ e a l fre qu e n c ie s1 , it g ive s
rise to a ra th e r w e ll-stru c tu re d sp e c tru m in th e p re se n c e
o f b ra ke -squ e a l. T h is p e rm its th e u se o f m o d ifi e d in fo rm a tio n th e o re tic to o ls (like e n tro p y) to fo rm a n a priori
d e c isio n o n th e p re se n c e o f a squ e a l e ve n t [3, 5 ].
4000
2000
0
0
0.5
1
1.5
2
2.5
Time [s]
3
3.5
(b) D e te c tio n a nd lo c a liz a tio n re sult
Figu re 3: Localization on a m ov ing v e hicle
th e c o rre c t m a p p in g o f e ve n ts to th e ir so u rc e s. M e a su re m e n ts m a d e in a c tu a l c o n d itio n s o f u se in d ic a te th a t th e
p ro p o se d syste m is ro b u st a g a in st d istu rb in g fa c to rs su ch
a s re ve rb e ra tio n a n d n o ise .
References
[1] C .H. K n a p p a n d G .C . C a rte r, “ T h e g e n e ra liz e d c o rre la tio n m e th o d fo r e stim a tio n o f tim e d e la y” IE E E
T ran s. A cou stics, S peech, S ign al P rocessin g, vo l. 24,
p p . 320 – 327 , 19 7 6 .
E xp erim enta l results
In th e fo llo w in g e xa m p le th e lo c a liz e d squ e a l e ve n ts a re
p lo tte d d ire c tly u p o n th e sp e c tro g ra m o f th e sig n a l. T h e
o rd in a te o f e a ch m a rke r re p re se n ts th e fre qu e n c y o f th e
squ e a l e ve n t a n d th e h o riz o n ta l e xte n t d e fi n e s th e le n g th
o f th e e ve n t.
[2] M . B ra n d ste in a n d D . W a rd (e d s.), “ M ic ro p h o n e Arra ys: S ig n a l Pro c e ssin g T e ch n iqu e s a n d Ap p lic a tio n s”.
S p rin g e r Ve rla g , B e rlin , 20 0 1.
[3] C . S h a n n o n , “ A M a th e m e tic a l T h e o ry o f C o m m u n ic a tio n ”, B e ll S yste m s T e ch n ic a l J o u rn a l, vo l. 27 , p p .
37 9 -423 a n d 6 23-6 5 6 , J u ly a n d O c to b e r, 19 48 .
T h e m e a su re m e n ts w e re m a d e o n a m o vin g VW -T o u ra n .
T h e F F T siz e w a s 10 24, th e sig n a ls w e re w in d o w e d w ith
a Ha n n w in d o w a t a n o ve rla p o f 7 5 % . T h e d a ta sh o w n in
F ig u re 3 c o rre sp o n d s to a m e a su re m e n t w h e re o n ly th e
b ra ke o n th e fro n t, rig h t w h e e l w a s ‘a c tive ’
[4] P. M . C la rkso n a n d G . A. W illia m so n , “ O rd e r sta tistic s a n d a d a p tive fi lte rin g ,” in S ign al P rocessin g
M ethods for A u dio, Images an d T elecommu n ication s
(P. C la rkso n a n d H. S ta rk, e d s.), vo l. 28 4, Ac a d e m ic
Pre ss, 19 9 5 .
C o nclusio ns
T h e syste m p re se n te d is c a p a b le o f d e te c tin g a n d lo c a liz in g m u ltip le n a rro w -b a n d , p o ssib ly o ve rla p p in g a c o u stic
e ve n ts. T h e u se o f m u ltip le m ic ro p h o n e a rra ys e n a b le s
[5 ] P. Re n e ve y a n d A. D ryg a jlo . “ En tro p y b a se d vo ic e
a c tivity d e te c tio n in ve ry n o isy c o n d itio n s”, Pro c . Eu ro sp e e ch , Eu ro p e a n C o n fe re n c e o n S p e e ch C o m m u n ic a tio n a n d T e ch n o lo g y, S e p t. 20 0 1.
1 The lo w e r fre q ue nc ie s c o nta ining m o to r no ise a re ne g le c te d in
o ur c o nside ra tio ns.
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