TAP CHi KHOA HOC VA CONG NGHE Tap48, s6 2, 2010 Tr. 11-22
KIEM SOAT TliNG ON TICH CU'C SU" DUNG MANG NQRON MO LOAI 2
HUYNH VAN T U A N , T R A N Q U 6 C CU'O'NG, DU'aNG HOAl NGHTA,
I , . N G U Y E N HCru PHU'aNG
• »
1. GlCn THIEU
Nguyen li chung ciia cac he thdng kiem soat tieng dn tich cue (active noise control - ANC) la tao ra tieng dn thii cap cd cung bien dp nhung ngugc pha vdi tieng dn so cap sao cho tieng dn so cap va tieng dn thii cap triet tieu lan nhau tai •somg can kiem soat tieng dn. Hinh 1 trinh bay he thdng ANC hdi tiep trong dd bd dieu khien cd nhiem •vu tao ra tieng dn thii cap cd ciing bien do nhung ngugc pha vdi tieng dn so cap tai micro tdng hgp.
Ngudn
tieng dn (J Micro tdng hgp
Bd dieu khien Fuzzy neural Hinh L He thong ANC hoi tiep
Ket qua nghien ciiu ve cac he thdng ANC tuyen tinh dung lpc FIR cd the tim thay trong [1].
Gan day nhieu tac gia da de xuat cac phuong phap khac nhau de giai quyet van de phi tuyen tren dudng tmyen thii cap: [6] su dung mang truyen thang nhieu ldp, [7, 9] gidi thieu iing dung cua mang ham co sd xuyen tam (radial basis ftmction - RBF), [8] sir dung mang neuron md. Mat khac gan day cac tap md loai hai da dugc phat trien [9, 10]. Khac vdi tap md loai mdt, tap md loai hai dugc bieu dien bdi cac ham thanh vien bat dinh va do do cho phep md ta tdt hon cac dai lug'ng bat dinh.
Muc tieu cua bai bao nay la gidi thieu he thdng ANC hdi tiep thich nghi dung mang noron md loai 2. Giai thuat cap nhat true tuyen cac trgng sd cua mang dugc xae dinh dimg phuang phap giam dp ddc (steepest descent). Dieu kien hdi tu ciia giai thuat dugc thiet lap dua vao ly thuyet dn dinh Lyapunov. Phan cdn lai ciia bai bao dugc bd cue nhu sau: phan 2 gidi thieu so luge mang noron md loai 2 dang khoang, phan 3 trinh bay he thdng ANC hdi tiep diing mang noron md loai 2, phan 4 trinh bay cac ket qua md phdng, trong dd phuang phap dung mang noron md loai 2 dugc so sanh vdi cac phuong phap khac nhu lpc FIR, mang perceptron, mang noron md loai 1. Phan 5 kit luan bai bao.
2. MANG NORON MOf LOAI 2
^U'[^<,
Lap 1 Lop 2 Lop 3
yj-^y.
Lop 4 L6p 5 /fiw/; 2. Cau tnic mang naron md loai 2.
Hinh 2 md ta mang noron md loai 2 (type 2 fiizzy neural network - T2FNN) vdi L ngd vao va mpt ngd ra. Mang ed 5 ldp
Ldp 1: Tiep nhan cac tin hieu vao d(k),...,d{k-L-i-l)
Lop 2: Xae dinh cae chan tren va chan dudi ciia cac ham thanh vien cua cac tin hieu vao.
Vi du cac chan tren jl.. va cac chan dudi |l.. ciia ham thanh vien ciia tap md loai 2 thii j cua tin hieu vao thu i dugc xae dinh bdi
id(k-i + l)-myf
|a,, =exp^ —
2a„. ^ y = e x p i -
(d(k-i + l)-m.jf
2^7
(1)vdi r = 1,2,...,!,; [i--, \i,, OyVa. Oy la cac hang sd. Hinh 3 va 4 trinh bay cac ham thanh vien ciia cac tap md loai 2 trong hai trudng hgp Oy = Oy, My > nty (hinh 3) va Wy - my, Oy > Oy (hinh 4).
-2
Hinli
5 -1 -0,5 0 0,5 1 1,5
3. Tap md loai 2 vdi a = g , m > m,
.15 .1 -0 5 ,0 0.5
Hinh 4. Tap ma loai 2 vdi m., = m
.j=rn,j, o^>a,^
12
Ldp 3: Sd ph4n tu cua ldp nay bing sd luat hgp thanh N. Neu ta dien dich phep giao diing luat PRO, tin hieu ra tuong iing d phan tii thii n (1 < n < N) la tap md loai 2 vdi ham thanh vien xae dinh bai cac chan tren va chan dudi
1^ " =
U\^uU^j
(2)Ldp 4 : Chuyen tap md loai 2 sang tap md loai 1. Cac gia tri J,, va y, (hinh 2) dugc xae dinh dung phuang phap tam ciia tap hgp (center - o f - set) [8, 9, 10]
i M:"< + t r < i r ^; + t ^'^"
Vr = n = \ n = R + \ N , y, = — n = L+\ (3)
ZM:"+ z r z r + z r
n = \ n = R + \ n = \ n = 14-1
vdi 1 < R < N-1 va 1 < L < N-1. Trong dd w" va w", n = l,...,N, la trgng sd cua mang dugc cap nhat true tuyen trong qua trinh huan luyen.
Dinh nghia cac vecto Nxl:
<^-=-R—'-^^li'y . . ^ ^ - ^ -
,[i , . . . , i i , i i , | j ..,r]
zr+ z r
,!=1 n=R + l
^ / = - [—I —9 — I L+l L + 2 iV ]
> , | I - , . . . , | I ,[i ,[l ,...,11 J
zr+ z r
11=1 n=L+l
[ 1 2 N Y [ 1 2 N Y
w,. ^[w,.,w,.,...,w,. \ , Wj = [w,,Wi ,... ,w, \ . Ta cd the viet lai (3) dudi dang ma tran nhu sau:
y,. (k) = (s?l (k)w,. (k), y, (k) = ^[ (k)w, (k)
Ldp 5: Ldp nay (ldp ra) cd chiic nang xae dinh tin hieu ra y(k) (giai md)
(4)
(5)
(6)
(7)
(8)
3. HE THONG ANC HOI TIE? THICH NGHI DUNG NORON MO LOAI 2
He thdng ANC hdi tiep thich nghi diing mang noron md loai 2 (T2FNN) nhu hinh 5.
Trong dd, G(z) la trayen dat cua dudng trayen thtr cap tir loa thit cap den micro tdng hgp trong hinh 1, G(z) la md hinh ciia G(z), FxLMS (filtered-x least mean square) la giai thuat cap nhat bp trpng sd w", w" ciia mang, S{ ) bieu dien tinh phi tuyen cua khau chap hanh, S{ ) la md hinh ciia S{ ) . Trong tradng hgp khau chap hanh cd tinh bao hda, ta cd the xap xi S{ ) bdi ham tansig nhu sau:
S(y)^- •1
i+e-^y
vdi yl la tham sd cua ham tansig (A dugc chpn bang 2 de s{y) ed dp ddc bSng 1 tai y = 0).
d(k)
(9)
dfk)
e(k)
d(k)
JL
Sid)
T2FNN
"XT"
y(k)
G{z)
d(k) d'(k)
Siy) u(k) G(z) v(k)
S{y) G(z) FxLMS
n o
Tit hinh 5, ta cd:
vol
Hinh 5. He thong ANC diing mang T2FNN
e(k) = d{k)-v(k)
M
v(^) = Y^g(m)u(k-m)
ra = 0
g ( m ) , m - 0,1,2,.. . , M la dap iing xung cua G(z), u(k) = 2
1 + e -ly(k) 1 Dinh nghia ham muc tieu
1 . 2 ,
J(k)^-e\k).
(10)
(11)
(12)
(13) Cac trpng sd w", vv" ciia mang noron md loai 2 dugc udc lugng bing each cue tiiu hda J(k) dimg phuong phap giam dp ddc [1, 2, 3, 4, 5]. Ta cd ket qua sau
Dinh li:
a) Gidi thudt hudn luyen de quy cue tieu hoa J dugc xdc dinh bdi
14
Wi{k-\-'^=Wi(k)-\--T](ik)'^g(m)\[-u-(k-m)y),(k-m)
w. ak+l) = w,Xk)+lTp(k)tg(^i^-i^\k-m)y>,.(k-m)
2 m=0
(14) (15) trong do T] Id toc do hoi tu {r]>0).
b) Bieu kien dii de gidi thudt (14), (15) hoi tu dugc xdc djnh bdi 0 < 77 <
V M
Yj{m)[\-u\k-m)]
LnJ=0 J 2
r
\^(k-m) + (p}.(k-m)
(16)
vdi (]),, ([),. dugc nghia d (4) vd (5).
Chimg minh.
a) Xae dinh giai thuat huan luyen
Cac trpng sd mang noron md dugc udc lugng bang each cue tieu hda J(k) dinh nghia d (13) dung phuang phap steepest descent [1 - 5]
w,(k + 1) = w,(k)-Tj
w,.ik + 1) = w,.(k)-Tj
(17)
(18) vdi JJ la tdc dd hdi tu (/^ > O) •
Ap dung cdng thiic chudi ddi vdi cac phuang trinh (17) va (18), ta dugc:
dJ
dJ trong do:
dJ de dv du de dv du dy dJ de dv du de dv du dy
dy_
dw I ' dy
1 M r -|
= --e(k)Y,g{m)\i-u'(k-m)\\>,(k-m) (19)
m = 0
1 " r 1 M
-e(k)Y, gim)\[ -u^k -m)^,.(k - m) (20)
m=0
du Ae-^y 9y (l-fe Tu (19) va (20) ta cd (14) va (15).
b) Xae dinh dieu kien hdi tu cua giai thuat Tir (13), tacd:
•2y{k)
^[l-u\k)].
(21)j(k)=\y(k)=\{d(k)-v(k)r
(22)Dinh nghia
hJ(k) = J(k +1) - J(k) = \_[e(k +1) - e(k)][e(k +1) + e(k)] = \^e(k)[2e{k) + ^e(k)\ (23)
VOl
Mk)=e{k+\)-e{k) = de_
dwf
^,(k)-\- de dw,.
„ „ . . deM^ dv du(k-m)^dy(k-ni\
m'Xk)-—2^^:; ^^ 1 —^^
dv,„=odu{k-m) dy(k-rn) [[ di^
/ ^ - l -
dy(k-ni) dw,. M
=—Mk) 4
A/{k)=—r]e(ki
= -.^e\ki
Y^mll-u\k-m)]
111=0
f^m\\-u\k-m)-\
=0
f^ml\-u\k-m)-\
[(j)^(A:-/n)-F(t)^(A:-m)
^'i {k - ni) -I- ([)' (A: - ni) xl2.e{k)—^y\e{k) Y^ml\-u\k-m)\
(24) [^](k-ni)+i^](k-m)
f,{k-}7i)+d,ik-m) x 2 - - t i Y^ml\-u\k-m)-\ f,(k-m)+d;{k-m) (25) Vi y ( ^ ) = — e ^ (A:) > 0 khi ^J(k) < 0 , J(k) giam ^ e(k) ^ 0 , do dd hr (25) ta cd dieu kien hdi tu sau
^-,'i
M
Yj(m)\\-u^(k-m)\
n!=0
^(k-m)+^^(k-m) >0 (26)
ttr (26) ta dugc (16).
4. KET QUA MO PHONG
Muc nay trinh bay kit qua md phdng trong dd he thdng ANC dung mang noron md loai 2 dugc so sanh vdi cac he thdng ANC sau:
a. He thdng ANC diing loc thich nghi FIR truyen thong [2,3]
Giai thuat huan luyen [3]:
w(k +1) = w(k) + \^e(k)Y,g{m)D(k - m) vd\b{k)-[d(k), d(k-\), ..., J ( A : - m ) ] ^ la vecto tin hieu ngd vao.
b. He thong ANC dung mang perceptron [4]
Vdi ham tich hgp tuyin tinh va ham tac ddng sigmoid ludng cue (tangsig):
2 ,, net(k) = w ' {k)D(k); yik) = f{net(k)) = j — ^ nel{k)
16
Giai thuat hu4n luyen [4]
(k +1) = w(k) + - r i e ( A : ) X g(w)[l ~y-(k- m)\b(k - m).
2 m=0 c. H e thdng A N C diing mang noron mcr loai 1 [5]
Khdng gian ngd vao dugc chia thanh 5 tap md vdi ham thanh vien Gaussian cd trpng tam lan lugt la - 1 ; -0,5; 0; 0,5; 1 va phuong sai 0,3 (hinh 6).
-0.8 -0 6 -0,4 -0 2 0 0,2 0.4 0.6 0.8
Hinh 6. Cac tap md Gaussian loai 1 Hinh 7. Cau tnic mang noron md loai 1 Cau tnic cua mang noron md loai 1 tmyen thang gdm 5 ldp nhu hinh 7.
Ldp 1: (Ldp vao) a = d- .
Ldp 2: (Ldp md boa) a'^' = exp
Ot Ldp 3: (Ldp luat hpp thanh) ci ~ Yi.^'
i (3)
Ldp 4: (Ldp chuan boa) a = :==-^, (4)
Ldp 5: Ldp ra J^ = <3*^' = Z*^/*^'—/ •
Cac dinh nghia: vv(A:) = [w,(A:), w^ik), ..., w,,(k)Y.
A^'\k) = y'\kl a^'\k-l), ..., d'\k-n + l)J
vdi n: sd luat hgp thanh.
Giai thuat huan luyen [5]: (ham tich hgp tuyen tinh va ham tac ddng tuyen tinh) w(k + l) = w(k) + r\e(k)^g(m)A^''\k-m)
M
=0
d. He thdng ANC dung mang noron mo- loai 2 : • ) Mang noron md loai 2 ed mdt niit ngd vao vdi 5 tap md, cac thdng sd trpng tam m bat dinh va phuong sai o ciia ham thanh vien Gaussian dugc chpn:
m = {[-1.15, - 0 . 8 5 ] , [ - 0 . 6 5 , - 0 . 3 5 ] , [ - 0 . 1 5 , 0.15],[0.35, 0.65],[0.85, l . i s ] } a = [0.4, 0.4, 0.4, 0.4, 0.4].
Cac thdng sd md phdng nhu sau: ham trayen dat ciia tieng dn thii cap G(z) = 0 . 5 / z " ; bang sd hpc dugc chpn tren co sd phuang trinh (16) la T) = 0,8; tan sd lay m4u la 8 KHz.
4.1. Mo phdng 1
Ngudn tieng dn don tan vdi tan sd 140Hz (thudng xuat hien d dpng co ciia xe dtd 1600 cc [10]). Cac ket qua trinh bay trong hinh 8 va bang 1.
Bdng 1
MSB (dB)
Tieng dn so cap +17
FIR -2
Perceptron -17
Md loai 1 -24
Md loai 2 -49 trong dd MSB (Mean Square Error) la trang binh binh phuong sai sd, MSE dugc xae dinh:
MSE = —^ef(n) ^ MSE(dB) = lOlog,g(MSE).
N /=i
Dua vao bang 1, ta thay phuang phap diing md loai 2 hieu qua nhat do mang noron md loai 2 cho phep md hinh hda va giam tdi thieu tinh bat dinh ciia he thdng logic md tren co sd luat hgp thanh, ham thudc cua tap md loai 2 la khdng gian 3 chieu cd kha nang do mtrc dp ngau nhien dieu nay lam cho logic md loai 2 cd kha nang md hinh hda tinh bat dinh mdt each true tiep.
4.2. Mo phong 2
Hinh 9 trinh bay ket qua md phdng tradng hgp tieng dn da tan (tdng hgp cua 6 tan sd:
61 Hz, 140 Hz, 180 Hz, 260 Hz, 350 Hz va 500 Hz). Ta thay vdi he thdng dung mang noron md loai 1, cudng do tieng dn giam tit 10 dB - 25 dB trong •vung tan sd can kiem soat tieng dn nhtmg lai tang len trong •vung tan sd cao ttr 20 dB - 30 dB. Vdi he thdng diing mang noron md loai 2, cudng dp tieng dn giam hr 5 dB - 30 dB.
Mdt vai nhdm tac gia da dung phuong phap hdi tiep de kiem soat tieng dn: T. Meurers, S.M. Veres, and S.J. Elliott [2] sir dung lge thich nghi trong mien tan sd, ket qua tieng dn don tan sd giam tir 15 dB - 30 dB; Bharath M. Siravara [3] dung lpc FIR trong mien thdi gian, ket qua tieng dn da tan sd giam hr 10-16dB. So sanh vdi nhdm tac gia trong [2] va [3], viec sir dung noron md loai 2 trong kiem soat tieng dn dat hieu qua cao, tieng dn giam 66dB trong trudng hgp ngudn tieng dn don tan sd va tieng dn da tan sd giam ttr 5 dB - 30 dB.
Tieng on so cap
20 r
0 -
1 1 1 1 1 1 1 1 '
i I -2\6B L : • J -.L I -
i .illffi f W i l l l l X _
l|i!|f' n ^Iffif^^
50 100 150 200 25D 300 350 400 450 500 Tan so [Hz]
0 50 100 150 200 250 300 350 400 450 500 Tan so [Hz]
f
!
-17;dB
4 m\ i \m m m ^m m m
• 0 50 100 150 200 250 300 350 400 450 500 Tan SD [Hz]
"0 50 100 150 200 250 300 350 400 450 500 Tan so [Hz]
f ff
; -4
: /
tf[fl
giciB ; ;
1^ ' ^
ftf • ^
31ta|if« 'p m i | | l m
50 100 150 200 250 300 350 400 450 500 T a n so [Hz]
Hinh 8. Ket qua mo phong tieng on dan tan.
(a) Tieng on sa cap;
(b) ANC dung loc thich nghi FIR;
(c) ANC dung mang noron;
(d) ANC dung mang noron md loai 1;
(e) ANC dimg mang noron md loai 2.
4.3. Mo phong 3
Hieu qua ciia khau bd chinh bao hda. Bien do khau bd chinh dugc chgn la ± 0,5. Tan sd tieng dn 150 Hz. Ket qua md phdng dugc the hien trong mien thdi gian (hinh 10a, 10b) va miin tan sd (hinh 11). Ta thay khi khdng bd chinh, tieng dn tdng hgp tang cao ban tiing dn sa c4p khoang 2dB. Khi cd bd chinh, tieng dn tdng hgp giam khoang 15dB so vdi tieng dn so cap. Kit qua md phdng cho thay he thdng ANC cd bd chinh cho bd khuech dai am tan lam viec hieu qua.
he thdng giam dugc tieng dn ngay khi bd khuech dai cdng suat am tan bi bao hda do tieng dn ngd vao tang cao.
20
-ANC OFF
• ANC loai 1
•ANC loai 2
-^^i^vs^PSs-:^
^-^Q^-f^
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency (kHz)
Hinh 9. Cac tin hieu vdi nguon tieng on da tan the hien trong mien tan sd
Primary noise Primary noise
0 0.01 0.02 0,03 0.04 0.05 0,06 0,07 0,08 0,09 0,1 Secondary noise
0 0,01 0.02 0,03 0,04 0,05 0,0B 0,07 0.08 0.09 0.1 Secondary noise
0 0 01 0.02 0.03 0 04 0.05 0 06 0.07 0 08 0 09 0 1 Residual noise
0 0 01 0 02 0 03 0 04 0.05 0 OE 0.07 0 08 0 09 0 1 T(me(s)
0 0.01 0.02 0.03 0.04 0.05 0 06 0.07 0.08 0.09 0.1 Residual noise
0 0.01 0 02 0.03 0.04 0.05 0 06 0.07 0.08 0 09 01 Tinne(s)
Hinh 10a. Ket qua khi khong bo chinh Hinh 10b. Ket qua khi co bo chinh
20
//;«/! 77. (a) Tieng on sa cap; (b) Tieng on tong hgp khi khong bo chinh;
(c) Tieng on tong hop khi c6 bo chinh.
Mv:ri,.^.,:w ^,.,; 5. KET LUAN
Bai bao da gidi thieu he thdng kiem soat tieng dn tich cue hdi tiep diing mang noron md loai 2. Diem mdi eiia he thdng ANC de nghi nhu sau:
- Viec su dung khau bd chinh bao hda cua khau chap hanh;
- Viec sii dung mang noron md loai 2.
Dua vao phuong phap giam dp ddc, bai bao da xay dung giai thuat huan luyen mang noron md loai 2. Su hdi tu eua giai thuat huan luyen da dugc khao sat. Cac ket qua md phdng cho thay:
- He thdng de nghi ed the boat ddng mdt each hieu qua. Cac ket qua thuc nghiem se dugc gidi thieu trong tuong lai gan;
- So sanh vdi cac phuong phap khac, viee sir dung mang noron md loai 2 trong he thdng ANC dat hieu qua cao nhat.
TAX LIEU THAM KHAO
1. S. M. Kuo and D. R. Morgan - Active noise control: A tutorial revie'w, Proc. IEEE 87 (6) (1999).
2. T. Meurers, S. M. Veres, and S. J. Elliott - Frequency Selective Feedback for Active Noise Confrol, IEEE Control Systems Magazine 22 (4) (2002) 32-40.
3. Bharath M. Siravara - Subband Feedback Active Noise Cancellation, Master thesis. The University of Texas at Dallas, August, 2002.
4. Duong Hoai Nghia, Huynh Van Tuan - Active Noise Control Using Neural Network, The Intemational Symposium On Electrical-Electronic Engineering (ISEE) University of Teehnology-Ho Chi Minh City, Vietnam, 2007.
5. Huynh Van Tuan, Duong Hoai Nghia - A fuzzy neural network feedback active noise controller. The 10* Intemational Conference on Control, Automation, Robotics and Vision, ICARCV 2008, Hanoi, 2008.
6. John Canfield - Active Disturbance Cancelation In Nonhnear Dynamical Systems Using Neural Netvi'ork, University of New Hampshire, December, 2003.
7. C. A. Silva, J. M. Sousa, and J. M. G. Sau da Costa - Active Noise Control Based On Fuzzy Models, 4* European Conference on Noise Control Euronoise 2001, Para, 2001, pp. 14-17.
8. Qi-Zhi Zhang, Woon-Seng Gan, Ya-li Zhou - Adaptive Recurrent Fuzzy Neural Networks For Active Noise Control, Elsevier, Joumal of sound and Vibration 296, 2006 935-948, 2 June 2006.
9. Nilesh N. Kamik, Jerry M. Mendel - Type-2 Fuzzy Logic Systems, Software, IEEE Trans, on fiizzy systems 7 (6) (1999).
10. Qilian Liang, Jerry M. Mendel - Interval Type-2 Fuzzy Logic Systems: Theory and Design, IEEE Trans, on fuzzy systems 8 (5) (2000).
11. Cheng-Yuan Chang - Enhanced digital filter design for active noise control, Ph.D Thesis, Ching Yun University, Taiwan, 7-2000.
12. C. Y. Chang, F. B. Luoh - Enhancement of active noise control using neural-based fihered-X algorithm, Joumal of Sound and Vibration 305 (2007) 348-356.
SUMMARY
AN ACTIVE NOISE CONTROLLER USING TYPE-2 FUZZY NEURAL NETWORK This paper presents a feedback active noise control system using type-2 fiizzy neural network. The new features of the proposed system are: firstly we introduce a saturation compensator for the actuator and secondly we use a type 2 fuzzy neural network to estimate the nonlinearity of the secondary path transfer ftmction. Online dynamic back-propagation learning algorithm based on the error gradient descent method is proposed. The condition of convergence of the proposed algorithm is derived using a discrete Lyapunov fimction. Simulation results show that the proposed method is effective.
Dia chi: Nhdn bdi ngdy 12 thdng 6 ndm 2008 Huynh Van Tuan, Nguyin Hiiu Phuong,
Tradng Dai hgc Khoa hgc tu nhien, DHQG Tp.HCM.
Tran Qudc Cudng,
Trudng Dai hgc Tien Giang. "
Duong Hoai Nghia,
Tradng Dai hgc Bach khoa, DHQG Tp.HCM.
22
