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发表于 2011-3-29 13:24:52
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回复 2# debra - V) X3 q4 z0 k) S9 p
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; a& ?8 p1 k1 v) V; e %打开指定文件,并对信号进行Pon分析计算0 g) D4 k; ?* [/ X8 S
function [M, Amp, Fre, damp, Pha, main_f, main_damp, x, xc, y, Amp_Response, er, all, N, dt]=x_svdprony(x_in, dt, fL, showfigure): b6 V2 M! M' e
format long;
# V0 y0 I9 ?! x3 B) V* U x = x_in';/ Y. P- h# I& b- R4 S
cpu=cputime;! [7 d- d6 g3 V3 Q
N=size(x,1);
8 y0 K: S! ^/ W4 m; D% W b %取N/2的整数部分为初始的P
3 E- T; A9 G6 X6 v3 l; R: I P=floor(N/2);: G: \" M5 z$ e* {0 e$ m# K
" L: G7 a9 b6 r7 ~/ @7 B1 D
%去直流环节
: q1 g+ j7 i) h* n! p x_Sum = 0;' u: W) _, f( v4 e/ A; Z3 C9 n/ S
for i=1:N
, {% e, Y% |; C/ F. A# l x_Sum = x_Sum + x(i);" e# X: A; }' E0 i* F/ N
end
! U9 \+ K" Z% k, y* u x_av = x_Sum / N;. I0 Z" G+ m5 T5 S' M2 X% s
if x_av > 10E-109 F* ]& T; T: k9 ^( r( o7 Y
for i=1:N, G/ w/ L8 b# U2 w. ?: S4 c: B
x(i) = x(i) - x_av;5 u* E+ w1 i1 ~' A' ?. h1 n
end- B% J7 j7 X- ^- d5 C) U
end7 q( P) {& D) M4 W; `0 \! }9 w0 f
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! @% v; |8 n1 \ g) ^ %滤波环节+ j# J: R. @; K& H
%fL=1;
3 }$ t$ w9 C% b9 X; t5 i/ ? if fL>1
* p0 |7 p5 ]$ {9 j% X b for i=fL+1:N. L. P# `$ M( A: Z t9 f+ h X( u
x(i-fL)=0;
9 ?+ N3 b' p5 ?! }3 `$ [1 [ for j=1:fL
6 p$ N5 t" S1 l- A6 k4 J x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);$ d) @$ |8 q6 K" e+ ?
end
0 X0 r3 A/ ^- c0 O end
) w% _" y& Z- ?! o! z2 z* H: b end q ^ k X, H f/ s
N=N-fL;
5 f& u9 F% \3 b' U1 ? tt=0:1:N-1;" a6 ^9 s1 U# }4 ? c4 i; p
Q7 w1 i! A' Y/ ?. b %P要求为偶数! M0 g9 N5 {: {1 Z, M( D& }
if mod(P, 2) ~= 0
. Y: r8 H$ I7 l1 ?% i( r; ^) c P = P - 1;9 H2 P* ]+ [: b( _0 N+ M( S
end
/ `7 S# X# l1 R, ^0 U 7 v# p- _! G" g
P1=P;- u Y6 B- W- g. S
if mod(P, 2) == 0% _- Y7 z! _, w* H' c# g/ I
% Generate R,生成样本矩阵( m+ X1 d( x e% k2 ?5 l; @- W
for i=1:P1% w+ E7 m0 y4 e$ X! D
for j=1:P1+1
+ S) n q" C. u I2 J" z ss=0;: z* G7 C0 z- \8 w/ c8 z
for k=P1:N-1% z N; L& S8 ]6 _# Y& }
%前向预测误差
" `$ w' H8 z0 C ss=ss+x(k+2-j,1)*x(k+1-i,1);
4 e& q/ j" V# d1 s8 `/ H3 {9 U %后向预测误差" A4 } l& J/ W0 F
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);: I0 D% \& p i+ b1 E
%同时考虑双向误差
6 l! u3 p D* u2 }$ Q# A1 S5 C %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j); $ Y& A* w# m) H; o* c
end 1 D* ~3 q% Z$ x/ r
R(i,j)=ss;; P; ]' H0 T4 j' e: [5 u
end
/ D% Z1 F# {0 x& I end2 q( i& f' g4 p" ]
% divide R into R1 and R2, and get A; R1*A=R2;
# T, D% V+ Z9 E+ z) K# K# T for i=1:P) Y* `( A8 q- z( K
for j=1:P: p! ^; Q0 T+ {' A9 Z4 S
R1(i,j)=R(i,j+1);5 Z6 q; B6 m" S
end
+ ^# p# X( N# b' a end, Z8 ^# ?1 P& \: ^
for i=1:P
$ k# T" @; F0 ?0 D R2(i)=R(i,1);
* m5 k! }2 A* \2 y3 W& W( i8 }, r end+ O6 o6 e0 A; a0 h! Y9 z
3 [3 y# \* O4 `
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%/ } j( ~. @8 s; u" V# J
%首先进行SVD分解
6 c+ K' T2 a @, [) h [u,s,v]=svd(R1);
6 m. }4 T; R7 O. U0 e4 s* k( U %根据奇异值确定实际的阶数M+ K$ C( s0 D1 n5 W6 L' h6 o0 T
M=0;. A% f$ J# {* i; z5 S
%计算全部奇异值的均方和- Z* f# G4 {; z% l2 o' n
Sum_SVD=0;
2 H/ t, m2 ^, O for i=1:P
4 q4 i/ L" a1 Y# p! @4 ]" ` Sum_SVD = Sum_SVD+s(i,i)^2;( ^! }0 r d& y' k" \& D
end1 S" g y1 F/ h6 l
cur_sum = 0;
# @/ V5 B* O, o J i=1;" m5 P% J* B- h/ X& H$ v5 v
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P, F Q) ` M5 Q, x p
cur_sum = cur_sum + s(i,i)^2;# K2 D$ Z0 T' h& x5 g; v2 R. A: n9 ~
M = M + 1;% S) Q2 @ b w( U
i = i + 1;
; @$ V- B( L" E! c end5 H0 p% Y6 A3 c; h' n! s
%输出预测的阶数M# \/ P0 Q3 z! v8 O" [5 B- L. L
M;
! Q0 p2 I% n- B& c% V' o %生成Sp矩阵" ^& K' u j0 p7 L. j
Sp=zeros(M+1, M+1);6 {5 h/ U, \% K2 z
for j=1:M " ^) G4 ^3 P. ^/ s% b/ O
for i=1:(P-1)-M+1
( {/ r* C5 ]! @$ v i& _+ P Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';
! a$ }5 `! x f- y3 q8 T end8 j7 s/ M* P9 b) L" W/ B5 B
end8 ~3 J" V. q% M" f9 D, C
% R A! y$ l+ F9 G6 d
%根据公式生成最佳最小二乘解
+ s. C7 u' S/ J) u$ l7 { Sp_inv=inv(Sp);
* ?9 S* {( K9 B2 W/ J# `# y2 H9 k if isinf(Sp_inv(1,1)) == 16 G" F. c2 v; V5 ]
Sp_inv = pinv(Sp);; Q! O0 a# a3 Z" d. T" I7 ` Z
end
: B7 |* v1 t9 @ 1 @, ]& j: d; o1 b% S8 i% q+ }7 n
a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);$ C7 B) w6 _" L _8 K
P = M; W! w3 Y i. {, U8 }6 g
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
( U e$ X$ ^! i ^ % Get Zi
5 |% M6 y: a0 |% ^0 N cof_SVD(1)=1;
( u- F2 l6 L. {. i; A3 b for i=1:M9 \2 S! l6 V6 }, Q% B0 A$ H; k
cof_SVD(i+1)=a_SVD(i);$ c8 a4 P, s! f& f" t
end! J4 m2 W0 d! {6 }9 C9 l! u5 y
Z=roots(cof_SVD);
/ t. C1 \# b7 D2 S }8 L 4 e6 R0 q; N6 E% ^1 O- {9 T
% Get y,y should be very close to x
/ f5 D: B( f/ _5 X5 Y# z, e. s for i=1:P$ r9 R5 A* W8 W
y(i)=x(i);
$ T/ a( d9 E7 }( |0 `& ]' j P end
7 \5 k1 N; O1 c8 G& A' [3 P P 3 D6 m( z/ N: o9 z( J; O& n$ y$ D
for i=P+1:N6 n6 ? C; x( `# q
y(i)=0;
; l/ C/ V0 `# v2 B; f end. Z! ?' U5 a$ r2 l- W
for i=P+1:N
: J7 L& h# k3 c& h5 L, u for j=1:P
2 b1 W) {- h3 z4 u+ k, a, B y(i)=y(i)-a_SVD(j)*x(i-j);% P, E% K1 B/ P Z1 L( D! N3 R* y
end
: k5 M# P: M. N# Z; N' M end" ^$ C Q# D9 E6 p
: p Z7 N0 o1 i7 @$ D % Get B0 g0 e/ M! F# H2 O& E
for i=1:N4 y; Y, y+ Y+ r. e9 F& {& Z
for j=1:P: r, X6 ^ @: b$ H7 w+ F
Fy(i,j)=Z(j)^(i-1);& ^# H% }9 {5 E
end
+ H: q: w: h0 Q end
' ~0 Y2 \$ L$ l4 h; {, X0 w Fz=Fy';
3 V6 E( D- x& @$ m# ^ FH=Fy'*Fy;: _; P) ^' [: g6 w
Fn=inv(FH);+ _, h- c7 U/ @. J; N; e6 | C
B = inv(Fy'*Fy)*Fy'*y';$ z$ h6 c1 b3 P) J. E8 k
! _9 j4 Y5 W& n4 {0 M0 Q5 J % Calculate Amplitude, Phasor, Frequency and damp
0 n/ L6 I$ h; H0 n7 v for i=1:P
+ ^& R2 U% n% H+ t$ V: |4 y, H" s Amp(i)=abs(B(i));) @' i5 q) G/ T' s3 E" f
Pha(i)=atan(imag(B(i))/real(B(i)));" M7 k' g5 p: |3 B. i5 s
Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);
5 ^3 m0 h4 ~4 I- C; L! M% ^; d damp(i)=log(abs(Z(i)))/dt;9 q0 |; A4 D/ P4 t! _5 y
end
y' j* m3 G+ D %调试用的代码
- C7 V) L2 v. O9 V0 [) V8 `" m. I if isnan(Amp(1)) == 1
$ l! ]* p0 Q* l! X2 x4 u# b' R error('幅值的求解出现错误!');
8 e5 D( Q$ |9 H# x end
" r9 y( x5 l2 N9 J/ M3 i6 U8 z 2 i* c, T1 x' }, H; S# j
% Get xc,verify if xc is nearly equal to x
+ k- V. X* m! ]/ u: E7 | for i=1:P w, d8 e3 w$ o! r* B7 a
if(real(B(i))>=0.0)
; S$ W) W0 P/ W/ c9 O" T bth(i)=Pha(i);9 T1 B/ F% j( Q
else
; U" Y. k I5 c! H6 n9 } bth(i)=pi+Pha(i);
( M1 o& j: g2 f: l& H1 V6 e, Z end3 O9 o: L' `; F( P$ ~
end$ r" M1 q- f- f. ]/ j/ z
%对Pha重新幅值
$ f$ b4 V; w& q' i& c: C% } for i=1:P8 I# g; [/ l. A
if Pha(i) < 0, {3 Q _+ A8 ]' J& [, P: W: `8 Z
Pha(i) = Pha(i) + 2*pi;
" s9 U; O% t+ q+ `( e# @ end
; p( v0 S; C; e: Z end; `! X' {" O6 v0 T. l+ N
0 [. I: x5 Y3 w* q for i=1:N
( j& l0 Z+ j3 P. k6 w# b7 I" s xc(i)=0.0;, [/ R7 v/ W/ l1 V# l
for j=1:P- S, d' P4 H8 S% T- y0 |
xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));: n' J/ O3 K2 o: `8 B2 {; s
end
X! X: [3 v0 Y+ r: p end5 w3 K/ k5 _3 d
% if showfigure == 1
0 ~# C$ l/ E% _' c3 Y, V- ^% %显示特征根的位置 W; I5 n' Z5 |3 O; y! G
% figure;
- Y- w, _1 {& i/ c8 J% plot(damp, 2*pi*Fre, 'r*');
) T2 b1 X4 c3 g: P2 |& N% end$ u, ~5 |/ b6 {' V
8 p# m- t9 Q4 k3 T) T! H9 \ xj=xc';) U* t% _) t$ X/ d4 W1 M
er=0;: c0 e6 {& W8 J& {/ z4 ~
all = 0; h2 z. |+ D& l6 W: m y$ {1 w" F9 z
for i=1:N 6 Y& v) c; ]+ W. j+ q, L, Y. B8 F
er=er+(x(i)-xc(i))^2;7 o( {8 S" _8 m
all = all+x(i)^2;4 }1 q9 W7 @" B' c# K
end
0 H9 t7 U: C2 H5 n SNR=-20*log(sqrt(er/all));% Z7 ]" O. \/ ?
* V, p0 L* v" B: s4 Q U1 d' B % Calculate Prony spectrum7 o' q x7 k+ w2 d- i- h
%频谱的取值范围为0-5Hz
7 S7 u' x' v& U/ [ f=0:0.01:4.99;
8 u8 j% q5 }7 h M9 i* }$ Z9 F) U for j=1:size(f,2)
7 w+ C4 B% C% E0 P* y) a. T1 ?/ k$ w sptr(j)=0; E; E! Z3 a7 j5 E# r3 Q4 Y+ W
sptr1(j)=0;! g* b$ T2 [7 G1 R( ?
sptr2(j)=0;0 f8 K+ `; E3 [: R
angl(j)=0;5 A& d, |9 E' `6 M6 P n4 I# |
tmpangle = 0;
. e `" s0 N" b( ~. q& a7 ` for k=1:P) d" q$ ? x# c" o/ t
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));' B9 s- F* r$ W
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
/ F& a D3 g$ t3 q7 r end
" K2 S" L! A- L; i! | sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);, {: E5 k7 F2 r. o
tmpangle = atan2(sptr1(j),sptr2(j));
4 j+ B# }4 j$ O$ V4 z+ n angl(j) = tmpangle*360/pi;
. i* l4 L( }9 T/ Z end
9 J. t2 f8 \9 z( [$ d" x& i7 o$ s %对幅频响应进行归一化,并且寻找主导频率模式: O6 I) o+ D, r( E
%寻找sptr的最大值
# V: H& ?0 J4 n; o max_sptr=0;
, @1 S) t. }) `; n3 x* h main_f=0;
7 Q* i9 v. A; j& |& z for j=1:size(f,2)
* {% I; ~" Q4 ]; G* l if sptr(j) > max_sptr
1 z9 T/ V8 ~/ Y: c5 v( m max_sptr = sptr(j);
, B, n1 t* `1 Q$ s %主导频率出现在最大幅频响应位置5 M6 [$ r& ^. }/ F: M- t1 H0 U3 B. S
if f(j) ~= 0;1 d" b- j; p& K. |
main_f = f(j);8 Y. Q, J; t8 [
else
3 A2 m- ]& ]( E1 t) U max_sptr = 0;& X* u5 k: v" ^7 x8 T. w. R+ C
end
, C! E4 ]4 o9 U9 J1 H: L+ G( u end
8 d2 C4 ]9 F9 K1 S7 ]2 m) a end
. q. Y" q* G% p8 E main_f;
! U1 S @( m5 A o, [ %找出真正计算的频率值
6 `5 T+ N* S1 [+ h, i$ D" _$ q f_err = 10;
+ z* D5 w# i5 M9 Z6 D, L& h$ ` f_main = 0;$ {+ @8 E& N/ p* g4 j
for i=1:size(Amp, 2). z+ i: C- O# A" P. W/ ~2 a
if abs(main_f - Fre(i)) < f_err( W- ^% H7 D# [
f_main = Fre(i);
k2 B5 k6 N* H7 e. ?7 b) n" C damp_main = damp(i);2 s# j1 u/ t$ y7 J
f_err = abs(main_f - Fre(i));
: N$ l" G6 S/ h# l5 G v* Z end
" |! J/ P6 P* e, n$ A8 F5 H% i end
' W4 M5 Z% J, o( P) k! ~ main_f = f_main;. b9 Z& _' ^7 | h1 Q
main_damp = damp_main;
, j# y* z: o4 N) ]! Q %进行归一化
/ e- T) R) q. \: q! [* m3 T for j=1:size(f,2)/ X! W, w. B0 r. G. x5 O+ c4 D1 Z
sptr(j)=sptr(j)/max_sptr;0 u: s2 ?, o7 v- p7 X5 {3 m: H
Amp_Response(j) = sptr(j);
* w& g( L7 }# ~, s0 d+ @6 T end' c4 x! o% A: y1 V0 _0 E1 ]4 b3 @' J
" a) J4 e- Y/ I5 n for i=1:size(f,2)
_0 k6 J+ @/ J* P% n$ v: O& M/ d if angl(i) > 0
0 k/ ` s) U2 L" c0 Z! @ angl(i)=angl(i)-360;8 h7 p2 ~0 m( t+ V, U" s
end. d w3 ?1 d a: M4 N
end0 t: @# l* M1 |
- w' y; }2 F) x l* p/ t" f if showfigure == 1( N# {+ Z; F4 |# ?' P8 Z2 T/ e" ^! X. T
%在一个图上显示时域拟和曲线和Prony频谱分布
3 \9 J) e$ n3 j1 ` figure;
; [4 O7 p$ X) h g, K subplot(2,1,1);
3 C, Y' z F6 a( X' ? %plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b'); v6 U. I7 P2 r, j) K- m
plot(tt,x(1:N),'r', tt,xc, '*b');
$ t) T% t, f& e$ ?0 F% `" u/ j subplot(2,1,2);
8 x' u" u3 M( l* V plot(f,sptr);# B7 ?: V0 j- M9 C6 a# \6 e: i
%subplot(2,2,3);. o8 ~$ b; g B/ H7 T$ Y K. s& [( T
%plot(f,sptr);/ J+ X7 }% e7 W8 v: ~
%subplot(2,2,4);$ k7 N2 v O$ Z' Y
%plot(f,angl);) h2 @* c H# W
end4 K: t" C8 R7 X
1 Z' g4 x" M4 i m: b: J# v
cpu=cputime-cpu;2 c0 V$ ^; v5 A8 v
format short;
1 H! J1 e3 y6 C( l" z0 Q6 S4 q end |
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