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楼主 |
发表于 2011-3-29 13:24:52
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回复 2# debra 5 B+ d+ ]! j% E. q' u$ T" |, Z( d7 f
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6 L! ]. h* r8 @' v %打开指定文件,并对信号进行Pon分析计算# Q% J0 S- `. X
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)
( \- ~* K* y ^. n1 n8 A. N format long;, h# m, S% L6 K; \( W: T
x = x_in';
- C4 X* k* X( h( C) u9 Q& K cpu=cputime;
) p' i! e1 {/ X7 M# E$ Q N=size(x,1);+ p( x, l1 j7 q7 e/ T
%取N/2的整数部分为初始的P0 P D' q3 D# C2 D5 q7 v
P=floor(N/2);1 k& Z" c4 h2 D* d7 ~! i* W
4 t5 c3 ~# ?6 M D- k+ Q$ @ %去直流环节
% p, L* E! b& U& s# f: ^) R0 {! f& K x_Sum = 0;
9 R3 f+ G* ^/ F$ E0 d' N! x for i=1:N. D' K- q; d8 b, K
x_Sum = x_Sum + x(i);
: e9 Z. @8 [5 p, O end 1 o$ K; k/ r' f' f
x_av = x_Sum / N;! |2 [6 n1 v. c: F5 a6 @; ]
if x_av > 10E-105 K. [' O+ B$ W0 e8 A
for i=1:N
( T( I1 b5 |* N) f! v9 l x(i) = x(i) - x_av;
1 c: @/ X( P& j4 F( i; ^, L2 t- D end2 M1 x6 v' m+ E
end
( ]9 Z% L% p7 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%# l+ S' x- j" T* W, `
%滤波环节
, L6 k5 Q$ z5 J( x; j L# f. h0 O %fL=1;
' C: Z* q* M! Z O$ `- g if fL>1: J0 x1 o: \- s9 L% ^. @
for i=fL+1:N
2 \: n* t7 k M- J8 D) \: J x(i-fL)=0;
& m4 c* b9 ]1 x- o for j=1:fL6 T8 ^% W1 b+ C5 t
x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);
E% Q. E9 S4 Q( B1 l# s" y end8 ~! K' M+ s: [ K6 u5 G; Z' Y8 Z
end2 Y) K7 s6 ~1 u8 i
end
% l* H, n2 I4 Y N=N-fL;
+ s9 L0 z7 u) u$ C( } tt=0:1:N-1;
; Z/ r$ q3 r* y$ N* e" j V% E ! O& w3 {6 x8 |7 _+ S/ B
%P要求为偶数& I+ y3 Q1 O+ ~ c& o0 t6 c5 E
if mod(P, 2) ~= 0* ~$ c8 ~+ v* N* [
P = P - 1;
" M0 b" ~7 n& r; ?3 `+ a, W7 F4 e end: h4 _5 [3 q8 A
. \) L X8 q$ ^ P1=P;
: y6 I/ p8 o! k1 W6 e) Z if mod(P, 2) == 0
6 ]; }1 P, K* d, x! n! S9 w6 d4 r % Generate R,生成样本矩阵, w9 d6 }; N* ` i$ d0 S9 I3 c
for i=1:P1
" j" Z2 d5 g4 h3 h, m1 a. { for j=1:P1+1
* x* K. G9 h4 C. o1 W2 H3 g ss=0;7 ]5 w% \7 M" T: d. z5 c
for k=P1:N-1$ x+ `, K0 m% F- h' J6 @3 L: ~
%前向预测误差- |$ j- n7 r5 A; O4 T
ss=ss+x(k+2-j,1)*x(k+1-i,1);
, F( K1 x6 t/ s+ l: o %后向预测误差% L, j/ K' b+ ~2 ~
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
6 s1 [" {3 C+ h/ E %同时考虑双向误差
5 V$ }4 S J2 | %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
0 m z& _* i7 @; J2 q/ ^ end _- U! x' @$ V5 g! n* O1 f
R(i,j)=ss;
% e1 m1 o6 h0 N' L$ i, A# M end# u6 a2 |- ]+ B
end
& Q, U3 X9 t, w$ b- F- r( J/ m: I % divide R into R1 and R2, and get A; R1*A=R2;
5 Y( L8 [+ X' ^$ d6 l for i=1:P
0 k8 a, D+ j7 Z8 G7 V# \: Y4 x for j=1:P
# P% B1 t8 y2 a+ s R1(i,j)=R(i,j+1);
4 P# w/ _: I1 b- V+ e end
z+ U$ [* s, j m! E end
( B- i; A! P; t. F4 Q for i=1:P* L/ ~( a, s& {9 t9 s- e
R2(i)=R(i,1);& K7 O" y8 h$ c) T8 U( t; Q M
end
3 X% O+ E( ~0 z- V$ D# X$ ?( L
; I5 {7 h% p. b0 u" H %添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 w; k# [* k8 X; w/ d( {6 K %首先进行SVD分解! m* E) g/ l9 g
[u,s,v]=svd(R1);7 S" K5 p8 d& R5 [7 l
%根据奇异值确定实际的阶数M
; a- T: w1 w8 x4 n M=0;" r% V6 g2 |$ [' m7 P) |
%计算全部奇异值的均方和
0 G0 B0 `, F d9 F6 C# @- v Sum_SVD=0;
" j9 m" }6 k1 K$ Q for i=1:P) K% ]' F* h' c( G# Q
Sum_SVD = Sum_SVD+s(i,i)^2;) |4 X- @3 O! U ^- M! V) o2 g! o- K) w
end# q, q% P* e$ t9 D/ [/ ]! V
cur_sum = 0;: N/ ?- l3 G$ j' E5 Y. P
i=1;4 [* K. u! w' F! p3 t$ [
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P
# m1 p+ v6 m7 w: |1 s0 D) n cur_sum = cur_sum + s(i,i)^2;
/ }# d/ t0 z) m! m% M M = M + 1;. S; O) Y9 x% Y0 \% [9 N4 }
i = i + 1;4 P8 L `3 \- S8 k8 b3 n$ G9 N- l
end0 @0 t' H; c5 x4 n: p
%输出预测的阶数M
/ s( k! ~" c7 f$ y$ o( b M; N' a# F: t. C. T
%生成Sp矩阵! P8 }: [' H/ l( W5 F0 d6 R3 R
Sp=zeros(M+1, M+1);
7 y: A6 l! m, }9 M- r for j=1:M & |; G% u3 i: I6 K, D- r
for i=1:(P-1)-M+12 w9 Y/ \3 g1 O' N0 U0 ^
Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';8 _1 ^0 R9 t. P. M/ C* t9 o: y
end
/ f0 F( U8 N5 }2 b6 e- y) M# Z" { end% p# i/ Y5 g3 K# g$ ` _
: m& G& x% z: p8 V
%根据公式生成最佳最小二乘解
. T+ Y" t. T8 ` Sp_inv=inv(Sp);8 c n2 j8 V7 B) i. Q$ Y8 r! y
if isinf(Sp_inv(1,1)) == 1
$ d7 Q- W) d3 M1 R+ Q3 P5 A, Z Sp_inv = pinv(Sp);. b9 |. {' K: N$ e6 R; y
end+ \4 H6 g3 H& v& v5 o0 M9 R
' [: t( k! n4 a% W9 B. n a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
( r7 N# b9 X$ Y w P = M;
; ?. d2 s/ y9 S( h! a; B2 s/ R %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6 H3 ~& f- n8 J! ^9 [ P/ U+ G4 w. x % Get Zi
$ h* m7 y: t2 J! b- M cof_SVD(1)=1;
' z: C, g2 [% H7 ~* j2 S for i=1:M
4 x7 r6 E% z, V1 s7 g7 A cof_SVD(i+1)=a_SVD(i);
; z- I$ |0 E- | end
$ u7 Y; Q6 A2 Z- p0 c0 f Z=roots(cof_SVD);
4 b, @# x7 P* f. o: I
& F. ^& O! Q& [& ?9 X % Get y,y should be very close to x
9 c6 F1 F R. J F/ P! ?# @ for i=1:P
# ^$ s/ w- o0 P$ { ~1 M! q y(i)=x(i);, T) I$ F: t. [
end8 b# ] I$ |) D: p6 P& q- Q
9 u$ _( C9 J* W" g; c for i=P+1:N& R3 \( `7 h* L9 Q: x* ~2 M
y(i)=0;
- S+ r) |* J$ ~( `4 o. V/ M- j end1 _8 C3 i" s5 X( ~" g4 R9 ]& o8 C
for i=P+1:N: s7 @' b. {& d5 n& {, q" `
for j=1:P0 `9 t7 c: [- b
y(i)=y(i)-a_SVD(j)*x(i-j);; |; j$ T' ~. ^# N% H; ?, q* r! O- T
end
4 d+ M% \1 _7 k8 A end- T5 L5 k+ k6 d
! S5 m# k. X6 k/ [( ?9 R: x6 p % Get B
) f. A( L4 i* n; ~+ d for i=1:N
0 y- i% u3 s5 i for j=1:P2 a# m' q4 J6 f( `, u T
Fy(i,j)=Z(j)^(i-1);. Y' c' O7 E# Z3 }
end3 K$ [3 z( {: Q3 @8 Y
end
; H+ T: ?, t' i- M! W Fz=Fy';8 O" f* t+ |$ F _5 t% ]! R: }' k
FH=Fy'*Fy;
4 n7 Q3 o) O8 I! ` Fn=inv(FH);$ c- S5 t/ v6 s |* |. H) S
B = inv(Fy'*Fy)*Fy'*y';* J) G6 Q/ A+ L6 t* \5 J6 s5 E
Q9 w! M* E/ M$ \( l% c( O % Calculate Amplitude, Phasor, Frequency and damp
" v# m- E' _- d) M9 i! x for i=1:P
7 \: I2 y/ _8 x& q+ v6 Z Amp(i)=abs(B(i));
) R9 s3 ^# I5 i3 c" q Pha(i)=atan(imag(B(i))/real(B(i)));
8 o) s( H. U2 ^: q( w3 U; c- f$ }( t Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);' [& M) Z% W8 ?8 ^
damp(i)=log(abs(Z(i)))/dt;( R" K. X7 o$ r
end
?. M+ \& }# q0 y& w9 ? %调试用的代码
6 [" N4 h w5 c; ~1 s4 Q! n3 ]2 d/ Z if isnan(Amp(1)) == 19 n) ^3 y; R% O) [; I/ r
error('幅值的求解出现错误!');
7 ~$ B: a: g# H, ]% x. X end
* A* A/ t+ _/ p2 H' z3 Z / l* M/ W F. W& p' t* B
% Get xc,verify if xc is nearly equal to x
0 T+ _) z, d$ l) M; j for i=1:P( R, {+ k w( e8 ?
if(real(B(i))>=0.0)
# r: q; R: o7 K/ a) F bth(i)=Pha(i);& l% r N5 q+ {- }) A% K
else4 T6 ~' {( o! w# V' r8 q5 p4 `3 V
bth(i)=pi+Pha(i);! Z: a; {' k1 I9 S( z6 q
end$ a/ L5 K) B. Q( ~
end
% P6 p" P6 t# P$ A# C1 C! G# ~ %对Pha重新幅值) u% S6 \( N6 ]" I8 W J" a
for i=1:P
7 z$ x) v, X C8 L% v if Pha(i) < 0) {5 L9 U& J; G: v, a/ X) G8 s
Pha(i) = Pha(i) + 2*pi;
: X. R9 C+ i. F$ v$ G- p end- R; f, n9 Y3 S4 {1 G1 c
end
% A2 p4 V0 v# B6 C2 a # e2 K4 y Z+ n, V( D1 G
for i=1:N2 c! S8 ?; ^3 s+ p
xc(i)=0.0;
5 W1 T) V& k P for j=1:P
. M7 r5 S d. H0 H7 K& } xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));
8 G3 R' m. L+ g) \9 Q# G4 { end! K( b; a# C. K3 D$ Q( D
end# w: B# d3 [( x! ~( I9 L
% if showfigure == 1
G; Y7 a9 z( V7 Q3 `2 R) v% %显示特征根的位置& F% m3 F. t' j
% figure;" x, E$ `" b0 s8 j( o! w6 B
% plot(damp, 2*pi*Fre, 'r*');
C l5 a7 P' |: G3 y0 i' V% end, {. y2 Y3 S* R0 E
; W! V9 M4 x2 O: f. o7 L xj=xc';
7 p8 V" W8 a8 }( c# B er=0;
# n) y( B2 \4 T all = 0;
/ Z/ ?+ e1 N! P1 {$ k for i=1:N
3 c" {* {6 i' s1 N, h+ I er=er+(x(i)-xc(i))^2;
2 F) B2 y) P. M4 L2 \, `+ T9 I all = all+x(i)^2;
1 O( R3 ^' p7 { ?" ~8 S$ ^ end
( Z0 y# {1 G" y SNR=-20*log(sqrt(er/all));" |& S& A6 T3 q( L) Y
- M- E( D8 P1 x
% Calculate Prony spectrum- @/ G/ r- O( k$ X% B, y
%频谱的取值范围为0-5Hz
% q. m1 G& O' j, K1 Y+ k* o f=0:0.01:4.99;
! a- J9 Y& m; { for j=1:size(f,2)0 ^& ?, |! ~+ T
sptr(j)=0;
* u3 H0 `+ X& r# E sptr1(j)=0;
6 V" q$ V! X$ ^0 a3 i- \$ g1 f sptr2(j)=0;- G/ ^- p2 ]. j5 V" r$ h6 z* R; ~
angl(j)=0;
: p9 ~6 O- c2 M tmpangle = 0;( w1 n! i5 M) o" S: Y0 T1 z ~ i% ^& i
for k=1:P I3 f3 t9 ?6 h$ D1 Y- F
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));7 s" S: r4 d& t3 O {; w2 k* \
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));0 O2 D5 f# A W. k
end
7 @/ ]4 b$ @4 d" m( E sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);7 n* ~, z& L3 }( {- Y
tmpangle = atan2(sptr1(j),sptr2(j));
; k/ g) B6 g3 d8 [) l angl(j) = tmpangle*360/pi;" |5 _: X3 V; o+ R/ @+ g* _
end( e1 D* ^$ t9 @$ l+ S# K
%对幅频响应进行归一化,并且寻找主导频率模式
3 K6 H4 O! H' O( H %寻找sptr的最大值
u6 ^# f4 X/ h) z max_sptr=0;
7 k9 g# m3 ?9 ` main_f=0;3 k6 t; o1 l6 a" _
for j=1:size(f,2)
9 x5 e( n( k5 S+ c, D+ A if sptr(j) > max_sptr
% D8 s/ c# S6 `1 {, Q. p max_sptr = sptr(j);9 n( D- E1 `* ]0 \: T* E4 }+ i- X4 u
%主导频率出现在最大幅频响应位置
1 K5 s3 Q9 B# K! d$ D if f(j) ~= 0;% w; Y1 z; P; A) J
main_f = f(j);2 F" V/ [3 b0 x! `- w+ Q
else
, z, f# d4 l6 {% Z" i( X0 { R$ u max_sptr = 0;
$ q: J/ Z4 t1 V; ~# u end3 r3 Y* b, f6 g% p" ^2 F# j
end
1 l. p7 |0 B9 d+ a1 K- W end# u/ u- N4 Q2 u- j- }
main_f;$ |8 c1 s5 O% \+ h/ U
%找出真正计算的频率值4 Z% X' N0 J- W8 V( l8 D' D# u& W# _
f_err = 10;
. m3 [( \+ Q0 l f_main = 0;
. A- j- l2 R; L' R for i=1:size(Amp, 2)# A9 d$ v- a2 f+ W: P
if abs(main_f - Fre(i)) < f_err5 P9 v. l* A$ P& a
f_main = Fre(i);
5 M% @1 {" l$ z5 G8 u damp_main = damp(i);; B C6 S0 W6 Q6 x
f_err = abs(main_f - Fre(i)); [' D: W( M7 u9 h
end: c- P7 {) e$ ~- c/ S# `( u- C
end
) k* S* z K, ?1 y5 ] main_f = f_main;3 x1 u4 H; U2 f! \9 l5 p
main_damp = damp_main;; O' z4 N f- D5 V1 \
%进行归一化
6 o% U O4 v1 n# u* A9 o for j=1:size(f,2), t4 n# G; v p6 ]+ M/ ~
sptr(j)=sptr(j)/max_sptr;
& k! ^+ _( Y6 t$ j$ v Amp_Response(j) = sptr(j);4 K1 z7 z/ G9 n5 b8 @- W
end5 @: N2 c6 l/ S2 K
; s; |6 d% A- V3 q
for i=1:size(f,2)
2 \* D; Y: J1 [) w if angl(i) > 0+ ]* q3 T4 l; r/ r9 f( L2 R
angl(i)=angl(i)-360;* t* N5 `# Q& x1 s- x+ Z) D3 X$ K
end: s) X' i/ Z/ O" r& P% ?
end
2 N9 o7 ?" t( s9 d$ }/ q
K: H/ g( \2 W) {3 e if showfigure == 1
4 u' d/ {3 {9 b1 R$ R; w! @9 j3 j %在一个图上显示时域拟和曲线和Prony频谱分布$ s$ K& Z# y7 t4 C6 Y! S
figure;7 v0 h5 L2 ^6 \& s% P2 b
subplot(2,1,1);
: D1 E+ I K% a" l8 M %plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');& b, d% W7 D+ A& M
plot(tt,x(1:N),'r', tt,xc, '*b');
0 k% `0 A, `+ L& w: z) R subplot(2,1,2);$ U0 p- x9 I% t
plot(f,sptr);
& A) c" [( ]* D% Q* Z# H %subplot(2,2,3);4 m3 P# ^2 g4 F* I ?
%plot(f,sptr);
2 h) i# @; O: v3 b" M2 _ %subplot(2,2,4);
' ^ b6 Q0 O. h+ a; M2 p9 S' v %plot(f,angl);% C3 x/ Z0 X$ I$ k% [" u
end6 U# V' a2 ?8 A4 L) G9 _1 V
7 j6 u- n) O* N* z" Y2 m
cpu=cputime-cpu;* j$ J- Z& X* P; u
format short;
& h6 A% g# Q. e/ @/ r; N) {/ | Z end |
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