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发表于 2011-3-29 13:24:52
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回复 2# debra 9 [9 F3 i' R. p3 r
& p F/ S, f/ E" E
6 {0 u; G3 d# ~: k" L* W/ ~ %打开指定文件,并对信号进行Pon分析计算
/ P3 X3 b6 t, `8 w0 F- Rfunction [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)
, }: S' G1 L; n$ ^5 @1 w format long;
# n5 r% l6 q" c6 m% d x = x_in';" g" I9 O+ E. T" ^9 R% A% X
cpu=cputime;
$ D& j" L- B; r; r N=size(x,1);+ d8 x3 w9 P# E
%取N/2的整数部分为初始的P
4 X# U& I2 r0 P7 R7 b8 I' R P=floor(N/2);/ @9 z4 |4 |0 R P4 ~
+ q7 ]8 d$ f. D; @5 q9 V
%去直流环节1 d% d5 Q4 {; U0 X. l, d* @
x_Sum = 0;8 W! ~9 o* H& ^- W2 e2 m
for i=1:N
0 L. r6 D, M* f7 k! t- S5 C x_Sum = x_Sum + x(i);: t9 C( q8 E$ `
end
2 L; Z3 o* y) e x_av = x_Sum / N;
7 T" c y& X/ g if x_av > 10E-10
}' O8 V" x1 U# m# F for i=1:N
. I# N2 M( W6 A! L9 `8 ~- b x(i) = x(i) - x_av;
+ P' `: b5 y5 c end
( d9 _3 @, R$ K: t3 D3 { end- i3 Z" m$ q6 ]' b; F, ?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%) @. R/ h P7 ~
%滤波环节
0 s+ s" B& R/ t1 @/ l2 j %fL=1; r/ c+ s# Y, c- u0 s+ D
if fL>1
5 r( o7 w% x1 }5 B7 K3 z8 A for i=fL+1:N
! j8 d- j% u+ { x(i-fL)=0;$ m$ s& i% R. l' R9 E0 s" G
for j=1:fL% u- H# G9 b1 k5 I) |+ k
x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);
( H: s; o( C7 Y end
/ z% B8 v7 c W- e; c end& n, _: [" ]; _! J0 ^, r0 ~1 M$ g
end) H& P: O! S) _& _# @. g) y$ Z% ?
N=N-fL;& a$ a' N( g1 w3 w6 S8 O+ ]6 j' i+ Y
tt=0:1:N-1;
% I2 |5 v3 {" W: f
: F# p! B1 @) L6 i- l& z %P要求为偶数$ V5 g' h8 a( n& k( o# ]- i
if mod(P, 2) ~= 0
9 {0 ^2 W9 F" K P = P - 1;' C) ~3 g5 N/ u- Q! ^
end2 @$ A9 Y+ b6 B. p3 r
5 [+ L$ s* \) U' v' k' |% `
P1=P;1 d1 U2 A7 [0 O! _1 W
if mod(P, 2) == 07 l$ z: S K; W' K. f
% Generate R,生成样本矩阵
! [, p' g$ V& \ for i=1:P1
' G9 m! ~! g2 W for j=1:P1+12 x" D7 t- E J
ss=0;
1 _% j9 s& g2 O for k=P1:N-12 a3 C! ?0 o; {5 H" n; H/ p ]
%前向预测误差) x, n0 N; O R, c4 c% E! K; k
ss=ss+x(k+2-j,1)*x(k+1-i,1);
3 r! l$ j y2 M4 Z %后向预测误差. s* u- i% u6 T! B2 l
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
$ ~8 q, @: _. A %同时考虑双向误差
$ Y; i5 _- _9 G %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
! |" N: _, x. D. i8 t* H end 2 Z+ E8 a' B1 |& R8 x6 n$ x6 b
R(i,j)=ss;
( V% F/ |, M+ g end
1 i. M' H# H W/ n4 @9 P+ q3 N' _ end
0 P: |) P) n m K+ Q- `% r, R' G % divide R into R1 and R2, and get A; R1*A=R2;
8 G' ]6 Y+ i* B5 y+ Y) |# G6 f* X, i for i=1:P
! H/ V4 d' E& N$ ^: h for j=1:P _4 S$ s1 N/ @5 @" n# c7 U2 d
R1(i,j)=R(i,j+1);+ f, _' Y7 ?2 A2 c: X( d6 ?
end/ i* \; I. e5 B7 v7 |. o6 {
end
* B- d ]7 h/ t- o3 ^/ c, r for i=1:P4 e# H; q3 s" Z m9 |# `
R2(i)=R(i,1);
' A% l: @8 V. K. i7 ~6 k1 E end
7 @" I% S5 ~- E: `: i% V" J& c ( f9 T U% n, w! N# O. l) p
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 j0 I& G7 ~2 j. d( ]) l2 O
%首先进行SVD分解
) C$ Q# k6 U% S' j8 M' x [u,s,v]=svd(R1);! A5 I0 k# d) a R) v" K' a
%根据奇异值确定实际的阶数M
# G. c) q' u* x0 } M=0;: k7 c. W) c" a; v4 P; B4 t0 |
%计算全部奇异值的均方和6 V( r5 ^7 [* C: M% p" q; H
Sum_SVD=0;
z. d8 q, X+ p* y6 \' r for i=1:P1 S% ~7 b; t8 |. M% ]
Sum_SVD = Sum_SVD+s(i,i)^2;! d( B J# E' A* N! k
end- M# M7 a0 l4 C& r! D9 |) ^
cur_sum = 0;
1 u t$ W9 b5 T! @: B, {: C i=1;
) v! D$ G( y9 s% F" d3 @3 C b while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P# [, X4 J3 |; F2 j' t
cur_sum = cur_sum + s(i,i)^2;
3 v- s T6 T1 S! z" A M = M + 1;$ [% P7 p$ U) _, Y' v
i = i + 1;
5 {! u) X1 P) m Z6 k( x end
\! m% p& s- K2 m4 R: Y9 ]' X %输出预测的阶数M* G1 ^( k7 a% r- `
M;. p& V8 @7 X" P; U) f5 g
%生成Sp矩阵9 k0 X* U4 z' b1 v( j3 ^ u+ U
Sp=zeros(M+1, M+1);
# r3 m4 {! t8 j! H for j=1:M ' @2 x" B4 f2 }& d' q9 ^- K
for i=1:(P-1)-M+1
: H3 z6 B- x7 { Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';; f L5 ]$ f9 R" {( }0 p8 K
end7 K* ]$ v0 H/ G" t3 z1 X
end) g0 r' I( q5 T2 A; ^; Z
! L `( s5 `" q& W
%根据公式生成最佳最小二乘解
, X: A5 G% S2 J Sp_inv=inv(Sp);' E. z! K) K5 h3 M
if isinf(Sp_inv(1,1)) == 1
% c2 d2 k' h ~0 z Sp_inv = pinv(Sp);8 z! G T' T X" b
end
4 N, |5 E7 z7 @2 h1 d3 k u+ s3 ~- ^0 m3 d
a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1); A2 |" ?( V$ m' R2 ~
P = M;' Q& @ K/ q l
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0 M% ?1 E) E, {/ I % Get Zi3 R. X4 {9 P5 q3 K5 H6 K
cof_SVD(1)=1;
5 I8 k1 x+ X) t* U& B for i=1:M
2 S# V2 X' B3 N cof_SVD(i+1)=a_SVD(i);$ x6 r# z6 p( g/ F
end
! u9 l' V* U& s! S$ Y, R8 t Z=roots(cof_SVD);: Z4 q( \0 a0 j( r8 N# y
: d/ v; I2 P- c8 } % Get y,y should be very close to x1 e9 A( V3 v, }1 K: R# @
for i=1:P
! d' q, M5 E) ]/ }' e% o2 p y(i)=x(i);4 k6 \( l% g* g- O2 E0 @! M7 {
end
+ u2 k2 a! z% @7 Z# Z# ]9 ? 9 A# N' v5 M0 }5 d+ v) J3 E
for i=P+1:N; y) m! ^1 B2 |1 T: a a6 ~
y(i)=0;$ H: D" d7 F! R; a- O7 O4 {: ]
end" k3 `) a/ S; }& i/ E0 P
for i=P+1:N6 z/ p- A- O; U* B5 W4 D
for j=1:P& O. ^& e) t& A/ J- t
y(i)=y(i)-a_SVD(j)*x(i-j);; F) J, C7 [& }% X
end
3 z0 r8 [8 m4 g: W$ O end2 F5 t5 b5 o; i% @7 ?/ a C; B" ]1 J/ W
`( @$ W# P0 U" x0 w4 z
% Get B
/ r* Z/ E* j K, r/ M+ O6 i4 z for i=1:N
. H1 y7 V: E+ x3 ?2 s) B8 b. ` for j=1:P
; I8 x: T' r- {3 j( E Fy(i,j)=Z(j)^(i-1);
- R3 B. O4 `3 }6 R2 R8 r8 V) n end
9 u2 Q$ _& o; L& B* N% F+ @ end" G$ y$ `, H. F% ~ o5 j; X i% `
Fz=Fy';
* n7 J2 N4 \+ K* I' Q" V$ _ FH=Fy'*Fy;2 T& T' L b' _5 C- m
Fn=inv(FH);
% p- J5 R$ ~+ F# j& k! G0 q B = inv(Fy'*Fy)*Fy'*y';
8 L$ X1 u1 V8 z4 K6 j
* @3 y2 x; a7 Y3 ?1 T- Z % Calculate Amplitude, Phasor, Frequency and damp7 D- E4 U; z1 m& q8 ?
for i=1:P' [- k4 `6 Z, N( ^$ l# m
Amp(i)=abs(B(i));
' o; E3 S) k# c" A Pha(i)=atan(imag(B(i))/real(B(i)));% h0 p: u6 x% D2 ~8 A3 W6 \
Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);
~* a% N5 l* f& o z damp(i)=log(abs(Z(i)))/dt;6 Z% }* T/ f/ T {! `7 s
end
$ Q w0 f) h- ?) d5 s/ Z% x& w %调试用的代码+ E |2 _0 X/ J) m4 k: s, p5 |7 O# l
if isnan(Amp(1)) == 1
. a, O! |: A+ e, K5 W4 v a; g3 T4 z. j error('幅值的求解出现错误!');% ]. j! O) ~4 k8 |. c3 n
end0 k/ t& }/ R1 Y! m( W8 m
{8 e- q% z2 S( c5 z/ e* e$ g* n % Get xc,verify if xc is nearly equal to x% u9 z+ v" B8 V% j* @2 n5 [- y
for i=1:P
$ Z c; J0 M: I8 G$ [9 ~# ? if(real(B(i))>=0.0); W1 ~. W0 \6 I& n, S& Y$ r9 x
bth(i)=Pha(i);
* o, w0 G+ k3 V j else
8 j w: n5 Y1 K; q+ G0 W' l bth(i)=pi+Pha(i);
& H2 H, ~, u4 u+ A; R- } end& R" B$ |2 |7 G$ W0 K1 x4 {$ n
end2 F* d. }( P! x1 n( v( ]
%对Pha重新幅值
) |: B9 A T3 N8 v for i=1:P
! q5 p: Q5 W5 z! \# K2 M4 J if Pha(i) < 0
! d1 u! T) M9 R$ K6 V Pha(i) = Pha(i) + 2*pi;
6 g7 V+ E" s$ b+ I5 Q. L# Q end
, Q: ~& W8 b& Q/ } end
d% ~; {: @* l% t B( a5 B" a& O. O
for i=1:N& Z. @" [ r; p, {
xc(i)=0.0;# P5 b! F) c/ t! Z$ h
for j=1:P
# {7 ?! A, O/ i+ [3 E: w xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));
0 N# g0 u- l+ }/ q5 Q end; V$ ~% G% }3 j$ r5 M2 V+ ]/ b: S
end _) p: W5 y6 N4 f
% if showfigure == 1
2 o9 d4 O6 Q3 s8 J% %显示特征根的位置6 \+ P) |, c; @/ S0 c9 I* m+ j+ I7 Y
% figure;$ f) d0 A- a) @" d7 P% }% i% g! f
% plot(damp, 2*pi*Fre, 'r*');6 f5 q. ~; F/ |) p
% end
6 j3 s8 ]' J2 s- D2 X' n 3 O, s. }9 r3 Z' q- j
xj=xc';
! \! c6 q; I* y- f er=0;6 T9 _! h+ V/ \* L
all = 0;* J2 S! G4 s+ h2 m0 e# p0 _
for i=1:N
* T2 r9 d" z4 w/ \3 J er=er+(x(i)-xc(i))^2;
6 z* x$ P2 v: o, `* @ all = all+x(i)^2;
3 U# A# S, @: ? end
v8 |9 B& [* L" ?1 F; h0 _! m SNR=-20*log(sqrt(er/all));0 j. {. L7 [$ j5 Z T
- c3 b$ ~( N5 ^8 ]! V. z
% Calculate Prony spectrum
2 b1 ~! n3 x7 L, ~ %频谱的取值范围为0-5Hz
: f: {' s) F, q; [% U- W& h5 h" n f=0:0.01:4.99; \1 k0 E" s" s* O8 A
for j=1:size(f,2)
/ p* {, U5 [+ Y% y sptr(j)=0;
; u0 Z% S5 A$ Y7 C; ? sptr1(j)=0;* u/ L+ h5 e" D( _8 N
sptr2(j)=0;
' U9 ~4 b9 {( F, p: T angl(j)=0;7 w" h4 `& c* V1 X" s& R( O
tmpangle = 0;
0 S: K v) y5 c- ] for k=1:P
! b* [( B$ I/ L: J2 F sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));2 r: x& x, T0 j0 D$ m5 g3 _; T2 }
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
: @; i" f$ c0 W! `) }, j end% j& }- X, A$ g$ G$ H. w
sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);
4 }5 n; {2 [% j& m% ^6 d" ]& g tmpangle = atan2(sptr1(j),sptr2(j));1 \4 Z$ x1 o J9 m. h- c# l3 A
angl(j) = tmpangle*360/pi;
( z) m: D4 N- m end
( ~: g) [! ]' X- t %对幅频响应进行归一化,并且寻找主导频率模式% h D" x {2 @5 l- w& U' v4 P
%寻找sptr的最大值5 D2 |* @4 z# @9 o0 z
max_sptr=0;
1 L% c/ h& T- p/ D3 t7 S main_f=0;
/ x. R; ?. W; @2 ~( Z% i! D1 ? for j=1:size(f,2)
# |3 I! `. d k if sptr(j) > max_sptr1 p% y2 C" m$ \
max_sptr = sptr(j);
" W" [8 _$ s5 V3 X1 h6 N9 a% U# h/ Z/ J %主导频率出现在最大幅频响应位置( l- x8 ]- x4 F, Q) F" r+ B2 }
if f(j) ~= 0;# ^. @) k' s1 O7 r; ^9 y2 B
main_f = f(j);1 }) i# \- G8 E) t* n: o" l" w8 r
else3 d1 K7 j) R" O" B. ?
max_sptr = 0; f6 n2 g) Q6 [. b2 C$ D$ y$ `
end; t& g0 j0 Y9 R- n G
end2 A- P0 }1 T- _6 t
end
) S* S" B E) O8 R7 b6 L3 n9 [ main_f;
$ O7 k1 l9 P4 Q$ n %找出真正计算的频率值/ S3 \6 n8 @7 y$ i3 c/ w% s! G
f_err = 10;1 Q" Y$ [5 M. w" \
f_main = 0;: ~( C* K% A0 |2 U+ m X1 W4 R
for i=1:size(Amp, 2)
. g; G8 O: @6 w: F5 ~1 b' x2 E if abs(main_f - Fre(i)) < f_err
U# O( \; }3 n" ?! d f_main = Fre(i);
% W& Z2 k, v1 g, m6 S0 O damp_main = damp(i);
; z0 B+ F7 G! n/ Y7 D f_err = abs(main_f - Fre(i));. L2 J/ I; I1 Z
end* W6 [, [; V, Z* U5 v) e* g% e0 L* w
end H: W. l" K* E0 i5 o6 Q
main_f = f_main;* q$ w, m6 c9 t: @# l! U3 m
main_damp = damp_main;
" ]7 f: I- a. G. `5 ~* m %进行归一化) L' {8 w; X" |- H
for j=1:size(f,2)- T+ c. R0 F, u5 x
sptr(j)=sptr(j)/max_sptr;
+ P# r0 B+ ]) C3 B% i Amp_Response(j) = sptr(j);
, p# Z0 |' w% k4 t% I end
0 a! w; i i8 G7 j# w
; C* t2 q/ L1 j) E: a for i=1:size(f,2)
5 @; n+ ] T, m* P if angl(i) > 03 {9 ~9 y! w2 `, d, M' B$ Y
angl(i)=angl(i)-360;
; g8 ~1 o9 _! m) V3 L8 _ end4 ~% n3 m1 G1 ~& \3 z# c
end/ z) n6 A* X$ ]) S: \
5 T# T# Q9 k* B7 k- _ I if showfigure == 1
: O z8 ]8 `& B+ \ %在一个图上显示时域拟和曲线和Prony频谱分布
( b! g/ H! T3 L5 j J; ~ figure;
' M+ v! Y; R9 u9 _+ C- u subplot(2,1,1);; {" u; \8 P' c) e
%plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');
( x8 z: w# b+ P& S: C3 e plot(tt,x(1:N),'r', tt,xc, '*b');
, |) e. B/ G9 V0 j7 K9 ^ subplot(2,1,2);8 T0 C0 M6 _/ Q5 i/ \
plot(f,sptr);
6 u) G( X' b; w+ U/ I %subplot(2,2,3);# @3 \8 i' [5 t
%plot(f,sptr);
* D A3 ]; u Q3 H6 o %subplot(2,2,4);9 N2 U* ?( L, @; d+ w4 c- Y0 ?
%plot(f,angl);1 C/ W& D6 _0 g7 F# T% y
end
9 b; \8 v* s X + F4 d+ U k3 K% O
cpu=cputime-cpu;0 U- v. t. d) {# k
format short;
7 p9 Z) |+ j( o: q end |
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