|
|
楼主 |
发表于 2011-3-29 13:24:52
|
显示全部楼层
回复 2# debra
& j% i( {! M; W& E* {6 Z+ B) q5 f$ a2 s. H- Y I- i
3 w8 Y# c& m# w( e# q %打开指定文件,并对信号进行Pon分析计算6 i* }! Y) I' ?* I7 v
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)
! T+ h6 U- T+ D* Z7 b4 C3 m+ X/ ?+ | format long;, X& u0 O$ L/ t1 Z& W
x = x_in';
. [4 J- [+ w4 R/ ^ cpu=cputime;
" r, g( b' _ {* l/ ?2 c; O# b N=size(x,1);
; O2 F n6 O7 D( d/ d2 O %取N/2的整数部分为初始的P, H1 l- U$ `2 B; e3 X5 s
P=floor(N/2);
/ J6 Z0 r4 q* j% I' m 8 S% K' ?) T" A2 e+ ]
%去直流环节
7 T L) G \" B8 X* L3 H9 O x_Sum = 0;- m+ }$ w% K) i7 V/ S% \
for i=1:N
7 e1 v; U5 L9 w% \ x_Sum = x_Sum + x(i);
1 q; o& [+ F) @3 h end
* ^& X9 `& f6 I% {: B- s# J x_av = x_Sum / N;
C% m$ I* H7 b+ B if x_av > 10E-10& o8 O/ y; a% z+ ?: P) _
for i=1:N
" ~6 s' h- d0 m) I' o" J7 V x(i) = x(i) - x_av;
+ h3 `. ?! x { end
5 `- K r! O% \& J9 H' [ end
' @0 G# N5 J4 X %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%( n3 e. F2 U; A( |- g
%滤波环节
5 H: Y. ^ |7 n$ s* |8 h6 H% O( o %fL=1;* T; v- c) d' p, u9 o+ J0 \, U* K
if fL>1
+ a4 {; _' v5 Z for i=fL+1:N
3 l; E! @2 R8 k5 ?% b x(i-fL)=0;
! m, ~4 x7 Q7 v) b* T' U for j=1:fL
7 {7 a3 i) t6 W* w x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);0 G; Z& `: k+ N2 P7 q
end
- O1 W, p' k" x1 e& V. c4 L end
* e( Q8 q# c( u! c r o; X end6 S3 J2 E6 d' C' n0 c
N=N-fL;7 m2 @" O1 u+ D3 n# l$ |
tt=0:1:N-1;! Y) { t5 u2 o
6 J6 D6 G* P+ s' ?8 @& C$ x0 L %P要求为偶数
0 q* ~4 U3 b" L/ m; W if mod(P, 2) ~= 0" {7 k/ `8 N! y+ J# l5 H
P = P - 1;7 X4 h1 e* I7 p# f, x3 a# Z
end
1 t) ]& Y& G3 I. ^' o* X) b 4 X9 \9 W$ n/ Z. z
P1=P;, I6 L' Y1 k# I) j
if mod(P, 2) == 05 S$ k2 G* n! m h5 e" C
% Generate R,生成样本矩阵
( I6 v, p5 z; P! H for i=1:P1
. w9 d- R! L8 z$ P* p for j=1:P1+1
* \5 c0 c- r$ A2 C) i4 t9 J9 V- ` ss=0;
, y# T3 O% ]5 I2 }5 \ for k=P1:N-1
+ ~: H3 s1 e; ^ %前向预测误差
4 V' C! q. N/ t+ @ ss=ss+x(k+2-j,1)*x(k+1-i,1);* }) `5 t+ B( J. @* h5 N) {7 o$ \# _# u
%后向预测误差
) ^( `. T" n' P% A% l %ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);4 |( o+ G8 P- Z* }
%同时考虑双向误差% I: ]1 v' `$ s' g3 r
%ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
+ V: @- E+ L6 b" H end
( H1 q/ C- V8 k. B0 e. c R(i,j)=ss;1 {8 c- l. G1 x2 d* {6 N9 R9 U
end
0 n1 G4 R0 i+ z# O$ V" T+ e8 m5 n end
; m% ~( z) A. r+ I9 m % divide R into R1 and R2, and get A; R1*A=R2;* |$ |7 `( K% `" P- M$ s
for i=1:P/ {. n# V7 M3 v# S0 H
for j=1:P
6 d3 @% d( \% n7 r' I R1(i,j)=R(i,j+1); i* D% }2 t0 E1 }9 `
end
* W3 A' r8 f4 Y# Z1 k8 p end
1 X! H* {6 b6 G, {* Y* o+ r. z for i=1:P! t. ?; d7 n8 t3 S! C' r5 y
R2(i)=R(i,1);
5 [6 {+ r& C W; e5 w end
i/ X/ n- \% ^
# d) R7 H1 D$ j8 B* a+ O %添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2 l7 b/ a8 j/ _$ P m8 S$ n
%首先进行SVD分解' ^5 O6 j' Z0 u: a
[u,s,v]=svd(R1);% p4 ~; Q2 C3 n0 d: t
%根据奇异值确定实际的阶数M
- t0 i' n* ~- j! ?5 F M=0;1 i e( n; l" [, Z. y
%计算全部奇异值的均方和2 x8 |. X; d" q2 e6 I
Sum_SVD=0;
: `6 z/ E3 p' c( C8 Z for i=1:P
5 \' h _% c _ {) d Sum_SVD = Sum_SVD+s(i,i)^2;; S7 n& m9 U9 X% t4 ]* f1 J
end
/ I6 x8 R% u# c# h/ T' O+ u# d, a cur_sum = 0;
: M& U+ H e e. D1 T6 x8 n i=1;
; V! I2 _. I j: ]+ t while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P
$ p* r$ Y2 G' X1 U% f cur_sum = cur_sum + s(i,i)^2;) N8 a, f& K3 D! s# r
M = M + 1;0 H U8 ?6 c4 T1 h
i = i + 1;7 m K. k* j6 `9 W+ a. w
end ^( v9 L+ z' q+ f6 ~
%输出预测的阶数M4 X0 x9 X+ U" u6 |& Y9 S
M;
" Y, K& p: p6 V$ V, {+ ^- { %生成Sp矩阵* m* M; U0 K" }% D1 u5 {
Sp=zeros(M+1, M+1);
5 s% R1 S/ D7 h! b for j=1:M
& t/ @6 l0 o( K for i=1:(P-1)-M+1
4 T6 a0 k, s3 W( B% F" | Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';
9 K; i; ]0 \+ ^" w8 Q end1 p# u1 ~: `4 H( M0 p* J+ f A& |
end5 T1 Q6 G6 P M( `5 j) E
' ?3 O4 L2 |8 j4 y4 a# [3 W8 X) }
%根据公式生成最佳最小二乘解
2 S+ A+ V1 w- {3 E. u# d2 G Sp_inv=inv(Sp);
' N$ Q v6 I" s! a- c if isinf(Sp_inv(1,1)) == 1
5 C* A! n5 M* E& Z& ~ Sp_inv = pinv(Sp);
: A4 f. ]# L; q4 ?4 O6 ~) T0 z# l end2 }, ^# l: u$ }8 H; ~! A
0 V* v; {% d; A9 p a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
2 B" E2 T6 S1 i1 C8 F/ `4 P# q9 @, W P = M;/ v8 x% v) n+ [% o r$ D+ Q: j
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%' i4 Y& T( r9 F- S1 P0 q- J
% Get Zi4 F% H4 u" h4 c# T. f
cof_SVD(1)=1;
# _. b! W4 ?6 g4 q. h for i=1:M
8 n. s; B9 j. D/ N cof_SVD(i+1)=a_SVD(i);
" b( a" j$ G* K W/ m. Y f end
# f& t( \9 |( r" s" N N1 |5 o4 j Z=roots(cof_SVD);% Y0 [$ F3 F2 B) A1 M+ _ _
3 [( a, t! L! L. ]4 o$ ]4 t) }2 A; Z
% Get y,y should be very close to x
& j2 N) o4 H! T+ e8 _% b for i=1:P
- k. w1 d: V8 P% }/ x* H4 N* ~ y(i)=x(i);5 C; i% ^: z& Z' e" V- _) s& Z- Z4 D
end
( M2 O4 D8 k+ r4 c7 |
; b& @' w; O7 g$ k! C for i=P+1:N
0 o3 Z$ G6 g7 `( M y(i)=0;7 I/ `& h# X ^( T% [
end
4 ?, ~ o& M" _# q$ y for i=P+1:N4 |0 i! Z: z5 A7 h4 O) U& ^
for j=1:P* x' ^+ N( O$ D8 t6 Y C
y(i)=y(i)-a_SVD(j)*x(i-j);! Y+ b# a* J9 J( T) o" Y5 O4 G
end
# L% T1 f7 y. {: a# I) d" A: T end+ R9 X9 @, A4 o: o; \( a
: K. Z; _+ n9 [7 c( G- {
% Get B
% j% G) e, M6 h* \4 A- v for i=1:N: E( _% P* X. b
for j=1:P
" n0 P1 E# i, {# e2 Q Fy(i,j)=Z(j)^(i-1);& R# l4 u! [1 j! u
end
5 y- [# O4 G! o ?+ E+ A$ ^9 J end: P9 Q. t6 _5 U8 t
Fz=Fy';
/ L2 v& C7 U' \+ O( P* O c5 F FH=Fy'*Fy;
( \( G1 f% i0 d8 ^ Fn=inv(FH);+ t; w) {, n$ f1 ^6 X; [& d; K- Z
B = inv(Fy'*Fy)*Fy'*y';6 u! p( ~+ Q F8 i: c, V
6 n. ?/ k9 | Y, C1 _$ m% Q % Calculate Amplitude, Phasor, Frequency and damp
) c. @4 U! n# K7 ~2 f9 \8 c* Z9 ?8 K for i=1:P
; i4 ~$ ~( v v: b' Q# P# G# u8 ? Amp(i)=abs(B(i));* P* P! M( I4 n
Pha(i)=atan(imag(B(i))/real(B(i)));
% ^( `8 t: U Q9 ^ Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);
/ Y; N4 r6 x3 B; u damp(i)=log(abs(Z(i)))/dt;
# X) I4 s$ h: z P, o, o end
1 q9 ?7 T3 v2 w9 l %调试用的代码
; W. c1 ^6 k$ v/ Q. Y8 @ if isnan(Amp(1)) == 13 X9 X& Y9 t8 H' p
error('幅值的求解出现错误!');- M6 N4 l7 t- Y
end
# J! F( r! t' A& V* u & {. l9 r% H( c$ V
% Get xc,verify if xc is nearly equal to x# Y9 F* F4 m( v
for i=1:P9 N$ R0 Q# h9 H
if(real(B(i))>=0.0)' n k1 X. F% C4 I! X
bth(i)=Pha(i);/ x8 B/ ~) v3 W: I4 |
else
& o, ]9 w0 t5 q! x" X9 O* l bth(i)=pi+Pha(i);- a+ A$ [. M7 p# a0 w3 X. o
end
, `; l/ x0 |( |2 u end
6 M+ P$ ?& P' v3 F; y %对Pha重新幅值. G2 j; O: I, C; U9 }
for i=1:P
1 R$ v3 @: j& o, \8 ]* | if Pha(i) < 0
3 w& N+ h* F7 f) N: ]; |: w, o) D) p Pha(i) = Pha(i) + 2*pi;
2 B7 a0 I5 E3 a" T end
' m2 s2 | r" R% c end
2 A9 x$ ^) m* C+ W6 U. h6 h
8 j2 }# _3 [9 D+ i/ a* Y9 S for i=1:N3 p9 D" p; d- Q
xc(i)=0.0; }. f2 n' N4 d- s7 J! ]4 h
for j=1:P5 V/ O1 N) }. ~$ v
xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));
! o) r& M1 t3 Q6 ~ end
5 W' B, u+ q$ r$ M; o% b4 ^ end
$ N9 }+ Q) o9 O% if showfigure == 1! N" S7 J+ b# D5 N3 b$ p5 _
% %显示特征根的位置2 G) m; u( f. z) g) i6 c
% figure;
5 x9 u9 l. ~, v7 W$ [% Y& l$ `% plot(damp, 2*pi*Fre, 'r*');
" l6 H$ V/ |5 `9 u% end$ k! D' g0 J( s: D1 Y
$ Y/ {0 R. }- |* I; ], I e
xj=xc';
3 n, q4 O& ^ R; B4 V er=0;! W7 T% {, H: D: d8 k& S1 ?
all = 0;
0 [9 \6 |# v# p" J9 Y0 U4 { for i=1:N ) j6 d8 x3 ~, Q2 p7 o
er=er+(x(i)-xc(i))^2;0 n! D( e l! q+ ]3 F V
all = all+x(i)^2;
) Q( n n8 R. s+ d end
o7 b# u% {$ P, ~7 H( E n0 N SNR=-20*log(sqrt(er/all));1 Y n" J, N0 T* G: e
8 }4 `( S* w, w. e0 |' V" }; M9 j % Calculate Prony spectrum
4 K4 K5 Q( h: c( S9 N9 i %频谱的取值范围为0-5Hz
" V t0 y4 B/ S& `# {. o f=0:0.01:4.99;
g. r4 M9 b" N& A# y& [, i for j=1:size(f,2)
6 q* x5 }' u# X2 l# f8 y5 d; A sptr(j)=0;
5 d! x, o. l6 i5 V( _' i7 o" a sptr1(j)=0;: w+ ^! h4 J0 l# R
sptr2(j)=0;( g" W5 |1 i2 L3 V# U) @6 b* u, |2 k# s
angl(j)=0;
+ c: x) _' C) d% o, e! E' X8 T tmpangle = 0;4 L8 U" l! g- t) d: Q
for k=1:P
0 l8 z' @, _: n, j5 d& Q" | sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));0 S: B4 P$ q$ x* f0 v. O5 A
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));( d n w2 I- R& n/ @# i# e
end
! X3 v$ i. z% K2 M- P% b* E sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);" h' {; \! J, H: ?% K
tmpangle = atan2(sptr1(j),sptr2(j));
n: _2 M- C1 Y angl(j) = tmpangle*360/pi;
$ Y7 C% E5 [5 U$ N- j' r0 C end
) p5 W! u7 u# O8 N8 j( f. U: C! W %对幅频响应进行归一化,并且寻找主导频率模式8 W: C$ j& B* B% `5 @
%寻找sptr的最大值
7 n6 T$ j9 ?' l- F4 v; P max_sptr=0;
: G3 c4 h1 ^8 q2 j+ u% G T0 l main_f=0;
( [1 w- I% G0 C' H' @ for j=1:size(f,2), m1 T- Y$ Z/ O4 J: k, h! g
if sptr(j) > max_sptr* W: i2 @- l; w+ ?% x- a
max_sptr = sptr(j);
6 W# R3 D$ l0 d6 b %主导频率出现在最大幅频响应位置
3 S) j$ S0 J% f! m if f(j) ~= 0;
& d0 p/ ?: _; }7 j main_f = f(j);
/ ~+ Y6 ? C7 o; ]" T2 V4 s, W else* P5 T( k6 P' M4 n0 G
max_sptr = 0;* a% I: H2 Z4 y, L
end* e2 m, Z% u3 Q# A
end
5 x5 q8 g( \4 J3 } end
% {* Y! H5 Z1 i! x2 t, s! S main_f;
1 C3 b, w4 |) h! H7 [3 U# g& D- Z1 k0 P %找出真正计算的频率值
9 q! y- d% L& u# h s' C8 v f_err = 10;
. O0 [, T' f% }7 W$ B f_main = 0;
( T- h7 d) l; m1 |& _ M& e for i=1:size(Amp, 2)! H+ s4 d8 t+ J8 a$ M6 Q' |
if abs(main_f - Fre(i)) < f_err
, k2 _, M9 Y4 G! {: R& @+ [ f_main = Fre(i);
; m) r* x8 T! `0 Z# n damp_main = damp(i);
3 L1 L) i3 f1 N% u% n2 v) N! W f_err = abs(main_f - Fre(i));4 k- Q/ v& U6 x8 I1 H% t
end
' {5 D- B9 v5 M) T" o end* O9 Y* v, K% S% W) C# R
main_f = f_main;
; } l" G5 }% V2 g! E6 ] main_damp = damp_main;
* @ I6 j% l+ H5 M %进行归一化* F9 E* W6 l9 n! n `, s
for j=1:size(f,2)8 k4 w- X4 k8 @! I
sptr(j)=sptr(j)/max_sptr;& ~* Z( h; v% h
Amp_Response(j) = sptr(j);/ v! k7 X T3 X3 {# h+ D
end
# B+ R4 e& C1 H9 M& C6 ^) ]
* G3 M/ R& H4 \' z. c! s for i=1:size(f,2)+ G) Z; C0 U+ Q7 S+ u/ d6 _
if angl(i) > 0
+ [2 M1 I4 P& q6 @ angl(i)=angl(i)-360;
! v; e. F6 R: o0 [, @ end
# W ]" i! p4 A- ? end
b* S9 |0 o2 g' l5 Y/ M6 H 3 I7 G# N. O6 k5 I- J
if showfigure == 1
* a) Z+ H6 X) F9 P% ]% m y2 T %在一个图上显示时域拟和曲线和Prony频谱分布* \, H9 e. j0 ]
figure;1 D& O" d% X ^1 G
subplot(2,1,1);
- D# {1 x/ a6 b7 L %plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');$ e" c$ X' m p% N Z! J/ y( H: f
plot(tt,x(1:N),'r', tt,xc, '*b');
. J, T$ l( p* w: b( y r3 i# q subplot(2,1,2);
t b7 ?, l; z' M plot(f,sptr);% Y/ u- U" ?8 v: n& v5 W
%subplot(2,2,3);7 |; Z4 k' C4 n. s* o
%plot(f,sptr);
0 z3 e& w( a4 Q$ h3 s8 v6 F$ l %subplot(2,2,4);. z) F8 g9 k+ K( w0 N. K
%plot(f,angl);
. |- ?0 ?& T) \) f end
$ f4 |# G; e' W; z! H: Y / D& |( k2 s' O
cpu=cputime-cpu;
7 T8 u3 V/ k6 ]1 E format short;
1 {6 S5 E# k! Q6 K7 ^2 r' @ end |
|