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楼主 |
发表于 2011-3-29 13:24:52
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回复 2# debra
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%打开指定文件,并对信号进行Pon分析计算# f0 L# r3 u7 ^/ {0 L5 A! O
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)
, Y! F% ]' [3 ~2 { f format long;/ |; T9 w6 }1 y; b
x = x_in';) v* h- N o1 @2 N2 U' N% ?6 [
cpu=cputime;- p! H; r: g/ b+ A8 J1 L" T
N=size(x,1);
$ ]$ A2 s7 @" | %取N/2的整数部分为初始的P
+ l: X. [: z0 O9 t, v" D P=floor(N/2);
1 [% \/ [$ z \# y
. H2 J) u# ~5 }) Y3 ?6 Q %去直流环节
8 p1 I. j! m. i5 E, {/ ^* P5 m x_Sum = 0;/ ~2 [, g& l- d" w% }1 }
for i=1:N
* Q4 ~! v$ D( h! E; u x_Sum = x_Sum + x(i);
5 a2 g1 D2 C ~7 |8 r; P end
6 J7 u: L+ u$ |; p x_av = x_Sum / N;0 l) {+ |- _; E. r+ N
if x_av > 10E-10
# G2 u, p2 A1 _ for i=1:N c1 D# C: M) a" r/ l) ?1 q9 J, t/ ?. x% Y
x(i) = x(i) - x_av;
' S$ ]8 `3 ^1 i: P1 E# Y; E7 ?- P% T end
O) g+ L/ E* _% a! v. X( h( w end9 z' v, Z( o, q2 W2 ^ P
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 U2 H, n/ N# v
%滤波环节
9 j1 e4 ^- }. h2 n9 O, ~) @ %fL=1;
3 s8 U" F* _2 M' C! a if fL>1
4 K9 b$ L# S5 H8 Y; |0 E9 w- w for i=fL+1:N7 a. Y# h& f/ _' ?" ^" x
x(i-fL)=0; ?, `' G9 w+ Q' j
for j=1:fL
' y/ y) Z6 O4 x$ W x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);0 T4 Z3 N+ n0 L
end
7 e% K4 P; k9 \ end) ~. G* a! i0 Z1 s! @
end" y1 k% X, z% l
N=N-fL;
# \6 R; p$ z5 n9 d: Y/ |- [ tt=0:1:N-1;
) Y$ L ~6 _4 w3 [7 Y
* X5 Q; n" m& ?" H7 c3 B %P要求为偶数
+ u, v3 q" U& c% \7 u5 t6 c if mod(P, 2) ~= 09 J, z* K- R; R" {
P = P - 1;" O/ E7 c* x. I! W! B$ h( l/ d
end
/ e' d- C5 T- {5 h
2 e6 l9 [3 Q% [7 {9 ~4 H P1=P;/ O+ P6 i& z- K1 t
if mod(P, 2) == 0
( p* B3 m" a* n; |! |6 e! d % Generate R,生成样本矩阵0 d! O) {: D+ Q0 E+ d U" n
for i=1:P1- |2 n5 e" W7 `
for j=1:P1+1
q7 ?2 {/ J( G* S# h' `8 i4 M% B# P ss=0;
0 ~% l: M G" S* h2 b& v( |4 I' K for k=P1:N-1) ]. W4 \5 X8 b1 \0 {2 [# p8 V
%前向预测误差
' I( ]+ K- m. _! ~8 ?/ f; R ss=ss+x(k+2-j,1)*x(k+1-i,1);
9 a/ j% ]* H- S. |; E %后向预测误差! U) A" a, C( `
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
3 P9 g( R7 y. }! ~' w$ j& p %同时考虑双向误差, ] @' c) |* V9 O" g
%ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j); 4 g& m5 [+ C+ l1 Y( |
end & W' Q, ^( A6 Y$ g3 E1 f' Y
R(i,j)=ss;
- m3 l/ j4 r/ J, o8 ?9 e1 m' G3 | end
1 P | Q) P7 ? end5 A0 |; u) o) V9 M* T2 t
% divide R into R1 and R2, and get A; R1*A=R2;
8 W8 O; o7 J8 |4 ^" v for i=1:P, ^9 ]0 ^; w( L9 Q. U
for j=1:P6 Y) p7 U0 _7 K
R1(i,j)=R(i,j+1);
9 `% _$ S& N( W. j- C end. ~. ?, B* I, |8 @3 e: R+ e
end
% e! j x: {- x' l& h$ v7 u3 i" v$ h for i=1:P
( U. q$ p$ s( f9 j1 {- X' u R2(i)=R(i,1);& l& N2 r6 x& C; G' b
end
( h+ s+ h9 l6 m- V
2 [8 m- H/ a) c/ P R: s8 | %添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%4 P, U6 U. U! h% s& x: t/ J5 ]' d4 l
%首先进行SVD分解 ?6 C+ Z0 e6 `' k K2 m" n7 j
[u,s,v]=svd(R1);, b& l$ ]6 v+ o& h: i
%根据奇异值确定实际的阶数M
4 y8 ?7 x/ W0 @9 ]: G; H5 N: M3 H0 P M=0;
k* e! }6 u" m% p3 Y8 g4 O' q %计算全部奇异值的均方和* `$ o( D5 Q$ v, y+ [! w% y
Sum_SVD=0;1 O) }- b& B& w9 Z2 u
for i=1:P
0 d9 h" Q- q! j! D5 f* Z: Q* E Sum_SVD = Sum_SVD+s(i,i)^2;& H L9 d+ \6 m4 D$ ^( j* h2 g
end( G6 ?: h/ h7 x* b. Z
cur_sum = 0;
- _$ n+ S0 V) J8 f5 s i=1;* A C$ {+ |: B4 C
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P
9 v# w5 a7 K& g" R% \; ?+ f0 B1 V cur_sum = cur_sum + s(i,i)^2;- ?+ p# @* v5 v- [/ M6 _1 r% u, s
M = M + 1;, @; {+ p1 H* J" T& U
i = i + 1;
& h. |! Z- N; \7 Z end
" C, @. o5 B% K5 N' |+ p8 E- G1 O1 s4 i %输出预测的阶数M: w( X- `$ W7 X6 [
M;
! V5 S+ l" ^' C' l1 ]- { %生成Sp矩阵; `' a" U f) ^3 s, j P3 {
Sp=zeros(M+1, M+1);" u: Y, ?+ N8 w2 X/ p
for j=1:M % u3 h5 ^7 i& Q0 k! N0 e1 b
for i=1:(P-1)-M+1! u' ?. j, d$ A/ N# e* y/ @5 m2 e2 G
Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';" r8 [) e5 r( o7 I3 P: A
end
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%根据公式生成最佳最小二乘解% p5 F0 o# F: b# |% q4 X
Sp_inv=inv(Sp);
3 [ ~1 a# K: U% Y if isinf(Sp_inv(1,1)) == 1
3 m" @5 y; N0 {0 ]7 U Sp_inv = pinv(Sp);
1 b' B8 h; @# |# Q( z$ t. z end- d# E) K9 W2 s
. r, r& U; _8 U; v0 l- J a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);4 ~+ z. y' \7 p, H2 I* f, J
P = M;
% z3 M/ N: P+ C, ^- r %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2 M( z* i" R" A+ m
% Get Zi
1 `4 }8 P" O9 ~ B; ]- U; D cof_SVD(1)=1;1 A/ ?! O# `6 a" e0 ^
for i=1:M, \+ g0 {* M) q* Y0 ~
cof_SVD(i+1)=a_SVD(i);
3 E3 J v2 x" R! Q4 @* W! \ end/ e% p6 x. |$ B8 F4 p
Z=roots(cof_SVD);
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% Get y,y should be very close to x9 `, j6 n* K1 X$ v! J" x
for i=1:P
3 L5 i* ~/ L6 X, l6 z& ? y(i)=x(i);
: v0 O; x6 |9 z; Q8 \5 o end
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- t" K! `7 U) w for i=P+1:N
$ u# U" T( y. {% m0 [ y(i)=0;
4 _2 K7 `/ w0 L. O end
* ^" s4 Y1 R4 p- U4 i& t( ]5 F for i=P+1:N% B1 C' z0 R$ U j/ v
for j=1:P6 e' ~) l: }9 Y b* c& u" U
y(i)=y(i)-a_SVD(j)*x(i-j);
- o5 ?9 k# d) J8 B9 A+ M end' \( o. l$ }, z! d# m: e1 h; @) [
end8 t W# G; s/ ~
}( p1 ?" |. r, m5 w& y# @2 O
% Get B2 j4 @; u& O9 P$ T) Z* t
for i=1:N
3 e2 B2 T4 u) \% U; G for j=1:P0 k" v9 o% q4 r6 E" F
Fy(i,j)=Z(j)^(i-1);7 q! V+ }) Z$ M4 M$ B7 P1 S' ?( H
end/ Z* M M. O# I: j1 S
end! V0 R" a1 O' Z( m. m, e9 {+ f
Fz=Fy';6 Q8 ~: d9 t4 F( S; ~4 ~
FH=Fy'*Fy;
0 e' _% n) S4 _* s" v- | Fn=inv(FH);
% r& L3 s8 l& [9 j1 R B = inv(Fy'*Fy)*Fy'*y';0 u: N/ e. j" l$ v
+ l( y9 k% w, ]# o6 E! Q$ x % Calculate Amplitude, Phasor, Frequency and damp2 j. f! ^; x! g
for i=1:P
4 t* R$ E4 v& N8 g6 b% s% Y$ d Amp(i)=abs(B(i));
2 H/ q5 G2 y T+ |$ Q; k, F Pha(i)=atan(imag(B(i))/real(B(i)));
; F; ]. w4 I! c! W( v3 V6 V/ T Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);
& p9 Y* c9 w7 M1 E% q& l; Q damp(i)=log(abs(Z(i)))/dt;# C3 `1 U- J" ~ c: q, Q1 L4 `
end; B1 p3 }; J) ]8 h' H$ Z
%调试用的代码
& c' E. F7 U% ?/ O1 j if isnan(Amp(1)) == 10 v, t) b" g6 n4 D# x
error('幅值的求解出现错误!');, u: _8 L1 f0 h. R1 Q
end
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$ k, M7 w/ a4 s, k# P % Get xc,verify if xc is nearly equal to x
7 o1 ^/ [" X8 T) v5 n for i=1:P
, g7 w+ V& o+ W0 x" O7 s2 C4 Y" z if(real(B(i))>=0.0)) G+ x- Y4 j4 L- U. U) O7 [
bth(i)=Pha(i);
* {1 \, [, [1 ] u% m8 ?3 t else
9 y6 I: t; T7 [3 k4 b/ m bth(i)=pi+Pha(i);9 M/ C/ o' o7 Y6 w6 I
end
C8 w( j* }6 d& j s end
# I g9 w6 l, [: g5 [: _! } %对Pha重新幅值, S( A8 o8 H" t
for i=1:P+ e! _: s3 d6 c0 \9 q; j+ a( y( j" X
if Pha(i) < 0
: q/ E2 l. ^) j- S Pha(i) = Pha(i) + 2*pi;
. B) q( }5 K @1 E: Z end
$ b b# R% ^& V* n end- _! j, h: S) d* e
, s& p! H) b# ]& A$ ]( A9 m6 k
for i=1:N
8 x* C, P' O( }8 U& w* { xc(i)=0.0;
) N+ E! W- A9 J: i for j=1:P/ X& a6 f7 r9 m
xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));/ Y& e i8 ]1 k5 @5 I d
end
- R* N# z0 I4 a O" E* L6 d# s end
; r- b: }' v z. }7 v% if showfigure == 1' }# f! S1 ?. {, w N+ s
% %显示特征根的位置8 e2 m5 i$ I& ^8 C3 H- D1 p
% figure;; T" D. @; x6 f: W$ g8 p) O
% plot(damp, 2*pi*Fre, 'r*');; H# t+ a( R% x7 t/ @( x* L+ M
% end
% p J2 R0 @+ V% B) f4 e
9 c; ^4 ~( ?- Z5 y$ s. a4 B xj=xc';
, u& G. {- `* w( r& ^ er=0;; D" _) j1 R. \: d7 ]1 i
all = 0;
+ U3 q* C5 l( g) r7 A- x5 u for i=1:N ' O( L7 |! s% o8 ?8 K5 y: v8 ?/ H- a
er=er+(x(i)-xc(i))^2;( k' Q- O! t- S. e. Y% n6 L" ]
all = all+x(i)^2;# X& o' v! B1 X: R. l7 R* r5 v
end
- ~" j; o+ `) `8 ^/ m2 M2 I. R SNR=-20*log(sqrt(er/all));
" }0 s& Q8 s4 [; q1 X ) Q8 K. z! ]: G
% Calculate Prony spectrum
+ l8 o$ ?) s: ?; M. I %频谱的取值范围为0-5Hz
+ |9 V. F5 U3 e f=0:0.01:4.99;& N s" |- ?' z! i" L
for j=1:size(f,2)3 z: `, O2 w! j' M
sptr(j)=0;* n, P1 S$ i' K3 l
sptr1(j)=0;; `; \7 Y- B- v2 f. k3 E
sptr2(j)=0; l" c8 N) I/ v
angl(j)=0;
- d% }" P8 q9 I; B+ g4 ? tmpangle = 0;2 {5 |6 P2 t4 f% j
for k=1:P
' X6 g5 @5 @9 ^6 N/ Q sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));/ v# ?) ^+ k$ d1 e M
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
6 `9 E* C$ D- ~ end
% L& b; {: Q0 X, C sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);
* N7 O, X. T* J Z" t5 i tmpangle = atan2(sptr1(j),sptr2(j));: t5 g& }, ~! M W
angl(j) = tmpangle*360/pi;
0 b2 L( O* {* O6 [( S9 p- P$ x end
0 [0 M V% z# p2 H %对幅频响应进行归一化,并且寻找主导频率模式1 g& X( w$ r) U2 Z7 v
%寻找sptr的最大值. T* k$ f; v! {/ Z) s7 d7 F
max_sptr=0;. E% K! _$ ]- y% I+ A
main_f=0;: }9 N L; \, ?4 Y9 i/ O4 |
for j=1:size(f,2)- l( s2 ]/ @1 I) g( z* C
if sptr(j) > max_sptr
$ R9 ~! O6 K( f max_sptr = sptr(j);5 [1 l r% ~0 {
%主导频率出现在最大幅频响应位置* X+ P5 |" O( g* W& V# B
if f(j) ~= 0;
+ Z4 H+ e& V' F5 g. G main_f = f(j);
/ r5 m( z/ `# ^5 G, I5 v4 Q else5 t. n/ x' m' f: v' K6 ~, q
max_sptr = 0;$ i$ O( j: f n0 P% H/ P
end% X4 Y% ~* u' l8 Y* G& c9 i
end' u3 J4 l# y2 { R& R; a
end, ~ l6 R' G; Z T) x" K
main_f;
; L" ~ K9 m7 e9 }3 R+ I; d %找出真正计算的频率值5 q( d. a" N- e2 u* a# @
f_err = 10;
/ Z( M R" I6 x" F2 e" e f_main = 0;
8 z3 R! Z& u& ]6 U }' X for i=1:size(Amp, 2)( h$ _2 C% b. E. D0 a! O' ]- g
if abs(main_f - Fre(i)) < f_err6 E4 b3 }8 F- `- Q8 \- i
f_main = Fre(i);: S. T$ U- M3 L J% S/ X* ~+ E
damp_main = damp(i);. L# y& s# I" o& F- P. V, \
f_err = abs(main_f - Fre(i));8 _- e' U& y( S1 ~8 P# M
end4 ^9 M; a+ K( o7 j- P
end
$ K4 S8 I" ~$ I) Q: H; N; q/ O main_f = f_main;5 t" c* p+ E0 l% h+ z! H( ^7 p
main_damp = damp_main;
0 A/ j0 c( @! W* ]! | %进行归一化3 X7 d3 D- n$ D" M
for j=1:size(f,2)
$ a5 h( z% a& @8 I' ]* e; v sptr(j)=sptr(j)/max_sptr;
, u( T, X, [/ B4 w) z Amp_Response(j) = sptr(j);4 f) i$ H( d' h
end
- `4 l; v3 N5 n6 J; F) C1 O9 _
8 A- R) v: f1 H2 }; _* B u for i=1:size(f,2)
7 S+ Q+ W X3 l8 d if angl(i) > 0
- O k# O8 w, B9 f: ]( E' v. ?/ ] angl(i)=angl(i)-360;8 F5 @1 d; J3 `' v7 m! |# \% j8 v# ]: ]
end
9 Q! m' r) P, R end# w1 C& c( R5 B1 V+ B$ g. t! K
6 a' A. g- o- ^0 s/ b- B
if showfigure == 1
1 o) c7 b2 ]0 h. \" W %在一个图上显示时域拟和曲线和Prony频谱分布
8 s8 ~7 T$ y& T/ w6 b figure;
) ]( X1 ^2 h: U; m subplot(2,1,1);8 T- p3 x5 h q, k
%plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');
6 T# v0 p I* n plot(tt,x(1:N),'r', tt,xc, '*b');
7 ~. e/ n5 q) m+ g5 E0 L4 w subplot(2,1,2);$ U6 r! K3 s9 O/ w) z3 z
plot(f,sptr);6 ~9 }/ O/ E3 l
%subplot(2,2,3);
. d. G) T. O, _, U/ w4 B' t %plot(f,sptr);0 h v4 Z8 Z5 n
%subplot(2,2,4);; T1 W, q0 a% Q6 `* o) |& k' J. S
%plot(f,angl);1 d2 l5 j" K( p! C6 B. H9 r) ?. _
end
; M( i9 S0 u& R7 I, J ) F6 n% t" u- }: f
cpu=cputime-cpu;8 ~% I2 e5 J' V
format short;7 \* L& p$ U0 g5 ~" k. e! v
end |
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