|
|
楼主 |
发表于 2011-3-29 13:24:52
|
显示全部楼层
回复 2# debra
! p! \! |, y8 D! R6 K
; r% K$ M& U% L; M" C* t
0 O, f% ~0 n- M J5 n3 A2 C- k1 p %打开指定文件,并对信号进行Pon分析计算
* w( N3 N* K9 c, L: [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)# X6 j9 \& g: F) V6 R. o/ t
format long;
& W0 ?, D1 r7 m- U, t! y x = x_in';
! B3 V' \8 m: _) v cpu=cputime;0 K0 `/ `9 Z* f: O/ f
N=size(x,1);7 I3 \& K3 J. `4 _6 x( q
%取N/2的整数部分为初始的P) \2 p/ D$ S. K; r& K. u
P=floor(N/2);5 l5 }; r, v$ I) @% i4 Y& W! v
% W3 B0 N& W. a1 s% O7 Y7 y5 Q %去直流环节
9 Q1 u! h W2 d1 @) H( B ^ x_Sum = 0;
3 R# R/ P- g* h! R( m for i=1:N
$ l" m @) _) D x_Sum = x_Sum + x(i);/ m$ {) x3 l8 P6 I9 i' J
end # `0 e# H; R7 C% {
x_av = x_Sum / N;
! ~. }- P2 f. C& [5 Y5 Y, m, e if x_av > 10E-10
- U3 q+ a Z1 H) N$ u i% \6 Z for i=1:N3 [' @' [8 L' d) @" ^
x(i) = x(i) - x_av;
9 | Q B! W+ _, m/ T end
& X+ Y/ R M2 ~4 L end
; m9 r+ q0 k/ t1 V) { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1 ?) ^# i& |2 P
%滤波环节6 w/ T( \. S( m2 L
%fL=1;4 G# C! S7 U: _1 W* H( L
if fL>1
* _* J6 T0 ^. t& |$ r for i=fL+1:N, N& A4 `, u& N$ J
x(i-fL)=0;
5 Y* v1 G2 m X; n" t9 C for j=1:fL; p8 b- g8 V* K9 i; [+ u
x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);
5 C' W0 B. ?4 M* l end2 e9 [5 x9 h! y2 ]4 I$ s
end
E. F6 n( ~* f8 F' [% r# a end6 |% `4 \/ b, z. I0 M
N=N-fL;, ~) R( n* }. p( W1 L7 x
tt=0:1:N-1;, W, X* i6 f6 I& c, `& W- D
5 T+ V0 q% Q# Z3 R
%P要求为偶数8 K7 z& b8 ^& f! p( N4 r$ m
if mod(P, 2) ~= 08 ]/ K: y8 X; D: c2 O0 n: r
P = P - 1;3 ~6 F X9 W. d' R) P* D% Z; }
end
( y8 { s" c5 [; e % T# w. H3 i9 ^, ?9 _
P1=P;
7 q6 r) T# Q3 Q y if mod(P, 2) == 0
1 p6 {% ^4 Q! A- V) b+ f; ] % Generate R,生成样本矩阵4 J. A; k+ s9 V8 b/ L
for i=1:P1
! i6 E0 n! _/ V( L# m for j=1:P1+1
* f' m* ?) A% n+ P ss=0;
3 ?8 b" N7 F" W8 M# o for k=P1:N-1! ?2 k1 E7 O9 q+ R
%前向预测误差9 [3 x% |! B/ S# d2 S! ^
ss=ss+x(k+2-j,1)*x(k+1-i,1);
. ^2 [. @6 Z8 J, Y$ ^ u %后向预测误差6 w" W" q- K+ Q8 A0 j# `
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);; O" b; B% W* `: h
%同时考虑双向误差
7 V8 b" |0 @9 J9 r %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
6 a& [0 W: Y u* o W- e2 Z+ P end
) L% j% M5 A' d3 S; a8 Y& E4 ?. H R(i,j)=ss;
' o- F, `, V/ G1 W7 E# F end" E' O9 _8 g: w! v2 R; T# x0 ]
end8 l2 O* D, f2 [' u: \7 S# M I9 c
% divide R into R1 and R2, and get A; R1*A=R2; x8 c7 D( a! Y; K% }
for i=1:P
2 C# U' q8 p& {& D& A0 Z for j=1:P
$ K7 Z7 c, L' B( J1 X1 f% ~ R1(i,j)=R(i,j+1);) Y" E4 J1 b3 r V4 a/ v+ K' g
end6 N" o, ]0 p4 \7 Z
end) `; W8 I) z' m0 E8 ~, U
for i=1:P, Q" X0 u- t& U" ?, l
R2(i)=R(i,1);. ~2 P2 W( T7 \2 z' W) Y2 J
end# p( J8 l9 B+ w
' e$ T- A4 C \' b( E, R" K2 |
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 K8 ]& L: ~& V0 Q [6 D# ~
%首先进行SVD分解- S$ n* ^* c) j' x4 ?
[u,s,v]=svd(R1);
% ]2 q) {3 E! h. ^/ Q! B: y %根据奇异值确定实际的阶数M/ Y1 I) |3 Z! U/ d5 n# i9 q
M=0;
% x5 L# ^. a, Z' F %计算全部奇异值的均方和
7 b% W! L- ^3 _* m3 ~ Sum_SVD=0;/ B l8 u( A' B/ w3 f: X
for i=1:P
: |6 P7 m" C* r' ] Sum_SVD = Sum_SVD+s(i,i)^2;; H( z$ O5 P9 m$ @. `2 v; g
end
' e4 }) T& \& v# g: w0 E4 Z# s cur_sum = 0;$ K! f& ~% f% b4 D& @' a) Z6 {
i=1;
& X. Q5 [5 k& W! M$ q2 B6 v2 } while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P3 h$ f9 R" c b7 [) M. t
cur_sum = cur_sum + s(i,i)^2;/ o8 { y2 A9 N2 m
M = M + 1;- n/ G: X* ^3 U6 r$ T% `
i = i + 1;
7 z; T$ k& h/ y3 J end
* q! f$ {. y. @! K- u, G %输出预测的阶数M
# U' L k) N3 N. R: B M;
6 j& P2 ]/ h0 }; X7 r$ Y2 F4 W. W %生成Sp矩阵1 ^/ h: s& Z) E5 V2 @# ?" n& W8 ]
Sp=zeros(M+1, M+1);
$ S$ T. D* X5 G" F2 c1 G) c for j=1:M ' ~' g5 `$ w! V9 t% k. D
for i=1:(P-1)-M+1! ` h r; ]& v6 T3 Y
Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';9 d4 l7 K# V% E9 q$ z
end
2 Y3 R* o% D. Z$ I. x end6 F+ P- y# D5 y+ d6 q! W3 c c
, T4 ^3 g* }3 I: I0 }% j& L
%根据公式生成最佳最小二乘解& b8 ?* I4 V* z
Sp_inv=inv(Sp);
, i% p4 x J5 d if isinf(Sp_inv(1,1)) == 1
4 ?+ X( Q ^& `6 ?: E2 R0 K4 l Sp_inv = pinv(Sp);, F; V/ t2 V7 q
end
2 g& h3 g' B9 J; a 6 w. [4 Z% Z+ P* Z
a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
, s6 B9 `, ~1 Z3 n3 N! { P = M;
4 ]( b7 F3 @, h: R% R) w %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
l2 E$ c3 y/ t2 T9 g % Get Zi$ |' N$ h, f0 J( [8 L% H# f E
cof_SVD(1)=1;
! Q% t% Z8 ~2 e% @2 m! N for i=1:M/ r# Z. Z* D2 D3 I2 d- a; l, n( d3 s
cof_SVD(i+1)=a_SVD(i);
4 G( A( V7 H! q7 ~0 y end
$ F) ~; h" p! {! ] U. R8 r Z=roots(cof_SVD);
8 `) q' t. R( L3 a* t' o ; [* F2 L5 d; R) \- T
% Get y,y should be very close to x
- t3 w5 s5 v& r: u3 X for i=1:P6 S. ^. ]% {- \4 f
y(i)=x(i);) K3 U1 X. j8 r/ A3 O9 u3 N1 r
end
4 j- C' o k: }
+ H, p; O2 y1 h7 O for i=P+1:N) Q) y9 c" D' O) S
y(i)=0;
5 o- F( r) i% r _ end4 e# Y9 K3 y9 F8 x
for i=P+1:N5 D9 d, {+ Q5 W7 J4 D
for j=1:P
0 O: q4 ^: f7 w3 F y(i)=y(i)-a_SVD(j)*x(i-j);
' w% y3 M# ^" V$ ^0 k9 G: B end
8 k& m8 m" T8 O# j: t) H$ W end
, K8 A9 B3 ]& R r$ @: Z
" \, H5 C; A! |1 O8 p6 B % Get B& s: d, `! s! y3 H; o
for i=1:N
* g/ N! l4 }8 n3 q, L: m for j=1:P
/ t, A4 l& W! O) x1 p Fy(i,j)=Z(j)^(i-1);
9 e' s+ B. Z p! v7 c C* O end
0 `. i2 R' H& j: H, K7 K end
2 x9 j% K4 G) k( g! A# O- Y: F7 d+ L1 T- I Fz=Fy';" A5 K$ i) u. q, O2 \- J' @; A
FH=Fy'*Fy;
4 L# w' t Y2 _5 C" q# a Fn=inv(FH);
8 j! T: y- N/ h: w( g0 K B = inv(Fy'*Fy)*Fy'*y';
4 |0 S9 s! M# V4 f/ d# e ) h. z) `5 k4 f/ F: I! P
% Calculate Amplitude, Phasor, Frequency and damp8 r, M' S/ _( G3 E. F3 e
for i=1:P
$ C+ ~3 t+ A! y. o. Q% E Amp(i)=abs(B(i));$ v: N7 F: g6 E1 T& Q
Pha(i)=atan(imag(B(i))/real(B(i)));# j' {! ~ g1 F: ~( l) x% m
Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);# l5 V! O2 p( x& }; k! h
damp(i)=log(abs(Z(i)))/dt;+ ]0 K$ L& S/ Z/ r. x
end( k8 z1 Z7 S4 P4 z6 v! q( _+ q
%调试用的代码2 M7 p' d- u' C! x/ g" R
if isnan(Amp(1)) == 1
j9 ?' _( L6 b) J. k- f error('幅值的求解出现错误!');
- x( v4 V. O; `: R end M4 x: U5 |& ?( L9 E j
i$ D; S5 |" Q3 U; z % Get xc,verify if xc is nearly equal to x" M1 l5 p; f6 c, A8 N/ p$ }
for i=1:P( b+ Z2 z. y3 J$ c
if(real(B(i))>=0.0)
' v/ n7 p2 i9 W6 B/ c$ ^ bth(i)=Pha(i);
& L& g( ~8 d9 f3 [ else: X) [) o2 ?/ c! M0 @+ u) o$ \6 R
bth(i)=pi+Pha(i);$ a* [4 e/ |6 O) q) u7 A
end
% _2 _0 V1 [2 ?, n- ?, x" m end
1 m+ u, ` v8 I' j %对Pha重新幅值
: O1 N" p" R* ?& j- \8 S% G for i=1:P
3 c" [4 F( ?% ^ a9 W% f" j: u if Pha(i) < 0) [- B P! f$ H5 j! F
Pha(i) = Pha(i) + 2*pi;
+ B* [& d* x$ x3 l6 o; e end
3 ]9 C0 b2 X) P8 {! P' q: W* C end) |9 r" U$ W1 U7 d
0 y: A& b6 B' k( u8 B% w& ?3 I9 ` D for i=1:N
& a& [6 t5 Y) m% x, }& Q/ |0 t xc(i)=0.0;6 f( r; s; A0 W$ u
for j=1:P
F; p: F ]1 K/ c xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));6 G7 A& w8 u" N1 A6 \* S4 R
end
m, P6 |: {- o8 `) R end
7 C4 \" i( ~) K( K' J+ \/ T7 R% if showfigure == 1* ]& J5 n( B2 P3 ~4 _$ C
% %显示特征根的位置
& u; {+ d0 D1 f+ i0 Y/ A$ H3 }0 h% figure;1 ?2 K+ w+ S+ n' \
% plot(damp, 2*pi*Fre, 'r*');
. s& q0 v; F$ v/ v/ h, }) T7 n% end
# h" m+ m" l, U/ j) @2 s3 q
; x& v; _2 s' ^ xj=xc';2 p& ]3 E3 e5 q4 J/ D) {4 ?
er=0;& v0 X1 M. N+ y
all = 0;
9 N# _4 i- }1 {* U% F& e; _ for i=1:N
0 A/ b. f, G { er=er+(x(i)-xc(i))^2;
! S; a1 X" V' F! [( y all = all+x(i)^2;1 e0 t# M4 f" r3 j! O+ G
end4 `: ]" P: M) @7 V' v, @' t
SNR=-20*log(sqrt(er/all));
% @, G( A" ^7 m1 d0 m' Y( _
; {5 |1 N. ]/ c# S* ]. l0 p9 R % Calculate Prony spectrum4 ^; U1 @6 V2 {- A7 f' C
%频谱的取值范围为0-5Hz
- i/ U: O9 y0 n4 k( f f=0:0.01:4.99;8 `5 T$ b4 X# ?! S N3 ]* c
for j=1:size(f,2)" b1 c0 q4 _5 E& _. A
sptr(j)=0;* m6 m0 O& ]' t3 N
sptr1(j)=0;( b3 H4 |: K" K2 I
sptr2(j)=0;, u7 ~+ k1 D9 |% H
angl(j)=0;4 {) V* d u7 k# A
tmpangle = 0;
- s" @. f, m( w) v. U/ i for k=1:P% K+ c( g' y' ` v4 v
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));6 p5 @# d! F* R" r3 N3 p+ u; m g
sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
! i/ I3 W, i& `2 e4 F" _ end0 p7 v& B/ R, H) d* j
sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);4 v E0 T0 L V1 b+ k
tmpangle = atan2(sptr1(j),sptr2(j));
! Y0 t3 F) M0 l/ N" x5 L angl(j) = tmpangle*360/pi;
V; q# K& O" ^5 `/ F end
% R# \8 z; i5 R- l0 C' F# b( Q) J %对幅频响应进行归一化,并且寻找主导频率模式
5 {0 U9 p" @8 u) i %寻找sptr的最大值
+ F- |5 n* x; d& n: Q max_sptr=0;, z7 b* Q9 j! S( F6 C7 p6 B
main_f=0;
9 e5 Z4 ~6 }9 _6 C8 d3 m for j=1:size(f,2)
; q2 { T1 m4 U: ^1 g& P/ a if sptr(j) > max_sptr
s# p; L4 z! ~, l/ B6 U3 _0 q9 z max_sptr = sptr(j);
3 V+ A0 Y) n: D) t %主导频率出现在最大幅频响应位置
! {8 [: U. [) Y& ? W, L T if f(j) ~= 0;8 N; ?- a$ X( a2 H
main_f = f(j);2 a T0 L" f4 l4 o) K
else; k( j# D% ?- w! T7 }; X- L& U% J
max_sptr = 0;2 R% r. B" R( V5 A: K+ h
end
0 `+ G8 G$ Q- C% K end
; i' n4 M7 H# d end* K/ J' A9 U* f1 W( D
main_f;
7 [, b4 ^6 S! `$ E8 g %找出真正计算的频率值
) M8 G- d! B: |& {" c+ S; ` f_err = 10;
% C4 R/ K4 x, ?5 W1 S f_main = 0;
/ l: u, u# O' X5 Q) a" M+ b+ ^* P for i=1:size(Amp, 2)& U& y+ R0 u+ W! x1 z! A* u4 G
if abs(main_f - Fre(i)) < f_err7 ]1 u& W% q* Y3 G: {
f_main = Fre(i);
! l# y) |. l( c8 [# P damp_main = damp(i);
( | B1 M7 `& G7 w E6 z f_err = abs(main_f - Fre(i));
% p) T# O2 V+ W; O* w) W9 G7 K$ | end$ H+ f) {9 `( w) Q# U* ?& I
end
S9 i7 j$ v) u, Z9 p2 Q9 I | main_f = f_main;/ J. a) {9 O$ Y/ q* a4 {
main_damp = damp_main;
( W1 ?# k# i3 j+ ]; M6 r4 n %进行归一化$ n6 ]+ N# T0 \2 a' @. z2 e
for j=1:size(f,2)
, x3 F2 N3 L' ~ G; Q- q2 Q sptr(j)=sptr(j)/max_sptr;
7 O1 S% U0 U- o' b { _% s Amp_Response(j) = sptr(j);
+ G! U2 o) m* _; u* {/ ] end
1 d3 c5 ?$ _; h. v ) X* d5 i% w5 l) n
for i=1:size(f,2)# G# V: u% g- R
if angl(i) > 0
+ }6 Y% m3 w+ f( m+ W angl(i)=angl(i)-360;
' H) S! f' T2 f end
1 i4 |% ^, }) G) g `. z0 z end
* e0 T, L4 t) M5 z% L . D L, R. o5 h. B4 a5 X
if showfigure == 1
" w3 i1 |3 c+ Z( X %在一个图上显示时域拟和曲线和Prony频谱分布
# m4 l- K6 ?+ s7 C; l7 Q, Z4 \ figure;
: Q3 B x& _; U subplot(2,1,1);
" {/ ?* k C) n, ?. `* X %plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');
4 T# e, R4 S' W! B plot(tt,x(1:N),'r', tt,xc, '*b');
* ?( V" ~: L8 y7 l0 f subplot(2,1,2);( o2 J' k' _0 a- [3 z5 O1 u9 ]9 T% {
plot(f,sptr);
% Y# ?4 \$ m, q" l4 x5 O %subplot(2,2,3);
, r3 g4 H1 E6 d %plot(f,sptr);
! i* @' Z0 J: V$ }9 m2 x %subplot(2,2,4);
" p, K* w+ X/ i# }) H( k% P %plot(f,angl);, X' R) H8 t' U/ O; }: Q
end
# A' r* L! v6 E0 l' e5 v- i- [' U 6 Z" y% O: y T0 }1 \# C: E
cpu=cputime-cpu;
: \' ?$ m* a, t/ M( H$ G$ c; C format short;
# X9 Z- Z* I7 i7 ^' l4 g end |
|