|
|
楼主 |
发表于 2011-3-29 13:24:52
|
显示全部楼层
回复 2# debra l7 d3 ?7 y, ^4 R* l
! z- q( g7 E+ M8 A
4 K: _5 Y, r8 j5 H2 X% U! m8 G
%打开指定文件,并对信号进行Pon分析计算
+ P1 C' X! m4 qfunction [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)* r) c- f- a& r
format long;0 M6 ~5 v) G' K9 G: }$ q! J8 \
x = x_in';8 \3 U: X) L- y- e
cpu=cputime;7 \) ]! d# w. u2 m2 W+ ?6 B v
N=size(x,1);
0 A4 ^$ e1 g" v: H o% Z) | %取N/2的整数部分为初始的P# z3 I# `5 {9 O, E, ?' }+ C9 ?' E
P=floor(N/2);
* y9 @' ~4 X) a7 R* J" v , Y* G. a: w3 T5 R# i
%去直流环节8 g b8 ]; @' ]2 d+ Z
x_Sum = 0;7 w; X8 D8 \# j( U) ?) p% s
for i=1:N
+ G6 H$ j$ i0 ~+ H- U- x x_Sum = x_Sum + x(i);
6 o- T& Q* N) q3 C: g! V9 n end - m1 K# M+ f' y+ Z& r% T! ~( r
x_av = x_Sum / N;! d$ k- a! t! `9 W/ w
if x_av > 10E-10# c: f- |5 I* f5 n
for i=1:N6 g- a/ O: s& x8 \$ d+ c6 W
x(i) = x(i) - x_av;. g. s4 t m5 T& y
end
. X+ ^. h3 x2 M' T# F end; `9 `5 z% q5 I+ [) }4 y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0 K" l" m7 C7 Z8 q; k5 l0 b) v i %滤波环节! j6 Y) Q- Q( {/ i8 I" H
%fL=1;1 W l0 |# b4 x. O2 f
if fL>1( t6 |3 w4 `. M4 A7 W3 U5 c- _ d
for i=fL+1:N" T* f# ?' i( ~% J, C) r
x(i-fL)=0;
7 i, x" w) _% f% r8 }* p for j=1:fL
* m. F- C7 X& S s# O- K O x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);; Z @0 ]7 b! V- e- v3 O
end5 t% Q# [# y. W; F& E* R# ^
end4 N, J. u4 G+ t5 w/ m2 F8 l* Q
end
7 e/ }0 j$ ~* G- v/ i- ?" l& k N=N-fL;
) P4 G, n( D0 j4 B2 B* v tt=0:1:N-1;) X1 t* I- t" k! Y/ [/ ]/ V
& m: o' ]6 z( r' Z %P要求为偶数
/ [ J7 H% P Y if mod(P, 2) ~= 07 Y9 @( y; a. ^/ q* E* g
P = P - 1;5 f; ]; h6 A8 B$ M
end F/ } O& Q" K3 \8 `
6 k3 u) ?) o: f P1=P;
3 y6 l2 \$ q- } if mod(P, 2) == 0# M$ V, E+ n% x) a& a m0 M: F: ?
% Generate R,生成样本矩阵7 m# j" y; ~: ~' f- g
for i=1:P1- O9 v& v! M0 L: B! \3 I l1 r
for j=1:P1+1
) X' p; b. t7 @+ F* G. ]( a( ] ss=0;/ Y+ r& n* ]7 q: O
for k=P1:N-1
5 S( H9 _3 F# Z; q4 J+ ? %前向预测误差
1 e2 I& M% S& e ss=ss+x(k+2-j,1)*x(k+1-i,1);; e! y! u) P) @
%后向预测误差7 p8 o7 \9 a* l% |6 ^9 N4 d2 t/ B
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
& e$ x; L3 z$ M* ?; Y9 \1 W %同时考虑双向误差8 P* v {6 d3 U4 h; v
%ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j);
) {9 v! m+ n, d# {3 h% ` end
) S8 R3 S7 u% }6 g R(i,j)=ss;$ M) \" X9 P! K) n) b
end. L0 Y( w6 [% m( L
end" o9 J/ f9 ^1 f; K. Y( C
% divide R into R1 and R2, and get A; R1*A=R2;7 j( [) t( w' ~) P7 J# r3 h
for i=1:P
% v0 f4 O1 e: \. ] for j=1:P7 F2 K7 E1 z& M* {& k5 `( a
R1(i,j)=R(i,j+1);1 h1 j6 [1 `) X
end* z4 V5 F( |" M9 T4 G
end
H# o% p+ m# d- V `, _/ V for i=1:P
7 y1 h, G* N2 c R2(i)=R(i,1);: n( x$ L/ W" G) _" ]
end2 C) |" A) g! Z l+ O- D
0 Z* ~ o" `2 x# G1 ?% X
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%! L( m5 l& o% r' N3 u. S5 ~4 r0 I
%首先进行SVD分解
2 k1 O# e# b) Y7 h [u,s,v]=svd(R1);. _; F T! t. P+ j) O( }
%根据奇异值确定实际的阶数M$ u! J) v7 T2 ?' t. n, v
M=0;& e9 O/ i0 v b2 M1 m" F
%计算全部奇异值的均方和9 ^: ^) @% Y+ f( J
Sum_SVD=0;2 W3 e# t5 N/ Z+ u2 D5 G
for i=1:P( h) a5 ?' i% c+ j4 V
Sum_SVD = Sum_SVD+s(i,i)^2;# |8 R6 c* B6 d. T" P
end6 w( ^# `; b* `" F0 O. \
cur_sum = 0;8 @' y1 ?5 q: ?! l# Y& m+ [# V
i=1;5 b) ?/ w; ^* _* }
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P, @. k5 |3 K4 c1 U( n
cur_sum = cur_sum + s(i,i)^2;
& t, U9 D1 t. b$ m/ _* m# V M = M + 1;
! R; v y c& W z: l/ K+ j i = i + 1;6 ^! \5 X/ Z2 D0 c+ h& j
end
! t7 y5 h& m9 c6 @3 P %输出预测的阶数M1 V/ |, Q, a0 _8 W( b
M;
1 Y" B# w& T' P" b' L! q %生成Sp矩阵! X3 b; W3 w6 Z, k; z& G. h) |
Sp=zeros(M+1, M+1);
( g2 y5 B) I2 O' r' ^/ n2 @! z for j=1:M
3 w* r$ u0 f1 @, u0 G6 | for i=1:(P-1)-M+1
0 @/ X1 c+ f# \6 @0 U# i Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';3 O5 h% {7 A5 l' s
end
/ ^4 a2 w/ d; j* f end! v$ u+ A6 X5 y
5 _, B% m" J4 S( C" B
%根据公式生成最佳最小二乘解4 r. ^- {2 n, X" N6 T2 B
Sp_inv=inv(Sp); `4 u% U. x8 o# U0 x
if isinf(Sp_inv(1,1)) == 1) b5 c+ U7 t1 e4 O
Sp_inv = pinv(Sp);
! |# A2 |3 ?' b end, f" x9 J- C# H$ }' I
1 A" S- m& T# }- Q a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
' W/ B% z/ K/ M3 a* P( M- M7 O& }9 e P = M;# U3 x/ O+ w$ X
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%6 v+ O0 N; n1 j9 i7 R8 R$ I& a: n
% Get Zi2 ~, H7 |# R- t
cof_SVD(1)=1;
6 m" J# Y/ ?$ a ~' M+ I: l O3 o for i=1:M% _9 Q2 s0 _( L
cof_SVD(i+1)=a_SVD(i);' ?: L2 P) |" W( G# t$ Z
end
2 a0 H: a) y3 j. j Z=roots(cof_SVD);
) p+ X1 X z8 l* M
( p B$ j# A* I+ h' c % Get y,y should be very close to x
) M$ h" X" E4 Y ? ^" K' ]3 p for i=1:P
( C! V1 p% N/ n y(i)=x(i);: Z+ T2 c7 p: w/ z, Z* m/ j. s
end" | N6 `* P9 r* G
d$ F+ J# l% L, V7 ? for i=P+1:N
. N0 w/ ^3 Z3 F8 N( U0 p5 g y(i)=0;
! c) n; e* B+ i/ ^4 ~, ^3 r" w end2 P, Y2 h* J J% L' ^. z: ~) @
for i=P+1:N
: p: d& Y# g$ Y' \ for j=1:P
3 P& S7 d0 t Y7 @ y(i)=y(i)-a_SVD(j)*x(i-j);
& f; F, g( [0 K- Q% E. b4 o end/ T# C; m0 \8 y2 \8 O6 e
end
$ r$ h; a6 s A8 V" f
( t4 o: w7 r7 z % Get B4 ?" n) ~& Y, t5 X# P' ^7 c2 ]
for i=1:N
X- r: L1 h/ V. c- M* o for j=1:P. \7 [' x7 k( ~% g4 g9 X
Fy(i,j)=Z(j)^(i-1);8 b- x% P+ ] z$ k
end
0 ]& w7 C* b+ F, x' n% a end: t2 G, c) j$ J( V8 T6 T) r
Fz=Fy';
9 s% o% U" z, g8 M FH=Fy'*Fy;
$ Q/ P5 c' T: i4 j Fn=inv(FH);- ]1 g* ^. h0 @' U9 Y1 r! Q
B = inv(Fy'*Fy)*Fy'*y';
[: t4 j' f0 T: s! c8 L9 D3 k
+ m, N2 L$ {9 |0 Y % Calculate Amplitude, Phasor, Frequency and damp2 A6 D& n2 S. M) D: @; Y
for i=1:P9 W8 z7 Z8 V& ` [- E) h
Amp(i)=abs(B(i));
. Q. k5 E, {0 V8 E8 ?/ |1 ^ Pha(i)=atan(imag(B(i))/real(B(i)));
/ D- a; m8 f- I Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);( ?, q; G& P: K' \
damp(i)=log(abs(Z(i)))/dt;* t% c$ o9 j6 P2 g# v2 l* D2 k4 p
end& l0 m. G G) j/ b6 z, b2 W) O& l
%调试用的代码8 @* E! n% @% k5 c8 a
if isnan(Amp(1)) == 1
b* P( l4 K3 L" X, ` error('幅值的求解出现错误!');
! x) ]6 C* w' j. h/ D end
: f& h$ {' M2 [) R1 b9 s, n/ H
) z; h' u7 O( s* q9 y5 }0 w % Get xc,verify if xc is nearly equal to x
. X5 d; v+ s% Z' m' v3 d for i=1:P
/ b, n1 H# u. S# x& M if(real(B(i))>=0.0)0 l2 Y: X8 o1 l" [
bth(i)=Pha(i);
0 p/ ]0 V3 G. Z* N4 l0 L else
/ {* P: g9 [ l3 r, i3 D& v m* t( F0 F bth(i)=pi+Pha(i);
+ j+ W. ]8 G5 A/ G2 r: \ end
& |5 \6 Q q3 X6 M2 n3 U end
# e& T4 X) Z5 W2 |, E) U# O' v %对Pha重新幅值
& N% ^9 k* Z u for i=1:P
3 Z4 s! I0 ^5 [' N if Pha(i) < 0
* b' W4 D6 }7 C% a7 { Pha(i) = Pha(i) + 2*pi;4 G0 T; W' m% C/ a; H6 E) O4 I
end* j* b+ \" m3 o+ {6 w4 L
end6 C7 Y8 R) w) e/ z2 v* l- j
5 N( n: e: W. ^5 O
for i=1:N
6 y v! Z1 |' `* d/ j. M xc(i)=0.0;
3 k* H$ h& a) V$ b+ x& G) a1 O for j=1:P' H# X& y' ~1 G% M+ x# i! @$ a
xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));% R( d# k* M# O4 m5 d( ^
end
" h: |8 ~8 c3 v8 K1 t. j8 m7 s% y& Z end0 l6 R* z* Q y) H2 b4 J
% if showfigure == 1
) i+ X3 b0 a E5 _. J4 Z% %显示特征根的位置/ Y+ Y, s8 q7 W. J8 U
% figure;
9 c0 o: j6 L. e& f+ w8 n L4 ~3 g% plot(damp, 2*pi*Fre, 'r*');
6 ^; `% @' M5 w( S% v' r% end% N( E' t: s6 |+ B
) _9 M+ w4 V6 h" r xj=xc';
: R7 N6 f" m* _5 m) O- p er=0;" Z e. y: A/ N
all = 0;; W% Q7 j5 e" f8 q) p/ _
for i=1:N
$ H4 z2 R( c. Z/ y5 z# K9 i# {" b er=er+(x(i)-xc(i))^2;
* \& d6 J: T) c5 }! e" ? all = all+x(i)^2;
- v0 F' y" B% S' x end
0 I" Q; f7 h' @3 H SNR=-20*log(sqrt(er/all));5 y: v$ Z$ ]+ Q5 G8 Z# x8 W! x
6 s6 [7 ^/ f2 V; D3 K % Calculate Prony spectrum P% F. Q0 u, F+ d. k# n) U# \
%频谱的取值范围为0-5Hz9 \2 o) V& b. @! _! @' |
f=0:0.01:4.99;
3 ~; Y0 w6 s* P" W for j=1:size(f,2)
- j+ I+ y- u' J8 w5 G9 L sptr(j)=0;7 c' G6 k2 M! P) w
sptr1(j)=0;4 d4 b0 R1 e3 j7 ^, k
sptr2(j)=0; I+ Z6 z% g/ t" |
angl(j)=0;
7 K7 A& \* O# c: e4 ~2 B& D. } tmpangle = 0;
- d' S6 V& E1 Y7 F for k=1:P' y- \8 v8 Y! `2 R
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
9 ~: P* s5 s; Z( E- G1 l, } M sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));1 T: f% L$ V% R) l
end
$ H# Q. {: |' Z- Z, a6 { sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);
* t* \$ U; R ?* L tmpangle = atan2(sptr1(j),sptr2(j));$ N/ w* P G0 b3 @9 {: T! |
angl(j) = tmpangle*360/pi;
m0 a0 h( z$ l) L2 b5 P+ O- e8 I end
5 ]( G5 M4 ]$ e- ^, ^/ \2 {+ l %对幅频响应进行归一化,并且寻找主导频率模式% y. E9 m0 k; e& b" t
%寻找sptr的最大值
; K' q( @+ W, ?$ p8 B- O max_sptr=0;% ^' q6 X; L9 w b
main_f=0;0 l' t- d- K' d, N% I
for j=1:size(f,2)
5 i7 L# O! W) {. `! p/ o if sptr(j) > max_sptr3 X. V% |3 w. ]' ?# j. l
max_sptr = sptr(j);
m0 ^8 p5 \" s/ K8 _ %主导频率出现在最大幅频响应位置$ k' f# A1 q7 V; X; ?2 }
if f(j) ~= 0; w1 a7 o1 v/ G* i
main_f = f(j);
' s0 t7 E) H6 b3 A else
' D0 E) R& M% ^; k& \4 c. H& h max_sptr = 0;
$ |* m! V% R5 i# c) k$ a end
' Z! L# |1 ?, ]! y3 C6 o0 J" U end/ z( p( a4 o. S' H1 }# C
end
7 b8 J& J4 M( U# P, v main_f;
; ?, [& h) W- e' e- Z4 Y %找出真正计算的频率值- B$ ^% k- T' }
f_err = 10;
$ Q' j- V7 J$ A- `$ E f_main = 0;: L3 r; x- ?# K9 Q/ U
for i=1:size(Amp, 2)
4 y. X$ L/ a! b& D0 t C/ n if abs(main_f - Fre(i)) < f_err( z) p9 A2 X7 R* ]! ~/ r) o; _, u
f_main = Fre(i);/ c0 L1 E: f' h4 f! q
damp_main = damp(i);
' w# u/ ?# w; f. P% u f_err = abs(main_f - Fre(i));2 o& U$ Q! t0 h0 I
end
0 u% j5 h# r) a- n8 c end! I: Q5 w$ P9 L- ?( m: @: A
main_f = f_main;7 {! o/ S9 t/ v* g8 H
main_damp = damp_main;6 Y) ~; ~; i6 D; O8 l
%进行归一化 e3 F7 R' {* U* P' a9 Y2 o
for j=1:size(f,2)8 o( N0 L# j. n. F' _
sptr(j)=sptr(j)/max_sptr;8 \& G$ J. F. g& d7 u6 @7 p
Amp_Response(j) = sptr(j);
* |8 {7 @& S/ k end2 ~- w* _9 Y: i6 ]% n: A
8 C' ~+ ~4 T, k( o' z! n
for i=1:size(f,2) F* A, |2 h/ K& w2 f+ [
if angl(i) > 0
& m& z% j% [; a0 G angl(i)=angl(i)-360;
; @) V6 e: d1 x end
8 @- ^% H: T2 G2 @/ _2 U' r end
2 `2 A9 m# v! I: h- Z: G9 y3 v
' T C+ ~# T. J$ |* C+ x q if showfigure == 13 W3 K; c; N; P
%在一个图上显示时域拟和曲线和Prony频谱分布$ O0 t, n/ C& j$ |( F* `' X! W6 A2 O
figure;: p* V% p& M; B6 q/ [8 l
subplot(2,1,1);5 t. [) ?( Y$ p' \3 @ X
%plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');
# B3 K$ e# C( y- P plot(tt,x(1:N),'r', tt,xc, '*b');; U) I% J8 ^3 u3 [' Z; G4 W5 K
subplot(2,1,2);9 ` N0 `7 `5 e) N4 L* m% G$ o
plot(f,sptr);' y3 l4 j0 f- Y' X( |
%subplot(2,2,3);
+ Y/ X2 M- i/ [9 ?% _/ n5 d5 O %plot(f,sptr);+ |/ k5 C4 [. S9 M' w# k
%subplot(2,2,4);: B# o7 V0 m0 `$ P& R" M
%plot(f,angl);. A3 X* L8 U0 |, G6 d
end5 U$ h( H0 X5 m( |6 w- V/ F& y$ G
: }# }# D7 T: E/ |% X6 R, H cpu=cputime-cpu;6 O' G) X7 C8 G, A# r& o" J
format short;
# k, D+ T' q: n' R end |
|