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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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5 K. ?7 e: e: Z. ] N %打开指定文件,并对信号进行Pon分析计算$ J+ v( E/ C C P
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)( X! A n s( Y4 L w
format long;
- Q- t/ Q/ N! ?7 p9 |: u @. [ x = x_in';
5 x4 D# @; D( e/ q0 R8 S cpu=cputime;1 y7 F, g+ T1 @7 K" K
N=size(x,1);5 q* [( j) k4 H! X+ J) }# }5 m! ^
%取N/2的整数部分为初始的P/ M/ k4 d( ^' y" G, n
P=floor(N/2);
9 q( ? Z8 x8 f: Q: C0 D. l# h + G( Q5 C6 O% X
%去直流环节" E' f! m# q4 a: A; P$ D- B2 l7 k
x_Sum = 0;$ ^1 M5 U) m, y/ S9 Y/ }2 U
for i=1:N
3 |9 p+ V# z+ w. i x_Sum = x_Sum + x(i);
1 B7 v5 D# x$ ] end
- L& u I9 u* i/ p x_av = x_Sum / N;
- e; y1 M& v2 x+ }5 Q if x_av > 10E-108 X+ H* K0 i9 N! G
for i=1:N) O% ]) T; M3 L
x(i) = x(i) - x_av;
. A$ d+ r! p9 D8 V1 A4 z end' I8 e% { f2 w+ ]( {: _
end# _- B" V9 i$ f) a2 m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
$ G: C9 U! a' T5 Z% D7 \ %滤波环节# p7 y/ G- W3 B- {2 x- @# K2 p
%fL=1;
, }8 w. U5 F# ?0 |" [/ w! i if fL>13 R w8 x3 M" y# p
for i=fL+1:N
) C9 M" r/ p' y# l8 J7 g x(i-fL)=0;
3 N7 H9 E3 e$ {. n t for j=1:fL4 _5 w7 T+ y1 J
x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);
9 F. }% U& h! @ end% D0 v& i5 o. j; s1 j$ o& W
end
6 O# W# k: x$ q, D; g& Y end
: W; |0 O3 i7 l: _ N=N-fL;
: b" ]) l1 b* I2 I8 s tt=0:1:N-1;
2 D& }1 H1 r9 {4 b5 Q3 D. z6 [ % B* Z. H; N) q# A' X
%P要求为偶数
5 a, A: S5 h8 V/ u" r if mod(P, 2) ~= 0
6 K% c3 U: o. |; z/ | P = P - 1;( C, [; g/ g! E# E2 j4 s2 K
end# N: {( D0 i- A. R! \; q/ P7 F6 I
; H. ^* Q( y) b9 V
P1=P;& K3 k' H! ?2 \( x" q1 o% A3 F* i0 w M
if mod(P, 2) == 0; Q N0 B8 }2 V+ ]1 [: F1 C1 v" `
% Generate R,生成样本矩阵
: }) W; B* g+ G U for i=1:P1
, I" a" B( |8 d for j=1:P1+1: ~/ _7 n+ _( l; W& u
ss=0;0 S. p* d# f5 m# r
for k=P1:N-1
7 h' V8 F8 Z/ z: w %前向预测误差 h% r8 N$ v% j
ss=ss+x(k+2-j,1)*x(k+1-i,1);
4 y8 W( @; E0 F/ p' i9 v %后向预测误差) c5 p" p! I, E& C# V
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
! _1 }1 ?/ S" W- @ %同时考虑双向误差6 ^! E& t& q) f- w4 b7 r2 r
%ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j); 7 p# O& w, Y0 K4 T. A& _
end
, E0 f1 Z; X& c. s' U% T! } R(i,j)=ss;
4 D$ F1 F8 o+ L0 Y7 M end1 I' `* z% U5 q
end" B6 a V' ?5 \$ p ?4 w2 R
% divide R into R1 and R2, and get A; R1*A=R2;
6 a: _' r1 D& C6 A2 s R, I- \ for i=1:P
- o( n' A0 ?$ J* `+ p" h2 @ S for j=1:P
+ d* f/ l7 k& g R1(i,j)=R(i,j+1);6 y P1 B' x. Z9 V7 s( I" z
end7 u' ?/ {+ {1 |( U7 k3 P
end
; ^9 J; i/ ]% H& a for i=1:P7 M* ~4 ^1 Z1 P
R2(i)=R(i,1);: v9 t5 D7 M/ E0 H: U3 |
end; J" T/ H. X n6 ~
3 q7 _1 ^* L+ `: k
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%* R+ v2 y1 m+ E7 L5 Q1 M8 h
%首先进行SVD分解
$ D& A' N4 z* F7 m [u,s,v]=svd(R1);' \7 q" \2 e1 f* ]/ W, R
%根据奇异值确定实际的阶数M$ S' V5 Y s& [& O' L
M=0;
% o% z3 n( B* ^2 p9 l5 V+ J %计算全部奇异值的均方和
' h5 U ^; u9 D$ G4 x8 H Sum_SVD=0;
5 y% c* w3 r: ?' G( e1 E for i=1:P
* c( ~9 s& ?1 w! o- p8 X Sum_SVD = Sum_SVD+s(i,i)^2;
0 Z1 F% y. M6 {+ [4 X- J end) j- Z' b( e+ A6 |
cur_sum = 0;5 g& e) n$ h2 m% F
i=1;; v2 H) `* R4 W% U! v( a
while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P
+ _6 E0 A9 Q9 v4 r L cur_sum = cur_sum + s(i,i)^2;0 u% m0 x9 k) j8 s8 |
M = M + 1;9 C5 p' D& E! w- G8 l6 |
i = i + 1;
, |, I' l& Y7 u) B7 P! O2 R end+ R6 X. d( C1 M/ l3 G7 t
%输出预测的阶数M
; ~0 \0 `: p; ]% I$ R M;
' b# _ `3 M s- a %生成Sp矩阵0 Z3 n- R i# q0 K* N
Sp=zeros(M+1, M+1);- A9 |9 a5 r7 C) x* M
for j=1:M 2 Y5 J2 k j0 x; V
for i=1:(P-1)-M+1
6 h0 J! v3 N+ o( _# F3 V$ d7 c3 c Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';6 \+ ^ ^! ]- j! ~: T4 G
end
3 O2 I( b$ w1 Z" H, Z. A end
$ S; A+ J S9 R$ V- z 4 B; U( T2 x. u- f0 o) r- ]
%根据公式生成最佳最小二乘解0 `. T/ C! j& t1 @( m0 |
Sp_inv=inv(Sp);4 u6 R. i: Q5 k8 c1 R3 s0 \
if isinf(Sp_inv(1,1)) == 1$ B3 l6 K8 W0 S$ a6 X# ~: _3 O4 M
Sp_inv = pinv(Sp);* ?7 l6 I. ~) c( v( Z. p( l
end# g) U7 ^" ]! ^$ p
! @0 r* A4 [, j4 A, D5 T a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);
`4 \. k ?! R P = M;! r# p' V8 T1 m3 h/ g
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
9 b4 W% G/ n1 `) c* m % Get Zi) |& v! d o! ?' r
cof_SVD(1)=1;/ G* w5 `: \( E( G
for i=1:M
F& H. f9 K: _4 I: d) P6 e' z cof_SVD(i+1)=a_SVD(i);
0 V7 G5 ~ o9 `, T! Y G0 b end" J5 T0 l" q( S1 ^# u
Z=roots(cof_SVD);
# I% r% u8 M0 Z/ `1 h4 _ - L, z" P! Y* c# p+ ^) K
% Get y,y should be very close to x
6 I$ K9 x: @; N' W/ T for i=1:P7 @, c8 U, u: J
y(i)=x(i);
. E! C! s' D7 `4 w$ q' X. } end X/ q- b t% r* o6 I+ S7 K0 F3 e
0 V1 M6 c6 ~/ z
for i=P+1:N2 h" e4 _ m0 V- S/ L0 W0 v( {
y(i)=0;
: l- y0 z, n' \% D& Y; J+ { end6 \5 W9 L6 a5 [' j5 T
for i=P+1:N1 T% y3 f0 y; I( Q4 I5 e3 H% B+ ]
for j=1:P
, {$ S! R6 X5 G7 \6 q y(i)=y(i)-a_SVD(j)*x(i-j);
1 e. K. R# R2 U) V' `7 V' b end
- C. J4 c0 N! g3 L( g end9 _- o. ?8 k0 {8 e; }; [
" y' N" y& s' z' q0 ` x
% Get B% T( _% f) x0 e$ j1 i5 o
for i=1:N8 { b% G1 N& O, Y+ Q4 T
for j=1:P5 s% C \ U4 b+ U+ |
Fy(i,j)=Z(j)^(i-1);+ ]4 n- `4 C1 I
end
! U" A" i$ Z! N. U9 W8 M0 i2 o end3 T) Q- ?- I( {2 p, M
Fz=Fy';
Y, A8 y: H7 `& O- I' w# J# ?8 ^; q FH=Fy'*Fy;
4 X1 I5 z% P# e* z% W j2 m8 S; V Fn=inv(FH);
. F' g. u, ?- Q; Y5 n* G" z B = inv(Fy'*Fy)*Fy'*y';+ V4 {& d* M. O
' s' K0 H/ u- J f! | } % Calculate Amplitude, Phasor, Frequency and damp$ X7 c6 `: d! @1 V6 V2 `$ j* B
for i=1:P
+ W, W) m! g( J8 f% j' k Amp(i)=abs(B(i));( t8 F- B8 H5 @1 I% c
Pha(i)=atan(imag(B(i))/real(B(i)));
" g' u5 T& j8 J/ C5 T0 i* ? Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);; J# l. J0 ?, m( n/ n4 r, N4 l
damp(i)=log(abs(Z(i)))/dt;( \( L( c$ p3 P9 ]
end( _. E. L* E, a5 }) G: n* @6 V% N
%调试用的代码
! w: C& a7 h8 B4 z2 e$ W if isnan(Amp(1)) == 1
% C# o/ y6 }6 G( a; j# | error('幅值的求解出现错误!');
4 }8 i, R3 X# b' A. a" H end( M0 g1 i- k$ R3 g" M ]
; E9 \' E- `- k# W% ?2 T9 l9 {# P % Get xc,verify if xc is nearly equal to x
9 N! p: A# e1 H for i=1:P
/ H% c+ o: F; P- E$ Y w: X' I. | if(real(B(i))>=0.0)- b) S" s) D z
bth(i)=Pha(i);, ]6 V2 B# P' U9 v* H4 P9 B
else; U0 Q3 O: W+ Y# {6 j# B- I
bth(i)=pi+Pha(i);5 ]& M; I6 h" S" M
end
( J0 C2 u! ?0 r: x b1 {# G/ ~ end5 P3 u+ |" K$ B1 M- F0 V0 l
%对Pha重新幅值+ q1 Z% ^) z6 p$ b5 ^: C
for i=1:P
) ~1 S7 C V" { if Pha(i) < 0
9 N9 W9 F a+ I7 V5 @ Pha(i) = Pha(i) + 2*pi;
) A7 ]9 _6 {7 }9 m4 {/ Y end" Q' y- ~. l0 l S+ m) j8 ?
end( g) x4 [4 R( k' h! B
, m! S1 L0 ?+ Q- H$ ~# } for i=1:N
@: {8 T. }8 j+ R O7 ?6 a% d xc(i)=0.0;. ~; a0 |0 F7 z0 {, N6 c2 Y8 ^* f
for j=1:P# _; I) o9 j W! Z$ J6 B* m$ v
xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));% E; V( I3 i9 x: o' v! G" c
end* c$ W; Y( M" W$ V6 B
end1 b. x; l& }( S' ]! \2 r# |8 @7 q
% if showfigure == 1
6 C, V' {% l$ L. w) ]6 O1 |% %显示特征根的位置
3 H% y, M0 X) Z3 S+ ]% figure;' h4 c* v# b+ a- E1 N m
% plot(damp, 2*pi*Fre, 'r*');
$ s" q3 j+ A( G2 Y( a8 x% end+ O2 C' `0 |$ @, J& E# p6 q
7 U. ]! O- P; T; [9 T
xj=xc';
6 U' l5 K+ w3 b er=0;: p* s3 Z9 q1 S. T! m) L; y$ S) c
all = 0;
9 H8 O/ [% X) ~% } for i=1:N 8 z% l# K1 K8 _1 }1 q( ]
er=er+(x(i)-xc(i))^2;
) _' ^$ M# I# o* e, z, n6 W: j. l all = all+x(i)^2;3 S0 a1 i( n9 j# N" n9 h
end& k' b4 i3 X4 v; L
SNR=-20*log(sqrt(er/all));" H) ]3 d }; V; {3 \# ~' u8 i1 n
% [6 z. w( F: g % Calculate Prony spectrum _6 j% L7 y& X6 n2 H. I. e
%频谱的取值范围为0-5Hz7 U% j z, k1 l0 e: h: D# w
f=0:0.01:4.99;$ l" e# u% {: L d8 g$ q1 Y
for j=1:size(f,2): p0 `; o# C# i l8 i! v8 Z
sptr(j)=0;+ h0 D: J5 i1 K. `* {
sptr1(j)=0;
/ z# H ^' L; B+ @. D0 @) [ sptr2(j)=0;
2 [ D6 z1 `! f w: E8 ]7 C2 L angl(j)=0;
0 C+ Y" n- O' u1 D' F6 v' v tmpangle = 0;8 I# J( e$ m( J& x- n* {& e0 f" ?
for k=1:P
; R& j# v6 }2 W; L( l sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
3 r& @% m) \3 V2 b: L sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
5 o1 O, \( Z6 w' V, Y5 z end
7 A4 U; C& F- z+ z1 f. D" `: W sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);
2 y% v1 [8 x: I1 j6 Y2 r( A tmpangle = atan2(sptr1(j),sptr2(j)); \2 w A% H# j. p1 Z
angl(j) = tmpangle*360/pi;2 D( i9 a+ K; F; d7 ~0 Y" t
end
. V2 D7 Q7 t; a$ Y4 t %对幅频响应进行归一化,并且寻找主导频率模式5 s5 r$ G! \( ^+ f- z# F
%寻找sptr的最大值5 c# G6 F+ H" G1 b
max_sptr=0;
0 {- u% j- Q/ U main_f=0;
/ s+ h, T, Q/ E5 y$ l- n1 Z2 {0 V2 Z for j=1:size(f,2)
! x3 k3 L- P0 \' s+ p5 ^& R0 N; D if sptr(j) > max_sptr4 L( t+ I$ n5 X: j6 j
max_sptr = sptr(j);
. }2 v! C1 }. O& |- G) l %主导频率出现在最大幅频响应位置! H" f+ [) b R" K$ L, K1 _
if f(j) ~= 0;- q; e7 L. E& c
main_f = f(j);% g2 ^5 j# M7 @! R0 a1 y
else: V' K/ D. C) x( u6 d7 ^
max_sptr = 0;
3 i1 D) D4 F0 V$ @1 I+ M end" A& [/ i; B+ R5 X/ E
end
" [) g8 ~( R( {* ?* P end* ?( p* H# q& X3 g# U; j. l) P
main_f;% [3 A4 ?3 m- X! D' J. X; p
%找出真正计算的频率值
: G# _1 V! T" T f_err = 10;
0 c! \# D) P+ w9 V+ i/ d f_main = 0;
/ X: v/ z( \5 e0 \6 j. N# | for i=1:size(Amp, 2)
% g% Z* [6 G6 A' z+ `) W4 H if abs(main_f - Fre(i)) < f_err
# N6 i$ h; Q2 E" [2 f+ Z f_main = Fre(i);- r( S' G; a1 R3 W7 \' @2 D
damp_main = damp(i);( Z& X) z4 T u' {3 m; o& K
f_err = abs(main_f - Fre(i));
0 Q* m' A) _0 ^- @7 u4 Z( t end. b4 \# r$ A2 Y) ]
end; s# O* j# ?; b; D1 z8 _
main_f = f_main;
$ _: Q" {; P% P: a main_damp = damp_main;$ j: ?4 u* {% r. f3 L" D: m
%进行归一化7 D- {3 I" i3 z/ v& K& K6 X+ q
for j=1:size(f,2)
7 H+ ]/ z+ p( s/ O( o: Q5 k sptr(j)=sptr(j)/max_sptr;
1 y5 @. y9 L2 k# ^ O. k' y Amp_Response(j) = sptr(j);
) c! }: k$ e- ^8 V# Q% l end/ {$ L9 Z: T& B6 z
# \0 V; u& b8 G/ @8 L. F9 e4 i+ s
for i=1:size(f,2)
& ]: u( v) G6 k- g$ i x( } if angl(i) > 0
6 ^$ m$ r" T$ ?' {/ v8 B angl(i)=angl(i)-360;
* X; Q+ k3 Y0 x5 u5 |' g end
% q$ T' k% }7 Z R9 v8 _0 Z end; o4 F* A" N1 }0 P
2 l" L! [7 d# i% | if showfigure == 1
7 J+ p; P6 w. d; C: N; u. s; p: E/ { %在一个图上显示时域拟和曲线和Prony频谱分布
! t" t1 Y0 I5 d% k figure;
( h! d9 Z5 @' k; D+ y subplot(2,1,1);
+ i5 D4 ~( e" H3 M% q6 P! z$ p4 } %plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');
4 w: {) g* Q ?; d. n plot(tt,x(1:N),'r', tt,xc, '*b');
! ]% {1 ]4 Q! z/ e. O( Y1 ]% Y subplot(2,1,2);
- p2 J, |' Z+ j1 H1 n3 w/ h# H plot(f,sptr);
0 R- s R* C3 N% L %subplot(2,2,3);* A* Q5 N* A ^) G1 U8 v( _
%plot(f,sptr);7 r- T0 H- e2 C! z# Y5 I- X3 C! E
%subplot(2,2,4);7 l$ k$ j, M# r. V% u
%plot(f,angl);
* k- n* U& m8 }( U0 ~0 i- Y8 R' M end1 Y3 S3 @# O# f* `5 q x5 g! x
' N, h8 G6 ` _+ ]
cpu=cputime-cpu;
( B' }3 F! @* Y0 a3 |* t& a8 ` format short;$ W* v( H: Q9 v& R# r* O+ o( d
end |
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