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发表于 2011-3-29 13:24:52
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回复 2# debra $ a/ i. g9 T0 W" l+ T0 z1 [
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6 q! z5 b( z: J* Y- _4 N1 J %打开指定文件,并对信号进行Pon分析计算( _* a2 `9 o9 L! b$ @" }( g2 T/ i
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)
7 Z/ y! W) J9 P* N format long;
* J( E" M' ^/ Q9 A# U x = x_in';# m' \3 @" m' F( Y; h
cpu=cputime; k; Y* p8 s& |. C5 w% s
N=size(x,1);
7 Z4 ]' {6 B. X9 N# f" D6 ~ %取N/2的整数部分为初始的P
2 X/ Y* I: X+ v+ A+ _7 } P=floor(N/2); \1 Q1 o0 s8 F' V: ^* A
. y- V% U& s) f. K1 L. |; h1 L %去直流环节6 _% e- h* I$ h" `! M ?* M
x_Sum = 0;
* Z; x2 p8 ~6 G" ~ for i=1:N& r W8 |$ }7 B% Z+ k: o6 p( i
x_Sum = x_Sum + x(i);" j* e" |3 ?1 i1 x- t, t8 k
end
" R h7 N3 L0 ^ x_av = x_Sum / N;
; I3 w' _0 `$ y) A/ i& H if x_av > 10E-10 P7 {; R$ W$ l- J7 [2 i/ ]' y/ e
for i=1:N
3 J( g+ i( }' _- q! |$ z x(i) = x(i) - x_av;6 e& N, A# ^- p. [7 i4 a
end1 h" S, S, p: }, f7 e
end
; D0 H$ t0 y k. {5 c %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%& B" Y& n* O) C# V2 a
%滤波环节, L- c+ o4 ]1 F
%fL=1;$ \& G9 f5 b( H1 |! `
if fL>1
( F6 p# ~( k" D0 e2 X [3 v for i=fL+1:N
. c* H6 v, @& i, o% d x(i-fL)=0;2 T; [' n' `; [ K, C1 C
for j=1:fL- L4 l, F" Y6 c( C
x(i-fL) = x(i-fL)+(1/fL)*x(i-j+1);; w2 @0 \+ h+ x- L# p/ c
end7 [0 H3 d; i p; _. r8 P
end
: X3 i" o! B% | end
8 U G$ @9 @7 [& q) a' J7 A& I N=N-fL;9 b) P2 y- `% @& u, D
tt=0:1:N-1;! D4 O1 {+ @8 f
# n r5 O- ?/ X3 k9 u% M1 [$ I
%P要求为偶数
3 q2 E- W# m4 t9 `" M% ` if mod(P, 2) ~= 0- X+ J" e# P0 e3 {+ }3 ~+ y# [
P = P - 1;( K# A: P& n9 _ n
end1 W0 N" c6 a5 E# e3 A9 d
5 V+ D- @4 v f; v/ C" D" X
P1=P;
( p" K$ G8 i8 x U$ u if mod(P, 2) == 0
+ _. X- @* N% p! n2 D/ C: E % Generate R,生成样本矩阵
% _8 X4 o6 |# r8 D for i=1:P1. `, ^' I; }6 ? {% b. ~! M
for j=1:P1+16 W# R0 M! R/ f2 u$ g( `' F
ss=0;
! p0 O, o0 [' U0 S, F* B9 U8 | for k=P1:N-1
; G( F* P6 s2 e: i, A6 p0 H+ x %前向预测误差
* h6 ?4 f5 K& S& R/ B; W! F ss=ss+x(k+2-j,1)*x(k+1-i,1);
' M* z6 L; N" i4 F %后向预测误差$ ]8 `4 v, g8 j5 h$ V5 V4 r
%ss=ss+x(k+1-P1+i)*x(k+1-P1-1+j);
# E% w+ v, j" f" X; }3 N- _ %同时考虑双向误差
$ H* ~8 b3 s& z6 ^/ `" M %ss=ss+x(k+2-j,1)*x(k+1-i,1)+x(k+1-P1+i)*x(k+1-P1-1+j); % v3 i6 j3 C$ e0 w
end
! f4 w; q; X: R. Q R(i,j)=ss;' ?" ~! a2 I J$ E1 ~( \% {& y
end* u- H4 [8 \# N- v; Y- p6 C
end! a Q! u" t; q6 K
% divide R into R1 and R2, and get A; R1*A=R2;0 ]$ Z: u8 O* I7 A
for i=1:P" q7 D$ g2 i4 g% g
for j=1:P4 E! V- p1 m! y) x
R1(i,j)=R(i,j+1);3 _! J& I2 A4 o
end7 Y$ p. S! ^# W8 `+ F
end
& A5 X) }* r- m/ g for i=1:P3 u4 k4 h( O9 J, K, p7 N
R2(i)=R(i,1);+ ? C$ K9 i1 N8 \0 @
end
& ?6 V, a1 W6 l w7 Z ' E9 X- H; I4 g9 @7 I' N; Q
%添加的代码,使用SVD-TLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
; m/ i( f9 A. P' V6 M/ |/ J %首先进行SVD分解8 J& c3 ^! @7 m6 Y* Z/ {
[u,s,v]=svd(R1);
! T U* V' }# ^* ?9 o( F! X3 D %根据奇异值确定实际的阶数M' d, A% _9 X/ P j0 O. ]+ M
M=0;
' x2 o$ Z8 R6 E3 a' r8 N %计算全部奇异值的均方和
6 j7 }9 ?& k5 I- E4 D+ u Sum_SVD=0;7 s$ C3 w4 e; t- c$ }# P* d* K
for i=1:P6 @" J- A; V- ?. h0 O
Sum_SVD = Sum_SVD+s(i,i)^2;
O8 R, L0 |: n6 L' O8 W end, K5 ?- N* y6 T
cur_sum = 0;9 X+ p f0 a/ C& L! n, p
i=1;
/ G, H2 |( G- T) A while 1 - sqrt(cur_sum/Sum_SVD) > 0.000001 & i<=P& y8 W1 m& m8 n( C& j$ z
cur_sum = cur_sum + s(i,i)^2;
& C% C. Q" W( }2 T4 Z: X7 S: _ p M = M + 1;
% b) p; b/ P$ U. I, F3 q9 F i = i + 1;
$ t4 F: d5 \/ J( @1 I end
/ \2 k6 K7 R2 g% [+ e# J %输出预测的阶数M, T8 z/ `2 Y7 Y# D+ Z& a3 A
M;
3 s: a' }- @& W- o! | %生成Sp矩阵6 @% q& h" V% M( A
Sp=zeros(M+1, M+1);) d( `6 y' a3 _& }6 E# R8 Z
for j=1:M , Y; r9 Z- d* o: w: t/ \
for i=1:(P-1)-M+1
" A0 v4 Y7 `0 y9 j; ]+ s9 [ Sp = Sp+s(j,j)^2*v(i:i+M,j)*v(i:i+M,j)';
8 G1 n- s0 Y" }( p8 R$ t, M end4 N0 Z2 \/ B. W
end& H, a k* n! g
6 s/ w5 I5 X a% X! ^( t %根据公式生成最佳最小二乘解$ ^5 v5 \4 x1 D1 d0 @
Sp_inv=inv(Sp); i7 F6 j5 ^, K N- G/ y2 g# Q# S. C
if isinf(Sp_inv(1,1)) == 1
2 Y) _% Q* y: n8 p9 k- Q J Sp_inv = pinv(Sp);
6 i/ z9 Y2 R3 Z2 Q end
% b( c0 i/ p3 w( ~8 ~% X T Q6 ~ & m3 M4 ]$ o! X; w. s* i7 i' X
a_SVD = Sp_inv(1+1:M+1, 1)/Sp_inv(1,1);0 J4 o/ _( o* M7 { y) n0 p
P = M;7 v, f: e8 Y: } n8 B
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%# y M7 \1 E" Y6 n. W
% Get Zi
% {) U D( b" `# Q, w9 _ cof_SVD(1)=1;1 l8 J4 K' B0 i5 R! g
for i=1:M
4 b0 Z9 R' ~: y y& O% [; j- V5 Z4 c cof_SVD(i+1)=a_SVD(i);
8 _6 N$ K) O+ U! y! c/ w end
9 q* @+ v4 l" H3 f4 f9 J, e8 t h Z=roots(cof_SVD);
. J. @( j/ j0 |9 A+ i
. w+ N+ F/ S' m7 B* G/ ~* S7 Q % Get y,y should be very close to x8 G9 k' [2 y. H
for i=1:P9 Q; w9 h+ z& W4 G' k0 Z$ P
y(i)=x(i);# r5 m: o0 } E4 E6 @
end! z( {# u& u, ]
! M$ g: F/ _/ [7 L
for i=P+1:N1 L- V3 M, X# z; F
y(i)=0;0 b# s+ L! z |) V0 [7 e/ m4 W% N% I( k
end
0 z' ?( |$ R9 `& ~# j2 Z) ~+ u; p for i=P+1:N
~# f2 R1 s U% `1 P: ? for j=1:P1 h6 _& S: I j; R
y(i)=y(i)-a_SVD(j)*x(i-j);3 O# r8 r+ Z1 h/ m
end
1 G3 e+ D& ]( Y$ Z8 j6 e end) v; T7 ~% l# `. h: F
: Y5 y% |9 B% x! f4 m % Get B
; P& p% F2 w4 t9 Y; O for i=1:N! {' `' X5 a1 Q. M- j0 F
for j=1:P
' G- \ S: g6 P' X$ x" y Fy(i,j)=Z(j)^(i-1);! U3 y6 F2 \1 t+ K
end9 O: C3 H. w" u4 P# r3 [, d
end
% L0 J8 ~8 x: F1 I3 E- W Fz=Fy';% `1 {7 n2 N! C9 b& n6 l2 r& c, a/ \
FH=Fy'*Fy;# f+ ] ]0 E) F0 a5 ~
Fn=inv(FH);
& A Y, b9 i. Z8 N: m: A B = inv(Fy'*Fy)*Fy'*y';
2 R N }* b& o0 f) Y- E0 n7 v
& m8 @+ E# }; G% \9 ]7 G' u$ m % Calculate Amplitude, Phasor, Frequency and damp
+ C6 F5 j7 d& T for i=1:P
* g E9 M0 I7 ~3 T3 V! Z, A Amp(i)=abs(B(i));
2 |: s- j$ j, O4 d$ m9 C# ? Pha(i)=atan(imag(B(i))/real(B(i)));
8 Q% C* `7 g3 ^7 l" j Fre(i)=atan(imag(Z(i))/real(Z(i)))/(2*pi*dt);+ a, y, f. O7 ~1 M3 Q9 T* v( ~4 s
damp(i)=log(abs(Z(i)))/dt;$ V) l% U9 D# a0 v& A% W* F7 E) g) a
end! }" n( K1 Z6 P9 N" n6 U
%调试用的代码+ l! B5 K7 Q- p
if isnan(Amp(1)) == 12 [9 p6 d# M1 P% B* b
error('幅值的求解出现错误!');* r" o2 X! v9 D+ y. r
end
: [/ d# N3 i* t: J5 l; N # L9 _4 F8 u' I# @& r
% Get xc,verify if xc is nearly equal to x
1 V9 O4 h5 z u/ y9 ?4 ` for i=1:P
; ^- w1 y. o; e if(real(B(i))>=0.0)
$ x: {7 P% X: x0 o) x bth(i)=Pha(i);
! K$ f B, {5 W3 `1 f+ { else
5 c7 ^* ?" E3 L5 p& n1 n0 W. g bth(i)=pi+Pha(i);
1 Q" g8 Z0 R# O( q5 ^! h end# S. s a* l4 Y# [% n) {
end
* Y t8 Z! r0 H6 z. T: e; q %对Pha重新幅值- K- y" u; l0 ~5 N
for i=1:P
5 A2 z: p9 @. Q) N* q1 Z, d/ E if Pha(i) < 0
; m, W% G; J7 e/ l( X Pha(i) = Pha(i) + 2*pi;
/ k9 N$ n5 {; h end
/ K! F0 t1 B! A) Z end
6 h, a5 ], R, l I/ _% S 4 x5 b# {' c2 _2 \
for i=1:N
& ^6 ?# |2 S" D# W' P& f$ u xc(i)=0.0;
, J" b' H. O( P/ G: e* ~: Q for j=1:P
) u3 f: |( t/ ^" G7 ? xc(i)=xc(i)+Amp(j)*exp(damp(j)*(i-1)*dt)*cos(2*pi*Fre(j)*(i-1)*dt+bth(j));
2 ? K- _5 ^: ^7 W* ] end
1 w+ g8 S" Q2 Q% X3 F) Q end
# u: W! D0 S/ x9 Q$ [- E% if showfigure == 1
" I0 g5 b% K' x' Q* z# w% %显示特征根的位置
) L& t ~$ U y$ E" i' i8 Q( D% figure;
" g/ D8 G- q- k3 B. \) E: X6 W) K) J# S% plot(damp, 2*pi*Fre, 'r*');* R/ R5 P: g0 I
% end* H- w0 i) }0 e! G! M6 T
0 Q2 o" ]4 Y8 H& P( y
xj=xc';
+ Y' j' x5 b9 q; h/ H; O! o er=0;
) L9 w U% }) k1 X; c% P. M all = 0;& \7 l+ j% P3 j) ]) E' z+ J
for i=1:N 9 s7 {3 f! @* U' S6 S4 t
er=er+(x(i)-xc(i))^2;
7 e8 X1 A! b; z' W1 {; r9 i all = all+x(i)^2; }5 K0 O9 E2 @
end
: J1 Z- e+ F. y0 n1 x! S( ~& W SNR=-20*log(sqrt(er/all));) W- ]9 K$ i/ v3 c6 f8 y% o/ |
7 y$ N$ t9 c! P: m& H s % Calculate Prony spectrum3 `9 J8 I& q; V( l5 |5 ?# `
%频谱的取值范围为0-5Hz
+ S: d2 Y2 K1 z4 w* Z! \# L* u3 A f=0:0.01:4.99;
0 d) Y% a g0 _9 q/ s) \ for j=1:size(f,2)- a* R [& o8 e6 m7 T r
sptr(j)=0; n I6 H6 F' b6 X" t
sptr1(j)=0;
, n) e6 [3 n3 H1 c6 Q sptr2(j)=0;0 V" b @& _" V7 |
angl(j)=0;
5 C" H$ n0 q# v3 h! `2 w tmpangle = 0;8 A& ]) q) A1 ?& T! z1 v8 P2 t
for k=1:P j3 k U d2 G8 l" \
sptr1(j)=sptr1(j)+Amp(k)*cos(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
! r9 M: R5 E$ E# g2 K4 q! H sptr2(j)=sptr2(j)+Amp(k)*sin(bth(k))*(2*damp(k)/(damp(k)^2+(2*pi*(f(j)-Fre(k)))^2));
; E1 y2 \- D8 g3 c- G* C. G7 ` end
3 c& T. v( E' m sptr(j)=sqrt(sptr1(j)^2+sptr2(j)^2);3 H; r; C2 x/ {: H( S. d
tmpangle = atan2(sptr1(j),sptr2(j));
' m/ Y2 a9 v3 r, R& c+ Q angl(j) = tmpangle*360/pi;
0 k% W& y& R# t8 @/ o' U end1 _; O4 x! ~. k
%对幅频响应进行归一化,并且寻找主导频率模式
: G5 G2 Z7 l; P8 M %寻找sptr的最大值 c& M! j q' j) M! z
max_sptr=0;
) o. a7 e: F( I/ r% @2 P l7 b main_f=0;
. A1 h8 c W' a/ z for j=1:size(f,2)8 t# _9 |% Q- \5 `
if sptr(j) > max_sptr
5 S2 w2 k+ l5 E+ O( \1 w% [ max_sptr = sptr(j);
. F: s( {/ F4 B2 l1 E9 q, L: O %主导频率出现在最大幅频响应位置
5 r1 Q) h! u' U0 f if f(j) ~= 0;0 F$ V9 B# g$ T3 z: x d" U
main_f = f(j);
$ p, X' d/ E% c( j4 y' n else1 I) A; z* s W' H ~
max_sptr = 0;
( `) [5 g: a+ s" x9 D1 K end
/ e; `8 t# _* m$ ~, u# F1 u' K/ a& k end- {0 C, j& n* }. V1 Z* F3 N
end& v3 }7 {3 B; x* U* w, Q
main_f;* t0 I" q7 t6 v# h; C5 N* k( c6 e1 h
%找出真正计算的频率值4 q4 ?4 o& |$ y( }. \, |
f_err = 10;% _7 v8 G+ g: {+ Z
f_main = 0;- ]4 f5 E2 h5 i1 s% O' V" A$ J
for i=1:size(Amp, 2)9 [+ g0 R' x2 G& U3 Q- c7 F
if abs(main_f - Fre(i)) < f_err* q3 B, P7 ?: z* U# O0 A3 y; ]
f_main = Fre(i);
* k" ~7 t4 h) q( m4 k' c9 x# { damp_main = damp(i);
) }" f7 I0 R4 T0 `% d" X8 c f_err = abs(main_f - Fre(i));
; X, p* }/ L) U; t s/ f6 d- s% O7 c end
R8 J) ~! Q9 p% j end
6 Y2 T8 I' f7 O9 X* d6 ? main_f = f_main;
0 T: b( q1 [: Y( A main_damp = damp_main;; v5 e3 [2 B5 v
%进行归一化
- O& S0 D# c2 j. X( A6 I' w8 i for j=1:size(f,2)
$ t4 \" u0 {3 x- h) f3 } sptr(j)=sptr(j)/max_sptr;9 |; e2 \, H$ ~4 @+ z
Amp_Response(j) = sptr(j);6 e9 m+ u: H' v1 ]1 ~/ T
end
+ j! P j. H0 W ^1 O6 U# M; h
) N k% Y$ Y* X4 k5 G8 R for i=1:size(f,2)0 C5 U) ?3 `% t+ O
if angl(i) > 00 _* D$ h0 J$ v1 h
angl(i)=angl(i)-360;
7 A5 b c+ T2 \' ]& f+ D end$ v6 S) M1 a4 A( B* g
end3 z+ @3 [* }7 C# r" v! L
( k% g1 ~& B# z! V- ? if showfigure == 1( X) c2 m6 ]$ H# f! P# \
%在一个图上显示时域拟和曲线和Prony频谱分布
' U% ?" p {0 A3 `5 _5 f, K- `9 J figure;
/ g. [9 Z0 M( s: P [ subplot(2,1,1);4 `2 l8 J' n, _5 `2 `3 h z
%plot(tt,x(1:N),'b', tt,y, 'r', tt,xc, '*b');. f5 J: Z5 O% p3 l4 ~5 L5 b, Z
plot(tt,x(1:N),'r', tt,xc, '*b');2 |( u" S2 \* L" L! y
subplot(2,1,2);6 O* l$ i4 N6 {: N: `! _- p
plot(f,sptr);
j; `! H* o- z7 C' e6 A' Y %subplot(2,2,3);, n5 E+ |. `6 E" ^0 k# i
%plot(f,sptr);
+ B& X- {: a; B% i %subplot(2,2,4);
4 O- U" {# ~% @0 o %plot(f,angl);8 ^& I, q0 W) P' M4 _( D
end
* A/ r/ c r( @ g
3 J2 k" X. o% b% l3 a) @ cpu=cputime-cpu;
- P& @, R$ P5 a3 K1 b# J3 } format short;4 T% J4 i7 K6 }7 F" U) h! l" _7 l7 w
end |
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