结构模态识别+多测点频域贝叶斯+快速Bayesian

function pcov=cov(nf1,nf2,nn,fs,x,mpv_S,sigma2,DD,D,mshape,beta,d,dof) z=x(2); mpv_fi=mshape; nf=nf2-nf1+1; for k=nf1:nf2 j=k-nf1+1; fk(j)=(k-1)/nn*fs; gama(j)=mpv_S*DD(j)/sigma2;%signal-to-noise factor Dnf(j)=4*(beta(j)^3-beta(j)*(1-2*z^2))/fk(j);%eq(43) Dnz(j)=8*z*beta(j)^2;%eq(44) Dnff(j)=4*(3*beta(j)^2-1+2*z^2)/(fk(j)^2);%eq(45) Dnzz(j)=8*beta(j)^2;%eq(46) Dnfz(j)=16*z*beta(j)/fk(j);%eq(47) Df(j)=-Dnf(j)*DD(j)^2; Dz(j)=-Dnz(j)*DD(j)^2; lnDf(j)=-4*DD(j)/fk(j)*(beta(j)^3-beta(j)*(1-2*z^2));%eq(48) lnDz(j)=-8*z*beta(j)^2*DD(j);%eq(49) lnDff(j)=4*fk(j)^(-2)*(4*DD(j)^2*(beta(j)^3-beta(j)*(1-2*z^2))^2-DD(j)*(3*beta(j)^2-1+2*z^2));%eq(50) lnDzz(j)=8*beta(j)^2*DD(j)*(8*z^2*beta(j)^2*DD(j)-1);%eq(51) lnDfz=16*fk(j)^(-1)*z*beta(j)*(beta(j)^4-1)*DD(j)^2;%eq(52) Dff(j)=lnDff(j)*DD(j)+Df(j)^2/DD(j); Dzz(j)=lnDzz(j)*DD(j)+Dz(j)^2/DD(j); Dfz(j)=2*Dz(j)*Df(j)/DD(j)-Dnfz(j)*DD(j)^2; B(j)=1/(1+1/gama(j));%eq(55) Bnf(j)=-gama(j)^(-1)/DD(j)*Df(j);%eq(58) Bnz(j)=-gama(j)^(-1)/DD(j)*Dz(j); BnS(j)=-1/gama(j)*mpv_S^(-1);%eq(59) Bnsigma(j)=1/gama(j)/sigma2;%eq(60) Bnff(j)=1/gama(j)*DD(j)*Dnff(j);%eq(61) Bnzz(j)=1/gama(j)*DD(j)*Dnzz(j); BnSS(j)=2/gama(j)/mpv_S^2; Bnsigma2(j)=0;%eq(63) Bnfz(j)=1/gama(j)*DD(j)*Dnfz(j);%eq(64) BnfS(j)=1/mpv_S*1/gama(j)*1/DD(j)*Df(j);%eq(65) BnzS(j)=1/mpv_S*1/gama(j)*1/DD(j)*Dz(j); Bnfsig(j)=-1/gama(j)/sigma2*1/DD(j)*Df(j);%eq(66) Bnzsig(j)=-1/gama(j)/sigma2*1/DD(j)*Dz(j);%eq(66) BnSsig(j)=-1/gama(j)/sigma2*1/mpv_S;%eq(67) Bff(j)=2*B(j)^3*Bnf(j)^2-B(j)^2*Bnff(j); Bzz(j)=2*B(j)^3*Bnz(j)^2-B(j)^2*Bnzz(j); BSS(j)=2*B(j)^3*BnS(j)^2-B(j)^2*BnSS(j); Bsigma(j)=-Bnsigma(j)*B(j)^2; Bsigma2(j)=2*B(j)^3*Bnsigma(j)^2; Bf(j)=-B(j)^2*Bnf(j); Bz(j)=-B(j)^2*Bnz(j); Bs(j)=-B(j)^2*BnS(j); Bfsig(j)=2*B(j)^3*Bnf(j)*Bnsigma(j)-B(j)^2*Bnfsig(j); Bzsig(j)=2*B(j)^3*Bnz(j)*Bnsigma(j)-B(j)^2*Bnzsig(j); Bssig(j)=2*B(j)^3*BnS(j)*Bnsigma(j)-B(j)^2*BnSsig(j); Bfz(j)=2*B(j)^3*Bnf(j)*Bnz(j)-B(j)^2*Bnfz(j); Bfs(j)=2*B(j)^3*Bnf(j)*BnS(j)-B(j)^2*BnfS(j); Bzs(j)=2*B(j)^3*Bnz(j)*BnS(j)-B(j)^2*BnzS(j); q(j)=mpv_fi'*reshape(D(:,j),dof,dof)*mpv_fi; end %derivatives of Ld and Lq for k=nf1:nf2 j=k-nf1+1; A(:,j)=1/(1+1/gama(j))*D(:,j); Ldff(j)=(1+1/gama(j))^(-1)*1/DD(j)*Dff(j)-(1+1/gama(j))^(-2)*(1/DD(j)*Df(j))^2; Ldzz(j)=(1+1/gama(j))^(-1)*1/DD(j)*Dzz(j)-(1+1/gama(j))^(-2)*(1/DD(j)*Dz(j))^2; Ldss(j)=(1+1/gama(j))^(-2); Ldsig2(j)=1/gama(j)^2*(1+1/gama(j))^(-2); Lqff(j)=Bff(j)*q(j); Lqzz(j)=Bzz(j)*q(j); Lqss(j)=BSS(j)*q(j); Lqsig21(j)=Bsigma(j)*q(j); Lqsig22(j)=Bsigma2(j)*q(j); Ldfz(j)=(1+1/gama(j))^(-1)*1/DD(j)*Dfz(j)-(1+1/gama(j))^(-2)*DD(j)^(-2)*Df(j)*Dz(j);%eq74 Ldfs(j)=1/gama(j)*(1+1/gama(j))^(-2)*1/DD(j)*Df(j); Ldzs(j)=1/gama(j)*(1+1/gama(j))^(-2)*1/DD(j)*Dz(j); Ldfsig(j)=1/gama(j)*(1+1/gama(j))^(-2)*1/DD(j)*Df(j); Ldzsig(j)=1/gama(j)*(1+1/gama(j))^(-2)*1/DD(j)*Dz(j); Ldssig(j)=1/gama(j)*(1+1/gama(j))^(-2); Lqffi2(:,j)=Bf(j)*D(:,j); Lqzfi2(:,j)=Bz(j)*D(:,j); Lqsfi2(:,j)=Bs(j)*D(:,j); Lqsigfi2(:,j)=Bsigma(j)*D(:,j); end l=1:nf; A=reshape(sum(A,2),dof,dof); Ldff=sum(Ldff(l),2); Ldzz=sum(Ldzz(l),2); Ldss=-sum(Ldss(l),2)/mpv_S^2; Ldsig2=-(nf+sum(Ldsig2(l),2))/(sigma2^2); Lqff=-sum(Lqff(l),2)/sigma2; Lqzz=-sum(Lqzz(l),2)/sigma2; Lqss=-sum(Lqss(l),2)/sigma2; Lqsig2=2*(d-mpv_fi'*A*mpv_fi)/sigma2^3+2*sum(Lqsig21(l),2)/(sigma2)^2-sum(Lqsig22(l),2)/sigma2;%eq72 Lqfi2=-2*(A-2*mpv_fi*mpv_fi'*A+4*mpv_fi'*A*mpv_fi*mpv_fi*mpv_fi'-2*A*mpv_fi*mpv_fi'-mpv_fi'*A*mpv_fi*eye(dof))/sigma2;%eq73 Ldfz=sum(Ldfz(l),2); Ldfs=sum(Ldfs(l),2)/mpv_S; Ldzs=sum(Ldzs(l),2)/mpv_S; Ldfsig=-sum(Ldfsig(l),2)/sigma2; Ldzsig=-sum(Ldzsig(l),2)/sigma2; Ldssig=-sum(Ldssig(l),2)/mpv_S/sigma2;%eq77 Lqfsig=sum(Bf(l).*q(l),2)/sigma2^2-sum(Bfsig(l).*q(l),2)/sigma2; Lqzsig=sum(Bz(l).*q(l),2)/sigma2^2-sum(Bzsig(l).*q(l),2)/sigma2; Lqssig=sum(Bs(l).*q(l),2)/sigma2^2-sum(Bssig(l).*q(l),2)/sigma2; Lqffi=2*(sum(Bf(l).*q(l),2)*mpv_fi'-mpv_fi'*reshape(sum(Lqffi2(:,l),2),dof,dof))/sigma2; Lqzfi=2*(sum(Bz(l).*q(l),2)*mpv_fi'-mpv_fi'*reshape(sum(Lqzfi2(:,l),2),dof,dof))/sigma2; Lqsfi=2*(sum(Bs(l).*q(l),2)*mpv_fi'-mpv_fi'*reshape(sum(Lqsfi2(:,l),2),dof,dof))/sigma2; Lqsigfi=2*(mpv_fi'*A-sum(B(l).*q(l),2)*mpv_fi')/sigma2^2+2/sigma2*(sum(Bsigma(l).*q(l),2)*mpv_fi'-mpv_fi'*reshape(sum(Lqsigfi2(:,l),2),dof,dof)); Lqfz=-1/sigma2*sum(Bfz(l).*q(l),2); Lqfs=-1/sigma2*sum(Bfs(l).*q(l),2); Lqzs=-1/sigma2*sum(Bzs(l).*q(l),2); Lff=Ldff+Lqff; Lfz=Ldfz+Lqfz; Lfs=Ldfs+Lqfs; Lfsig=Ldfsig+Lqfsig; Lffi=Lqffi; Lzz=Ldzz+Lqzz; Lss=Ldss+Lqss; Lsig2=Ldsig2+Lqsig2; Lfi2=Lqfi2; Lzsig=Ldzsig+Lqzsig; Lzs=Ldzs+Lqzs; Lzfi=Lqzfi; Lssig=Ldssig+Lqssig; Lsfi=Lqsfi; Lsigfi=Lqsigfi; H=[Lff Lfz Lfs Lfsig Lffi;Lfz Lzz Lzs Lzsig Lzfi;Lfs Lzs Lss Lssig Lsfi;Lfsig Lzsig Lssig Lsig2 Lsigfi;Lffi' Lzfi' Lsfi' Lsigfi' Lfi2]; [basis,kv]=eig(H); c=0; for j=1:5 c=c+1/kv(j,j)*basis(:,j)*basis(:,j)'; end f_cov=sqrt(c(1,1))/x(1)*100; z_cov=sqrt(c(2,2))/x(2)*100; s_cov=sqrt(c(3,3))/mpv_S*100; sig_cov=sqrt(c(4,4))/sigma2*100; pcov=[f_cov;z_cov;s_cov;sig_cov]';