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灰色预测模型matlab程序灰色模型预测是在数据不呈现一定规律下可以采取的一种建模和预测方法，其预测数据与原始数据存在一定的规律相似性%下面程序是灰色模型GM(1,1)程序二次拟合和等维新陈代谢改进预测程序,matlab6.5,使用本程序请注明，程序存储为gm1.m%x=[5999,5903,5848,5700,7884];gm1(x);测试数据%二次拟合预测GM(1,1)模型functiongmcal=gm1(x)sizexd2=size(x,2);%求数组长度k=0;fory1=xk=k+1;ifk1x1(k)=x1(k-1)+x(k);%累加生成z1(k-1)=-0.5*(x1(k)+x1(k-1));%z1维数减1，用于计算Byn1(k-1)=x(k);elsex1(k)=x(k);endend%x1,z1,k,yn1sizez1=size(z1,2);%size(yn1);z2=z1';z3=ones(1,sizez1)';YN=yn1';%转置%YNB=[z2z3];au0=inv(B'*B)*B'*YN;au=au0';%B,au0,auafor=au(1);ufor=au(2);ua=au(2)./au(1);%afor,ufor,ua%输出预测的au和u/a的值constant1=x(1)-ua;afor1=-afor;x1t1='x1(t+1)';estr='exp';tstr='t';leftbra='(';rightbra=')';%constant1,afor1,x1t1,estr,tstr,leftbra,rightbrastrcat(x1t1,'=',num2str(constant1),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(ua),rightbra)%输出时间响应方程%******************************************************%二次拟合k2=0;fory2=x1k2=k2+1;ifk2kelseze1(k2)=exp(-(k2-1)*afor);endend%ze1sizeze1=size(ze1,2);z4=ones(1,sizeze1)';G=[ze1'z4];X1=x1';au20=inv(G'*G)*G'*X1;au2=au20';%z4,X1,G,au20Aval=au2(1);Bval=au2(2);%Aval,Bval%输出预测的A,B的值strcat(x1t1,'=',num2str(Aval),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(Bval),rightbra)%输出时间响应方程nfinal=sizexd2-1+1;%决定预测的步骤数5这个步骤可以通过函数传入%nfinal=sizexd2-1+1;%预测的步骤数1fork3=1:nfinalx3fcast(k3)=constant1*exp(afor1*k3)+ua;end%x3fcast%一次拟合累加值fork31=nfinal:-1:0ifk311x31fcast(k31+1)=x3fcast(k31)-x3fcast(k31-1);elseifk310x31fcast(k31+1)=x3fcast(k31)-x(1);elsex31fcast(k31+1)=x(1);endendendx31fcast%一次拟合预测值fork4=1:nfinalx4fcast(k4)=Aval*exp(afor1*k4)+Bval;end%x4fcastfork41=nfinal:-1:0ifk411x41fcast(k41+1)=x4fcast(k41)-x4fcast(k41-1);elseifk410x41fcast(k41+1)=x4fcast(k41)-x(1);elsex41fcast(k41+1)=x(1);endendendx41fcast,x%二次拟合预测值%***精度检验pC************//////////////////////////////////k5=0;fory5=xk5=k5+1;ifk5sizexd2elseerr1(k5)=x(k5)-x41fcast(k5);endend%err1%绝对误差xavg=mean(x);%xavg%x平均值err1avg=mean(err1);%err1avg%err1平均值k5=0;s1total=0;fory5=xk5=k5+1;ifk5sizexd2elses1total=s1total+(x(k5)-xavg)^2;endends1suqare=s1total./sizexd2;s1sqrt=sqrt(s1suqare);%s1suqare,s1sqrt%s1suqare残差数列x的方差s1sqrt为x方差的平方根S1k5=0;s2total=0;fory5=xk5=k5+1;ifk5sizexd2elses2total=s2total+(err1(k5)-err1avg)^2;endends2suqare=s2total./sizexd2;%s2suqare残差数列err1的方差S2Cval=sqrt(s2suqare./s1suqare);Cval%nnn=0.6745*s1sqrt%CvalC检验值k5=0;pnum=0;fory5=xk5=k5+1;ifabs(err1(k5)-err1avg)0.6745*s1sqrtpnum=pnum+1;%ppp=abs(err1(k5)-err1avg)elseendendpval=pnum./sizexd2;pval%p检验值%arr1=x41fcast(1:6)%预测结果为区间范围预测步长和数据长度可调整程序参数进行改进