数学建模社区-数学中国
标题:
帮忙做下统计显著性检验和K值的误差以及灵敏度分析
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作者:
箫剑→残念
时间:
2016-10-25 16:50
标题:
帮忙做下统计显著性检验和K值的误差以及灵敏度分析
function parafit
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% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
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% k6->k6 k7->k7
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% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
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% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
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% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);
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% dLadt = k(7)*C(Hmf);
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%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
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clear all
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clc
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format long
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% t/min Glc Fru Fa La HMF/ mol/L
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Kinetics=[0 0.25 0 0 0 0
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15 0.2319 0.01257 0.0048 0 2.50E-04
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30 0.19345 0.027 0.00868 0 7.00E-04
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45 0.15105 0.06975 0.02473 0 0.0033
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60 0.13763 0.07397 0.02615 0 0.00428
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90 0.08115 0.07877 0.07485 0 0.01405
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120 0.0656 0.07397 0.07885 0.00573 0.02143
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180 0.04488 0.0682 0.07135 0.0091 0.03623
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240 0.03653 0.06488 0.08945 0.01828 0.05452
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300 0.02738 0.05448 0.09098 0.0227 0.0597
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360 0.01855 0.04125 0.09363 0.0239 0.06495];
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k0 = [0.0000000005 0.0000000005 0.0000000005 0.00000000005 0.00005 0.0134 0.00564 0.00001 0.00001 0.00001]; % 参数初值
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lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限
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ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
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x0 = [0.25 0 0 0 0];
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yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
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% warning off
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% 使用函数 ()进行参数估计
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[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
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fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
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fprintf('\tk1 = %.11f\n',k(1))
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fprintf('\tk2 = %.11f\n',k(2))
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fprintf('\tk3 = %.11f\n',k(3))
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fprintf('\tk4 = %.11f\n',k(4))
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fprintf('\tk5 = %.11f\n',k(5))
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fprintf('\tk6 = %.11f\n',k(6))
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fprintf('\tk7 = %.11f\n',k(7))
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fprintf('\tk8 = %.11f\n',k(8))
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fprintf('\tk9 = %.11f\n',k(9))
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fprintf('\tk10 = %.11f\n',k(10))
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fprintf(' The sum of the squares is: %.1e\n\n',fval)
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k_fm= k;
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% warning off
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% 使用函数lsqnonlin()进行参数估计
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[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
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lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
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ci = nlparci(k,residual,jacobian);
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fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
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fprintf('\tk1 = %.11f\n',k(1))
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fprintf('\tk2 = %.11f\n',k(2))
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fprintf('\tk3 = %.11f\n',k(3))
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fprintf('\tk4 = %.11f\n',k(4))
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fprintf('\tk5 = %.11f\n',k(5))
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fprintf('\tk6 = %.11f\n',k(6))
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fprintf('\tk7 = %.11f\n',k(7))
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fprintf('\tk8 = %.11f\n',k(8))
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fprintf('\tk9 = %.11f\n',k(9))
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fprintf('\tk10 = %.11f\n',k(10))
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fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
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k_ls = k;
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output
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warning off
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% 以函数fmincon()估计得到的结果为初值,使用函数lsqnonlin()进行参数估计
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k0 = k_fm;
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[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
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lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
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ci = nlparci(k,residual,jacobian);
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fprintf('\n\n以fmincon()的结果为初值,使用函数lsqnonlin()估计得到的参数值为:\n')
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fprintf('\tk1 = %.11f\n',k(1))
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fprintf('\tk2 = %.11f\n',k(2))
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fprintf('\tk3 = %.11f\n',k(3))
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fprintf('\tk4 = %.11f\n',k(4))
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fprintf('\tk5 = %.11f\n',k(5))
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fprintf('\tk6 = %.11f\n',k(6))
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fprintf('\tk7 = %.11f\n',k(7))
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fprintf('\tk8 = %.11f\n',k(8))
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fprintf('\tk9 = %.11f\n',k(9))
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fprintf('\tk10 = %.11f\n',k(10))
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fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
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k_fmls = k;
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output
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tspan = [0 15 30 45 60 90 120 180 240 300 360];
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[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
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figure;
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plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
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figure;plot(t,x(:,2:5));
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p=x(:,1:5)
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hold on
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plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
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function f = ObjFunc7LNL(k,x0,yexp)
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tspan = [0 15 30 45 60 90 120 180 240 300 360];
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[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
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y(:,2) = x(:,1);
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y(:,3:6) = x(:,2:5);
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f1 = y(:,2) - yexp(:,2);
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f2 = y(:,3) - yexp(:,3);
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f3 = y(:,4) - yexp(:,4);
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f4 = y(:,5) - yexp(:,5);
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f5 = y(:,6) - yexp(:,6);
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f = [f1; f2; f3; f4; f5];
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function f = ObjFunc7Fmincon(k,x0,yexp)
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tspan = [0 15 30 45 60 90 120 180 240 300 360];
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[t x] = ode45(@KineticEqs,tspan,x0,[],k);
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y(:,2) = x(:,1);
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y(:,3:6) = x(:,2:5);
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f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
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+ sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
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+ sum((y(:,6)-yexp(:,6)).^2) ;
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function dxdt = KineticEqs(t,x,k)
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dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
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dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
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dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
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dLadt = k(7)*x(5);
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dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
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dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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