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MatlabÄâºÏ·´Ó¦¶¯Á¦Ñ§²ÎÊý½á¹ûÆ«²îºÜ´ó°¡£¬Çó´óÉñÖ¸µã³ÌÐòµ±ÈçºÎÐÞ¸Ä ÒÑÓÐ1È˲ÎÓë
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×î½üÒ»Ö±ÔÚÄâºÏ·´Ó¦¶¯Á¦Ñ§²ÎÊý£¬»¨Á˺ܴ󹦷òÊÔ×űàºÃÁË´úÂ룬ȴʼÖÕ²»ÄܵóöÎÄÏ×ÖеIJÎÊý½á¹û£¬Çó´óÉñ°ïæָµãһϳÌÐò¡£Ôڴ˰ÝлÁË¡£ code: function KineticsEst5 clear all clc k0 = [0.5 0.5 0.5 0.5 0.5 0.5]; % ²ÎÊý³õÖµ lb = [0 0 0 0 0 0]; % ²ÎÊýÏÂÏÞ ub = [+inf +inf +inf +inf +inf +inf]; % ²ÎÊýÉÏÏÞ x0 = [4.96 24.43 26.32 17 38.72]; ExpData = ... [ 0 4.96 24.43 26.32 5 5.635 28.29 30.715 10 6.31 32.15 35.11 15 6.77 34.225 34.98 20 7.23 36.3 34.85 25 7.065 39.285 33.525 30 6.9 42.27 32.2 35 7.08 45.46 29.7 40 7.26 48.65 27.2 50 8 51.215 24.495 60 8.74 53.78 21.79 75 8.605 58.01 19.12 90 8.47 62.24 16.45 ] yexp = ExpData(:,2:4); % ʹÓú¯Êýfmincon()½øÐвÎÊý¹À¼Æ [k,fval,flag] = fmincon(@ObjFunc4Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp); fprintf(\\\'\\\\nʹÓú¯Êýfmincon()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\\\\n\\\') fprintf(\\\'\\\\tk1 = %.4f\\\\n\\\',k(1)) fprintf(\\\'\\\\tk2 = %.4f\\\\n\\\',k(2)) fprintf(\\\'\\\\tk3 = %.4f\\\\n\\\',k(3)) fprintf(\\\'\\\\tk4 = %.4f\\\\n\\\',k(4)) fprintf(\\\'\\\\tk5 = %.4f\\\\n\\\',k(5)) fprintf(\\\'\\\\tk6 = %.4f\\\\n\\\',k(6)) fprintf(\\\' The sum of the squares is: %.1e\\\\n\\\\n\\\',fval) k_fmincon = k; % ÒÔº¯Êýfmincon()¹À¼ÆµÃµ½µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ k0 = k_fmincon; [k,resnorm,residual,exitflag,output,lambda,jacobian] = ... lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp); ci = nlparci(k,residual,jacobian); fprintf(\\\'\\\\n\\\\nÒÔfmincon()µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\\\\n\\\') fprintf(\\\'\\\\tk1 = %.4f ¡À %.4f\\\\n\\\',k(1),ci(1,2)-k(1)) fprintf(\\\'\\\\tk2 = %.4f ¡À %.4f\\\\n\\\',k(2),ci(2,2)-k(2)) fprintf(\\\'\\\\tk3 = %.4f ¡À %.4f\\\\n\\\',k(3),ci(3,2)-k(3)) fprintf(\\\'\\\\tk4 = %.4f ¡À %.4f\\\\n\\\',k(4),ci(4,2)-k(4)) fprintf(\\\'\\\\tk5 = %.4f ¡À %.4f\\\\n\\\',k(5),ci(5,2)-k(5)) fprintf(\\\'\\\\tk6 = %.4f ¡À %.4f\\\\n\\\',k(6),ci(6,2)-k(6)) fprintf(\\\' The sum of the squares is: %.1e\\\\n\\\\n\\\',resnorm) % ------------------------------------------------------------------ function f = ObjFunc4Fmincon(k,x0,yexp) tspan = [0,5,10,15,20,25,30,35,40,50,60,75,90]; [t x] = ode45(@KineticEqs,tspan,x0,[],k); y(:,1:3) = x(:,1:3); f = sum((y(:,1)-yexp(:,1)).^2) + sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2); % ------------------------------------------------------------------ function f = ObjFunc4LNL(k,x0,yexp) tspan = [0,5,10,15,20,25,30,35,40,50,60,75,90]; [t x] = ode45(@KineticEqs,tspan,x0,[],k); y(:,1:3) = x(:,1:3); f1 = y(:,1) - yexp(:,1); f2 = y(:,2) - yexp(:,2); f3 = y(:,3) - yexp(:,3); f = [f1; f2; f3]; % ------------------------------------------------------------------ function dxdt = KineticEqs(t,x,k) dxdt = ... [ (k(1)*x(1)+k(6)*x(3)) (k(2)*x(1)+k(5)*x(3)) (k(3)*x(1)+k(4)*x(2)-(k(5)+k(6))*x(3)) (-(k(1)+k(2)+k(3))*x(1)) (-k(4)*x(2)) ]; |
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