人工智能matlab仿真

1、1.函數(shù)優(yōu)化4x122.僅143x6,2,4 x?2 4x2 4x2該二元6次函數(shù)式一個(gè)多峰函數(shù)，共有6個(gè)極值，其中有兩個(gè)極值點(diǎn)對(duì)應(yīng)的 函數(shù)取值為最小值。試求解函數(shù)的極值點(diǎn)(1)設(shè)計(jì)思路本題采用遺傳算法，遺傳算法搜索最優(yōu)解的方法是模仿生物的進(jìn)化過程，遺傳算法主要使用選擇算子、交叉算子與變異算子來模擬生物進(jìn)化，從而產(chǎn)生一代又一代的種群。遺傳算法具有通用、并行、穩(wěn)健、簡單與全局優(yōu)化能力強(qiáng)等突 出優(yōu)點(diǎn)，適用于解決復(fù)雜、困難的全局優(yōu)化問題(2)程序流程圖(3)實(shí)驗(yàn)程序function objV=objectFunction(pop) m=size(pop,1);for i=1:mobjV(i,1)=4

2、*pop(i,1)A2-2.1*pop(i,1)A4+(1/3)*pop(i,1)A6+pop(i,1)*pop(i,2)-4*po p(i,2)A2+4*pop(i,2)A4;end%J始化clc;clear;pc=0.7;pm=0.05;NIND=20;MAXGEN=1000;NVAR=2;PRECI=40;GGAP=0.9;短叉率%變異率%個(gè)體數(shù)目%最大遺傳代數(shù)%變量維數(shù)峨量二進(jìn)制數(shù)%弋溝trace_min=zeros(MAXGEN,1);trace_max=zeros(MAXGEN,1);%每代極小值%!代極大值%#群初始化FieldD=rep(PRECI,1,NVAR);-1,-1;

3、1,1;rep(1;0;1;1,1,NVAR);%K 域掃描Chrom=crtbp(NIND,NVAR*PRECI);%計(jì)算第0代函數(shù)適應(yīng)度，尋找最優(yōu)個(gè)體gen=0;pop=bs2rv(Chrom,FieldD);objV=objectFunction(pop);minY=min(objV);%各二進(jìn)制初始種群轉(zhuǎn)化為十進(jìn)制%計(jì)算函數(shù)適應(yīng)度%i數(shù)適應(yīng)度最小值即函數(shù)最小值maxY=max(objV);POP(:,:,gen+1)=pop(1:end,1:end);%進(jìn)化過程while gen<MAXGENFitnV=ranking(-objV);SelCh=select('sus&#

4、39;,Chrom,FitnV,GGAP);%擇SelCh=recombin('xovsp',SelCh,pc);%!組SelCh=mut(SelCh,pm);藏異popnew=bs2rv(SelCh,FieldD);渤一代種群objVSel=objectFunction(popnew); % 計(jì)算子代目標(biāo)函數(shù)值 Chrom,objV=reins(Chrom,SelCh,1,1,objV,objVSel); gen=gen+1; if minY>min(objV)%W找當(dāng)前極小值minY=min(objV);y,i=min(objV)；x=bs2rv(Chrom,Fiel

5、dD);xmin(1,:)=x(i,:);disp('對(duì)應(yīng)最小自變量取值：',num2str(x(i,:)disp('對(duì)應(yīng)最小值:',num2str(y)%輸出最優(yōu)個(gè)體%輸出最優(yōu)個(gè)體endif maxY<max(objV)%!找當(dāng)前極大值maxY=max(objV);Y,I=max(objV);X=bs2rv(Chrom,FieldD);xmax(1,:)=X(I,:);disp('對(duì)應(yīng)最大自變量取值：',num2str(X(I,:)disp('對(duì)應(yīng)最大值:',num2str(Y)end%俞出最優(yōu)個(gè)體%俞出最優(yōu)個(gè)體trace

6、_min(gen,1)=minY;trace_max(gen,1)=maxY;end%畫圖%保存當(dāng)前極小值%呆存當(dāng)前極大值figureplot(1:gen,trace_min(:,1); hold on%畫進(jìn)化過程圖plot(1:gen,-1.031570364,'r-');figure(2)plot(1:gen,trace_max(:,1);hold on%i標(biāo)函數(shù)在區(qū)間最小值plot(1:gen32333,'r-');%目標(biāo)函數(shù)在區(qū)間最大值(4)運(yùn)行結(jié)果優(yōu)化函數(shù)如圖所示:由優(yōu)化函數(shù)圖可知，此函數(shù)存在 2個(gè)極小值點(diǎn)，4個(gè)極大值點(diǎn)4個(gè)最大值為:對(duì)應(yīng)x1,x2最大

7、自變量取值：-0.99543-0.91298對(duì)應(yīng)函數(shù)最大值：2.5798對(duì)應(yīng)x1,x2最大自變量取值：-0.92829-0.99328對(duì)應(yīng)函數(shù)最大值：2.97對(duì)應(yīng)x1,x2最大自變量取值：-0.989-0.99817對(duì)應(yīng)函數(shù)最大值：3.1879對(duì)應(yīng)x1,x2最大自變量取值：-0.99168-0.99925對(duì)應(yīng)函數(shù)最大值：3.20472個(gè)最小值為：對(duì)應(yīng)x1,x2最小自變量取值：-0.0447820.76447對(duì)應(yīng)函數(shù)最小值：-0.99772對(duì)應(yīng)x1,x2最小自變量取值：0.11984-0.66623對(duì)應(yīng)函數(shù)最小值：-1.01022.體重約70kg的某人在短時(shí)間喝下2瓶啤酒后，隔一段時(shí)間測量他的血

8、液中酒精含量(mg/100mL),得到以下數(shù)據(jù)：時(shí)間/(h)0.250.50.7511.522.533.544.5567酒精含量/3068758282776868585150413835時(shí)間/(h)8910111213141516酒精含量282518151210774根據(jù)酒精在人體血液分解的動(dòng)力學(xué)規(guī)律可知，血液中酒精濃度與時(shí)間的關(guān)系可表示為:qt rtk e e試根據(jù)表中數(shù)據(jù)求出參數(shù)k、q、r。(1)設(shè)計(jì)思路本題采用遺傳算法，遺傳算法搜索最優(yōu)解的方法是模仿生物的進(jìn)化過程，遺傳算法主要使用選擇算子、交叉算子與變異算子來模擬生物進(jìn)化，從而產(chǎn)生一 代又一代的種群。遺傳算法具有通用、并行、穩(wěn)健、簡單與

9、全局優(yōu)化能力強(qiáng)等突 出優(yōu)點(diǎn)，適用于解決復(fù)雜、困難的全局優(yōu)化問題。(2)程序流程圖(3)實(shí)驗(yàn)程序:%求函數(shù)適應(yīng)度子程序function objV=objectFunction(pop,Data)m=size(pop,1);n=size(Data,1);for i=1:mfor j=1:nC0,1)=abs(pop(i,1)*(exp(pop(i,2)*(-1)*Data0,1)-exp(pop(i,3)*(-1)*Data0,1)-Data0,2); endobjV(i,1)=mean(C);end%求方差子程序function RESM=variance(a,a_1)M=size(a,1);y

10、=0;y_1=0;for i=1:My_1=y_1+(a(i,1)-a_1(i,1)A2； end RESM=sqrt(y_1/M);%交叉率 尬異率 %尸體數(shù)目%主程序 load Data %始化 pc=0.7; pm=0.05; NIND=500;%i大遺傳代數(shù)MAXGEN=2000;NVAR=3;PRECI=20;GGAP=0.9;超量維數(shù) 被量二進(jìn)制數(shù)%弋購trace=zeros(MAXGEN,1);%!代最優(yōu)值%中群初始化FieldD=rep(PRECI,1,NVAR);100,0,0;150,1,3;rep(1;0;1;1,1,NVAR);燼域掃描呢建初始種群Chrom=crtbp

11、(NIND,NVAR*PRECI);%計(jì)算第0代函數(shù)適應(yīng)度，尋找最優(yōu)個(gè)體gen=0;%各二進(jìn)制初始種群轉(zhuǎn)化為十進(jìn)制%計(jì)算函數(shù)適應(yīng)度%函數(shù)適應(yīng)度最小值即最優(yōu)值pop=bs2rv(Chrom,FieldD);objV=objectFunction(pop,Data);minY=min(objV);%進(jìn)化過程while gen<MAXGENFitnV=ranking(-objV);SelCh=select('sus',Chrom,FitnV,GGAP);SelCh=recombin('xovsp',SelCh,pc);SelCh=mut(SelCh,pm);po

12、pnew=bs2rv(SelCh,FieldD);objVSel=objectFunction(popnew,Data); %處擇%1組異名新一代種群計(jì)算子代目標(biāo)函數(shù)值Chrom,objV=reins(Chrom,SelCh,1,1,objV,objVSel);gen=gen+1;if minY>min(objV)%l找當(dāng)前最優(yōu)個(gè)體endminY=min(objV);trace(gen,1)=minY;% 呆存當(dāng)前最優(yōu)個(gè)體end%結(jié)果輸出Y,I=min(objV);X=bs2rv(Chrom,FieldD);Xmin(1,:)=X(I,:);disp('對(duì)應(yīng)自變量取值：,num2

13、str(X(I,:)喻出最優(yōu)個(gè)體m=size(Data,1);for i=1:m喻出最優(yōu)個(gè)體的函數(shù)擬合值Y(i,1)=Xmin(1,1)*(exp(-1)*Xmin(1,2)*(Data(i,1)-exp(-1)*Xmin(1,3)*(Data(i,1);ARE(i,1)=Data(i,2)-Y(i,1);endRESM=variance(Data(:,2),Y);disp('方差：',num2str(RESM)%十算方差%畫圖figure刎進(jìn)化過程圖plot(1:gen,trace(:,1);figure(2);%畫出期望值與擬合值曲線plot(Data(:,1),Data(

14、:,2),'rd-'); hold onplot(Data(:,1),Y,'b*-')xlabel('時(shí)間');ylabel('酒精含量');legend('期望值',擬合值);figure(3)plot(Data(:,1),ARE,'rd-') xlabel('時(shí)間');ylabel('誤差');(4)運(yùn)行結(jié)果進(jìn)行20次的多項(xiàng)式擬合后圖如下:OTro的30明1=-七如月所以，對(duì)應(yīng)自變量取值：k=113.3353q=0.1841013r=2.206932方差：3.37

15、483.設(shè)計(jì)一個(gè)神經(jīng)網(wǎng)絡(luò)，并對(duì)輸入信號(hào)進(jìn)行預(yù)測。輸入為一線性調(diào)頻信號(hào)，信號(hào) 采樣時(shí)間為2s,采樣頻率為1000Hz,起始到信號(hào)的瞬時(shí)為0Hz, 1s時(shí)的瞬 時(shí)頻率為150Hz。(1)本題采用三層BP神經(jīng)網(wǎng)絡(luò)。第一步，網(wǎng)絡(luò)初始化。給各連接權(quán)值分別賦一個(gè)區(qū)間的隨機(jī)數(shù)， 設(shè)定誤差函數(shù)e,給定計(jì)算精度值和最大學(xué)習(xí)次數(shù) Mo第二步，隨機(jī)選取第2000個(gè)輸入樣本，前1900作為訓(xùn)練中¥本最后100做測 試。第三步，計(jì)算隱含層各神經(jīng)元的輸入和輸出。第四步，利用網(wǎng)絡(luò)期望輸出和實(shí)際輸出，計(jì)算誤差函數(shù)對(duì)輸出層的各神經(jīng)元 的偏導(dǎo)數(shù)a。第五步利用隱含層到輸出層的連接權(quán)值、 輸出層和隱含層a的輸出計(jì)算誤差函數(shù)

16、對(duì)隱含層各神經(jīng)元的偏導(dǎo)數(shù) bo第六步，利用輸出層各神經(jīng)元的a和隱含層各神經(jīng)元的輸出來修正連接權(quán)值wo第七步：利用隱含層各神經(jīng)元的 a和輸入層各神經(jīng)元的輸入修正連接權(quán)。(2)神經(jīng)網(wǎng)絡(luò)算法流程圖：(3)實(shí)驗(yàn)程序%設(shè)計(jì)一個(gè)神經(jīng)網(wǎng)絡(luò)，并對(duì)輸入信號(hào)進(jìn)行預(yù)測1s時(shí)的瞬時(shí)%信號(hào)采樣時(shí)間為2s,采樣頻率為1000Hz ,起始到信號(hào)的瞬時(shí)為 0Hz,頻率為150Hzclc;clear;time=0:0.001:2;y=chirp(time,0,1,150,'linear');y=y'time=time'm=size(y,1);%網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)以前四個(gè)時(shí)刻預(yù)測第五個(gè)時(shí)刻fo門=1:1

17、896X(i,1)=y(i,1);X(i,2)=y(i+1,1);X(i,3)=y(i+2,1);X(i,4)=y(i+3,1);Y(i,1)=y(i+4,1); end %網(wǎng)絡(luò)訓(xùn)練 s=size(Y,2);P=X't=Y'%數(shù)據(jù)歸一化pn,minX,maxX=premnmx(p);%各數(shù)據(jù)歸一化tn,minY,maxY=premnmx(t);%各數(shù)據(jù)歸一化啕“練網(wǎng)絡(luò)net=newf(minmax(pn),8,s,'tansig','purelin','trainlm');net.trainParam.goal=0.001;net

18、.trainParam.epochs=800;net=train(net,pn,tn);yn =sim(net,pn);Yn = postmnmx(yn,minY,maxY);y_train=Yn'%訓(xùn)練誤差train_number=size(X,1);for i=1:train_numberARE(i,1)=Y(i,1)-y_train(i,1);end%網(wǎng)絡(luò)測試數(shù)據(jù)fo門=1:97X_test(i,1)=y(i+1900,1);X_test(i,2)=y(i+1901,1);X_test(i,3)=y(i+1902,1);X_test(i,4)=y(i+1903,1);Y_test

19、(i,1)=y(i+1904,1);end%網(wǎng)絡(luò)測試q=X_test'u=Y_test'qn=tramnmx(q,minX,maxX);y_tr=sim(net,qn);y_trr=postmnmx(y_tr,minY,maxY);y_test=y_trr'train_number=size(X,1);test_number=size(X_test,1);test_number=size(X_test,1);%測試誤差for i=1:test_numberARE_1(i,1)=Y_test(i,1)-y_test(i,1);end%畫圖figure。)； plot(Y,

20、'rd-');hold onplot(y_train,'b*-')legend('訓(xùn)練樣本輸出期望值,'訓(xùn)練樣本輸出預(yù)測值');axis(0 500 -1.5 1.5)figure(2);plot(Y,'rd-');hold onplot(y_train,'b*-')legend('訓(xùn)練樣本輸出期望值,'訓(xùn)練樣本輸出預(yù)測值);axis(501 1000 -1.5 1.5)figure(3);plot(Y,'rd-');hold onplot(y_train,'b*-&

21、#39;)legend('訓(xùn)練樣本輸出期望值,'訓(xùn)練樣本輸出預(yù)測值');axis(1001 1500 -1.5 1.5)figure(4);plot(Y,'rd-');hold onplot(y_train,'b*-')legend('訓(xùn)練樣本輸出期望值,'訓(xùn)練樣本輸出預(yù)測值');axis(1501 1900 -1.5 1.5)figure(5);plot(ARE,'b*-');axis(0 500 -0.2 0.2)figure(6);plot(ARE,'b*-');axis(50

22、1 1000 -0.2 0.2)figure(7);plot(ARE,'b*-');axis(1001 1500 -0.2 0.2)figure(8);plot(ARE,'b*-');axis(1501 1900 -0.2 0.2)figure(9);plot(ARE_1,'b*-');figure(10);plot(Y_test,'rd-');hold onplot(y_test,'b*-')(4)運(yùn)行結(jié)果下圖分別為0-1900樣本分成4組的訓(xùn)練過程1.5訓(xùn)練樣本輸出期望值一訓(xùn)練樣本輸出預(yù)測值$ ¥播 ) 1+* + !:*:* If+.+ tt+.s*一 _ _ _wV'腳H +-*+室05010015020025030035040045050