灰色预测模型及MATLAB实例

Love The Way You Lie 2022-03-22 04:49 276阅读 0赞

灰色预测模型及MATLAB实例推荐下面的:  
[https://www.cnblogs.com/somedayLi/p/9543202.html][https_www.cnblogs.com_somedayLi_p_9543202.html]

[https://www.cnblogs.com/yocichen/p/9348946.html][https_www.cnblogs.com_yocichen_p_9348946.html]

function y=gm11() 
    %建立符号变量a(发展系数)和b(灰作用量)
    syms a b ;
    GG=[];
    c = [a b]';
     
    %原始数列 A
    %A = [41462, 28969, 32251, 47694, 32265, 27819, 33539, 36994];%VA
    %A=[70999	71282	85415	93747	101423	109150	115276	119349];%OH
    %A=[89981	86793	78577	72096	77318	75351	72376	68751];%PA
    %A=[29588	28285	27502	26820	27077	25811	26530	28870];%KY
    %A=[8668	9310	9429	9062	6926	5345	5405	3672];%WV
    %A=[240698 232146 234767.3 238130.8 40988.7 40345.4 39819.1 39392.8]%sum
    
    x=xlsread('VACountry-new.xlsx')
    for k= 1:118
         A =x(k,:)
    n = length(A);
     
    %对原始数列 A 做累加得到数列 B
    B = cumsum(A);
     
    %对数列 B 做紧邻均值生成
    for i = 2:n
        C(i) = (B(i) + B(i - 1))/2;
    end
    C(1) = [];
     
    %构造数据矩阵
    B = [-C;ones(1,n-1)];
    Y = A; Y(1) = []; Y = Y';
     
    %使用最小二乘法计算参数 a(发展系数)和b(灰作用量)
    c = inv(B*B')*B*Y;
    c = c';
    a = c(1); b = c(2);
     
    %预测后续数据
    F = []; F(1) = A(1);
    for i = 2:(n+10) %这里10代表向后预测的数目，如果只预测一个的话为1
        F(i) = (A(1)-b/a)/exp(a*(i-1))+ b/a;
    end
     
    %对数列 F 累减还原,得到预测出的数据
    G = []; G(1) = A(1);
    for i = 2:(n+10) %10同上
        G(i) = F(i) - F(i-1); %得到预测出来的数据
    end
     
    disp('预测数据为：');
    G
    GG=[GG;G];
    
    end
    xlswrite('VACountryyuce.xlsx',GG)
    
    %模型检验
     
    H = G(1:8); %这里的10是已有数据的个数
    %计算残差序列
    epsilon = A - H
     
    %法一：相对残差Q检验
    %计算相对误差序列
    delta = abs(epsilon./A);
    %计算相对误差Q
    disp('相对残差Q检验：')
    Q = mean(delta)
     
    %法二：方差比C检验
    disp('方差比C检验：')
    C = std(epsilon, 1)/std(A, 1)
     
    %法三：小误差概率P检验
    S1 = std(A, 1);
    tmp = find(abs(epsilon - mean(epsilon))< 0.6745 * S1);
    disp('小误差概率P检验：')
    P = length(tmp)/n
     
    %绘制曲线图
    t1 = 2010:2017;
    t2 = 2010:2027;
    plot(t1, A,'ro'); hold on;
    plot(t2, G, 'g-');
    xlabel('年份'); ylabel('污水量/亿吨');
    legend('实际污水排放量','预测污水排放量');
    title('长江污水排放量增长曲线'); %都用自己的
    grid on;

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NDg2NTAx_size_16_color_FFFFFF_t_70]

[https_www.cnblogs.com_somedayLi_p_9543202.html]: https://www.cnblogs.com/somedayLi/p/9543202.html
[https_www.cnblogs.com_yocichen_p_9348946.html]: https://www.cnblogs.com/yocichen/p/9348946.html
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NDg2NTAx_size_16_color_FFFFFF_t_70]: /images/20220322/c0e47ff86d89416a8a7c3e71119dc8de.png