灰色系统预测滑坡位移MATLAB代码,灰色预测法matlab详解,matlab

clc;clear;%建立符号变量a(发展系数)和b(灰作用量) %原始数列 A A = [188.136,198.305,173.051,228.814,215.983,249.153,279.661,284.746,268.746,315.254,345.763,399.186,391.525,416.949,452.542,452.542,493.22,550.22,544.068,574.576,605.085,666.102,711.864,867.627,823.729,874.576,910.169,935.593,986.441,1042.37,1103.39,1330.49,1205.08,1250.85,1301.69,1347.46,1383.05,1418.64,1418.64]; 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+39) 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+39) G(i) = F(i) - F(i-1); %得到预测出来的数据 end disp('预测数据为：'); G %模型检验 H = G(1:39); %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+10) %绘制曲线图 t1 = (1:1:39); t2 = (1:1:78); plot(t1, A, 'ro'); hold on; plot(t2, G, 'g-'); xlabel('时间'); ylabel('累计位移量/mm'); legend('ZG34实测累计位移量','ZG34预测累计位移量'); grid on;