Matlab tips (27) grey prediction

Preface

MATLAB Learning about image processing is very friendly , You can start from scratch , There are many encapsulated functions that can be called directly for basic image processing , This series of articles is mainly to introduce some of you in MATLAB Some concept functions are commonly used in routine demonstration ！

Color prediction model is through a small amount of 、 Incomplete information , A prediction method of establishing a mathematical model to make a prediction . It is based on the past and present development laws of objective things , With the help of scientific methods, describe and analyze the future development trend and situation , And form scientific assumptions and judgments .

It is a method to predict the system with uncertain factors . Grey prediction identifies the difference of development trend between system factors , That is, correlation analysis , And generate and process the original data to find the law of system change , Generate data sequences with strong regularity , Then the corresponding differential equation model is established , So as to predict the future development trend of things . The grey prediction model is constructed by a series of quantitative values reflecting the characteristics of the prediction object observed at the same time interval , Predict the characteristic quantity at a certain time in the future , Or the time to reach a characteristic quantity .

The example encountered when searching for data , Here to share ,MATLAB Version is MATLAB2015b.

One . MATLAB Simulation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： Grey prediction program 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-27
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% I.  Clear environment variables 
clear all
clc

tic
%Matlab Grey prediction program ：
%y=input(' Please input data ');

y=[29.8 30.11 41.05 70.12 77.79 77.79 104.82 65.22 82.7 100.79]
n=length(y);
yy=ones(n,1);
yy(1)=y(1);
for i=2:n
yy(i)=yy(i-1)+y(i) 
end
B=ones(n-1,2);
for i=1:(n-1)
B(i,1)=-(yy(i)+yy(i+1))/2;
B(i,2)=1;
end
BT=B';
for j=1:(n-1)
    YN(j)=y(j+1);
end
YN=YN';
A=inv(BT*B)*BT*YN;
a=A(1);
u=A(2);
t=u/a;
t_test=input(' Enter the number to be predicted ');
i=1:t_test+n;
yys(i+1)=(y(1)-t).*exp(-a.*i)+t;
yys(1)=y(1);
for j=n+t_test:-1:2
    ys(j)=yys(j)-yys(j-1);
end
x=1:n;
xs=2:n+t_test;
yn=ys(2:n+t_test);
plot(x,y,'^r',xs,yn,'*-b');
det=0;
for i=2:n
det=det+abs(yn(i)-y(i));
end
det=det/(n-1);
disp([' The percent absolute error is ：',num2str(det),'%']);
disp([' Predictive value for ：',num2str(ys(n+1:n+t_test))]);
% Please input data  [29.8 30.11 41.05 70.12 77.79 77.79 104.82 65.22 82.7 100.79]
toc

Two . Simulation results

y =

   29.8000   30.1100   41.0500   70.1200   77.7900   77.7900  104.8200   65.2200   82.7000  100.7900


yy =

   29.8000
   59.9100
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
  326.6600
    1.0000
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
  326.6600
  431.4800
    1.0000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
  326.6600
  431.4800
  496.7000
    1.0000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
  326.6600
  431.4800
  496.7000
  579.4000
    1.0000


yy =

   29.8000
   59.9100
  100.9600
  171.0800
  248.8700
  326.6600
  431.4800
  496.7000
  579.4000
  680.1900

 Enter the number to be predicted 6
 The percent absolute error is ：14.5128%
 Predictive value for ：110.5718      120.8171      132.0116      144.2434      157.6086      172.2122
 Time has passed  1.866326  second .

3、 ... and . Summary

Gray scale prediction in prediction application , Such as weather forecast 、 earthquake prediction 、 Pest forecast, etc , Domestic scholars have made many useful studies . Simply take a note of the example of gray prediction analysis , It may be used later . Learn one every day MATLAB Little knowledge , Let's learn and make progress together ！