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This article mainly introduces the relevant knowledge of "how to achieve grey prediction in Matlab". The editor shows you the operation process through actual cases, and the operation method is simple, fast and practical. I hope this article "how to achieve grey prediction in Matlab" can help you solve the problem.

Model introduction

A little bit about the principle:

Grey prediction for the data with weak trend, accumulate the original data and get the new data with obvious trend to fit, assuming that the original data is:

Then the data in the new dataset X (1) is:

It is generally believed that the cumulative data follow an exponential distribution, so let's directly assume:

It is not done to carry out a nonlinear fitting directly, but since the second grade of primary school, the teacher has taught us that, like this exponential function fitting, the effect of changes in various parameters on the overall curve is very different, ah, the direct fitting error will be very large, how can it be integrated into a linear fitting? I have tried direct fitting, which can generally describe the trend and make a prediction, but the error will be a little larger than the grey prediction.

The exponential function generally conforms to a differential equation:

It is easy to solve ordinary differential equations:

In this way, we only need to find the two constants of aforce u to get x (1) (t), we can get X (1) sequence, and then we can get X (0) sequence by item-by-item difference.

When k ≤ t ≤ KPI 1, there are:

The differential equation before it is brought back is:

In fact, linear fitting is fine, of course, we can also use the least square method to pretend to analyze it, so that:

Basic code

The core code is very short, only six lines, the code gives detailed comments, the basic drawing or MATLAB style is relatively simple, and the image modification code will be given later.

X0 = [15 16.1 17.3 18.4 18.7 19.1 19.9 21.3 22.5]; tweak 1) 9;% original data independent variable range pt=10:12;% predicted data independent variable range X1=cumsum (X0);% cumulative generation trend obvious new series Z=X1 (1:end-1) + diff (X1). / 2 % mean, that is, (X1 (1:end-1) + X1 (2:end)). / 2a_u=polyfit (- ZLECHING X0 (2:end), 1);% axiu = (BackgroundB)\ BZLING Y a=a_u (1); u=a_u (2); P = (X1 (1)-uCanda). / exp (a.* ([tpenpt]-1)) + UA % to find X1 fitting value P = [P (1), diff (P)];% X1 to make item-by-item difference to calculate predicted value% drawing plot ([tminute pt], P <...'>); hold onplot ('tmemX0') legend ('predicted value', 'true value')

Basic code + modifier X0 = [15 16.1 17.3 18.4 18.7 19.1 19.9 21.3 22.5]; tweak 1var 9;% original data independent variable range pt=10:12;% predicted data independent variable range X1=cumsum (X0);% cumulative generation trend obvious new sequence Z=X1 (1:end-1) + diff (X1). / 2 % mean, that is, (X1 (1:end-1) + X1 (2:end)). / 2a_u=polyfit (- ZLECHING X0 (2:end), 1);% axiu = (BackgroundB)\ BZLING Y a=a_u (1); u=a_u (2); P = (X1 (1)-uCanda). / exp (a.* ([tpenpt]-1)) + UA % find X1 fitting value P = [P (1), diff (P)];% X1 make item-by-item difference to get predicted value% drawing plot ([tPowerpt], P < 82124179]. 'MarkerEdgeColor',],' LineWidth',2,'MarkerSize',16) hold onplot (t recorder X0 pensiondMee. Curiosity pensionary Colorado, [169 page64 pr 71]. / 255 recorder MarkerFaceColorboy, [169 pr 64 pr 71]. / 255 pr... 'MarkerEdgeColor', [1meme 1],' LineWidth',2,'MarkerSize',16)% add legend lgd=legend ('fitting result','original data'); lgd.Location='best';lgd.FontSize=16;% coordinate region decorates ax=gca;grid on;box offax.LineWidth=2;ax.Color= [249250245]. / 255 coordinate region decorated with ax=gca;grid on;box offax.LineWidth=2;ax.Color= [249250245]. Ax.FontName='Cambria';ax.FontSize=14

This is the end of the introduction on "how to achieve Grey Prediction in Matlab". Thank you for your reading. If you want to know more about the industry, you can follow the industry information channel. The editor will update different knowledge points for you every day.

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