CN106296434B - Grain yield prediction method based on PSO-LSSVM algorithm - Google Patents

Grain yield prediction method based on PSO-LSSVM algorithm Download PDF

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CN106296434B
CN106296434B CN201610684306.2A CN201610684306A CN106296434B CN 106296434 B CN106296434 B CN 106296434B CN 201610684306 A CN201610684306 A CN 201610684306A CN 106296434 B CN106296434 B CN 106296434B
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杨铁军
杨娜
朱春华
樊超
傅洪亮
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Abstract

A grain yield prediction method based on a PSO-LSSVM algorithm sequentially comprises the following steps: acquiring the grain yield and the value of a main influence factor in a known year; smoothing the original data of the grain yield and the main influence factors; obtaining a prediction model according to a least squares support vector machine model
Figure DEST_PATH_IMAGE002
(ii) a Solving penalty factor by iterative algorithm
Figure DEST_PATH_IMAGE004
Width of sum kernel
Figure DEST_PATH_IMAGE006
(ii) a Solving a Lagrange multiplier and a variable value b; solving radial basis kernel functions
Figure DEST_PATH_IMAGE008
A value of (d); substituting the solved Lagrange multiplier, variable value b and radial basis function into the prediction model
Figure 733441DEST_PATH_IMAGE002
And calculating the predicted value of the grain yield of the nth year by using the model. The invention discloses a grain yield prediction method based on a PSO-LSSVM algorithm, which can predict the grain yield with high prediction precision and can improve the prediction accuracy of the grain yield in China.

Description

Grain yield prediction method based on PSO-LSSVM algorithm
Technical Field
The invention belongs to the field of grain yield prediction, and particularly relates to a grain yield prediction method based on a PSO-LSSVM algorithm.
Background
Accurate prediction of grain yield can provide basis for government decision, and grain yield data are typical small sample data, are easily affected by uncertainty factors and are represented as a complex nonlinear system.
At present, methods for predicting grain yield at home and abroad are various and mainly comprise a regression analysis method, a time series method and an artificial neural network method. The regression analysis method can carry out causal analysis on variables, when the method is applied to grain yield prediction, main influence factors of the grain yield can be found, but the method is only suitable for short-term prediction because all the influence factors cannot be fully considered. The time-series method is short in calculation time consumption, low in requirement on the quantity of historical data and capable of reflecting continuous changes of yield. However, most models established by the method are models based on linear data, and the grain time series data are often represented as nonlinear features, so that the prediction accuracy is not high. The artificial neural network method is a nonlinear prediction method, has high parallel processing and fault-tolerant capability, and is widely applied at present. However, the neural network requires a large data sample, and the grain yield data belongs to small sample data, so that the phenomena of overfitting of the result, weak generalization capability and the like often occur in the prediction process.
In conclusion, the existing grain yield prediction methods have the problem of large or small grain yield, and the grain yield prediction method with high prediction precision is provided, and has important significance for grain prediction.
Disclosure of Invention
The invention aims to provide a grain yield prediction method with high prediction accuracy based on a PSO-LSSVM algorithm.
In order to solve the technical problems, the invention provides the following technical scheme: a grain yield prediction method based on a PSO-LSSVM algorithm sequentially comprises the following steps:
(1) acquiring the grain yield and the value of a main influence factor in a known year;
(2) smoothing the grain yield and the primary influence factor of the known year obtained in the step (1);
(3) obtaining a prediction model according to a least squares support vector machine model
Figure GDA0003351038480000011
Wherein f (x)n) Is the grain yield of the nth yearAmount, xiIs the value of the impact factor of year i, xnIs the value of the impact factor for the nth year; alpha is alphai(i is 1, …, n) is the lagrange multiplier, b is the variable value, k (x)n，xi) Is a radial basis kernel function;
(4) solving a penalty factor gamma and the width sigma of the kernel function through an iterative algorithm;
(5) solving a Lagrange multiplier and a variable value b;
(6) solving radial basis kernel function k (x)n，xi) A value of (d);
(7) substituting the solved Lagrange multiplier, variable value b and radial basis function into the prediction model
Figure GDA0003351038480000021
And calculating f (x) using the modeln) Namely the predicted value of the grain yield of the nth year; wherein i is the year of the grain yield and the influence factor value which can be inquired, the main influence factor is known in the nth year, and the grain yield is to be predicted.
The method for obtaining the main influence factors comprises the following steps: and calculating the correlation degree between the influence factors and the grain yield according to the values of the grain yield and the influence factors, and comparing the correlation degrees between the influence factors and the grain yield, wherein the influence factor with the maximum correlation degree is the main influence factor.
In the step (2), the method for smoothing the grain yield and the main influence factors in the step (1) comprises the following steps:
1) respectively carrying out differential processing on the grain yield and the original data of the main influence factors;
2) respectively calculating the fluctuation average values p and py of the grain yield and the main influence factors according to the differential processing of the step 1);
3) obtaining the grain yield and the value of the main influence factor after smoothing treatment, and respectively calculating fluctuation values p1 and py1 between the grain yield and the value of the main influence factor in two adjacent years by Lp-Lp1 and Yp-Yp 1;
there are three cases for grain yield:
in the first case: p1 > p, and Lp < Lp1, let Lp1 be Lp + p;
in the second case: p1 > p, and Lp > Lp1, let Lp1 be Lp-p;
in the third case: p1 < p, then Lp1 ═ Lp 1;
there are three cases for the values of the main impact factors:
in the first case: py1 > py, and Yp < Yp1, then Yp1 ═ Yp + py;
in the second case: py1 > py, and Yp > Yp1, then Yp1 ═ Yp-py;
in the third case: py1 < py, then Yp1 ═ Yp 1;
wherein Lp is the grain yield of the nth-m years; lp1 is the grain yield of n-m +1 year; yp is the original value of the main influence factor of the nth-m years; yp1 is the original value of the n-m +1 year primary factor.
Solving a penalty factor gamma and the width sigma of the kernel function by an iterative optimization method:
step 1, obtaining a fitness function according to a prediction model as follows:
Figure GDA0003351038480000022
in the formula yiIs the actual value of the grain yield in the ith year,
Figure GDA0003351038480000023
the predicted value of the grain yield in the ith year; n is a radical ofAAnd NBRespectively training samples and testing sample numbers;
step 2, updating the particle speed and position according to the following formula;
Figure GDA0003351038480000031
wherein x isi(t+1)＝xi(t)+vi(t+1)
In the formula, t is the iteration number, ω is a non-negative number, called inertia weight, and controls how much previous velocity of each generation of velocity update of the particle is kept. c. C1And c2Is a non-negative constant, called acceleration factor. v. ofiIs the velocity of the particlesDegree, vi∈[-vmax，vmax]，vmaxIs a constant, set by the user to limit the velocity, x, of the particleiIs the position of the particle. r is1And r2Is between [0, 1 ]]A random number in between.
Figure GDA0003351038480000032
And gbestRespectively determining a current individual optimal value and a current population optimal value according to a test error obtained by the trained LSSVM for the test sample set;
step 3, analyzing the result after each iteration, and using the current fitness value fit [ i ] obtained by the iteration]And individual extremum
Figure GDA0003351038480000033
Make a comparison if
Figure GDA0003351038480000034
Then use fit [ i]Is replaced by
Figure GDA0003351038480000035
Using its fitness value fit [ i ]]And global extreme gbestComparison, if fit [ i]＞gbestThen use fit [ i]Replace g by droppingbestMeanwhile, updating the speed and the position of the particles according to the step 2;
and 4, outputting the optimal solution of the parameters if the fitness function value reaches the prediction precision or reaches the preset maximum iteration times, finishing the optimization, and if the fitness function value does not reach the preset maximum iteration times, turning to the step 2 to search again.
The method for solving the Lagrange multiplier and the variable value b comprises the following steps: according to the formula
Figure GDA0003351038480000036
Solving b according to the formula
Figure GDA0003351038480000037
Solving alpha; wherein the content of the first and second substances,
Figure GDA0003351038480000038
is 1iInversion of the matrix, Q is an i × i square matrix of the major influence factors, where the i-th row and i-column have the values xi×xi，EiIs an identity matrix of order j, yiIs the value of grain yield in the i-th year; gamma is a penalty factor.
The solving method of the radial basis function comprises the following steps: using the formula k (x)n，xi)＝exp{-||xn-xi||2/σ2) Solving, wherein xiIs the value of the impact factor of year i, xnIs the value of the impact factor for the nth year.
Through the technical scheme, the invention has the beneficial effects that:
1. the prediction model combines the PSO algorithm and the least square support vector machine model, and simultaneously carries out smoothing treatment on the original data, so that the prediction precision is obviously improved, and the prediction model has important significance for improving the grain yield prediction accuracy.
2. By determining the values of the main influence factors, the prediction of the grain yield is greatly simplified.
3. In the solution method of the penalty factor gamma and the width sigma of the kernel function, the optimal value is obtained through iterative optimization, and the prediction precision of the prediction model is further improved.
Drawings
FIG. 1 is a flow chart of a prediction method according to the present invention.
Detailed Description
A grain yield prediction method based on a PSO-LSSVM algorithm is disclosed, as shown in figure 1, the method sequentially comprises the following steps:
(1) and acquiring the grain yield and the value of the main influence factor of the known year, wherein the grain yield and the value of the main influence factor of the known year can be known through the existing literature records.
The method for judging whether the influence factors are main influence factors comprises the following steps: and calculating the correlation degree between the influence factors and the grain yield according to the grain yield and the influence factors, wherein the influence factor with the maximum correlation degree with the grain yield is a main influence factor. The method for calculating the correlation degree between the influence factors and the grain yield is mature prior art. The calculation of the correlation between the influence factors and the grain yield can refer to the chinese patent application with application number "201510985352.1".
(2) Smoothing the acquired grain yield of the known year and the acquired original data of the main influence factors, wherein the smoothing method comprises the following steps:
firstly, respectively carrying out differential processing on the grain yield and the original data of the main influence factors;
secondly, respectively calculating a fluctuation average value p of the grain yield and a fluctuation average value py of the main influence factors according to the differential processing of the step 1);
and step three, obtaining the grain yield and the values of the main influence factors after smoothing treatment: calculating a fluctuation value p1 between grain yields of two adjacent years by using Lp-Lp1, and calculating a main influence factor py1 of two adjacent years by using Yp-Yp 1; wherein Lp is the grain yield of the m-th year; lp1 is the grain yield in m +1 year; yp is the original value of the m-year major influence factor; yp1 is the original value of the m +1 year primary factor (m ═ 1,2,3 … n-2).
There are three cases for grain yield:
in the first case: if p1 > p, and Lp < Lp1, then p1 is equal to Lp + p;
in the second case: if p1 > p, and Lp > Lp1, then p1 is equal to Lp-p;
in the third case: if p1 < p, Lp1 ═ Lp 1;
there are three cases for the values of the main impact factors:
in the first case: if py1 > py, and Yp < Yp1, then Yp1 is equal to Yp + py;
in the second case: if py1 > py, and Yp > Yp1, then Yp1 is equal to Yp-py;
in the third case: if py1 < py, Yp1 ═ Yp 1;
the grain yield and the fluctuation value of the main influence factor are reduced through smoothing processing, so that the prediction precision is improved.
(3) Obtaining the prediction according to the least square support vector machine modelTest model
Figure GDA0003351038480000051
Wherein f (x)n) Is the n-year grain yield, xiIs the value of the impact factor of year i, xnIs the value of the impact factor for the nth year; alpha is alphai(i is 1, …, n) is the lagrange multiplier, b is the variable value, k (x)n，xi) Is a radial basis kernel function; the prediction model is derived according to the least squares method.
(4) Solving a penalty factor gamma and the width sigma of the kernel function through an iterative algorithm;
the solution method of the penalty factor gamma and the width sigma of the kernel function is as follows:
solving a penalty factor gamma and the width sigma of the kernel function by an iterative optimization method:
step 1, obtaining a fitness function according to a prediction model as follows:
Figure GDA0003351038480000052
wherein yi is the actual value of the grain yield in the ith year,
Figure GDA0003351038480000053
the predicted value of the grain yield in the ith year; n is a radical ofAAnd NBRespectively training samples and testing sample numbers;
step 2, updating the particle speed and position according to the following formula;
Figure GDA0003351038480000054
wherein x isi(t+1)＝xi(t)+vi(t+1)
In the formula, t is the iteration number, ω is a non-negative number, called inertia weight, and controls how much previous velocity of each generation of velocity update of the particle is kept. c. C1And c2Is a non-negative constant, called acceleration factor. v. ofiIs the velocity, v, of the particlei∈[-vmax，vmax]，vmaxIs constant and is set by the userTo limit the velocity, x, of the particlesiIs the position of the particle. r is1And r2Is between [0, 1 ]]A random number in between.
Figure GDA0003351038480000055
And gbestRespectively determining a current individual optimal value and a current population optimal value according to a test error obtained by the trained LSSVM for the test sample set;
step 3, analyzing the result after each iteration, and obtaining the current fitness value fit [ j ] by using the iteration]And individual extremum
Figure GDA0003351038480000056
Make a comparison if
Figure GDA0003351038480000057
Then use fit [ i]Is replaced by
Figure GDA0003351038480000058
Using its fitness value fit [ i ]]And global extreme gbestComparison, if fit [ i]＞gbestThen use fit [ i]Replace g by droppingbestMeanwhile, the speed and the position of the particles are updated according to the step 3;
and 4, outputting the optimal solution of the parameters if the fitness function value reaches the prediction precision or reaches the preset maximum iteration times, finishing the optimization, and turning to the step 3 to search again if the fitness function value does not reach the conditions.
And as for the random numbers rand (1, 1), the random numbers rand are automatically generated by a computer, are not influenced by human in the prediction process, and unknown grain products can be obtained according to the prediction model as long as the values of known main influence factors and the grain yield exist.
(5) Solving the Lagrange multiplier and the variable value b, wherein the solving method of the Lagrange multiplier and the variable value b comprises the following steps: according to the formula
Figure GDA0003351038480000061
Solving b according to the formula
Figure GDA0003351038480000062
(where i ═ 1,2, n-1), solving for α; wherein the content of the first and second substances,
Figure GDA0003351038480000063
is 1iInversion of the matrix, Q is an i × i square matrix of the major influence factors, where the i-th row and i-column have the values xi，xiIs the value of the primary influencing factor in year i, yiIs the value of grain yield in the i-th year; gamma is a penalty factor.
(6) Solving radial basis kernel function k (x)n，xi) The solving method of the radial basis function is as follows: using the formula k (x)n，xi)＝eXp{-||xn-xi||2/σ2Solving, wherein xiIs the value of the impact factor of year i, xnIs the value of the impact factor of the nth year, wherein n is the year for which the value of the main impact factor is known and the grain yield is to be predicted. Wherein xnReference is made to the chinese patent application having application number "201510985352.1".
(7) Substituting the solved Lagrange multiplier, variable value b and radial basis function into a formula
Figure GDA0003351038480000064
And calculating the predicted value of the nth year by using the model; wherein i is the year of the grain yield and the value of the main influence factor which can be inquired, the value of the main influence factor of the nth year is known, and the grain yield is to be predicted.
According to the steps, the grain yield in 2011, 2012 and 2013 is predicted, the grain yield in the three years is also predicted by using the existing LS-SVM, SVM and ARIMA models, and the prediction result is shown in the following table 1:
TABLE 1 comparison of grain yield predictions
Figure GDA0003351038480000065
According to the prediction result, the real value is compared with the prediction result, wherein the prediction error is shown in table 2:
TABLE 2 average relative error comparison
Prediction model The prediction method of the invention PSO-LSSVM LSSVM SVM ARIMA
Average relative error (%) 0.7 0.8 1.23 1.56 1.73
As can be seen from tables 1 and 2, the ARIMA prediction model has the lowest precision, the average relative error is 1.73%, the SVM model has the nonlinear advantage, the prediction precision is improved a little compared with the ARIMA, and the average relative error is 1.56%; the LSSVM has the advantages that because the model parameters needing to be determined are less than those of the SVM, the relation between the complexity and the generalization capability of the model is well coordinated, and the prediction precision is also obviously improved; the PSO-LSSVM prediction model finds the optimal parameters in the LSSVM model by introducing a particle swarm optimization algorithm, the model precision is improved again, the prediction result also shows that the model has excellent performance, the average relative error is 0.8 percent, the prediction method of the invention performs smoothing treatment on the original data used by the PSO-LSSVM prediction model, the average relative error is minimum, and the prediction effect is also optimal.
The invention discloses a grain yield prediction method based on a PSO-LSSVM algorithm, which can predict the grain yield, combines the PSO algorithm and a least square support vector machine model, and simultaneously carries out smooth processing on original data, so that the prediction precision is obviously superior to that of the traditional LSSVM, SVM and ARIMA models, the prediction result of the grain yield in China can be improved, and guidance is provided for grain consumption, planting and purchasing.

Claims (2)

1. A grain yield prediction method based on a PSO-LSSVM algorithm is characterized by comprising the following steps: the method sequentially comprises the following steps:
(1) acquiring the grain yield and the value of a main influence factor in a known year;
(2) smoothing the grain yield and the primary influence factor of the known year obtained in the step (1);
(3) obtaining a prediction model according to a least squares support vector machine model
Figure FDA0003361401500000011
Wherein f (x)n) Is the n-year grain yield, xiIs the value of the main influencing factor of year i, xnIs the value of the primary influencing factor for year n; alpha is alphai(i is 1, …, N) is the lagrange multiplier, b is the variable value, k (x)n，xi) Is a radial basis kernel function;
(4) iteratively solving a penalty factor gamma and the width sigma of the kernel function through a PSO algorithm;
(5) solving a Lagrange multiplier and a variable value b;
(6) solving radial basis kernel function k (x)n，xi) A value of (d);
(7) substituting the solved Lagrange multiplier, variable value b and direction-releasing basis function into the prediction model
Figure FDA0003361401500000012
And calculating f (x) using the modeln) Namely the predicted value of the grain yield of the nth year; wherein i is the year of the grain yield and the influence factor value which can be inquired, the main influence factor is known in the nth year, and the grain yield is to be predicted; the method for obtaining the main influence factors comprises the following steps: calculating the correlation degree between the influence factors and the grain yield according to the grain yield and the values of the influence factors, and comparing the correlation degrees between the influence factors and the grain yield, wherein the influence factor with the maximum correlation degree is a main influence factor;
in the step (2), the method for smoothing the grain yield and the main influence factors in the step (1) comprises the following steps:
1) respectively carrying out differential processing on the grain yield and the original data of the main influence factors;
2) respectively calculating the fluctuation average values p and py of the grain yield and the main influence factors according to the differential processing of the step 1);
3) obtaining the grain yield and the value of the main influence factor after smoothing treatment, and respectively calculating fluctuation values p1 and py1 between the grain yield and the value of the main influence factor in two adjacent years by Lp-Lp1 and Yp-Yp 1;
there are three cases for grain yield:
in the first case: p1 > p, and Lp < Lp1, let Lp1 be Lp + p;
in the second case: p1 > p, and Lp > Lp1, let Lp1 be Lp-p;
in the third case: p1 < p, then Lp1 ═ Lp 1;
there are three cases for the values of the main impact factors:
in the first case: py1 > py, and Yp < Yp1, then Yp1 ═ Yp + py;
in the second case: py1 > py, and Yp > Yp1, then Yp1 ═ Yp-py;
in the third case: py1 < py, then Yp1 ═ Yp 1;
wherein Lp is the grain yield of the m-th year; lp1 is the grain yield in the m +1 year; yp is the original value of the m-year major influence factor; yp1 is the original value of the main influence factor in the m +1 th year, and the value range of m is 1 to (N-1).
2. The grain yield prediction method based on the PSO-LSSVM algorithm as claimed in claim 1, wherein: the solving method of the radial basis function comprises the following steps: using the formula k (x)n，xi)＝exp{-||xn-xi||2/σ2Solving, wherein xiIs the value of the main influencing factor of year i, xnIs the value of the main influencing factor of the nth year.
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