CN112862208A - Rainfall time series forecasting model - Google Patents
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- 238000000714 time series forecasting Methods 0.000 title abstract description 5
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- 238000012216 screening Methods 0.000 claims abstract description 6
- 238000003062 neural network model Methods 0.000 claims description 6
- 238000012549 training Methods 0.000 claims description 6
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Abstract
A rainfall time series forecasting model belongs to the technical field of hydrological weather forecasting and early warning. The method adopts the homogenesis function to carry out simulation prediction, can improve the deficiency of prediction of the sequence extreme value, and greatly improves the fitting and prediction effects of the extreme value. The uncertainty in the screening process is avoided by adopting the optimal subset, and the forecasting precision is improved by the BP neural network. The method can be widely applied to the prediction of the precipitation.
Description
Technical Field
The invention relates to a rainfall time series forecasting model, and belongs to the technical field of hydrological weather forecasting and early warning.
Background
The rainfall change has direct influence on the runoff of the surface river, and can provide reference for the prediction and prevention of flood disasters. In addition, the precipitation is related to agricultural development and grain safety, and the research on the precipitation and temperature change of years has important significance on global change. The averaging function is an important method for simulating and predicting the time sequence in the hydrological climate, can improve the shortage of predicting the extreme value of the sequence, greatly improves the fitting and predicting effects of the extreme value, and is widely applied to the prediction of the precipitation. But the problems of uncertainty of screening, low forecasting precision and the like exist.
Is described. The bp (back propagation) neural network is a concept proposed by scientists including Rumelhart and McClelland in 1986, is a multi-layer feedforward neural network trained according to an error back propagation algorithm, and is the most widely applied neural network. In the BP network, a plurality of (one or more) layers of neurons are added between an input layer and an output layer, the neurons are called hidden units, the hidden units are not directly connected with the outside, but the state change of the hidden units can affect the relation between the input and the output, and each layer can have a plurality of nodes. In the past decades, artificial neural networks have been widely used in the fields of system modeling, fault diagnosis and control, pattern recognition, financial forecasting, hydrology, and the like. The artificial neural network method has reliable prediction effect, and can achieve the expected effect by using less meteorological data.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a rainfall time series forecasting model to improve the forecasting precision.
The technical scheme adopted by the invention is as follows: a model for time series forecast of rainfall, comprising the steps of:
s1, extending the original time sequence by using a homogenesis function method to obtain an extended sequence;
original time series:
x(t)={x(1),x(2),…,x(N)}
first order difference sequence of original time series:
Δx(t)=x(t+1)-x(t),t=1,2,…,N-1;
second order difference sequence of original time sequence:
ΔΔx(t)=Δ2x(t)=Δx(t+1)-Δx(t),t=1,2,…,N-2;
wherein N is the number of the original time sequences;
s2, calculating a mean value generating function of the original time sequence, the first order difference sequence and the second order difference sequence by using the following formula;
wherein i is 1, 2, …, l; l is not less than 1 and not more than M and nlINT (N/3), wherein INT represents an integer;
s3, performing periodic continuation calculation on the first-order and second-order difference homodyne function sequences and the original sequence homodyne function sequence by using the following formula;
wherein: t is 1, 2, L, N;
s4, calculating an accumulated continuation sequence by using the following formula to fit the trend of upward increasing and downward decreasing in the time sequence to obtain an accumulated continuation sequence matrix;
wherein X (1) represents a starting value representing an original time series, t ═ 2,3, …, N;
s5, deleting and selecting the obtained continuation sequences by an optimal subset regression method to select an optimal subset; and screening independent variables according to the continuation sequence;
s6, establishing unary regression of each continuation sequence and the original sequence time, and calculating a CSC value of a double-scoring criterion, wherein the CSC value balances the quality of a variable by a quantity forecasting score and a trend forecasting score, aiming at enabling the sum of the quantity score and the trend score to be maximum; satisfy the requirement ofRoughly selecting the sequence of (a) as a predictor, wherein alpha is a significance level;
s7, extracting the number of independent variables when the formed subsets regress to the CSC value to the maximum according to the optimal subset combination of different independent variable numbers and a double-scoring criterion;
s8, taking the independent variable as the input of the 3-layer BP neural network, and taking the original sequence as the network output; the key for determining the BP neural network node is the determination of the hidden layer node; obtaining n input layer nodes and m output layer nodes through training, establishing a neural network model, and carrying out training solution on the neural network model; and obtaining a BP neural network forecasting model.
The invention has the beneficial effects that: the method adopts the homogenesis function to carry out simulation prediction, can improve the deficiency of prediction of the sequence extreme value, and greatly improves the fitting and prediction effects of the extreme value. The uncertainty in the screening process is avoided by adopting the optimal subset, and the forecasting precision is improved by the BP neural network. The method can be widely applied to the prediction of the precipitation.
Detailed Description
The rainfall of a certain city in south of the Yangtze river from 1995 to 2010 is taken as data:
TABLE 11993 annual rainfall in a city to 2010
Year of year | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 |
rainfall/mL | 1821 | 1542 | 1687 | 1631 | 1661 | 1925 | 1378 | 1614 | 1712 |
Year of year | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
rainfall/mL | 1920 | 1120 | 1213 | 1278 | 1294 | 1382 | 1340 | 1571 | 1607 |
S1, extending the original time sequence by using a homogenesis function method to obtain an extended sequence;
original time series:
x(t)={x(1),x(2),…,x(N)}
first order difference sequence of original time series:
Δx(t)=x(t+1)-x(t),t=1,2,…,N-1;
second order difference sequence of original time sequence:
ΔΔx(t)=Δ2x(t)=Δx(t+1)-Δx(t),t=1,2,…,N-2;
wherein N is the number of the original time sequences;
s2, calculating a mean value generating function of the original time sequence, the first order difference sequence and the second order difference sequence by using the following formula;
wherein i is 1, 2, …, l; l is not less than 1 and not more than M and nlINT (N/3), wherein INT represents an integer;
s3, performing periodic continuation calculation on the first-order and second-order difference homodyne function sequences and the original sequence homodyne function sequence by using the following formula;
wherein: t is 1, 2, L, N;
s4, calculating an accumulated continuation sequence by using the following formula to fit the trend of upward increasing and downward decreasing in the time sequence to obtain an accumulated continuation sequence matrix;
wherein X (1) represents a starting value representing an original time series, t ═ 2,3, …, N;
s5, deleting and selecting the obtained continuation sequences by an optimal subset regression method to select an optimal subset; and screening independent variables according to the continuation sequence;
s6, establishing unary regression of each continuation sequence and the original sequence time, and calculating a CSC value of a double-scoring criterion, wherein the CSC value balances the quality of a variable by a quantity forecasting score and a trend forecasting score, aiming at enabling the sum of the quantity score and the trend score to be maximum; satisfy the requirement ofThe sequence of (a) is roughly selected as a predictor, wherein alpha is a significance level, and alpha is 0.01;
s7, extracting the number of independent variables when the formed subsets regress to the CSC value to the maximum according to the optimal subset combination of different independent variable numbers and a double-scoring criterion;
s8, taking the independent variable as the input of the 3-layer BP neural network, and taking the original sequence as the network output; the key for determining the BP neural network node is the determination of the hidden layer node; the role function of the node adopts a Sigmoid function, and the model of the function is as follows:
f(x)=1/(1+e-x)
obtaining n input layer nodes and m output layer nodes through training, establishing a neural network model, and carrying out training solution on the neural network model; and obtaining a BP neural network forecasting model.
TABLE 2 comparison of the prediction results of the method of the present application with the stepwise regression of the averaging function
As can be seen from the above table, the method used in the present application has smaller relative error and absolute error and higher accuracy than the step-by-step regression method using the homodyne function.
Claims (1)
1. A model for time series forecast of rainfall, comprising the steps of:
s1, extending the original time sequence by using a homogenesis function method to obtain an extended sequence;
original time series:
x(t)={x(1),x(2),…,x(N)}
first order difference sequence of original time series:
Δx(t)=x(t+1)-x(t),t=1,2,…,N-1;
second order difference sequence of original time sequence:
ΔΔx(t)=Δ2x(t)=Δx(t+1)-Δx(t),t=1,2,…,N-2;
wherein N is the number of the original time sequences;
s2, calculating a mean value generating function of the original time sequence, the first order difference sequence and the second order difference sequence by using the following formula;
wherein i is 1, 2, …, l; l is not less than 1 and not more than M and nlINT (N/3), wherein INT represents an integer;
s3, performing periodic continuation calculation on the first-order and second-order difference homodyne function sequences and the original sequence homodyne function sequence by using the following formula;
wherein: t is 1, 2, L, N;
s4, calculating an accumulated continuation sequence by using the following formula to fit the trend of upward increasing and downward decreasing in the time sequence to obtain an accumulated continuation sequence matrix;
wherein X (1) represents a starting value representing an original time series, t ═ 2,3, …, N;
s5, deleting and selecting the obtained continuation sequences by an optimal subset regression method to select an optimal subset; and screening independent variables according to the continuation sequence;
s6, establishing unary regression of each continuation sequence and the original sequence time, and calculating a CSC value of a double-scoring criterion, wherein the CSC value balances the quality of a variable by a quantity forecasting score and a trend forecasting score, aiming at enabling the sum of the quantity score and the trend score to be maximum; satisfy the requirement ofRoughly selecting the sequence of (a) as a predictor, wherein alpha is a significance level;
s7, extracting the number of independent variables when the formed subsets regress to the CSC value to the maximum according to the optimal subset combination of different independent variable numbers and a double-scoring criterion;
s8, taking the independent variable as the input of the 3-layer BP neural network, and taking the original sequence as the network output; the key for determining the BP neural network node is the determination of the hidden layer node; obtaining n input layer nodes and m output layer nodes through training, establishing a neural network model, and carrying out training solution on the neural network model; and obtaining a BP neural network forecasting model.
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刘莉;叶文;: "基于BP神经网络时间序列模型的降水量预测", 水资源与水工程学报, no. 05, pages 156 - 159 * |
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