CN112862208A - Rainfall time series forecasting model - Google Patents

Rainfall time series forecasting model Download PDF

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CN112862208A
CN112862208A CN202110239798.5A CN202110239798A CN112862208A CN 112862208 A CN112862208 A CN 112862208A CN 202110239798 A CN202110239798 A CN 202110239798A CN 112862208 A CN112862208 A CN 112862208A
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张潮
贺挺
詹全忠
钱峰
殷悦
陈真玄
杨柳
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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

Rainfall time series forecasting model
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;
Figure BDA0002961677100000021
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;
Figure BDA0002961677100000022
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;
Figure BDA0002961677100000031
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 of
Figure BDA0002961677100000032
Roughly 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;
Figure BDA0002961677100000041
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;
Figure BDA0002961677100000042
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;
Figure BDA0002961677100000051
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 of
Figure BDA0002961677100000052
The 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
Figure BDA0002961677100000061
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;
Figure FDA0002961677090000011
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;
Figure FDA0002961677090000012
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;
Figure FDA0002961677090000021
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 of
Figure FDA0002961677090000022
Roughly 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.
CN202110239798.5A 2021-03-04 2021-03-04 Rainfall time series forecasting model Pending CN112862208A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102495937A (en) * 2011-10-18 2012-06-13 南京信息工程大学 Prediction method based on time sequence

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102495937A (en) * 2011-10-18 2012-06-13 南京信息工程大学 Prediction method based on time sequence

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
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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