CN116108961A - Drought prediction method and system based on ARIMA-SVM model - Google Patents
Drought prediction method and system based on ARIMA-SVM model Download PDFInfo
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Abstract
The invention provides an ARIMA-SVM model-based drought prediction method and system, which relate to the technical field of drought prediction and comprise the steps of obtaining an initial drought index at each moment in a next preset time period according to a time sequence and an ARIMA (p, d, q) model after order determination; respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain a residual prediction value of each initial drought index; and determining the sum of the initial drought index and the residual error predicted value corresponding to the same moment as a predicted drought index, obtaining a predicted drought index sequence in the next preset time period, and determining the drought degree of the area to be predicted in the next preset time period. According to the method, the drought degree is predicted through the ARIMA (p, d, q) model after the order determination, and the prediction error of the ARIMA (p, d, q) model is predicted by using the support vector machine, so that the objectivity of drought prediction is improved.
Description
Technical Field
The invention relates to the technical field of drought prediction, in particular to a drought prediction method and a drought prediction system based on an ARIMA-SVM (differential integration moving average autoregressive-support vector machine, autoregressive Integrated Moving Average-Support Vector Machine) model.
Background
With the exception of global climate change, drought events are more frequent, and serious losses are caused to society, economy and ecology. Regional drought often causes global effects, and drought has become the most widely affected natural disaster. Drought has serious effects on socioeconomic performance and has attracted considerable attention from countries around the world. At present, the loss assessment and prediction of drought are mainly realized by obtaining data in the form of field investigation, expert interviews and statistical data and combining qualitative and quantitative models (including models such as economic models beneficial to input-output models, hydrologic economic models and the like and models of risk loss degree based on a risk assessment principle).
However, current research is mainly in agriculture, including the farming and animal industries, and other aspects have less drought damage research, such as municipal domestic water, travel industry, and industry. In addition, the loss caused by drought on social economy and ecology lacks compared with the systematic quantitative research, and although a qualitative and quantitative evaluation combined method is adopted during evaluation and prediction, the quantitative evaluation model is mostly a statistical model, is influenced by factors such as regions, human factors and the like, has poor universality, and cannot evaluate and predict drought conditions in real time, efficiently and objectively.
Disclosure of Invention
The invention aims to provide an ARIMA-SVM model-based drought prediction method and an ARIMA-SVM model-based drought prediction system, which can improve the efficiency and objectivity of drought prediction and improve the accuracy of drought prediction.
In order to achieve the above object, the present invention provides the following solutions:
an ARIMA-SVM model-based drought prediction method, comprising:
acquiring a time sequence of a region to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; the drought index is used for measuring the drought degree;
obtaining an initial drought index at each moment in a next preset time period according to the time sequence and the ARIMA (p, d, q) model after the order setting; parameters of the fixed-order ARIMA (p, d, q) model are determined according to a historical time sequence; the parameters comprise an autoregressive order p, a moving average order q and a differential order d;
respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain residual prediction values of each initial drought index; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index;
determining the sum of the initial drought index and the residual error predicted value corresponding to the same moment as a predicted drought index to obtain a predicted drought index sequence in the next preset time period;
and determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
Preferably, before the obtaining the time sequence of the area to be predicted, the method further includes:
acquiring a historical time sequence of a region to be predicted; the elements in the time sequence are historical drought indexes of the area to be predicted;
performing stationarity processing on the historical time sequence by using a difference algorithm to obtain a difference order d and a stationarity processed historical time sequence;
respectively constructing a moving average model MA (q) and an autoregressive moving average model ARMA (p, q) according to the historical time sequence after the stable treatment;
fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after the order determination.
Preferably, before the obtaining the time sequence of the area to be predicted, the method further includes:
acquiring a plurality of historical initial drought indexes; the historical initial drought index is obtained according to a historical time sequence and an ARIMA (p, d, q) model after order determination;
and training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
Preferably, before obtaining the initial drought index at each moment in the next preset time period according to the time sequence and the ARIMA (p, d, q) model after the step, the method further comprises:
and carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
An ARIMA-SVM model-based drought prediction system, comprising:
the time sequence acquisition module is used for acquiring the time sequence of the area to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; the drought index is used for measuring the drought degree;
the initial drought index determining module is used for obtaining an initial drought index of each moment in the next preset time period according to the time sequence and the ARIMA (p, d, q) model after the order setting; parameters of the fixed-order ARIMA (p, d, q) model are determined according to a historical time sequence; the parameters comprise an autoregressive order p, a moving average order q and a differential order d;
the residual prediction value determining module is used for respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain residual prediction values of the initial drought indexes; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index;
the predicted drought index sequence determining module is used for determining that the sum of the initial drought index and the residual error predicted value corresponding to the same moment is the predicted drought index, and obtaining a predicted drought index sequence in the next preset time period;
and the drought degree prediction module is used for determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
Preferably, the system further comprises:
the historical time sequence acquisition module is used for acquiring a historical time sequence of the area to be predicted; the elements in the time sequence are historical drought indexes of the area to be predicted;
the first stationarity processing module is used for carrying out stationarity processing on the historical time sequence by utilizing a difference algorithm to obtain a difference order d and a stationarity processed historical time sequence;
the sub-model building module is used for building a moving average model MA (q) and an autoregressive moving average model ARMA (p, q) according to the historical time sequence after the stable treatment;
and the order determining module is used for fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after order determination.
Preferably, the system further comprises:
the historical initial drought index acquisition module is used for acquiring a plurality of historical initial drought indexes; the historical initial drought index is obtained according to a historical time sequence and an ARIMA (p, d, q) model after order determination;
the residual prediction model determining module is used for training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
Preferably, the system further comprises:
and the second stationarity processing module is used for carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the drought prediction method and system based on the ARIMA-SVM model, the drought degree is predicted through the ARIMA (p, d, q) model after order determination, and the residual prediction value is obtained by utilizing the trained support vector machine model to correct the prediction error of the ARIMA (p, d, q) model, so that the efficiency and objectivity of drought prediction are improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of an ARIMA-SVM model-based drought prediction method in an embodiment of the invention;
fig. 2 is a linear classification diagram of a support vector machine in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide an ARIMA-SVM model-based drought prediction method and an ARIMA-SVM model-based drought prediction system, which can improve the efficiency and objectivity of drought prediction.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The invention provides an ARIMA-SVM model-based drought prediction method, which comprises the following steps:
step 101: acquiring a time sequence of a region to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; drought index is used to measure the degree of drought.
Step 102: obtaining an initial drought index at each moment in a next preset time period according to the time sequence and the ARIMA (p, d, q) model after the order setting; parameters of the ARIMA (p, d, q) model after the order determination are determined according to the historical time sequence; the parameters include an autoregressive order p, a moving average order q, and a differential order d.
Step 103: respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain a residual prediction value of each initial drought index; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index.
Step 104: and determining the sum of the initial drought index and the residual predictive value corresponding to the same moment as the predicted drought index to obtain a predicted drought index sequence in the next preset time period.
Step 105: and determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
The drought prediction method based on ARIMA-SVM model provided by the invention, before step 101, further comprises:
acquiring a historical time sequence of a region to be predicted; the elements in the time series are the historical drought index of the area to be predicted.
And carrying out stationarity processing on the historical time sequence by using a difference algorithm to obtain a difference order d and a stationarity processed historical time sequence.
A moving average model MA (q) and an autoregressive moving average model ARMA (p, q) are respectively constructed according to the historical time sequence after the stationary treatment.
Fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after the order determination.
Furthermore, before step 101, the method further includes:
acquiring a plurality of historical initial drought indexes; the historical initial drought index is derived from a historical time series and a scaled ARIMA (p, d, q) model.
And training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
Prior to step 102, further comprising:
and carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
Specifically, the method comprises the following steps:
step one, constructing an autoregressive model.
Aiming at drought historical data (such as disaster area, drought population and the like) of the drought region in the near-N years, an ARIMA-SVM-based drought prediction model of the region is built according to the drought historical data of the region in the near-N years. First for arbitrary time series { X } t ，t∈T}，X t The drought index at time T, T representing the time series length, is called the p-order autoregressive model (AR (p)) if the following conditions are satisfied:
X t ＝φ 0 +φ 1 X t-1 +φ 2 X t-2 +...+φ p X t-p +ε t (1)
wherein phi is 0 ,φ 1 ,...,φ p Are all the first parameters to be estimated, phi p ≠0，ε t White noise sequence with average value of 0, white noise sequence and X t-i I=1, 2,3. When phi is 0 At=0, the p-order autoregressive model AR (p) is the decentered model.
And step two, constructing a moving average model.
First for arbitrary time series { X } t t∈T, the condition that the following is satisfied is called a q-order moving average model (MA (q)):
X t ＝μ-θ 1 ε t-1 -θ 2 ε t-2 -...-θ a ε t-a +ε t (2)
wherein θ 1 ，θ 2 ，...，θ a Are all the second parameters to be estimated, theta q ≠0，ε t A white noise sequence with a mean value of 0. When the random error μ=0, the q-order moving average model MA (q) is a decentered model.
Step three, an autoregressive moving average model, namely a combined model of an autoregressive model AR (p) and a moving average model MA (q), is built and is called ARMA (p, q).
The autoregressive moving average model is expressed as:
wherein when
ARMA (p, q) is the decentralised model.
In the drought prediction evaluation, most of time series data are unstable and are non-stable time series. The ARMA (p, q) model proposed in step one to step three cannot be used normally. A differential approach is taken before fitting so that the non-stationary time series becomes stationary time series.
And step five, a differential calculation process. First for arbitrary time series { X } t T ε T, the following conversion is performed:
equation 4 is a first order differential operation conversion. From this, d-order differential conversion can be obtained:
Step six, constructing a differential integration moving average autoregressive model ARIMA (p, d, q). Non-stationary time series { X } t t.epsilon.T } satisfies the following conditions:
wherein, the liquid crystal display device comprises a liquid crystal display device,
representing a time series { X } t T epsilon T, and a stable time sequence obtained after d-level differential transformation, wherein E (x) represents expectations; var represents variance; phi (B) =1-phi 1 B-φ 2 B 2 -...-φ p B p Is an autoregressive coefficient polynomial, wherein θ (B) =1- θ 1 B-θ 2 B 2 -...-θ q B q Is a moving average coefficient polynomial. The core formula of the differential integration moving average autoregressive model ARIMA (d, p, q) is +.>
The other 4 are the pair formulas
Interpretation of the medium parameters satisfying the condition, equation E (ε) t ) =0 represents the expected computation of white noise sequence samples with an average value of 0. Formula Var (ε) t )＝σ 2 Variance calculation of white noise sequence samples representing a mean of 0. Formula E (ε, ε) s ) =0, s+.t represents a single sample and a sequence of samples ε s Is used for the calculation of the expected calculation of (a). Formula->
Representing sequence sample X s And (3) expected calculation of individuals with non-stationary time series.
And seventhly, adopting an ARIMA (p, d, q) model to complete drought prediction, obtaining a difference value between a predicted value and an actual measured value, and adopting a support vector machine regression model to predict the difference value between the predicted value and the actual measured value.
And step eight, establishing a support vector machine regression model. Firstly, a group of training data sets (x 1, y 1), (x 2, y 2), (x 3, y 3), (xm, yn) }, wherein the abscissa of the training data sets is ARIMA (p, d, q) model predictive value, the ordinate is the difference between the actual drought index value and ARIMA (p, d, q) model predictive value, and the input quantity x is mapped to a function phi (x) to obtain a regression function
w T And b is an intercept, the data is fitted by using the function in a high-dimensional characteristic space H, and a kernel function is introduced to obtain the effect of nonlinear regression. In the fitting process, a hyperplane meeting the classification requirement is searched for separating the two types of data, so that the hyperplane ensures the classification accuracy and simultaneously maximizes the distance between the data on two sides of the training data set and the hyperplane.
As shown in FIG. 2, the training set of points on the two-dimensional plane has two different types of points, and the goal of the linear classification is to separate the two different types of points in the training set using one hyperplane so that the hyperplane is farther from both types of data points, thereby enabling classification of data with greater confidence. The straight super plane is w T Phi (x) +b=0, the broken line hyperplane obliquely above is w T Phi (x) +b=1, the broken line hyperplane obliquely below is w T Phi (x) +b= -1. And the sum of the distances from two types of data in the training data set to the straight line hyperplane is
If the classification hyperplane can properly classify two types of data, then: the term "w" is a weight norm, and w represents a weight.
y i Representing the ordinate value.
Step nine, correctly classifying two types of data in the number set by utilizing a hyperplane, and meeting the following constraint while having classification intervals:
l represents the ordinate range.
The above linear classification can correctly classify two types of data under ideal conditions, and in fact, when the number of the hyperplane divisions is set, a certain fitting error exists, so that a relaxation variable is introduced, and at the moment, the regression function is as follows:
wherein ε is i Represents the ith as a relaxation variable, C>0 is the penalty parameter.
Step ten, in order to solve the above-mentioned optimization problem, a lagrangian function is established:
wherein alpha is i Is the ith Lagrangian multiplier; alpha is the Lagrangian multiplier; epsilon is the relaxation variable.
Step eleven, finally reintroducing kernel function
Finally, the nonlinear fitting function is obtained as follows:
step twelve, therefore, the final result of the ARIMA-SVM model-based drought prediction is the sum of ARIMA model-based drought prediction values and SVM model-based drought prediction values.
In addition, the invention also provides a drought prediction system based on the ARIMA-SVM model, which comprises the following steps:
the time sequence acquisition module is used for acquiring the time sequence of the area to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; drought index is used to measure drought degree;
the system comprises an initial drought index determining module, a fixed-order ARIMA (p, d, q) model, a historical time sequence determining module and a differential order determining module, wherein the initial drought index determining module is used for obtaining an initial drought index at each moment in a next preset time period according to the time sequence and the fixed-order ARIMA (p, d, q) model;
the residual prediction value determining module is used for respectively inputting a plurality of initial drought indexes into the residual prediction model to obtain residual prediction values of each initial drought index; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index;
the predicted drought index sequence determining module is used for determining the sum of the initial drought index and the residual error predicted value corresponding to the same moment as the predicted drought index to obtain a predicted drought index sequence in the next preset time period;
and the drought degree prediction module is used for determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
The historical time sequence acquisition module is used for acquiring a historical time sequence of the area to be predicted; the elements in the time sequence are the historical drought indexes of the areas to be predicted;
the first stationarity processing module is used for carrying out stationarity processing on the historical time sequence by utilizing a differential algorithm to obtain a historical time sequence after the differential order d and the stationarity processing;
the sub-model construction module is used for respectively constructing a moving average model MA (q) and an autoregressive moving average model ARMA (p, q) according to the historical time sequence after the stable treatment;
the order determining module is used for fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after order determination.
The historical initial drought index acquisition module is used for acquiring a plurality of historical initial drought indexes; the historical initial drought index is obtained according to a historical time sequence and an ARIMA (p, d, q) model after order determination;
the residual prediction model determining module is used for training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
And the second stationarity processing module is used for carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (8)
1. An ARIMA-SVM model-based drought prediction method, the method comprising:
acquiring a time sequence of a region to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; the drought index is used for measuring the drought degree;
obtaining an initial drought index at each moment in a next preset time period according to the time sequence and the ARIMA (p, d, q) model after the order setting; parameters of the fixed-order ARIMA (p, d, q) model are determined according to a historical time sequence; the parameters comprise an autoregressive order p, a moving average order q and a differential order d;
respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain residual prediction values of each initial drought index; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index;
determining the sum of the initial drought index and the residual error predicted value corresponding to the same moment as a predicted drought index to obtain a predicted drought index sequence in the next preset time period;
and determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
2. The ARIMA-SVM model based drought prediction method according to claim 1, further comprising, prior to said obtaining the time series of areas to be predicted:
acquiring a historical time sequence of a region to be predicted; the elements in the time sequence are historical drought indexes of the area to be predicted;
performing stationarity processing on the historical time sequence by using a difference algorithm to obtain a difference order d and a stationarity processed historical time sequence;
respectively constructing a moving average model MA (q) and an autoregressive moving average model ARMA (p, q) according to the historical time sequence after the stable treatment;
fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after the order determination.
3. The ARIMA-SVM model based drought prediction method according to claim 2, further comprising, prior to said obtaining the time series of areas to be predicted:
acquiring a plurality of historical initial drought indexes; the historical initial drought index is obtained according to a historical time sequence and an ARIMA (p, d, q) model after order determination;
and training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
4. The ARIMA-SVM model based drought prediction method according to claim 1, further comprising, before obtaining an initial drought index for each moment in a next preset time period from the time series and the ordered ARIMA (p, d, q) model:
and carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
5. An ARIMA-SVM model-based drought prediction system, the system comprising:
the time sequence acquisition module is used for acquiring the time sequence of the area to be predicted; the elements in the time sequence are drought indexes of the areas to be predicted; the drought index is used for measuring the drought degree;
the initial drought index determining module is used for obtaining an initial drought index of each moment in the next preset time period according to the time sequence and the ARIMA (p, d, q) model after the order setting; parameters of the fixed-order ARIMA (p, d, q) model are determined according to a historical time sequence; the parameters comprise an autoregressive order p, a moving average order q and a differential order d;
the residual prediction value determining module is used for respectively inputting a plurality of initial drought indexes into a residual prediction model to obtain residual prediction values of the initial drought indexes; the residual prediction model is obtained by training a support vector machine by utilizing a historical initial drought index;
the predicted drought index sequence determining module is used for determining that the sum of the initial drought index and the residual error predicted value corresponding to the same moment is the predicted drought index, and obtaining a predicted drought index sequence in the next preset time period;
and the drought degree prediction module is used for determining the drought degree of the area to be predicted in the next preset time period according to the predicted drought index sequence.
6. The ARIMA-SVM model based drought prediction system as set forth in claim 5, further comprising:
the historical time sequence acquisition module is used for acquiring a historical time sequence of the area to be predicted; the elements in the time sequence are historical drought indexes of the area to be predicted;
the first stationarity processing module is used for carrying out stationarity processing on the historical time sequence by utilizing a difference algorithm to obtain a difference order d and a stationarity processed historical time sequence;
the sub-model building module is used for building a moving average model MA (q) and an autoregressive moving average model ARMA (p, q) according to the historical time sequence after the stable treatment;
and the order determining module is used for fitting the moving average model MA (q) and the autoregressive moving average model ARMA (p, q) to obtain an ARIMA (p, d, q) model after order determination.
7. The ARIMA-SVM model based drought prediction system as set forth in claim 6, further comprising:
the historical initial drought index acquisition module is used for acquiring a plurality of historical initial drought indexes; the historical initial drought index is obtained according to a historical time sequence and an ARIMA (p, d, q) model after order determination;
the residual prediction model determining module is used for training the support vector machine model by taking a plurality of historical initial drought indexes as input and taking the difference between the historical drought indexes and the historical initial drought indexes as output to obtain a residual prediction model.
8. The ARIMA-SVM model based drought prediction system as set forth in claim 5, further comprising:
and the second stationarity processing module is used for carrying out stationarity processing on the time sequence by utilizing a differential algorithm.
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