CN111242210A - Short-term load prediction method based on improved Shapley value model - Google Patents

Short-term load prediction method based on improved Shapley value model Download PDF

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CN111242210A
CN111242210A CN202010020729.0A CN202010020729A CN111242210A CN 111242210 A CN111242210 A CN 111242210A CN 202010020729 A CN202010020729 A CN 202010020729A CN 111242210 A CN111242210 A CN 111242210A
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刘海涛
孙晓
许伦
张潮
顾思
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Abstract

The invention discloses a short-term load prediction method based on an improved Shapley value model, which reconstructs non-stationary loads through Hilbert-Huang (HHT) transformation to obtain random, periodic and trend components; and determining the weight distribution of each prediction method of combined prediction by improving the shape value model, applying the weight distribution to the prediction of random, periodic and trend components respectively, and superposing the obtained prediction components to obtain a final prediction value. Compared with the existing prediction method, the prediction method provided by the invention has higher accuracy and stability.

Description

Short-term load prediction method based on improved Shapley value model
Technical Field
The invention relates to the technical field of load prediction of a power system, in particular to a short-term load prediction method based on an improved Shapley value model.
Background
In the operation control and the planning management of the power system, the load prediction determines the reasonable arrangement of power generation, transmission and distribution, and is an important component of the power system planning. The primary application of short-term conformance prediction is, among other things, to provide data to a power generation planning program that is used to determine operating scenarios that meet safety requirements, operating constraints, and natural environments and equipment. How to improve the prediction accuracy is the center and the key point of the current short-term load prediction theory and method.
Some researchers propose the idea of predicting by a combined prediction model aiming at the problem of low prediction precision of a single prediction method, and aim at the problem that the single prediction method simultaneously predicts three components with different stable characteristics to generate larger errors, the combined prediction method can effectively combine the advantages of each prediction method to improve the prediction precision, and the difficulty is the problem of weight distribution.
For example, the invention patent with the patent number CN201811334912.7 provides a wind power convergence tendency state-based quantization method based on an improved shape value, which aims at the problems that the convergence effect prediction accuracy is low only by using wind measurement data and meteorological data, and the traditional shape value method still participates in combination when the deviation of a single model prediction result is too large. Compared with a single prediction model, the method for predicting the wind power continuous output curve by combining the states can more accurately describe the wind power convergence trend, and provides a certain theoretical basis for planning the outgoing transmission capacity after the wind power base is expanded. However, such methods are more suitable for load prediction of the power system in a stable operation environment, and are not suitable for prediction capability of complex load data with unstable characteristics in an actual operation process, and the weight distribution method included in the methods is also not suitable for a short-term load prediction method.
With the further advance of national power grids, the intellectualization level of a user terminal on a demand side is continuously improved, the time sequence characteristics of user loads are obviously changed, short-term load data have the characteristic of non-stationarity, and the single load prediction model and the conventional combined prediction model ignore the time sequence characteristics of the load data and are difficult to achieve satisfactory prediction accuracy. How to more accurately and scientifically analyze and mine the internal characteristics of the load under the new situation and improve the accuracy of short-term load prediction needs to be solved urgently.
Disclosure of Invention
The invention aims to provide a short-term load prediction method based on an improved Shapley value model, which reconstructs non-stationary loads through Hilbert-Huang (HHT) transformation to obtain random, periodic and trend components; and determining the weight distribution of each prediction method of combined prediction by improving the shape value model, applying the weight distribution to the prediction of random, periodic and trend components respectively, and superposing the obtained prediction components to obtain a final prediction value. Compared with the existing prediction method, the prediction method provided by the invention has higher accuracy and stability.
To achieve the above object, with reference to fig. 1, the present invention provides a short-term load prediction method based on an improved sharley value model, where the short-term load prediction method includes:
s1: decomposing the load data presenting unstable characteristics through empirical mode decomposition to obtain a limited number of intrinsic mode functions;
s2: obtaining a time-frequency curve corresponding to each intrinsic mode function through Hilbert transform;
s3: reconstructing each intrinsic mode function into random, periodic and trend components according to the principle that the overlapping of each time-frequency curve is minimum;
s4: predicting the random, periodic and trend components by respectively adopting an improved shapey value combination prediction method to obtain prediction components corresponding to the random, periodic and trend components;
s5: and superposing the prediction components corresponding to the random, periodic and trend components to obtain the final prediction component.
In a further embodiment, in step S1, the decomposing the load data exhibiting unstable characteristics by empirical mode decomposition to obtain a finite number of eigenmode functions includes the following steps:
s11: setting l as 1;
s12: interpolating the load data by a cubic spline function to obtain an envelope e thereonmax(t) and the lower envelope emin(t) calculating the mean ml(t)；
S13: obtaining a candidate mode function sequence c through load power S (t) decompositionl(t)：
cl(t)＝S(t)-ml(t)
S14: judgment cl(t) whether the mean value of the upper envelope line and the lower envelope line generated by respectively fitting the local maximum value point and the local minimum value point is equal to zero or not is met, if not, c is carried outl(t) determining as new S (t), repeating the steps S12 to S13 until the condition is satisfied to obtain the mode function sequence cl(t)；
S15: removing c from the load curve S (t)l(t) component obtains remainder r (t), and the calculation formula is as follows:
r(t)＝S(t)-cl(t)；
s16: taking r (t) as a new S (t), adding 1 to l, repeating the steps S12 to S16, and calculating to obtain other candidate mode function sequences cl(t) until r (t) the sequence of mode functions cannot be reisolated;
at this time, each natural mode function cl(t) and the remainder r (t) satisfy the following equation:
Figure RE-GDA0002421279240000021
where num is the total number of candidate mode function sequences, and s (t) is the initial load power.
In a further embodiment, in step S2, the process of obtaining the time-frequency curve corresponding to each eigenmode function through hilbert transform includes the following steps:
s21: the eigenmode function cl(t) and
Figure RE-GDA0002421279240000022
convolution is carried out to obtain an all-pass phase shift network
Figure RE-GDA0002421279240000023
The calculation formula is as follows:
Figure RE-GDA0002421279240000024
s22: by the eigenmode function cl(t) and all-pass phase shifting network
Figure RE-GDA0002421279240000025
Common structure analysis signal zl(t), the calculation formula is as follows:
Figure RE-GDA0002421279240000026
wherein, al(t) is a function of the amplitude of the wave,
Figure RE-GDA0002421279240000031
is a phase function;
s23: calculating an amplitude function al(t), the calculation formula is as follows:
Figure RE-GDA0002421279240000032
s24: calculating instantaneous frequency fl(t), the calculation formula is as follows:
Figure RE-GDA0002421279240000033
in a further embodiment, in step S4, the predicting step of predicting the random, periodic, and trend components by respectively using an improved shape value combination prediction method includes the following steps:
s41: predicting the component k by adopting a plurality of prediction methods to obtain a prediction error set Fk；
S42: by a set of prediction errors F for component kkObtain all subsets thereof, i.e. combined error values Ek(*)；
S43: calculating Shapley values E for component k for each prediction methodik；
S44: calculating to obtain a prediction weight set W aiming at the component kk；
S45: according to a set W of predicted weights for component kkAnd calculating to obtain the prediction result of the component k.
In a further embodiment, in step S44, the calculation obtains a set W of prediction weights for component kkFurther comprising the steps of:
judging the predicted weight set WkIf yes, removing the prediction method with the weight value being a negative value, returning to the step S42, and recalculating the prediction weight value set W for the component kkOtherwise, the process proceeds to step S45, and the prediction result of the component k is calculated.
In a further embodiment, in step S4, the predicting step of predicting the random, periodic, and trend components by respectively using an improved shape value combination prediction method includes the following steps:
gray prediction, an Elman neural network and an SVM are adopted for combined prediction, the weight distribution of each prediction method is determined by improving a Shapley value method, and a combined prediction model is as follows:
Yk＝ωAKYAK+ωBKYBK+ωCKYCK
in the formula: y iskIs the combined predicted value in state k; omegaAK、ωBK、ωCKThe weights of the grey prediction, the Elman neural network and the SVM are respectively under the component k; y isAK、YBK、YCKThe predicted values of the three prediction methods under the component k are respectively.
In a further embodiment, the step of determining the weight distribution of each prediction method by improving the sharey value method by using gray prediction, Elman neural network and SVM to perform combined prediction comprises the following steps:
s401: let set I ═ {1, 2, 3}, any subset p, q that set I contains, it represents any combination in 3 kinds of prediction methods, e (p), e (q) represent each internal defect prediction error;
for any subset p, q of set I, there is:
E(p)+E(q)≥E(p∪q)；
s402: is provided with
Figure RE-GDA0002421279240000034
X is to beiDefined as the error, x, of the prediction model of the i-th type after the cooperation is completedi≤E(i)；
E (3) represents the total error of the combined prediction of 3 prediction models due to internal defects, i.e. E (3) ═ Σi∈Ixi；
S403: definition EiThe average value of the absolute values of the errors generated by the ith prediction model, and E is the sum of the errors of the combined predictions, then there are:
Figure RE-GDA0002421279240000041
Figure RE-GDA0002421279240000042
in the formula: the number of samples is expressed as m, and the absolute value of the error generated by the sigma-th sample of the ith prediction model is expressed as eiσN is the total number of prediction models;
s404: weights are assigned based on the sharey value method according to the following formula:
Figure RE-GDA0002421279240000043
Figure RE-GDA0002421279240000044
in the formula: ω | p | represents a weighting factorSub, p- { i } represents a removal model i 'in the combination, and i' represents a certain load prediction model participating in combination prediction; e'tThe error amount of the ith prediction model is a Shapley value, | p | is the number of the prediction methods in the combined prediction model;
and calculating the weight distribution of each prediction method in the combined prediction model by the following formula:
Figure RE-GDA0002421279240000045
compared with the prior art, the technical scheme of the invention has the following remarkable beneficial effects:
(1) in the load prediction with larger fluctuation characteristics, the load is reconstructed through HHT transformation to obtain components with concentrated fluctuation characteristics and stable change frequency, and the reconstructed components are respectively predicted, so that the influence of load fluctuation on the load prediction is effectively reduced.
(2) The weight of each prediction method in the combined prediction is determined by improving a Shapley value method, the prediction values of the three components after reconstruction are superposed to obtain a final prediction result, and compared with a single prediction model and an unmodified Shapley value combined prediction model, the prediction accuracy and the algorithm stability are greatly improved.
(3) After the load data is reconstructed, the weight values corresponding to the components are set for each component, and the combined prediction model is adopted for prediction.
It should be understood that all combinations of the foregoing concepts and additional concepts described in greater detail below can be considered as part of the inventive subject matter of this disclosure unless such concepts are mutually inconsistent. In addition, all combinations of claimed subject matter are considered a part of the presently disclosed subject matter.
The foregoing and other aspects, embodiments and features of the present teachings can be more fully understood from the following description taken in conjunction with the accompanying drawings. Additional aspects of the present invention, such as features and/or advantages of exemplary embodiments, will be apparent from the description which follows, or may be learned by practice of specific embodiments in accordance with the teachings of the present invention.
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The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:
fig. 1 is a flowchart of a short-term load prediction method based on an improved shape value model.
FIG. 2 is a schematic of historical load data for training and testing.
Fig. 3 is a schematic diagram of the eigenmode components of the 30-day data in the historical load data after EMD decomposition.
Fig. 4 is a schematic diagram of a time-frequency curve of each eigenmode component after hilbert transformation.
FIG. 5 is a diagram illustrating random, periodic, trend component conditions.
FIG. 6 is a schematic diagram showing the comparison between the prediction result of the present method and the prediction results of other methods.
Fig. 7 shows a weight assignment result obtained by using the shape value model (table 1).
Fig. 8 shows the weight assignment result obtained by using the improved shape value model (table 2).
Fig. 9 shows a comparison of the prediction results of the respective methods (table 3).
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
As shown in fig. 1, the short-term load prediction method based on the improved shape value model provided by the present invention includes the following steps:
step 1, decomposing the load data presenting unstable characteristics through Empirical Mode Decomposition (EMD) to obtain a limited number of Intrinsic Mode Functions (IMF).
The Hilbert-Huang (HHT) transformation can decompose the load presenting the unstable characteristic into several inherent modal components with different characteristic time scales by EMD decomposition according to the unstable time sequence characteristics in the load, and the instantaneous frequency-time curve of each modal component can be obtained by the Hilbert transformation, so that conditions are provided for the reconstruction of the load curve.
The method adopts the load data shown in fig. 2, extracts 18 days of data (96 times per day) as an example for analysis, and performs EMD decomposition on 18 × 96 data to obtain each eigenmode component, as shown in fig. 3, the specific steps are as follows:
1) interpolating the initial load data by a cubic spline function to obtain an envelope e thereonmax(t) and the lower envelope emin(t) calculating the mean m1(t)。
2) Obtaining a candidate mode function sequence c through load power P (t) decomposition1(t)：
c1(t)＝S(t)-m1(t) (1)
3) Judgment c1(t) whether the mean value of the upper envelope line and the lower envelope line generated by respectively fitting the local maximum value point and the local minimum value point is equal to zero or not is met, if not, c is carried out1(t) regarding the S (t) as a new one, and repeating the steps 1) and 2) until the condition is met to obtain a mode function sequence c1(t)。
4) Removing c from the load curve S (t)1(t) component obtains remainder r (t), and the calculation formula is as follows:
r(t)＝S(t)-c1(t) (2)
5) taking r (t) as a new S (t), repeating the steps 1), 2), 3) and 4), and calculating to obtain other candidate mode function sequences cl(t) until r (t) the sequence of mode functions cannot be reisolated.
At this time, each natural mode function cl(t) and the remainder r (t) satisfy the following equation:
Figure RE-GDA0002421279240000051
and 2, obtaining a time-frequency curve corresponding to each intrinsic mode function through Hilbert transformation.
For the eigenmode component c after EMD decompositionlHilbert transform is performed to obtain the instantaneous frequency of each modal component, and the result is shown in fig. 4, which mainly comprises the following steps:
1) the eigenmode function cl(t) and
Figure RE-GDA0002421279240000061
convolution is carried out to obtain an all-pass phase shift network
Figure RE-GDA0002421279240000062
The calculation formula is as follows:
Figure RE-GDA0002421279240000063
2) by the eigenmode function cl(t) and all-pass phase shifting network
Figure RE-GDA0002421279240000064
Jointly constructing an analytic signal, wherein the calculation formula is as follows:
Figure RE-GDA0002421279240000065
3) calculating an amplitude function according to the following formula:
Figure RE-GDA0002421279240000066
4) calculating the instantaneous frequency according to the following formula:
Figure RE-GDA0002421279240000067
and 3, reconstructing each eigenmode function into random, periodic and trend components according to the principle that the overlapping of each time-frequency curve is minimum, wherein the result is shown in fig. 5.
And 4, predicting the random, periodic and trend components by respectively adopting an improved shapey value combination prediction method to obtain prediction components corresponding to the random, periodic and trend components.
The combined prediction model is as follows:
Yk＝ωAKYAK+ωBKYBK+ωCKYCK(8)
in the formula: y iskIs the combined predicted value in state k; omegaAK,ωBK,ωCKThe weights of the grey prediction, the Elman neural network and the SVM are respectively under the component k; y isAK，YBK，YCKThe predicted values of the three prediction methods under the component k are respectively.
In order to obtain the weight of each prediction method, the patent constructs a shapeley weight model and defines the following:
1) any subset p, q included in the I set (I ═ {1, 2, 3}) is represented by any combination of the 3 methods, and e (p), e (q) represent each internal defect prediction error.
2) For any subset p, q of I, there is:
E(p)+E(q)≥E(p∪q) (9)
3) is provided with
Figure RE-GDA0002421279240000068
Defining the error of the ith prediction model generated after the cooperation is completed as xi，xi≤E(i)。
4) E (3) represents the total error of the combined prediction of 3 prediction models due to internal defects, i.e. E (3) ═ Σi∈Ixi。
Definition EiThe average value of the absolute values of the errors generated by the ith prediction model, and E is the sum of the errors of the combined predictions, then there are:
Figure RE-GDA0002421279240000069
Figure RE-GDA00024212792400000610
in the formula: sample(s)The number is represented as m; the absolute value of the error generated by the ith sample of the prediction model is denoted as eiσAnd n is the total number of prediction models.
Equations (12) and (13) represent equations for assigning weights based on the sharley value method:
Figure RE-GDA00024212792400000611
Figure RE-GDA0002421279240000071
in the formula: ω | p | represents a weighting factor, p- { i } represents a removal model in the combination, i' represents a certain load prediction model participating in the combined prediction; e'tThe error amount of the i model, namely the Shapley value, | p | is the number of the prediction methods in the combined prediction model.
The weight assignment of each prediction method in the combined prediction model can be calculated by equation (14):
Figure RE-GDA0002421279240000072
aiming at the prediction precision influenced by the excessive error of a certain prediction method, a Shapley value model is improved, the prediction method represented by a negative weight coefficient is abandoned, the weight distribution is carried out again on the residual combined prediction residual methods, and the prediction method with the poor prediction result is prevented from interfering the combined prediction result. The weight assignment result obtained by using the shape value model is shown in table 1. The weight assignment results obtained by using the improved shape value model are shown in table 2.
And 5, superposing the prediction components corresponding to the random, periodic and trend components to obtain the final prediction component.
In order to verify the performance of the prediction method provided by the invention, the non-stationary load is predicted in a short term by adopting three schemes of a single prediction model, an unmodified Shapley combined prediction model and an improved Shapley value combined prediction model, and comparative analysis is carried out from two aspects of model accuracy and stability. The comparison results are shown in fig. 6 and table 3, and the results show that the prediction method provided by the invention has higher accuracy and stability.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily defined to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, as the disclosed concepts and embodiments are not limited to any one implementation. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims (7)

1. A short-term load prediction method based on an improved Shapley value model is characterized by comprising the following steps:
s1: decomposing the load data presenting unstable characteristics through empirical mode decomposition to obtain a limited number of intrinsic mode functions;
s2: obtaining a time-frequency curve corresponding to each intrinsic mode function through Hilbert transform;
s3: reconstructing each intrinsic mode function into random, periodic and trend components according to the principle that the overlapping of each time-frequency curve is minimum;
s4: predicting the random, periodic and trend components by respectively adopting an improved shapey value combination prediction method to obtain prediction components corresponding to the random, periodic and trend components;
s5: and superposing the prediction components corresponding to the random, periodic and trend components to obtain the final prediction component.
2. The method for short-term load prediction based on the modified sharley value model as claimed in claim 1, wherein in step S1, the process of decomposing the load data exhibiting unstable characteristics through empirical mode decomposition to obtain a limited number of eigenmode functions includes the following steps:
s11: setting l as 1;
s12: interpolating the load data by a cubic spline function to obtain an envelope e thereonmax(t) and the lower envelope emin(t) calculating the mean ml(t)；
S13: obtaining a candidate mode function sequence c through load power S (t) decompositionl(t)：
cl(t)＝S(t)-ml(t)
S14: judgment cl(t) whether the mean value of the upper envelope line and the lower envelope line generated by respectively fitting the local maximum value point and the local minimum value point is equal to zero or not is met, if not, c is carried outl(t) determining as new S (t), repeating the steps S12 to S13 until the condition is satisfied to obtain the mode function sequence cl(t)；
S15: removing c from the load curve S (t)l(t) component obtains remainder r (t), and the calculation formula is as follows:
r(t)＝S(t)-cl(t)；
s16: taking r (t) as a new S (t), adding 1 to l, repeating the steps S12 to S16, and calculating to obtain other candidate mode function sequences cl(t) until r (t) the sequence of mode functions cannot be reisolated;
at this time, each natural mode function cl(t) and the remainder r (t) satisfy the following equation:
Figure FDA0002360680210000011
where num is the total number of candidate mode function sequences.
3. The method for short-term load prediction based on the modified sharley value model as claimed in claim 1, wherein in step S2, the step of obtaining the time-frequency curves corresponding to the eigenmode functions through hilbert transform comprises the following steps:
s21: the eigenmode function cl(t) and
Figure FDA0002360680210000012
convolution is carried out to obtain an all-pass phase shift network
Figure FDA0002360680210000013
The calculation formula is as follows:
Figure FDA0002360680210000014
s22: by the eigenmode function cl(t) and all-pass phase shifting network
Figure FDA0002360680210000021
Common structure analysis signal zl(t), the calculation formula is as follows:
Figure FDA0002360680210000022
wherein, al(t) is a function of the amplitude of the wave,
Figure FDA0002360680210000023
is a phase function;
s23: calculating an amplitude function al(t), the calculation formula is as follows:
Figure FDA0002360680210000024
s24: calculating instantaneous frequency fl(t), the calculation formula is as follows:
Figure FDA0002360680210000025
4. the method for predicting short-term load based on the modified sharley value model according to claim 1, wherein in step S4, the step of predicting the random, periodic and trend components by using the modified sharley value combination prediction method respectively to obtain the prediction components corresponding to the random, periodic and trend components comprises the following steps:
s41: predicting the component k by adopting a plurality of prediction methods to obtain a prediction error set Fk；
S42: by a set of prediction errors F for component kkObtain all subsets thereof, i.e. combined error values Ek(*)；
S43: calculating Shapley values E for component k for each prediction methodik；
S44: calculating to obtain a prediction weight set W aiming at the component kk；
S45: according to a set W of predicted weights for component kkAnd calculating to obtain the prediction result of the component k.
5. The method according to claim 4, wherein in step S44, the calculating obtains a set W of predicted weights for component kkFurther comprising the steps of:
judging the predicted weight set WkIf yes, removing the prediction method with the weight value being a negative value, returning to the step S42, and recalculating the prediction weight value set W for the component kkOtherwise, the process proceeds to step S45, and the prediction result of the component k is calculated.
6. The method for predicting short-term load based on the modified sharley value model according to claim 1, wherein in step S4, the step of predicting the random, periodic and trend components by using the modified sharley value combination prediction method respectively to obtain the prediction components corresponding to the random, periodic and trend components comprises the following steps:
gray prediction, an Elman neural network and an SVM are adopted for combined prediction, the weight distribution of each prediction method is determined by improving a Shapley value method, and a combined prediction model is as follows:
Yk＝ωAKYAK+ωBKYBK+ωCKYCK
in the formula: y iskIs the combined predicted value in state k; omegaAK、ωBK、ωCKThe weights of the grey prediction, the Elman neural network and the SVM are respectively under the component k; y isAK、YBK、YCKThe predicted values of the three prediction methods under the component k are respectively.
7. The method of claim 6, wherein the combined prediction using gray prediction, Elman neural network and SVM, and the determining of the weight distribution of each prediction method by the modified Shapley value method comprises the following steps:
s401: let set I ═ {1, 2, 3}, any subset p, q that set I contains, it represents any combination in 3 kinds of prediction methods, e (p), e (q) represent each internal defect prediction error;
for any subset p, q of set I, there is:
E(p)+E(q)≥E(p∪q)；
s402: is provided with
Figure FDA0002360680210000031
X is to beiDefined as the error, x, of the prediction model of the i-th type after the cooperation is completedi≤E(i)；
E (3) represents the total error of the combined prediction of 3 prediction models due to internal defects, i.e. E (3) ═ Σi∈Ixi；
S403: definition EiThe average value of the absolute values of the errors generated by the ith prediction model, and E is the sum of the errors of the combined predictions, then there are:
Figure FDA0002360680210000032
Figure FDA0002360680210000033
in the formula: the number of samples is expressed as m, and the absolute value of the error generated by the sigma-th sample of the ith prediction model is expressed as eiσN is the total number of prediction models;
s404: weights are assigned based on the sharey value method according to the following formula:
Figure FDA0002360680210000034
Figure FDA0002360680210000035
in the formula: ω | p | represents a weighting factor, p- { i } represents a removal model in the combination, i' represents a certain load prediction model participating in the combined prediction; e'tThe error amount of the ith prediction model is a Shapley value, | p | is the number of the prediction methods in the combined prediction model;
and calculating the weight distribution of each prediction method in the combined prediction model by the following formula:
Figure FDA0002360680210000036
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