CN114881283A - Training method of solar-term change forecasting model, and solar-term change forecasting method and device - Google Patents

Training method of solar-term change forecasting model, and solar-term change forecasting method and device Download PDF

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CN114881283A
CN114881283A CN202210324832.3A CN202210324832A CN114881283A CN 114881283 A CN114881283 A CN 114881283A CN 202210324832 A CN202210324832 A CN 202210324832A CN 114881283 A CN114881283 A CN 114881283A
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李林阳
乔书波
徐海龙
林家乐
彭华东
杨显赐
李松伟
宋开放
郭文卓
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Abstract

The application discloses a training method of a daily variation forecasting model, a daily variation forecasting method and a daily variation forecasting device. The training method comprises the following steps: fitting the first historical solar length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a solar length extrapolation value of a first target time point based on an obtained first fitting curve, wherein the first fitting residual sequence comprises fitting residuals corresponding to a plurality of first historical time points respectively; determining a fitting residual error corresponding to the first target time point based on the date extrapolation value and the date actual value of the first target time point; performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation; and training the solar-length change forecasting model by taking the first phase space representation as a training sample and taking the fitting residual error corresponding to the first target time point as a label corresponding to the training sample.

Description

Training method of solar-term change forecasting model, and solar-term change forecasting method and device
Technical Field
The application relates to the technical field of computers, in particular to a training method of a solar-length change forecasting model, a solar-length change forecasting method and a device.
Background
The earth rotation rate changes, and the long-term change shows that the earth rotation speed slowly becomes smaller, the period term is from several days to several decades, and the phenomenon is called Day Length (Day of Day) change. The change of the day length is an important Earth Rotation Parameter (ERP), is a necessary parameter for mutual conversion between an Earth reference system and an celestial sphere reference system, and has important application in the fields of deep space exploration, deep space satellite navigation, satellite positioning and the like. The earth rotation motion is influenced by the comprehensive actions of ocean, atmospheric ocean current, crust, core and mantle, and presents complex nonlinear change, but the day-length change obtained by the space measurement technology cannot be obtained in real time.
The demand for the change of the day length is increasing due to the high-speed development in the fields of deep space exploration, space navigation and the like, and therefore, a high-precision forecasting scheme for the change of the day length is urgently needed.
Disclosure of Invention
The embodiment of the application aims to provide a training method of a solar-term change forecasting model, a solar-term change forecasting method and a device, which are used for realizing high-precision forecasting of solar-term change.
In order to achieve the above purpose, the following technical solutions are adopted in the embodiments of the present application:
in a first aspect, an embodiment of the present application provides a method for training a daily variation prediction model, including:
fitting a first historical daily length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a daily length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical daily length change sequence comprises daily length actual values of a plurality of first historical time points, and the first fitting residual sequence comprises fitting residuals corresponding to the plurality of first historical time points respectively;
determining a fitting residual corresponding to the first target time point based on the date extrapolated value and the date actual value of the first target time point;
performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and training the solar-length change forecasting model by taking the first phase space representation as a training sample and taking a fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
According to the embodiment of the application, the characteristic that the daily length change sequence usually comprises an obvious linear trend term and a main period term is utilized, the first historical daily length change sequence is fitted based on the preset fitting algorithm, and the obtained first fitting curve can reflect the daily length change trend and can be further used for daily length prediction; secondly, considering that the solar length change sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the solar length change sequence, the precision of a forecast result obtained by forecasting the solar length change only according to the first fitting curve is not high, for this reason, the fitting precision can be reflected by using the residual error between the solar length fitting value and the solar length actual value of each time point, the solar length extrapolated value of the first target time point is obtained by extrapolation based on the first fitting curve, the fitting residual error corresponding to the first target time point is determined based on the solar length extrapolated value and the solar length actual value of the first target time point, the first fitting residual error sequence comprising the residual errors between the solar length fitting values and the solar length actual values of a plurality of first historical time points and the residual error corresponding to the first target time point are used for training the solar length change forecasting model, so that the solar length change forecasting model can fully learn the nonlinear characteristics of the first historical solar length change sequence, residual error prediction can be carried out, and then the accurate day length prediction value can be obtained by utilizing the residual error predicted by the day length change prediction model and the day length extrapolation value obtained by fitting extrapolation based on the preset fitting algorithm; furthermore, considering that the solar length change time sequence has the characteristics of overall presentation certainty and randomness, when the solar length change prediction model is trained, the fitting residual between the first fitting curve and the first historical solar length change sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitting residual sequence, so that the rules hidden in the first historical solar length change sequence can be excavated, the obtained phase space representation retains more potential characteristic information in the first historical solar length change sequence, then the obtained phase space representation is used as a training sample, the fitting residual corresponding to the first target time point is used as a label corresponding to the training sample, the solar length change prediction model is trained, more knowledge can be learned by the solar length change prediction model, and the residual prediction accuracy of the solar length change prediction model is further improved, therefore, the high-precision forecast of the change of the day length is realized.
In a second aspect, an embodiment of the present application provides a method for forecasting a change in day length, including:
fitting a second historical daily length change sequence based on a preset fitting algorithm, and determining a second fitting residual sequence and a daily length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical daily length change sequence comprises daily length actual values of a plurality of second historical time points, and the second fitting residual sequence comprises fitting residuals corresponding to the second historical time points respectively;
performing phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, wherein the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of the first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and determining a predicted daily length value of the second target time point based on the extrapolated daily length value and the forecast residual error of the second target time point.
According to the embodiment of the application, the characteristic that the solar length change sequence usually comprises an obvious linear trend term and a main period term is utilized, the second historical solar length change sequence is fitted based on the preset fitting algorithm, the obtained second fitting curve can reflect the solar length change trend, and then the solar length extrapolation value of the second target time point is obtained by extrapolation based on the second fitting curve; secondly, considering that the change of the solar length sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the change of the solar length sequence, the precision of a prediction result obtained by predicting the change of the solar length according to a first fitting curve is not high, and the trained change of the solar length prediction model can accurately predict the residual error of a future time point based on the fitting residual errors of historical time points, so that the prediction residual error of a second target time point can be obtained based on a second fitting residual error sequence and a change of the solar length prediction model, wherein the second fitting residual error sequence comprises the residual errors between the fit values of the solar length of a plurality of second historical time points and the actual values of the solar length, and then the solar length of the second target time point can be accurately predicted based on the prediction residual error and the extrapolated value of the solar length of the second target time point; in addition, considering that the solar-length change time sequence has the characteristics of overall presentation certainty and randomness, when residual prediction is carried out by using the solar-length change prediction model, the phase space reconstruction is carried out on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence, the rules hidden in the second historical solar-length change sequence can be excavated, the obtained phase space represents that more potential characteristic information in the second historical solar-length change sequence is reserved, and then the obtained phase space represents is input into the solar-length change prediction model, so that the obtained prediction residual of the second target time point is more accurate, and the solar-length change is highly accurately predicted.
In a third aspect, an embodiment of the present application provides a training device for a daily variation prediction model, including:
the first fitting module is used for fitting a first historical solar length change sequence based on a preset fitting algorithm and determining a first fitting residual sequence and a solar length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical solar length change sequence comprises solar length actual values of a plurality of first historical time points, and the first fitting residual sequence is used for representing a fitting residual between the first fitting curve and the first historical solar length change sequence;
the first determining module is used for determining a fitting residual error corresponding to the first target time point based on the date length extrapolated value and the date length actual value of the first target time point;
the first reconstruction module is used for carrying out phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and the training module is used for training the solar length change forecasting model by taking the first phase space representation as a training sample and taking the fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
In a fourth aspect, an embodiment of the present application provides a device for forecasting daily variation, including:
the second fitting module is used for fitting a second historical solar length change sequence based on a preset fitting algorithm and determining a second fitting residual sequence and a solar length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical solar length change sequence comprises solar length actual values of a plurality of second historical time points, and the second fitting residual sequence is used for representing a fitting residual between the second fitting curve and the second historical solar length change sequence;
the second reconstruction module is used for carrying out phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
the first forecasting module is used for inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of a first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and the second forecasting module is used for determining a day length forecast value of the second target time point based on the day length extrapolation value and the forecast residual error of the second target time point.
In a fifth aspect, an embodiment of the present application provides an electronic device, including:
a processor;
a memory for storing the processor-executable instructions;
wherein the processor is configured to execute the instructions to implement the method of the first or second aspect.
In a sixth aspect, the present application provides a computer-readable storage medium, where instructions in the storage medium, when executed by a processor of an electronic device, enable the electronic device to perform the method according to the first aspect or the second aspect.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
fig. 1 is a schematic flowchart of a method for training a daily variation prediction model according to an embodiment of the present application;
fig. 2 is a schematic flowchart of a method for training a daily variation prediction model according to another embodiment of the present application;
fig. 3 is a schematic structural diagram of a daily variation prediction model according to an embodiment of the present application;
fig. 4 is a schematic flowchart of a method for forecasting diurnal variation according to an embodiment of the present application;
fig. 5 is a schematic flowchart of a method for forecasting a change in day length according to another embodiment of the present application;
fig. 6 is a schematic structural diagram of a training apparatus for a daily variation prediction model according to an embodiment of the present application;
fig. 7 is a schematic structural diagram of a device for forecasting variation in solar length according to an embodiment of the present application;
fig. 8 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following specific embodiments of the present application and the accompanying drawings. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application are capable of operation in sequences other than those illustrated or described herein. In addition, "and/or" in the specification and claims means at least one of connected objects, and a character "/" generally means that a front and rear related object is in an "or" relationship.
In order to realize high-precision forecast of the change of the solar length, the embodiment of the application aims to provide a training scheme of a solar length change forecasting model, and the characteristic that a solar length change sequence usually comprises an obvious linear trend item and a main period item is utilized, a first historical solar length change sequence is fitted based on a preset fitting algorithm, and an obtained first fitting curve can reflect the change trend of the solar length and can be further used for carrying out solar length prediction; secondly, considering that the solar length change sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the solar length change sequence, the precision of a forecast result obtained by forecasting the solar length change only according to the first fitting curve is not high, for this reason, the fitting precision can be reflected by using the residual error between the solar length fitting value and the solar length actual value of each time point, the solar length extrapolated value of the first target time point is obtained by extrapolation based on the first fitting curve, the fitting residual error corresponding to the first target time point is determined based on the solar length extrapolated value and the solar length actual value of the first target time point, the first fitting residual error sequence comprising the residual errors between the solar length fitting values and the solar length actual values of a plurality of first historical time points and the residual error corresponding to the first target time point are used for training the solar length change forecasting model, so that the solar length change forecasting model can fully learn the nonlinear characteristics of the first historical solar length change sequence, residual error prediction can be carried out, and then the accurate day length prediction value can be obtained by utilizing the residual error predicted by the day length change prediction model and the day length extrapolation value obtained by fitting extrapolation based on the preset fitting algorithm; furthermore, considering that the solar length change time sequence has the characteristics of overall presentation certainty and randomness, when the solar length change prediction model is trained, the fitting residual between the first fitting curve and the first historical solar length change sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitting residual sequence, so that the rules hidden in the first historical solar length change sequence can be excavated, the obtained phase space representation retains more potential characteristic information in the first historical solar length change sequence, then the obtained phase space representation is used as a training sample, the fitting residual corresponding to the first target time point is used as a label corresponding to the training sample, the solar length change prediction model is trained, more knowledge can be learned by the solar length change prediction model, and the residual prediction accuracy of the solar length change prediction model is further improved, therefore, the high-precision forecast of the change of the day length is realized.
The embodiment of the application further provides a daily variation forecasting scheme, wherein the characteristic that a daily variation sequence usually comprises an obvious linear trend term and a main period term is utilized, a preset fitting algorithm is used for fitting a second historical daily variation sequence, an obtained second fitting curve can reflect the daily variation trend, and then extrapolation is carried out based on the second fitting curve to obtain a daily extrapolation value of a second target time point; secondly, considering that the change of the solar length sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the change of the solar length sequence, the precision of a prediction result obtained by predicting the change of the solar length according to a first fitting curve is not high, and the trained change of the solar length prediction model can accurately predict the residual error of a future time point based on the fitting residual errors of historical time points, so that the prediction residual error of a second target time point can be obtained based on a second fitting residual error sequence and a change of the solar length prediction model, wherein the second fitting residual error sequence comprises the residual errors between the fit values of the solar length of a plurality of second historical time points and the actual values of the solar length, and then the solar length of the second target time point can be accurately predicted based on the prediction residual error and the extrapolated value of the solar length of the second target time point; in addition, considering that the solar-length change time sequence has the characteristics of overall presentation certainty and randomness, when residual prediction is carried out by using the solar-length change prediction model, the phase space reconstruction is carried out on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence, the rules hidden in the second historical solar-length change sequence can be excavated, the obtained phase space represents that more potential characteristic information in the second historical solar-length change sequence is reserved, and then the obtained phase space represents is input into the solar-length change prediction model, so that the obtained prediction residual of the second target time point is more accurate, and the solar-length change is highly accurately predicted.
It should be understood that the training method for the solar length change forecasting model and the solar length change forecasting model provided in the embodiments of the present application may be executed by an electronic device or software installed in the electronic device, and specifically may be executed by a terminal device or a server device.
The technical solutions provided by the embodiments of the present application are described in detail below with reference to the accompanying drawings.
Referring to fig. 1, a flow chart of a method for training a daily variation prediction model according to an embodiment of the present application is shown, where the method includes the following steps:
s102, fitting the first historical day length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a day length extrapolation value of a first target time point based on a first fitting curve obtained through fitting.
Wherein the first historical daily length change sequence comprises daily length actual values of a plurality of first historical time points. Because the change sequence of the solar term usually comprises an obvious linear trend term and a main period term, the first historical change sequence of the solar term is fitted based on a preset fitting algorithm, and a first fitting curve capable of reflecting the change trend of the solar term can be obtained.
The first fitting residual sequence comprises fitting residuals corresponding to a plurality of first historical time points, and the fitting residuals corresponding to the first historical time points are used for representing the difference between the daily length actual value of the first historical time point and the daily length fitting value of the first historical time point on the first fitting curve.
In the above S102, extrapolation is performed based on the first fitted curve, so as to obtain a date length extrapolated value of the first target time point, and for each first historical time point, a fitted residual corresponding to the first historical time point is obtained based on a difference between a date length fitted value of the first historical time point on the first fitted curve and a date length actual value of the first historical time point; further, based on the fitting residual corresponding to each first historical time point, a first fitting residual sequence can be generated.
Considering that the solid tide and the sea tide are one of the main motivating factors of the earth rotation change, in order to obtain a more accurate daily length prediction result, optionally, as shown in fig. 2, before the first historical daily length change sequence is fitted, the harmonic terms in the first historical daily length change sequence may be further subtracted to obtain the first historical daily length change sequence that is not affected by the harmonic terms, that is, the corrected first historical daily length change sequence, and specifically, the harmonic terms in the first historical daily length change sequence may be subtracted according to the IERS2010 specification. Accordingly, in S102, the modified first historical solar-term change sequence is fitted based on a preset fitting algorithm, so as to obtain a first fitting curve.
Further, after obtaining the first fitted residual sequence based on the first fitted curve obtained by fitting, normalization processing may be performed on the first fitted residual sequence, and the specifically adopted normalization processing method may include various normalization methods commonly used in the art, which is not limited in this application embodiment.
In practical application, the preset fitting algorithm may adopt any appropriate algorithm capable of fitting the time series in the field, and may specifically be selected according to actual needs, which is not limited in the embodiment of the present application. Optionally, considering that a Least square method (LS) can better extract periodic components in the time sequence, and the first historical solar length change sequence includes an obvious main periodic term, based on this, the preset fitting algorithm may include a Least square method, so that the first historical solar length change sequence can be fitted more accurately, which is beneficial to improving the extrapolation accuracy. Specifically, the specific implementation of extrapolating the first historical solar-length change sequence by using the least square method is shown in the following formula (1):
Figure BDA0003572992480000101
wherein f (t) represents the extrapolated value of the day length at time t, a 0 And represents a point in time, a 1 Representing a parameter representing a linear trend, c i And d i Representing a period term parameter, T i Indicating the number of cycle entries.
And S104, determining a fitting residual corresponding to the first target time point based on the date extrapolation value and the date actual value of the first target time point.
Specifically, the difference between the extrapolated value of the day length of the first target time point and the actual value of the day length may be determined as the fitting residual corresponding to the first target time point.
And S106, performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation.
The essence of the phase space is a state space which can restore the original power system and is constructed according to a set of time sequences with limited length, and in the phase space, the evolution process of any component is influenced by other components related to the phase space. Therefore, in the reconstructed phase space, the evolution information of the whole system is hidden by the change process of each component.
In the embodiment of the application, considering that the solar-length change time sequence has the characteristics of overall presentation certainty and randomness, when the solar-length change prediction model is trained, the fitting residual between the first fitting curve and the first historical solar-length change sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitting residual sequence, so that the rules hidden in the first historical solar-length change sequence are excavated, the obtained phase space represents that more potential feature information in the first historical solar-length change sequence is reserved, the solar-length change prediction model can learn more knowledge, the prediction accuracy of the solar-length change prediction model is improved, and the high-precision prediction of the solar-length change is realized. In addition, the delay time and the embedding dimension are related to the quality of a reconstruction space, and further related to the prediction precision of a subsequent daily variation prediction model, and therefore, the first fitted residual sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitted residual sequence, so that a high-quality first phase space representation is obtained.
In an alternative implementation, to perform high-quality phase-space reconstruction on the first fitted residual sequence, the step S106 may be specifically implemented as: and for each fitting residual in the first fitting residual sequence, reconstructing the fitting residual into vector representation in a phase space based on the embedding dimension and the delay time matched with the first fitting residual sequence, and further generating first phase space representation based on the vector representation of each fitting residual in the first fitting residual sequence in the phase space.
For example, with a first fitting residual sequence { x } 1 ,x 2 ,x 3 ,...,x N For example, assuming that the embedding dimension matching the first fitted residual sequence is m, and the delay time matching the first fitted residual sequence is τ, we can get a vector representation X of the ith fitted residual in the phase space j ＝[x j ,x j+τ ,...,x j+(m-1)τ ]And the resulting first phase space representation T is:
Figure BDA0003572992480000111
in this embodiment of the present application, the embedding dimension and the delay time that match the first fitted residual sequence may be determined in any appropriate manner, and may be specifically selected according to actual needs, which is not limited in this embodiment of the present application. In an alternative implementation, in order to accurately determine the embedding dimension and the delay time that match the first fitted residual sequence, the embedding dimension and the delay time may be determined using a C-C algorithm, taking into account that the embedding dimension and the delay time have a strong correlation. Specifically, S106 may include:
s161, splitting the first fitting residual sequence into a plurality of mutually disjoint subsequences.
Specifically, the first fitting residual sequence { x } is still above 1 ,x 2 ,x 3 ,...,x N For example, the first fitted residual sequence can be split intoThe following mutually disjoint subsequences:
Figure BDA0003572992480000121
wherein x is 1 ,x 2 ,...,x τ And respectively representing each subsequence with the length N/tau, tau representing delay time, N representing the length of the first fitting residual error sequence, and N being an integer multiple of tau.
S162, determining the correlation integral of the first fitting residual sequence based on a plurality of mutually disjoint subsequences.
Wherein the associated integral of the first fitted residual sequence represents the probability that the distance between any two subsequences in the phase space is smaller than the radius r.
Specifically, the associated integral of the first fitted residual sequence can be determined by the following equation (4):
Figure BDA0003572992480000122
wherein, the correlation integral of the C (m, N, r, τ) first fitting residual sequence, | | X i -X j || ∞ Representing a sequence of neutrons X in phase space i And subsequence X j R represents a radius, θ (-) represents a Heaviside unit function, which satisfies: if x is less than 0, θ (x) is 0; if x is not less than 0, θ (x) is 1.
S163, based on the correlation integral, determines a test statistic function and a test statistic deviation function of the first fitted residual sequence.
Specifically, the test statistic function of the first fitted residual sequence is shown in equation (5) below:
Figure BDA0003572992480000123
wherein S (m, N, r, τ) represents the test statistic function of the first fitted residual sequence, r represents the embedding dimension, r represents the radius, and N represents the first fitted residual sequenceLength of difference sequence, τ denotes delay time, C l Representing the associated integral of the first fitted residual sequence.
And S164, determining a test statistic mean value and a test statistic deviation mean value of the first fitting residual sequence based on the test statistic function and the candidate embedding dimensions.
The test statistic mean value of the first fitting residual sequence is used for representing the mean value of the test statistic corresponding to the first fitting residual sequence in each candidate embedding dimension, and the test statistic deviation mean value of the first fitting residual sequence is used for representing the mean value of the test statistic deviation corresponding to the first fitting residual sequence in each candidate embedding dimension.
According to the statistical theory of BDS (Brock-Decher-Scheinkman), if the time sequence { x } 1 ,x 2 ,x 3 ,…,x N Is a random variable, then the statistic is S (m, r, τ) and is constantly zero at N infinity. However, the actually observed time series is necessarily correlated and the number is limited, and S (m, r, τ) - τ can reflect the autocorrelation characteristics of the time series, and in the embodiment of the present application, the autocorrelation characteristics of the first fitted residual sequence. When S (m, r, τ) - τ pass through the first time or differ the least for all radii r, the reconstructed points in phase space are considered to be uniformly distributed, and the reconstructed phase space is considered to be the most reasonable. Defining test statistic bias:
ΔS(m,τ)＝max{S(m,r i ,τ)}-min{S(m,r j ,τ)} (6)
where Δ S (m, τ) represents the test statistic deviation, which represents the maximum of the test statistic deviations for all radii r of S (m, r, τ) - τ.
And (3) obtaining reasonable values of each parameter in the S by applying BDS statistics, wherein N is 3000, m is 2-5, r is k.sigma/2, k is less than or equal to 3, and sigma is the mean square error of the sequence. The resulting mean test statistic and mean test statistic deviation can be obtained as follows:
Figure BDA0003572992480000131
wherein the content of the first and second substances,
Figure BDA0003572992480000132
represents the mean of the test statistic for the first fitted residual sequence,
Figure BDA0003572992480000133
the mean of the test statistic deviation, m the embedding dimension, and τ the delay time, representing the first fitted residual sequence.
And S165, determining the delay time matched with the first fitting residual sequence based on the test statistic mean value and/or the test statistic deviation mean value.
Specifically, the following components can be mixed
Figure BDA0003572992480000134
First zero point of
Figure BDA0003572992480000135
As a delay time matched to the first fitted residual sequence.
And S166, determining the embedding dimension matched with the first fitting residual sequence based on the preset mapping relation between the delay time and the embedding dimension and the delay time matched with the first fitting residual sequence.
Specifically, the preset mapping relationship between the delay time and the embedding dimension may be: tau is w (m-1) τ, wherein τ w Denotes a delay time window, τ denotes a delay time, and m denotes an embedding dimension. Wherein the delay time window τ w Specifically, may be S cor (τ) global minimum point.
The embodiment of the present application shows a specific implementation manner of the above S106. Of course, it should be understood that S106 may also be implemented in other manners, and this is not limited in this embodiment of the application.
The chaotic system is sensitive to the initial state of motion, the chaotic time sequence becomes unpredictable step by step for a long time along with the alternation of time, the chaotic sequence is a time sequence with the organic unification of determinacy and randomness, the state of motion diverges less in the initial stage, and the chaos can be predicted in a short time. Based on this, in another embodiment of the present application, as shown in fig. 2, before the step S106, a chaos characteristic determination is further performed on the first fitted residual sequence to identify whether the first fitted residual sequence belongs to a chaos time sequence, and further, in a case that the first fitted residual sequence is the chaos time sequence, based on an embedding dimension and a delay time matched with the first fitted residual sequence, a phase space reconstruction is performed on the first fitted residual sequence, so as to dig out more hidden laws in the first historical change-over-date sequence, so that the obtained phase space representation can retain more potential feature information in the first historical change-over-date sequence, and further improve the prediction accuracy of the change-over-date prediction model.
In the embodiment of the present application, any appropriate manner may be adopted to determine whether the first fitting residual sequence is the chaotic time sequence, which may be specifically selected according to actual needs, and the embodiment of the present application does not limit this. Because the Lyapunov index represents the law of the power system evolving in the orbit between adjacent points in the phase space, if the index is greater than 0, the orbit divergence is represented, and based on this, as shown in fig. 2, in an optional implementation manner, the Lyapunov index of the first fitting residual sequence can be subjected to chaotic discrimination. Specifically, phase space reconstruction can be performed on the first fitted residual sequence based on a preset embedding dimension and a preset delay time, so that a second phase space representation is obtained; then, determining a Lyapunov index of the first fitting residual sequence based on a minimum data quantity method and a second phase space representation; further, whether the first fitted residual sequence is a chaotic time sequence is determined based on the Lyapunov exponent of the first fitted residual sequence.
More specifically, if there is a Lyapunov exponent greater than 0 in the Lyapunov exponents of the first fitted residual sequence or the maximum Lyapunov exponent is greater than 0, it may be determined that the first fitted residual sequence is a chaotic time sequence.
It should be noted that, the determination of the Lyapunov exponent of the first fitted residual sequence based on the minimum data measure method and the second phase spatial representation can be implemented in various ways commonly used in the art, and will not be described in detail herein.
And S108, training the solar-length change forecasting model by taking the first phase space representation as a training sample and the fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
Considering that the solar length change sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the solar length change sequence, and the prediction result obtained by predicting the solar length change according to the first fitting curve is not high in precision, so that the first phase space can be represented as a training sample, the fitting residual error corresponding to the first target time point is taken as a label corresponding to the training sample, the solar length change prediction model is trained, the solar length change prediction model can fully learn the nonlinear characteristics of the first historical solar length change sequence, residual error prediction can be carried out, and then the accurate solar length prediction value can be obtained by utilizing the residual error predicted by the solar length change prediction model and the solar length extrapolated value obtained by fitting and extrapolating based on the preset fitting algorithm.
In an alternative implementation manner, as shown in fig. 2, the S108 may be specifically implemented as:
and S181, inputting the training sample into the daily variation prediction model to obtain a prediction residual error of the first target time point.
And inputting the first phase space representation into the solar length change forecasting model, and forecasting residual errors by the solar length change forecasting model based on the first phase space representation to obtain the forecast residual errors of the first target time point. The forecast residual error of the first target time point is used for representing the deviation between the day length forecast value and the day length actual value of the first target time point, and the deviation can reflect the accuracy of day length forecast for the first target time point.
And S182, determining the forecast loss of the solar-length change forecast model based on the forecast residual error of the first target time point and the label corresponding to the training sample.
The prediction loss of the solar-term change prediction model is used for representing the difference between the prediction residual output by the solar-term change prediction model aiming at the input training sample and the label corresponding to the input training sample, and can represent the residual prediction precision of the solar-term change prediction model.
Specifically, since the prediction residual of the first target time point is expressed in the phase space, in order to accurately determine the prediction loss of the solar length change prediction model, the phase space reconstruction may be performed on the label corresponding to the first phase space representation, and the prediction loss of the solar length change prediction model is determined based on the prediction residual of the first target time point and the respective phase space representations of the label corresponding to the first phase space representation.
For example, similar to the above-described way of performing the phase-space reconstruction on the first fitted residual sequence, the first phase-space representation T is as follows:
Figure BDA0003572992480000161
similarly, a phase space representation of the tag corresponding to the first phase space representation can be obtained, namely:
Figure BDA0003572992480000162
where D represents the phase space representation of the corresponding label, N represents the length of the first fitted residual sequence, and τ represents the delay time.
It should be noted that, in practical applications, the prediction loss of the daily variation prediction model can be expressed based on Mean Absolute Error (MAE) and Absolute Error (AE), that is to say:
Figure BDA0003572992480000163
AE j ＝|p j -o j | (11)
wherein p is j Representing the prediction residual at the j-th time point, o j Representing the fitting residual error of the jth time point, and i representing the forecast span; n is the length of the first fitted residual sequence; MAE i Representing the average of forecast spans iMean absolute error, AE j Representing the absolute difference between the predicted residual and the fitted residual for the j-th time point.
It can be understood that the training sample reconstructed by using the phase space and the corresponding label have the advantages of a traditional recursion mode (that is, the result of each prediction needs the prediction value of the previous prediction as input data) and an interval mode (that is, interval data processed by down-sampling is adopted for prediction during prediction), that is, in the prediction process, the sequence can be predicted in multiple steps only by training to obtain a daily change prediction model, so that the method has high prediction efficiency, the trained daily change prediction model is simple, can be rapidly converged, has a fast prediction rate and the like, and the delay time and the embedding dimension can be obtained according to formula solution, so that the process of artificial participation in network training is greatly reduced, and the autonomous prediction and self-adaptive capacity of the network are improved.
And S183, optimizing model parameters of the solar-term change forecasting model based on the forecasting loss of the solar-term change forecasting model.
The model parameters of the solar-term change forecasting model may specifically include, but are not limited to: the number of nodes in each network layer in the solar-term change forecasting model, the connection relation and the connection weight among the nodes in different network layers, the threshold corresponding to the nodes in each network layer and the like.
In order to obtain the solar-term change forecasting model with high forecasting precision, a Back Propagation (BP) algorithm can be adopted, and model parameters of the solar-term change forecasting model are adjusted based on the forecasting loss of the solar-term change forecasting model.
More specifically, when adjusting the model parameters of the solar length change forecasting model, the forecasting loss caused by each network layer can be determined by adopting an error back propagation algorithm based on the forecasting loss of the solar length change forecasting model and the current relevant parameters of each network layer; and then, aiming at reducing the forecast loss of the daily variation forecast model, adjusting the relevant parameters of each network layer by layer.
It should be noted that the above-mentioned process is only a single adjustment process, and in practical applications, multiple adjustments may be required, so that the above-mentioned steps S181 to S183 may be repeated multiple times until the preset training stop condition is met, thereby obtaining the final daily variation prediction model. The preset training stopping condition may be that the prediction loss of the daily variation prediction model is smaller than a preset loss threshold, or may also be that the adjustment times reach preset times, and the like, which is not limited in the embodiment of the present application.
The embodiment of the present application shows a specific implementation manner of the above S108. Of course, it should be understood that S108 may also be implemented in other manners, and this is not limited in this embodiment of the application.
In the embodiment of the present application, the daily variation prediction model may have a structure with any appropriate structure, and may be specifically set according to actual needs, which is not limited in the embodiment of the present application. In view of the natural advantages of the back-propagation neural network in nonlinear sequence prediction, in an alternative implementation, the variation of the solar length prediction model may include a back-propagation neural network, and specifically, as shown in fig. 3, the variation of the solar length prediction model may include an input layer, an output layer, and an implied layer.
In order to try to train a compact network structure by reducing the number of neurons in the hidden layer as much as possible under the condition of satisfying the prediction accuracy, before S108, the method in the above embodiment may further include: determining the number of neurons contained in an input layer and an output layer in the back propagation neural network based on the delay time matched with the first fitting residual sequence; determining the number of neurons contained in a hidden layer in a back propagation neural network based on the number of neurons contained in an input layer and an output layer respectively; and constructing a solar-term change forecasting model based on the number of the neurons contained in the input layer, the output layer and the hidden layer in the back propagation neural network.
Specifically, to accurately extract the hidden nonlinear features in the first phase spatial representation, the number of neurons in the input layer may be determined to be equal to the delay time, and the number of neurons in the output layer may be further determined based on the number of neurons in the input layer, e.g., as shown in fig. 3, if the delay time of the first phase spatial representation is τ, then it may be determined thatThe number of neurons in the input layer is tau; since there is a correlation between the number of neurons in the hidden layer and the number of neurons in the input layer and the output layer, the number of neurons in the hidden layer can be determined as
Figure BDA0003572992480000181
Wherein h represents the number of neurons in the hidden layer, m 1 Indicates the number of neurons in the input layer, n 1 The number of the neurons in the output layer is shown, alpha represents a preset regulation constant, and alpha is more than or equal to 1 and less than or equal to 10.
According to the training method of the solar-term change forecasting model, the characteristic that a solar-term change sequence usually comprises an obvious linear trend item and a main period item is utilized, the first historical solar-term change sequence is fitted based on a preset fitting algorithm, and an obtained first fitting curve can reflect the solar-term change trend and can be used for carrying out solar-term prediction; secondly, considering that the solar length change sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the solar length change sequence, the precision of a forecast result obtained by forecasting the solar length change only according to the first fitting curve is not high, for this reason, the fitting precision can be reflected by using the residual error between the solar length fitting value and the solar length actual value of each time point, the solar length extrapolated value of the first target time point is obtained by extrapolation based on the first fitting curve, the fitting residual error corresponding to the first target time point is determined based on the solar length extrapolated value and the solar length actual value of the first target time point, the first fitting residual error sequence comprising the residual errors between the solar length fitting values and the solar length actual values of a plurality of first historical time points and the residual error corresponding to the first target time point are used for training the solar length change forecasting model, so that the solar length change forecasting model can fully learn the nonlinear characteristics of the first historical solar length change sequence, residual error prediction can be carried out, and then the accurate day length prediction value can be obtained by utilizing the residual error predicted by the day length change prediction model and the day length extrapolation value obtained by fitting extrapolation based on the preset fitting algorithm; furthermore, considering that the solar length change time sequence has the characteristics of overall presentation certainty and randomness, when the solar length change prediction model is trained, the fitting residual between the first fitting curve and the first historical solar length change sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitting residual sequence, so that the rules hidden in the first historical solar length change sequence can be excavated, the obtained phase space representation retains more potential characteristic information in the first historical solar length change sequence, then the obtained phase space representation is used as a training sample, the fitting residual corresponding to the first target time point is used as a label corresponding to the training sample, the solar length change prediction model is trained, more knowledge can be learned by the solar length change prediction model, and the residual prediction accuracy of the solar length change prediction model is further improved, therefore, the high-precision forecast of the change of the day length is realized.
Based on the method for training the solar-length change forecasting model shown in the above embodiments of the present application, the solar-length change forecasting model obtained by training can be used for forecasting the solar-length change. The following describes in detail the application process based on the solar-term change forecasting model.
The embodiment of the application also provides a method for forecasting the variation of the solar length, which can be used for forecasting the variation of the solar length based on a model for forecasting the variation of the solar length trained by the method shown in fig. 1. Referring to fig. 4, a flow chart of a method for forecasting a change in day length according to an embodiment of the present application is schematically shown, where the method includes the following steps:
s402, fitting the second historical day length change sequence based on a preset fitting algorithm, and determining a second fitting residual sequence and a day length extrapolation value of a second target time point based on a second fitting curve obtained through fitting.
Wherein the second historical daily length change sequence comprises daily length actual values of a plurality of second historical time points. Because the solar-term change sequence usually comprises an obvious linear trend term and a main period term, fitting is carried out on the second historical solar-term change sequence based on a preset fitting algorithm, and a second fitting curve capable of reflecting the solar-term change trend can be obtained.
The second fitting residual sequence comprises fitting residuals corresponding to a plurality of second historical time points, and the fitting residuals corresponding to the second historical time points are used for representing the difference between the daily length actual value of the second historical time points and the daily length fitting value of the second historical time points on the second fitting curve.
The specific implementation manner of S402 is similar to the specific implementation manner of S102, and specifically, reference may be made to the description of S102, and detailed description is not repeated here.
Considering that the solid tide and the sea tide are one of the main motivating factors of the earth rotation change, in order to obtain a more accurate forecast result, optionally, as shown in fig. 5, before the second historical solar term change sequence is fitted, the harmonic terms in the second historical solar term change sequence may be further subtracted to obtain the second historical solar term change sequence that is not affected by the harmonic terms, that is, the modified second historical solar term change sequence, and specifically, the harmonic terms in the second historical solar term change sequence may be subtracted according to the IERS2010 specification. Accordingly, in the above S402, the modified second historical solar-term change sequence is fitted based on a preset fitting algorithm, so as to obtain a second fitting curve.
Further, after obtaining a second fitted residual sequence based on a second fitted curve obtained by fitting, the first fitted residual sequence may also be subjected to a normalization processing, and the specifically adopted normalization processing method may include various normalization methods commonly used in the art, which is not limited in the embodiment of the present application.
In practical application, the preset fitting algorithm may adopt any appropriate algorithm capable of fitting the time series in the field, and may specifically be selected according to actual needs, which is not limited in the embodiment of the present application. Optionally, considering that a Least square method (LS) can better extract periodic components in the time sequence, and the first historical solar length change sequence includes an obvious main periodic term, based on this, the preset fitting algorithm may include a Least square method, so that the first historical solar length change sequence can be fitted more accurately, which is beneficial to improving the extrapolation accuracy.
S404, based on the embedding dimension and the delay time matched with the second fitting residual sequence, carrying out phase space reconstruction on the second fitting residual sequence to obtain a third phase space representation.
The specific implementation manner of S404 is similar to the specific implementation manner of S106, and specifically, reference may be made to the description of S106, and detailed description is not repeated here.
The chaotic system is sensitive to the initial state of motion, the chaotic time sequence becomes unpredictable step by step for a long time along with the alternation of time, the chaotic sequence is a time sequence with the organic unification of determinacy and randomness, the state of motion diverges less in the initial stage, and the chaos can be predicted in a short time. Based on this, in another embodiment of the present application, as shown in fig. 5, before the step S404, a chaos characteristic determination is further performed on the second fitted residual sequence to identify whether the second fitted residual sequence belongs to the chaos time sequence, and further, in a case that the second fitted residual sequence is the chaos time sequence, based on the embedding dimension and the delay time matched with the second fitted residual sequence, the phase space reconstruction is performed on the second fitted residual sequence, so as to dig out more hidden rules in the second historical change-over-date sequence, so that the obtained phase space representation can retain more potential feature information in the second historical change-over-date sequence, and further improve the prediction accuracy of the change-over-date prediction model.
In the embodiment of the present application, a manner of performing chaos discrimination on the second fitted residual sequence is similar to the manner of performing chaos characteristic discrimination on the first fitted residual sequence in the embodiment shown in fig. 1, and specific implementation manners of performing chaos characteristic discrimination on the first fitted residual sequence in the embodiment shown in fig. 1 may be specifically referred to, and will not be described in detail here.
And S406, inputting the third phase space representation into a pre-trained solar length change prediction model to obtain a prediction residual error of the second target time point.
The method comprises the steps that a daily change forecasting model is obtained by training a first phase space representation based on a first fitting residual sequence and a fitting residual of a first target time point, the first fitting residual sequence is obtained by fitting a first historical daily change sequence, the fitting residual of the first target time point is determined based on a daily extrapolated value and a daily actual value of the first target time point, and the daily extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical daily change sequence.
And the forecast residual error of the second target time point is used for representing the deviation between the day length forecast value and the day length actual value of the second target time point. The trained solar length change prediction model can accurately predict the residual error of a future time point based on the fitting residual error of the historical time point, and accordingly, the third phase space representation is input into the solar length change prediction model, and the prediction residual error of the second target time point can be obtained.
And S408, determining a day length forecast value of the second target time point based on the day length extrapolation value and the forecast residual error of the second target time point.
Specifically, as shown in fig. 5, the predicted daily value of the second target time point is obtained by adding the extrapolated daily value of the second target time point to the prediction residual.
Alternatively, as shown in fig. 5, in consideration that the solid tide and the sea tide are one of the main excitation factors of the earth rotation change, in order to obtain a more accurate day length prediction result, after adding the extrapolated value of the day length of the second target time point to the prediction residual, the harmonic term in the second historical day length change sequence may be further added to the obtained result, and the result after adding the harmonic term is determined as the day length prediction value of the second target time point.
According to the method for forecasting the change of the solar length, the characteristic that the change sequence of the solar length usually comprises an obvious linear trend term and a main period term is utilized, the second historical change sequence of the solar length is fitted based on a preset fitting algorithm, the obtained second fitting curve can reflect the change trend of the solar length, and then extrapolation is carried out based on the second fitting curve to obtain the solar length extrapolation value of the second target time point; secondly, considering that the change of the solar length sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the change of the solar length sequence, the precision of a prediction result obtained by predicting the change of the solar length according to a first fitting curve is not high, and the trained change of the solar length prediction model can accurately predict the residual error of a future time point based on the fitting residual errors of historical time points, so that the prediction residual error of a second target time point can be obtained based on a second fitting residual error sequence and a change of the solar length prediction model, wherein the second fitting residual error sequence comprises the residual errors between the fit values of the solar length of a plurality of second historical time points and the actual values of the solar length, and then the solar length of the second target time point can be accurately predicted based on the prediction residual error and the extrapolated value of the solar length of the second target time point; in addition, considering that the solar-length change time sequence has the characteristics of overall presentation certainty and randomness, when residual prediction is carried out by using the solar-length change prediction model, the phase space reconstruction is carried out on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence, the rules hidden in the second historical solar-length change sequence can be excavated, the obtained phase space represents that more potential characteristic information in the second historical solar-length change sequence is reserved, and then the obtained phase space represents is input into the solar-length change prediction model, so that the obtained prediction residual of the second target time point is more accurate, and the solar-length change is highly accurately predicted.
The foregoing description has been directed to specific embodiments of this disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
In addition, in correspondence with the method for training the solar term change prediction model shown in fig. 1, the embodiment of the present application also provides a device for training the solar term change prediction model. Referring to fig. 6, a schematic structural diagram of a training apparatus for a daily variation prediction model according to an embodiment of the present application is provided, where the apparatus 600 includes:
a first fitting module 610, configured to fit a first historical solar length change sequence based on a preset fitting algorithm, and determine a first fitted residual sequence and a solar length extrapolated value of a first target time point based on an obtained first fitted curve, where the first historical solar length change sequence includes solar length actual values of a plurality of first historical time points, and the first fitted residual sequence is used to represent a fitted residual between the first fitted curve and the first historical solar length change sequence;
a first determining module 620, configured to determine a fitting residual corresponding to the first target time point based on the extrapolated value of the day length and the actual value of the day length of the first target time point;
a first reconstructing module 630, configured to perform phase space reconstruction on the first fitted residual sequence based on the embedding dimension and the delay time that are matched with the first fitted residual sequence, so as to obtain a first phase space representation;
the training module 640 is configured to train the variation of solar length forecast model by using the first phase space representation as a training sample and using the fitting residual corresponding to the first target time point as a label corresponding to the training sample.
According to the training device of the solar-term change forecasting model, the characteristic that a solar-term change sequence usually comprises an obvious linear trend item and a main period item is utilized, the first historical solar-term change sequence is fitted based on a preset fitting algorithm, and an obtained first fitting curve can reflect the solar-term change trend and can be used for carrying out solar-term prediction; secondly, considering that the solar length change sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the solar length change sequence, the precision of a forecast result obtained by forecasting the solar length change only according to the first fitting curve is not high, for this reason, the fitting precision can be reflected by using the residual error between the solar length fitting value and the solar length actual value of each time point, the solar length extrapolated value of the first target time point is obtained by extrapolation based on the first fitting curve, the fitting residual error corresponding to the first target time point is determined based on the solar length extrapolated value and the solar length actual value of the first target time point, the first fitting residual error sequence comprising the residual errors between the solar length fitting values and the solar length actual values of a plurality of first historical time points and the residual error corresponding to the first target time point are used for training the solar length change forecasting model, so that the solar length change forecasting model can fully learn the nonlinear characteristics of the first historical solar length change sequence, residual error prediction can be carried out, and then the accurate day length prediction value can be obtained by utilizing the residual error predicted by the day length change prediction model and the day length extrapolation value obtained by fitting extrapolation based on the preset fitting algorithm; furthermore, considering that the solar length change time sequence has the characteristics of overall presentation certainty and randomness, when the solar length change prediction model is trained, the fitting residual between the first fitting curve and the first historical solar length change sequence is subjected to phase space reconstruction based on the embedding dimension and the delay time matched with the first fitting residual sequence, so that the rules hidden in the first historical solar length change sequence can be excavated, the obtained phase space representation retains more potential characteristic information in the first historical solar length change sequence, then the obtained phase space representation is used as a training sample, the fitting residual corresponding to the first target time point is used as a label corresponding to the training sample, the solar length change prediction model is trained, more knowledge can be learned by the solar length change prediction model, and the residual prediction accuracy of the solar length change prediction model is further improved, therefore, the high-precision forecast of the change of the day length is realized.
Optionally, the first reconstruction module includes:
a first reconstruction submodule for reconstructing the fitted residuals into a vector representation in a phase space based on the embedding dimension and delay time matched with the first fitted residual sequence for each of the first fitted residual sequences;
a first generation submodule for generating the first phase space representation based on a vector representation in phase space of each of the sequence of fitted residuals.
Optionally, the apparatus 600 further comprises:
a splitting sub-module configured to split the first fitted residual sequence into a plurality of mutually disjoint sub-sequences before the reconstruction module performs phase space reconstruction on the first fitted residual sequence based on the embedding dimension and the delay time that match the first fitted residual sequence;
a correlation integral determination sub-module for determining a correlation integral of the first fitted residual sequence based on the plurality of mutually disjoint sub-sequences;
the first statistic submodule is used for determining a test statistic function and a test statistic deviation function of the first fitting residual sequence based on the correlation integral;
a second statistical submodule for determining a test statistic mean and a test statistic deviation mean of the first fitted residual sequence based on the test statistic function and a plurality of candidate embedding dimensions, wherein the test statistic mean is used for representing an average value of test statistics corresponding to the first fitted residual sequence in each candidate embedding dimension, and the test statistic deviation mean is used for representing an average value of test statistic deviations corresponding to the first fitted residual sequence in each candidate embedding dimension;
a delay time determination submodule for determining a delay time matched to the first fitted residual sequence based on the test statistic mean and/or the test statistic deviation mean;
and the embedding dimension determining submodule is used for determining the embedding dimension matched with the first fitting residual sequence based on a preset mapping relation between the delay time and the embedding dimension and the delay time matched with the first fitting residual sequence.
Optionally, the apparatus 600 further comprises:
a third reconstruction module, configured to perform phase space reconstruction on the first fitted residual sequence based on a preset embedding dimension and a preset delay time before the first reconstruction module performs phase space reconstruction on the first fitted residual sequence based on the embedding dimension and the delay time that are matched with the first fitted residual sequence, so as to obtain a second phase space representation;
an exponent determining module, configured to determine a Lyapunov exponent of the first fitted residual sequence based on a minimum data measure method and the second phase spatial representation;
the chaos discrimination module is used for determining whether the first fitting residual sequence is a chaos time sequence based on the Lyapunov exponent of the first fitting residual sequence;
the first reconstruction module is used for performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence if the first fitting residual sequence is a chaotic time sequence.
Optionally, the training module comprises:
a residual error forecasting submodule, configured to input the training sample into the solar length change forecasting model, so as to obtain a forecast residual error of the first target time point;
a loss determination submodule, configured to determine a prediction loss of the solar-length change prediction model based on the prediction residual at the first target time point and the label corresponding to the training sample;
and the optimization submodule is used for optimizing the model parameters of the solar-term change forecasting model based on the forecasting loss of the solar-term change forecasting model.
Optionally, the variation of solar length forecasting model comprises a back propagation neural network;
the apparatus 600 further comprises:
a first neuron determination submodule, configured to determine, before the training module trains the change of length of day prediction model by using the first phase space representation as a training sample and using a fitting residual corresponding to the first target time point as a label corresponding to the training sample, the number of neurons included in each of an input layer and an output layer in the back propagation neural network based on a delay time matched with a first fitting residual sequence;
the second neuron determination submodule is used for determining the number of neurons contained in an implicit layer in the back propagation neural network based on the number of neurons contained in the input layer and the output layer respectively;
and the construction submodule is used for constructing the solar-length change forecasting model based on the number of the neurons contained in the input layer, the output layer and the hidden layer in the back propagation neural network.
Optionally, the preset fitting algorithm comprises a least squares method.
Obviously, the training device for the solar-term change forecasting model provided in the embodiment of the present application can be used as an execution subject of the training method for the solar-term change forecasting model shown in fig. 1, and thus the functions of the training method for the solar-term change forecasting model in fig. 1 can be realized. Since the principle is the same, the description will not be repeated here.
In addition, the embodiment of the present application further provides a variation in solar terms forecasting device corresponding to the variation in solar terms forecasting method shown in fig. 4. Referring to fig. 7, a schematic structural diagram of a device for forecasting variation in solar length according to an embodiment of the present application is provided, where the device 700 may include:
a second fitting module 710, configured to fit a second historical solar length change sequence based on a preset fitting algorithm, and determine a second fitted residual sequence and a solar length extrapolated value of a second target time point based on an obtained second fitted curve, where the second historical solar length change sequence includes solar length actual values of a plurality of second historical time points, and the second fitted residual sequence is used to represent a fitted residual between the second fitted curve and the second historical solar length change sequence;
a second reconstruction module 720, configured to perform phase space reconstruction on the second fitted residual sequence based on the embedding dimension and the delay time that are matched with the second fitted residual sequence, so as to obtain a third phase space representation;
a first forecasting module 730, configured to input the third phase space representation into a pre-trained longest-range change forecasting model to obtain a forecast residual of the second target time point, where the longest-range change forecasting model is obtained by training a first phase space representation based on a first fitting residual sequence and a fitting residual of a first target time point, the first fitting residual sequence is obtained by fitting a first historical longest-range change sequence, the fitting residual of the first target time point is determined based on a longest-range extrapolated value and a longest-range actual value of the first target time point, and the longest-range extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical longest-range change sequence;
a second forecasting module 740, configured to determine a predicted daily value of the second target time point based on the extrapolated daily value and the forecast residual of the second target time point.
According to the device for forecasting the change of the solar length, the characteristic that the change sequence of the solar length usually comprises an obvious linear trend term and a main period term is utilized, the second historical change sequence of the solar length is fitted based on a preset fitting algorithm, the obtained second fitting curve can reflect the change trend of the solar length, and then extrapolation is carried out based on the second fitting curve to obtain the solar length extrapolation value of the second target time point; secondly, considering that the change of the solar length sequence also has obvious nonlinear characteristics, the preset fitting algorithm cannot fully utilize the nonlinear characteristics of the change of the solar length sequence, the precision of a prediction result obtained by predicting the change of the solar length according to a first fitting curve is not high, and the trained change of the solar length prediction model can accurately predict the residual error of a future time point based on the fitting residual errors of historical time points, so that the prediction residual error of a second target time point can be obtained based on a second fitting residual error sequence and a change of the solar length prediction model, wherein the second fitting residual error sequence comprises the residual errors between the fit values of the solar length of a plurality of second historical time points and the actual values of the solar length, and then the solar length of the second target time point can be accurately predicted based on the prediction residual error and the extrapolated value of the solar length of the second target time point; in addition, considering that the solar-length change time sequence has the characteristics of overall presentation certainty and randomness, when residual prediction is carried out by using the solar-length change prediction model, the phase space reconstruction is carried out on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence, the rules hidden in the second historical solar-length change sequence can be excavated, the obtained phase space represents that more potential characteristic information in the second historical solar-length change sequence is reserved, and then the obtained phase space represents is input into the solar-length change prediction model, so that the obtained prediction residual of the second target time point is more accurate, and the solar-length change is highly accurately predicted.
Obviously, the device for forecasting the variation of the solar length provided by the embodiment of the present application can be used as the execution main body of the method for forecasting the variation of the solar length shown in fig. 4, and therefore, the function of the method for forecasting the variation of the solar length in fig. 4 can be realized. Since the principle is the same, the description will not be repeated here.
Fig. 8 is a schematic structural diagram of an electronic device according to an embodiment of the present application. Referring to fig. 8, at a hardware level, the electronic device includes a processor, and optionally further includes an internal bus, a network interface, and a memory. The Memory may include a Memory, such as a Random-Access Memory (RAM), and may further include a non-volatile Memory, such as at least 1 disk Memory. Of course, the electronic device may also include hardware required for other services.
The processor, the network interface, and the memory may be connected to each other via an internal bus, which may be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, an EISA (Extended Industry Standard Architecture) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 8, but that does not indicate only one bus or one type of bus.
And the memory is used for storing programs. In particular, the program may include program code comprising computer operating instructions. The memory may include both memory and non-volatile storage and provides instructions and data to the processor.
The processor reads a corresponding computer program from the nonvolatile memory to the memory and then runs the computer program to form the training device of the solar-term change forecasting model on a logic level. The processor is used for executing the program stored in the memory and is specifically used for executing the following operations:
fitting a first historical solar length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a solar length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical solar length change sequence comprises solar length actual values of a plurality of first historical time points, and the first fitting residual sequence is used for representing a fitting residual between the first fitting curve and the first historical solar length change sequence;
determining a fitting residual corresponding to the first target time point based on the date extrapolated value and the date actual value of the first target time point;
performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and training the solar-length change forecasting model by taking the first phase space representation as a training sample and taking a fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
Or the processor reads the corresponding computer program from the nonvolatile memory to the memory and then runs the computer program to form the solar-term change forecasting device on the logic level. The processor is used for executing the program stored in the memory and is specifically used for executing the following operations:
fitting a second historical solar length change sequence based on a preset fitting algorithm, and determining a second fitting residual sequence and a solar length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical solar length change sequence comprises solar length actual values of a plurality of second historical time points, and the second fitting residual sequence is used for representing a fitting residual between the second fitting curve and the second historical solar length change sequence;
performing phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, wherein the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of the first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and determining a predicted daily length value of the second target time point based on the extrapolated daily length value and the forecast residual error of the second target time point.
The method performed by the training apparatus for a model for forecasting the variation in solar length as disclosed in the embodiment of fig. 1 of the present application or the method performed by the apparatus for forecasting the variation in solar length as disclosed in the embodiment of fig. 4 of the present application can be applied to or implemented by a processor. The processor may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or by instructions in the form of software. The Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and combines hardware thereof to complete the steps of the method.
The electronic device may further execute the method shown in fig. 1 and implement the function of the training apparatus for a daily variation prediction model in the embodiment shown in fig. 1, or the electronic device may further execute the method shown in fig. 4 and implement the function of the training apparatus for a daily variation prediction model in the embodiment shown in fig. 4, which is not described herein again in this embodiment of the present application.
Of course, besides the software implementation, the electronic device of the present application does not exclude other implementations, such as a logic device or a combination of software and hardware, and the like, that is, the execution subject of the following processing flow is not limited to each logic unit, and may also be hardware or a logic device.
Embodiments of the present application also provide a computer-readable storage medium storing one or more programs, where the one or more programs include instructions, which when executed by a portable electronic device including a plurality of application programs, enable the portable electronic device to perform the method of the embodiment shown in fig. 1, and are specifically configured to:
fitting a first historical solar length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a solar length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical solar length change sequence comprises solar length actual values of a plurality of first historical time points, and the first fitting residual sequence is used for representing a fitting residual between the first fitting curve and the first historical solar length change sequence;
determining a fitting residual corresponding to the first target time point based on the date extrapolated value and the date actual value of the first target time point;
performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and training the solar-length change forecasting model by taking the first phase space representation as a training sample and taking a fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
Alternatively, the portable electronic device can be caused to perform the method of the embodiment shown in fig. 4, and is specifically configured to perform the following operations:
fitting a second historical solar length change sequence based on a preset fitting algorithm, and determining a second fitting residual sequence and a solar length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical solar length change sequence comprises solar length actual values of a plurality of second historical time points, and the second fitting residual sequence is used for representing a fitting residual between the second fitting curve and the second historical solar length change sequence;
performing phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, wherein the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of the first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and determining a predicted daily length value of the second target time point based on the extrapolated daily length value and the forecast residual error of the second target time point.
In short, the above description is only a preferred embodiment of the present application, and is not intended to limit the scope of the present application. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.

Claims (10)

1. A method for training a solar-term change forecasting model is characterized by comprising the following steps:
fitting a first historical daily length change sequence based on a preset fitting algorithm, and determining a first fitting residual sequence and a daily length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical daily length change sequence comprises daily length actual values of a plurality of first historical time points, and the first fitting residual sequence comprises fitting residuals corresponding to the plurality of first historical time points respectively;
determining a fitting residual corresponding to the first target time point based on the date extrapolated value and the date actual value of the first target time point;
performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and training the solar-length change forecasting model by taking the first phase space representation as a training sample and taking a fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
2. The method of claim 1, wherein the phase-space reconstructing the first fitted residual sequence based on the embedding dimension and the delay time matched to the first fitted residual sequence to obtain a first phase-space representation comprises:
reconstructing, for each of the first sequence of fitted residuals, the fitted residual as a vector representation in phase space based on the embedding dimension and delay time that match the first sequence of fitted residuals;
generating the first phase space representation based on a vector representation in phase space of each of the sequence of fitted residuals.
3. The method of claim 1, wherein prior to phase-space reconstructing the first fitted residual sequence based on embedding dimensions and delay times matched to the first fitted residual sequence, the method further comprises:
splitting the first fitted residual sequence into a plurality of mutually disjoint subsequences;
determining an associated integral of the first fitted residual sequence based on the plurality of mutually disjoint subsequences;
determining a test statistic function and a test statistic deviation function of the first fitted residual sequence based on the correlation integral;
determining a test statistic mean value and a test statistic deviation mean value of the first fitted residual sequence based on the test statistic function and a plurality of candidate embedding dimensions, wherein the test statistic mean value is used for representing an average value of test statistics corresponding to the first fitted residual sequence in each candidate embedding dimension, and the test statistic deviation mean value is used for representing an average value of test statistic deviations corresponding to the first fitted residual sequence in each candidate embedding dimension;
determining a delay time matching the first fitted residual sequence based on the test statistic mean and/or the test statistic deviation mean;
and determining the embedding dimension matched with the first fitting residual sequence based on a preset mapping relation between the delay time and the embedding dimension and the delay time matched with the first fitting residual sequence.
4. The method of claim 1, wherein prior to phase-space reconstructing the first fitted residual sequence based on embedding dimensions and delay times matched to the first fitted residual sequence, the method further comprises:
performing phase space reconstruction on the first fitting residual sequence based on a preset embedding dimension and a preset delay time to obtain a second phase space representation;
determining a Lyapunov exponent of the first fitted residual sequence based on a minimum data volume method and the second phase spatial representation;
determining whether the first fitted residual sequence is a chaotic time sequence based on a Lyapunov exponent of the first fitted residual sequence;
the phase space reconstructing the first fitted residual sequence based on the embedding dimension and the delay time matched with the first fitted residual sequence comprises:
and if the first fitting residual sequence is a chaotic time sequence, performing phase space reconstruction on the first fitting residual sequence based on the embedding dimension and delay time matched with the first fitting residual sequence.
5. The method according to claim 1, wherein the training the daily variation prediction model with the first phase space representation as a training sample and the fitting residual corresponding to the first target time point as a label corresponding to the training sample comprises:
inputting the training sample into the daily variation forecasting model to obtain a forecasting residual error of the first target time point;
determining the forecast loss of the daily variation forecast model based on the forecast residual error of the first target time point and the label corresponding to the training sample;
and optimizing the model parameters of the solar length change forecasting model based on the forecasting loss of the solar length change forecasting model.
6. The method of claim 1, wherein the daily variation prediction model comprises a back propagation neural network;
before training the solar length variation forecasting model by using the first phase space representation as a training sample and using the fitting residual corresponding to the first target time point as a label corresponding to the training sample, the method further includes:
determining the number of neurons respectively contained in an input layer and an output layer in the back propagation neural network based on the delay time matched with the first fitting residual sequence;
determining the number of neurons contained in a hidden layer in the back propagation neural network based on the number of neurons contained in the input layer and the output layer respectively;
and constructing the solar-term change forecasting model based on the number of the neurons respectively contained in the input layer, the output layer and the hidden layer in the back propagation neural network.
7. The method of any one of claims 1 to 6, wherein the predetermined fitting algorithm comprises a least squares method.
8. A method for forecasting variation of solar length is characterized by comprising the following steps:
fitting a second historical daily length change sequence based on a preset fitting algorithm, and determining a second fitting residual sequence and a daily length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical daily length change sequence comprises daily length actual values of a plurality of second historical time points, and the second fitting residual sequence comprises fitting residuals corresponding to the second historical time points respectively;
performing phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, wherein the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of the first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and determining a predicted daily length value of the second target time point based on the extrapolated daily length value and the forecast residual error of the second target time point.
9. A training device for a model for forecasting diurnal variation, comprising:
the first fitting module is used for fitting a first historical daily length change sequence based on a preset fitting algorithm and determining a first fitting residual sequence and a daily length extrapolated value of a first target time point based on an obtained first fitting curve, wherein the first historical daily length change sequence comprises daily length actual values of a plurality of first historical time points, and the first fitting residual sequence comprises residual errors between the daily length actual values of the plurality of first historical time points and corresponding daily length fitting values on the first fitting curve;
the first determining module is used for determining a fitting residual error corresponding to the first target time point based on the date length extrapolated value and the date length actual value of the first target time point;
the first reconstruction module is used for carrying out phase space reconstruction on the first fitting residual sequence based on the embedding dimension and the delay time matched with the first fitting residual sequence to obtain a first phase space representation;
and the training module is used for training the solar length change forecasting model by taking the first phase space representation as a training sample and taking the fitting residual error corresponding to the first target time point as a label corresponding to the training sample.
10. A device for forecasting variation in solar length, comprising:
the second fitting module is used for fitting a second historical daily length change sequence based on a preset fitting algorithm and determining a second fitting residual sequence and a daily length extrapolated value of a second target time point based on an obtained second fitting curve, wherein the second historical daily length change sequence comprises daily length actual values of a plurality of second historical time points, and the second fitting residual sequence comprises residual errors between the daily length actual values of the plurality of second historical time points and corresponding daily length fitting values on the second fitting curve;
the second reconstruction module is used for carrying out phase space reconstruction on the second fitting residual sequence based on the embedding dimension and the delay time matched with the second fitting residual sequence to obtain a third phase space representation;
the first forecasting module is used for inputting the third phase space representation into a pre-trained solar length change forecasting model to obtain a forecast residual error of the second target time point, the solar length change forecasting model is obtained by training a first phase space representation based on a first fitting residual error sequence and a fitting residual error of a first target time point, the first fitting residual error sequence is obtained by fitting a first historical solar length change sequence, the fitting residual error of the first target time point is determined based on a solar length extrapolated value and a solar length actual value of the first target time point, and the solar length extrapolated value of the first target time point is obtained by fitting and extrapolating the first historical solar length change sequence;
and the second forecasting module is used for determining a day length forecast value of the second target time point based on the day length extrapolation value and the forecast residual error of the second target time point.
CN202210324832.3A 2022-03-30 2022-03-30 Training method of solar-term change forecasting model, and solar-term change forecasting method and device Pending CN114881283A (en)

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