Earth fluid effective angular momentum time sequence reconstruction method and device

Abstract

The invention provides an earth fluid effective angular momentum time sequence reconstruction method and device. The earth fluid effective angular momentum time sequence reconstruction method comprises the steps that earth fluid effective angular momentum is obtained, an original earth fluid effective angular momentum time sequence is obtained through linear interpolation, spectral analysis is conducted through fast Fourier transform, and an inherent periodic term is obtained; setting a lag window length based on an annual swing period and a Marcher swing period, performing singular value decomposition grouping and reconstruction, and obtaining a period time sequence, a trend time sequence and a residual time sequence; performing spectral analysis on the periodic time sequence, the trend time sequence and the residual time sequence obtained by decomposition through fast Fourier transform, judging whether the spectral characteristics are the same as those obtained by spectral analysis or not, and if not, continuing to decompose the periodic term; otherwise, reconstructing the earth fluid effective angular momentum time sequence. According to the method, a singular spectrum analysis scheme for setting a stable lag window is provided, signal integrity can be ensured, signal aliasing is avoided, and the extraction precision of quasi-periodic signals is improved; meanwhile, the data fusion consistency is ensured, and the earth fluid effective angular momentum reconstruction precision is improved.

Description

Technical Field

[0001] The invention belongs to the field of space geodesy and relates to a technical solution for reconstructing the effective angular momentum time series of earth fluid based on singular spectrum analysis extracted from inherent periodic terms. Background Art

[0002] With the development of space geodetic technology, the accuracy and time resolution of the determination of the Earth's rotation parameters have been continuously improved, allowing people to observe the influence of various dynamic effects such as the atmosphere, ocean, and hydrology on the Earth's rotation changes. In particular, short-term changes in the Earth's rotation are inseparable from the effects of physical excitation sources such as the atmosphere, ocean, land water, and sea level. Due to the conservation of angular momentum of the system composed of the solid Earth and fluid layers, the redistribution and relative movement of materials in the atmosphere, ocean, land water, and other layers will cause the exchange of angular momentum. The effective angular momentum (EAM, also known as the excitation function) of the Earth's fluid can quantitatively characterize the contribution of these excitation sources to the Earth's rotation changes. Among them, the EAM data set contains four effective angular momentum components: atmospheric angular momentum (AAM), hydrological angular momentum (HAM), oceanic angular momentum (OAM), and sea level effective angular momentum (SLAM).

[0003] With the establishment and improvement of geodynamic models, the prediction accuracy of the effective angular momentum of the earth's fluid has been greatly improved. The prediction method that integrates the effective angular momentum of the atmosphere and the ocean can better handle the high-frequency random changes of the earth's rotation, thereby significantly improving the short-term prediction of the earth's rotation parameters. It can be seen that the importance of sorting out and studying the effective angular momentum of the earth's fluid to improve the prediction accuracy of the earth's rotation parameters is self-evident.

[0004] 1. Currently, the commonly used methods for analyzing the time-varying characteristics of the effective angular momentum of the earth's fluid include the least squares fitting method, empirical mode decomposition, etc., which are usually combined with the Earth Orientation Parameters Combined04 (EOP C04) series for analysis to better understand the changes in the earth's rotation. However, due to the differences in the time resolution of different data sets, this brings certain challenges to the analysis. For example, the time resolution of the EOP C04 series is 24h (00:00UTC), while the time resolution of AAM and OAM is 3h (00:00UTC), and the time resolution of HAM and SLAM is 24h (12:00UTC).

[0005] 2. Singular spectrum analysis SSA is an effective method for extracting quasi-periodic signals from time series, in which the appropriate lag window length is crucial for extracting the inherent periodic term. If the window length is too long, it will increase the training time of the decomposition model and reduce the reconstruction accuracy; if the window length is too short, it will not be able to fully capture the effective information in the time series. Summary of the invention

[0006] In view of the above problems of the prior art, the present invention proposes a technical solution for reconstructing the effective angular momentum time series of the earth fluid based on singular spectrum analysis extracted from inherent periodic terms.

[0007] The present invention provides a method for reconstructing the time series of effective angular momentum of earth fluid, which performs the following process:

[0008] Obtain the effective angular momentum EAM of the earth fluid, obtain the original time series of the effective angular momentum of the earth fluid by linear interpolation, perform spectrum analysis by fast Fourier transform, and obtain the inherent periodic term;

[0009] The lag window length is set based on the annual swing and Chandler swing cycles, and singular value decomposition grouping and reconstruction are performed to obtain the periodic time series, trend time series and residual time series;

[0010] The spectrum analysis of the decomposed periodic time series, trend time series and residual time series is performed through fast Fourier transform to determine whether the spectrum characteristics are the same as those obtained by spectrum analysis. If not, the periodic terms are further decomposed; otherwise, the effective angular momentum time series of the earth's fluid is reconstructed.

[0011] Moreover, the original earth fluid effective angular momentum time series obtained by linear interpolation includes the first equatorial component, the second equatorial component and the axial component.

[0012] Moreover, the hysteresis window length is set to 6 years.

[0013] Moreover, the singular value decomposition grouping and reconstruction include establishing a trajectory matrix based on the original earth fluid effective angular momentum time series, calculating the eigenvalues ​​of the covariance matrix corresponding to the trajectory matrix, and obtaining the eigenvector; projecting the time series onto the eigenvector to obtain the corresponding time principal component; and performing adaptive weighted reconstruction based on the eigenvector and the signal strength.

[0014] Moreover, when there is a one-dimensional time series of length N and a lag window of length M, N is the length of the original earth fluid effective angular momentum time series, and the trajectory matrix X is expressed as follows:

[0015]

[0016] Among them, x1, x2,…x Nare the corresponding observation values ​​of time sampling points 1, 2…, N in the time series.

[0017] Moreover, by calculating the trajectory matrix X, the corresponding covariance matrix T X The eigenvalues ​​of are obtained, and M eigenvalues ​​are arranged in descending order from large to small. M , and the eigenvector E j,k , project the time series onto the feature vector E j,k On the top, we get the corresponding time principal component a i,k , i is the time series index, j is the data label in the window, and k is the index of the time empirical orthogonal function.

[0018] Furthermore, the adaptive weighted reconstruction based on the feature vector and the signal strength includes introducing a weight function w(λ j ), use the kth principal component to reconstruct the signal component of the kth layer,

[0019]

[0020] In the formula, the weight function w(λ j ) is defined as

[0021] On the other hand, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for reconstructing the timing series of effective angular momentum of earth fluid when executing the program.

[0022] On the other hand, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for reconstructing the time series of effective angular momentum of earth fluid as described above.

[0023] On the other hand, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method for reconstructing the time series of effective angular momentum of earth fluid as described above.

[0024] Compared with the prior art, the technical solution proposed by the present invention has the following advantages:

[0025] 1) A linear interpolation method is proposed, which can effectively solve the problem of inconsistent temporal resolution of different data sets and ensure the alignment and consistency of data fusion and analysis timestamps, thereby improving the accuracy of reconstruction of the effective angular momentum of the Earth's fluid.

[0026] 2) A singular spectrum analysis method with a stable hysteresis window is proposed. This method can avoid signal aliasing while ensuring signal integrity, thereby improving the extraction accuracy of quasi-periodic signals.

[0027] The solution of the present invention is simple and convenient to implement, has strong practicality, solves the problems of low practicality and inconvenience in actual application existing in related technologies, can improve user experience, and has important market value. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of an embodiment of the present invention;

[0029] Figure 2 is an original time series diagram of effective angular momentum of earth fluid according to an embodiment of the present invention;

[0030] Figure 3 is a schematic diagram of the spectrum analysis results of the original time series of the equatorial component of the effective angular momentum of the earth fluid according to an embodiment of the present invention;

[0031] Figure 4 is a schematic diagram of the spectrum analysis results of the original time series of the axial component of the effective angular momentum of the earth fluid according to an embodiment of the present invention;

[0032] Figure 5 is a schematic diagram of the reconstruction result of the inherent periodic term of the equatorial component 1 based on the singular spectrum analysis according to an embodiment of the present invention;

[0033] Figure 6 is a schematic diagram of spectrum analysis results of the equatorial component 1 according to an embodiment of the present invention;

[0034] Figure 7 is a schematic diagram of the reconstruction result of the inherent periodic term of the equatorial component 2 based on the singular spectrum analysis according to an embodiment of the present invention;

[0035] Figure 8 is a schematic diagram of the spectrum analysis result of the equatorial component 2 of an embodiment of the present invention;

[0036] Fig. 9 is a schematic diagram of the reconstruction result of the natural periodic term of the axial component based on the singular spectrum analysis according to an embodiment of the present invention;

[0037] Fig.10 is a schematic diagram of the spectrum analysis result of the axial component of an embodiment of the present invention;

[0038] Fig.11 It is a schematic diagram comparing the axial component reconstruction and the original time series results according to an embodiment of the present invention.

[0039] Fig.12 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, characteristics and effects of the present invention.

[0041] See also Figure 1 The embodiment of the present invention provides a method for reconstructing the time series of effective angular momentum of earth fluid, comprising the following steps:

[0042] a) First, obtain the effective angular momentum data set of the earth fluid (EAM = AAM + OAM + HAM + SLAM), and obtain the original earth fluid effective angular momentum time series (including equatorial component 1, equatorial component 2 and axial component) by linear interpolation method, as follows: Figure 2 As shown; then use fast Fourier transform to analyze its spectrum and obtain its inherent periodic terms (including anniversary terms, half-anniversary terms and 1 / 3 anniversary terms, etc.), see Figure 3 and Figure 4 .

[0043] For the sake of reference, the above step a (taking HAM as an example) is explained in detail as follows:

[0044] First, the observation epoch of HAM (12:00UTC) is converted to the epoch corresponding to EOP C04 (00:00UTC) by linear interpolation method. The calculation process is as follows:

[0045]

[0046] In the formula, HAM 00：00UTC is the value corresponding to the 00:00 UTC epoch, HAM0 is the value corresponding to the assumed 0 epoch, HAM1 is the value corresponding to the assumed 1 epoch, T1 and T0 are epochs 1 and 0 respectively, T 00：00UTC is the 00:00 UTC epoch.

[0047] Secondly, the time series of the effective angular momentum of the original earth fluid x is analyzed based on the Fast Fourier Transform (FFT). Γ , its spectrum analysis can be expressed by Fourier series expansion:

[0048]

[0049] Where: A l is the spectrum amplitude value of the lth harmonic component of the signal, x Γ is the time series of the effective angular momentum of the original Earth fluid at the Γth moment, and n is the number of observations.

[0050] b) Secondly, a 6-year hysteresis window length is embedded, that is, the window length is 2190. Considering that the annual swing and Chandler swing periods are the main inherent periodic items, the present invention proposes to preferably set the hysteresis window length to 6 years, because the window length can satisfy the multiples of the annual swing and Chandler swing periods at the same time, and if the hysteresis window length is set too long, it will cause the system to react slowly to new trends and short-term changes, affecting timeliness and accuracy. On the contrary, if it is too short, it will be easily disturbed by noise and outliers, affecting stability. Therefore, the present invention proposes to take the least common multiple of the annual swing and Chandler swing periods to set the hysteresis window length.

[0051] Then perform singular value decomposition grouping and reconstruction to obtain period time series, trend time series and residual time series, see Figure 5 , Figure 7 and Fig. 9 .

[0052] Furthermore, the embodiment of the present invention preferably proposes a detailed implementation of step b as follows:

[0053] Step b1: There is a one-dimensional time series {x i}, assuming the window length is Among them, M is 2190, and N is the length of the original earth fluid effective angular momentum time series. Then the trajectory matrix X can be written as:

[0054]

[0055] Among them, x1, x2,…x N are the sequences {x i}The corresponding observation values ​​of time sampling points 1, 2…, N in .

[0056] Step b2: Covariance matrix T of trajectory matrix X X It can be written as:

[0057]

[0058] Where: element By calculating the covariance matrix T X The eigenvalues ​​of , and the M eigenvalues ​​arranged in descending order from large to small are obtained. M , and the corresponding eigenvector E j,k , where the eigenvector E j,k It is orthogonal, so it is called the Temporal Empirical Orthogonal Function (T-EOF);

[0059] Project the time series to the feature vector E j,kThe corresponding temporal principal component (T-PC) can be obtained, denoted as a i,k :

[0060]

[0061] Where: 0≤i≤NM,1≤j≤M, i is the time series index, j is the data label in the window, and k is the index of the time empirical orthogonal function, which is used to identify the time principal component corresponding to the eigenvalue. The time series is decomposed by SSA to determine the reconstructed component (RC) from T-EOF and T-PC.

[0062] Step b3: From step b2, we know that the eigenvalue λ corresponding to the eigenvector j represents the weight of each characteristic component, so the present invention proposes a method based on the characteristic vector E j,k The adaptive weighted reconstruction method based on signal strength is to introduce a weight function w(λ j ), then the signal component of the kth layer is reconstructed using the kth principal component, which is:

[0063]

[0064] Where: weight function w(λ j ) is defined as j represents the data label within the window.

[0065] c) Finally, the frequency spectrum of the periodic time series, trend time series and residual time series is analyzed by fast Fourier transform to determine whether the frequency spectrum characteristics are the same as those in step a) (see Figure 6 , Figure 8 and Fig.10 ), that is, whether the period and amplitude of the component reconstructed by SSA are the same as the period and amplitude of the original time series. If they are not the same, return to repeat step b) to continue decomposing the periodic term; otherwise, stop the iteration and reconstruct the effective angular momentum time series of the earth fluid.

[0066] In specific implementation, in order to determine whether the spectrum characteristics are the same as those in step a), the corresponding threshold of the total contribution rate of the periodic term can be set according to the actual situation, and is preferably set to 0.60 in the embodiment. That is, if the total contribution rate of the periodic term is lower than the preset corresponding threshold of 0.60, then return to repeat step b) to continue decomposing the periodic term.

[0067] By comparing the present invention with the existing method for reconstructing the effective angular momentum time series of the earth's fluid based on the least squares fitting method, the present invention method has a better reconstruction effect on the effective angular momentum time series of the earth's fluid than the least squares fitting method. Taking the axial component as an example, Fig.11The present invention proposes a singular spectrum analysis method for setting a stable hysteresis window to reconstruct the axial component time series. The results show that the axial component time series obtained by the method of the present invention through the reconstructed component is highly consistent with the original time series.

[0068] In order to facilitate understanding of the technical effect of the present invention, a software platform was established using the above principle to reconstruct the time series of the effective angular momentum of the earth's fluid using the new method, and actual data and simulation data were used to verify it. Taking the axial component as an example, Table 1 statistically shows the contribution rate and total contribution rate of the inherent periodic terms obtained by decomposing the original sequence using the singular spectrum analysis method and the least squares method.

[0069] Table 1 Comparison of the contribution of the two methods to the decomposition of the original time series

[0070]

[0071] In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the scope of protection of the present invention.

[0072] A possible embodiment is a system for reconstructing the time series of effective angular momentum of earth fluids, comprising the following modules:

[0073] The first module is used to obtain the effective angular momentum EAM of the earth fluid, obtain the original time series of the effective angular momentum of the earth fluid by linear interpolation, and perform spectrum analysis using fast Fourier transform to obtain the inherent periodic term;

[0074] The second module is used to set the lag window length based on the annual swing and Chandler swing cycles, perform singular value decomposition grouping and reconstruction, and obtain the cycle time series, trend time series and residual time series;

[0075] The third module is used to perform spectrum analysis on the decomposed periodic time series, trend time series and residual time series through fast Fourier transform to determine whether the spectrum characteristics are the same as those obtained by spectrum analysis. If not, continue to decompose the periodic terms; otherwise, reconstruct the effective angular momentum time series of the earth's fluid.

[0076] In specific implementation, the above system can be realized in hardware and sold as a market product.

[0077] The device for reconstructing the effective angular momentum of earth fluid provided by the present invention is described below. The device for reconstructing the effective angular momentum of earth fluid described below and the method for reconstructing the effective angular momentum of earth fluid described above can be referred to each other.

[0078] Fig.12An example of a physical structure diagram of an electronic device is shown in FIG. Fig.12 As shown, the electronic device may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may call logic instructions in the memory to execute the method for reconstructing the timing of effective angular momentum of earth fluids.

[0079] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0080] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the method for reconstructing the timing series of the effective angular momentum of the earth fluid provided by the above-mentioned methods.

[0081] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the method for reconstructing the time series of effective angular momentum of earth fluid provided by the above-mentioned methods.

[0082] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0083] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reconstructing the time series of effective angular momentum of earth fluids, characterized by: Carry out the following process, Obtain the effective angular momentum EAM of the earth fluid, obtain the original time series of the effective angular momentum of the earth fluid by linear interpolation, and perform spectrum analysis using fast Fourier transform to obtain the inherent periodic term; The lag window length is set based on the annual swing and Chandler swing cycles, and singular value decomposition grouping and reconstruction are performed to obtain the periodic time series, trend time series and residual time series; The spectrum analysis of the decomposed periodic time series, trend time series and residual time series is performed through fast Fourier transform to determine whether the spectrum characteristics are the same as those obtained by spectrum analysis. If not, the periodic terms are further decomposed; otherwise, the effective angular momentum time series of the earth's fluid is reconstructed.

2. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 1, characterized in that: The original earth fluid effective angular momentum time series obtained by linear interpolation includes the first equatorial component, the second equatorial component and the axial component.

3. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 1, characterized in that: The hysteresis window length is set to 6 years.

4. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 1, characterized in that: The singular value decomposition grouping and reconstruction includes establishing a trajectory matrix according to the original earth fluid effective angular momentum time series, calculating the eigenvalues ​​of the covariance matrix corresponding to the trajectory matrix to obtain the eigenvector; projecting the time series onto the eigenvector to obtain the corresponding time principal component; and performing adaptive weighted reconstruction based on the eigenvector and the signal strength.

5. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 4, characterized in that: When there is a one-dimensional time series of length N and a lag window length of M, N is the length of the original earth fluid effective angular momentum time series, and the trajectory matrix X is expressed as follows: Among them, x1, x2,…x N are the corresponding observation values ​​of time sampling points 1, 2…, N in the time series.

6. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 5, characterized in that: By calculating the trajectory matrix X and the corresponding covariance matrix T X The eigenvalues ​​of are obtained, and M eigenvalues ​​are arranged in descending order from large to small. M , and the eigenvector E j,k , project the time series onto the feature vector E j,k On the top, we get the corresponding time principal component a i,k , i is the time series index, j is the data label in the window, and k is the index of the time empirical orthogonal function.

7. The method for reconstructing the time series of effective angular momentum of earth fluid according to claim 6, characterized in that: The adaptive weighted reconstruction based on the feature vector and the signal strength includes introducing a weight function w(λ j ), use the kth principal component to reconstruct the signal component of the kth layer, In the formula, the weight function w(λ j ) is defined as 8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for reconstructing the time series of effective angular momentum of earth fluid as described in any one of claims 1 to 7 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for reconstructing the time series of effective angular momentum of earth fluids as claimed in any one of claims 1 to 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by a processor, the method for reconstructing the time series of effective angular momentum of earth fluids as claimed in any one of claims 1 to 7 is implemented.

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