A method for reconstructing discontinuous data of time-varying gravity field model based on machine learning

Abstract

This application relates to a method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning, including the following steps: S1: Invert the equivalent water height of the basin by using the spherical harmonic coefficient method, and obtain the original time series data of the terrestrial water storage change in the basin through filtering; S2: Perform seasonal decomposition on the original time series data TWSA t to generate a periodic term C with linear characteristics t , a highly non-linear trend term T t and a residual term R t ; S3: Establish and train an ARIMA-LSTM combined model composed of an autoregressive moving average model (ARIMA) and a long short-term memory neural network (LSTM), and then perform data reconstruction at the grid scale and the basin scale; S4: Calculate the difference ε t , and use indicators to evaluate the accuracy of the model results. This application uses a combined model for prediction, which reduces the weight of the neural network results and avoids the unstable influence brought by a single neural network, and has the advantage of high prediction accuracy.

Description

Technical Field

[0001] The present invention relates to the field of satellite gravity applications, and more specifically to a method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning. Background Art

[0002] At present, the data of the time-varying gravity field model comes from gravity satellite observation data. However, due to the calibration of gravity satellite instruments or satellite attitude adjustment, the satellite is affected by space weather, resulting in some missing data, that is, data discontinuity. When the time-varying gravity field model is used for application analysis, it is necessary to manually supplement the discontinuous data. There are many methods for reconstructing time-varying gravity field data, among which the deep learning model long short-term memory neural network (LSTM) is widely used.

[0003] Long short-term memory neural network (LSTM) is used to reconstruct the discontinuous data of the time-varying gravity field model. Data preprocessing is required first. The processed data is divided into training set and test set according to a certain ratio; then the model is built and trained, the training set is input into the model, and the hyperparameters of the neural network model are adjusted to finally obtain the reconstructed time-varying gravity field model data according to the optimal model. Due to the complex characteristics of time series, the existing technology also uses a deep learning neural network composed of multi-layer LSTM to recursively predict the missing information of the time-varying gravity field, or reconstructs the equivalent water height through a multi-layer perceptron.

[0004] The ARIMA model is a time series forecasting method. It is a method that compiles and analyzes time series and makes analogies or extensions based on the development process, direction and trend reflected in the time series. It is currently widely used in financial analysis and other fields and can be used to predict non-stationary time series. The model is expressed as ARIMA(p, d, q):

[0005]

[0006]

[0007] Where A(z) represents AR(p), B(z) represents MA(q), and X t For output, is the delay operator, d is the difference processing of the observed data d times, is the backward shift operator at time t.

[0008] The time series data of the time-varying gravity field has strong seasonal changes, and its own historical changes are regular. In theory, it can be predicted and reconstructed using time series prediction methods. However, since the time-varying gravity field data is greatly affected by natural influences such as temperature and precipitation and various human activities, the generated time series contains a lot of noise and complex laws. When using a single time series prediction model, due to the various types of functional relationships that may exist within various types of data, the model cannot fully grasp the historical change laws of the data, the output structure is not robust enough, the accuracy is not high enough, and the generalization ability is not strong enough. Although the use of a single neural network model can capture the laws and relationships of sequence changes over time, the model uses back propagation and activation functions, and there is still the problem of gradient explosion or disappearance. It may not be possible to obtain the optimal solution, resulting in a significant reduction in the prediction effect. The same hyperparameter setting will result in different solutions because the LSTM model itself is a randomly initialized parameter, and the model has poor stability and low accuracy. Summary of the invention

[0009] In view of the defects of the existing technology using a single model, the purpose of the present invention is to provide a method for reconstructing intermittent data of a time-varying gravity field model based on machine learning. By utilizing multiple models, the accuracy of the reconstructed time-varying gravity field data is improved, and the results are made more consistent with the actual situation. At the same time, it can adapt to data reconstruction work in more regions and improve the stability and universality of the reconstructed model.

[0010] A method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning, comprising the following steps:

[0011] S1: Use the spherical harmonic coefficient method to invert the equivalent water height of the basin, and obtain the original time series data of the terrestrial water storage change in the basin through filtering;

[0012] S2: TWSA of the original time series data t Perform seasonal decomposition to generate a periodic term C with linear characteristics t , a highly nonlinear trend term T t and the residual term R t , the calculation formula is:

[0013] TWSA t =C t +T t +R t

[0014] S3: Establish and train an ARIMA-LSTM combined model consisting of an autoregressive moving average model (ARIMA) and a long short-term memory neural network (LSTM), and then reconstruct data at the grid scale and the basin scale. The data reconstruction includes: for the periodic term C t, use the ARIMA model to fit it to get the periodic item forecast value For the trend term T t and the residual term R t Use the LSTM model for fitting to obtain the trend item prediction values and the residual predicted value The periodic item forecast value Trend item forecast value and the residual predicted value Add together the predicted time series data TWSA;

[0015] S4: Calculate the difference ε t :

[0016]

[0017] For the difference ε t ,The accuracy of the model results is evaluated using four indicators ,including Pearson correlation coefficient (CC), Nash efficiency coefficient (NSE), mean absolute percentage error (MAPE) and root mean square

[0018] As a further solution of the present invention: the formula for inverting the equivalent water height of the basin using the spherical harmonic coefficient method is as follows:

[0019]

[0020] Where Δh(θ,λ) is the equivalent water height; θ and λ are the co-latitude and longitude of the point to be calculated; a is the radius of the earth; ρ e and ρ w Represent the density of the earth and water respectively; ΔC nm With ΔS nm represents the change of nth order and mth order spherical harmonic coefficients; k n represents the corresponding n-order load Love number; is the fully normalized Legendre function; W n With W m is the smoothing kernel function related to order and suborder;

[0021] After inverting the equivalent water height of the basin, a combined filtering method consisting of a FAN filter with a radius of 300 km and a decorrelation filter of P3M15 was selected to obtain the time series data of the changes in the terrestrial water storage in the basin.

[0022] As a further solution of the present invention: the data required for the combined model training include terrestrial water storage change data at the basin scale and the grid (1°×1°) scale. The basin scale is the average of the grid point values ​​of the entire basin, and the grid scale is the point-like spatial distribution of the data in units of 1°.

[0023] As a further solution of the present invention: the Pearson correlation coefficient (CC) evaluates the linear relationship between the predicted TWSA and the true value of GRACE-TWSA, the Nash efficiency coefficient (NSE) is used to measure the degree of fit of the model; the mean absolute percentage error (MAPE) is used to estimate the deviation between the predicted TWSA and the true value of GRACE-TWSA, and the root mean square error (RMSE) measures the absolute size of the error, and the calculation formula is as follows:

[0024]

[0025]

[0026]

[0027]

[0028] In the formula, σ y , are the sample standard deviations of GRACE observations and predictions, respectively.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. The present invention uses a combination of multiple models and takes advantage of the advantages of different models. ARIMA is a linear relationship model suitable for predicting linear and non-stationary sequences. LSTM is a neural network model that can find highly nonlinear functional relationships in sequences. Usually, time series are affected by too many factors and their own laws are relatively complex. The equivalent water height of the basin is inverted by the spherical harmonic coefficient method, and the original time series data of the terrestrial water storage changes in the basin are obtained by filtering and seasonal decomposition is performed. It can be decomposed into periodic terms with linear characteristics, highly nonlinear trend terms and residual terms. The decomposed multiple sequences are simpler than the original sequences. Different methods are used for prediction according to the mathematical characteristics of different sequences. For periodic terms, ARIMA prediction is used, and for trend terms and residual terms, LSTM prediction is used. The predicted time series data is obtained after summing, and the prediction effect is good.

[0031] 2. The ARIMA-LSTM combined model of the present invention can improve the stability, applicability and accuracy of TWSA reconstruction compared with a single model, reduce the weight of the neural network results, and avoid the unstable influence caused by a single neural network; at the same time, the decomposition sequence can reduce the complexity of the data, making it easier for the model to learn the characteristics of the data, facilitating the reconstruction work and improving the accuracy of data reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is the technical roadmap of the present invention;

[0033] Figure 2 The TWSA time series of 11 river basins and regions around the world for 23 months from July 2015 to May 2017 predicted by the ARIMA model, LSTM model and ARIMA-LSTM combined model;

[0034] Figure 3 Nash efficiency coefficients of TWSA reconstructed by ARIMA model, LSTM model and ARIMA-LSTM combined model compared with GRACE satellite observations;

[0035] Figure 4 TWSA (1°×1°) grid maps reconstructed in the Amazon River basin by the ARIMA model, LSTM model, and ARIMA-LSTM combined model. DETAILED DESCRIPTION

[0036] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the preferred embodiments are only for illustrating the present invention, rather than for limiting the protection scope of the present invention.

[0037] Figure 1 As the technical roadmap of the present invention, the present invention uses the method of seasonal decomposition of time series, combines the respective advantages of the ARIMA model and the LSTM neural network model, and constructs a new ARIMA-LSTM combined model.

[0038] The data is provided by the Gravity Recovery and Climate Experiment (GRACE) satellite jointly developed by the National Aeronautics and Space Administration (NASA) and the German Aerospace Center (DLR) under the Earth System Science Pathfinder Program. The satellite measures irregular changes in the gravity field and provides monthly global terrestrial water storage change (TWSA) data in the form of equivalent water height. The official GRACE data sets are produced by the Jet Propulsion Laboratory (JPL), the Center for Space Research (CSR) at the University of Texas at Austin, and the German Research Center for Geosciences (GFZ), with a resolution of 400km. The invention obtains GRACE equivalent water height data calculated by the Level-2 spherical harmonic coefficient method (SH) based on CSR from April 2002 to May 2017 (the service time of the GRACE satellite is from April 2002 to June 2017) for 162 months. The SH data are all Rlease-06 versions, and the CSR SH products are gridded at a scale of 1°×1°. Due to satellite battery and instrument failures, a total of 20 months of GRACE-TWSA data were lost. Therefore, after calculating TWSA, cubic spline interpolation was used to fill the missing parts, increasing the amount of training data to reduce the difficulty of model training. A total of 182 months of data from April 2002 to May 2017 were used as training sample data to ensure data continuity. For Level-2 CSR SH data, some necessary post-processing procedures were applied after geocentric correction, including the need to replace the C10 term in the spherical harmonic coefficients with the value calculated by the method of Swenson et al. and the need to replace the solution obtained by satellite laser ranging (SLR) because the GRACE satellite cannot determine the exact value of the C20 term, using a Gaussian smoothing filter with a radius of 300 km to denoise high-order noise, applying decorrelation filtering to remove the correlation of spherical harmonic coefficients, glacier rebound correction (GIA), atmospheric load correction (GAD) and background field correction including deducting the corresponding average model.

[0039] Example

[0040] First, the spherical harmonic coefficient method is used to invert the equivalent water height of the basin, and the time series data of the terrestrial water storage change in the basin is obtained by filtering. The calculation formula of the equivalent water height is:

[0041]

[0042] Where Δh(θ,λ) is the equivalent water height; θ and λ are the co-latitude and longitude of the point to be calculated; a is the radius of the earth; ρ e and ρ w Represent the density of the earth and water respectively; ΔC nm With ΔS nm represents the change of nth order and mth order spherical harmonic coefficients; k n represents the corresponding n-th order load Love number; is the fully normalized Legendre function; W n With W m is a smoothing kernel function related to order and suborder.

[0043] The time series data of 159 months from April 2002 to June 2015 were used as the model training set, and the data of 23 months from July 2015 to May 2017 were used as the model test set. The data required for model training include the time series of terrestrial water storage changes at the basin scale and grid (1°×1°) scale. The basin scale is the average of the grid point values ​​of the entire basin, and the grid scale is the point-like spatial distribution of the data in units of 1°. The above data are used as input variables, and the ARIMA-LSTM combined model is used to learn the autocorrelation factors of the data and make predictions. The test set is used to verify the prediction effect of the model.

[0044] Then, the original time series is seasonally decomposed to obtain the periodic term C with linear characteristics. t , a highly nonlinear trend term T t and the residual term R t , for the original time series TWSA t , which can be composed of the above three items:

[0045] TWSA t =C t +T t +R t

[0046] For C t Item, use ARIMA model to fit it to get the forecast value of periodic item Then use the LSTM model to analyze the complex trend term T t and the residual term R t The series are fitted separately to obtain the trend item forecast value and the residual predicted value The periodic item forecast value Trend item forecast value and the residual predicted value Add the predicted time series data TWSA, and then calculate the difference ε t :

[0047]

[0048] The Pearson correlation coefficient (CC) is used to evaluate the linear relationship between the predicted TWSA and the true value of GRACE-TWSA, and the Nash efficiency coefficient (NSE) is used to measure the degree of fit of the model; the mean absolute percentage error (MAPE) is used to estimate the deviation between the predicted TWSA and the true value of GRACE-TWSA, and the root mean square error (RMSE) is used to measure the absolute size of the error. The formula is as follows:

[0049]

[0050]

[0051]

[0052]

[0053] Among them, σ y , are the sample standard deviations of GRACE observations and reconstructions, respectively.

[0054] Comparative Example 1

[0055] The ARIMA combined model is used to learn the autocorrelation factors of the data and make predictions, and the other steps are the same as those in the embodiment.

[0056] Comparative Example 2

[0057] The LSTM combination model is used to learn the autocorrelation factors of the data and make predictions, and the other steps are the same as those in the embodiment.

[0058] The embodiment is compared with comparative examples 1 and 2. The ARIMA model, the LSTM model and the ARIMA-LSTM combined model are based on the TWSA data obtained from the GRACE satellite at the regional scale and grid scale from July 2015 to May 2017 reconstructed from historical data (April 2002 to June 2015). The four indicators of NSE, CC, RMSE and MAPE are used to evaluate the accuracy and conduct comparative analysis of the model effect.

[0059] Figure 2 The TWSA time series of 11 basins and regions in the world for 23 months from July 2015 to May 2017 predicted by the ARIMA model, LSTM model and ARIMA-LSTM combined model are as follows. The 11 basins and regions in the world are the Amazon River Basin, the Ob River Basin, the North China Plain, the Lena River Basin, the Yenisei River Basin, the Mississippi River Basin, the Congo River Basin, the Mackenzie River Basin, the Nile River Basin, the Chad River Basin and the Volga River Basin.

[0060] Depend on Figure 2It can be seen that the reconstruction effects of each model in each major river basin are relatively good, and as the prediction time moves backward, the prediction accuracy of the three models gradually decreases, and the single model (ARIMA model and LSTM model) decreases most seriously, and the ARIMA-LSTM combination model decreases less. This is most obvious in the Amazon River Basin, Yenisei River Basin, Chad River Basin and North China Plain. In the Congo River Basin, the change pattern of its time series is more complicated. The effect of the statistical model ARIMA model will be significantly worse than the model containing neural network as time moves backward.

[0061] Table 1

[0062]

[0063] Table 2

[0064]

[0065]

[0066] Table 3

[0067]

[0068] Table 4

[0069]

[0070] Tables 1 to 4 show the NSE values, MAPE values, RMSE values ​​and CC values ​​of the three models for reconstructing TWSA and comparing them with GRACE observations. According to Table 1, the ARIMA-LSTM model has the best reconstruction effect in all large basins, and more than 72% of the basins can achieve NSE indicators of more than 80% modeling degree. The average NSE in all basins is 0.827, which is much better than 0.642 of the ARIMA model and 0.668 of the LSTM model, indicating that the model can simultaneously learn linear and nonlinear relationships in time series. According to the MAPE index, it can be seen that the error percentage of the relative truth value of the ARIMA-LSTM model in most basins is the smallest, with an average of 1.03%, which is less than 2.38% of the LSTM model and 1.70% of the ARIMA model. According to the RMSE index, it can be seen that the absolute error of the ARIMA-LSTM model is the smallest in all basins, with an average of 1.673cm, which is smaller than the 2.453cm of the LSTM model and the 2.675cm of the ARIMA model. In the Amazon River Basin, 3.833cm is even close to one-third of the ARIMA model error (9.211cm). The ARIMA model can only reach an NSE index of 50% in most basins, and the average NSE in all basins is 0.642, which is consistent with the fact that the ARIMA model can only have good learning performance for linear autocorrelation sequence structures. According to the MAPE and RMSE indicators, the ARIMA model (1.70% / 2.675cm) and the LSTM model (2.38% / 2.453cm) have their own advantages and disadvantages, especially in the Amazon River Basin, Ob ​​River Basin, Mississippi River Basin, Nile River Basin and Volga River Basin, the ARIMA model has higher accuracy because the periodic signals with linear characteristics in these basins are significantly stronger, which is suitable for prediction using this model. The NSE value of the LSTM model exceeds that of the ARIMA model in most areas, and the average NSE is 0.668, indicating that the neural network is more effective than the statistical model in predicting TWSA. Finally, combined with the average CC index of each model (ARIMA / 0.865, LSTM / 0.892, ARIMA-LSTM / 0.932), it is found that no matter which model has good predictive ability, its prediction value has a strong linear correlation with the GRACE observation value. The ARIMA-LSTM combination model can achieve more than 90% CC index in more than 72% of the basins, which is consistent with the NSE index performance, while the single neural network LSTM can only reach 54%, and the single ARIMA model is 45%. Therefore, the ARIMA-LSTM combination model performs better and can further improve the effect of TWSA prediction.

[0071] Depend on Figure 3It can be seen that for each river basin, the NSE value is generally Single ARIMA Model < Single Neural Network LSTM Model < ARIMA-LSTM Combined Model. The single neural network LSTM model shows low NSE values of 0.011 and 0.358 in the Ob River Basin and the North China Plain, both of which are inferior to the prediction effects of the other two models in the same region. This indicates that the equivalent water height sequence in this area is relatively complex. In addition to the periodic signal, the non-linear signal may have weak autocorrelation, which can be seen from the large and less regular changes in the TWSA curve in this region. It is difficult for the model to capture the change characteristics of its signal.

[0072] Figure 4

[0073] According to the above comparison results, it can be seen that:

[0074]

[0075]

[0076] Combining the above time series line charts, four indicators and grid charts, it can be found that the ARIMA-LSTM combination model can improve the stability, applicability and accuracy of TWSA reconstruction compared with a single model.

[0077] The above description is only a part of the preferred specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can combine, replace or change the technical solutions and inventive concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning, characterized in that: The following steps are involved: S1: Use the spherical harmonic coefficient method to invert the equivalent water height of the basin, and obtain the original time series data of the terrestrial water storage change in the basin through filtering; S2: TWSA of the original time series data t Perform seasonal decomposition to generate a periodic term C with linear characteristics t , a highly nonlinear trend term T t and the residual term R t , the calculation formula is: TWSA t =C t +T t +R t S3: Establish and train an ARIMA-LSTM combined model consisting of an autoregressive moving average model (ARIMA) and a long short-term memory neural network (LSTM), and then reconstruct data at the grid scale and the basin scale. The data reconstruction includes: for the periodic term C t , use the ARIMA model to fit it to get the periodic item forecast value For the trend term T t and the residual term R t Use the LSTM model for fitting to obtain the trend item prediction values and the residual predicted value The periodic item forecast value Trend item forecast value and the residual predicted value Add together the predicted time series data TWSA; S4: Calculate the difference ε t : For the difference ε t ,The accuracy of the model results is evaluated using four indicators ,including Pearson correlation coefficient (CC), Nash efficiency coefficient (NSE), mean absolute percentage error (MAPE) and root mean square 2. The method according to claim 1, characterized in that In step S1, the formula for inverting the equivalent water height of the basin using the spherical harmonic coefficient method is as follows: Where Δh(θ,λ) is the equivalent water height; θ and λ are the co-latitude and longitude of the point to be calculated; a is the radius of the earth; ρ e and ρ w Represent the density of the earth and water respectively; ΔC nm With ΔS nm represents the change of nth order and mth order spherical harmonic coefficients; k n represents the corresponding n-order load Love number; is the fully normalized Legendre function; W n With W m is the smoothing kernel function related to order and suborder; After inverting the equivalent water height of the basin, a combined filtering method consisting of a FAN filter with a radius of 300 km and a decorrelation filter of P3M15 was selected to obtain the time series data of the changes in the terrestrial water storage in the basin.

3. The method according to claim 1, characterized in that In step S3, the data required for the combined model training include terrestrial water storage change data at the basin scale and the grid 1°×1° scale. The basin scale is the average of the grid point values ​​of the entire basin, and the grid scale is the point-like spatial distribution of the data in units of 1°.

4. The method according to claim 1, characterized in that In step S4, the Pearson correlation coefficient (CC) evaluates the linear relationship between the predicted TWSA and the true value of GRACE-TWSA, and the Nash efficiency coefficient (NSE) is used to measure the degree of fit of the model; the mean absolute percentage error (MAPE) is used to estimate the deviation between the predicted TWSA and the true value of GRACE-TWSA, and the root mean square error (RMSE) measures the absolute size of the error, and the calculation formula is as follows: In the formula, σ y , are the sample standard deviations of GRACE observations and predictions, respectively.

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