CN117273062A - Method for reconstructing intermittent data of time-varying gravity field model based on machine learning - Google Patents

Abstract

The application relates to a method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning, which comprises the following steps: s1: inverting the equivalent water height of the river basin by adopting a spherical harmonic coefficient method, and obtaining original time sequence data of land water reserve change of the river basin through filtering; s2: for original time series data TWSA _t Seasonal decomposition is performed to generate a periodic term C with linear characteristics _t Highly nonlinear trend term T _t And residual term R _t The method comprises the steps of carrying out a first treatment on the surface of the S3: autoregressive moving average model (ARIMA) and long and short term memory neural network (LSTM) are built and trainedThe ARIMA-LSTM combined model is formed, and then data reconstruction of the grid scale and the drainage basin scale is carried out; s4: calculating the difference epsilon _t And performing precision evaluation of the model result by using the index. The method adopts the combined model to predict, so that the weight of the neural network result is reduced, the unstable influence caused by a single neural network is avoided, and the method has the advantage of high prediction precision.

Description

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

Technical field

The 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 technique

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 data missing, that is, there are data discontinuities. When using the time-varying gravity field model When performing application analysis, it is necessary to manually complete 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.

Long short-term memory neural network (LSTM) is used to reconstruct time-varying gravity field model discontinuous data. Data preprocessing is required first. The processed data is divided into training set and test set according to a certain proportion; then model construction and model training are performed, and the training set is input model, and by adjusting the hyperparameters of the neural network model, the reconstructed time-varying gravity field model data is finally obtained according to the optimal model. Due to the complex characteristics of time series, existing technologies also use deep learning neural networks combined with multi-layer LSTMs to recursively predict missing information in time-varying gravity fields, or reconstruct equivalent water heights through multi-layer perceptrons.

The summation autoregressive moving average (ARIMA) model is a time series forecasting method. By compiling and analyzing time series, analogies or extensions are made based on the development process, direction and trend reflected in the time series. It is currently widely used in financial analysis and other fields. , can be used to predict non-stationary time series. The model is expressed as ARIMA(p,d,q):

Among them, A(z) represents AR(p), B(z) represents MA(q), X _t is the output, is the delay operator, d is the differential processing of the observation data d times,/> is the backward shift operator of time t.

The time series data of the time-varying gravity field has strong seasonal changes, and its own historical changes are regular. In theory, time series prediction methods can be used for prediction and reconstruction. However, because the time-varying gravity field data is subject to factors such as temperature , precipitation and other natural impacts and human activities have a greater impact. The generated time series contains a lot of noise and complex patterns. When using a single time series prediction model, due to the multiple types of functional relationships that may exist within various types of data, , causing the model to be unable to fully grasp the historical change patterns of the data, the output structure is not robust enough, the accuracy is not high enough, and the generalization ability is not strong. Although using a single neural network model can capture the patterns and relationships of the sequence changes over time, the model Using backpropagation and activation functions, there is still the problem of gradient explosion or disappearance, and the optimal solution may not be obtained, resulting in a greatly reduced prediction effect; the same hyperparameter setting will have different solutions because the LSTM model itself has random initialization parameters. The model has poor stability and low accuracy.

Contents of the invention

In view of the shortcomings of using a single model in the existing technology, the purpose of the present invention is to provide a method for reconstructing discontinuous data of a time-varying gravity field model based on machine learning, using multiple models to improve the accuracy of the reconstructed time-varying gravity field data, so that the results It is more consistent with the real situation, and can adapt to data reconstruction work in more areas, improving the stability and universality of the reconstruction model.

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

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 changes in the basin through filtering;

S2: Perform seasonal decomposition on the original time series data TWSA _t to generate the periodic term C _t with linear characteristics, the 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 combination model composed of an autoregressive moving average model (ARIMA) and a long short-term memory neural network (LSTM), and then perform grid-scale and watershed-scale data reconstruction. The data reconstruction includes: Periodic term C _t , use the ARIMA model to fit it to obtain the predicted value of the periodic term For the trend term T _t and the residual term R _t , the LSTM model is used to fit the trend term T t and the residual term R t to obtain the predicted value of the trend term/> and the predicted value of the residual term/> Predict the periodic value/> Trend item forecast value/> and the predicted value of the residual term/> The predicted time series data TWSA is added together;

S4: Calculate the difference ε _t :

For the difference ε _t , four indicators are used to evaluate the accuracy of the model results: Pearson correlation coefficient (CC), Nash efficiency coefficient (NSE), mean absolute percentage error (MAPE) and root mean square error (RMSE). .

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:

In the formula, Δh(θ,λ) is the equivalent water height; θ and λ are the colatitude and longitude of the point to be calculated; a is the radius of the earth; ρ _e and ρ _w represent the earth density and water density respectively; ΔC _nm and ΔS _nm represents the change of n-th order m-th spherical harmonic coefficient; k _n represents the corresponding n-th order load Loew number; is a fully normalized Legendre function; W _n and W _m are smooth kernel functions related to order and order;

After inverting the equivalent water height of the basin, a combined filtering method formed by the FAN filter with a radius of 300km and the decorrelation filter of P3M15 was used to obtain the time series data of the land water storage changes in the basin through filtering.

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. The network scale is a point-like spatial distribution of data in units of 1°.

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, and the Nash efficiency coefficient (NSE) is used to measure the fitting degree 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. The calculation formula is as follows:

In the formula, σ _y , are the sample standard deviations of GRACE observed values and predicted values respectively.

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

1. This invention uses a combination of multiple models to take advantage 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 the sequence, usually in time. The series is affected by too many factors, and its own rules are relatively complex. The original time series data, which is obtained by using the spherical harmonic coefficient method to invert the equivalent water height of the basin, and filtering to obtain the changes in land water storage in the basin, can be decomposed seasonally. 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, use ARIMA forecasting uses LSTM forecasting for trend items and residual items. After summing, the predicted time series data is obtained, and the forecasting effect is good.

2. Compared with a single model, the ARIMA-LSTM combined model of the present invention can improve the stability, applicability and accuracy of TWSA reconstruction, reduce the weight of the neural network results, and avoid the unstable effects brought by a single neural network; at the same time, the decomposed sequence can Reducing data complexity makes it easier for the model to learn the characteristics of the data, facilitates reconstruction work, and improves the accuracy of data reconstruction.

Description of the drawings

Figure 1 is a technical roadmap of the present invention;

Figure 2 shows 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, the LSTM model and the ARIMA-LSTM combined model;

Figure 3 shows the Nash efficiency coefficient of TWSA reconstructed by ARIMA model, LSTM model and ARIMA-LSTM combined model compared with GRACE satellite observations;

Figure 4 shows the TWSA (1° × 1°) grid map reconstructed by the ARIMA model, the LSTM model and the ARIMA-LSTM combined model in the Amazon River Basin.

Detailed ways

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 and are not intended to limit the scope of the present invention.

Figure 1 is the technical roadmap of the present invention. The present invention uses the method of seasonal decomposition of time series and combines the respective advantages of the ARIMA model and the LSTM neural network model to construct a new ARIMA-LSTM combined model.

The data comes from the Gravity Recovery and Climate Experiment (GRACE) satellite, jointly developed by NASA and the German Aerospace Center (DLR) under the Earth System Science Pathfinder program, by measuring irregular changes in the gravity field. Monthly global terrestrial water storage changes (TWSA) data are provided in a water-efficient format. The official GRACE dataset is 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 creates the Level-2 spherical harmonic coefficient method (SH) calculation based on CSR for 162 months from April 2002 to May 2017 (the service time of the GRACE satellite is from April 2002 to June 2017). GRACE equivalent water height data. SH data are all version Rlease-06, and CSR SH products are gridded at a scale of 1° × 1°. A total of 20 months of GRACE-TWSA data were lost due to satellite battery and instrument failures. Therefore, after calculating TWSA, cubic spline interpolation was used to supplement the missing parts, increasing the amount of training data to reduce the training difficulty of the model. A total of 182 months from April 2002 to May 2017 were used. The data is used as training sample data to ensure the continuity of the data. 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 coefficient with the value calculated by the method of Swenson et al. and the GRACE satellite cannot determine the accuracy of the C20 term. value, it is necessary to replace the solution obtained by satellite laser ranging (SLR), use a Gaussian smoothing filter with a radius of 300km to denoise high-order noise, apply a decorrelation filter to remove the correlation of spherical harmonic coefficients, and glacier rebound correction (GIA ), atmospheric load correction (GAD) and background field correction include deducting the corresponding average model.

Example

First, the spherical harmonic coefficient method is used to invert the equivalent water height of the basin, and the time series data of the land water storage changes in the basin are obtained through filtering. The calculation formula of the equivalent water height is:

In the formula, Δh(θ,λ) is the equivalent water height; θ and λ are the colatitude and longitude of the point to be calculated; a is the radius of the earth; ρ _e and ρ _w represent the earth density and water density respectively; ΔC _nm and ΔS _nm represents the change of n-th order m-th spherical harmonic coefficient; k _n represents the corresponding n-th order load Loew number; is a fully normalized Legendre function; W _n and W _m are smooth kernel functions related to order and order.

A total of 159 months of time series data from April 2002 to June 2015 was used as the model training set, and a total of 23 months of data from July 2015 to May 2017 was 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 the grid (1° × 1°) scale. The basin scale is the average of the grid point values in the entire basin, and the grid scale is the data in 1° units. Point-like spatial distribution, the above data are used as input variables, and the ARIMA-LSTM combination 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.

Then, perform seasonal decomposition on the original time series to obtain the periodic term C _t with linear characteristics, the highly nonlinear trend term T _t and the residual term R _t . For the original time series TWSA _t , it can be composed of the above three items:

TWSA _t =C _t +T _t +R _t

For the C _t term, use the ARIMA model to fit it to obtain the predicted value of the periodic term. Then use the LSTM model to fit the complex trend term T _t and residual term R _t sequences respectively to obtain the predicted value of the trend term/> and the predicted value of the residual term/> Predict the periodic value/> Trend item forecast value/> and the predicted value of the residual term/> Add the predicted time series data TWSA, and then calculate the difference ε _t :

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

Among them, σ _y , are the sample standard deviations of GRACE observed values and reconstructed values respectively.

Comparative example 1

Use ARIMA to combine models to learn the autocorrelation factors of the data and make predictions. Other steps are the same as in the embodiment.

Comparative example 2

Use LSTM to combine models to learn the autocorrelation factors of the data and make predictions. Other steps are the same as in the embodiment.

The examples were compared with Comparative Example 1 and Comparative Example 2. The ARIMA model, LSTM model and ARIMA-LSTM combined model were reconstructed from July 2015 to 2017 based on historical data (April 2002 to June 2015). Regional-scale and grid-scale TWSA data obtained from the GRACE satellite in May. Four indicators, NSE, CC, RMSE and MAPE, are used to conduct accuracy evaluation and comparative analysis of model effects.

Figure 2 shows 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, the LSTM model and the ARIMA-LSTM combined model. The 11 river basins and regions in the world are the Amazon River Basin, the Ob River Basin, the North China Plain, the Lena River Basin, the Yenisey River Basin, the Mississippi River Basin, the Congo River Basin, the Mackenzie River Basin, the Nile River Basin, and the Chad River Basin. and the Volga River Basin.

As can be seen from Figure 2, the reconstruction effects of each model in each major watershed are relatively good, and as the prediction time moves back, the prediction accuracy of the three models gradually decreases, and the single model (ARIMA model and LSTM model) declines most seriously. The ARIMA-LSTM combined model has a smaller decline, which is most obvious in the Amazon River Basin, Yenisey River Basin, Chad River Basin and North China Plain, while in the Congo River Basin, the change pattern of its time series is more complex, and the statistical model The performance of the ARIMA model will be significantly worse than the model containing neural networks over time.

Table 1

Table 2

table 3

Table 4

Tables 1 to 4 respectively show the NSE value, MAPE value, RMSE value and CC value of the three models reconstructed TWSA compared with the GRACE observation value. According to Table 1, it can be seen that the ARIMA-LSTM model has the best reconstruction effect in all large watersheds, and more than 72% of the watersheds can achieve the NSE index of more than 80% of the modeling level. The average NSE value in all watersheds is 0.827, which is much better than The ARIMA model is 0.642 and the LSTM model is 0.668, indicating that the model can simultaneously learn linear relationships and nonlinear relationships in time series. According to the MAPE index, it can be seen that the relative true value error percentage of the ARIMA-LSTM model is the smallest in most watersheds. , the mean value is 1.03%, which is smaller 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 value 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, the absolute error of 3.833cm is even close to the ARIMA model error. (9.211cm) one-third. The ARIMA model can only reach 50% of the NSE index in most watersheds, and the average NSE value in all watersheds is 0.642, which is consistent with the situation 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) each 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 is more accurate. High because these basins have significantly stronger periodic signals with linear characteristics and are suitable for prediction using this model. The NSE value of the LSTM model exceeds that of the ARIMA model in most areas, with an average NSE value of 0.668, indicating that the neural network's prediction ability for TWSA is more effective than the statistical model. Finally, combined with the average CC indicators of each model (ARIMA/0.865, LSTM/0.892, ARIMA-LSTM/0.932), it was found that no matter which model has good prediction ability, its prediction values have a strong linear correlation with the GRACE observation value, ARIMA- The LSTM combined model can achieve more than 90% of the CC index in more than 72% of the watersheds, which is consistent with the NSE index performance, while the single neural network LSTM can only achieve 54%, and the single ARIMA model is 45%, so the ARIMA-LSTM combined model The performance is even better and can further improve the effect of TWSA prediction.

As can be seen from Figure 3, for each watershed, the NSE value is usually a single ARIMA model < a single neural network LSTM model < an ARIMA-LSTM combination model, while the single neural network LSTM model has low NSE values of 0.011 and 0.358 in the Ob River Basin and the North China Plain. , are not as good as the prediction effects of the other two models in the same area, indicating that the equivalent water height sequence in this area is more complex. In addition to the periodic signal, the nonlinear signal may have weak autocorrelation. This can be seen from the TWSA curve in this area. It can be seen from the huge changes and weak regularity that the model cannot grasp the changing characteristics of its signals.

Figure 4 shows the grid diagram reconstructed by the three models in the Amazon River Basin. Since the Amazon Basin is the largest river basin in the world, and the Amazon River Basin has large annual changes in water levels, significant seasonal changes in spatiotemporal distribution, and strong physical signals, it is convenient for the model. Learn its changing rules, and the calculated grid chart can intuitively express the learning effect of the model. Due to space limitations, four periods with even distribution in the reconstruction time period (October 2015, April 2016, October 2016, April 2017) are selected. It can be seen that the three models can respond better in space. The trend and periodicity of TWSA, and the high correlation between images. The results of the ARIMA-LSTM combined model are closest to the true value, are the smoothest in space, have the fewest faults, and show the best reconstruction effect. At the same time, as time goes by, errors gradually accumulate, and the gap with the true value becomes larger. The ARIMA model over-intensifies the signal strength, making the reconstruction value of the overall area too large. At the same time, the signal is not smooth enough in space, and the gap between it and the true value is large. Although the LSTM model can grasp the overall changing trend of TWSA and has smoother reconstruction results than the ARIMA model, it is not stable enough and produces more error signals.

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

From the model performance indicators for reconstructing GRACE TWSA, we can see that the ARIMA-LSTM combination model has excellent generalization ability in TWSA time series reconstruction. It has shown good accuracy in the reconstruction of multiple watersheds, and the average NSE and CC values have reached 0.827/0.932, which has good effect on time series of different river basins. The reconstruction accuracy of the ARIMA-LSTM combined model is stable. Compared with the ARIMA model and the LSTM model, it has general advantages and is better than the two single models in the reconstruction of different watersheds.

Spatially, the ARIMA-LSTM combined model has a similar spatial pattern to the output of the single model, but has the best correlation with the true value, in terms of spatial smoothness, trend and period due to the other two models.

Based on the line chart, four indicators and grid chart of the above time series, it can be found that the ARIMA-LSTM combined model can improve the stability, applicability and accuracy of TWSA reconstruction compared with a single model.

The above are only some of the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can, within the technical scope disclosed in the present invention, use the technology of the present invention. Any combination, equivalent substitution or change of the solutions and their inventive concepts shall be covered by the protection scope of the present invention.

Claims (4)

1. The method for reconstructing intermittent data of the time-varying gravity field model based on machine learning is characterized by comprising the following steps:

s1: inverting the equivalent water height of the river basin by adopting a spherical harmonic coefficient method, and obtaining original time sequence data of land water reserve change of the river basin through filtering;

s2: for original time series data TWSA _t Seasonal decomposition is performed to generate a periodic term C with linear characteristics _t Highly nonlinear trend term T _t And residual term R _t The calculation formula is as follows:

TWSA _t ＝C _t +T _t +R _t

s3: establishing and training an ARIMA-LSTM combined model consisting of an autoregressive moving average model (ARIMA) and a long-short-term memory neural network (LSTM), and then carrying out data reconstruction of a grid scale and a drainage basin scale, wherein the data reconstruction comprises the following steps: for period item C _t Fitting the ARIMA model to obtain a period term predicted valueFor trend term T _t And residual term R _t Fitting by using an LSTM model to obtain trend item predicted values +.>And residual term predictor->Predicted value of period term->Trend term predictive value->And residual term predictor->Adding to obtain predicted time sequence data TWSA;

s4: calculating the difference epsilon _t ：

For the difference epsilon _t The accuracy of the model results was assessed using four indices, pearson Correlation Coefficient (CC), nash efficiency coefficient (NSE), mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE).

2. The method of claim 1, wherein in step S1, the equation for inverting the equivalent water height of the basin using the spherical harmonic coefficient method is as follows:

wherein Δh (θ, λ) is the equivalent water height; θ and λ are the residual latitude and longitude of the point to be calculated; a is the earth radius; ρ _e And ρ _w Representing the earth density and the water density, respectively; ΔC _nm And delta S _nm Representing the change of the spherical harmonic coefficient of the order n and m; k (k) _n Representing the corresponding n-order load lux;is a fully normalized Legend function; w (W) _n And W is equal to _m Is a smooth kernel function related to the order and the order;

after the equivalent water height of the river basin is inverted, a combined filtering method formed by FAN filtering with the radius of 300km and decorrelation filtering of P3M15 is selected, and time sequence data of land water reserve change of the river basin is obtained through filtering.

3. The method of claim 1, wherein in step S3, the data required for the combined model training includes land water reserves change data of a drainage basin scale and a grid (1 °. Times.1°) scale, the drainage basin scale is an average of grid point values of the whole drainage basin, and the grid scale is a punctiform spatial distribution in units of 1 °.

4. The method of claim 1, wherein in step S4, the pearson Correlation Coefficient (CC) evaluates a linear relationship between predicted TWSA and a GRACE-TWSA true value, and the nash efficiency coefficient (NSE) is used to measure the fitting degree of the model; the Mean Absolute Percentage Error (MAPE) is used for estimating the deviation of the predicted TWSA and the GRACE-TWSA true value, the Root Mean Square Error (RMSE) is used for measuring the absolute magnitude of the error, and the calculation formula is as follows:

in sigma _y ,Sample standard deviations of GRACE observations and predictions, respectively.