A short-term daily precipitation prediction method of high-dimensional space-time information fusion

Abstract

The application discloses a short-term daily precipitation prediction method based on high-dimensional space-time information fusion, extracts characteristic components of different frequencies of daily precipitation sequence data by using wavelet packet conversion; expands the dimension of the characteristic components based on a phase space reconstruction method; determines the optimal reconstruction dimension of the characteristic components by using a Cao method, and restores the chaotic attractor of each sequence; maps the information embedded in the non-delayed attractor to the delayed attractor of the target variable through a nonlinear dynamic system model; simulates the nonlinear mapping between the non-delayed attractor and the delayed attractor by using a CNN-LSTM model, fuses the space-time information, and obtains a coupling prediction model; repeatedly embeds to form a prediction set of the target variable, and obtains the final prediction result of the coupling prediction model. Compared with the existing deep learning model technology, the application can greatly improve the accuracy of short-term daily precipitation prediction with only a small amount of training samples, and has great reliability and application potential.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of atmospheric science, in particular to the technical field of weather forecast, and specifically relates to a short-term daily precipitation forecast method based on high-dimensional spatiotemporal information fusion. BACKGROUND

[0002] In the field of weather forecast, in recent years, various climate numerical models such as CFSv2.0, ECWMF_System4, BCC_CSM, etc. are applied in daily business, but the prediction results of the dynamic model for the interannual variation of precipitation are not ideal, and the simulation results for precipitation anomalies are poor, which has certain limitations. Therefore, data-driven models are increasingly valued, which mainly include statistical and dynamic downscaling methods, artificial intelligence models, etc.

[0003] The statistical downscaling method takes large-scale numerical prediction products as prediction factors, and establishes a statistical model between regional prediction quantities and large-scale prediction factors using historical data to realize the use of numerical prediction products. However, the statistical downscaling method is difficult to capture the complex nonlinear characteristics of the daily precipitation sequence, and has limited applicability and is difficult to extrapolate. In machine learning models, artificial neural networks and BP neural networks are widely used in precipitation prediction due to their strong adaptability and nonlinear processing capabilities, but these models belong to the shallow learning category and have limited practicality, and have some shortcomings such as local optimization, poor convergence, overfitting, and strong dependence on parameters.

[0004] Deep neural networks have received extensive attention due to their ability to capture nonlinear interdependent relationships and are widely used in meteorological and hydrological forecasting. In particular, the recurrent neural network (RNN) model has an advantage in processing sequence models, and the long short-term memory model (LSTM) has significantly improved the performance of the recurrent neural network, which can effectively capture the dependence between different positions in the sequence model. However, deep learning models usually require a large amount of labeled data for training, and if there is only a small amount of labeled data, they will perform poorly or even fail, and the amount of single-site precipitation observation data at most weather stations cannot meet the requirements of deep learning models for the number of training samples, which restricts the further application of deep neural networks in precipitation prediction. SUMMARY

[0005] The present application aims to at least partially solve one of the technical problems in the related art.

[0006] One object of the present application is to provide a short-term daily precipitation forecast method based on high-dimensional spatiotemporal information fusion, which couples deep learning models and nonlinear dynamic system models to improve the accuracy of daily precipitation prediction under small sample conditions.

[0007] In order to achieve the above object, the application provides a high-dimensional space-time information fusion short-term daily precipitation prediction method, comprising:

[0008] S1, wavelet packet conversion is used to extract high-frequency and low-frequency signals of daily precipitation sequence data, and characteristic components of different frequencies are obtained;

[0009] S2, the dimension of the characteristic component is expanded based on the phase space reconstruction method, and the original high-dimensional data feature space is reshaped;

[0010] S3, the optimal reconstruction dimension of the characteristic component is determined by using Cao method, and the chaotic attractor of each sequence is recovered;

[0011] S4, through the nonlinear dynamic system model, the space-time information is exchanged, and the information embedded in the non-delayed attractor is mapped into the delayed attractor of the target variable;

[0012] S5, the nonlinear mapping between the non-delayed attractor and the delayed attractor is simulated by using the CNN-LSTM model, the space-time information is fused, and the coupling prediction model is obtained;

[0013] S6, the prediction set of the target variable is formed by repeating embedding, the nonlinear mapping of step S5 is selected by repeating a plurality of random combinations, the prediction set of the target variable is formed, and the final prediction result of the coupling prediction model is obtained.

[0014] The further preferred technical scheme of the application is that step S1 uses wavelet packet conversion to extract high-frequency and low-frequency signals of daily precipitation sequence data, and obtains characteristic components of different frequencies; the specific method is:

[0015] The high-frequency and low-frequency signals in the daily precipitation sequence data are extracted by using wavelet packet conversion, the corresponding frequency band and frequency spectrum are adaptively selected according to the signal characteristics, and the characteristic component sequence of different frequencies in the daily precipitation sequence is obtained;

[0016] Wavelet packet conversion includes wavelet packet decomposition and wavelet packet reconstruction, and the wavelet packet decomposition is represented as:

[0017] ;

[0018] Wherein, 、 is the wavelet packet coefficient; is the scale parameter, ; 、 is the translation parameter; is the frequency parameter, ; 、 are low-pass and high-pass filters in wavelet packet decomposition respectively;

[0019] Wavelet packet reconstruction is represented as:

[0020] ;

[0021] wherein, is the wavelet packet coefficient after wavelet packet reconstruction; 、 is the low-pass and high-pass filter set after wavelet packet reconstruction; 、 is the wavelet packet coefficient before reconstruction, which is obtained by the wavelet packet decomposition formula.

[0022] As preferred, step S2 enlarges the dimension of the feature component based on the phase space reconstruction method, reshapes the original high-dimensional data feature space; the specific method is:

[0023] The time series is embedded in a high-dimensional space for reconstruction, expressed as:

[0024] ;

[0025] wherein, is the embedding dimension, is the delay time, is the reconstruction matrix, is the time series.

[0026] As preferred, step S3 uses Cao method to determine the optimal reconstruction dimension of the feature component, and restores the chaotic attractor of each sequence; the specific method is:

[0027] S31, for each time series of feature components, the distance between each point and its nearest neighbor point is calculated under different embedding dimensions, which is used to judge the nearest neighbor change of the point in space under different dimensions, expressed as , the calculation formula is:

[0028] ;

[0029] wherein, and are the th vector of the dimensional space and its nearest neighbor point, and are the th vector of the dimensional space and its nearest neighbor point, indicates the norm;

[0030] S32, gradually increase the embedding dimension, and recalculate the nearest neighbor distance ;

[0031] S32, calculate the mean value of ​ , and the change of ; ; and are calculated as:

[0032] ;

[0033] ;

[0034] wherein, represents the number of samples, represents the dimension of the phase space, represents the delay time; when tends to be stable, the value, i.e. the determined optimal embedding dimension;

[0035] S33, reconstructing the phase space of the feature components by using the determined optimal embedding dimension, to generate a high-dimensional representation of the chaotic attractor.

[0036] As preferred, step S4 exchanges the spatiotemporal information by a nonlinear dynamical system model, to map the information in the embedded non-delayed attractor into the delayed attractor of the target variable; the specific method is:

[0037] S41, constructing the delayed attractor and the non-delayed attractor of the high-dimensional system based on the embedding theorem according to the chaotic attractor obtained in step S3;

[0038] The delayed attractor is expressed as:

[0039] ;

[0040] wherein, is the dimension of the reconstructed attractor, is the delay time, and the delayed attractor is constructed by the target variable , and is predicted based on the delay embedding theorem;

[0041] The non-delayed attractor is expressed as:

[0042] ;

[0043] wherein, is the non-delayed attractor, is the time series of the original system.

[0044] S42, determining the reconstruction dimension of the non-delayed attractor and the delayed attractor according to the embedding theorem;

[0045] S43, mapping the information in the non-delayed attractor into the delayed attractor of the target variable through a nonlinear dynamic system model.

[0046] As preferred, step S5 simulates the nonlinear mapping between the non-delayed attractor and the delayed attractor by using a CNN-LSTM model, fuses the spatiotemporal information, and obtains a coupled prediction model; the specific method is:

[0047] S51, randomly selecting variables from high-dimensional data to generate a large number of randomly sampled non-delayed attractors, and pairing each randomly sampled non-delayed attractor with a delayed attractor of the target variable as a training sample;

[0048] S52, using the generated training samples, modeling and training the nonlinear mapping relationship between the non-delayed attractor and the delayed attractor based on the CNN-LSTM model, and the mapping predictor of the target variable is expressed as:

[0049] ;

[0050] wherein, is the mapping between the non-delayed and delayed attractors, , , is a variable randomly extracted from the time series of the original system.

[0051] As preferred, step S6 repeats the embedding to form a prediction set of the target variable, selects multiple random combinations to repeat the nonlinear mapping of step S5, forms a prediction set of the target variable, and obtains the final prediction result of the coupled prediction model; the specific method is:

[0052] S61, randomly selecting different variable combinations from the mapping relationship between the non-delayed attractor and the delayed attractor obtained in step S5, each combination representing a different prediction path;

[0053] S62, for each randomly selected variable combination, using the trained coupled model, repeating the embedding to form a prediction set of the target variable .

[0054] S63, statistically analyzing the prediction set to extract the final prediction result.

[0055] As preferred, step S63 statistically analyzes the prediction set to extract the final prediction result, and the specific method is:

[0056] Eliminating outliers exceeding the upper quartile and lower quartile in the prediction set;

[0057] Fitting the probability distribution of the prediction set by using a kernel function, and adopting a probability density function​ The expected value of the final prediction value is expressed as:

[0058] ;

[0059] Wherein, The differential of the independent variable .

[0060] Another aspect of the present application provides a non-transitory computer readable storage medium having stored thereon computer instructions to cause a computer to execute the high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method described above.

[0061] Still another aspect of the present application provides an electronic device comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus, and the processor invokes the logic instructions in the memory to execute the high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method described above.

[0062] Beneficial effects: The present application, in view of the objective fact that the precision of the traditional daily precipitation prediction model is low, fully excavates the advantages of the deep learning model and the nonlinear dynamic system model, and proposes the high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method. Compared with the existing deep learning model technology, the present application can greatly improve the accuracy of short-term daily precipitation prediction with only a small amount of training samples, and has great reliability and application potential. Specifically, the present application uses a deep learning model to extract the time feature information of the sequence, a nonlinear dynamic system to extract the spatial correlation feature information between the sequences, and couples the deep learning model and the nonlinear dynamic system model to fully utilize the advantages of the two types of models, while extracting the time and spatial feature information of the precipitation sequence, thereby improving the daily precipitation prediction accuracy under small sample conditions. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 is a flowchart of the high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method of the present application;

[0064] Figure 2 is a comparison chart of the daily precipitation prediction values and observed values of the Dingbian station obtained by the four models in Example 1;

[0065] Figure 3 is a comparison chart of the daily precipitation prediction values and observed values of the Guyuan station obtained by the four models in Example 1;

[0066] Figure 4 is a comparison chart of the daily precipitation prediction values and observed values of the Huanxian station obtained by the four models in Example 1;

[0067] Figure 5A comparison chart of the daily precipitation forecast and observation values ​​at Pingliang Station obtained by the four models in Example 1;

[0068] Figure 6 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Wugong Station obtained by the four models in Example 1;

[0069] Figure 7 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Xifeng Station obtained by the four models in Example 1;

[0070] Figure 8 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Yaoxian Station obtained by the four models in Example 1;

[0071] Figure 9 This is a comparison chart of the daily precipitation forecast values ​​and observation values ​​at Changwu Station obtained by the four models in Example 1. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0073] The following combination Figures 1-9 The present invention describes a short-term daily precipitation forecast method based on high-dimensional spatiotemporal information fusion.

[0074] To address the problem that the amount of precipitation observation data from a single site cannot meet the training sample requirements of deep learning models, several nonlinear dynamical system models have emerged. These models can capture spatial interaction information between variables in a high-dimensional framework and create a probability distribution of this interaction information through a mapping between non-delayed attractors and delayed attractors, thereby converting the spatial information of high-dimensional data into future information about the target variable. Nonlinear dynamical systems can fully extract the spatial correlation characteristics between meteorological and hydrological series at different sites, reduce the model's reliance on samples by expanding the sample dimensionality, and achieve good forecasting results even in high-dimensional, small sample conditions.

[0075] In summary, deep learning models can extract temporal feature information of sequences, while nonlinear dynamical systems can extract spatial correlation feature information between sequences. Therefore, if deep learning models and nonlinear dynamical system models can be coupled to fully utilize the advantages of both types of models and simultaneously extract temporal and spatial feature information of precipitation data sequences, it is a feasible way to improve the accuracy of daily precipitation prediction under small sample conditions. Based on this, the short-term daily precipitation prediction method of high-dimensional spatio-temporal information fusion is proposed in the present application.

[0076] Before detailing the technical solutions of the present application, first explain some technical terms involved in the present application, in order to facilitate the understanding of the technical solutions proposed in the present application.

[0077] 1. High-dimensional spatio-temporal information fusion: refers to integrating data from different sources and different time points (such as spatial correlation between precipitation sequences of different meteorological stations and temporal correlation information of precipitation sequences of the same station) to obtain more comprehensive analysis results.

[0078] 2. Short-term daily precipitation prediction: refers to predicting precipitation events in the near future (usually within 7 days).

[0079] 3. Wavelet packet decomposition: a signal processing technique used to decompose signals into different frequency components for better analysis and processing.

[0080] 4. Phase space reconstruction: reconstructs the dynamic behavior of a system in high-dimensional space by introducing time delays based on time series data.

[0081] 5. Takens' theorem: a mathematical theorem that provides a method to determine the minimum embedding dimension required to reconstruct the phase space from time series data.

[0082] 6. Cao's method: a method for determining the optimal embedding dimension of time series by evaluating the change in nearest neighbors at different embedding dimensions.

[0083] 7. Nonlinear dynamical system model: a mathematical model that describes the nonlinear relationship of a system's evolution over time, commonly used in the study of chaos theory.

[0084] 8. Deep learning model (CNN-LSTM): a deep learning model that combines convolutional neural networks (CNN) and long short-term memory networks (LSTM), suitable for processing data with spatio-temporal dependencies.

[0085] 9. Coupled prediction model (WPD-PSR-CL-NDM): a composite prediction model that integrates wavelet packet decomposition (WPD), phase space reconstruction (PSR), chaotic attractor (CL), and nonlinear dynamical system model (NDM).

[0086] 10. Embedding dimension: In phase space reconstruction, the minimum dimension needed to capture the full dynamic behavior of a system.

[0087] 11. Delayed attractor: An attractor constructed based on the target variable, reflecting the system's behavior over time.

[0088] 12. Non-delayed attractor: An attractor constructed based on the original system time series, reflecting the system's behavior in space.

[0089] 13. Kernel function: In statistical analysis, a class of functions used to estimate the probability density function, such as the Gaussian kernel.

[0090] 14. Root Mean Square Error (RMSE): A statistical measure of the difference between model predictions and actual observations.

[0091] 15. Mean Absolute Percentage Error (MAPE): Measures the proportion of prediction errors relative to actual values, used to assess the accuracy of predictions.

[0092] 16. Nash-Sutcliffe Efficiency (NSE): A statistical measure of the consistency between model predictions and actual observations.

[0093] 17. Correlation coefficient (R): A statistical measure of the degree of linear correlation between two variables.

[0094] Example 1: This embodiment provides a high-dimensional spatiotemporal information fusion short-term daily precipitation forecasting method, comprising:

[0095] S1, using wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data, and obtaining characteristic components of different frequencies; the specific method is:

[0096] Using wavelet packet transform to extract high-frequency and low-frequency signals in daily precipitation sequence data, and according to the signal characteristics, the corresponding frequency band and spectrum are selected adaptively to obtain the characteristic component sequence of different frequencies in the daily precipitation sequence;

[0097] Wavelet packet transform includes wavelet packet decomposition and wavelet packet reconstruction, and the wavelet packet decomposition is represented as:

[0098] ;

[0099] wherein, 、 is the wavelet packet coefficient; is the scale parameter, ; 、 is the translation parameter; is the frequency parameter, ; 、 are the low-pass and high-pass filters in wavelet packet decomposition, respectively;

[0100] The wavelet packet reconstruction is represented as:

[0101]

[0102] wherein, is the wavelet packet coefficient after wavelet packet reconstruction; are the low-pass and high-pass filter sets after wavelet packet reconstruction; is the wavelet packet coefficient before reconstruction, which is obtained by the wavelet packet decomposition formula.

[0103] S2, the dimension of the feature component is expanded based on the phase space reconstruction method, and the original high-dimensional data feature space is reshaped.

[0104] First, the core idea of phase space reconstruction and Takens theorem are described:

[0105] The core idea of phase space reconstruction is to find a corresponding state point for each time point in a higher-dimensional space based on the information in the time series data by selecting appropriate delay time and embedding dimension. The trajectories between these state points can reflect the dynamic characteristics of the system, including chaotic behavior and attractor structure.

[0106] Takens theorem shows that a dynamical system with the same topological properties as the original system can be reconstructed under appropriate time delay and embedding dimension. Based on Takens theorem, the time series is embedded into a high-dimensional space for reconstruction, represented as:

[0107]

[0108] wherein, is the embedding dimension, is the delay time, is the reconstruction matrix, is the time series.

[0109] S3, the optimal reconstruction dimension of the feature component is determined by the Cao method, and the chaotic attractor of each sequence is recovered.

[0110] The Cao method can solve the sensitivity of the false nearest neighbor method to noise and the subjective interference. When the embedding dimension is small, the projection of the attractor in space forms false nearest neighbors with the points around the attractor. Therefore, the embedding dimension is continuously increased until there are no false nearest neighbors, and the embedding dimension at this time is the optimal embedding dimension.

[0111] The specific method is: ​​​​

[0112] S31, for each characteristic component of each time series, the distance between each point and its nearest neighbor point is calculated at different embedding dimensions, for judging the nearest neighbor change of points in space at different dimensions, denoted as , the calculation formula is:

[0113] ;

[0114] wherein, and are the first vector of the m-dimensional space and its nearest neighbor point, and are the first vector of the m-dimensional space and its nearest neighbor point, and are the first vector of the m-dimensional space and its nearest neighbor point, ;

[0115] S32, gradually increase the embedding dimension, and recalculate the nearest neighbor distance ;

[0116] S32, calculate the mean value of , and ; and The calculation formula is:

[0117] ;

[0118] ;

[0119] wherein, represents the number of samples, indicates the dimension of the phase space, indicates the delay time.

[0120] When tends to be stable, the value of is the determined optimal embedding dimension;

[0121] When , it indicates that the time series is a random signal, and when , the optimal embedding dimension can be determined.

[0122] S33, using the determined optimal embedding dimension, the characteristic component is reconstructed in the phase space to generate a high-dimensional representation of the chaotic attractor.

[0123] S4, through the nonlinear dynamic system model, exchange space-time information, and map the information in the embedding non-delay attractor to the delay attractor of the target variable; the specific method is:​​​​

[0124] S41, based on the embedding theorem, constructing a delay attractor and a non-delay attractor of the high-dimensional system according to the chaotic attractor obtained in step S3;

[0125] First, the embedding theorem is described:

[0126] Suppose is a compact manifold with dimension. For smooth diffeomorphism and smooth function pair, the mapping is a widespread property, defined as follows:

[0127] ;

[0128] ;

[0129] wherein is the dimension of the reconstructed attractor, is the delay time, the delay attractor is constructed from the target variable and is predicted based on the delay embedding theorem;

[0130] The non-delay attractor is expressed as:

[0131] ;

[0132] wherein is the non-delay attractor, is the time series of the original system.

[0133] S42, according to the embedding theorem, determining the reconstruction dimension of the non-delay attractor and the delay attractor;

[0134] According to the embedding theorem, the dimension of the reconstructed attractor L is less than the dimension of the original system. The embedding theorem shows that the non-delay attractor reflects the spatial information and correlation information in the high-dimensional space. The delay attractor reflects the time information of the individual variable. In this embodiment, the reconstruction dimension L is set to 3, that is, a 3-dimensional delay attractor and a 3-dimensional non-delay attractor are reconstructed. The constructed delay attractor and non-delay attractor are as follows:

[0135] ;

[0136] ;

[0137] wherein is randomly extracted from the time series of the original system.

[0138] S43, mapping the information in the non-delayed attractor into the delayed attractor of the target variable through the nonlinear dynamic system model.

[0139] S5, simulating the nonlinear mapping between the non-delayed attractor and the delayed attractor by using the CNN-LSTM model, fusing the spatiotemporal information, and obtaining a coupling prediction model;

[0140] The traditional nonlinear dynamic system model uses Gaussian process regression to describe the mapping relationship between the non-delayed attractor and the delayed attractor. However, in high-dimensional space, Gaussian regression not only has the risk of overfitting, but also may capture noise in the data rather than the real pattern in the case of limited sample size. Therefore, the embodiment uses a combined deep learning model (CNN-LSTM) to capture the complex nonlinear mapping relationship between the non-delayed attractor and the delayed attractor. The generation process of the training sample of the coupling prediction model (WPD-PSR-CL-NDM) is as follows:

[0141] S51, randomly selecting variables from high-dimensional data to generate a large number of randomly sampled non-delayed attractors, and pairing each randomly sampled non-delayed attractor with the delayed attractor of the target variable as a training sample;

[0142] S52, using the generated training sample, modeling and training the nonlinear mapping relationship between the non-delayed attractor and the delayed attractor based on the CNN-LSTM model, and the mapping predictor of the target variable is expressed as:

[0143] ;

[0144] wherein, is the mapping between the non-delayed and delayed attractors, 、 、 is randomly extracted from the time series of the original system.

[0145] S6, repeating the embedding to form the prediction set of the target variable, selecting multiple random combinations of repeating step S5 to form the prediction set of the target variable, and obtaining the final prediction result of the coupling prediction model; the specific method is as follows:

[0146] S61, randomly selecting different variable combinations from the mapping relationship between the non-delayed attractor and the delayed attractor obtained in step S5, each combination representing a different prediction path;

[0147] S62, for each randomly selected variable combination, using the trained coupling model to repeatedly embed to form the prediction set of the target variable ;

[0148] S63, statistical analysis is performed on the prediction set to extract the final prediction result, including:

[0149] eliminating outliers exceeding the upper quartile and lower quartile in the prediction set;

[0150] fitting the probability distribution of the prediction set using a kernel function, and using the expected value of the probability density function as the final prediction value, expressed as:

[0151] ;

[0152] wherein, is the differential of the independent variable .

[0153] In this embodiment, daily precipitation forecasts of eight weather stations, namely Yaoxian, Xifeng, Wugong, Pingliang, Changwu, Huanxian, Guyuan and Dingbian, are taken as examples, a coupling model (WPD-PSR-CL-NDM) constructed by the present application is compared with three deep learning models: attention mechanism long short-term memory network (LSTM-Attention), time convolution network (TCN) and convolutional gated recurrent unit (CNN-GRU) to verify the effectiveness and robustness of the method of the present embodiment for short-term daily precipitation forecast. The daily precipitation data of the eight stations is from the China Meteorological Data Sharing Network. The specific method of applying the coupling model constructed by the present application is as follows: first, the daily precipitation sequences of the eight weather stations are divided into four sub-sequences [2, 0], [2, 1], [2, 2] and [2, 3] by using two-layer wavelet packets, and the reconstruction dimension of each component at a time delay of 1 is determined by using the Cao method; second, the reconstruction dimension of each component at a time delay of 1 is determined by using the Cao method, and the phase space of each component is reconstructed to recover the chaotic attractor of the sequence; finally, different components of the eight stations are taken as inputs into the WPD-PSR-CL-NDM coupling prediction model. In order to better test the effect of the WPD-PSR-CL-NDM coupling prediction model, two seven-day precipitation forecasts are carried out for the eight stations respectively, two training periods and two prediction periods are set, and the details are as follows: the training periods of Yaoxian, Xifeng, Wugong, Pingliang and Changwu stations are respectively from June 1, 2015 to August 23, 2017 and from June 1, 2017 to September 13, 2019, and the prediction periods are respectively from August 24, 2017 to August 30, 2017 and from September 14, 2019 to September 20, 2019; the training periods of Huanxian, Guyuan and Dingbian stations are respectively from June 1, 2015 to August 23, 2017 and from June 1, 2017 to August 21, 2019, and the prediction periods are respectively from August 24, 2017 to August 30, 2017 and from August 22, 2019 to August 28, 2019. The comparison results of daily precipitation forecast values and observed values of different stations in the two prediction periods are as followsFigures 2~9 as shown.

[0154] by Figures 2~9 It can be seen that the prediction effect of WPD-PSR-CL-NDM model at the seven stations is significantly better than that of LSTM-Attention, TCN and CNN-GRU model. At Yaoxian station, the WPD-PSR-CL-NDM model is better for the prediction of the observed value of precipitation, and better captures its trend, while the TCN model performs poorly, and fails to predict the trend of sudden changes in precipitation, with large prediction error. In Xifeng station, the LSTM-Attention model shows a lower prediction value for daily precipitation from August 24, 2017 to August 30, 2017, and TCN and CNN-GRU are not sensitive enough to the sudden increase in precipitation, failing to predict its trend in time. In Wugong station, all models can predict the trend of the increase in precipitation on August 29, 2017, but after the peak of precipitation, TCN and CNN-GRU fail to decrease in time, deviating from the actual situation and showing a large error; in the prediction from September 14, 2019 to September 20, 2019, the WPD-PSR-CL-NDM model can capture the trend of precipitation change, with smaller error than other models. In Pingliang station, the prediction effect of LSTM-Attention model is poor, and the prediction of TCN and CNN-GRU models on September 19, 2019 shows the opposite situation of the actual precipitation, with a very large prediction error. In Changwu station, the prediction error of all models is reduced in the period from August 24, 2017 to August 30, 2017. In Huanxian station, the LSTM-Attention model performs poorly, especially in its prediction on August 25, 2017, which shows the opposite situation of the observed value, deviating from the reality. In the prediction on August 26, 2019, only the WPD-PSR-CL-NDM model correctly predicts the trend of the increase in precipitation, while other models fail to accurately predict and show the opposite situation of the actual situation. In Guyuan station, the precipitation fluctuates greatly in the period from August 24, 2017 to August 30, 2017. On August 26, 2017 and August 27, 2019, the prediction of TCN and CNN-GRU models shows the opposite situation of the observed value, failing to accurately predict its trend. In Dingbian station, LSTM-Attention and TCN models show a large prediction error, and the CNN-GRU model also shows the opposite situation of the observed value. In summary, the prediction performance of WPD-PSR-CL-NDM model at the eight stations is better than that of the comparative models, which can effectively capture the trend of precipitation change, showing excellent prediction ability and high application value.

[0155] Further, the prediction performance of the LSTM-Attention, TCN, CNN-GRU and WPD-PSR-CL-NDM models at the eight stations was evaluated by the root mean square error (RMSE), mean absolute percentage error (MAPE), Nash coefficient (NSE) and correlation coefficient (R), and the calculation results are shown in Tables 1 and 2.

[0156] Table 1 Evaluation index results of the four models at the Pingliang, Xifeng, Changwu, Wugong and Yaoxian stations

[0157]

[0158] Table 2 Evaluation index results of the four models at the Dingbian, Guyuan and Huanxian stations

[0159]

[0160] It can be seen from Table 1 and Table 2 that the prediction performance of the WPD-PSR-CL-NDM model is significantly better than that of the LSTM-Attention, TCN and CNN-GRU models. At Pingli station, compared with the LSTM-Attention, TCN and CNN-GRU models, the RMSE value of the WPD-PSR-CL-NDM model is reduced by 28.53%~47.13%, the MAPE value is reduced by 60.14%~99%, in the case of negative NSE value of the TCN and CNN-GRU models, the NSE value of the WPD-PSR-CL-NDM model fluctuates around 0.5, and the R value is much higher than that of the comparative models. At Xifeng station, compared with the LSTM-Attention, TCN and CNN-GRU models, the RMSE value of the WPD-PSR-CL-NDM model is improved by 4.18%~51.25%, the MAPE value is improved by 15.5%~77.82%, in the case of negative NSE value of the comparative models, the NSE value of the WPD-PSR-CL-NDM model is positive, and the R value is greater than 0.5. At Changwu station, compared with the LSTM-Attention, TCN and CNN-GRU models, the RMSE value of the WPD-PSR-CL-NDM model is reduced by 11.87%~40.38%, the MAPE value is reduced by 5.6%~92.84%, and in the prediction stage of 2017.8.24~2017.8.30, the R value is as high as 0.96, and the prediction performance is excellent. At Wugong station, the RMSE value of the WPD-PSR-CL-NDM model is improved by 2.15%~43.32%, and the MAPE value is improved by 23%~79.51%. At Yaoxian station, the RMSE value of the WPD-PSR-CL-NDM model is improved by 5.99%~29.46%, and the MAPE value is improved by 15.67%~84.67%. At Dingbian station, the RMSE value of the WPD-PSR-CL-NDM model is improved by 30.21%~64.93%, and the MAPE value is improved by 26.38%~89.1%. At Guyuan station, the RMSE value of the WPD-PSR-CL-NDM model is improved by 3.94%~42.06%, and the MAPE value is improved by 23.57%~87.75%. At Huanxian station, the RMSE value of the WPD-PSR-CL-NDM model is improved by 35.74%~49.85%, and the MAPE value is improved by 0.8%~90.8%.In the prediction results of 2017.8.24~2017.8.30 at eight stations, the R value of the prediction result of the WPD-PSR-CL-NDM model fluctuates in the range of 0.6485~0.9634, the NSE value fluctuates in the range of 0.2927~0.6559 and is much higher than that of other comparative models; in the prediction results of 2019.9.14~2019.9.20, the R value of the prediction result of the WPD-PSR-CL-NDM model fluctuates in the range of 0.5082~0.8931, the NSE value fluctuates in the range of 0.2289~0.5357 and is much higher than that of other comparative models. In summary, the evaluation indexes of the WPD-PSR-CL-NDM model are significantly better than those of the comparative models, and can effectively solve the problems of large prediction error and low precision of the comparative models.

[0161] From the comprehensive analysis of the evaluation index calculation results in Tables 1 and 2, it can be seen that the prediction effect of the WPD-PSR-CL-NDM model is much better than that of other comparative models. The WPD-PSR-CL-NDM prediction model established in the present application predicts the daily precipitation sequence for the first time without any auxiliary information, and satisfactory prediction results are obtained. Therefore, the organic integration of spatiotemporal information based on deep learning and nonlinear dynamic system can effectively improve the prediction effect of daily precipitation, and has great application potential.

[0162] Embodiment 2: The present embodiment provides a non-transitory computer readable storage medium having computer instructions stored thereon, the computer instructions causing a computer to execute the short-term daily precipitation prediction method of high-dimensional spatiotemporal information fusion of embodiment 1.

[0163] Embodiment 3: The present embodiment provides an electronic device, which can include a processor, a communications interface, a memory and a communications bus, wherein the processor, the communications interface and the memory complete the communication among each other through the communications bus. The processor can call the logical instructions in the memory to execute the short-term daily precipitation prediction method of high-dimensional spatiotemporal information fusion of embodiment 1.

[0164] In addition, the logic instructions in the memory described above can be implemented in the form of software function units and sold or used as independent products, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0165] Embodiment 4: The embodiment provides a computer program product, the computer program product comprising a computer program, the computer program being stored on a non-transitory computer readable storage medium, and the computer program being executable by a processor to cause a computer to perform the short-term daily precipitation prediction method of high-dimensional space-time information fusion of embodiment 1.

[0166] The device embodiments described above are only schematic, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, that is, they can be located in one place, or can be distributed on multiple network units. Part or all of the modules can be selected according to actual needs to achieve the purpose of the embodiment scheme. Those skilled in the art can understand and implement without creative labor.

[0167] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be implemented by means of software and the necessary general hardware platform, and of course, can also be implemented by hardware. Based on such understanding, the above technical solutions essentially or the parts that contribute to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments.

[0168] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A short-term daily precipitation prediction method of high-dimensional space-time information fusion, characterized in that, The method comprises the following steps: S1, extracting high-frequency and low-frequency signals of daily precipitation sequence data by wavelet packet transform, and obtaining characteristic components of different frequencies; S2, expanding the dimension of the characteristic components based on the phase space reconstruction method, and remodeling the original high-dimensional data characteristic space; S3, determining the optimal reconstruction dimension of the characteristic components by the Cao method, and restoring the chaotic attractor of each sequence; S4, exchanging space-time information by a nonlinear dynamic system model, and mapping the information embedded in the non-delayed attractor into the delayed attractor of the target variable; S5, simulating the nonlinear mapping between the non-delayed attractor and the delayed attractor by a CNN-LSTM model, fusing the space-time information, and obtaining a coupled prediction model; S6, repeatedly embedding to form a prediction set of the target variable, selecting multiple random combinations of the nonlinear mapping of step S5, forming a prediction set of the target variable, and obtaining the final prediction result of the coupled prediction model.

2. The high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method according to claim 1, characterized in that, Step S1 utilizes wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data, and obtains characteristic components of different frequencies. The specific method is: Wavelet packet transform is used to extract high-frequency and low-frequency signals in daily precipitation sequence data, and corresponding frequency bands and spectra are adaptively selected according to signal characteristics to obtain characteristic component sequences of different frequencies in daily precipitation sequence data. Wavelet packet decomposition is represented as: ； wherein , are wavelet packet coefficients; is a scale parameter, ; , is a translation parameter; is a frequency parameter, ; , are low-pass and high-pass filters in wavelet packet decomposition, respectively; Wavelet packet reconstruction is represented as: ； wherein are the wavelet packet coefficients after wavelet packet reconstruction; , are the low-pass and high-pass filter banks after wavelet packet reconstruction; , are the wavelet packet coefficients before reconstruction, obtained by the wavelet packet decomposition formula.

3. The high-dimensional spatiotemporal information fusion based short-term daily precipitation forecasting method according to claim 1, characterized in that, Step S2 expands the dimension of the characteristic components based on the phase space reconstruction method, and remodels the original high-dimensional data characteristic space. The specific method is: The time series Embedding into a high-dimensional space for reconstruction, denoted as: ； wherein, is an embedding dimension, is a delay time, is a reconstruction matrix, is a time series.

4. The high-dimensional spatiotemporal information fusion based short-term daily precipitation forecasting method according to claim 1, characterized in that, Step S3 utilizes the Cao method to determine the optimal reconstruction dimension of the characteristic components, and restores the chaotic attractor of each sequence. S31、For each time series feature component, the distance between each point and its nearest neighbor point is calculated at different embedding dimensions, which is used to determine the nearest neighbor change of the point in space at different dimensions, denoted as The calculation formula is: ； wherein and are the first vector of an n-dimensional space and its closest point, and are the first vector of an n-dimensional space and its closest point, denotes the norm; S32, increase embedding dimension step by step, and recalculate the nearest neighbor distance ; S32, calculate the average of , and the change of ; and the calculation formula is:​ ； ； wherein, represents the number of samples, represents the dimension of the phase space, represents the delay time; when tends to stabilize, the value, i.e. the determined optimal embedding dimension; S33, using the determined optimal embedding dimension, reconstructing the phase space of the characteristic components to generate a high-dimensional representation of the chaotic attractor.

5. The high-dimensional spatio-temporal information fusion based short-term daily precipitation forecasting method according to claim 1, characterized in that, Step S4 exchanges space-time information by a nonlinear dynamic system model, and maps the information embedded in the non-delayed attractor into the delayed attractor of the target variable. S41, based on the embedding theorem, constructing a delayed attractor and a non-delayed attractor of a high-dimensional system according to the chaotic attractor obtained in step S3; The delayed attractor is represented as: ； wherein, is the dimension of the reconstructed attractor, is the delay time, the delay attractor is constructed from the target variable and is predicted based on the delay-embedding theory; The non-delayed attractor is represented as: ； wherein, is a non-delayed attractor, is a time series of the original system; S42, according to the embedding theorem, determining the reconstruction dimension of the non-delayed attractor and the delayed attractor; S43, mapping the information in the non-delayed attractor into the delayed attractor of the target variable by a nonlinear dynamic system model.

6. The high-dimensional spatiotemporal information fusion based short-term daily precipitation forecasting method according to claim 5, characterized in that, Step S5 simulates the nonlinear mapping between the non-delayed attractor and the delayed attractor by a CNN-LSTM model, fuses the space-time information, and obtains a coupled prediction model. S51, randomly selecting variables from high-dimensional data to generate a large number of randomly sampled non-delayed attractors, and pairing each randomly sampled non-delayed attractor with the delayed attractor of the target variable as a training sample; S52, utilize the generated training samples, based on the CNN-LSTM model, to model and train the nonlinear mapping relationship between the non-delayed attractor and the delayed attractor, and the mapping predictor of the target variable is expressed as: ； wherein, is the mapping between the non-delayed and delayed attractors, , , are randomly drawn from the time series of the original system.

7. The high-dimensional spatiotemporal information fusion based short-term daily precipitation forecasting method according to claim 6, characterized in that, Step S6 repeatedly embeds to form a prediction set of the target variable, selects multiple random combinations of the nonlinear mapping of step S5, forms a prediction set of the target variable, and obtains the final prediction result of the coupled prediction model. S61, randomly selecting different variable combinations from the mapping relationship between the non-delayed attractor and the delayed attractor obtained in step S5, each combination representing a different prediction path; S62, for each randomly selected combination of variables, using the trained coupling model, repeating the embedding to form a prediction set of target variables ;​ S63, performing statistical analysis on the prediction set to extract the final prediction result.

8. The high-dimensional spatiotemporal information fusion short-term daily precipitation prediction method according to claim 7, characterized in that, Step S63 performs statistical analysis on the prediction set to extract the final prediction result, and the specific method is: Eliminate outliers exceeding the upper and lower quartiles in the prediction set; The probability distribution of the prediction set is predicted using a kernel function fitting, using the expected value of the probability density function as the final prediction value, denoted as: ； wherein is the derivative of the argument . 9.A non-transitory computer readable storage medium having stored thereon computer instructions to cause a computer to execute the high-dimensional spatiotemporal information fusion short-term daily precipitation forecasting method of any one of claims 1-8.

10. An electronic device comprising: A processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus, and the processor calls the logical instructions in the memory to execute the high-dimensional spatiotemporal information fusion short-term daily precipitation forecasting method of any one of claims 1-8.

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