Short-term daily rainfall forecasting method based on high-dimensional spatio-temporal information fusion

Abstract

The invention discloses a short-term daily rainfall forecasting method based on high-dimensional spatio-temporal information fusion. The method comprises the following steps: extracting characteristic components of different frequencies of daily rainfall sequence data by using wavelet packet conversion; expanding the dimension of the feature component based on a phase-space reconstruction method; determining the optimal reconstruction dimension of the feature component by using a Cao method, and recovering the chaotic attractor of each sequence; mapping the information embedded in the non-delay attractor to the delay attractor of the target variable through a nonlinear power system model; using a CNN-LSTM model to simulate nonlinear mapping between a non-delay attractor and a delay attractor, and fusing the spatio-temporal information to obtain a coupling forecasting model; and repeatedly embedding to form a prediction set of the target variables, and obtaining a final prediction result of the coupling prediction model. Compared with an existing deep learning model technology, the method can greatly improve the accuracy of short-term daily rainfall forecast only through a small number of training samples, and has high reliability and application potential.

Description

Technical Field

[0001] The present invention relates to the field of atmospheric science and technology, in particular to the field of meteorological forecasting technology, and specifically to a short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion. Background Art

[0002] In the field of meteorological forecasting, in recent years, a variety of objective prediction products such as CFSv2.0, ECWMF_System4, BCC_CSM and other climate numerical models at home and abroad have been used in daily operations, but the forecast results of dynamic models for interannual changes in precipitation are not ideal, and the simulation results for precipitation anomalies are poor, which has certain limitations. Therefore, data-driven models are increasingly valued, and data-driven models mainly include statistical and dynamic downscaling methods, artificial intelligence models, etc.

[0003] The statistical downscaling method uses large-scale numerical forecast products as forecast factors, and uses historical data to establish a statistical model between regional forecast quantities and large-scale forecast factors to achieve the use of numerical forecast products. However, the statistical downscaling method is difficult to capture the complex nonlinear characteristics of daily precipitation series, has limited applicability, and is very difficult to extrapolate. Among 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. However, these models belong to the shallow learning category, have limited practicality, and have some shortcomings, such as local optimality, poor convergence, overfitting, and strong dependence on parameters.

[0004] Deep neural networks have attracted widespread attention due to their ability to capture nonlinear interdependencies and have been widely used in the field of meteorological and hydrological forecasting. In particular, the recursive neural network (RNN) model has shown its advantages in the processing of sequence models; and the long short-term memory model (LSTM) has also significantly improved the performance of recursive neural networks, which can effectively capture the dependencies between different positions in the sequence model. However, deep learning models usually require a large amount of labeled data for training. If there is only a small amount of labeled data, they will perform poorly or even fail. The amount of precipitation observation data at a single site of most meteorological stations cannot meet the requirements of the deep learning model for the number of training samples, which restricts the further application of deep neural networks in the field of precipitation forecasting. Summary of the invention

[0005] The present invention aims to solve one of the technical problems existing in the related art at least to a certain extent.

[0006] One object of the present invention is to provide a short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion, coupling a deep learning model with a nonlinear dynamic system model to improve the accuracy of daily precipitation forecasting under small sample conditions.

[0007] In order to achieve the above-mentioned purpose, the present invention provides a short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion, comprising:

[0008] S1. Use wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data and obtain characteristic components of different frequencies;

[0009] S2, expand the dimension of feature components based on phase space reconstruction method and reshape the original high-dimensional data feature space;

[0010] S3, using the Cao method to determine the optimal reconstruction dimension of the characteristic components and restore the chaotic attractor of each sequence;

[0011] S4, through the nonlinear dynamic system model, the spatiotemporal information is exchanged to map the information embedded in the non-delay attractor to the delay attractor of the target variable;

[0012] S5. Use the CNN-LSTM model to simulate the nonlinear mapping between non-delayed attractors and delayed attractors, integrate the spatiotemporal information, and obtain a coupled prediction model.

[0013] S6. Repeat embedding to form a prediction set of the target variable, select multiple random combinations to repeat the nonlinear mapping of step S5, form a prediction set of the target variable, and obtain the final prediction result of the coupled prediction model.

[0014] A further preferred technical solution of the present invention is that step S1 uses wavelet packet transformation to extract high-frequency and low-frequency signals of daily precipitation sequence data to obtain 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 wavelet packet transformation, and the corresponding frequency bands and spectra are adaptively selected according to the signal characteristics to obtain the characteristic component sequences of different frequencies in the daily precipitation sequence.

[0016] Wavelet packet transformation includes wavelet packet decomposition and wavelet packet reconstruction. Wavelet packet decomposition is expressed as:

[0017]

[0018] in, is the wavelet packet coefficient; j is the scale parameter, j∈{i,i-1,L,1}; l, k are the translation parameters; n is the frequency parameter, n∈{2 j -1,2 j -2,L,0};h k-2l , g k-2l They are respectively the low-pass and high-pass filters in wavelet packet decomposition;

[0019] Wavelet packet reconstruction is expressed as:

[0020]

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

[0022] Preferably, step S2 expands the dimension of the characteristic component based on the phase space reconstruction method to reshape the original high-dimensional data characteristic space; the specific method is:

[0023] The time series {x1,x2,…,x N} is embedded into a high-dimensional space for reconstruction, expressed as:

[0024] X=[x i ,x i+t ,…,x i+(d-1)t ];

[0025] Where d is the embedding dimension, t is the delay time, X is the reconstruction matrix, {x i ,i=1,2,…,N} is a time series.

[0026] Preferably, step S3 uses the Cao method to determine the optimal reconstruction dimension of the characteristic component and restore the chaotic attractor of each sequence; the specific method is:

[0027] S31. For each characteristic component of the time series, the distance between each point and its nearest neighbor is calculated in different embedding dimensions to determine the change of the nearest neighbor of the point in space in different dimensions, expressed as α(i,m), and the calculation formula is:

[0028]

[0029] Among them, x m (i) and is the i-th vector and its nearest point in the m-dimensional space, x m+1 (i) and is the i-th vector and its nearest point in the m+1 dimensional space, ||·|| represents the norm;

[0030] S32, gradually increase the embedding dimension and recalculate the nearest neighbor distance α(i,m);

[0031] S32. Calculate the mean value E(m) of α(i,m) and E1(m) used to represent the change of E(m); the calculation formulas of E(m) and E1(m) are:

[0032]

[0033] Where n represents the number of samples, m represents the dimension of the phase space, and τ represents the delay time. When E1(m) tends to be stable, the value of m is the optimal embedding dimension.

[0034] S33. Using the determined optimal embedding dimension, the phase space of the characteristic components is reconstructed to generate a high-dimensional representation of the chaotic attractor.

[0035] Preferably, step S4 exchanges spatiotemporal information through a nonlinear dynamic system model to map the information embedded in the non-delay attractor to the delay attractor of the target variable; the specific method is:

[0036] S41, constructing a delayed attractor and a non-delayed attractor of a high-dimensional system based on the chaotic attractor obtained in step S3 and the embedding theorem;

[0037] The delayed attractor is expressed as:

[0038] K=(x f (t),x f (t+τ),…,x f (t+(L-1)τ));

[0039] Where L is the dimension of the reconstructed attractor, τ is the delay time, and the delay attractor K is determined by the target variable x f (t) construct and make predictions based on delayed embedding theory;

[0040] The non-delayed attractor is expressed as:

[0041] O=(x i1 (t),x i2 (t),L,x ip (t));

[0042] Among them, O is a non-delayed attractor, {x ij ,j=1,2,L,p} is the time series of the original system.

[0043] S42. According to the embedding theorem, determine the reconstruction dimensions of the non-delayed attractor and the delayed attractor;

[0044] S43. Through the nonlinear dynamic system model, the information in the non-delay attractor is mapped to the delay attractor of the target variable.

[0045] Preferably, step S5 uses the CNN-LSTM model to simulate the nonlinear mapping between the non-delay attractor and the delay attractor, and integrates the spatiotemporal information to obtain a coupled prediction model; the specific method is:

[0046] 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;

[0047] S52. Using the generated training samples, based on the CNN-LSTM model, the nonlinear mapping relationship between non-delay attractors and delayed attractors is modeled and trained. The target variable x f The mapping predictor of (t) is expressed as:

[0048] x f (t+τ)=ψ(x i (t),x j (t),x k (t));

[0049] where ψ is the mapping between non-delayed and delayed attractors, x i (t), x j (t), x k (t) is a variable randomly selected from the time series of the original system.

[0050] Preferably, step S6 is repeated to embed a prediction set of the target variable, multiple random combinations are selected to repeat the nonlinear mapping of step S5 to form a prediction set of the target variable, and the final prediction result of the coupled prediction model is obtained; the specific method is:

[0051] S61, randomly selecting different variable combinations from the mapping relationship between the non-delay attractor and the delay attractor obtained in step S5, each combination representing a different prediction path;

[0052] S62. For each randomly selected variable combination, use the trained coupling model to repeatedly embed the target variable X s (t) prediction set

[0053] S63. Perform statistical analysis on the prediction set to extract the final prediction result.

[0054] Preferably, step S63 performs statistical analysis on the prediction set to extract the final prediction result, and the specific method is as follows:

[0055] Eliminate outliers that are outside the upper and lower quartiles of the prediction set;

[0056] Use the kernel function to fit the probability distribution of the prediction set and use the probability density function The expected value of is taken as the final prediction value, expressed as:

[0057]

[0058] Here, dx is the differential of the independent variable x.

[0059] Another aspect of the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, the computer instructions enabling a computer to execute the above-mentioned short-term daily precipitation forecasting method by integrating high-dimensional spatiotemporal information.

[0060] On the other hand, the present invention 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 calls the logic instructions in the memory to execute the above-mentioned high-dimensional spatiotemporal information fusion short-term daily precipitation forecasting method.

[0061] Beneficial effects: In view of the objective fact that the accuracy of traditional daily precipitation forecast models is relatively low, the present invention fully exploits the advantages of deep learning models and nonlinear dynamic system models, and proposes a short-term daily precipitation forecast method that integrates high-dimensional spatiotemporal information. Compared with existing deep learning model technology, the present invention only requires a small number of training samples to greatly improve the accuracy of short-term daily precipitation forecasts, and has greater reliability and application potential. Specifically, the present invention uses a deep learning model to extract the temporal feature information of a sequence, and a nonlinear dynamic system to extract the spatial correlation feature information between sequences, and couples the deep learning model and the nonlinear dynamic system model, making full use of the advantages of the two types of models, while extracting the temporal and spatial feature information of the precipitation sequence, and improving the accuracy of daily precipitation forecasts under small sample conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of the short-term daily precipitation forecasting method of the present invention with high-dimensional spatiotemporal information fusion;

[0063] Figure 2 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Dingbian Station obtained by the four models in Example 1;

[0064] Figure 3 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Guyuan Station obtained by the four models in Example 1;

[0065] Figure 4 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Huanxian Station obtained by the four models in Example 1;

[0066] Figure 5 A comparison chart of the daily precipitation forecast and observation values ​​of Pingliang Station obtained by the four models in Example 1;

[0067] Figure 6 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Wugong Station obtained by the four models in Example 1;

[0068] Figure 7A comparison chart of daily precipitation forecast values ​​and observed values ​​at Xifeng Station obtained by the four models in Example 1;

[0069] Figure 8 A comparison chart of daily precipitation forecast values ​​and observed values ​​at Yao County Station obtained by the four models in Example 1;

[0070] Fig. 9 This is a comparison chart of the daily precipitation forecast values ​​and observation values ​​of Changwu Station obtained by the four models in Example 1. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments 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 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.

[0072] Combine the following Figure 1-Figure 9 The present invention describes a short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion.

[0073] In order to solve the problem that the amount of precipitation observation data at a single site cannot meet the requirements of the deep learning model for the number of training samples. Some nonlinear dynamic system models have emerged. Nonlinear dynamic system models can capture the spatial interaction information between variables from a high-dimensional framework, and create a probability distribution of interaction information through mapping between non-delayed attractors and delayed attractors, converting the spatial information of high-dimensional data into future information of the target variable. Nonlinear dynamic systems can fully extract the spatial correlation feature information between meteorological and hydrological sequences at different sites, reduce the model's dependence on samples by expanding the dimension of samples, and achieve good forecasting results under high-dimensional small sample conditions.

[0074] In general, deep learning models can extract temporal feature information of sequences, and nonlinear dynamic systems can extract spatial correlation feature information between sequences. Therefore, if the deep learning model and the nonlinear dynamic system model can be coupled, and the advantages of the two types of models can be fully utilized, and the temporal and spatial feature information of the precipitation data sequence can be extracted at the same time, it must be a feasible way to improve the accuracy of daily precipitation forecast under small sample conditions. Based on this, a short-term daily precipitation forecast method with high-dimensional spatiotemporal information fusion is proposed in this application.

[0075] Before describing the technical solution of the present application in detail, some technical terms involved in the present application are first explained to facilitate understanding of the technical solution proposed in the present application.

[0076] 1. High-dimensional spatiotemporal information fusion: refers to integrating data from different sources and different time points (such as the spatial correlation between precipitation sequences at different meteorological stations and the temporal correlation information of precipitation sequences at the same station) to obtain more comprehensive analysis results.

[0077] 2. Short-term daily precipitation forecast: refers to the prediction of precipitation events in the upcoming short period of time (usually within 7 days).

[0078] 3. Wavelet packet decomposition: A signal processing technique used to decompose a signal into components of different frequencies for better analysis and processing.

[0079] 4. Phase space reconstruction: Based on time series data, the dynamic behavior of the system is reconstructed in a high-dimensional space by introducing time delays.

[0080] 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.

[0081] 6. Cao method: A method for determining the optimal embedding dimension of a time series by evaluating the changes in the nearest neighbors under different embedding dimensions.

[0082] 7. Nonlinear dynamic system model: A mathematical model that describes the nonlinear relationship of the system's evolution over time, often used in the study of chaos theory.

[0083] 8. Deep learning model (CNN-LSTM): A deep learning model that combines convolutional neural network (CNN) and long short-term memory network (LSTM), suitable for processing data with spatiotemporal dependencies.

[0084] 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 dynamic system model (NDM).

[0085] 10. Embedding dimension: In phase space reconstruction, the minimum dimension required to capture all the dynamic characteristics of the system.

[0086] 11. Delay attractor: An attractor constructed based on the target variable that reflects the behavior of the system over time.

[0087] 12. Non-delayed attractor: An attractor constructed based on the time series of the original system, reflecting the spatial behavior of the system.

[0088] 13. Kernel function: In statistical analysis, a type of function used to estimate probability density functions, such as the Gaussian kernel.

[0089] 14. Root mean square error (RMSE): A statistical indicator that measures the difference between the model's predicted values ​​and the actual observed values.

[0090] 15. Mean relative error (MAPE): measures the ratio of the forecast error to the actual value and is used to evaluate the accuracy of the forecast.

[0091] 16. Nash coefficient (NSE): A statistical indicator that measures the consistency between model predictions and actual observations.

[0092] 17. Correlation coefficient (R): A statistical indicator that measures the degree of linear correlation between two variables.

[0093] Embodiment 1: This embodiment provides a short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion, comprising:

[0094] S1. Use wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data and obtain characteristic components of different frequencies. The specific method is:

[0095] The high-frequency and low-frequency signals in the daily precipitation sequence data are extracted by wavelet packet transformation, and the corresponding frequency bands and spectra are adaptively selected according to the signal characteristics to obtain the characteristic component sequences of different frequencies in the daily precipitation sequence.

[0096] Wavelet packet transformation includes wavelet packet decomposition and wavelet packet reconstruction. Wavelet packet decomposition is expressed as:

[0097]

[0098] in, is the wavelet packet coefficient; j is the scale parameter, j∈{i,i-1,…,1}; l, k are the translation parameters; n is the frequency parameter, n∈{2 j -1,2 j -2,…,0};h k-2l , g k-2l They are respectively the low-pass and high-pass filters in wavelet packet decomposition;

[0099] Wavelet packet reconstruction is expressed as:

[0100]

[0101] in, is the wavelet packet coefficient after wavelet packet reconstruction; is the low-pass and high-pass filter bank after wavelet packet reconstruction; is the wavelet packet coefficient before reconstruction, obtained by the wavelet packet decomposition formula.

[0102] S2. Based on the phase space reconstruction method, the dimension of the feature component is expanded and the original high-dimensional data feature space is reshaped.

[0103] First, the core idea of ​​phase space reconstruction and Takens theorem are explained:

[0104] The core idea of ​​phase space reconstruction is to find a corresponding state point for each time point in a higher-dimensional space by selecting appropriate delay time and embedding dimension according to the information in the time series data. The trajectories between these state points can reflect the dynamic characteristics of the system, including chaotic behavior and attractor structure.

[0105] 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 {x1,x2,…,x N} is embedded into a high-dimensional space for reconstruction, expressed as:

[0106] X=[x i ,x i+t ,…,x i+(d-1)t ];

[0107] Where d is the embedding dimension, t is the delay time, X is the reconstruction matrix, {x i ,i=1,2,…,N} is a time series.

[0108] S3. Use Cao method to determine the optimal reconstruction dimension of characteristic components and restore the chaotic attractor of each sequence.

[0109] Cao's method can solve the problem of the false nearest neighbor method's sensitivity to noise and subjective interference. When the embedding dimension is small, the projection of the attractor in space and the points around the attractor form false nearest neighbor points. Therefore, the embedding dimension is continuously increased until there are no false nearest neighbor points, and the embedding dimension at this time is the optimal embedding dimension.

[0110] The specific method is:

[0111] S31. For each characteristic component of the time series, the distance between each point and its nearest neighbor is calculated in different embedding dimensions to determine the change of the nearest neighbor of the point in space in different dimensions, expressed as α(i,m), and the calculation formula is:

[0112]

[0113] Among them, x m (i) and is the i-th vector and its nearest point in the m-dimensional space, x m+1(i) and is the i-th vector and its nearest point in the m+1 dimensional space, ||·|| represents the norm;

[0114] S32, gradually increase the embedding dimension and recalculate the nearest neighbor distance α(i,m);

[0115] S32. Calculate the mean value E(m) of α(i,m) and E1(m) used to represent the change of E(m); the calculation formulas of E(m) and E1(m) are:

[0116]

[0117] Among them, n represents the number of samples, m represents the dimension of the phase space, and τ represents the delay time.

[0118] When E1(m) tends to be stable, the value of m is determined as the optimal embedding dimension;

[0119] When E1(m)=1, it means that the time series is a random signal, and the optimal embedding dimension can be determined only when E1(m)≠1.

[0120] S33. Using the determined optimal embedding dimension, the phase space of the characteristic components is reconstructed to generate a high-dimensional representation of the chaotic attractor.

[0121] S4. Through the nonlinear dynamic system model, the spatiotemporal information is exchanged to map the information embedded in the non-delay attractor to the delay attractor of the target variable. The specific method is:

[0122] S41, constructing a delayed attractor and a non-delayed attractor of a high-dimensional system based on the chaotic attractor obtained in step S3 and the embedding theorem;

[0123] First, the embedding theorem is explained:

[0124] Assume V is a compact manifold with dimension d. For (φ,h), φ:V→V smooth diffeomorphisms and h:V→smooth function pairs, the mapping is a general property, defined as follows:

[0125] ψ φ,h (X)=[h(X),h(φ(X)),…,h(φ L-1 (X))];

[0126] K=(x f (t),x f (t+τ),…,x f (t+(L-1)τ));

[0127] Where L is the dimension of the reconstructed attractor, τ is the delay time, and the delay attractor K is determined by the target variable xf (t) construct and make predictions based on delayed embedding theory;

[0128] The non-delayed attractor is expressed as:

[0129] O=(x i1 (t),x i2 (t),L,x ip (t));

[0130] Among them, O is a non-delayed attractor, {x ij ,j=1,2,L,p} is the time series of the original system.

[0131] S42. According to the embedding theorem, determine the reconstruction dimensions of the non-delayed attractor and the delayed attractor;

[0132] According to the embedding theorem, the dimension of the reconstructed attractor L is smaller than the dimension of the original system. The embedding theorem shows that the non-delay attractor reflects the spatial information and association 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, the reconstruction has a 3-dimensional delay attractor and a 3-dimensional non-delay attractor. The constructed delay attractor and non-delay attractor are as follows:

[0133] K=(x f (t),x f (t+τ),x f (t+2τ));

[0134] O=(x i (t),x j (t),x s (t));

[0135] where x i (t),x j (t),x s (t) is randomly drawn from the time series of the original system.

[0136] S43. Through the nonlinear dynamic system model, the information in the non-delay attractor is mapped to the delay attractor of the target variable.

[0137] S5. Use the CNN-LSTM model to simulate the nonlinear mapping between non-delayed attractors and delayed attractors, integrate the spatiotemporal information, and obtain a coupled prediction model.

[0138] The traditional nonlinear dynamic system model uses Gaussian process regression to describe the mapping relationship between non-delay attractors and delayed attractors. However, in high-dimensional space, Gaussian regression not only has the risk of overfitting, but also may capture the noise in the data rather than the real pattern when the number of samples is limited. Therefore, this embodiment uses a combined deep learning model (CNN-LSTM) to capture the complex nonlinear mapping relationship between non-delay attractors and delayed attractors. The generation process of the coupled prediction model (WPD-PSR-CL-NDM) training samples is:

[0139] 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;

[0140] S52. Using the generated training samples, based on the CNN-LSTM model, the nonlinear mapping relationship between non-delay attractors and delayed attractors is modeled and trained. The target variable x f The mapping predictor of (t) is expressed as:

[0141] x f (t+τ)=ψ(x i (t),x j (t),x k (t));

[0142] where ψ is the mapping between non-delayed and delayed attractors, x i (t), x j (t), x k (t) is randomly selected from the time series of the original system.

[0143] S6, repeat embedding to form a prediction set of the target variable, select multiple random combinations to repeat the nonlinear mapping of step S5, form a prediction set of the target variable, and obtain the final prediction result of the coupled prediction model; the specific method is:

[0144] S61, randomly selecting different variable combinations from the mapping relationship between the non-delay attractor and the delay attractor obtained in step S5, each combination representing a different prediction path;

[0145] S62. For each randomly selected variable combination, use the trained coupling model to repeatedly embed the target variable X s (t) prediction set

[0146] S63, performing statistical analysis on the prediction set and extracting the final prediction results, including:

[0147] Eliminate outliers that are outside the upper and lower quartiles of the prediction set;

[0148] Use the kernel function to fit the probability distribution of the prediction set and use the probability density function The expected value of is taken as the final prediction value, expressed as:

[0149]

[0150] Here, dx is the differential of the independent variable x.

[0151] In this embodiment, the daily precipitation forecast of eight meteorological stations, including Yaoxian, Xifeng, Wugong, Pingliang, Changwu, Huanxian, Guyuan and Dingbian, is taken as an example, and the coupling model (WPD-PSR-CL-NDM) constructed by the present invention is compared with three deep learning models: long short-term memory network (LSTM-Attention) with attention mechanism, temporal convolutional network (TCN), and convolutional gated recurrent unit (CNN-GRU) to verify the effectiveness and robustness of the method of this embodiment for short-term daily precipitation forecast. The daily precipitation data of the eight stations are derived from the China Meteorological Data Sharing Network. The specific method of applying the coupling model constructed by the present invention is as follows: first, a two-layer wavelet packet is used to divide the daily precipitation series of eight meteorological stations into four subsequences of [2,0], [2,1], [2,2] and [2,3], and the Cao method is used to determine the reconstruction dimension of each component when the time delay is 1; secondly, the Cao method is used to determine the reconstruction dimension of each component when the time delay is 1, and the phase space of each component is reconstructed to restore the chaotic attractor of its sequence; finally, the different components of the eight stations are substituted as input into the WPD-PSR-CL-NDM coupling forecasting model. In order to better test the effect of the WPD-PSR-CL-NDM coupled forecast model, two seven-day precipitation forecasts were conducted for the eight stations, and two training periods and two forecast periods were set. The setting details are as follows: the training periods of Yaoxian, Xifeng, Wugong, Pingliang and Changwu stations are from June 1, 2015 to August 23, 2017 and from June 1, 2017 to September 13, 2019, respectively, and the forecast periods are from June 1, 2017 to September 13, 2019, respectively. The training period for Huanxian, Guyuan and Dingbian stations was from June 24, 2015 to August 23, 2017 and from June 1, 2017 to August 21, 2019, respectively, and the forecast period was from August 24, 2017 to August 30, 2017 and from August 22, 2019 to August 28, 2019, respectively. The comparison results of daily precipitation forecast values ​​and observation values ​​at different stations in the two forecast periods are shown in Figure 2. Figures 2 to 9 shown.

[0152] Depend on Figures 2 to 9It can be seen that the forecasting effect of the WPD-PSR-CL-NDM model at the seven stations is significantly better than that of the LSTM-Attention, TCN and CNN-GRU models. At Yaoxian Station, the WPD-PSR-CL-NDM model forecasts the observed value of precipitation well and captures its trend well, while the TCN model performs poorly and fails to timely forecast the direction of sudden changes in precipitation, resulting in large forecast errors. At Xifeng Station, the LSTM-Attention model's forecast of daily precipitation from August 24, 2017 to August 30, 2017 shows a low forecast value. TCN and CNN-GRU are not sensitive enough to the sudden increase in precipitation and fail to timely forecast the precipitation change trend. At Wugong Station, all models were able to predict the trend of precipitation increase on August 29, 2017 in a timely manner, but after the peak of precipitation, the TCN and CNN-GRU models failed to fall back in time, which was seriously out of touch with reality and showed a large error; in the forecast from September 14, 2019 to September 20, 2019, the WPD-PSR-CL-NDM model was able to capture the changing trend of precipitation, with a smaller error than other models. At Pingliang Station, the forecast effect of the LSTM-Attention model was poor, and the forecasts of the TCN and CNN-GRU models on September 19, 2019 were opposite to the actual precipitation, with a very large forecast error. At Changwu Station, the mismeasurement errors of all models were reduced from August 24, 2017 to August 30, 2017. At Huanxian Station, the LSTM-Attention model performed poorly, especially on August 25, 2017, when its forecast was opposite to the observed value, which was seriously out of touch with reality. In the forecast on August 26, 2019, only the WPD-PSR-CL-NDM model correctly predicted the trend of increasing precipitation, while other models failed to accurately predict and presented a situation opposite to reality. At Guyuan Station, the precipitation fluctuations in Guyuan from August 24, 2017 to August 30, 2017 were large. On August 26, 2017 and August 27, 2019, the TCN and CNN-GRU models showed opposite forecasts for the observed values ​​and failed to accurately predict their trends. At Dingbian Station, the LSTM-Attention and TCN models showed large forecast errors, and the CNN-GRU model also showed a forecast value opposite to the observed value. In summary, the forecast performance of the WPD-PSR-CL-NDM model at the eight stations is better than that of the comparison model. It can effectively capture the trend of precipitation changes, shows excellent forecasting ability, and has high application value.

[0153] Furthermore, the forecast performance of LSTM-Attention, TCN, CNN-GRU and WPD-PSR-CL-NDM models at eight sites was evaluated by root mean square error (RMSE), mean relative error (MAPE), Nash coefficient (NSE) and correlation coefficient (R). The calculation results are shown in Tables 1 and 2.

[0154] Table 1 Evaluation index results of the four models at Pingliang, Xifeng, Changwu, Wugong and Yaoxian stations

[0155]

[0156] Table 2 Evaluation index results of the four models at Dingbian, Guyuan and Huanxian stations

[0157]

[0158] It can be seen from Tables 1 and 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 Pingliang Station, compared with LSTM-Attention, TCN and CNN-GRU, the RMSE value of the WPD-PSR-CL-NDM model decreased by 28.53% to 47.13%, and the MAPE value decreased by 60.14% to 99%. When the NSE values ​​of the TCN and CNN-GRU models were negative, the NSE value of the WPD-PSR-CL-NDM model fluctuated around 0.5, and the R value was much higher than that of the comparison model. At Xifeng Station, compared with LSTM-Attention, TCN and CNN-GRU, the RMSE value of the WPD-PSR-CL-NDM model improved by 4.18% to 51.25%, and the MAPE value improved by 15.5% to 77.82%. When the NSE values ​​of the comparison models were all negative, the NSE values ​​of the WPD-PSR-CL-NDM model were all positive, and the R values ​​were all greater than 0.5. At Changwu Station, compared with LSTM-Attention, TCN and CNN-GRU, the RMSE value of the WPD-PSR-CL-NDM model decreased by 11.87% to 40.38%, and the MAPE value decreased by 5.6% to 92.84%. In addition, during the forecast period of 2017.8.24 to 2017.8.30 at this station, the R value was as high as 0.96, and the forecast performance was excellent. At Wugong Station, the RMSE value of the WPD-PSR-CL-NDM model improved by 2.15% to 43.32%, and the MAPE value improved by 23% to 79.51%. At Yaoxian Station, the RMSE value of the WPD-PSR-CL-NDM model improved by 5.99% to 29.46%, and the MAPE value improved by 15.67% to 84.67%. At Dingbian Station, the RMSE value of the WPD-PSR-CL-NDM model improved by 30.21% to 64.93%, and the MAPE value improved by 26.38% to 89.1%. At Guyuan Station, the RMSE value of the WPD-PSR-CL-NDM model improved by 3.94% to 42.06%, and the MAPE value improved by 23.57% to 87.75%. At Huanxian Station, the RMSE value of the WPD-PSR-CL-NDM model improved by 35.74% to 49.85%, and the MAPE value improved by 0.8% to 90.8%.In the forecast results of eight stations from August 24, 2017 to August 30, 2017, the R value of the WPD-PSR-CL-NDM model forecast results fluctuated in the range of 0.6485 to 0.9634, and the NSE value fluctuated in the range of 0.2927 to 0.6559, which was much higher than other comparison models; in the forecast results from September 14, 2019 to September 20, 2019, the R value of the WPD-PSR-CL-NDM model forecast results fluctuated in the range of 0.5082 to 0.8931, and the NSE value fluctuated in the range of 0.2289 to 0.5357, which was much higher than other comparison models. In summary, the evaluation indicators of the WPD-PSR-CL-NDM model are significantly better than those of the comparison models, which can effectively solve the shortcomings of large forecast errors and low precision of the comparison models.

[0159] Comprehensive analysis of the evaluation index calculation results in Tables 1 and 2 shows that the forecasting effect of the WPD-PSR-CL-NDM model far exceeds that of other comparison models. The WPD-PSR-CL-NDM forecasting model established in the present invention forecasts the daily precipitation series for the first time without any auxiliary information, and obtains satisfactory forecasting results. Therefore, the organic fusion of spatiotemporal information based on deep learning and nonlinear dynamic systems can effectively improve the forecasting effect of daily precipitation, and has great application potential.

[0160] Embodiment 2: This embodiment provides a non-transitory computer-readable storage medium on which computer instructions are stored. The computer instructions enable a computer to execute a short-term daily precipitation forecasting method of high-dimensional spatiotemporal information fusion according to Embodiment 1.

[0161] Embodiment 3: This embodiment provides an electronic device, which may include: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus. The processor may call the logic instructions in the memory to execute a short-term daily precipitation forecasting method of high-dimensional spatiotemporal information fusion in Embodiment 1.

[0162] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0163] Embodiment 4: This embodiment provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a short-term daily precipitation forecasting method with high-dimensional spatiotemporal information fusion according to Embodiment 1.

[0164] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0165] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion, characterized in that: include: S1. Use wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data and obtain characteristic components of different frequencies; S2, expand the dimension of feature components based on phase space reconstruction method and reshape the original high-dimensional data feature space; S3, using the Cao method to determine the optimal reconstruction dimension of the characteristic components and restore the chaotic attractor of each sequence; S4, through the nonlinear dynamic system model, the spatiotemporal information is exchanged to map the information embedded in the non-delay attractor to the delay attractor of the target variable; S5. Use the CNN-LSTM model to simulate the nonlinear mapping between non-delayed attractors and delayed attractors, fuse the spatiotemporal information, and obtain a coupled prediction model. S6. Repeat embedding to form a prediction set of the target variable, select multiple random combinations to repeat the nonlinear mapping of step S5, form a prediction set of the target variable, and obtain the final prediction result of the coupled prediction model.

2. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 1 is characterized in that: Step S1 uses wavelet packet transform to extract high-frequency and low-frequency signals of daily precipitation sequence data to obtain characteristic components of different frequencies; The specific method is: The high-frequency and low-frequency signals in the daily precipitation sequence data are extracted by wavelet packet transformation, and the corresponding frequency bands and spectra are adaptively selected according to the signal characteristics to obtain the characteristic component sequences of different frequencies in the daily precipitation sequence. Wavelet packet transformation includes wavelet packet decomposition and wavelet packet reconstruction. Wavelet packet decomposition is expressed as: in, is the wavelet packet coefficient; j is the scale parameter, j∈{i,i-1,…,1}; l, k are the translation parameters; n is the frequency parameter, n∈{2 j -1,2 j -2,L,0};h k-2l , g k-2l They are respectively the low-pass and high-pass filters in wavelet packet decomposition; Wavelet packet reconstruction is expressed as: in, is the wavelet packet coefficient after wavelet packet reconstruction; is the low-pass and high-pass filter bank after wavelet packet reconstruction; is the wavelet packet coefficient before reconstruction, which is obtained by the wavelet packet decomposition formula.

3. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 1 is characterized in that: Step S2 expands the dimension of the feature component based on the phase space reconstruction method to reshape the original high-dimensional data feature space; The specific method is: The time series {x1,x2,…,x ％ } is embedded into a high-dimensional space for reconstruction, expressed as: X=[x ( ,x (+t ,L,x (+(+-1)t -; Where d is the embedding dimension, t is the delay time, X is the reconstruction matrix, {x ( ,i=1,2,L,N} is a time series.

4. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 1 is characterized in that: Step S3 uses the Cao method to determine the optimal reconstruction dimension of the characteristic component and restore the chaotic attractor of each sequence; the specific method is: S31. For each characteristic component of the time series, the distance between each point and its nearest neighbor is calculated in different embedding dimensions to determine the change of the nearest neighbor of the point in space in different dimensions, expressed as α(i,m), and the calculation formula is: Among them, x8(i) and is the i-th vector and its nearest point in the m-dimensional space, x 8+1 (i) and is the i-th vector and its nearest point in the m+1-dimensional space, ∥·∥ represents the norm; S32, gradually increase the embedding dimension and recalculate the nearest neighbor distance α(i,m); S32. Calculate the mean value E(m) of α(i,m) and E1(m) used to represent the change of E(m); the calculation formulas of E(m) and E1(m) are: Where n represents the number of samples, m represents the dimension of the phase space, and τ represents the delay time. When E1(m) tends to be stable, the value of m is the optimal embedding dimension. S33. Using the determined optimal embedding dimension, the phase space of the characteristic components is reconstructed to generate a high-dimensional representation of the chaotic attractor.

5. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 1 is characterized in that: Step S4 exchanges spatiotemporal information through a nonlinear dynamic system model, and maps the information embedded in the non-delay attractor to the delay attractor of the target variable; the specific method is: S41, constructing a delayed attractor and a non-delayed attractor of a high-dimensional system based on the chaotic attractor obtained in step S3 and the embedding theorem; The delayed attractor is expressed as: K=@x A (t),x A (t+τ),L,x A (t+(L-1)τ)C; Where L is the dimension of the reconstructed attractor, τ is the delay time, and the delay attractor K is determined by the target variable x A (t) construct and make predictions based on delayed embedding theory; The non-delayed attractor is expressed as: O=@x (1 (t),x (2 (t),L,x (E (t)C; Among them, O is a non-delayed attractor, {x (j ,j=1,2,L,p} is the time series of the original system. S42. According to the embedding theorem, determine the reconstruction dimensions of the non-delayed attractor and the delayed attractor; S43. Through the nonlinear dynamic system model, the information in the non-delay attractor is mapped to the delay attractor of the target variable.

6. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 5 is characterized in that: Step S5 uses the CNN-LSTM model to simulate the nonlinear mapping between the non-delay attractor and the delay attractor, and integrates the spatiotemporal information to obtain a coupled prediction model. The specific method is: 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; S52. Using the generated training samples, based on the CNN-LSTM model, the nonlinear mapping relationship between non-delay attractors and delayed attractors is modeled and trained. The target variable x A The mapping predictor of (t) is expressed as: x A (t+τ)=ψ@x ( (t),x j (t),x k (t)C; where ψ is the mapping between non-delayed and delayed attractors, x ( (t), x j (t), x k (t) is randomly selected from the time series of the original system.

7. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 6 is characterized in that: Step S6 repeats 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: S61, randomly selecting different variable combinations from the mapping relationship between the non-delay attractor and the delay attractor obtained in step S5, each combination representing a different prediction path; S62. For each randomly selected variable combination, use the trained coupling model to repeatedly embed the target variable X H (t) prediction set S63. Perform statistical analysis on the prediction set to extract the final prediction result.

8. The short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion according to claim 7 is characterized in that: Step S63 performs statistical analysis on the prediction set to extract the final prediction result. The specific method is as follows: Eliminate outliers that are outside the upper and lower quartiles of the prediction set; Use the kernel function to fit the probability distribution of the prediction set and use the probability density function The expected value of is taken as the final prediction value, expressed as: Here, dx is the differential of the independent variable x.

9. A non-transitory computer-readable storage medium having computer instructions stored thereon, the computer instructions enabling a computer to execute the short-term daily precipitation forecasting method based on high-dimensional spatiotemporal information fusion as described in any one of claims 1 to 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 communicate with each other via the communication bus, and the processor calls the logic instructions in the memory to execute the short-term daily precipitation forecasting method of high-dimensional spatiotemporal information fusion as described in any one of claims 1-8.

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