High-precision rainfall prediction method based on sfdl sequence feature decomposition and dendritic learning model

Abstract

The application provides a high-precision rainfall prediction method based on SFDL sequence feature decomposition and a dendritic learning model, through SFDL sequence feature decomposition technology, original rainfall time series data is accurately disassembled into a trend item, a seasonal item and a residual item, long-term change law, periodic fluctuation and irregular disturbance characteristics are captured respectively, hierarchical modeling of complex sequences is realized, for the residual item after decomposition, an improved dendritic learning model DNM is introduced, the bionic structure and multiplication unit characteristics of the model can efficiently fit nonlinear relationships, meanwhile, model parameters are optimized by combining a BP algorithm, the prediction ability for chaotic data is improved, the SFDL decomposition accuracy is optimized by local weighted regression LOESS, the original feature correlation of data is reserved, and the high-dimensional mapping effect of time series data is improved by adopting phase space reconstruction PSR preprocessing; through modular design, a decomposition-prediction-fusion process is integrated, the model structure is simplified, the calculation complexity is reduced, and the real-time prediction demand and the engineering deployment feasibility are considered.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence and time series analysis technology, specifically involving a high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model. Background Technology

[0002] Rainfall is a core meteorological factor reflecting regional climate characteristics and hydrological cycle. Its changing trend is directly related to flood control and drought relief scheduling, agricultural production planning, urban water conservancy project construction and ecological environment protection. Accurate rainfall prediction can not only provide government departments with a scientific basis for disaster prevention and mitigation decision-making, but also provide key support for agricultural irrigation, water resource allocation and geological disaster early warning. Therefore, researching high-precision and high-robust rainfall prediction methods has important practical significance and application value. However, the spatiotemporal variation of rainfall is affected by multiple factors such as atmospheric circulation, topography, water vapor transport and seasonal alternation, and exhibits significant nonlinear, non-stationary, chaotic and temporal fluctuation characteristics, which limits the modeling accuracy and adaptability of traditional prediction models under complex meteorological conditions.

[0003] In early research, traditional statistical models and classical learning models were the mainstream approaches for rainfall prediction. For example, prediction frameworks built based on statistical methods such as the Autoregressive Integral Moving Average (ARIMA) model and exponential smoothing model, while capable of capturing basic trends in stationary time series, lacked the ability to fit nonlinear fluctuations and chaotic characteristics of rainfall, making them ill-suited for extreme events such as sudden heavy rainfall. Researchers used Support Vector Machines (SVM) to construct rainfall-related prediction models, improving nonlinear fitting through kernel function mapping. However, SVM, as a small-sample learning method, has a complex mathematical model and low training efficiency when processing large-scale time series data. Furthermore, ZM... Yaseen et al. (2018) proposed a monthly rainfall prediction model that integrates ANFIS and the Firefly Optimization Algorithm. Although it has the potential to handle certain complex problems, it is prone to overfitting and getting stuck in local optima during training, and its stability is insufficient. It is worth noting that the Dendritic Neuron Model (DNM) has shown good potential in time series prediction, and the effectiveness of its learning algorithm has been verified. However, its application alone lacks targeted data preprocessing and is difficult to adapt to the complex time series characteristics of rainfall. On the other hand, the sequence decomposition method based on LOESS efficiently extracts trend and seasonal features, but it has not been combined with the dendritic model to form a dedicated solution for rainfall prediction.

[0004] With the development of artificial intelligence technology, deep learning models are widely used in rainfall prediction. For example, DHNguyen et al. (2021) improved the radar rainfall prediction method based on LSTM to enhance the time-dependent acquisition capability. However, LSTM has strict requirements on the amount of data, and its computational cost is high and convergence is slow in long-sequence scenarios. The Autoformer model proposed by HX Wu et al. (2021) performs well in time series prediction, but its MAPE index for rainfall prediction is poor, and the visualization and interpretability of the results are insufficient. Some studies combine CNN and LSTM to build hybrid models, which can jointly model multi-dimensional meteorological factors, but the structure is complex and the engineering deployment is difficult. Other studies use VMD and Elman networks to predict rainfall, but the decomposition method and the adaptability of rainfall time series characteristics still need to be improved. Although traditional numerical weather prediction (NWP) methods have a certain degree of interpretability, their accuracy and efficiency under complex meteorological conditions are difficult to meet the actual needs.

[0005] Despite some progress in existing research, there are still shortcomings: traditional statistical models and NWP methods are difficult to adapt to the chaotic characteristics and nonlinear fluctuations of rainfall, resulting in large prediction biases for extreme rainfall events; classic machine learning models have limited capacity for processing large-scale data, and dendritic models alone lack preprocessing support; deep learning models are often structurally complex and computationally expensive, making it difficult to meet the needs of real-time deployment; data preprocessing lacks specificity, existing decomposition methods are unable to simultaneously capture local fluctuations and long-term trends, and the models lack adaptability.

[0006] Therefore, addressing the shortcomings of existing rainfall forecasting methods in adapting to the chaotic characteristics of time series, separating multi-scale fluctuations, and balancing model efficiency and generalization ability, this study proposes a targeted improvement scheme: First, the maximum Lyapunov exponent and phase space reconstruction technique are introduced to transform chaotic time series into a phase space that explicitly expresses dynamic relationships, thereby enhancing the model's understanding of nonlinear fluctuations. Second, the STL seasonal-trend decomposition method is used to accurately decompose the original series into seasonal, trend, and residual components, achieving separate modeling of features at different time scales. Based on this, a simplified dendritic neuron (DL) model is constructed, significantly improving training efficiency while retaining its biomimetic and anti-overfitting characteristics. Finally, through the organic combination of STL and DL, a robust forecasting framework is formed that can adaptively extract the inherent patterns of multi-source meteorological data and possesses both forecast accuracy and cross-regional generalization ability. Summary of the Invention

[0007] The purpose of this invention is to provide a high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model, to solve the technical problem of rainfall prediction under complex conditions of multi-regional, multi-meteorological variable coupling and frequent extreme weather events. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model proposed in this invention is characterized by the following specific steps:

[0008] S1: Multi-source data acquisition and preprocessing. Hourly rainfall data from NCDC, ECMWF, GHCN, and NASA, along with auxiliary meteorological data, were collected to construct the original time series. Data filtering, chaotic characteristic verification, normalization, and outlier handling were performed. The original time series expression is as follows:

[0009]

[0010] Where T is the time step and C is the feature dimension.

[0011] S2: Phase space reconstruction. Set the reconstruction dimension m=2 and the time delay τ=1 to transform the preprocessed one-dimensional sequence into a high-dimensional input vector and target vector, making the hidden dependencies of the time series data explicit.

[0012] The input vector is:

[0013]

[0014] The target vector is:

[0015] Where M is the length of the reconstructed data.

[0016] S3: By combining the SFDL sequence feature decomposition algorithm with Locally Weighted Regression (LOESS), the time series data corresponding to the high-dimensional input vector is decomposed into trend terms. Seasonal items With residuals These correspond to long-term change patterns, periodic fluctuations, and irregular disturbances, respectively. Local weighted regression aims to minimize the weighted mean square error. Core parameters are used to adjust decomposition accuracy and preserve the original data characteristics and correlations. The optimal configuration of the LOESS core parameters was determined through multiple parameter combinations and the Friedman test. Neighborhood parameters... Adaptive adjustment rules are adopted. Take the distance from the target point The farthest indivual As weight boundaries Press at time Calculate the weight function parameters. Based on this dynamic determination, the tricube weights are... according to: The calculation involves setting a LOSS convergence threshold. LOESS smoothing stops when the difference between two adjacent iterations is less than this threshold, balancing decomposition accuracy and efficiency. The LOESS decomposition is only used to optimize the accuracy of the temporal decomposition; the residual terms after decomposition are not considered part of the final result. When inputting the DNM* model, the mean squared error (LOSS) of the BP algorithm is uniformly used for parameter optimization to ensure that the error is controllable throughout the process and that the parameters in the decomposition and prediction stages are coordinated.

[0017] S4: DNM * Dendritic Network Modeling and Component Fusion:

[0018] The residual term Rt obtained from SFDL decomposition is input into the improved dendritic neuron model DNM for nonlinear prediction. At the same time, targeted processing is performed on the seasonal term St and the trend term Tt. The calculation of each layer of DNM is performed according to the following logic:

[0019] The synaptic layer uses a linear activation function instead of the traditional Sigmoid function, calculated as follows:

[0020]

[0021] in For synaptic weights, For the threshold, Input features for the residual terms.

[0022] The branch layer performs a product operation on the output of the synaptic layer, using the following formula:

[0023] Where N is the number of input features.

[0024] The cell membrane layer directly outputs the branching layer results, that is:

[0025] The residual prediction results are obtained by activating the cell somatic layer using the Sigmoid function, and the formula is as follows:

[0026]

[0027] in For positive integers, The threshold of the cell body layer;

[0028] The backpropagation (BP) algorithm is used to optimize the parameters of the DNM model, with a learning rate η=0.01 and a loss function equal to the mean squared error between the predicted and actual values. The synaptic weights are iteratively updated using gradient descent. With threshold ;

[0029] In the processing and fusion of each component, the seasonal term St remains unchanged from its original decomposition, while the trend term Tt is fitted using a cubic continuous polynomial function with least squares, as shown in the formula:

[0030]

[0031] Where k, l, m, and n are the fitting parameters, which are solved by the least squares method;

[0032] residuals The above DNM model was used to predict the results. The final prediction result is the sum of the three components, namely:

[0033] ;

[0034] S5: Inverse normalization. Based on the min-max normalization transformation rule, inverse normalization is performed on the fused prediction results to restore the true rainfall scale.

[0035] Furthermore: In step 1, the chaotic characteristics verification uses the Wolf method to calculate the maximum Lyapunov exponent MLE of the sequence, and only sequences with MLE < 1 are selected for subsequent modeling to adapt to the chaotic characteristics of rainfall.

[0036] Furthermore: the normalization process in step 1 uses MATLAB's mapminmax function to perform min-max normalization, mapping the data to the [0,1] interval, and simultaneously records the transformation rules for inverse normalization, as shown in the following formula:

[0037] Where MIN and MAX are the minimum and maximum values ​​of the sequence x(t), respectively, and the transformation rules are recorded synchronously.

[0038] These are denoted as st1 and st2, and are used for inverse normalization.

[0039] Furthermore: In step 1, outlier handling combines the 3σ principle with meteorological background knowledge to eliminate outliers that exceed the reasonable range of 0~4 mm / min.

[0040] Furthermore, the inverse normalization in step 5 is achieved by using the mapminmax function to scale the normalized predicted values ​​back to the maximum value (MAX) and minimum value (MIN) of the original sequence, ensuring that the output results are consistent with the actual rainfall.

[0041] Furthermore, the multi-source data includes rainfall monitoring data from four authoritative meteorological data sources: NCDC, ECMWF, GHCN, and NASA. The dataset length is uniformly 600, and it is divided into 70% training set, 10% validation set, and 20% test set in chronological order.

[0042] Furthermore: In step S4, the optimal parameter combination for DNM was determined by screening 24 candidate parameters using a Friedman test. =1、 =1 and η=0.01 are the optimal parameter combinations.

[0043] Furthermore: the parameter update formula for the BP algorithm in step S4 is:

[0044]

[0045] Where k is the number of training rounds, , This represents the gradient change.

[0046] Furthermore: the specific expression for the loss function of DNM in step S4 is as follows:

[0047]

[0048] Where Tp is the actual value and Op is the predicted value.

[0049] Compared with existing technologies, this application has the following main technical advantages: By using SFDL sequence feature decomposition technology, the original rainfall time series data is accurately decomposed into trend terms, seasonal terms, and residual terms, respectively capturing long-term variation patterns, periodic fluctuations, and irregular disturbance characteristics, thus achieving hierarchical modeling of complex sequences; for the residual terms after decomposition, an improved dendritic learning model (DNM*) is introduced, whose biomimetic structure and multiplication unit characteristics can efficiently fit nonlinear relationships, while the BP algorithm is combined to optimize model parameters, improving the predictive ability for chaotic data;

[0050] The accuracy of SFDL decomposition is optimized by using Local Weighted Regression (LOESS) to preserve the original features and correlations of the data, and the high-dimensional mapping effect of time series data is improved by using Phase Space Reconstruction (PSR) preprocessing. The decomposition-prediction-fusion process is integrated through modular design, which simplifies the model structure and reduces the computational complexity, while taking into account the real-time prediction requirements and the feasibility of engineering deployment.

[0051] This invention can significantly improve the accuracy, anti-interference ability, and multi-regional adaptability of rainfall forecasting. It exhibits stronger generalization ability when facing the coupling of multiple meteorological variables, extreme rainfall events, and dynamic changes of different climate systems. Through this method, high-precision short-term and medium-term rainfall forecasts can be achieved, providing reliable technical support for flood control and drought relief scheduling, agricultural production planning, geological disaster early warning, and optimal allocation of water resources. It overcomes the problems of large prediction deviation, high computational cost, and insufficient capture of complex time series features in existing technologies. Attached Figure Description

[0052] Figure 1 This is a visualization of the prediction results of this invention;

[0053] Figure 2 This is a flowchart of the high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model of the present invention. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments. However, the present invention can be implemented in many different ways and should not be construed as limited to the embodiments shown; rather, these embodiments provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0055] Example 1, as Figure 1 As shown, a high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model is characterized by the following specific steps:

[0056] S1: Multi-source data acquisition and preprocessing. Hourly rainfall data and auxiliary meteorological data from NCDC, ECMWF, GHCN, and NASA were collected to construct the original time series. Data filtering, chaotic characteristic verification, normalization, and outlier handling were performed. The multi-source data included rainfall monitoring data from four authoritative meteorological data sources: NCDC, ECMWF, GHCN, and NASA. The dataset length was uniformly 600 bytes and divided into a 70% training set, a 10% validation set, and a 20% test set according to time sequence. Outlier handling combined the 3σ principle with meteorological background knowledge to remove outliers exceeding the reasonable range of 0~4 mm / min. The original time series expression is as follows:

[0057]

[0058] Where T is the time step and C is the feature dimension;

[0059] In step 1, the chaotic characteristics verification uses the Wolf method to calculate the maximum Lyapunov exponent MLE of the sequence, and only sequences with MLE < 1 are selected for subsequent modeling to adapt to the chaotic characteristics of rainfall.

[0060] The normalization process in step 1 uses MATLAB's mapminmax function to perform min-max normalization, mapping the data to the [0,1] interval, and simultaneously recording the transformation rules for inverse normalization, as shown in the following formula:

[0061] Where MIN and MAX are the minimum and maximum values ​​of the sequence x(t), respectively, and the transformation rules are recorded synchronously.

[0062] These are denoted as st1 and st2, and are used for inverse normalization;

[0063] S2: Phase space reconstruction. Set the reconstruction dimension m=2 and the time delay τ=1 to transform the preprocessed one-dimensional sequence into a high-dimensional input vector and target vector, making the hidden dependencies of the time series data explicit.

[0064] The input vector is:

[0065]

[0066] The target vector is:

[0067] Where M is the length of the reconstructed data;

[0068] S3: By combining the SFDL sequence feature decomposition algorithm with Locally Weighted Regression (LOESS), the time series data corresponding to the high-dimensional input vector is decomposed into trend terms. Seasonal items With residuals These correspond to long-term change patterns, periodic fluctuations, and irregular disturbances, respectively. Local weighted regression aims to minimize the weighted mean square error. Core parameters are used to adjust decomposition accuracy and preserve the original data characteristics and correlations. The optimal configuration of the LOESS core parameters was determined through multiple parameter combinations and the Friedman test. Neighborhood parameters... Adaptive adjustment rules are adopted. Take the distance from the target point The farthest indivual As weight boundaries Press at time Calculate the weight function parameters. Based on this dynamic determination, the tricube weights are... according to: The calculation involves setting a LOSS convergence threshold. LOESS smoothing stops when the difference between two adjacent iterations is less than this threshold, balancing decomposition accuracy and efficiency. The LOESS decomposition is only used to optimize the accuracy of the temporal decomposition; the residual terms after decomposition are not considered part of the final result. When inputting the DNM* model, the mean squared error (LOSS) of the BP algorithm is uniformly used for parameter optimization to ensure that the error is controllable throughout the process and that the parameters in the decomposition and prediction stages are coordinated.

[0069] S4: DNM * Dendritic Network Modeling and Component Fusion:

[0070] The residual term Rt obtained from SFDL decomposition is input into the improved dendritic neuron model DNM for nonlinear prediction. At the same time, targeted processing is performed on the seasonal term St and the trend term Tt. The calculation of each layer of DNM is performed according to the following logic:

[0071] The synaptic layer uses a linear activation function instead of the traditional Sigmoid function, calculated as follows:

[0072]

[0073] in For synaptic weights, For the threshold, Input features for the residual terms.

[0074] The branch layer performs a product operation on the output of the synaptic layer, using the following formula:

[0075] Where N is the number of input features.

[0076] The cell membrane layer directly outputs the branching layer results, that is:

[0077] The residual prediction results are obtained by activating the cell somatic layer using the Sigmoid function, and the formula is as follows:

[0078]

[0079] in For positive integers, The threshold of the cell body layer;

[0080] In step S4, the optimal parameter combination for DNM was determined by screening 24 candidate parameters using the Friedman test. =1、 =1 and η=0.01 are the optimal parameter combinations.

[0081] The backpropagation (BP) algorithm is used to optimize the parameters of the DNM model, with a learning rate η=0.01 and a loss function equal to the mean squared error between the predicted and actual values. The synaptic weights are iteratively updated using gradient descent. With threshold ;

[0082] The parameter update formula for the BP algorithm is:

[0083]

[0084] Where k is the number of training rounds, , This represents the gradient change.

[0085] The specific expression for the loss function of DNM is:

[0086]

[0087] Where Tp is the actual value and Op is the predicted value.

[0088] In the processing and fusion of each component, the seasonal term St remains unchanged from its original decomposition, while the trend term Tt is fitted using a cubic continuous polynomial function with least squares, as shown in the formula:

[0089]

[0090] Where k, l, m, and n are the fitting parameters, which are solved by the least squares method;

[0091] residuals The above DNM model was used to predict the results. The final prediction result is the sum of the three components, namely:

[0092] ;

[0093] S5: Inverse normalization, based on the min-max normalization transformation rule, performs inverse normalization operation on the fused prediction results to restore the true rainfall scale;

[0094] In step 5, the inverse normalization is achieved by using the mapminmax function to scale the normalized predicted values ​​back to the maximum value (MAX) and minimum value (MIN) of the original sequence, ensuring that the output results are consistent with the actual rainfall.

[0095] By adopting the above technical solution:

[0096] Considering the need for meteorological departments and related units to formulate resource allocation and risk prevention strategies in advance based on future rainfall trends in flood control and drought relief scheduling, agricultural production planning, and geological disaster early warning, this patent aims to utilize multi-source historical meteorological data to make high-precision predictions of future rainfall, with the optimization objective of minimizing prediction errors.

[0097] in, Represents the actual observed value. This represents the model's predicted value, where n is the total number of samples.

[0098] Hourly monitoring data from January 2015 to December 2018 were obtained from NCDC (National Climate Data Center), ECMWF (European Centre for Medium-Range Weather Forecasts), GHCN (Global Historical Climate Network), and NASA (National Aeronautics and Space Administration). The core feature was rainfall, with auxiliary meteorological features such as temperature, humidity, air pressure, and wind speed also included. The raw data underwent filtering; after retaining the core features, the length of each dataset was uniformly reduced to 600 bytes to remove redundant information. The Wolf method was used to calculate the maximum Lyapunov exponent (MLE) for each sequence, and only sequences with MLE < 1 were selected for subsequent modeling. To accommodate the chaotic nature of rainfall time-series data, min-max normalization was performed using the MATLAB `mapminmax` function, mapping the data to the [0,1] interval. The min-max normalization formula is as follows:

[0099]

[0100] Wherein, MIN and MAX are the minimum and maximum values ​​of the sequence x(t), respectively, and the synchronous recording transformation rules are denoted as st1 and st2;

[0101] To enhance the capture of temporal dependencies, perform phase space reconstruction (PSR), setting the reconstruction dimension m=2 and the time delay τ=1, and generate input and target vectors:

[0102] Phase Space Reconstruction (PSR) Input Vector Formula

[0103]

[0104] Formula for the target vector of phase space reconstruction (PSR):

[0105]

[0106] During the forecasting phase, the mapminmax function is used to perform inverse normalization to restore the true rainfall scale.

[0107] The STLDNM (STL-based Dendritic Neuron Model*) architecture is adopted, combining STL sequence decomposition with the improved dendritic neuron model DNM to achieve end-to-end prediction. The preprocessed sequence is decomposed into trend terms using the STL algorithm. Seasonal items With residuals The decomposition formula is:

[0108]

[0109] Among them, the seasonal term St remains unchanged from the original decomposition result; the trend term Tt is fitted using a cubic continuous polynomial function with least squares fitting, and the formula for fitting the cubic continuous polynomial of the trend term is:

[0110]

[0111] in, l, m, and n are the fitting parameters, which are obtained using the least squares method;

[0112] The residual term Rt is input into the DNM model for nonlinear prediction. The calculation process for each layer of the DNM is as follows: The synaptic layer uses a linear activation function, the formula of which is:

[0113]

[0114] The branch layer performs a product operation on the output of the synaptic layer, that is:

[0115]

[0116] The cell membrane layer directly outputs the branching layer results:

[0117]

[0118] The cell somatic layer is activated by the sigmoid function, as shown in the formula:

[0119]

[0120] The optimal parameter combination for verification is: =1、 =1.

[0121] The final prediction result is the sum of three components:

[0122]

[0123] Then, the Transformer encoder captures long-range dependencies and periodic patterns. Finally, the ADNM module performs nonlinear fusion and dynamic weighted response to output a global feature vector.

[0124] The DNM model was trained using the backpropagation (BP) algorithm with a learning rate η set to 0.01. The loss function was defined as the mean squared error (MSE) between the predicted and actual values. The formula for the BP algorithm's mean squared error (MSE) loss function is as follows:

[0125]

[0126] During training, synaptic weights are iteratively updated using gradient descent. With threshold The updated formula is:

[0127]

[0128]

[0129] Where k is the number of training rounds, , The gradient change was used to screen 24 candidate parameters using the Friedman test, and the final parameter was determined. =1、 =1 and η=0.01 are the optimal parameter combinations to ensure optimal model performance;

[0130] Each dataset was divided into 70% training set, 10% validation set, and 20% test set in chronological order to ensure consistency between training and testing. The experimental environment was MATLAB R2020a software, and the hardware configuration was Intel(R) Core(TM) i5-9500U 3.0GHz processor and 8GB memory. All comparison models MLPNN, ANFIS, Elman, SVR, and Autoformer used the same data preprocessing method, input and output dimensions, and number of training iterations to ensure fairness in the comparison.

[0131] The predictive performance of the models was evaluated using multi-dimensional metrics, and the above technical solutions were validated. Five mainstream time series prediction models were selected: Multilayer Perceptron Neural Network (MLPNN), Adaptive Neural Fuzzy Inference System (ANFISL), Support Vector Regression (SVR), Recurrent Neural Network (Elman), and Autoformer.

[0132] Specifically: Since there is currently no unified standard test set for rainfall prediction, this patent specifically selected rainfall monitoring data from four authoritative meteorological data sources—NCDC, ECMWF, GHCN, and NASA—as experimental samples, covering the complete period from 2015 to 2018. The data includes hourly rainfall records and corresponding meteorological characteristics. After screening, the length of each dataset was uniformly set to 600, covering different climate systems and regional characteristics, which can fully reflect the rainfall variation patterns under different geographical environments and climatic conditions. In terms of experimental setup, each dataset was divided into 70% training set, 10% validation set, and 20% test set in chronological order to ensure the consistency of model training and testing time. All comparison models adopted the same data normalization processing method, input window configuration based on phase space reconstruction PSR, embedding dimension 2, time delay 1, and prediction step size. They were trained under the same hardware environment—Intel(R) Core (TM) i5-9500U 3.0GHz, 8GB memory, and hyperparameter optimization standards—to ensure the fairness and repeatability of the comparison results.

[0133] To comprehensively evaluate the predictive performance of various models, this patent selects four key indicators: Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Nash Coefficient (NSE). MSE and MAE measure the absolute magnitude of prediction bias, MAPE reflects the relative proportion of prediction error, and NSE measures the statistical degree of model fit. By calculating these indicators on four major rainfall datasets, the prediction accuracy, stability, generalization ability, and computational efficiency of the method of this invention and mainstream models under multi-regional and multi-climatic conditions can be systematically evaluated.

[0134] Indicator 1: MSE:

[0135] (54)

[0136] Indicator 2: MAE

[0137] (55)

[0138] Indicator 3: MAPE:

[0139] (56)

[0140] Indicator 4: NSE:

[0141]

[0142] in The total number of samples, This is the actual value. These are predicted values.

[0143] The experimental results for the six models on each dataset are shown in Table 1:

[0144]

[0145] Table 1

[0146] As shown in Table 1, the STLDL model demonstrates significant advantages in rainfall prediction from four major meteorological data sources: NCDC, ECMWF, GHCN, and NASA, across the four core indicators of MSE, MAPE, MAE, and NSE. The error indices of MSE, MAPE, and MAE are all significantly lower than those of the comparative models such as MLPNN, ANFIS, and Elman, with MAPE remaining consistently low. The magnitude of the error is far superior to the higher error levels of other models; the NSE index is closer to 1 (reaching 0.920 on the GHCN dataset), reflecting a stronger correlation between the predicted and actual values. In comparison, the error indices of models such as MLPNN and ANFIS are generally high, and some models (such as ANFIS with negative NSE values ​​on the GHCN and NASA datasets) even struggle to effectively fit sequence features; while SVR performs close to STLDL in MSE on some datasets, its overall error index and stability are inferior to the former; Autoformer shows some performance in some MSE results, but its MAPE, NSE, and other indices are all inferior to STLDL, with a significant gap in overall performance. This confirms that STLDL has better prediction accuracy and stability across multiple data sources and multiple index dimensions, making it suitable for rainfall prediction needs under different climatic conditions.

[0147] In summary, the STLDL model proposed in this patent can effectively reduce prediction errors in complex non-stationary and chaotic rainfall time series, significantly improve prediction accuracy, stability and generalization ability, and provide reliable technical support for flood control and drought relief scheduling, agricultural production planning, urban water conservancy project construction and geological disaster early warning. It has good engineering application value and promotion significance.

[0148] The above embodiments illustrate only one implementation of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model, characterized in that, The specific steps are as follows: S1: Multi-source data acquisition and preprocessing. Hourly rainfall data from NCDC, ECMWF, GHCN, and NASA, along with auxiliary meteorological data, were collected to construct the original time series. Data filtering, chaotic characteristic verification, normalization, and outlier handling were performed. The original time series expression is as follows: Where T is the time step and C is the feature dimension; S2: Phase space reconstruction. Set the reconstruction dimension m=2 and the time delay τ=1 to transform the preprocessed one-dimensional sequence into a high-dimensional input vector and target vector, making the hidden dependencies of the time series data explicit. The input vector is: The target vector is: Where M is the length of the reconstructed data; S3: By combining the SFDL sequence feature decomposition algorithm with Locally Weighted Regression (LOESS), the time series data corresponding to the high-dimensional input vector is decomposed into trend terms. Seasonal items With residuals These correspond to long-term change patterns, periodic fluctuations, and irregular disturbances, respectively. Local weighted regression aims to minimize the weighted mean square error. Core parameters are used to adjust decomposition accuracy and preserve the original data characteristics and correlations. The optimal configuration of the LOESS core parameters was determined through multiple parameter combinations and the Friedman test. Neighborhood parameters... Adaptive adjustment rules are adopted. Take the distance from the target point The farthest indivual As weight boundaries Press at time Calculate the weight function parameters. Based on this dynamic determination, the tricube weights are... according to: The calculation involves setting a LOSS convergence threshold. LOESS smoothing stops when the difference between two adjacent iterations is less than this threshold, balancing decomposition accuracy and efficiency. The LOESS decomposition is only used to optimize the accuracy of the temporal decomposition; the residual terms after decomposition are not considered part of the final result. When inputting the DNM* model, the mean squared error (LOSS) of the BP algorithm is used for parameter optimization to ensure that the error is controllable throughout the process and that the parameters in the decomposition and prediction stages are coordinated. S4: DNM Dendritic Network Modeling and Component Fusion The residual term Rt obtained from SFDL decomposition is input into the improved dendritic neuron model DNM for nonlinear prediction. At the same time, targeted processing is performed on the seasonal term St and the trend term Tt. The calculation of each layer of DNM is performed according to the following logic: The synaptic layer uses a linear activation function instead of the traditional Sigmoid function, calculated as follows: in For synaptic weights, For the threshold, Input features for the residual terms; The branch layer performs a product operation on the output of the synaptic layer, using the following formula: Where N is the number of input features; The cell membrane layer directly outputs the branching layer results, that is: The residual prediction results are obtained by activating the cell somatic layer using the Sigmoid function, as shown in the formula: in For positive integers, The threshold of the cell body layer; The backpropagation (BP) algorithm is used to optimize the parameters of the DNM model, with a learning rate η=0.01 and a loss function equal to the mean squared error between the predicted and actual values. The synaptic weights are iteratively updated using gradient descent. With threshold ; In the processing and fusion of each component, the seasonal term St remains unchanged from its original decomposition, while the trend term Tt is fitted using a cubic continuous polynomial function with least squares, as shown in the formula: Where k, l, m, and n are the fitting parameters, which are solved by the least squares method; residuals The improved dendritic neuron (DNM) model was used for nonlinear prediction. To improve the adaptive accuracy and stability of the prediction results, the final fusion method was adjusted to a dynamic weighted fusion mechanism with error compensation added: based on the seasonal term. Trend items Fitted values ​​and residual terms Historical prediction errors of predicted values, adaptively allocated dynamic weights , , (The smaller the error, the greater the weight, satisfying...) + + = 1), and simultaneously introduce an error compensation term based on historical fusion bias. (Constructed by smoothing the error from the previous time step using exponential smoothing), the final prediction result is a combination of dynamic weighted fusion and error compensation, i.e. S5: Inverse normalization. Based on the min-max normalization transformation rule, inverse normalization is performed on the fused prediction results to restore the true rainfall scale.

2. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that, The chaotic characteristics verification in step 1 uses the Wolf method with embedding dimension = 2 and time delay = 1. The maximum Lyapunov exponent MLE of the sequence is calculated, and only sequences with MLE < 1 are selected for subsequent modeling to adapt to the chaotic characteristics of rainfall.

3. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that, The normalization process in step 1 uses MATLAB's mapminmax function to perform min-max normalization, mapping the data to the [0,1] interval, and simultaneously recording the transformation rules for inverse normalization, as shown in the formula below: Where MIN and MAX are the minimum and maximum values ​​of the sequence x(t), respectively, and the transformation rules are recorded synchronously. These are denoted as st1 and st2, and are used for inverse normalization.

4. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that, The outlier handling in step 1 combines the 3σ principle with meteorological background knowledge to remove outliers that exceed the reasonable range of 0~4 mm / min.

5. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that: In step 5, the inverse normalization is achieved by using the mapminmax function to scale the normalized predicted values ​​back to the maximum value (MAX) and minimum value (MIN) of the original sequence, ensuring that the output results are consistent with the actual rainfall.

6. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that: The multi-source data includes rainfall monitoring data from four authoritative meteorological data sources: NCDC, ECMWF, GHCN, and NASA. The dataset length is uniformly 600 bytes and is divided into 70% training set, 10% validation set, and 20% test set in chronological order.

7. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 1, characterized in that: In step S4, the optimal parameter combination for DNM was determined by screening 24 candidate parameters using the Friedman test. =1、 =1 and η=0.01 are the optimal parameter combinations.

8. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 7, characterized in that, The parameter update formula for the BP algorithm in step S4 is: Where k is the number of training rounds, , This represents the gradient change.

9. The high-precision rainfall prediction method based on SFDL sequence feature decomposition and dendritic learning model according to claim 8, characterized in that, The specific expression for the loss function of DNM in step S4 is as follows: Where Tp is the actual value and Op is the predicted value.

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