A Static Equilibrium Shoreline Prediction Method for Capes and Bays Based on CNN-BiLSTM

Abstract

This invention discloses a method for predicting the static equilibrium shoreline of headlands and bays based on CNN-BiLSTM, belonging to the fields of coastal engineering and remote sensing information. The method includes: acquiring remote sensing images, tidal and wave data, and constructing training and testing sample sets; establishing a polar coordinate system with the headland diffraction point as the origin, uniformly selecting feature points along the shoreline and calculating their parameters, and constructing a multi-dimensional feature system by correlating dynamic data; building a CNN-BiLSTM hybrid model, using CNN to extract spatial features between feature points and BiLSTM to capture the temporal evolution of the shoreline, and training and integrating the model; using SHAP value analysis to quantify the independent and interactive contributions of each dynamic factor and identify core influencing factors; and finally predicting the static equilibrium shoreline morphology based on measured data. This invention achieves high-precision and interpretable prediction of the equilibrium shoreline of headlands and bays, effectively revealing the mechanism of multi-dynamic coupling.

Description

Technical Field

[0001] This invention belongs to the field of coastal engineering and remote sensing information technology, and in particular relates to a method for predicting the static equilibrium shoreline of headlands and bays based on CNN-BiLSTM. Background Technology

[0002] In existing technologies, methods for predicting the static equilibrium shoreline of headlands and bays can be mainly divided into physical model methods, empirical formula methods, and traditional machine learning methods. Physical model methods simulate coastal dynamic processes by constructing physically scaled models, and their advantage lies in their clear physical meaning. Empirical formula methods, such as the Coastal Engineering Research Council (CERC) formulas, establish the correlation between shoreline changes and dynamic factors based on the statistical regularities of observed data, and are characterized by their ease of application. Traditional machine learning methods, such as Support Vector Machines (SVM) and Random Forests, can handle multi-dimensional coastal dynamic and morphological data, and to a certain extent improve the data-driven prediction capabilities.

[0003] However, all of the aforementioned existing technologies have significant drawbacks. Physical modeling methods are time-consuming and costly, and struggle to reproduce the complex coupling effects between multiple dynamic factors such as waves and tides in real-world environments. Empirical formula methods typically rely on specific geological and dynamic conditions, lacking universality and failing to effectively capture and predict the temporal evolution of shoreline morphology. While traditional machine learning methods can handle multi-factor data, their model architectures are weak in extracting temporally dependent features and struggle to clearly reveal and quantify the interaction contribution mechanisms between different dynamic factors, leading to ambiguous physical meanings in the prediction results and failing to meet the demands of high-precision design and analysis in coastal engineering. Furthermore, although recent research has applied deep learning models such as Convolutional Neural Networks (CNNs) or Long Short-Term Memory (LSTMs), these often use single models in isolation, failing to fully integrate the advantages of spatial feature extraction and bidirectional temporal dependency capture, thus remaining limited in prediction accuracy and mechanism interpretation. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a static equilibrium shoreline prediction method for headlands and bays based on CNN-BiLSTM, thereby resolving the issues present in the existing technologies.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for predicting static equilibrium shoreline of headlands and bays based on CNN-BiLSTM, comprising:

[0006] S1. Select a static equilibrium cape or bay, and collect remote sensing images, tidal data, and wave data; preprocess the remote sensing images and extract the annual coastline; calculate the annual average dynamic parameters based on the tidal data and the wave data; construct a dataset containing training samples and test samples.

[0007] S2. Establish a polar coordinate system with the headland diffraction point as the origin, transform the coastline of each year to the polar coordinate system, and uniformly select multiple feature points along each coastline; calculate the polar coordinates, length and angle parameters of each feature point, and associate them with the corresponding dynamic parameters to generate training and testing sets;

[0008] S3. Based on the parameters obtained in step S2, construct a multidimensional input feature system; use the relative rate of change of the length of the feature points as the target variable, and standardize the input and target data;

[0009] S4. Construct a hybrid model consisting of a convolutional neural network layer, a bidirectional long short-term memory network layer, and a fully connected layer; train the hybrid model using the training set to obtain the final prediction model;

[0010] S5. Based on the trained model, the SHAP value analysis method is used to calculate the independent contribution value and interaction contribution value of each dynamic parameter to identify the core dynamic factors;

[0011] S6. Input the measured shoreline and dynamic data into the final prediction model and output the static equilibrium shoreline prediction result.

[0012] Preferably, in step S1, the preprocessing of the remote sensing image includes radiometric calibration, atmospheric correction, geometric correction, study area cropping, and annual median composite; the tidal data is derived from a global tidal model, and the wave data is derived from wave reanalysis data.

[0013] Preferably, in step S2, the number of feature points selected uniformly is 20.

[0014] Preferably, in step S3, the multidimensional input feature system includes basic features, differential features, time-varying features, statistical features, smoothing features, and normalized features.

[0015] Preferably, the basic features include the length, angle, tidal range, wave height, wave direction, wave period, and cape opening direction of each feature point; the differential features are the length and angle differences between adjacent feature points; the time variation features are the annual average changes in the length and angle of the feature points; the statistical features are the statistics of the feature point length; the smoothing features are the multi-year rolling average of the feature point length; and the normalization features are parameters obtained by normalizing the length and dynamic parameters.

[0016] Preferably, in step S4, the convolutional neural network layer uses a one-dimensional convolutional kernel to extract spatial features between feature points; the bidirectional long short-term memory network layer uses a two-layer cascaded structure to capture temporal dependencies.

[0017] Preferably, the training process of the hybrid model employs the Huber loss function, the Adam optimizer, and introduces dropout layers, L1-L2 regularization, and dynamic learning rate adjustment strategies.

[0018] Preferably, in step S5, the formula for calculating the interaction contribution value is:

[0019] ;

[0020] in, It is the interaction contribution value of factors i and j. It is the total contribution value when i and j work together. It is the sum of the contributions of i and j acting independently.

[0021] Preferably, after step S6, an accuracy verification step is included, in which the prediction results are evaluated using mean absolute error, root mean square error, and coefficient of determination.

[0022] Secondly, the present invention also provides a CNN-BiLSTM-based static equilibrium shoreline prediction system for headlands and bays, comprising a data acquisition module, a preprocessing module, a feature engineering module, a model building and training module, a contribution analysis module, and a prediction output module connected in sequence, for implementing the method described in the first aspect.

[0023] Compared with the prior art, the present invention has the following advantages and technical effects:

[0024] This invention establishes a polar coordinate system with the headland diffraction point as the origin and selects feature points to transform complex shoreline morphology into structured data, laying the foundation for high-precision modeling. By constructing a CNN-BiLSTM hybrid model, the CNN layer is used to extract spatial correlation features between feature points, and the BiLSTM layer is used to effectively capture the long-term and short-term temporal dependencies of shoreline evolution, achieving deep fusion and collaborative prediction of spatiotemporal features, thereby significantly improving the prediction accuracy of balanced shoreline morphology. At the same time, by introducing the SHAP value analysis method, the independent and interactive contributions of each dynamic factor are quantified, giving the model prediction results a clear physical mechanism explanation.

[0025] To address the shortcomings of existing methods in quantifying the interactions between factors, this invention specifically employs the SHAP value analysis method. This method not only calculates the independent contribution value of a single factor, but also quantifies the interactive contribution value between any two dynamic factors (such as wave height and wave direction) through a formula. This allows for the identification of dominant factors and core synergistic factor pairs, clearly revealing the multi-dynamic coupling mechanism that influences the equilibrium shoreline morphology.

[0026] This invention enhances the universality of the method by constructing a training set based on long-term historical observation data from multiple regions, enabling the model to learn general laws that transcend the experience of specific regions. Through the design of the BiLSTM network, it can effectively learn and predict the dynamic process of the shoreline evolving towards an equilibrium state under dynamic action, overcoming the limitations of static empirical formulas.

[0027] This invention is driven by historical remote sensing and reanalysis data, and achieves rapid prediction through a trained hybrid model. It completely avoids the expensive construction and long experimental cycle required by physical model methods, and provides an efficient, economical and reliable technical means for engineering applications. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0029] Figure 1 This is a flowchart of the static equilibrium shoreline prediction method for headlands and bays based on CNN-BiLSTM, according to an embodiment of the present invention.

[0030] Figure 2 This is a fitting graph of the measured values ​​and predicted values ​​of the test set in an embodiment of the present invention;

[0031] Figure 3 This is a heatmap of the contribution matrix of the dynamic factor in an embodiment of the present invention. Detailed Implementation

[0032] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0034] Example 1

[0035] like Figure 1As shown, this embodiment provides a method for predicting static equilibrium shoreline of headlands and bays based on CNN-BiLSTM, including:

[0036] S1. Select a static equilibrium cape or bay, and collect remote sensing images, tidal data, and wave data; preprocess the remote sensing images and extract the annual coastline; calculate the annual average dynamic parameters based on the tidal data and the wave data; construct a dataset containing training samples and test samples.

[0037] Furthermore, in step S1, the preprocessing of the remote sensing image includes radiometric calibration, atmospheric correction, geometric correction, study area cropping, and annual median composite; the tidal data comes from a global tidal model, and the wave data comes from wave reanalysis data.

[0038] Specifically, step S1 includes:

[0039] S101. Data collection scope determination: Static equilibrium capes and bays that have been in a stable dynamic environment for a long time are selected as the research object to ensure that there is no interference from large-scale artificial coastal projects (such as breakwaters and land reclamation) in the study area, and that the evolution of the coastline is in a natural equilibrium state.

[0040] S102. Multi-source data acquisition: Remote sensing imagery, tidal data, and wave data of the study area were acquired. The remote sensing imagery used was Landsat series (Landsat5 / 7 / 8 / 9) satellite imagery with a spatial resolution of 30m and a temporal coverage of one scene per month. The tidal data used the TPXO9-atlas-v5 global tidal model with a spatial resolution of 0.1°×0.1°. The wave data used was EAR5 (wave reanalysis data developed by the European Centre for Medium-Range Weather Forecasts) with a temporal resolution of 6 hours, including parameters such as significant wave height, wave period, and wave direction.

[0041] S103. Remote sensing image preprocessing: The original remote sensing images are sequentially processed by radiometric calibration, atmospheric correction, study area cropping, band combination, and annual median composite. Among them, radiometric calibration uses the satellite's built-in calibration coefficients to convert the original brightness value (DN) of each pixel into apparent reflectance. Atmospheric correction uses the FLAASH model to eliminate the effects of atmospheric scattering and absorption. Study area cropping is based on the administrative division vector boundary. Band combination uses RGB (4 / 3 / 2) false color combination. Annual median composite is obtained by screening monthly images with cloud cover of less than 1% and calculating the annual median of each pixel to obtain cloud-free annual images.

[0042] S104. Shoreline Extraction and Vectorization: Based on the preprocessed annual remote sensing image, the coastline is extracted using object-oriented classification combined with edge detection algorithm. First, image objects are generated through multi-scale segmentation. Land and water are distinguished based on vegetation index (NDVI) and water body index (MNDWI). Then, Canny edge detection is used to extract the land-water boundary. After manual correction to eliminate noise, an annual coastline shapefile vector file is generated.

[0043] S105. Extraction of hydrodynamic parameters: Harmonic constants of 13 astronomical tidal constituents (M2, S2, N2, K2, K1, O1, P1, Q1, etc.) in the study area were extracted from the TPXO9-atlas-v5 model. Hourly tidal level data were reconstructed using tidal harmonic analysis methods, and the annual average tidal range was calculated. Hourly effective wave height, wave period, and wave direction data were extracted from EAR5 wave data. After quality control (outlier removal), the annual average values ​​were calculated to obtain the annual average wave height, wave period, and wave direction parameters.

[0044] S106. Sample set division: A dataset was constructed based on the number of study areas, and a total of 17 typical static equilibrium bays were selected, of which 12 were used as training samples and 5 were used as test samples; each sample contained annual coastline data and corresponding dynamic parameter data from 2004 to 2024.

[0045] S2. Establish a polar coordinate system with the headland diffraction point as the origin, transform the coastline of each year to the polar coordinate system, and uniformly select multiple feature points along each coastline; calculate the polar coordinates, length and angle parameters of each feature point, and associate them with the corresponding dynamic parameters to generate training and testing sets;

[0046] Furthermore, in step S2, the number of feature points selected uniformly is 20.

[0047] Specifically, step S2 includes:

[0048] S201. Establishment of polar coordinate system: With the diffraction point of the cape as the origin, establish a polar coordinate system (ρ, θ), where the polar radius ρ is the straight-line distance from the feature point to the origin, and the polar angle θ is the angle between the line connecting the feature point and the origin and the reference direction.

[0049] S202. Coastline Standardization Processing: Import the coastline shapefiles of each year into the CAD-3D platform, perform coordinate transformation based on the polar coordinate system to unify the coastlines of all years under the same coordinate system; use a spatial sampling algorithm to uniformly select 20 feature points along each coastline, and adaptively adjust the sampling interval according to the coastline length to ensure that the feature points can completely represent the morphological features of the coastline.

[0050] S203. Calculation of feature point parameters: Calculate the polar radius ρ and polar angle θ of each feature point, and obtain the length and angle parameters of each feature point by combining the shoreline extraction results; associate the dynamic parameters extracted in step (1), match the corresponding annual average tidal range, wave height, wave period and wave direction data for each feature point, and measure and record the headland opening direction parameters at the same time.

[0051] S204. Dataset Construction: Using the year as the time dimension and each feature point as the spatial dimension, the above parameters are integrated into structured data to generate training and test sets; the training set contains 5040 data points (12) × number of years (21) × number of feature points (20) and the test set contains 2100 data points (5) × number of years (21) × number of feature points (20).

[0052] S3. Based on the parameters obtained in step S2, construct a multidimensional input feature system; use the relative rate of change of the length of the feature points as the target variable, and standardize the input and target data;

[0053] Furthermore, in step S3, the multidimensional input feature system includes basic features, differential features, time-varying features, statistical features, smoothing features, and normalized features.

[0054] Furthermore, the basic features include the length, angle, tidal range, wave height, wave direction, wave period, and cape opening direction of each feature point; the differential features are the length and angle differences between adjacent feature points; the time variation features are the annual average changes in the length and angle of the feature points; the statistical features are the statistics of the feature point length; the smoothing features are the multi-year rolling average of the feature point length; and the normalization features are the parameters obtained by normalizing the length and dynamic parameters.

[0055] Specifically, step S3 includes:

[0056] S301. Feature System Construction: Construct an input feature system containing 6 types of features, as detailed below:

[0057] (1) Basic characteristics: including the length of monitoring point i (L1~L 20 (i=1~20), the angle of monitoring point i (A1~A) 20 The monitoring point i (i=1~20) contains 45 basic features, including the average tidal range, average significant wave height, wave direction, average wave period, and cape opening direction for the corresponding year. The length of monitoring point i provides basic length information, and the angle of monitoring point i reflects the direction of the coastline. The tidal range, wave height, wave direction, and wave period data are the hydrodynamic environmental parameters for the corresponding year, representing the introduced environmental influencing factors. The cape opening direction reflects the orientation of the coastline.

[0058] (2) Difference features: Calculate the length difference (length of the next feature point minus the length of the previous feature point, a total of 19 groups) and angle difference (angle of the next feature point minus the angle of the previous feature point, a total of 19 groups), for a total of 38 difference features;

[0059] (3) Time variation characteristics: Calculate the annual length variation (length of the current year minus the length of the previous year) and annual angle variation (angle of the current year minus the angle of the previous year) of each feature point, and take the average of the changes over the past 3 years as the feature, for a total of 40 time variation characteristics;

[0060] (4) Statistical characteristics: Calculate the length statistical parameters of 20 characteristic points, including the mean length, length standard deviation, maximum length, minimum length and length variation coefficient, a total of 5 statistical characteristics;

[0061] (5) Smoothing features: Calculate the 3-year rolling average of the length of each feature point (the average of the length of the current year, the previous year, and the previous two years), for a total of 20 smoothing features;

[0062] (6) Normalized features: Calculate the relative mean ratio of the length of each monitoring point (the length of a single feature point divided by the average length of all monitoring points in the year), and normalize the tidal range, wave height, and wave period (using minimum-maximum normalization to [0,1]), resulting in a total of 23 normalized features; the relative mean ratio of the length is the ratio of the length of a single monitoring point to the annual average length. Combined with the normalization of dynamic parameters, the influence of scale differences between different years and different monitoring points can be eliminated.

[0063] The above 6 categories of features total 45+38+40+5+20+23=171 input features.

[0064] S302. Target Variable Construction: The relative change rate of length of 20 feature points is used as the output target. The calculation method is: Relative change rate of length = (Length of feature points in the following year - Length of feature points in the current year) / (Length of feature points in the current year + 10) -8 This method converts absolute length changes into relative rates of change, eliminating the influence of differences in the order of magnitude of length between different feature points, while introducing a minimum value of 10 into the denominator. -8 To avoid division by zero errors and ensure computational stability.

[0065] S303. Data Standardization: The RobustScaler standardization method is used to preprocess the input features. This method eliminates the influence of outliers based on the quartile range. The formula is: Standardized data = (Original number - Median) / (Third quartile - First quartile). Independent RobustScaler instances are initialized for the input features (x) and the target variable (y) respectively. Standardization parameters are fitted based on their respective training set data to avoid data leakage and facilitate model training and result evaluation.

[0066] S4. Construct a hybrid model consisting of a convolutional neural network, a bidirectional long short-term memory network, and a fully connected layer; train the hybrid model using the training set to obtain the final prediction model;

[0067] Furthermore, in step S4, the convolutional neural network uses a one-dimensional convolutional kernel to extract spatial features between feature points; the bidirectional long short-term memory network uses a two-layer cascaded structure to capture temporal dependencies.

[0068] Furthermore, the training process of the hybrid model employs the Huber loss function and the Adam optimizer, and introduces dropout layers, L1-L2 regularization, and dynamic learning rate adjustment strategies.

[0069] Specifically, step S4 includes:

[0070] S401. Overall Model Architecture: A hybrid model consisting of an input layer, a spatial feature extraction module, a temporal feature extraction module, a fully connected output module, and a regularization layer is constructed. The model structure is as follows: Input layer → Convolutional neural network layer → Batch normalization layer → Dropout layer → Bidirectional long short-term memory network layer 1 → Batch normalization layer → Dropout layer → Bidirectional long short-term memory network layer 2 → Batch normalization layer → Dropout layer → Fully connected layer 1 → Batch normalization layer → Dropout layer → Output layer.

[0071] S402. Detailed design of each module;

[0072] (1) Input layer: The input data format is time series sample × time step × feature dimension, where the time series sample is the annual data sequence of each bay, the time step is set to 3 (using the data of the previous 3 years to predict the change rate of the 4th year), and the feature dimension is 171 (the number of input features constructed in step 3), that is, the input shape is (None, 3, 171).

[0073] (2) Spatial feature extraction module: A 1D convolutional layer is used to extract spatial correlation features between feature points. The kernel size is set to 3 (one-dimensional size, corresponding to the local window of the temporal / feature dimension), the kernel depth is 64, the activation function is ReLU function (to alleviate the gradient vanishing problem), and the padding method is all zero padding (to ensure that the input and output dimensions are consistent). After the output of the convolutional layer is processed by batch normalization (BatchNorm) (to accelerate training convergence), the Dropout layer (dropout rate 25%) is used to prevent overfitting.

[0074] (3) Temporal feature extraction module: A two-layer cascaded bidirectional long short-term memory network structure is used to capture temporal dependencies. The first layer BiLSTM has 128 units, and the activation function is the tanh function (to adapt to the nonlinear features of temporal data). The returned sequence is set to True (to provide temporal input for the next layer). After the output of the first layer is processed by BatchNorm and Dropout (dropout rate of 30%), it is input into the second layer BiLSTM. The second layer has 64 units, and the returned sequence is set to False (outputting global temporal features). Both layers of BiLSTM introduce L1-L2 regularization (first layer BiLSTM: L1 regularization coefficient 0.001, L2 regularization coefficient 0.001; second layer BiLSTM: L1 regularization coefficient 0.0005, L2 regularization coefficient 0.0005) and MaxNorm weight constraint (maximum value 3) to further suppress overfitting.

[0075] (4) Fully connected layer output module: The first fully connected layer has 32 neurons and the activation function is ReLU. After BatchNorm processing and Dropout (dropout rate of 20%), it is input into the second fully connected layer. The number of neurons in the output layer is 20 (corresponding to the change rate of 20 feature points). The tanh activation function is used to map the output to the [-1,1] interval, which matches the range of the standardized target variable.

[0076] S403. Model Compilation: The Adam optimizer is used, with an initial learning rate of 0.001. Gradient clipping (clipping value 1.0) is introduced to prevent gradient explosion. The monitoring metric is MAE. After training, MAE, RMSE, and R² (coefficient of determination) are used to comprehensively evaluate the model prediction results.

[0077] S404. Model Training: First, an early stopping strategy is used to monitor the validation set loss; if there is no decrease after 20 consecutive epochs, training is stopped and the optimal weights are restored. Second, a dynamic learning rate adjustment strategy is used to schedule the learning rate; if there is no decrease after 8 consecutive epochs, the learning rate is halved, with the minimum learning rate set to 10. -7 Third, the model is saved through a model checkpointing strategy, which saves the model weights with the minimum loss on the validation set during training.

[0078] S405. Model ensemble: A single model training is completed using independent training and test sets divided by coastline. During the prediction phase, the rate of change of 20 feature points is predicted 5 times repeatedly, and the average of each prediction result is taken as the final prediction output. This improves generalization ability and prediction stability by reducing the randomness of model prediction.

[0079] S5. Based on the trained model, the SHAP value analysis method is used to calculate the independent contribution value and interaction contribution value of each dynamic parameter to identify the core dynamic factors;

[0080] Specifically, step S5 includes:

[0081] S501. Screening of core dynamic factors: The annual average tidal range, annual average wave height, annual average wave direction, annual average wave period, and the direction of the cape opening were selected as core dynamic factors to analyze their influence mechanism on the rate of change of the shoreline.

[0082] S502. SHAP value calculation: Based on the trained ensemble model, the contribution of each dynamic factor is quantified by the SHAP (Shapley Additive ex Planations) value analysis method. The specific steps are as follows: (1) Construct a feature subset space and generate all possible feature combinations that include the target factor and exclude the target factor; (2) Calculate the model prediction value under each feature combination and compare the prediction difference when including and excluding the target factor; (3) Based on the Shapley value theory, calculate the independent contribution value of each dynamic factor according to the weight allocation of the feature subset (considering the size of the subset and the probability of occurrence).

[0083] S503. Calculation of Interaction Contribution Value: For any two dynamic factors, calculate their joint contribution value (using the SHAP value calculation method described above, treating the two factors as a whole feature), the formula is as follows:

[0084] ;

[0085] Interactive contribution value The larger the absolute value, the stronger the interaction.

[0086] S504. Core Factor Identification: Construct a factor contribution matrix based on independent contribution values ​​and interactive contribution values, and identify the dominant factor with the largest independent contribution value and the cooperating factor pair with the largest interactive contribution value; for example, if the independent contribution value of wave height is the largest, and the interactive contribution value between wave height and wave direction is the largest, then the dominant factor is wave height, and the core cooperating factor pair is wave height-wave direction.

[0087] S6. Input the measured shoreline and dynamic data into the final prediction model and output the static equilibrium shoreline prediction result.

[0088] Specifically, using the measured shoreline of the study area as input and combining it with dynamic data, the predicted shoreline change rate is obtained. Then, the predicted shoreline morphology is converted into a shapefile (shp) in a latitude and longitude coordinate system, and the characteristic parameters of the static equilibrium shoreline (length, angle, and coordinates of 20 feature points) and the contribution matrix of dynamic factors are output, providing complete data support for engineering applications.

[0089] S7. Model accuracy verification:

[0090] The prediction results were validated using measured shoreline data from 2024 on 5 test samples. Validation metrics included MAE (mean absolute error), RMSE (root mean square error), and R² (coefficient of determination). Simultaneously, a visualization method was used to compare the morphological differences between the predicted and measured shorelines, calculating the relative errors of morphological parameters such as shoreline length and tortuosity to comprehensively evaluate the prediction accuracy.

[0091] This embodiment provides a CNN-BiLSTM-based method for predicting static equilibrium shorelines in headlands and bays. By integrating CNN spatial feature extraction with BiLSTM's temporal dependency capture capabilities and combining it with SHAP dynamic factor contribution quantification, it achieves high-precision static equilibrium shoreline prediction, providing reliable technical support for coastal engineering practices.

[0092] Example 2

[0093] This embodiment takes typical capes and bays of Hainan Island (Qian'an Bay coast and Zhuwan coast) as the research object and implements the method described in Embodiment 1, including:

[0094] S1. Data Acquisition and Sample Construction: Landsat series images were collected during the study period, and the annual coastline was extracted after standardization preprocessing; tidal data were extracted from the TPXO9-atlas-v5 model, and the annual average tidal range was calculated (within the normal moderate tidal range range of the region); wave parameters were extracted from ECMWF data, and the annual average wave height, average wave period, and wave direction all conformed to the perennial hydrodynamic environment characteristics of the study area; a dataset of similar bays in Hainan Island was constructed, and it was divided into training and test sets at an 8:2 ratio, with the Qian'anhai coast and Zhuwan coast as independent validation samples.

[0095] S2. Data preprocessing: Establish a polar coordinate system with the headland diffraction point as the origin, select 20 feature points evenly according to the shoreline shape, and calculate the polar radius, polar angle, length and angle parameters of each feature point.

[0096] S3. Feature Engineering: Construct a 171-dimensional input feature system according to the invention steps, with the target variable being the relative rate of change of feature point length; use RobustScaler to standardize the data to eliminate the influence of outliers.

[0097] S4. Model Training: The CNN-BiLSTM model with the structure described in Example 1 was built and trained. After model integration, the validation set MAE was within the high accuracy range required by the project, the coefficient of determination (R²) was excellent, and the model fit was good. Figure 2 The fit between the predicted and measured values ​​of the test set is shown.

[0098] S5. Contribution Analysis: SHAP value analysis shows that the independent contribution value of wave height is the largest (as the dominant factor), and the interaction contribution value between wave height and wave period is the largest (as the core synergistic factor pair), clarifying the mechanism of action of the dynamic factor. Figure 3 Heatmap of the contribution matrix of the dynamic factor.

[0099] S6. Equilibrium Shoreline Output: Using measured shoreline and dynamic data as input values, the static equilibrium shoreline position is output after model prediction.

[0100] This invention conducted multiple sets of comparative experiments. In these experiments, CNN, LSTM, and BiLSTM models were introduced for testing, and the performance of each model was analyzed to verify the effectiveness of the proposed model in improving prediction performance.

[0101] The comparative experimental results are shown in Table 1. In the prediction results of the CNN model, the MAE value is 2.53 and the RMSE value is 2.76. Although CNN can efficiently extract local spatial features, it cannot effectively model temporal dependencies in the data. For prediction tasks with temporal features, its ability to capture data patterns is insufficient, ultimately resulting in a large prediction error. In the prediction results of the LSTM model, the MAE value is 2.49 and the RMSE value is 2.71. The LSTM model outperforms CNN, demonstrating good modeling ability for the contextual relationships in temporal data and capturing both long-term and short-term dependencies. However, it lacks the ability to accurately extract local features, leading to a still relatively large overall prediction error. In the prediction results of the BiLSTM model, the MAE value is 2.47 and the RMSE value is 2.68. Although the BiLSTM model outperforms CNN and LSTM in prediction performance, its effect on extracting local features from the data is still unsatisfactory. In the prediction results of the CNN-BILSTM combined model, the MAE value is 2.13 and the RMSE value is 2.29, significantly outperforming the above three models. CNN excels at extracting local spatial features from data, while BiLSTM effectively captures temporal dependencies in data. The fusion of the two achieves complementarity between feature extraction and dependency capture capabilities, taking into account both local detail feature extraction and dependency capture. Therefore, it has the smallest prediction error on the test set, while exhibiting the best generalization performance and prediction accuracy.

[0102] Table 1

[0103] Model Test set mean absolute error / m Test set root mean square error / m CNN 2.53 2.76 LSTM 2.49 2.71 BiLSTM 2.47 2.68 This invention 2.13 2.29

[0104] Example 3

[0105] Based on the same inventive concept, this embodiment provides a headland static equilibrium shoreline prediction system based on CNN-BiLSTM, including a data acquisition module, a preprocessing module, a feature engineering module, a model building and training module, a contribution analysis module, and a prediction output module connected in sequence, for implementing the method described in Embodiment 1.

[0106] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting static equilibrium shoreline of headlands and bays based on CNN-BiLSTM, characterized in that, Includes the following steps: S1. Select a static equilibrium cape or bay, and collect remote sensing images, tidal data, and wave data; preprocess the remote sensing images and extract the annual coastline; calculate the annual average dynamic parameters based on the tidal data and the wave data; construct a dataset containing training samples and test samples. S2. Establish a polar coordinate system with the headland diffraction point as the origin, transform the coastline of each year to the polar coordinate system, and uniformly select multiple feature points along each coastline; calculate the polar coordinates, length and angle parameters of each feature point, and associate them with the corresponding dynamic parameters to generate training and testing sets; S3. Based on the parameters obtained in step S2, construct a multidimensional input feature system; use the relative rate of change of the length of the feature points as the target variable, and standardize the input and target data; S4. Construct a hybrid model consisting of a convolutional neural network layer, a bidirectional long short-term memory network layer, and a fully connected layer; train the hybrid model using the training set to obtain the final prediction model; S5. Based on the trained model, the SHAP value analysis method is used to calculate the independent contribution value and interaction contribution value of each dynamic parameter to identify the core dynamic factors; S6. Input the measured shoreline and dynamic data into the final prediction model and output the static equilibrium shoreline prediction result.

2. The method according to claim 1, characterized in that, In step S1, the preprocessing of the remote sensing image includes radiometric calibration, atmospheric correction, geometric correction, study area cropping, and annual median composite; the tidal data comes from a global tidal model, and the wave data comes from wave reanalysis data.

3. The method according to claim 1, characterized in that, In step S2, 20 feature points are selected uniformly.

4. The method according to claim 1, characterized in that, In step S3, the multidimensional input feature system includes basic features, differential features, time-varying features, statistical features, smoothing features, and normalized features.

5. The method according to claim 4, characterized in that, The basic features include the length, angle, tidal range, wave height, wave direction, wave period, and cape opening direction of each feature point; the differential features are the length and angle differences between adjacent feature points; the time variation features are the annual average changes in the length and angle of the feature points; the statistical features are the statistics of the feature point length; the smoothing features are the multi-year rolling average of the feature point length; and the normalization features are the parameters obtained by normalizing the length and dynamic parameters.

6. The method according to claim 1, characterized in that, In step S4, the convolutional neural network layer uses a one-dimensional convolutional kernel to extract spatial features between feature points; the bidirectional long short-term memory network layer uses a two-layer cascaded structure to capture temporal dependencies.

7. The method according to claim 6, characterized in that, The training process of the hybrid model employs the Huber loss function and the Adam optimizer, and introduces dropout layers, L1-L2 regularization, and dynamic learning rate adjustment strategies.

8. The method according to claim 1, characterized in that, In step S5, the formula for calculating the interaction contribution value is: ； in, It is the interaction contribution value of factors i and j. It is the total contribution value when i and j work together. It is the sum of the contributions of i and j acting independently.

9. The method according to claim 1, characterized in that, Step S6 is followed by an accuracy verification step, which uses mean absolute error, root mean square error and coefficient of determination to evaluate the prediction results.

10. A static equilibrium shoreline prediction system for headlands and bays based on CNN-BiLSTM, characterized in that, It includes a data acquisition module, a preprocessing module, a feature engineering module, a model building and training module, a contribution analysis module, and a prediction output module connected in sequence, for implementing the method as described in any one of claims 1-9.

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