Method for predicting submarine slope instability under submarine groundwater discharge based on bayesian-cnn

Abstract

This invention provides a Bayesian-CNN-based method for predicting seabed slope instability under the influence of seabed groundwater drainage, belonging to the field of marine engineering geology. Addressing the difficulty of existing models in quantifying the nonlinear dynamic evolution of slope instability under the coupled effects of seabed groundwater drainage (SGD) and multiple factors such as waves, this invention constructs a multi-parameter dataset including water depth, wave height, wave period, salinity, turbidity, SGD rate, and erosion depth through in-situ observations. A safety factor Fs is calibrated using a fluid-structure interaction mechanism as a supervisory label. The feature vectors are reconstructed into 3×3 matrices and input into a convolutional neural network. Bayesian optimization is introduced to automatically adjust hyperparameters, and 3×1 convolutional kernels are used to extract features. Probabilistic prediction is achieved through Dropout layers and Monte Carlo sampling to quantify uncertainty. A weighted mechanism for key time periods is introduced into the loss function to enhance the identification of critical instability states. This invention achieves high-precision prediction, providing reliable support for marine engineering geological environment assessment.

Description

Technical Field

[0001] This invention relates to the fields of marine engineering geology and marine observation technology, and more specifically, to a method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN. Background Technology

[0002] Submarine groundwater discharge (SGD), a crucial process in the interaction between land and sea water, induces seepage effects that alter the stress state of the seabed, thus impacting submarine slope stability. Current mainstream research on submarine slope instability primarily focuses on near-bottom shear stress models generated by the combined hydrodynamic interactions of waves, seabed, and slope, as well as Newmark block models induced by seismic activity. However, existing models do not incorporate the dynamic impact of SGD on sediment transport, and particularly lack the ability to accurately predict slope instability under extreme hydrodynamic conditions. Recent studies indicate that the seepage intensity generated by SGD can reach 3-5 times that of wave-induced seepage, and the resulting vertical seepage uplift force can directly weaken the structural stability of surface sediments.

[0003] The Yellow River underwater delta in China, a typical active SGD (Self-Growth Depression) area, exhibits measured discharge fluxes of 0.5–3.2 m³ / (m·d) and seepage rates ranging from 2.5–15.6 cm / d, displaying significant spatiotemporal heterogeneity. In-situ observations conducted by our team in the Gudong sea area in April–May 2024 confirmed a significant positive correlation between SGD flux and seabed slope instability. However, due to limitations in seabed environmental monitoring technology, existing observation methods struggle to achieve long-term, large-scale, real-time monitoring of the instability process, making it difficult to accurately monitor key periods of slope instability. Traditional physical models suffer from low computational efficiency when dealing with the multi-field coupling of SGD seepage, wave loads, and dynamic seabed topography evolution, and are unable to describe the stochastic uncertainties of the seabed environment with a single deterministic numerical value. Therefore, a deep learning prediction model capable of integrating multi-source dynamic observation data and providing an assessment of instability risk probability is urgently needed.

[0004] To address the aforementioned technical bottlenecks, this study proposes a novel paradigm for predicting seafloor slope instability based on deep learning. By integrating the hyperparameter optimization capabilities of the Bayesian optimizer with the accuracy of probabilistic predictions from CNN neural networks, a dynamic prediction model for seafloor slope instability under SGD-dominated architecture can be effectively established. This method avoids the parameter sensitivity issues of traditional models and overcomes the spatiotemporal limitations of in-situ observations, providing new methodological support for the assessment of seafloor engineering geological environments. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN.

[0006] This invention is achieved through the following technical solution: a prediction method for seafloor slope instability under the action of seafloor groundwater discharge based on Bayesian-CNN, specifically including the following steps:

[0007] S1. Multi-parameter coupled observation and dataset construction:

[0008] Data on various seabed environmental parameters, including water depth, wave height, wave period, salinity, turbidity, SGD rate, and erosion depth, were collected through in-situ observations and a dataset was constructed.

[0009] S2. Calibration of the safety index Fs of the seabed slope based on the fluid-structure interaction mechanism:

[0010] Using the raw data collected in step S1, based on fluid-structure interaction theory, upward seepage force generated by SGD, cumulative effect of excess pore water pressure, and dynamic erosion feedback of the seabed, the slope safety factor Fs is calculated and calibrated using the limit equilibrium criterion, and a tag set is constructed.

[0011] S3. Data import and preprocessing, reconstruction and sample space partitioning:

[0012] The data obtained in steps S1 and S2 are imported and cleaned, smoothed, and standardized. Simultaneously, the one-dimensional feature vectors are reconstructed into two-dimensional matrices to adapt to the structural characteristics of the convolutional neural network. Finally, the 1000 sample sets are divided into training and validation sets in a 7:3 ratio.

[0013] S4, Bayesian-CNN Neural Network Model Construction:

[0014] The network structure includes a multi-scale feature extraction layer, a regularization module, a Bayesian random deactivation layer, and a regression output layer. A weighted loss function is introduced to enhance sensitivity to unstable critical states. Hyperparameters are automatically tuned through Bayesian optimization to improve the model's generalization ability and robustness in complex marine environments.

[0015] S5, Bayesian-CNN Neural Network Training:

[0016] S5-1, Training Strategy Configuration and Model Learning:

[0017] The neural network model constructed in step S4 is integrated and trained using the 700 sets of training samples divided in step S3.

[0018] S5-2, Implementation of Probabilistic Prediction Based on Monte Carlo Sampling

[0019] To overcome the problem that traditional deterministic neural networks have difficulty quantifying the randomness of the marine environment, this embodiment adopts a Monte Carlo sampling strategy when using 300 sets of data in the model prediction validation set;

[0020] S6. Prediction and Result Evaluation:

[0021] The model trained in step S5 is used to predict the safety factor of the test samples. This is achieved by evaluating overall error metrics such as root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. To evaluate the predictive performance of the model.

[0022] As a preferred option, step S1 specifically includes the following steps:

[0023] S1-1, Coupling effect of factors influencing submarine groundwater discharge:

[0024] Water depth D directly affects the discharge intensity of SGD by altering the hydraulic gradient between groundwater and seawater; the average seepage velocity of groundwater in sediments is expressed as:

[0025] ;

[0026] In the formula: The equivalent seepage velocity of seabed groundwater discharge is given in m / s; K is the permeability coefficient of seabed sediments in m / s. D is the head height of the terrestrial freshwater (m); D is the water depth (m). The density is that of fresh water. is the density of seawater; L is the equivalent flow path length (m) of groundwater from its land source to its discharge point.

[0027] As waves propagate near the shore, the alternating wave crests and troughs create periodic pressure disturbances on the seabed surface, resulting in a pumping effect on pore water. The wave-induced instantaneous additional pressure is expressed as:

[0028] ;

[0029] In the formula: Wave-induced pressure (Pa); : Gravitational acceleration (m / s²) Let m be the wave height, and take the significant wave height. or maximum wave height ; For wave number, satisfying ; The wavelength is m; Angular frequency, ; The wave period is s; The vertical height (m) above the seabed surface; These are the horizontal position coordinates;

[0030] The wave period further influences the pressure attenuation depth by controlling the wavelength, and this relationship is determined by the dispersion relation:

[0031] ;

[0032] In the formula: Wavelength (m); wave period (s); water depth (m);

[0033] The safety stability coefficient for submarine slope instability under SGD is a function driven by multiple parameters:

[0034] ;

[0035] By constructing a neural network, the safety stability coefficient of the seabed slope is predicted from the complex background of multi-parameter coupling.

[0036] S1-2, In-situ observation and dataset construction:

[0037] We obtained hydrodynamic parameters, pore water pressure, submarine groundwater discharge parameters, and seabed erosion depth for the study area. We also obtained datasets for training and testing the models, including: water depth D and significant wave height. Effective wave period , maximum wave height Maximum wave period Salinity (S), Turbidity SGD rate erosion depth ;

[0038] Calculation of groundwater discharge rate based on pore water pressure signal decomposition:

[0039] The collected pore water pressure sequence Perform wavelet transform:

[0040] ;

[0041] In the formula: These are the wavelet transform coefficients; For scale Translation The mother wavelet function; by reconstructing the wavelet scale, the pore water pressure signal is decomposed into high-frequency, short-period wave action components; low-frequency, long-period tidal action components; and the remaining groundwater runoff background components.

[0042] Based on the decomposed pore water pressure components, groundwater discharge rates corresponding to different dynamic mechanisms were calculated and uniformly converted into daily discharge rates per unit shoreline length; the total seafloor groundwater discharge rate was also calculated. Expressed as:

[0043] ;

[0044] In the formula: The total amount of subsea groundwater discharged per unit shoreline length (m³·m⁻¹·d⁻¹); This refers to the net discharge volume resulting from groundwater runoff directly entering the sea. The component of groundwater infiltration or discharge per unit shoreline length induced by wave action; The component of seawater-groundwater exchange per unit length of shoreline caused by tidal fluctuations;

[0045] As a preferred option, step S2 specifically includes the following steps:

[0046] S2-1. Effective slope angle correction under dynamic erosion feedback:

[0047] The sediment erosion phenomenon accompanying the active period of SGD (Sediment Degradation and Erosion) on the seabed is used to correct the initial slope angle in real time using the erosion depth Ds:

[0048] ;

[0049] In the formula: The corrected effective slope angle is expressed in rad. The initial slope angle; The erosion-slope correction factor is used to characterize the rate of change of slope per unit erosion depth, and is taken as 0.0005 rad / mm. The depth of seabed erosion (in mm) was obtained from in-situ observations.

[0050] S2-2, SGD Dynamic Evolution Model of Excess Pore Pressure Based on Seepage Mechanical Effects:

[0051] The heterogeneity of porosity and permeability coefficient in seafloor sediments means that the excess pore water pressure u generated by SGD cannot be considered a simple linear mapping of the discharge rate v. A modified expression based on Darcy's law and the effective stress principle is proposed:

[0052] ;

[0053] In the formula: The additional pore water pressure induced by SGD dynamic seepage (kPa); The rate of discharge of subsea groundwater is m³ / d; The initial permeability coefficient of the sediment; The current effective stress is given in kPa. The effective stress is referenced in kPa. This is the stress sensitivity coefficient; The dynamic viscosity of water (Pa) s; The specific weight of water is kN / m³. This refers to the wave-induced instantaneous pore pressure fluctuation component;

[0054] S2-3. Cumulative stability evaluation considering pore pressure dissipation hysteresis:

[0055] The instability of the seabed slope is caused by the cumulative effect of pore pressure due to prolonged high-intensity discharge; the cumulative pore pressure factor is defined. :

[0056] ;

[0057] In the formula: This is the cumulative strength coefficient; The pore pressure dissipation rate is determined by the sediment consolidation coefficient. The instantaneous pore water pressure is expressed in kPa.

[0058] Calculate Fs for each set of observation samples based on the Mohr-Coulomb limit equilibrium criterion:

[0059] ;

[0060] In the formula: The effective cohesion of the sediment is kPa; The total normal stress is kPa; This refers to the static pore water pressure. Accumulated excess pore pressure (kPa) for SGD; The wave dynamic pressure component is kPa; The effective internal friction angle of the sediment is rad / ; The sliding force is kPa;

[0061] Where: denominator: sliding force for

[0062] ;

[0063] In the formula: The saturated weight of the sediment is kN / m³; D is the water depth in meters.

[0064] Total normal stress ( )for

[0065] ;

[0066] SGD cumulative excess pore pressure for

[0067] ;

[0068] Wave dynamic pressure component for

[0069] .

[0070] As a preferred option, step S3 specifically includes the following steps:

[0071] S3-1. Based on the data source determined in steps S1 and S2, obtain the data containing the independent variable:

[0072] ,

[0073] and target variable

[0074] ,

[0075] Time series data matrix M;

[0076] S3-2, Data Cleaning and Z-Score Standardization:

[0077] The following preprocessing operations are performed on the collected multidimensional time series data matrix M to ensure the robustness of model training: data cleaning is performed, systematically removing sample records containing missing or infinite values ​​from the matrix to ensure that the values ​​of the input neurons are all valid, and then smoothing is performed.

[0078] To eliminate the weight imbalance caused by differences in physical dimensions among different features such as water depth (m), wave height (m), and discharge rate (m³ / d), a Z-Score normalization transformation is performed on the input feature vector X:

[0079] ,

[0080] In the formula: These are the standardized eigenvalues; The characteristic mean; The standard deviation of this feature;

[0081] S3-3, Sample set partitioning:

[0082] The 1000 calibrated samples were divided into two independent subsets in a fixed ratio of 7:3. The first 700 sets were used as the training set to update the neural network weights, and the last 300 sets were used as the validation set to evaluate the model's generalization performance.

[0083] S3-4, Zhang quantitative reconstruction:

[0084] Will The eigenvectors are reconstructed by tensor quantization according to their physical meaning. The two-dimensional matrix format is used as the input to the convolutional neural network.

[0085] ;

[0086] S3-5. The final training and test sample sets are both composed of the above sequences. The data preprocessing is completed, and the data is directly input into the Bayesian-CNN neural network for model training and prediction.

[0087] Furthermore, step S4 specifically includes the following steps:

[0088] S4-1, Model Structure Design:

[0089] The neural network, constructed using a convolutional CNN structure, is used for predicting the safety stability coefficient of seabed slope instability.

[0090] The network input is the time series data matrix M obtained in step S3-1; the input layer receives... A two-dimensional matrix, which is formed by steps S3-4 The feature vectors are obtained by tensor quantization reconstruction; multi-scale feature extraction layer, convolutional layer 1 adopts The convolutional kernel extracts macroscopic dynamic features and is padded with padding. The output feature channels are selected from [16, 32, 64]. A batch normalization layer is introduced to normalize the feature mapping. Convolutional layer 2 uses... The convolution kernel extracts subtle fluctuations between parameters, and the output feature channels are selected from [32, 64, 128].

[0091] Regularization and activation module: ReLU activation function is applied after each convolutional layer, and L2 regularization penalty term is introduced, with coefficients in... Selected from;

[0092] Bayesian Dropout Layer: A Bayesian Dropout layer is connected after the convolutional layer, and its dropout rate is selected in the range of [0.2, 0.5].

[0093] The regression mapping layer flattens the features through the Flatten layer, passes through the fully connected layer of neurons selected from [16, 32, 64], and finally outputs the prediction result of the seabed slope safety factor Fs by the single neuron Regression layer;

[0094] A key-period weighting mechanism is introduced into the loss function: higher weights are given to the prediction errors of sudden changes in seabed slope instability or sudden increases in wave height, thereby improving the model's ability to respond to extreme events; the loss function is defined as follows:

[0095]

[0096] In the formula: N is the sample size. This represents the true value of the safety stability coefficient of the seabed slope. This is the predicted value of the safety stability coefficient of the seabed slope. Weighting coefficients for key erosion periods;

[0097] S4-2, Setting Network Hyperparameters and Bayesian Optimization Range; Automatic adjustment of network hyperparameters using Bayesian optimization; Initial learning rate set on a logarithmic scale. The number of kernels in the first layer is selected from [16, 32, 64], and the number in the second layer is selected from [32, 64, 128]; the Dropout inactivation rate is uniformly distributed in [0.2, 0.5]; the L2 regularization coefficient is set to [0.2, 0.5] on a logarithmic scale. The number of neurons in the fully connected layer is [16, 32, 64]; the batch size is [16, 32, 64].

[0098] S4-3, Bayesian Optimization Configuration and Composite Objective Function; Bayesian optimization is performed for 30-50 iterations, with 5-10 sets of hyperparameters initially randomly sampled to construct a Gaussian process prior, and an expectation-enhanced acquisition function is used to guide the search. The objective function uses a composite error obtained through 5-fold cross-validation. ,in For critical region samples ( The mean square error weighted (weight 2.0) of ). Take 1.

[0099] As a preferred embodiment, step S5-1 specifically includes the following steps:

[0100] S5-1-1, Optimizer Selection and Learning Rate Scheduling: The Adam optimizer is selected, and its key hyperparameters are automatically tuned through Bayesian optimization: the initial learning rate is searched on a logarithmic scale within the range of [1×10⁻⁻¹]. 4 The first-order moment attenuation coefficient β1 is searched within [0.85, 0.95], and β2 is fixed at 0.999.

[0101] S5-1-2, Loss Function Calculation: The total loss is the sum of the weighted mean squared error and the L2 regularization term, i.e. Weight Based on the sample safety factor, the critical zone is set. Take 2.0, neighboring area Take 1.5 for the remainder, and 1.0 for the rest. L2 regularization coefficient. Bayesian optimization on the logarithmic scale Internal search.

[0102] As a preferred option, step S5-2 specifically includes the following steps:

[0103] S5-2-1, Repeated Sampling: During inference, the Bayesian random deactivation layer (Dropout layer) is kept active. For the input feature vector at the same time, K=50 random inferences are performed to generate a set of predicted values. .

[0104] S5-2-2, Expected Value Extraction: Using the formula... The predicted mean of the safety factor is calculated; this mean is used as the slope stability evaluation index of the final output of this invention.

[0105] S5-2-3, Confidence Interval Quantification: Calculate the standard deviation of 50 sampling results. ;

[0106] As a preferred option, step S6 specifically includes the following steps:

[0107] S6-1, Prediction:

[0108] After the neural network training is completed, predictions are made on the training and test sets to obtain the predicted value of the seabed slope instability safety stability coefficient for each sample. ;

[0109] S6-2. Result Evaluation and Error Analysis:

[0110] The overall error metrics include root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. ), used to comprehensively evaluate the overall predictive performance of the model.

[0111] This invention, by employing the above technical solutions, offers the following advantages compared to existing technologies: Based on a complete dataset obtained from in-situ observations, it enhances the ability to identify critical instability states by introducing a state-sensitive weighted loss function. Through Bayesian inference and Dropout random sampling, the model effectively characterizes the nonlinear response under the coupled effects of SGD and waves, quantifies and predicts risks, and solves the problem that traditional methods struggle to handle the randomness and nonlinear dynamic evolution of the marine environment. Ultimately, it forms a complete, reliable, and applicable method for predicting seabed slope instability under SGD in complex marine environments.

[0112] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0113] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0114] Figure 1 The overall flowchart of this invention is as follows:

[0115] Figure 2 This is the basic structure of a convolutional neural network;

[0116] Figure 3 This invention presents the changes over time of 1000 sets of training data obtained through long-term in-situ observations.

[0117] Figure 4 This is a comparison chart of the predicted and actual values ​​of the training set and test set obtained by training the model using in-situ observation data in this invention. Detailed Implementation

[0118] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0119] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0120] The following is combined Figures 1 to 4 The present invention provides a detailed description of the method for predicting seabed slope instability under the action of seabed groundwater discharge based on Bayesian-CNN, according to an embodiment of the present invention.

[0121] like Figure 1 As shown, the present invention proposes as follows Figure 1 As shown, this invention proposes a prediction method for seafloor slope instability under the influence of seafloor groundwater discharge based on Bayesian-CNN. This invention utilizes MATLAB R2024b software for neural network training; the related functions and parameters mentioned below are based on this software version. The prediction method for seafloor slope instability under the influence of seafloor groundwater discharge based on Bayesian-CNN specifically includes the following steps:

[0122] S1. Multi-parameter coupled observation and dataset construction:

[0123] Data on various seabed environmental parameters, including water depth, wave height, wave period, salinity, turbidity, SGD rate, and erosion depth, were collected through in-situ observations, and a dataset was constructed. The specific steps include:

[0124] S1-1, Coupling effect of factors influencing submarine groundwater discharge:

[0125] Water depth D directly affects the discharge intensity of SGD by altering the hydraulic gradient between groundwater and seawater; the average seepage velocity of groundwater in sediments is expressed as:

[0126] ;

[0127] In the formula: The equivalent seepage velocity of seabed groundwater discharge is given in m / s; K is the permeability coefficient of seabed sediments in m / s. D is the head height of the terrestrial freshwater (m); D is the water depth (m). The density is that of fresh water. is the density of seawater; L is the equivalent flow path length (m) of groundwater from its land source to its discharge point.

[0128] Wave action is a significant driver of short-term variations in SGD (Surface Gauge Discharge) in shallow waters. As waves propagate near the shore, the alternating crests and troughs create periodic pressure disturbances on the seabed surface, resulting in a pumping effect on pore water and significantly enhancing groundwater discharge. The wave-induced instantaneous additional pressure is expressed as:

[0129] ;

[0130] In the formula: Wave-induced pressure (Pa); : Gravitational acceleration (m / s²) Let m be the wave height, and take the significant wave height. or maximum wave height ; For wave number, satisfying ; The wavelength is m; Angular frequency, ; The wave period is s; The vertical height (m) above the seabed surface; These are the horizontal position coordinates;

[0131] The impact of waves on SGD is related not only to wave height but also closely to wave period. Wave period further influences pressure attenuation depth by controlling wavelength; this relationship is determined by the dispersion relation.

[0132] ;

[0133] In the formula: Wavelength (m); wave period (s); water depth (m);

[0134] The safety stability coefficient for submarine slope instability under SGD is a function driven by multiple parameters:

[0135] ;

[0136] By constructing a neural network, the safety stability coefficient of the seabed slope is predicted from the complex background of multi-parameter coupling.

[0137] S1-2, In-situ observation and dataset construction:

[0138] We obtained hydrodynamic parameters, pore water pressure, submarine groundwater discharge parameters, and seabed erosion depth for the study area. We also obtained datasets for training and testing the models, including: water depth D and significant wave height. Effective wave period , maximum wave height Maximum wave period Salinity (S), Turbidity SGD rate erosion depth ;

[0139] Calculation of groundwater discharge rate based on pore water pressure signal decomposition:

[0140] The groundwater discharge rate directly affects the pore water pressure distribution and effective stress state of slope soil, and is a crucial factor in controlling the safety and stability coefficient. To improve the accuracy of discharge rate calculation, this invention separates different dynamic causes based on pore water pressure time series.

[0141] The collected pore water pressure sequence Perform wavelet transform:

[0142] ;

[0143] In the formula: These are the wavelet transform coefficients; For scale Translation The mother wavelet function; by reconstructing the wavelet scale, the pore water pressure signal is decomposed into high-frequency, short-period wave action components; low-frequency, long-period tidal action components; and the remaining groundwater runoff background components.

[0144] Based on the decomposed pore water pressure components, groundwater discharge rates corresponding to different dynamic mechanisms were calculated and uniformly converted into daily discharge rates per unit shoreline length; the total seafloor groundwater discharge rate was also calculated. Expressed as:

[0145] ;

[0146] In the formula: The total amount of subsea groundwater discharged per unit shoreline length (m³·m⁻¹·d⁻¹); This refers to the net discharge volume resulting from groundwater runoff directly entering the sea. The component of groundwater infiltration or discharge per unit shoreline length induced by wave action; The component of seawater-groundwater exchange per unit length of shoreline caused by tidal fluctuations;

[0147] The result obtained through the above process As a quantitative representation of the groundwater discharge intensity in the study area, it was introduced into subsequent erosion evolution models and slope stability analyses, serving as an important mediating variable connecting hydrodynamic conditions and geological responses.

[0148] S2. Calibration of the safety index Fs of the seabed slope based on the fluid-structure interaction mechanism:

[0149] Using the raw data collected in step S1, based on fluid-structure interaction theory, the upward seepage force generated by SGD, the cumulative effect of excess pore water pressure, and the dynamic erosion feedback of the seabed, the slope safety factor Fs is calculated and calibrated using the limit equilibrium criterion, and a label set is constructed. Specifically, this includes the following steps:

[0150] S2-1. Effective slope angle correction under dynamic erosion feedback:

[0151] The sediment erosion phenomenon accompanying the active period of SGD (Sediment Degradation and Erosion) on the seabed is used to correct the initial slope angle in real time using the erosion depth Ds:

[0152] ;

[0153] In the formula: The corrected effective slope angle is expressed in rad. The initial slope angle is set according to the topography of the study area; in this embodiment, it is taken as... ; The erosion-slope correction factor is used to characterize the rate of change of slope per unit erosion depth, and is taken as 0.0005 rad / mm. The depth of seabed erosion (in mm) was obtained from in-situ observations.

[0154] S2-2, SGD Dynamic Evolution Model of Excess Pore Pressure Based on Seepage Mechanical Effects:

[0155] The heterogeneity of porosity and permeability coefficient in seafloor sediments means that the excess pore water pressure u generated by SGD cannot be considered a simple linear mapping of the discharge rate v. A modified expression based on Darcy's law and the effective stress principle is proposed:

[0156] ;

[0157] In the formula: The additional pore water pressure induced by SGD dynamic seepage (kPa); The rate of discharge of subsea groundwater is m³ / d; The initial permeability coefficient of the sediment; The current effective stress is given in kPa. The effective stress is referenced in kPa. This is the stress sensitivity coefficient; The dynamic viscosity of water (Pa) s; The specific weight of water is kN / m³. This refers to the wave-induced instantaneous pore pressure fluctuation component;

[0158] S2-3. Cumulative stability evaluation considering pore pressure dissipation hysteresis:

[0159] Instability of seafloor slopes is often not driven by instantaneous SGD peaks, but rather by the cumulative effect of pore pressure accumulation caused by prolonged high-intensity drainage; a cumulative pore pressure factor is defined. :

[0160] ;

[0161] In the formula: This is the cumulative strength coefficient; The pore pressure dissipation rate is determined by the sediment consolidation coefficient. The instantaneous pore water pressure is expressed in kPa.

[0162] This equation treats the seafloor slope as a complex system influenced by SGD uplift force, wave dynamic pressure, and dynamic erosion of the landform, and calculates Fs for each set of observation samples based on the Mohr-Coulomb limit equilibrium criterion:

[0163] ;

[0164] In the formula: The effective cohesion of the sediment is kPa; The total normal stress is kPa; This refers to the static pore water pressure. Accumulated excess pore pressure (kPa) for SGD; The wave dynamic pressure component is kPa; The effective internal friction angle of the sediment is rad / ; The sliding force is kPa;

[0165] Where: denominator: sliding force for

[0166] ;

[0167] In the formula: The saturated weight of the sediment is kN / m³; D is the water depth in meters.

[0168] Total normal stress ( )for

[0169] ;

[0170] SGD cumulative excess pore pressure for

[0171] ;

[0172] Wave dynamic pressure component for

[0173] .

[0174] S3. Data import and preprocessing, reconstruction and sample space partitioning:

[0175] The data obtained in steps S1 and S2 are imported and cleaned, smoothed, and standardized. Simultaneously, the one-dimensional feature vectors are reconstructed into two-dimensional matrices to adapt to the structural characteristics of the convolutional neural network. Finally, the 1000 sample sets are divided into training and validation sets in a 7:3 ratio. The specific steps include:

[0176] S3-1. Based on the data source determined in steps S1 and S2, obtain the data containing the independent variable:

[0177] ,

[0178] and target variable

[0179] ,

[0180] Time series data matrix M;

[0181] S3-2, Data Cleaning and Z-Score Standardization:

[0182] The following preprocessing operations are performed on the collected multidimensional time series data matrix M to ensure the robustness of model training: data cleaning is performed, systematically removing sample records containing missing or infinite values ​​from the matrix to ensure that the values ​​of the input neurons are all valid, and then smoothing is performed.

[0183] To eliminate the weight imbalance caused by differences in physical dimensions among different features such as water depth (m), wave height (m), and discharge rate (m³ / d), a Z-Score normalization transformation is performed on the input feature vector X:

[0184] ,

[0185] In the formula: These are the standardized eigenvalues; The characteristic mean; The standard deviation of this feature;

[0186] S3-3, Sample set partitioning:

[0187] The 1000 calibrated samples were divided into two independent subsets in a fixed ratio of 7:3. The first 700 sets were used as the training set to update the neural network weights, and the last 300 sets were used as the validation set to evaluate the model's generalization performance.

[0188] S3-4, Zhang quantitative reconstruction:

[0189] Will The eigenvectors are reconstructed by tensor quantization according to their physical meaning. The two-dimensional matrix format is used as input to the convolutional neural network. This mapping process aims to capture the nonlinear spatial coupling relationship between discharge rate, wave elements and geological parameters by utilizing the local receptive field depth of the convolutional neural network.

[0190] ;

[0191] S3-5. The final training and test sample sets are both composed of the above sequences. The data preprocessing is completed, and the data is directly input into the Bayesian-CNN neural network for model training and prediction.

[0192] S4, Bayesian-CNN Neural Network Model Construction:

[0193] The network structure includes a multi-scale feature extraction layer, a regularization module, a Bayesian random deactivation layer, and a regression output layer. A weighted loss function is introduced to enhance sensitivity to unstable critical states. Hyperparameters are automatically tuned through Bayesian optimization to improve the model's generalization ability and robustness in complex marine environments. Specifically, the following steps are included:

[0194] S4-1, Model Structure Design:

[0195] The neural network, constructed using a convolutional CNN structure, is used for predicting the safety stability coefficient of seabed slope instability.

[0196] The network input is the time series data matrix M obtained in step S3-1; the input layer receives... A two-dimensional matrix, which is formed by steps S3-4 The feature vectors are obtained by tensor quantization reconstruction; multi-scale feature extraction layer, convolutional layer 1 adopts The convolutional kernel extracts macroscopic dynamic features and is padded with padding. The output feature channels are selected from [16, 32, 64]. A batch normalization layer is introduced to normalize the feature mapping. Convolutional layer 2 uses... The convolution kernel extracts subtle fluctuations between parameters, and the output feature channels are selected from [32, 64, 128].

[0197] Regularization and activation module: ReLU activation function is applied after each convolutional layer, and L2 regularization penalty term is introduced, with coefficients in... Selecting from the middle to prevent overfitting;

[0198] Bayesian Dropout Layer: A Bayesian Dropout layer is connected after the convolutional layer, and its dropout rate is selected in the range of [0.2, 0.5].

[0199] The regression mapping layer flattens the features through the Flatten layer, passes through the fully connected layer of neurons selected from [16, 32, 64], and finally outputs the prediction result of the seabed slope safety factor Fs by the single neuron Regression layer;

[0200] A key-period weighting mechanism is introduced into the loss function: higher weights are given to the prediction errors of sudden changes in seabed slope instability or sudden increases in wave height, thereby improving the model's ability to respond to extreme events; the loss function is defined as follows:

[0201]

[0202] In the formula: N is the sample size. This represents the true value of the safety stability coefficient of the seabed slope. This is the predicted value of the safety stability coefficient of the seabed slope. Weighting coefficients for key erosion periods;

[0203] S4-2, Setting Network Hyperparameters and Bayesian Optimization Range; Automatic adjustment of network hyperparameters using Bayesian optimization; Initial learning rate set on a logarithmic scale. The number of kernels in the first layer is selected from [16, 32, 64], and the number in the second layer is selected from [32, 64, 128]; the Dropout inactivation rate is uniformly distributed in [0.2, 0.5]; the L2 regularization coefficient is set to [0.2, 0.5] on a logarithmic scale. The number of neurons in the fully connected layer is [16, 32, 64]; the batch size is [16, 32, 64].

[0204] S4-3, Bayesian Optimization Configuration and Composite Objective Function; Bayesian optimization is performed for 30-50 iterations, with 5-10 sets of hyperparameters initially randomly sampled to construct a Gaussian process prior, and an expectation-enhanced acquisition function is used to guide the search. The objective function uses a composite error obtained through 5-fold cross-validation. ,in For critical region samples ( The mean square error weighted (weight 2.0) of ). Take 1.

[0205] S5, Bayesian-CNN Neural Network Training:

[0206] S5-1, Training Strategy Configuration and Model Learning:

[0207] The neural network model constructed in step S4 is ensemble-trained using the 700 training set samples divided in step S3; specifically, the following steps are included:

[0208] S5-1-1, Optimizer Selection and Learning Rate Scheduling: The Adam optimizer is selected, and its key hyperparameters are automatically tuned through Bayesian optimization: the initial learning rate is searched on a logarithmic scale within the range of [1×10⁻⁻¹]. 4 The first-order moment attenuation coefficient β1 is searched within [0.85, 0.95], and β2 is fixed at 0.999.

[0209] S5-1-2, Loss Function Calculation: The total loss is the sum of the weighted mean squared error and the L2 regularization term, i.e. Weight Based on the sample safety factor, the critical zone is set. Take 2.0, neighboring area Take 1.5 for the remainder, and 1.0 for the rest. L2 regularization coefficient. Bayesian optimization on the logarithmic scale Internal search.

[0210] S5-2, Implementation of Probabilistic Prediction Based on Monte Carlo Sampling

[0211] To overcome the difficulty of traditional deterministic neural networks in quantifying the randomness of the marine environment, this embodiment employs a Monte Carlo sampling strategy for the model prediction validation set of 300 sets of data; specifically, it includes the following steps:

[0212] S5-2-1, Repeated Sampling: During inference, the Bayesian random deactivation layer (Dropout layer) is kept active. For the input feature vector at the same time, K=50 random inferences are performed to generate a set of predicted values. .

[0213] S5-2-2, Expected Value Extraction: Using the formula... The predicted mean of the safety factor is calculated; this mean is used as the slope stability evaluation index of the final output of this invention.

[0214] S5-2-3, Confidence Interval Quantification: Calculate the standard deviation of 50 sampling results. According to measured data, during the stable period of wave load, A smaller value (typically <0.01) indicates high confidence in the model prediction; however, during periods of sudden surges in SGD flux or strong wave disturbances, An increase to above 0.05 reflects the strong nonlinearity and high uncertainty of the response of the seafloor geological system.

[0215] S6. Prediction and Result Evaluation:

[0216] The model trained in step S5 is used to predict the safety factor of the test samples. This is achieved by evaluating overall error metrics such as root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. To evaluate the predictive performance of the model, the following steps are used:

[0217] S6-1, Prediction:

[0218] After the neural network training is completed, predictions are made on the training and test sets to obtain the predicted value of the seabed slope instability safety stability coefficient for each sample. The prediction process is based on the trained network parameters and the optimized hyperparameter combination, and the output prediction values ​​can be directly used for error analysis and model performance evaluation.

[0219] S6-2. Result Evaluation and Error Analysis:

[0220] The overall error metrics include root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. ), used to comprehensively evaluate the overall predictive performance of the model.

[0221] S6-3 Instance Prediction Results

[0222] In this embodiment of the invention, the output after training is as follows: Optimal parameters—learning rate: 0.009933, number of kernel convolutions: 18, RMSE=0.0825, MAE=0.0539. =0.8571.

[0223] The comprehensive evaluation shows that the model performs well in terms of overall prediction accuracy and sensitivity to key erosion stages. There are slight fluctuations in individual data, but the overall prediction performance meets the requirements of engineering applications.

[0224] S7 Visualization and Results Display

[0225] After completing model training and prediction, this invention visually displays the predicted values. Compared with the true value The differences are used to evaluate the model's predictive ability. The true and predicted values ​​on the training and test sets are compared in line or curve form (see attached). Figure 4 This can clearly reflect the predictive effect of the stable phase and the abrupt change phase.

[0226] Visualization results can intuitively identify prediction biases and provide a reference for network optimization or hyperparameter adjustment. The embodiments of this invention show that the overall trend of the predicted curve and the true value curve is highly consistent, and the prediction accuracy is significantly improved during key abrupt change stages, indicating that the Bayesian-CNN network has good reliability in predicting the stability coefficient of seabed slope instability.

[0227] In the description of this invention, the term "a plurality of" refers to two or more. Unless otherwise explicitly defined, the terms "upper," "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. The terms "connection," "installation," "fixing," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium. For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances.

[0228] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0229] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A prediction method for seafloor slope instability under the influence of seafloor groundwater discharge based on Bayesian-CNN, characterized in that... Specifically, it includes the following steps: S1. Multi-parameter coupled observation and dataset construction: Data on various seabed environmental parameters, including water depth, wave height, wave period, salinity, turbidity, SGD rate, and erosion depth, were collected through in-situ observations, and a dataset was constructed. The specific steps include: S1-1, Coupling effect of factors influencing submarine groundwater discharge: Water depth D directly affects the discharge intensity of SGD by altering the hydraulic gradient between groundwater and seawater; the average seepage velocity of groundwater in sediments is expressed as: ； In the formula: The equivalent seepage velocity of seabed groundwater discharge is given in m / s; K is the permeability coefficient of seabed sediments in m / s. D is the head height of the terrestrial freshwater (m); D is the water depth (m). The density is that of fresh water. is the density of seawater; L is the equivalent flow path length (m) of groundwater from its land source to its discharge point. As waves propagate near the shore, the alternating wave crests and troughs create periodic pressure disturbances on the seabed surface, resulting in a pumping effect on pore water. The wave-induced instantaneous additional pressure is expressed as: ； In the formula: Wave-induced pressure (Pa); : Gravitational acceleration (m / s²) Let m be the wave height, and take the significant wave height. or maximum wave height ; For wave number, satisfying ; The wavelength is m; Angular frequency, ; The wave period is s; The vertical height (m) above the seabed surface; These are the horizontal position coordinates; The wave period further influences the pressure attenuation depth by controlling the wavelength, and this relationship is determined by the dispersion relation: ； In the formula: Wavelength (m); wave period (s); water depth (m); The safety stability coefficient for submarine slope instability under SGD is a function driven by multiple parameters: ； By constructing a neural network, the safety stability coefficient of the seabed slope is predicted from the complex background of multi-parameter coupling. S1-2, In-situ observation and dataset construction: We obtained hydrodynamic parameters, pore water pressure, submarine groundwater discharge parameters, and seabed erosion depth for the study area. We also obtained datasets for training and testing the models, including: water depth D, significant wave height, and significant wave period. , maximum wave height Maximum wave period Salinity (S), Turbidity SGD rate erosion depth ; Calculation of groundwater discharge rate based on pore water pressure signal decomposition: The collected pore water pressure sequence Perform wavelet transform: ； In the formula: These are the wavelet transform coefficients; For scale Translation The mother wavelet function; by reconstructing the wavelet scale, the pore water pressure signal is decomposed into high-frequency, short-period wave action components; low-frequency, long-period tidal action components; and the remaining groundwater runoff background components. Based on the decomposed pore water pressure components, groundwater discharge rates corresponding to different dynamic mechanisms were calculated and uniformly converted into daily discharge rates per unit shoreline length; the total seafloor groundwater discharge rate was also calculated. Expressed as: ； In the formula: The total amount of subsea groundwater discharged per unit shoreline length (m³·m⁻¹·d⁻¹); This refers to the net discharge volume resulting from groundwater runoff directly entering the sea. The component of groundwater infiltration or discharge per unit shoreline length induced by wave action; The component of seawater-groundwater exchange per unit length of shoreline caused by tidal fluctuations; S2. Calibration of the safety index Fs of the seabed slope based on the fluid-structure interaction mechanism: Using the raw data collected in step S1, based on fluid-structure interaction theory, upward seepage force generated by SGD, cumulative effect of excess pore water pressure, and dynamic erosion feedback of the seabed, the slope safety factor Fs is calculated and calibrated using the limit equilibrium criterion, and a label set is constructed; specifically including the following steps: S2-1. Effective slope angle correction under dynamic erosion feedback: The sediment erosion phenomenon accompanying the active period of SGD on the seabed is used to correct the initial slope angle in real time using the erosion depth Ds: ； In the formula: The corrected effective slope angle is expressed in rad. The initial slope angle; The erosion-slope correction factor is used to characterize the rate of change of slope per unit erosion depth, and is taken as 0.0005 rad / mm. The depth of seabed erosion (in mm) was obtained from in-situ observations. S2-2, SGD dynamic evolution model of excess pore pressure based on seepage mechanics effect: The heterogeneity of porosity and permeability coefficient in seafloor sediments means that the excess pore water pressure u generated by SGD cannot be considered a simple linear mapping of the discharge rate v. A modified expression based on Darcy's law and the effective stress principle is proposed: ； In the formula: The additional pore water pressure induced by SGD dynamic seepage (kPa); The rate of discharge of subsea groundwater is m³ / d; The initial permeability coefficient of the sediment; The current effective stress is given in kPa. The effective stress is referenced in kPa. This is the stress sensitivity coefficient; The dynamic viscosity of water (Pa) s; The specific weight of water is kN / m³. This refers to the wave-induced instantaneous pore pressure fluctuation component; S2-3. Cumulative stability evaluation considering pore pressure dissipation hysteresis: The instability of the seabed slope is caused by the cumulative effect of pore pressure due to prolonged high-intensity discharge; the cumulative pore pressure factor is defined. : ； In the formula: This is the cumulative strength coefficient; The pore pressure dissipation rate is determined by the sediment consolidation coefficient. The instantaneous pore water pressure is expressed in kPa. F was calculated for each set of observation samples based on the Mohr-Coulomb limit equilibrium criterion. s : ； In the formula: The effective cohesion of the sediment is kPa; The total normal stress is kPa; This refers to the static pore water pressure. Accumulated excess pore pressure (kPa) for SGD; The wave dynamic pressure component is kPa; The effective internal friction angle of the sediment is rad / ; The sliding force is kPa; Where: denominator: sliding force for: ； In the formula: The saturated weight of the sediment is kN / m³; D is the water depth in meters. Total normal stress for: ； SGD cumulative excess pore pressure for: ； Wave dynamic pressure component for: ； S3. Data import and preprocessing, reconstruction and sample space partitioning: The data obtained in steps S1 and S2 are imported and cleaned, smoothed and standardized; at the same time, the one-dimensional feature vector is reconstructed into a two-dimensional matrix form to adapt to the structural characteristics of the convolutional neural network. Finally, the 1000 sets of samples are divided into training set and validation set in a 7:3 ratio. S4, Bayesian-CNN Neural Network Model Construction: The network structure includes a multi-scale feature extraction layer, a regularization module, a Bayesian random deactivation layer, and a regression output layer. A weighted loss function is introduced to enhance the sensitivity to unstable critical states. The hyperparameters are automatically tuned through Bayesian optimization to improve the model's generalization ability and robustness in complex marine environments. S5, Bayesian-CNN neural network training: S5-1, Training Strategy Configuration and Model Learning: The neural network model constructed in step S4 is integrated and trained using the 700 sets of training samples divided in step S3. S5-2, Implementation of Probabilistic Prediction Based on Monte Carlo Sampling: The Monte Carlo sampling strategy was used when the model prediction validation set consisted of 300 sets of data. S6. Prediction and Result Evaluation: The model trained in step S5 is used to predict the safety factor of the test samples; the overall error metrics, including root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination, are evaluated. To evaluate the predictive performance of the model.

2. The method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN as described in claim 1, characterized in that... Step S3 specifically includes the following steps: S3-1. Based on the data source determined in steps S1 and S2, obtain the data containing the independent variable: and target variable Time series data matrix M; S3-2, Data Cleaning and Z-Score Standardization: The following preprocessing operations are performed on the collected multidimensional time series data matrix M to ensure the robustness of model training: data cleaning is performed, sample records containing missing values ​​or infinite values ​​are systematically removed from the matrix, and then smoothing is performed. To eliminate the weight imbalance caused by differences in physical dimensions among different features including water depth m, wave height m, and discharge rate m³ / d, a Z-Score normalization transformation is performed on the input feature vector X: ， In the formula: These are the standardized eigenvalues; The characteristic mean; The standard deviation of this feature; S3-3, Sample set partitioning: The 1000 calibrated samples were divided into two independent subsets in a fixed ratio of 7:

3. The first 700 sets were used as the training set to update the neural network weights, and the last 300 sets were used as the validation set to evaluate the model's generalization performance. S3-4, Zhang quantitative reconstruction: Will The eigenvectors are reconstructed by tensor quantization according to their physical meaning. The two-dimensional matrix format is used as the input to the convolutional neural network: ； S3-5. The final training and test sample sets are both composed of the above sequences. The data preprocessing is completed and the data is directly input into the Bayesian-CNN neural network for model training and prediction.

3. The method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN as described in claim 2, characterized in that... Step S4 specifically includes the following steps: S4-1, Model Structure Design: The neural network, constructed using a convolutional CNN structure, is used for predicting the safety stability coefficient of seabed slope instability. The network input is the time series data matrix M obtained in step S3-1; the input layer receives... A two-dimensional matrix, which is derived from S3-4 The feature vectors are obtained through tensor quantization and reconstruction; the multi-scale feature extraction layer uses convolution in the first layer. The convolutional kernel extracts macroscopic dynamic features and is padded with padding. The output feature channels are selected from [16, 32, 64]. A batch normalization layer is also introduced to normalize the feature mapping. The second convolutional layer uses... The convolutional kernel extracts subtle fluctuations between parameters, and the output feature channels are selected from [32, 64, 128]. Regularization and activation module: ReLU activation function is applied after each convolutional layer, and L2 regularization penalty term is introduced, with coefficients in... Selected from; Bayesian random dropout layer: A Bayesian random dropout layer is connected after the convolutional layer, and its dropout rate is selected in [0.2, 0.5]. The regression mapping layer flattens the features through the Flatten layer, passes through the fully connected layer of neurons selected in [16,32,64], and finally outputs the prediction result of the seabed slope safety factor Fs by the single neuron Regression layer; A key-period weighting mechanism is introduced into the loss function: higher weights are given to the prediction errors of sudden changes in seabed slope instability or sudden increases in wave height, thereby improving the model's ability to respond to extreme events; the loss function is defined as follows: ； In the formula: N is the sample size. This represents the true value of the safety stability coefficient of the seabed slope. This is the predicted value of the safety stability coefficient of the seabed slope. Weighting coefficients for key erosion periods; S4-2, Setting Network Hyperparameters and Bayesian Optimization Range; Automatic adjustment of network hyperparameters using Bayesian optimization; Initial learning rate set on a logarithmic scale. The number of kernels in the first layer is selected from [16, 32, 64], and the number in the second layer is selected from [32, 64, 128]. The Dropout inactivation rate is uniformly distributed in [0.2, 0.5]. The L2 regularization coefficient is set to a value on the logarithmic scale. The number of neurons in the fully connected layer is [16, 32, 64]; the batch size is [16, 32, 64]. S4-3, Bayesian optimization configuration and composite objective function; Bayesian optimization is performed for 30-50 iterations, with 5-10 sets of hyperparameters initially randomly sampled to construct a Gaussian process prior, and an expectation-enhancing acquisition function is used to guide the search; the objective function uses a composite error obtained through 5-fold cross-validation. ,in Critical region sample The mean squared error is weighted, with a weight of 2.

0. Take 1.

4. The method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN as described in claim 1, characterized in that... Step S5-1 specifically includes the following steps: S5-1-1, Optimizer Selection and Learning Rate Scheduling: The Adam optimizer is selected, and its key hyperparameters are automatically tuned through Bayesian optimization: the initial learning rate is searched on a logarithmic scale within the range of [1×10⁻⁻¹]. 4 The first-order moment attenuation coefficient β1 is searched within the range of [0.85, 0.95], and β2 is fixed at 0.

999. S5-1-2, Loss Function Calculation: The total loss is the sum of the weighted mean squared error and the L2 regularization term, i.e. Weight Based on the sample safety factor, the critical zone is set. Take 2.0, neighboring area Take 1.5 for the L2 regularization coefficient, and 1.0 for the rest. Bayesian optimization on the logarithmic scale Internal search.

5. The method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN as described in claim 1, characterized in that... Step S5-2 specifically includes the following steps: S5-2-1, Repeated Sampling: During inference, the Bayesian random deactivation layer Dropout layer is kept active. For the input feature tensor at the same time, K=50 random inferences are performed to generate a set of predicted values. S5-2-2, Expected Value Extraction: Using the formula... The predicted mean of the safety factor is calculated; S5-2-3, Confidence Interval Quantification: Calculate the standard deviation of 50 sampling results. .

6. The method for predicting seabed slope instability under the influence of seabed groundwater discharge based on Bayesian-CNN according to claim 1, characterized in that... Step S6 specifically includes the following steps: S6-1, Prediction: After training the neural network, predictions are made on the training and test sets to obtain the predicted stability coefficient for each sample, indicating the potential for instability of the seabed slope. ; S6-2. Result Evaluation and Error Analysis: The overall error metrics include root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. It is used to comprehensively evaluate the overall predictive performance of the model.

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