A method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm

Abstract

This invention provides a method for assessing and analyzing the failure probability of seabed slopes based on a BP neural network algorithm. It utilizes stochastic finite element numerical simulations (SEM) under two scenarios: uncertainty in soil and rock parameters and uncertainty in wave loads, to obtain the safety factor or stability label of the seabed slope. Using soil and rock parameters and wave load uncertainty parameters as inputs, and the safety factor or stability label as outputs, a training set for a machine learning surrogate model is constructed. The BP neural network algorithm is then used to analyze and train the model for these two scenarios, transforming the complex and time-consuming Monte Carlo stochastic finite element numerical simulations into statistical relationships. This establishes a surrogate model for rapidly calculating the failure probability of seabed slopes, significantly reducing the computational cost of seabed slope reliability assessment, providing a basis for seabed slope engineering decisions, and better ensuring the safety of seabed slope engineering projects.

Description

Technical Field

[0001] This invention relates to the field of seabed slope reliability analysis, and more specifically, to a method for assessing and analyzing the failure probability of seabed slopes based on a BP neural network algorithm. Background Technology

[0002] Against the backdrop of marine infrastructure construction and marine resource utilization, seabed slope stability has gradually become one of the important issues in coastal and marine engineering. Landslides triggered by seabed slope instability, as a highly destructive marine geological hazard, threaten human engineering activities and the safety of life and property. With the development of marine oil and gas resources and the increase in offshore construction activities, the frequency of marine accidents is gradually increasing. Therefore, studying seabed slope stability and assessing its reliability is crucial for marine engineering site selection and the prevention of catastrophic accidents. Previous studies on seabed slope stability have mostly focused on deterministic studies, that is, using deterministic parameters to simulate the instability process of seabed slopes or to calculate the safety factor of seabed slopes. Existing research shows that many factors affecting slope stability are random (Rusydy et al., 2024; Xiong and Huang, 2022; Zhao, 2008). Using deterministic analysis may underestimate the instability risk or overestimate the safety factor, leading to biases in the understanding of slope stability. The reliability theory, based on probabilistic statistical methods, has been introduced into slope stability analysis (Tang et al., 1976; Tobutt, 1982; Vanmarcke, 1980). Reliability analysis methods (such as the Monte Carlo limit equilibrium method, the Monte Carlo stochastic finite element method, and the reliability index method) are used to solve for the probability of slope failure, i.e., the reliability (Aminpour et al., 2022; Griffiths et al., 2011; Zeng et al., 2022). This provides a useful reference index for engineering decision-making and disaster prevention and mitigation, and has achieved good results in land slope stability research (Obregon and Mitri, 2019; Wang and Goh, 2021). While probabilistic methods have begun to be applied in the stability analysis of submarine slopes... However, to simplify calculations, related works all employ the limit equilibrium method, considering only mechanical equilibrium conditions in the model solution, which makes it difficult to reflect the true stress-strain characteristics of the slope (Henkel, 1970; Nodine, 2007). The Monte Carlo stochastic finite element method differs; its slope stability evaluation is based on the slope's stress-strain state, resulting in more accurate and reliable calculations. However, direct Monte Carlo simulation is extremely costly, especially when the slope failure probability is low, such as 0.001, requiring at least 100,000 repeated calculations of random samples (Aminpour et al., 2023; Johari et al., 2015), which is generally unacceptable in engineering practice.Furthermore, the stability of seabed slopes is affected by many uncertainties, such as sediment properties, complex hydrodynamics, and earthquakes (Chenet et al., 2020a; Chen et al., 2020b). Existing studies have largely failed to consider the reliability of seabed slopes under the influence of uncertainties in external loads, especially under wave loads, where relevant research is even scarcer. Furthermore, considering the uncertainties of wave loads would significantly increase the computational cost of using the Monte Carlo stochastic finite element method for seabed slope reliability assessment. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides a method for evaluating and analyzing the failure probability of seabed slopes based on the BP neural network algorithm.

[0004] This invention is achieved through the following technical solution: a method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm, specifically including the following steps:

[0005] Step S1: Based on the distribution characteristics of soil and rock parameters and wave parameters, generate a random field of soil and rock parameters using the KL series expansion method, and generate random wave loads using the spectral representation method, which serve as material parameters and boundary conditions for the numerical model.

[0006] Step S2: Establish a numerical model for calculating the stability of the seabed slope, considering multiple uncertainty scenarios, coupling the generated random field and random process, and conducting direct Monte Carlo simulation;

[0007] Step S3: Using the generated random field and random process as input and the numerical simulation results as output, construct training samples to train the machine learning surrogate model, and carry out machine learning Monte Carlo simulation to calculate the slope stability, and compare it with direct Monte Carlo simulation.

[0008] Step S4: Compare the results of the established machine learning agent model with the results of the direct Monte Carlo simulation in step S2 to verify the usability of the model and evaluate the accuracy and time complexity of the machine learning agent model.

[0009] As a preferred option, step S1 specifically includes the following steps:

[0010] Step S1-1: The uncertainty of sediment intensity parameters in the model is characterized using a random field, with the exponential autocorrelation function used as the basic function for random field simulation. Its expression is:

[0011] (1)

[0012] In the formula, and They represent the first iThe unit and the first j The absolute distance between units in the horizontal and vertical directions; and These represent the autocorrelation distances in the horizontal and vertical directions, respectively. The larger the autocorrelation distance, the stronger the spatial correlation of the parameters.

[0013] Based on the autocorrelation function, a normally distributed random field is generated in a certain discrete domain. The KL series expansion method is used to discretize the normally distributed random field.

[0014] Suppose the research subjects are For the nth random field, for the nth For a random field, if the random field is a normal random field, then its KL discretization result is:

[0015] (2)

[0016] In the formula, To take into account random field averages with mean squared deviation Discrete values ​​of a normally distributed random field; These are spatial coordinates, which can be one-dimensional, two-dimensional, or three-dimensional. It is the number of terms in the series expansion of the random field; , These are the autocorrelation functions. The j-th eigenvalue and eigenfunction, ; To account for the cross-correlation between random fields, Its size is M×N;

[0017] When discretizing a random field using equation (2), the domain of the random field variables is defined by the Fredholm second-type integral equation. Solving for the eigenvalues ​​of the autocorrelation function and characteristic function conduct:

[0018] (3)

[0019] Furthermore, the log-normal distribution is used to describe the strength properties of soil and rock masses, while ensuring the non-negativity of the parameters; the normal random field generated by the KL series expansion method can be transformed into a log-random field through formula transformation:

[0020] (4)

[0021] In the formula, , , , and Here are the mean and standard deviation of the variable to be simulated. Coefficient of variation;

[0022] Steps S1-2, random wave simulation is obtained by superimposing a series of component waves determined by the wave spectrum; the JONSWAP spectrum is used to simulate random waves; the wave spectrum. Satisfy the following formula:

[0023] (5)

[0024] In the formula, ; ; ; ; f The wave frequency; The wave period corresponding to the peak point of the spectrum; and This represents the average wave height and average period of the first 1 / 3 of the largest waves in the wave train; This is the peak enhancement factor, with a value range of 1 to 7;

[0025] Random waves are composed of an infinite number of linear waves superimposed. Therefore, the wave height of a random wave acting on the sea level is expressed as:

[0026] (6)

[0027] (7)

[0028] ； ； (8)

[0029] In the formula, is a positive integer, N The larger the value, the higher the simulation accuracy. This represents the wave height of the i-th wave; This represents the average frequency of the i-th wave; Let be the initial phase of the i-th wave; Let represent the wave number of the i-th wave; since random waves consist of infinitely many linear waves, the pressure acting on the surface of the seabed soil is... Represented as:

[0030] (9)

[0031] As a preferred option, step S2 specifically includes the following steps:

[0032] The constitutive model for the instability of the seabed slope is described using the Biot porous elastic and Mohr-Coulomb models. The reliability of the model (characterized by failure probability) is calculated using the stochastic finite element method.

[0033] Step S2-1: Using Biot's consolidation equation as the governing equation for elastic calculation; for a two-dimensional plane seabed at a finite depth, when waves propagate on the seabed, considering the compressibility of the pore fluid and neglecting the soil inertial force term, the governing equation for the seabed soil is:

[0034] (10)

[0035] In the formula, ρ is the excess pore water pressure in the porous elastic medium; k is the permeability coefficient of the seabed; The volumetric strain of the seabed soil. ; Porosity; The density of seawater; Let be the compressibility coefficient of water. ,in; Let be the bulk modulus of water, and take 2 × 10⁻⁶. 9 Pa; Saturation; It is the hydrostatic pressure;

[0036] Based on Terzaghi's effective stress principle, the equilibrium equation for the two-dimensional plane strain model of the soil skeleton, characterized by the relationship between effective stress and pore pressure, is given by the following formula:

[0037] (11)

[0038] (12)

[0039] In the formula, yes The effective normal stress in the direction is Effective normal stress in the direction, On a plane perpendicular to the x-axis Shear stress in the direction;

[0040] Step S2-1: Based on the linear elasticity theory, the relationship between the effective elastic stress and the soil displacement is given by the following formula:

[0041] (13)

[0042] (14)

[0043] (15)

[0044] By substituting equations (13)-(15) into equations (11) and (12), the force balance equations finally become:

[0045] (16)

[0046] (17)

[0047] In the formula, u , v For the soil skeleton along x , z Displacement in direction; The excess pore water pressure in a porous elastic medium; The volumetric strain of the seabed soil; The shear modulus of the soil; Poisson's ratio; It is the Laplace operator;

[0048] Equations (10), (16), and (17) constitute a problem concerning three unknown variables. p , u and w The third-order partial differential equations need to be solved based on specific boundary conditions; finite thickness ( h The two-dimensional seabed boundary condition is: the effective normal stress perpendicular to the seabed surface. and shear stress The wave pressure on the seabed surface is 0. effect, , The seabed side is considered an impermeable boundary, which also restricts normal displacement. The seabed bottom is an impermeable rigid substrate. ;

[0049] Step S2-3: The initial stability problem of the seabed slope considering wave forces is treated as a plane strain problem and analyzed using a two-dimensional elastoplastic finite element method. An elastoplastic soil constitutive model obeying the Mohr-Coulomb yield criterion is adopted, and the shear strength is expressed as:

[0050] (18)

[0051] In the formula, and These are the effective cohesion and effective internal friction angle of the soil, respectively. Normal stress;

[0052] Based on the plastic failure state of the simulated unit in the above constitutive model, elastoplastic analysis of slope instability is performed to obtain the dynamic process and sliding results of slope instability; the safety factor of the slope is calculated by the strength reduction method, and the slope stability is analyzed by reducing the value of the shear strength parameter.

[0053] Assume the original strength index of the seabed slope soil is and Using the strength reduction factor (SRF) to reduce the strength index, the hypothetical strength indices are as follows:

[0054] (19)

[0055] (20)

[0056] Soil parameters are generated using the Monte Carlo simulation method. M sets of random field samples were obtained, and the stability analysis of the seabed slope under wave action was performed using the random finite element method (SFEM). The corresponding M sets of FS time series values ​​were then obtained, and the results were obtained using formula (21). ;

[0057] (21)。

[0058] Furthermore, the training of the machine learning agent model in step S3 includes the following steps:

[0059] Step S3-1 M The numerical simulation results were used as the training set, and the input variables were geotechnical parameters related to the number of mesh elements in the stochastic finite element model, including effective cohesion. and effective internal friction angle The values ​​and time history curves of random wave loads, the output variables are M Safety factor and stability label obtained from a set of numerical simulations;

[0060] Step S3-2: The training dataset is divided into a training set and a test set, with the training set accounting for 70% and the test set accounting for 30%, respectively. Based on the input and output of the training set, a data-driven initial security coefficient prediction proxy model and a stability label prediction proxy model are constructed, respectively.

[0061] Step S3-3: Use the machine learning grid search algorithm to find the optimal hyperparameters for the initial security coefficient prediction agent model and the stability label prediction agent model respectively. Find the optimal hyperparameters for the two corresponding machine learning models, use the optimal hyperparameters of the two models as the model pre-defined hyperparameters, retrain the model, and save the two models.

[0062] Step S3-4: Regenerate based on step S1 N A new set of cohesive random fields, internal friction angle random fields, and random wave time history loads, among which... The generated random data distribution is input into the optimal safety factor prediction proxy model and the stability label prediction proxy model saved in step S3-3, and outputs respectively. N Group safety factor and N Group stability labels and calculate failure probability based on formula (21);

[0063] Furthermore, in step S3-1, when the numerical simulation uses the binary classification method BCM to calculate only stability, the BPNN model outputs a stability label—0 for stable or 1 for unstable.

[0064] Furthermore, the evaluation of the proxy model and the assessment of its computational cost in step S4 specifically include the following steps:

[0065] Step S4-1, M The cohesive random field, internal friction angle random field, and random wave time history load distribution in the numerical simulation are input into the optimal safety factor prediction surrogate model and stability label prediction surrogate model saved in steps S3-4, and output respectively. M Group safety factor and M Group stability tags;

[0066] Step S4-2, based on output M The results of the safety factor group were compared with the closeness between the predicted values ​​and the actual values ​​of the surrogate model, as well as the accuracy and confusion matrix of the surrogate model in predicting the stability label of the seabed slope. The accuracy and generalization ability of the model were evaluated through 10-fold cross-validation and model evaluation indicators.

[0067] Step S4-3: Solving statistical direct Monte Carlo simulation, safety factor prediction surrogate model, and stability label prediction surrogate model. M Group safety factor, M The computation time of the group stability label was compared with the failure probability calculation time of different models to verify the efficiency of the machine learning agent model.

[0068] The present invention provides a method for calculating the failure probability of a seabed slope based on stochastic finite element numerical simulation combined with machine learning algorithms. By conducting multiple Monte Carlo stochastic finite element numerical simulations and machine learning algorithms, a multi-scenario reliability surrogate model of the seabed slope can be established, enabling accurate and rapid assessment of the failure probability of the seabed slope. Due to the adoption of the above technical solution, the present invention has the following beneficial effects compared with existing technologies:

[0069] (1) This invention considers the initial stability of the seabed slope under different uncertainty scenarios and establishes a reliability surrogate model for the seabed slope under wave scenarios;

[0070] (2) Compared with the existing methods for assessing and analyzing the failure probability of seabed slopes, the present invention is economical, time-saving, labor-saving, and the calculation results are more reasonable and reliable, and has a certain degree of novelty.

[0071] (3) The present invention is simple to operate and easy to apply in practice. The trained machine learning proxy model overcomes the problem of low computational efficiency of numerical simulation and provides a new method and idea for quickly and conveniently calculating the failure probability of seabed slopes under different scenarios.

[0072] 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

[0073] 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:

[0074] Figure 1 The flowchart shows the multi-scenario seabed slope failure probability assessment and analysis method based on the BPNN algorithm.

[0075] Figure 2 A typical implementation of inputting random field simulation and its statistical characteristics into a stochastic finite element numerical model;

[0076] Figure 3 A typical implementation of inputting a random wave load time history curve into a random finite element numerical model;

[0077] Figure 4 A comparison of the power spectrum and theoretical spectrum of simulated wave height time history curve sequences under different cutoff orders;

[0078] Figure 5 This is a schematic diagram illustrating two simulation scenarios of uncertainty.

[0079] Figure 6 The safety factor distribution and failure probability curves calculated by direct Monte Carlo simulation and BPNN surrogate model under random geotechnical parameter scenarios;

[0080] Figure 7 The FS distribution and failure probability curves calculated for direct Monte Carlo simulation and BPNN surrogate model under random wave loading scenario;

[0081] Figure 8 To determine the closeness between the true value of the predicted safety factor and the predicted label for the BPNN surrogate model, and to perform 10-fold cross-validation and evaluation metrics.

[0082] Figure 9 Predicting the confusion matrix of stability labels on the training and test sets and R-squared results for 10-fold cross-validation for a BPNN surrogate model. 2 ;

[0083] Figure 10 The computation time difference is between the stochastic finite element numerical model and the BPNN surrogate model. Detailed Implementation

[0084] 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.

[0085] 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.

[0086] The following is combined Figures 1 to 10 The failure probability assessment and analysis method of the seabed slope based on the BP neural network algorithm of the present invention will be described in detail in the embodiments of the present invention.

[0087] This invention proposes a method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm, which specifically includes the following steps:

[0088] Step S1: Based on the distribution characteristics of soil and rock parameters and wave parameters, a random field of soil and rock parameters is generated using the KL series expansion method, and a random wave load is generated using the spectral representation method, serving as the material parameters and boundary conditions for the numerical model; considering two uncertainties, soil parameters (such as...) and To address the randomness of slope plasticity parameters (cohesion and internal friction angle), the KL series expansion method was used to generate random fields for these two parameters. The specific steps included:

[0089] Step S1-1: The uncertainty of sediment intensity parameters in the model is characterized using a random field, with the exponential autocorrelation function used as the basic function for random field simulation. Its expression is:

[0090] (1)

[0091] In the formula, and They represent the first i The unit and the first j The absolute distance between units in the horizontal and vertical directions; and These represent the autocorrelation distances in the horizontal and vertical directions, respectively. The larger the autocorrelation distance, the stronger the spatial correlation of the parameters.

[0092] Based on the autocorrelation function, a normally distributed random field is generated in a certain discrete domain. The KL series expansion method is used to discretize the normally distributed random field.

[0093] Suppose the research subjects are For the nth random field, for the nth For a random field, if the random field is a normal random field, then its KL discretization result is:

[0094] (2)

[0095] In the formula, To take into account random field averages with mean squared deviation Discrete values ​​of a normally distributed random field; These are spatial coordinates, which can be one-dimensional, two-dimensional, or three-dimensional. It is the number of terms in the series expansion of the random field; , These are the autocorrelation functions. The j-th eigenvalue and eigenfunction, ; To account for the cross-correlation between random fields, Its size is M×N;

[0096] When discretizing a random field using equation (2), the domain of the random field variables is defined by the Fredholm second-type integral equation. Solving for the eigenvalues ​​of the autocorrelation function and characteristic function conduct:

[0097] (3)

[0098] Furthermore, the log-normal distribution is used to describe the strength properties of soil and rock masses, while ensuring the non-negativity of the parameters; the normal random field generated by the KL series expansion method can be transformed into a log-random field through formula transformation:

[0099] (4)

[0100] In the formula, , , , and Here are the mean and standard deviation of the variable to be simulated. Coefficient of variation;

[0101] Steps S1-2, random wave simulation is obtained by superimposing a series of component waves determined by the wave spectrum; the JONSWAP spectrum is used to simulate random waves; the wave spectrum. Satisfy the following formula:

[0102] (5)

[0103] In the formula, ; ; ; f The wave frequency; The wave period corresponding to the peak point of the spectrum; and This represents the average wave height and average period of the first 1 / 3 of the largest waves in the wave train; This is the peak enhancement factor, with a value range of 1 to 7;

[0104] Random waves are composed of an infinite number of linear waves superimposed. Therefore, the wave height of a random wave acting on the sea level is expressed as:

[0105] (6)

[0106] (7)

[0107] ； ； (8)

[0108] In the formula, is a positive integer, N The larger the value, the higher the simulation accuracy; This represents the wave height of the i-th wave; This represents the average frequency of the i-th wave; Let be the initial phase of the i-th wave; Let represent the wave number of the i-th wave; since random waves consist of infinitely many linear waves, the pressure acting on the surface of the seabed soil is... Represented as:

[0109] (9).

[0110] It should be noted that the relevant distances can be determined by referring to the static cone penetration test of the study area. In this embodiment, the parameters used are shown in Table 1. Both the effective cohesion and the effective internal friction angle are assumed to follow a log-normal distribution.

[0111] Figure 2 shows a typical implementation and distribution characteristics of effective cohesion and effective internal friction angle generated using the KL series expansion method and random field characteristic parameters. As can be seen from the figure, the generated cohesion and internal friction angle random fields have a long horizontal correlation distance and a short vertical correlation distance, which is consistent with the set values. From the probability density distribution diagram of the two parameters, the probability density distribution of both parameters shows a skewed distribution, which is consistent with the log-normal distribution. After taking the logarithm of the parameter values, the probability density shows a normal distribution. The mean and coefficient of variation of the simulated parameters are also consistent with the set parameter values.

[0112] Table 1. Stochastic Field Characteristic Parameters of Submarine Slope Soil and Rock Parameters

[0113]

[0114] It should be noted that, based on typical wave spectrum characteristics, the sea surface wave height time history curves at different locations were simulated using the JONSWAP spectrum, and the parameters used are shown in Table 2.

[0115] Table 2 Parameters required for random wave simulation

[0116]

[0117] Furthermore, the simulated spectrum of the random wave time sequence obtained by simulation is derived from the autocorrelation function and smoothed. It can be seen that the target spectrum and the smoothed spectrum fit well, which is the random wave time sequence obtained by simulation based on the linear wave superposition method.

[0118] In this embodiment, a typical time-history variation curve of wave height and wave pressure is shown in Figure 3. The power spectrum of the simulated sequence under different cutoff terms N is compared with the target JONSWAP spectrum to show their similarity. Figure 4 As shown, as N increases, the simulated spectrum gradually approaches the target spectrum; when N=300, the simulated spectrum is very close to the target spectrum; when N=800, the simulated spectrum is almost identical to the target spectrum.

[0119] Furthermore, the generated random soil and rock field and random wave are used as material parameters and boundary conditions of the numerical model, respectively; among them, the random soil and rock parameter field is assigned to the model as plastic material parameters, and the wave pressure time history curve is applied to the model as a load of the numerical model.

[0120] Step S2: Establish a numerical model for calculating the stability of the seabed slope, considering multiple uncertainty scenarios, coupling the generated random field and random process, and conducting direct Monte Carlo simulation; this embodiment addresses two different uncertainty scenarios (random soil parameter scenario and random wave load scenario). Figure 5 ), and conducted 1000 numerical simulation tests on the stability of the seabed slope based on direct Monte Carlo simulation. After establishing the geometric model, assigning material parameters, and applying boundary conditions, the numerical simulation of the seabed slope stability was carried out.

[0121] Specifically, the following steps are included:

[0122] The constitutive model for the instability of the seabed slope is described using the Biot porous elastic and Mohr-Coulomb models. The reliability of the model (characterized by failure probability) is calculated using the stochastic finite element method.

[0123] Step S2-1: First, perform stress equilibrium. Apply load under still water conditions as the first loading step in the finite element analysis to obtain the still water stress field generated by the weight of the soil and the buoyancy of the water, thus balancing the stress and obtaining the initial stress state after stress equilibrium. The Biot consolidation equation is used as the governing equation for elastic calculation. For a two-dimensional plane seabed at a finite depth, when waves propagate on the seabed, considering the compressibility of the pore fluid and neglecting the soil inertial force term, the governing equation for the seabed soil is:

[0124] (10)

[0125] In the formula, ρ is the excess pore water pressure in the porous elastic medium; k is the permeability coefficient of the seabed; The volumetric strain of the seabed soil. ; Porosity; The density of seawater; Let be the compressibility coefficient of water. ,in; Let be the bulk modulus of water, and take 2 × 10⁻⁶. 9 Pa; Saturation; It is the hydrostatic pressure;

[0126] Based on Terzaghi's effective stress principle, the equilibrium equation for the two-dimensional plane strain model of the soil skeleton, characterized by the relationship between effective stress and pore pressure, is given by the following formula:

[0127] (11)

[0128] (12)

[0129] In the formula, yes Effective normal stress in the direction, yes Effective normal stress in the direction, On a plane perpendicular to the x-axis Shear stress in the direction;

[0130] Step S2-2: Apply external loads, using wave force as the surcharge at the upper boundary of the model. Add the wave pressure at typical moments to the load module. Based on the aforementioned seabed constitutive model, realize the wave loading in the second analysis step. Based on linear elasticity theory, the relationship between effective elastic stress and soil displacement is given by the following formula:

[0131] (13)

[0132] (14)

[0133] (15)

[0134] By substituting equations (13)-(15) into equations (11) and (12), the force balance equations finally become:

[0135] (16)

[0136] (17)

[0137] In the formula, u , v For the soil skeleton along x , z Displacement in direction; The excess pore water pressure in a porous elastic medium; The volumetric strain of the seabed soil; The shear modulus of the soil; Poisson's ratio; It is the Laplace operator;

[0138] Equations (10), (16), and (17) constitute a problem concerning three unknown variables. p , u and w The third-order partial differential equations need to be solved based on specific boundary conditions; finite thickness ( h The two-dimensional seabed boundary condition is: the effective normal stress perpendicular to the seabed surface. and shear stress The wave pressure on the seabed surface is 0. effect, , The seabed side is considered an impermeable boundary, which also restricts normal displacement. The seabed bottom is an impermeable rigid substrate. ;

[0139] Step S2-3: Determine the stability of the seabed slope using the strength reduction method. This involves determining the effective cohesion of the soil. and effective internal friction angle The strength reduction factor (SRF) is implemented as the third analysis step. In this embodiment, the interval of the SRF is 0.01, and the failure of the finite element numerical calculation iteration is used as the failure criterion for the stability of the seabed slope. The initial stability problem of the seabed slope considering the wave force is regarded as a plane strain problem and analyzed by two-dimensional elastoplastic finite element analysis. An elastoplastic soil constitutive model that obeys the Mohr-Coulomb yield criterion is adopted, and the shear strength is expressed as:

[0140] (18)

[0141] In the formula, and These are the effective cohesion and effective internal friction angle of the soil, respectively. Normal stress;

[0142] Based on the plastic failure state of the simulated unit in the above constitutive model, elastoplastic analysis of slope instability is performed to obtain the dynamic process and sliding results of slope instability; the safety factor of the slope is calculated by the strength reduction method, and the slope stability is analyzed by reducing the value of the shear strength parameter.

[0143] Assume the original strength index of the seabed slope soil is and Using the strength reduction factor (SRF) to reduce the strength index, the hypothetical strength indices are as follows:

[0144] (19)

[0145] (20)

[0146] Using the Monte Carlo simulation method, 1000 sets of random field samples were generated for the soil parameters. The stability analysis of the seabed slope under wave action was performed using the stochastic finite element method (SFEM), and 1000 sets of FS time series values ​​were obtained. Subsequently, the results were obtained using formula (21). ;

[0147] (21)。

[0148] It should be noted that if it is only necessary to determine the stability of the seabed slope in its current state in order to calculate the reliability, the strength reduction method can be omitted, and the calculation can be performed only once (Binary Classification Method BCM). The model convergence is used as the criterion for stability, and a stability label (0 or 1) is output. This can significantly shorten the calculation time in reliability calculation.

[0149] Considering only the uncertainty of a single soil parameter, and treating the soil parameter as a random field for study, the slope angle of the seabed slope... α =5°, slope height H s =15 m; Deformation modulus E =30 MPa, Poisson's ratio ν =0.3; saturated specific gravity γ =20 kN / m 3 Effective internal friction angle φ =2°, effective cohesion c =20 kPa, corresponding to cohesive soil. Since the internal friction angle is small, it has little impact on the safety factor. In the model, only the effective cohesion of the plastic parameter is regarded as a random field, and its mean is taken as 20 kPa. The simulation parameters are shown in Table 1. Under still water conditions, 1000 Monte Carlo simulations were carried out using the COMSOL Multiphysics large-scale multiphysics simulation analysis software with the strength reduction method and the binary classification method, respectively. The safety factor values ​​of 1000 seabed slopes and the stability labels of 1000 seabed slopes were obtained.

[0150] Considering only the uncertainty of wave loads, the seabed is treated as a homogeneous soil. The model plastic parameters (effective cohesion and effective internal friction angle) are the mean values ​​of random field simulations. The simulation parameters of wave loads are based on the data in Table 2. 1000 random wave load time history curves are generated. Similarly, 1000 Monte Carlo simulations are performed using the COMSOL Multiphysics large-scale multiphysics simulation analysis software with the strength reduction method and binary classification method. The calculation time is 20s. The safety factor curve and stability label of the seabed slope under 1000 wave loads are obtained.

[0151] It should be noted that the finite element simulation solution software in this invention is not limited to the software used in this embodiment. Other software capable of solving the constitutive equation problem targeted by this invention can also perform this step.

[0152] Step S3: Use the generated random field and random process as input, and the numerical simulation results as output to construct training samples to train the machine learning surrogate model.

[0153] Specifically, in this embodiment, 1000 sets of random field parameters, random wave load parameters, and numerical simulation results are used as data. The training set and test set are divided in a 7:3 ratio. BPNN models under two uncertain scenarios are trained and hyperparameters are optimized. The optimal models under the two uncertain scenarios are used to predict the slope safety coefficient and stability label, and the failure probability is calculated.

[0154] For random geotechnical parameter scenarios, when using a BP neural network model for machine learning modeling, the input data is first subjected to principal component dimensionality reduction to 20 columns. After dimensionality reduction, 1000×20 features are used as input, and 1000×1 safety factors are used as input and output to train the model. After the model training is completed, 10,000 random field samples are generated using the KL series expansion method described in step 1, which are used as input to train the BPNN model to obtain 10,000 safety factor values. The safety factor distribution and failure probability curves of Direct Monte Carlo Simulation (Direct MC) and Machine Learning Monte Carlo Simulation (ML MC) are compared. Figure 6 In the probability density distribution diagram ( Figure 6 In (a) and (b) of the diagram, the histograms of both Direct MC and MLMC show an approximate normal distribution. However, the distribution curve of MLMC fits the theoretical distribution more smoothly and has a higher degree of agreement, thus improving the stability and accuracy of probability density estimation. In the cumulative distribution function diagram ( Figure 6 In (c) and (d) of the model, the step-like empirical distribution curves of both methods are quite close to the theoretical CDF, especially in the middle and tail sections where the fitting effect is better. Regarding the calculation of instability probability, the instability probability obtained by Direct MC is... =0.081, while the result of ML MC is =0.082, the difference between the two is minimal, indicating that the ML MC method can effectively reproduce the failure probability calculation results of Direct MC while ensuring computational accuracy. The gray shaded area in the figure represents the region where the safety factor is less than 1, that is, the probability range corresponding to the unstable state. Figure 6 Tables (e) and (f) compare the differences between Direct MC and ML MC in the instability probability convergence process. Direct MC converges more slowly and exhibits significant fluctuations, while ML MC converges faster and has smaller fluctuations, demonstrating its efficiency and stability in failure probability calculation.

[0155] For the scenario of random wave loading, a BPNN model is also used to establish a proxy model for calculating the failure probability of the seabed slope. The input data is the time series data of waves, and the output is the minimum safety factor value corresponding to the safety factor time history curve. During training, the weights and biases of the neural network are optimized through the BP algorithm so that the model can fit the training set data to the greatest extent. After the model training is completed, 10,000 random wave samples are generated and input into the BPNN model to obtain 10,000 safety factor values. The safety factor distribution and failure probability curves of Direct Monte Carlo Simulation (Direct MC) and Machine Learning Monte Carlo Simulation (ML MC) are compared. Figure 7 Under wave load, the minimum safety factor of the seabed slope still approximately follows a normal distribution, but the number of samples less than 1 is significantly increased compared to the still water condition. Similarly, the distribution curve of the machine learning Monte Carlo simulation is smoother, and the cumulative probability density functions of the direct Monte Carlo simulation and the machine learning Monte Carlo simulation are basically the same. The failure probability of the seabed slope determined by 1000 simulations is 0.204, and the failure probability determined by 10000 simulations is 0.212. Based on the law of large numbers and the convergence of the curve, the final calculated failure probability of the seabed slope is determined to be 0.212, which is significantly increased compared to the still water condition. This reflects that wave load significantly reduces the safety of the seabed slope, and also indicates that the contribution of random waves to the instability of the seabed slope is greater than that of random soil parameters.

[0156] Step S4: Compare the results of the established machine learning agent model with the results of the direct Monte Carlo simulation in step S2 to verify the usability of the model and evaluate the accuracy and time complexity of the machine learning agent model.

[0157] In this embodiment, 1000 sets of random parameters used in the numerical simulation are first input into the BPNN surrogate model for safety factor prediction, and the closeness between the predicted values ​​and the actual values ​​is compared (Figure 8). The FS prediction results show a very high degree of fit between the predicted and actual values. The coefficient of determination R0 for the training and test sets is... 2 The values ​​of 0.994 and 0.987 respectively indicate that the model can fully capture the nonlinear mapping relationship between the input features and the FS. The average R-value of 10-fold cross-validation is... 2 The model achieves a mean absolute error (MAE) of 0.9858, demonstrating its robustness and reliability. Regarding error metrics, the MAE for the training and test sets are 4.113 and 4.755, respectively, while the MSEs are 29.978 and 50.321, both at relatively low levels. The mean absolute percentage error (AAPE) also ranges from 0.102 to 0.121. This indicates that the BPNN not only converges well during training but also exhibits good generalization ability in independent tests.

[0158] Similarly, the 1000 sets of random parameters used in the numerical simulation were input into the stability prediction BPNN surrogate model as input data, in the prediction of stability labels ( Figure 9 The BPNN model also demonstrated high prediction accuracy. The training set confusion matrix showed that all unstable and stable samples were correctly classified, with an overall accuracy of 98.3% and an error rate of 1.7%. The test set prediction results were slightly lower than the training set, but still maintained high accuracy, with an accuracy of 97.3% and an error rate of only 2.7%. This indicates that the BPNN model can effectively distinguish between stable and unstable states. Furthermore, the results of the 10-fold cross-validation show an average R0... 2 The result of 0.9719 further demonstrates the accuracy and stability of the classification model.

[0159] The performance of the BPNN surrogate model was evaluated in terms of time complexity, comparing the time costs of the stochastic finite element method (SFEM) for solving the safety factor, the binary classification method (BCM) for calculating the slope stability label, and the machine learning surrogate model (BPNN) for alternative solutions. Taking the calculation time of a stochastic wave load scenario as an example, on a laptop with an Intel Core i5-5010U 2.3 GHz processor, Figure 10(a) shows the difference in stability calculation time between SRM and BCM. Without safety factor calculation, the average CPU time for each stochastic finite element simulation is 13 seconds. With SRM for safety factor calculation, the average CPU time for each stochastic finite element simulation reaches 65 seconds. The calculation time of the binary classification method is about 1 / 13 of that of the intensity reduction method. Figure 10 (b) Further extending to reliability analysis, the proposed BPNN surrogate model can reduce CPU computation time from hours to tens of seconds. The efficiency of BCM combined with the machine learning model is still better than that of FS computation. BPNN achieves approximately 10 times the efficiency of the traditional SFEM-FS method in failure probability calculation. 4 Multiples of 10 3 The time acceleration is several times faster, and this trend still holds true for large-scale MC samples. This reflects the significant advantages of machine learning surrogate models in avoiding repeated numerical solutions and quickly completing batch predictions, providing an efficient and feasible option for rapid risk assessment and real-time decision-making in subsequent seabed geological engineering.

[0160] 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.

[0161] 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.

[0162] 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 method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm, characterized in that... Specifically, it includes the following steps: Step S1: Based on the distribution characteristics of soil and rock parameters and wave parameters, a random field of soil and rock parameters is generated using the KL series expansion method, and a random wave load is generated using the spectral representation method, which serves as the material parameters and boundary conditions for the numerical model; specifically, this includes the following steps: Step S1-1: The uncertainty of sediment intensity parameters in the model is characterized using a random field, with the exponential autocorrelation function used as the basic function for random field simulation. Its expression is: (1) In the formula, and They represent the first i The unit and the first j The absolute distance between units in the horizontal and vertical directions; and These represent the autocorrelation distances in the horizontal and vertical directions, respectively. The larger the autocorrelation distance, the stronger the spatial correlation of the parameters. Based on the autocorrelation function, a normally distributed random field is generated in a certain discrete domain. The KL series expansion method is used to discretize the normally distributed random field. Suppose the research subjects are For the nth random field, for the nth For a random field, if the random field is a normal random field, then its KL discretization result is: (2) In the formula, To take into account the random field mean and standard deviation Discrete values ​​of a normally distributed random field; These are spatial coordinates, which can be one-dimensional, two-dimensional, or three-dimensional. It is the number of terms in the series expansion of the random field; , These are the autocorrelation functions. The j-th eigenvalue and eigenfunction, ; To account for the cross-correlation between random fields, Its size is M×N; When discretizing a random field using equation (2), the domain of the random field variables is defined by the Fredholm second-type integral equation. Solving for the eigenvalues ​​of the autocorrelation function and characteristic function conduct: (3) The strength properties of soil and rock masses are described using a log-normal distribution, while ensuring the non-negativity of the parameters; the normal random field generated by the KL series expansion method is transformed into a log-random field through formula transformation: (4) In the formula, , , , and Here are the mean and standard deviation of the variable to be simulated. Coefficient of variation; Steps S1-2, random wave simulation is obtained by superimposing a series of component waves determined by the wave spectrum; the JONSWAP spectrum is used to simulate random waves; the wave spectrum. Satisfy the following formula: (5) In the formula, ; ; ; f The wave frequency; The wave period corresponding to the peak point of the spectrum; and This represents the average wave height and average period of the first 1 / 3 of the largest waves in the wave train; This is the peak enhancement factor, with a value range of 1 to 7; Random waves are composed of an infinite number of linear waves superimposed. Therefore, the wave height of a random wave acting on the sea level is expressed as: (6) (7) ； ； (8) In the formula, is a positive integer, N The larger the value, the higher the simulation accuracy; This represents the wave height of the i-th wave; This represents the average frequency of the i-th wave; Let be the initial phase of the i-th wave; Let represent the wave number of the i-th wave; since random waves consist of infinitely many linear waves, the pressure acting on the surface of the seabed soil is... Represented as: (9)； Step S2: Establish a numerical model for calculating the stability of the seabed slope, considering multiple uncertainty scenarios, coupling the generated random field and random process, and conducting direct Monte Carlo simulation; specifically including the following steps: Step S2-1: Using Biot's consolidation equation as the governing equation for elastic calculation; for a two-dimensional plane seabed at a finite depth, when waves propagate on the seabed, considering the compressibility of the pore fluid and neglecting the soil inertial force term, the governing equation for the seabed soil is: (10) In the formula, ρ is the excess pore water pressure in the porous elastic medium; k is the permeability coefficient of the seabed; The volumetric strain of the seabed soil. ; Porosity; The density of seawater; Let be the compressibility coefficient of water. ,in; Let be the bulk modulus of water, and take 2 × 10⁻⁶. 9 Pa; Saturation; It is the hydrostatic pressure; Based on Terzaghi's effective stress principle, the equilibrium equation for the two-dimensional plane strain model of the soil skeleton, characterized by the relationship between effective stress and pore pressure, is given by the following formula: (11) (12) In the formula, yes Effective normal stress in the direction, yes Effective normal stress in the direction, On a plane perpendicular to the x-axis Shear stress in the direction; Step S2-1: Based on the linear elasticity theory, the relationship between the effective elastic stress and the soil displacement is given by the following formula: (13) (14) (15) By substituting equations (13)-(15) into equations (11) and (12), the force balance equations finally become: (16) (17) In the formula, u , v For the soil skeleton along x , z Displacement in direction; The excess pore water pressure in a porous elastic medium; The volumetric strain of the seabed soil; The shear modulus of the soil; Poisson's ratio; It is the Laplace operator; Equations (10), (16), and (17) constitute a problem concerning three unknown variables. p , u and w The third-order partial differential equations need to be solved based on specific boundary conditions; finite thickness ( h The two-dimensional seabed boundary condition is: the effective normal stress perpendicular to the seabed surface. and shear stress The wave pressure on the seabed surface is 0. effect, , The seabed side is considered an impermeable boundary, which also restricts normal displacement. The seabed bottom is an impermeable rigid substrate. ; Step S2-3: The initial stability problem of the seabed slope considering wave forces is treated as a plane strain problem and analyzed using a two-dimensional elastoplastic finite element method. An elastoplastic soil constitutive model obeying the Mohr-Coulomb yield criterion is adopted, and the shear strength is expressed as: (18) In the formula, and These are the effective cohesion and effective internal friction angle of the soil, respectively. Normal stress; Based on the plastic failure state of the above-mentioned elastoplastic soil constitutive model, elastoplastic analysis of slope instability is performed to obtain the dynamic process and sliding results of slope instability; the safety factor of the slope is calculated by the strength reduction method, and the slope stability is analyzed by reducing the value of the shear strength parameter. Assume the original strength index of the seabed slope soil is and Using the strength reduction factor (SRF) to reduce the strength index, the hypothetical strength indices are as follows: (19) (20) Soil parameters are generated using the Monte Carlo simulation method. M sets of random field samples were obtained, and the stability analysis of the seabed slope under wave action was performed using the stochastic finite element method (SFEM). The corresponding M sets of FS time series values ​​were then obtained, and the results were obtained using formula (21). ; (21) ； Step S3: Using the generated random field and random process as input and the numerical simulation results as output, construct training samples to train the machine learning surrogate model, and carry out machine learning Monte Carlo simulation to calculate the slope stability. Step S4: Compare the results of the established machine learning agent model with the results of the direct Monte Carlo simulation to verify the usability of the model and evaluate the accuracy and time complexity of the machine learning agent model.

2. The method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm according to claim 1, characterized in that... The training of the machine learning agent model in step S3 includes the following steps: Step S3-1 M The numerical simulation results were used as the training set, and the input variables were geotechnical parameters related to the number of mesh elements in the stochastic finite element model, including effective cohesion. and effective internal friction angle The values ​​and time history curves of random wave loads, the output variables are M Safety factor and stability label obtained from a set of numerical simulations; Step S3-2: The training dataset is divided into a training set and a test set, with the training set accounting for 70% and the test set accounting for 30%, respectively. Based on the input and output of the training set, a data-driven initial security coefficient prediction proxy model and a stability label prediction proxy model are constructed, respectively. Step S3-3: Use the machine learning grid search algorithm to find the optimal hyperparameters for the initial safety coefficient prediction agent model and the stability label prediction agent model respectively. Find the optimal hyperparameters for the two corresponding machine learning models, use the optimal hyperparameters of the two models as the model pre-defined hyperparameters, retrain the model, and save the two models. Step S3-4: Regenerate based on step S1 N A new set of cohesive random fields, internal friction angle random fields, and random wave time history loads, among which... The generated random data distribution is input into the optimal safety factor prediction proxy model and the stability label prediction proxy model saved in step S3-3, and outputs respectively. N Group safety factor and N The stability label is set, and the failure probability is calculated based on formula (21).

3. The method for assessing and analyzing the failure probability of a seabed slope based on a BP neural network algorithm according to claim 2, characterized in that... In step S3-1, when the numerical simulation uses the binary classification method BCM to calculate only stability, the BPNN model outputs a stability label—0 for stable or 1 for unstable.

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