Parameter probability inversion method and system based on SPH water-soil coupling scouring erosion
By combining the SPH and Bayesian-MCMC methods, the uncertainty of soil parameters is quantified, which solves the problem of high parameter uncertainty in existing scour and erosion models and realizes the probabilistic prediction and parameter reliability improvement of scour and erosion models.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING UNIV OF TECH
- Filing Date
- 2026-01-31
- Publication Date
- 2026-05-12
Smart Images
Figure CN122016449A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of numerical simulation and parameter identification technology in geotechnical engineering, specifically involving a parameter probability inversion method and system based on SPH water-soil coupled scour erosion. Background Technology
[0002] Water and sediment erosion is a key physical process in river evolution, coastal erosion, and geological disasters such as landslide dam failure. Accurate prediction of water and sediment erosion behavior is highly dependent on the reasonableness of the values of key soil mechanical parameters (such as the initial internal friction angle and erosion rate). However, these parameters are significantly uncertain due to factors such as spatial variability of soil, experimental costs, and measurement errors.
[0003] Traditional scour erosion models are mostly based on empirical or semi-empirical formulas. While these models can reflect the basic laws of scour erosion to some extent, they struggle to accurately describe the physical mechanisms involved and cannot effectively quantify the inherent uncertainties of the parameters. Existing SPH-based scour erosion research primarily focuses on model framework construction, algorithm efficiency optimization, and physical process reproduction. However, the determination of key parameters in the model typically still relies on limited physical experimental data or engineering experience. This reliance on empirical parameters has significant limitations: obtaining parameters for specific operating conditions through experiments is costly and has limited representativeness; empirical values are often subjective and fail to objectively reflect the inherent spatial variability and uncertainty of the parameters; and existing methods fail to incorporate parameter uncertainty into the model prediction framework, making it impossible to quantify their reliability for key scour erosion prediction indicators. Summary of the Invention
[0004] To address the problems of high soil parameter uncertainty, reliance on empirical values, and difficulty in quantifying prediction reliability in existing scour and erosion models, this invention provides a probabilistic parameter inversion method and system based on Smooth Particle Hydrodynamics (SPH) and Bayesian-Markov Chain Monte Carlo (MCMC) methods. This method constructs a probabilistic inversion framework combining Smooth Particle Hydrodynamics (SPH) and Bayesian-Markov Chain Monte Carlo (MCMC) methods. It simulates the large deformation and dynamic evolution of the soil-water interface during two-phase water-sediment flow scour and erosion using the SPH method. Bayesian theory is used to integrate prior knowledge and observational data, and the MCMC algorithm is employed to estimate the posterior probability distribution of key soil parameters (such as initial internal friction angle and erosion rate). This achieves the transformation from parameter uncertainty quantification to probabilistic prediction of scour and erosion models, improving the reliability of numerical simulation of scour and erosion and reducing reliance on empirical parameters. It effectively solves the technical challenge of existing methods in simultaneously simulating complex soil-water coupling processes and quantifying and inverting parameter uncertainties.
[0005] To achieve the above objectives, the present invention provides the following solution: A parametric probabilistic inversion method based on SPH (soil-water coupled erosion) is proposed, the method comprising: S1: Establish a numerical model of water-sediment two-phase flow scouring and erosion based on a unified SPH framework; S2: Construct a Bayesian-MCMC parameter inversion framework; S3: Construct a likelihood function based on physical experimental observation data to quantify the consistency between the prediction results of the numerical model of water-sediment two-phase flow scour and erosion and the observation data, and provide data constraints for Bayesian inference; S3: Perform MCMC iterative sampling within the Bayesian-MCMC parameter inversion framework; S4: Perform convergence diagnosis on the MCMC iterative sampling results, and perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters. S5: Predict the probability of erosion based on posterior statistical features of parameters.
[0006] Preferred methods for establishing numerical models of water-sediment two-phase flow erosion based on a unified SPH framework include: A unified SPH method is used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface is achieved through the interparticle normal contact force and tangential viscous force. A linear time-varying strength model is introduced to describe the strength decay of the soil during scouring, and its evolution formula is as follows: ; In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0007] Preferred methods for constructing a Bayesian-MCMC parameter inversion framework include: The numerical model of water-sediment two-phase flow scour and erosion is embedded into a Bayesian inference framework. The posterior distribution of parameters is updated through MCMC sampling. The core Bayesian formula is: ; In the formula, For the posterior distribution, The parameter vector to be inverted, As a prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
[0008] Preferably, MCMC sampling uses the Metropolis-Hastings algorithm, and an automated process of automatic parameter transfer, model invocation, and result extraction is achieved by developing a dedicated interface between Python and the LS-DYNA solver.
[0009] Preferably, convergence diagnosis is assessed by examining the stationarity of the parameter trajectory; posterior distribution analysis includes calculating the posterior mean, standard deviation, and plotting the posterior probability density function.
[0010] The present invention also provides a parametric probabilistic inversion system based on SPH water-soil coupled scour erosion, the system being used to implement the aforementioned method, the system comprising: a first construction module, a second construction module, a quantization module, an iterative sampling module, a diagnosis and analysis module, and a prediction module; The first construction module is used to establish a numerical model of water-sediment two-phase flow scour and erosion based on a unified SPH framework; The second building module is used to construct the Bayesian-MCMC parameter inversion framework; The quantization module is used to construct a likelihood function based on physical experimental observation data, which is used to quantify the consistency between the prediction results of the numerical model of water-sediment two-phase flow scour and erosion and the observation data, and to provide data constraints for Bayesian inference. The iterative sampling module is used to perform MCMC iterative sampling within the Bayesian-MCMC parameter inversion framework; The diagnosis and analysis module is used to perform convergence diagnosis on the MCMC iterative sampling results and to perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters. The prediction module is used to predict the probability of erosion based on the posterior statistical features of the parameters.
[0011] Preferably, the process of establishing a numerical model for water-sediment two-phase flow scour and erosion based on a unified SPH framework includes: A unified SPH method is used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface is achieved through the interparticle normal contact force and tangential viscous force. A linear time-varying strength model is introduced to describe the strength decay of the soil during scouring, and its evolution formula is as follows: ; In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0012] Preferably, the process of constructing the Bayesian-MCMC parameter inversion framework includes: The numerical model of water-sediment two-phase flow scour and erosion is embedded into a Bayesian inference framework. The posterior distribution of parameters is updated through MCMC sampling. The core Bayesian formula is: ; In the formula, For the posterior distribution, The parameter vector to be inverted, As a prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
[0013] Preferably, MCMC sampling uses the Metropolis-Hastings algorithm, and an automated process of automatic parameter transfer, model invocation, and result extraction is achieved by developing a dedicated interface between Python and the LS-DYNA solver.
[0014] Preferably, convergence diagnosis is assessed by examining the stationarity of the parameter trajectory; posterior distribution analysis includes calculating the posterior mean, standard deviation, and plotting the posterior probability density function.
[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: The advantage of this invention is that it can effectively quantify the uncertainty of parameters, enabling it to reflect the inherent spatial variability of soil parameters. The resulting parameter estimates are more consistent with reality, providing a more reliable input for subsequent probabilistic predictions.
[0016] The inversion method provided by this invention can control the prior distribution and sampling process of each parameter. Based on this method, the complexity and accuracy of the inversion can be freely adjusted, which is beneficial for parameter inversion analysis with different accuracy requirements.
[0017] Furthermore, the inversion approach provided by this invention enables the parametric inversion of scour erosion models. This method allows for the convenient and rapid acquisition of the posterior probability distribution of the parameters, aiding in understanding the uncertainty characteristics of the parameters. Simultaneously, each inversion process is based on random sampling, ensuring the statistical reliability of the inversion results. Attached Figure Description
[0018] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 This is a schematic diagram of the overall process of the parameter probability inversion method for the SPH soil erosion model in this embodiment of the invention; Figure 2 This is a schematic diagram of the geometric model of the SPH two-phase flow erosion meter according to an embodiment of the present invention; Figure 3 This is a flowchart of the algorithm for the Bayesian-MCMC parameter inversion framework according to an embodiment of the present invention; Figure 4 The diagram shows the posterior distribution of inversion parameters and the Markov chain trajectory in an embodiment of the present invention, where (a) is a schematic diagram of the posterior distribution of the initial internal friction angle, and (b) is the slope of the erosion rate. k A schematic diagram of the posterior distribution, (c) is a schematic diagram of the Markov chain of the initial internal friction angle, and (d) is a schematic diagram of the Markov chain of the erosion rate slope; Figure 5 This is a comparison chart of the model inversion prediction results and experimental results in an embodiment of the present invention, wherein (a) is t = 0.25s Water-Soil Interface Outline Comparison Diagram, (b) is t = 0.5s Water-soil interface contour line comparison diagram, (c) is t = 0.75s Water-Soil Interface Outline Comparison Diagram, (d) is t = 1.0s Water and soil interface outline comparison diagram. Detailed Implementation
[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0022] Example 1 This invention provides a probabilistic inversion method for parameters of water-sediment erosion based on SPH (Soil-Water Coupled Inversion) model, specifically involving a method for probabilistically determining parameters of a water-sediment erosion model based on an SPH and Bayesian-Markov Chain Monte Carlo (MCMC) inversion framework. The innovation of this method lies in integrating the traditional deterministic SPH model with the probabilistic Bayesian-MCMC inversion framework, forming a probabilistic inversion framework from physical modeling to parameter uncertainty quantification, such as... Figure 1 As shown, the inversion method mainly consists of the following two parts: (1) An SPH (Soil-Water Coupled Erosion) model was established. The unified SPH method was used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface was achieved through the normal contact force and tangential viscous force between particles. A linear time-varying intensity model was introduced to describe the strength decay of the soil during the erosion process. Its evolution formula is as follows: In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0023] (2) Construct a Bayesian-MCMC probability inversion framework, embed the SPH model into the Bayesian inference framework, and update the posterior distribution of parameters through MCMC sampling. Its core Bayesian formula is: In the formula, For the posterior distribution, The parameter vector to be inverted, As a prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
[0024] Compared to traditional methods that rely solely on empirical parameters or deterministic inversion, this method, by combining the two components mentioned above, can transform scour erosion parameters from a deterministic to a probabilistic distribution, thereby improving the reliability of parameter identification and the ability to quantify the uncertainty of prediction results. The specific implementation process is as follows: S1: Establish a numerical model of water-soil two-phase flow scouring and erosion based on the unified SPH method. The water-soil interface is coupled through normal contact force and tangential viscous force to simulate the peeling, transport and deposition process of soil particles under water flow impact, providing a forward modeling basis for subsequent parameter inversion.
[0025] S2: Construct a Bayesian-MCMC parameter inversion framework, define the parameters to be inverted, and set their prior probability distribution. The framework is built based on Bayes' theorem and the Metropolis-Hastings iterative sampling algorithm. Its function is to combine prior knowledge with observational data, update the parameters from deterministic values to probability distributions, and improve the reliability of the estimation and prediction results of scour erosion model parameters. S3: Construct a likelihood function based on physical experimental observation data (such as soil-water interface elevation) to quantify the consistency between the prediction results of the SPH erosion model and the observation data, and provide data constraints for Bayesian inference; S4: Perform MCMC iterative sampling within the Bayesian-MCMC framework. In each iteration, candidate parameters are input into the SPH model for forward modeling, and the Markov chain state is updated according to the Metropolis-Hastings criterion to approximate the posterior distribution of the parameters.
[0026] S5: Perform convergence diagnosis on the MCMC iterative sampling results, and perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters, such as the posterior mean and standard deviation, and complete the probability update of the parameters from the prior to the posterior. S6: Based on the posterior statistical characteristics of the parameters obtained in S5, predict the probability of erosion and evaluate the accuracy of the model prediction to quantify the uncertainty of the prediction results.
[0027] In this embodiment, the innovation of the method lies in constructing a framework that integrates the SPH erosion physical model with the Bayesian-MCMC probabilistic inversion framework. This framework quantifies and updates key soil parameters in the SPH model through probabilistic inversion, overcoming the limitations of traditional methods that rely on empirical values and struggle to assess prediction uncertainties.
[0028] In this embodiment, the SPH scour erosion model adopts a weakly compressible fluid model for the water phase, and its pressure-density relationship is described by the Murnaghan equation of state; the sediment phase adopts a Mohr-Coulomb elastoplastic constitutive model.
[0029] In this embodiment, as an improvement to the existing soil constitutive model, a linear time-varying strength model is introduced to physically characterize the dynamic attenuation of soil strength during scour. Its expression is as follows: ; In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0030] In this embodiment, the prior distribution of the parameters to be inverted in the Bayesian-MCMC parameter inversion framework is set based on literature and engineering experience; a likelihood function is constructed based on the assumption that the prediction error follows a normal distribution to quantify the consistency between the SPH model prediction and the observed data.
[0031] In this embodiment, the MCMC sampling adopts the Metropolis-Hastings algorithm, and an automated process of automatic parameter transfer, model calling and result extraction is realized by developing a dedicated interface between Python and the LS-DYNA solver.
[0032] In this embodiment, convergence diagnosis is evaluated by checking the stationarity of the parameter trajectory; posterior distribution analysis can obtain the posterior statistical characteristics of the parameters and is used for the final prediction of scour erosion probability and uncertainty quantification.
[0033] Example 2 This invention provides a probabilistic method for determining parameters of a water-sediment erosion model based on the SPH and Bayesian-Markov chain Monte Carlo (MCMC) inversion framework. This embodiment uses the classic Louvain dam-break erosion physics experiment as a reference to demonstrate the complete process and implementation effect of the method. The method includes: (1) Based on the geometric dimensions and physical conditions of the Louvain dam failure test, a numerical model of water-sediment two-phase flow scour and erosion based on the unified SPH framework was established. The schematic diagram of the model structure is shown in [reference needed]. Figure 2 In the two-phase hydro-sediment SPH erosion model, the water phase adopts a weakly compressible fluid model, and its pressure-density relationship is described by the Murnaghan equation of state: ; In the formula, P For the pressure of the water flow, γ =7 to ensure the stability of the simulation calculation. k Value of 0: , c 0 represents the speed of sound. v max The maximum flow velocity of the water. For reference density, The density of the water flow.
[0034] The sediment phase is modeled using the Mohr-Coulomb elastoplastic constitutive model, and its stress state expression is as follows: ; In the formula, τ max For shear stress, c For cohesion (in this embodiment) c = 0), σ It is normal stress. The friction angle within the soil.
[0035] To characterize the attenuation of soil strength under water shearing, this invention employs a simplified linear time-varying strength model, which primarily considers the internal friction angle of the soil. Decrease linearly over time: ; In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0036] (2) Define the parameter to be inverted as the initial internal friction angle of the soil. With erosion rate slope k ,Right now The prior probability distribution is set as an independent normal distribution based on engineering experience.
[0037] (3) Extract four characteristic moments from the Louvain physics experiment ( t The soil-water interface elevation data at 0.25s, 0.5s, 0.75s, and 1.0s were used as observation data. y A likelihood function was constructed based on the observed data. It was assumed that the model prediction error followed a normal distribution, and its standard deviation was determined to be 0.4 through trial and error. In the formula, N Represents the normal distribution density function. For experimental observation values, These are simulated predicted values. Let be the likelihood function. These are the parameters to be inverted in the model.
[0038] (4) The Metropolis-Hastings algorithm is used for MCMC sampling. The algorithm flow is as follows: Figure 3 As shown. The specific steps are as follows: (4.1) Parameter initialization: Set the initial values of the parameters. Number of iterations t = 1; (4.2) Proposal distribution setting: A Gaussian distribution is selected as the proposal distribution. ,in, As is currently the case, the acceptance rate is controlled within the ideal range of 20% to 40% by adjusting the scaling factor; (4.3) Generate candidate parameters: Draw candidate samples from the proposal distribution ; (4.4) Model Update and Computation: Candidate Samples The material parameters in the SPH model are automatically updated using Python and LS-DYNA software, and the solver is invoked to perform calculations. (4.5) Likelihood calculation: Extract the predicted elevation of the soil-water interface from the SPH calculation results, and substitute it into the likelihood function to calculate the acceptance probability. r ; (4.6) Accept / Reject Candidate Values: Based on the Metropolis criteria, Determine whether to accept candidate samples .
[0039] (5) After completing the preset number of MCMC iterations, perform convergence diagnosis on the generated Markov chain. The specific steps are as follows: (5.1) Discard the warm-up samples at the front end of the Markov chain to eliminate the influence of the initial values.
[0040] (5.2) Judge the stationarity of the parameter trajectory to evaluate the convergence status: observe whether the Markov chain of each parameter fluctuates around a certain mean in the later stage of iteration, without obvious trend deviation or long-term stagnation, and the fluctuation range of the chain tends to be stable within a reasonable range.
[0041] (5.3) The remaining samples after convergent diagnosis constitute the data from the posterior distribution. Independent sampling is used. Based on these samples, the posterior mean, standard deviation, and other statistical characteristics of the parameters can be calculated. The expression for calculating the posterior mean is: In the formula, The number of valid samples. For the first One sample, is the mean of the posterior distribution.
[0042] The expression for calculating the posterior standard deviation is: In the formula, The standard deviation of the posterior distribution. The number of valid samples. For the first One sample, is the mean of the posterior distribution.
[0043] (5.4) Plot the posterior probability density distribution as follows: Figure 4 As shown, this completes the quantitative characterization of parameter uncertainty.
[0044] (6) Based on the posterior distribution of soil parameters obtained from Bayesian-MCMC inversion, the probability of erosion process is predicted. The specific steps are as follows: (6.1) Using the mean of the posterior distribution of the parameters obtained by inversion as representative values, update the corresponding parameters (i.e., the initial internal friction angle and the erosion rate slope) in the SPH water-soil two-phase scour and erosion model, and rerun the numerical simulation to obtain the predicted water-soil interface profile.
[0045] (6.2) To quantify the deviation between the predicted results and the experimental observations, the root mean square error (RMSE) is used as the evaluation index, and its calculation formula is as follows: In the formula, This represents the total number of comparison points on the soil-water interface at the selected feature time. and The first Simulated interface elevation values at each location and Louvain's experimental observation values.
[0046] (6.3) Figure 5 The paper presents a comparison between the predicted soil-water interface contours at four typical time points, obtained based on the posterior mean of the inversion parameters, and the experimental data. The results show that the predicted curves are in high agreement with the experimental data, and the RMSE at each time point is small, verifying the effectiveness of the Bayesian inversion framework proposed in this invention in effectively constraining parameter uncertainties and improving the accuracy of erosion prediction.
[0047] The implementation of this embodiment fully demonstrates that the parameter probability inversion method provided by the present invention can effectively integrate observation data and prior knowledge to estimate the posterior probability distribution of key soil parameters, significantly reducing parameter uncertainty and providing a scientific basis for reliable prediction of water and sand erosion processes.
[0048] Example 3 The present invention also provides a parametric probabilistic inversion system based on SPH water-soil coupled scour erosion, the system being used to implement the method described in Embodiment 1, the system comprising: a first construction module, a second construction module, a quantization module, an iterative sampling module, a diagnosis and analysis module, and a prediction module; The first building module is used to establish a numerical model of water-sediment two-phase flow scour and erosion based on the unified SPH framework. The second building module is used to construct the Bayesian-MCMC parameter inversion framework; The quantization module is used to construct a likelihood function based on physical experimental observation data. It is used to quantify the consistency between the prediction results of the numerical model of water-sediment two-phase flow scour and erosion and the observation data, and to provide data constraints for Bayesian inference. The iterative sampling module is used to perform MCMC iterative sampling within the Bayesian-MCMC parameter inversion framework; The diagnosis and analysis module is used to perform convergence diagnosis on the MCMC iterative sampling results and to perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters. The prediction module is used to predict the probability of erosion based on the posterior statistical features of the parameters.
[0049] In this embodiment, the process of establishing a numerical model for water-sediment two-phase flow scour and erosion based on a unified SPH framework includes: A unified SPH method is used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface is achieved through the interparticle normal contact force and tangential viscous force. A linear time-varying strength model is introduced to describe the strength decay of the soil during scouring, and its evolution formula is as follows: ; In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at any given moment.
[0050] In this embodiment, the process of constructing the Bayesian-MCMC parameter inversion framework includes: The numerical model of water-sediment two-phase flow scour and erosion is embedded into a Bayesian inference framework. The posterior distribution of parameters is updated through MCMC sampling. The core Bayesian formula is: ; In the formula, For the posterior distribution, The parameter vector to be inverted, As a prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
[0051] In this embodiment, the MCMC sampling adopts the Metropolis-Hastings algorithm, and an automated process of automatic parameter transfer, model calling and result extraction is realized by developing a dedicated interface between Python and the LS-DYNA solver.
[0052] In this embodiment, convergence diagnosis is evaluated by checking the stationarity of the parameter trajectory; posterior distribution analysis includes calculating the posterior mean, standard deviation, and plotting the posterior probability density function.
[0053] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A parametric probabilistic inversion method for scour erosion based on SPH (Soil-Water Coupled) method, characterized in that, The method includes: S1: Establish a numerical model of water-sediment two-phase flow scouring and erosion based on a unified SPH framework; S2: Construct a Bayesian-MCMC parameter inversion framework; S3: Construct a likelihood function based on physical experimental observation data to quantify the consistency between the prediction results of the numerical model of water-sediment two-phase flow scour and erosion and the observation data, and provide data constraints for Bayesian inference; S3: Perform MCMC iterative sampling within the Bayesian-MCMC parameter inversion framework; S4: Perform convergence diagnosis on the MCMC iterative sampling results, and perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters. S5: Predict the probability of erosion based on posterior statistical features of parameters.
2. The method according to claim 1, characterized in that, Methods for establishing numerical models of water-sediment two-phase flow scour and erosion based on a unified SPH framework include: A unified SPH method is used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface is achieved through the interparticle normal contact force and tangential viscous force. A linear time-varying strength model is introduced to describe the strength decay of the soil during scouring, and its evolution formula is as follows: ； In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at time t.
3. The method according to claim 1, characterized in that, Methods for constructing a Bayesian-MCMC parameter inversion framework include: The numerical model of water-sediment two-phase flow scour and erosion is embedded into a Bayesian inference framework. The posterior distribution of parameters is updated through MCMC sampling. The core Bayesian formula is: ； In the formula, For the posterior distribution, Let be the parameter vector to be inverted. For the prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
4. The method according to claim 1, characterized in that, MCMC sampling uses the Metropolis-Hastings algorithm and automates the process of parameter transfer, model invocation, and result extraction by developing a dedicated interface between Python and the LS-DYNA solver.
5. The method according to claim 1, characterized in that, Convergence diagnosis is assessed by examining the stationarity of the parameter trajectory; posterior distribution analysis includes calculating the posterior mean, standard deviation, and plotting the posterior probability density function.
6. A parametric probabilistic inversion system based on SPH (Soil-Water Coupled Erosion) for scour and erosion, the system being used to implement the method described in any one of claims 1-5, characterized in that, The system includes: a first construction module, a second construction module, a quantization module, an iterative sampling module, a diagnosis and analysis module, and a prediction module; The first construction module is used to establish a numerical model of water-sediment two-phase flow scour and erosion based on a unified SPH framework; The second building module is used to construct the Bayesian-MCMC parameter inversion framework; The quantization module is used to construct a likelihood function based on physical experimental observation data, which is used to quantify the consistency between the prediction results of the numerical model of water-sediment two-phase flow scour and erosion and the observation data, and to provide data constraints for Bayesian inference. The iterative sampling module is used to perform MCMC iterative sampling within the Bayesian-MCMC parameter inversion framework; The diagnosis and analysis module is used to perform convergence diagnosis on the MCMC iterative sampling results and to perform posterior distribution analysis on the converged samples to obtain the posterior statistical characteristics of the parameters. The prediction module is used to predict the probability of erosion based on the posterior statistical features of the parameters.
7. The system according to claim 6, characterized in that, The process of establishing a numerical model for water-sediment two-phase flow scour and erosion based on a unified SPH framework includes: A unified SPH method is used to discretize the soil-water two-phase medium. Dynamic coupling of the soil-water interface is achieved through the interparticle normal contact force and tangential viscous force. A linear time-varying strength model is introduced to describe the strength decay of the soil during scouring, and its evolution formula is as follows: ； In the formula, The initial internal friction angle, k A coefficient characterizing the decay rate, t 0 is simplified to the starting time of the water flow. For the moment when the water flow is in effect, for The internal friction angle at time t.
8. The system according to claim 6, characterized in that, The process of constructing the Bayesian-MCMC parameter inversion framework includes: The numerical model of water-sediment two-phase flow scour and erosion is embedded into a Bayesian inference framework. The posterior distribution of parameters is updated through MCMC sampling. The core Bayesian formula is: ； In the formula, For the posterior distribution, Let be the parameter vector to be inverted. For the prior distribution, The normalization constant is For experimental observation data, Let be the likelihood function. y For observational data.
9. The system according to claim 6, characterized in that, MCMC sampling uses the Metropolis-Hastings algorithm and automates the process of parameter transfer, model invocation, and result extraction by developing a dedicated interface between Python and the LS-DYNA solver.
10. The system according to claim 6, characterized in that, Convergence diagnosis is assessed by examining the stationarity of the parameter trajectory; posterior distribution analysis includes calculating the posterior mean, standard deviation, and plotting the posterior probability density function.