Bayesian filtering prediction method for stress-strain relationship of geotechnical material
By using Bayesian filtering prediction methods and Gaussian process surrogate models, the problem of long time consumption in traditional Bayesian inversion is solved, and rapid and accurate prediction and uncertainty quantification of stress-strain relationships in geotechnical materials are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-29
- Publication Date
- 2026-04-10
AI Technical Summary
Traditional Bayesian inversion methods are too time-consuming in geotechnical engineering, leading to parameter estimation bias and posterior distribution distortion, making them unsuitable for effective application in engineering practice.
By employing a Bayesian filtering prediction method combined with a Gaussian process surrogate model, and dynamically quantifying parameter uncertainty through posterior updates and resampling of the multi-scale model parameter set, a Gaussian process surrogate model is constructed to replace discrete element simulation, thereby achieving fast and accurate stress-strain relationship prediction.
It achieves stress-strain relationship prediction within millisecond response time, reducing computational costs while maintaining high accuracy and uncertainty quantification, thus solving the problems of long processing time and low accuracy in traditional methods.
Smart Images
Figure CN121835392A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a Bayesian filtering prediction method for stress-strain relationships in geotechnical materials. Background Technology
[0002] In the field of geotechnical engineering, constructing constitutive models that can accurately describe the mechanical behavior of materials has always been the core foundation for supporting key engineering decisions such as slope stability analysis, foundation pit support design, and geological disposal of nuclear waste. In recent years, with the development of multi-scale simulation technology, researchers have gradually shifted from traditional phenomenological continuous medium models to bottom-up cross-scale modeling paradigms. For example, molecular dynamics or coarse-grained molecular dynamics can be used to characterize the hydration and expansion mechanism of clay minerals such as montmorillonite at the nanoscale, and then the discrete element method can be combined to simulate the contact mechanics and structural evolution of particle assemblies at the mesoscale.
[0003] However, in order to obtain a reliable posterior distribution, traditional Bayesian inversion methods usually require repeated forward simulations on thousands of parameter samples to calculate the likelihood value. A single high-precision discrete element simulation often takes several hours or even days, making the complete inversion process impractical in engineering practice. If the number of simulations is forcibly reduced or the model is simplified, it will lead to parameter estimation bias, posterior distribution distortion, and loss of the meaning of uncertainty quantification. Summary of the Invention
[0004] In view of the aforementioned existing problems, the present invention is proposed.
[0005] Therefore, this invention provides a Bayesian filtering prediction method for stress-strain relationship of geotechnical materials to solve the problem of repeatedly performing forward simulations on thousands of parameter samples to calculate likelihood values. A single high-precision discrete element simulation often takes several hours or even days, making the complete inversion process infeasible in engineering practice. If the number of simulations is forcibly reduced or the model is simplified, it will lead to parameter estimation bias, posterior distribution distortion, and loss of the quantitative meaning of uncertainty.
[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a Bayesian filtering prediction method for stress-strain relationships in geotechnical materials, comprising: The measured macroscopic response of the target geotechnical material under the set working conditions is obtained. The measured macroscopic response is obtained through experiments, which includes macroscopic stress-strain data and microstructure response data. Based on macroscopic stress-strain test data and microstructural response data, the initial value ranges of nanoscale GB potential parameters and mesoscale discrete element parameters are determined, an initial multiscale model parameter set is generated, and a joint likelihood function is constructed. Based on the joint likelihood function, a Bayesian filtering framework is introduced to perform posterior update on the initial multi-scale model parameter set to obtain the posterior distribution of the parameters. Sample points are selected from the posterior distribution of parameters, and discrete element simulation is called for each sample point to obtain the corresponding macroscopic stress-strain response, forming a training dataset. A Gaussian process surrogate model is then constructed based on the training dataset. A Gaussian process surrogate model is used to replace discrete element simulation to obtain macroscopic stress-strain prediction results for parameter samples in subsequent iterations; Based on the deviation between the predicted results output by the Gaussian process surrogate model and the measured macroscopic response, Bayesian resampling and weight adjustment are iteratively performed until the Euclidean distance of the parameter posterior mean vector is less than the preset tolerance threshold in three consecutive iterations, at which point the parameter posterior distribution is determined to have converged. The sequence of operations for constructing the joint likelihood function until the posterior distribution of the decision parameters converges is defined as multi-scale Bayesian inversion. The target soil and rock material whose posterior distribution converges is labeled as the calibrated soil and rock material. The convergence posterior distribution of the calibrated soil and rock material is used as the structured prior in the parameter inversion process of the new type of soil and rock material to generate the initial prior parameter set. A multi-scale Bayesian inversion process is performed on the initial prior parameter set to obtain a converged posterior parameter distribution. This posterior parameter distribution is then used to drive a Gaussian process surrogate model, outputting the stress-strain relationship prediction results. As a preferred embodiment of the Bayesian filtering prediction method for the stress-strain relationship of geotechnical materials described in this invention, the step of acquiring the measured macroscopic response of the target geotechnical material under a set working condition includes: macroscopic stress-strain data obtained through experiments, and microstructural response data, including: Vertical expansion force tests were conducted on the target soil and rock materials under saturated conditions with controlled dry density and water content. The original data of axial reaction force and deformation of the specimens over time under constant volume constraint were recorded. The raw data is normalized to form a pairing set of macroscopic stress values and corresponding axial strain values, and the pairing set is defined as the measured macroscopic response; X-ray tomography was performed on the same sample to obtain a three-dimensional particle image stack. Based on a stack of three-dimensional particle images, a particle contact network is constructed using image segmentation and particle recognition techniques, and three types of microstructural features are extracted from it: force chain direction distribution, aggregate principal axis orientation angle, and local porosity spatial field. Histogram statistics were performed on the three types of micro-features and L1 normalization was applied to obtain three probability mass functions. The three probability mass functions are fused with equal weights to form a single microstructure response data.
[0007] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the method involves: determining the initial value ranges of the nanoscale GB potential parameters and the mesoscale discrete element parameters based on macroscopic stress-strain test data and microscopic structural response data, generating an initial multi-scale model parameter set, and constructing a joint likelihood function, including: Based on the minimum location and depth of the montmorillonite free energy-separation distance curve, the physical feasible range of five key parameters in the nano-Gay-Berne potential was determined, including energy well depth, minimum effective radius, relative well depth ratio, cutoff radius, and interaction energy between montmorillonite and water. Based on the experimental results of wet particle packing angle calibration, the reasonable range of friction coefficient and adhesion force parameters in the microscopic discrete element model is derived in reverse. The range of values for each dimension of the nanoscale GB potential parameter is combined with the range of values for each dimension of the microscale discrete element parameter to form a multidimensional parameter space, where each dimension corresponds to an independent model parameter, and the upper and lower bounds of the space are determined by the physical feasible range of the corresponding parameter. The multidimensional parameter space is used as the search domain for subsequent quasi-random sampling, and Sobol low-discrepancy sequences are generated within the search domain. The initial parameter sample is expressed as: ; in, The parameter vector representing the multi-scale geotechnical material model is the first... One sample, To generate Group initial parameter sample; Assign the same initial importance weight to each group of samples. This forms the initial multi-scale model parameter set; For the parameter samples, the expansion process was run using a discrete element simulator to obtain the macroscopic stress-strain response and microstructural characteristics. Based on the discrepancy between the simulation results and the measured macroscopic response, an observation likelihood function based on a multivariate Gaussian distribution is constructed.
[0008] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the method involves introducing a Bayesian filtering framework based on a joint likelihood function to perform posterior updates on the initial multi-scale model parameter set, thereby obtaining the posterior distribution of the parameters, including: During the iteration process, the measured macroscopic response data is processed step by step. ; For each particle With current parameters Drive discrete element model to generate state prediction ; Calculate the likelihood value of the particle under the current observation. And combined with state transition probability Weights from the previous time step Update the importance weights; The weight updates follow the following recursive relationship: ; in, Indicates the first Real-time measured macroscopic response, Indicates the first The particle in the first Simulated output state at any given time. Modeling is performed using a multivariate Gaussian distribution. The dynamic evolution of the discrete element model is implicitly defined; After updating the weights of all particles, normalization is performed, and the effective sample size (ESS) is calculated. The expression is: ; in, For the effective sample size, For the first The normalized weights of each particle in the current iteration This represents the total number of particles; When the ESS falls below a preset threshold, system resampling is performed to mitigate particle degradation.
[0009] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the step of selecting sample points from the posterior distribution of parameters, performing discrete element simulation on each sample point to obtain the corresponding macroscopic stress-strain response, forming a training dataset, and constructing a Gaussian process surrogate model based on the training dataset includes: After the Bayesian filter converges, samples with high-weight parameters are selected from the particle set in descending order of weight as a representative set. For representative samples, the discrete element simulator is called to run the working condition simulation and generate macroscopic stress-strain curves; Pair parameter samples with response curves to construct an input-output training dataset; Based on the input-output training dataset, a Gaussian process regression model is established using the squared exponential covariance kernel function.
[0010] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the target geotechnical material whose labeled posterior distribution converges is a calibrated geotechnical material. The convergent posterior distribution of the calibrated geotechnical material is used as a structured prior in the parameter inversion process of new types of geotechnical materials to generate an initial prior parameter set, including: particle set And weighted storage as knowledge assets of calibrated geotechnical materials; Discrete approximation of the particle set yields an explicit expression for the posterior distribution, which is: ; in, Represents the parameter vector of a multi-scale model. Represents the entire observation data sequence. For the first Normalized weights of individual particles, It is the Dirac delta function; When dealing with new types of geotechnical materials, retrieve calibrated materials with similar mineral composition or engineering properties from historical databases; The retrieved posterior distribution is used as a structured prior to replace the traditional uniform prior distribution; Importance sampling is performed based on structured priors to generate an initial set of prior parameters.
[0011] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the step of performing a multi-scale Bayesian inversion process on the initial prior parameter set to obtain a converged posterior parameter distribution, and using the posterior parameter distribution to drive a Gaussian process surrogate model to output the stress-strain relationship prediction result includes: A multi-scale Bayesian inversion process is performed on the initial prior parameter set, including likelihood construction, weight update, resampling and convergence determination, to obtain the particle set; Calculating the macroscopic response function based on particle sets The posterior expectation is used as the predicted value; Simultaneously, the posterior variance is calculated to quantify the uncertainty of prediction; The expression for the posterior expectation is: ; in, The total number of particles, For the conditional expectation operator, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle; The expression for the posterior variance is: ; in, For conditional variance operators, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle. For posterior expectation; The posterior expectation curve is used as the stress-strain prediction result, and the posterior variance is used to construct the confidence interval to output the stress-strain relationship prediction product.
[0012] As a preferred embodiment of the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials described in this invention, the generation of the initial prior parameter set includes: First, X-ray diffraction analysis was performed on the target rock and soil material to determine the mineral type; Based on mineral category, retrieve the posterior distribution of all previously calibrated materials of the same type from the historical calibration database; A comprehensive transfer prior distribution is constructed by weighting multiple search results; In the initialization phase of the new inversion task, initial parameter samples are generated directly from the integrated priors, rather than being uniformly sampled from a wide physical range; The initial weights are still set to However, the parameter space has been focused on the high-probability region; The inversion process for new types of geotechnical materials can converge in fewer iterations.
[0013] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program is executed by the processor, it implements any step of the Bayesian filtering prediction method for stress-strain relationships of geotechnical materials as described in the first aspect of the present invention.
[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the Bayesian filtering prediction method for stress-strain relationships of geotechnical materials as described in the first aspect of the present invention.
[0015] The beneficial effects of this invention are as follows: It introduces a Bayesian filtering framework based on multivariate Gaussian likelihood, combines sequential weight update and ESS-driven resampling mechanism, dynamically quantifies parameter uncertainty and adaptively focuses on high-probability regions, avoids particle degradation while preserving the correlation between parameters, achieves stable and convergent posterior distribution estimation, extracts high-weight samples from the posterior distribution, calls discrete element simulation to generate training data, and constructs a Gaussian process surrogate model with uncertainty output capability, accelerating a single physical simulation that originally took several hours to a millisecond-level response, and completely decoupling the contradiction between computational cost and inversion accuracy. Attached Figure Description
[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. 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.
[0017] Figure 1 This is a flowchart of the Bayesian filtering prediction method for stress-strain relationship of geotechnical materials in Example 1; Figure 2 This is a schematic diagram of the multi-level sampling process of the GB potential parameter in Example 2; Figure 3 This is a schematic diagram of the multi-level sampling process of the EEPA model parameters in Example 2; Figure 4 This is a schematic diagram of the discrete element parameters resampled by Bayesian filtering at different iteration steps in Example 2; Figure 5 This is a schematic diagram illustrating the correlation and uncertainty between the GB potential parameters and the discrete element parameters in Example 2; Figure 6 This is a schematic diagram comparing the experimental and predicted expansion results under different mineral ratios in Example 2. Detailed Implementation
[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0019] 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 those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.
[0020] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.
[0021] Example 1, referring to Figure 1 This is the first embodiment of the present invention, which provides a Bayesian filtering prediction method for stress-strain relationships in geotechnical materials, comprising the following steps: S1. Obtain the measured macroscopic response of the target geotechnical material under the set working conditions. The measured macroscopic response is the macroscopic stress-strain data and microstructure response data obtained through experiments.
[0022] Furthermore, under saturated conditions of controlled dry density and water content, vertical expansion force tests were conducted on the target soil and rock materials, and the original data of axial reaction force and deformation of the specimens over time under constant volume constraints were recorded. The raw data is normalized to form a pairing set of macroscopic stress values and corresponding axial strain values, and the pairing set is defined as the measured macroscopic response; X-ray tomography was performed on the same sample to obtain a three-dimensional particle image stack. Based on a stack of three-dimensional particle images, a particle contact network is constructed using image segmentation and particle recognition techniques, and three types of microstructural features are extracted from it: force chain direction distribution, aggregate principal axis orientation angle, and local porosity spatial field. Histogram statistics were performed on the three types of micro-features and L1 normalization was applied to obtain three probability mass functions. The three probability mass functions are fused with equal weights to form a single microstructure response data.
[0023] It should be noted that the experimental and image processing workflows can acquire macro-micro response data simultaneously, ensuring that the two are strictly correlated in time and space. This provides a consistent and noise-controllable observational basis for multi-scale joint inversion, thereby improving the reliability of parameter calibration.
[0024] S2. Based on macroscopic stress-strain test data and microstructural response data, determine the initial value range of nanoscale GB potential parameters and mesoscale discrete element parameters, generate an initial multiscale model parameter set, and construct a joint likelihood function.
[0025] Furthermore, based on the minimum location and depth of the montmorillonite free energy-separation distance curve, the physical feasible ranges of five key parameters in the nano-Gay-Berne potential were determined, including energy well depth, minimum effective radius, relative well depth ratio, cutoff radius, and the interaction energy between montmorillonite and water. Based on the experimental results of wet particle packing angle calibration, the reasonable range of friction coefficient and adhesion force parameters in the microscopic discrete element model is derived in reverse. The range of values for each dimension of the nanoscale GB potential parameter is combined with the range of values for each dimension of the microscale discrete element parameter to form a multidimensional parameter space, where each dimension corresponds to an independent model parameter, and the upper and lower bounds of the space are determined by the physical feasible range of the corresponding parameter. The multidimensional parameter space is used as the search domain for subsequent quasi-random sampling, and Sobol low-discrepancy sequences are generated within the search domain. The initial parameter sample is expressed as: ; in, The parameter vector representing the multi-scale geotechnical material model is the first... One sample, To generate Group initial parameter sample; Assign the same initial importance weight to each group of samples. This forms the initial multi-scale model parameter set; For the parameter samples, the expansion process was run using a discrete element simulator to obtain the macroscopic stress-strain response and microstructural characteristics. Based on the discrepancy between the simulation results and the measured macroscopic response, an observation likelihood function based on a multivariate Gaussian distribution is constructed.
[0026] It should be noted that by constructing a multidimensional parameter space based on physically feasible intervals and using Sobol sequence sampling, the curse of dimensionality problem of traditional grid sampling can be avoided while ensuring coverage, thus greatly improving the exploration efficiency of initial samples.
[0027] S3. Based on the joint likelihood function, a Bayesian filtering framework is introduced to perform posterior updates on the initial multi-scale model parameter set, thereby obtaining the posterior distribution of the parameters.
[0028] Furthermore, during the iteration process, the measured macroscopic response data is processed time-by-time. ; For each particle With its current parameters Drive discrete element model to generate state prediction ; Calculate the likelihood value of the particle under the current observation. And combined with state transition probability Weights from the previous time step Update the importance weights; Weight updates follow the following recursive relationship: ; in, Indicates the first Real-time measured macroscopic response, Indicates the first The particle in the first Simulated output state at any given time. Modeling is performed using a multivariate Gaussian distribution. The dynamic evolution of the discrete element model is implicitly defined; After updating the weights of all particles, normalization is performed, and the effective sample size (ESS) is calculated. The expression is: ; in, For the effective sample size, For the first The normalized weights of each particle in the current iteration This represents the total number of particles; When the ESS falls below a preset threshold, system resampling is performed to mitigate particle degradation.
[0029] It should be noted that introducing the effective sample size (ESS) as a resampling trigger condition can dynamically maintain particle diversity, effectively alleviate the particle degradation problem in Bayesian filtering, and ensure the stability and convergence of the posterior distribution estimation.
[0030] S4. Select sample points from the posterior distribution of parameters, call discrete element simulation for each sample point to obtain the corresponding macroscopic stress-strain response, form a training dataset, and build a Gaussian process surrogate model based on the training dataset.
[0031] Furthermore, after the Bayesian filter converges, samples with high weight parameters are selected from the particle set in descending order of weight as a representative set. For representative samples, the discrete element simulator is called to run the working condition simulation and generate macroscopic stress-strain curves; Pair parameter samples with response curves to construct an input-output training dataset; Based on the input-output training dataset, a Gaussian process regression model is established using the squared exponential covariance kernel function.
[0032] It should be noted that the constructed Gaussian process surrogate model not only has high-precision fitting capabilities, but also outputs prediction uncertainty, providing an error-aware mechanism for likelihood evaluation in subsequent iterations. This is key to achieving the dual goals of computational acceleration and accuracy maintenance.
[0033] S5. Use a Gaussian process surrogate model to replace discrete element simulation and obtain macroscopic stress-strain prediction results for parameter samples in subsequent iterations.
[0034] Furthermore, in each Bayesian iteration, the parameter vector to be evaluated is input into the Gaussian process surrogate model, which directly outputs the corresponding macroscopic stress-strain prediction mean and variance, which are used to efficiently calculate the likelihood function and update the particle weights.
[0035] It should be noted that by using a Gaussian process surrogate model to replace discrete element simulation, the time required for single response prediction can be reduced from hours to milliseconds, thus reducing the overall computational cost by more than an order of magnitude while maintaining inversion accuracy.
[0036] S6. Based on the deviation between the predicted results output by the Gaussian process surrogate model and the measured macroscopic response, iteratively perform Bayesian resampling and weight adjustment until the Euclidean distance of the parameter posterior mean vector is less than the preset tolerance threshold in three consecutive iterations, and determine that the parameter posterior distribution has converged.
[0037] Furthermore, based on the deviation between the predicted results output by the Gaussian process surrogate model and the measured macroscopic response, Bayesian resampling and weight adjustment are iteratively performed until the Euclidean distance of the parameter posterior mean vector is less than the preset tolerance threshold in three consecutive iterations, at which point the parameter posterior distribution is determined to have converged.
[0038] It should be noted that using the average change of three consecutive iterations as the convergence criterion balances algorithm stability and termination sensitivity, effectively avoiding premature stopping or excessive iteration caused by a single fluctuation, and improving the robustness of the inversion results.
[0039] S7. Define the sequence of operations for constructing the joint likelihood function until the posterior distribution of the decision parameters converges as multi-scale Bayesian inversion.
[0040] Furthermore, multi-scale Bayesian inversion is encapsulated into a standardized computation module, supporting end-to-end joint inversion of nanoscale potential parameters, microscale contact parameters, and macroscale response data, thereby achieving self-consistent calibration of cross-scale model parameters and uncertainty transfer.
[0041] It should be noted that the defined multi-scale Bayesian inversion process realizes closed-loop synergistic optimization of the nanoscale potential function, the microscale contact model and the macroscopic mechanical response, and solves the core problems of "scale separation and parameter inconsistency" in traditional multi-scale modeling.
[0042] S8. The target soil and rock material whose posterior distribution converges is the calibrated soil and rock material. The convergence posterior distribution of the calibrated soil and rock material is used as the structured prior in the parameter inversion process of the new type of soil and rock material to generate the initial prior parameter set.
[0043] Furthermore, the particle set And weighted storage as knowledge of calibrated geotechnical materials assets; Discrete approximation of the particle set yields an explicit expression for the posterior distribution, which is: ; in, Represents the parameter vector of a multi-scale model. Represents the entire observation data sequence. For the first Normalized weights of individual particles, It is the Dirac delta function; When dealing with new types of geotechnical materials, retrieve calibrated materials with similar mineral composition or engineering properties from historical databases; The retrieved posterior distribution is used as a structured prior to replace the traditional uniform prior distribution; Importance sampling is performed based on structured priors to generate an initial set of prior parameters.
[0044] It should be noted that the weighted transfer mechanism based on physical property similarity enables the prior distribution of new types of geotechnical materials to focus on high-probability regions, shortening the inversion path, realizing a knowledge transfer paradigm of one-time calibration and multiple reuses, and improving the efficiency of engineering applications.
[0045] S9. Perform a multi-scale Bayesian inversion process on the initial prior parameter set to obtain a converged posterior parameter distribution. Use the posterior parameter distribution to drive the Gaussian process surrogate model and output the stress-strain relationship prediction results.
[0046] Furthermore, a multi-scale Bayesian inversion process is performed on the initial prior parameter set, including likelihood construction, weight update, resampling and convergence determination, to obtain the particle set; Calculating the macroscopic response function based on particle sets The posterior expectation is used as the predicted value; Simultaneously, the posterior variance is calculated to quantify the uncertainty of prediction; The expression for the posterior expectation is: ; in, The total number of particles, For the conditional expectation operator, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle; The expression for the posterior variance is: ; in, For conditional variance operators, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle. For posterior expectation; The posterior expectation curve is used as the stress-strain prediction result, and the posterior variance is used to construct the confidence interval to output the stress-strain relationship prediction product.
[0047] It should be noted that the output includes a complete prediction product containing posterior expectations and confidence intervals, which not only provides deterministic stress-strain relationships but also quantifies model uncertainty, providing a direct basis for geotechnical engineering risk assessment and reliability design.
[0048] This embodiment also provides a computer device applicable to the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as proposed in the above embodiment.
[0049] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.
[0050] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.
[0051] In summary, this invention introduces a Bayesian filtering framework based on multivariate Gaussian likelihood, combined with sequential weight updates and an ESS-driven resampling mechanism, to dynamically quantify parameter uncertainty and adaptively focus on high-probability regions. This preserves the correlation between parameters while avoiding particle degeneration, achieving stable and convergent posterior distribution estimation. High-weight samples are extracted from the posterior distribution, training data is generated using discrete element simulation, and a Gaussian process surrogate model with uncertainty output capability is constructed. This accelerates a single physical simulation, which originally took hours, to a millisecond-level response, completely decoupling the contradiction between computational cost and inversion accuracy. For Example 2, please refer to... Figures 2-6 This is a second embodiment of the present invention, which provides a method for cross-material Bayesian parameter migration and stress-strain relationship prediction for multiple types of bentonite, including: Bayesian methods include prior distribution, likelihood function, and posterior distribution, expressed as: ; in, This represents the posterior probability. Let be the probability density function of the prior distribution. Let be the likelihood function. The normalization coefficient is... Represents observation data, Indicates the assumed parameters; In Bayesian inference, the prior distribution represents the probability distribution of the model parameters before the observed data. Based on prior knowledge or assumptions, the prior distribution can be either an informative prior distribution with high information content or an uninformative prior distribution, such as a uniform or Jeffreys prior distribution. The likelihood function describes the probability of observed data occurring given the parameters and is used to reflect the degree of support of the data for the parameters. The posterior distribution is obtained by combining the prior distribution and the likelihood function through Bayes' theorem. It represents the probability distribution of the model parameters given the observed data. To solve the computational complexity of the posterior distribution, the Markov chain Monte Carlo method is usually used. By constructing a Markov chain, random sampling is performed to approximate the posterior distribution. Among them, the Metropolis-Hastings algorithm and Gibbs sampling are two major MCMC techniques. The latter can be regarded as a special case of the former. Bayesian filtering aims to use a series of measurement data Infer the hidden state at time t =( , Specifically, this involves solving for the marginal posterior distribution p. The expected value related to the calculation is expressed as: ; in, It is a pair with p An integrable function describes any quantity of interest that serves as a function of the model's state. Given a state-space model, the posterior distribution of the model parameters can be given using Bayes' theorem, expressed as: ; With state space The increase of can be rewritten as: ; When time t>0, the posterior distribution can be further rewritten in iterative form: ; Among them, the likelihood distribution and transfer distribution It can be determined by sampling from a given suggested density.
[0052] Based on Sequential Importance Sampling (SIS) Through the sample state set The importance weight of the assessment ,parameter Based on the probability density, sampled at t=0, the expression for the importance weight at time t is: ; Monte Carlo approximation for calculating posterior expectation and variance: ; ; It is worth noting that importance weight At each time step, the weights are normalized, and the sum of all weights is 1. Since the posterior distribution of the model parameters is unknown, in the first iteration (k=0), an uninformative probability density is typically used to uniformly explore the parameter space, i.e.: ; ; In order to identify all possible posterior patterns and effectively approximate the posterior probability density function, the initial sampling uses a quasi-random number uniform sampling parameter space. The probability density should include the measurement data from the iterations. For subsequent iterations, the result of the previous iteration should be used as the probability density for this iteration. The specific expression can be rewritten as follows: ; ; At this point, the sample state will evolve according to the deterministic equations of the model at different scales. The sample sequence in each iteration will be updated according to the latest measurement data, thus ensuring that the samples at each time step are based on the most accurate system information. When k > 0, the importance weights will also be adjusted according to the new probability density, expressed as follows: ; After each iteration, the effective sample size (ESS) needs to be calculated, and based on this, it needs to be determined whether resampling is necessary. The expression is: ; If the effective sample size is lower than the preset threshold, the samples and weights need to be reinitialized to optimize the starting conditions for subsequent iterations. For montmorillonite expansion models at different scales, a multi-level sampling algorithm can be used to effectively approximate the posterior probability density distribution. In the first iteration (k=0), quasi-random numbers are used to uniformly sample the parameter space. In subsequent iterations (k>0), the posterior distribution obtained in the previous iterations is selected as the probability density. New samples are drawn from the nonparametric Gaussian mixture model. Using the open-source GrainLearning code, the iterative sampling will gradually approach the latent posterior pattern until the posterior expectation converges. In the iterative Bayesian filtering framework, based on sample size and initial parameter range Input parameters, output the posterior distribution of model parameters; Extract from probability density Each parameter value, to carry out If k=0, set the corresponding importance weights and perform uniform sampling; if k>0, update the weights and perform resampling.
[0053] Setting the standard covariance parameter is used to adjust the model's sensitivity to prediction errors, thereby affecting the weight update speed and filtering effect.
[0054] For different times Update weights, likelihood function It follows a multivariate Gaussian distribution.
[0055] Calculate the effective sample size (ESS) if k=0 and ESS>20%, or k>0 and ESS has not reached its maximum value. use The importance weights of time points approximate the posterior distribution. The expression is: ; Calculate the posterior expectation and variance; Iterative Bayesian filtering and Gaussian mixture model have achieved good results in predicting the macroscopic expansion response and calibrating model parameters of MX-80 bentonite. This paper will further apply them to other types of bentonite such as GMZ001, Kunigel-V1 and FEBEX. By iteratively sampling the macroscopic expansion force-dry density results measured by Jia, Dixon and Villar, we gradually approach the posterior mode of the potential expansion stress-strain relationship. The GB potential parameters and discrete element model parameters of montmorillonite under different types of saturated bentonite are calibrated. The optimized model parameter set is listed in Table 1.
[0056] Table 1. Parameter sets of montmorillonite models calibrated under different types of bentonite. GB potential model parameter set
[0057] DEM model parameter set
[0058] To verify the applicability of the montmorillonite expansion model, this chapter uses a micro-particle expansion model to conduct discrete element simulations of expansive soil systems such as montmorillonite-sand mixtures and montmorillonite-kaolinite-sand mixtures, and compares the results with macroscopic experimental results. Information such as bentonite type, initial dry density, and mineral proportions under various working conditions is summarized, and the particle size distribution and physical property parameters of soil samples under corresponding working conditions are listed. For the montmorillonite-sand mixture system, domestic and foreign scholars have studied the macroscopic expansion characteristics of MX-80, GMZ, FEBEX bentonite, and Kunigel-V1 at different dry densities. Different types of bentonite have different montmorillonite content and cation exchange capacity. For the montmorillonite-kaolinite-sand mixture system, the typical expansive soil sites DK355+700 and DK429+350 along the route of the central canal in Handan, Hebei and Nanyang, Henan, and the Mombasa-Nairobi Standard Gauge Railway project in Kenya are selected as simulation objects.
[0059] To investigate the changes in macroscopic swelling rate and swelling force of soil samples with varying mineral content ratios under different target moisture contents and initial dry densities, cylindrical ring soil samples with a diameter of 61.8 mm and a height of 20 mm were prepared at mineral ratios of 3:1:6, 1:1:3, and 1:3:6. To ensure consistency between the soil samples and the discrete element model, the initial moisture content was set to 0%. In the vertical swelling rate test, data was collected in real time using a video monitoring device. If the difference in deformation readings recorded over two consecutive hours did not exceed 0.01 mm, the deformation was considered stable. Each test group included four parallel samples, and the average value was taken as the final test result. The expression for the swelling rate is: ; in, Let be the unloaded expansion rate at time t. The readings of the dilatometer gauges at the start of the experiment. Let t be the scale reading at time t. The initial height of the sample is 20 mm; Table 2 Mineral composition and initial dry density of soil samples under different working conditions
[0060] Table 3. Particle size distribution and physical properties of soil samples under different working conditions
[0061] For one-dimensional swelling force testing under constant volume, a constant volume swelling-permeability device was used. The constant volume swelling-permeability device includes a base, sample, piston, pressure sensor, water pipe, peristaltic pump, top cover, and reading instrument. The prepared ring sample was assembled into the sample groove using permeable stone. The pressure sensor was kept in pre-contact with the upper surface of the sample. Deionized water was introduced from the bottom of the test through the peristaltic pump. The change of swelling force in the reading instrument over time was recorded in real time using a camera device until the change of swelling force was less than 0.1 kPa over 24 consecutive hours. Four parallel swelling force tests were carried out for different dry densities and mineral ratios to obtain the swelling force time history curve of the soil sample.
[0062] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A Bayesian filtering prediction method for stress-strain relationships in soil and rock materials, characterized in that: Includes the following steps: The measured macroscopic response of the target geotechnical material under the set working conditions is obtained. The measured macroscopic response is obtained through experiments, which includes macroscopic stress-strain data and microstructure response data. Based on macroscopic stress-strain test data and microstructural response data, the initial value ranges of nanoscale GB potential parameters and mesoscale discrete element parameters are determined, an initial multiscale model parameter set is generated, and a joint likelihood function is constructed. Based on the joint likelihood function, a Bayesian filtering framework is introduced to perform posterior update on the initial multi-scale model parameter set to obtain the posterior distribution of the parameters. Sample points are selected from the posterior distribution of parameters, and discrete element simulation is called for each sample point to obtain the corresponding macroscopic stress-strain response, forming a training dataset. A Gaussian process surrogate model is then constructed based on the training dataset. A Gaussian process surrogate model is used to replace discrete element simulation to obtain macroscopic stress-strain prediction results for parameter samples in subsequent iterations; Based on the deviation between the predicted results output by the Gaussian process surrogate model and the measured macroscopic response, Bayesian resampling and weight adjustment are iteratively performed until the Euclidean distance of the parameter posterior mean vector is less than the preset tolerance threshold in three consecutive iterations, at which point the parameter posterior distribution is determined to have converged. The sequence of operations for constructing the joint likelihood function until the posterior distribution of the decision parameters converges is defined as multi-scale Bayesian inversion. The target soil and rock material whose posterior distribution converges is labeled as the calibrated soil and rock material. The convergence posterior distribution of the calibrated soil and rock material is used as the structured prior in the parameter inversion process of the new type of soil and rock material to generate the initial prior parameter set. A multi-scale Bayesian inversion process is performed on the initial prior parameter set to obtain a converged posterior parameter distribution. The posterior parameter distribution is then used to drive a Gaussian process surrogate model to output the stress-strain relationship prediction results.
2. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 1, characterized in that: The acquisition of the measured macroscopic response of the target geotechnical material under the set working conditions includes macroscopic stress-strain data and microstructural response data obtained through experiments, including: Vertical expansion force tests were conducted on the target soil and rock materials under saturated conditions with controlled dry density and water content. The original data of axial reaction force and deformation of the specimens over time under constant volume constraint were recorded. The raw data is normalized to form a pairing set of macroscopic stress values and corresponding axial strain values, and the pairing set is defined as the measured macroscopic response; X-ray tomography was performed on the same sample to obtain a three-dimensional particle image stack. Based on a stack of three-dimensional particle images, a particle contact network is constructed using image segmentation and particle recognition techniques, and three types of microstructural features are extracted from it: force chain direction distribution, aggregate principal axis orientation angle, and local porosity spatial field. Histogram statistics were performed on the three types of micro-features and L1 normalization was applied to obtain three probability mass functions. The three probability mass functions are fused with equal weights to form a single microstructure response data.
3. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 2, characterized in that: Based on macroscopic stress-strain test data and microstructural response data, the initial value ranges of the nanoscale GB potential parameters and mesoscale discrete element parameters are determined, an initial multiscale model parameter set is generated, and a joint likelihood function is constructed, including: Based on the minimum location and depth of the montmorillonite free energy-separation distance curve, the physical feasible range of five key parameters in the nano-Gay-Berne potential was determined, including energy well depth, minimum effective radius, relative well depth ratio, cutoff radius, and interaction energy between montmorillonite and water. Based on the experimental results of wet particle packing angle calibration, the reasonable range of friction coefficient and adhesion force parameters in the microscopic discrete element model is derived in reverse. The range of values for each dimension of the nanoscale GB potential parameter is combined with the range of values for each dimension of the microscale discrete element parameter to form a multidimensional parameter space, where each dimension corresponds to an independent model parameter, and the upper and lower bounds of the space are determined by the physical feasible range of the corresponding parameter. The multidimensional parameter space is used as the search domain for subsequent quasi-random sampling, and Sobol low-discrepancy sequences are generated within the search domain. The initial parameter sample is expressed as: ； in, The parameter vector representing the multi-scale geotechnical material model is the first... One sample, To generate Group initial parameter sample; Assign the same initial importance weight to each group of samples. This forms the initial multi-scale model parameter set; For the parameter samples, the expansion process was run using a discrete element simulator to obtain the macroscopic stress-strain response and microstructural characteristics. Based on the discrepancy between the simulation results and the measured macroscopic response, an observation likelihood function based on a multivariate Gaussian distribution is constructed.
4. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 3, characterized in that: The method, based on the joint likelihood function and incorporating a Bayesian filtering framework, performs posterior updates on the initial multi-scale model parameter set to obtain the posterior distribution of the parameters, including: During the iteration process, the measured macroscopic response data is processed step by step. ; For each particle With current parameters Drive discrete element model to generate state prediction ; Calculate the likelihood value of the particle under the current observation. And combined with state transition probability Weights from the previous time step Update the importance weights; The weight updates follow the following recursive relationship: ； in, Indicates the first Real-time measured macroscopic response, Indicates the first The particle in the first Simulated output state at any given time. Modeling is performed using a multivariate Gaussian distribution. The dynamic evolution of the discrete element model is implicitly defined; After updating the weights of all particles, normalization is performed, and the effective sample size (ESS) is calculated. The expression is: ； in, For the effective sample size, For the first The normalized weights of each particle in the current iteration This represents the total number of particles; When the ESS falls below a preset threshold, system resampling is performed to mitigate particle degradation.
5. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 4, characterized in that: The process of selecting sample points from the posterior distribution of parameters, performing discrete element simulation on each sample point to obtain the corresponding macroscopic stress-strain response, forming a training dataset, and constructing a Gaussian process surrogate model based on the training dataset includes: After the Bayesian filter converges, samples with high-weight parameters are selected from the particle set in descending order of weight as a representative set. For representative samples, the discrete element simulator is called to run the working condition simulation and generate macroscopic stress-strain curves; Pair parameter samples with response curves to construct an input-output training dataset; Based on the input-output training dataset, a Gaussian process regression model is established using the squared exponential covariance kernel function.
6. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 5, characterized in that: The target soil and rock material for the convergence of the labeled posterior distribution is the calibrated soil and rock material. The convergence posterior distribution of the calibrated soil and rock material is used as a structured prior in the parameter inversion process of the new type of soil and rock material to generate an initial prior parameter set, including: particle set And weighted storage as knowledge assets of calibrated geotechnical materials; Discrete approximation of the particle set yields an explicit expression for the posterior distribution, which is: ； in, Represents the parameter vector of a multi-scale model. Represents the entire observation data sequence. For the first Normalized weights of individual particles, It is the Dirac delta function; When dealing with new types of geotechnical materials, retrieve calibrated materials with similar mineral composition or engineering properties from historical databases; The retrieved posterior distribution is used as a structured prior to replace the traditional uniform prior distribution; Importance sampling is performed based on structured priors to generate an initial set of prior parameters.
7. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 6, characterized in that: The process involves performing a multi-scale Bayesian inversion on the initial prior parameter set to obtain a converged posterior parameter distribution. This posterior parameter distribution is then used to drive a Gaussian process surrogate model, outputting stress-strain relationship prediction results, including: A multi-scale Bayesian inversion process is performed on the initial prior parameter set, including likelihood construction, weight update, resampling and convergence determination, to obtain the particle set; Calculating the macroscopic response function based on particle sets The posterior expectation is used as the predicted value; Simultaneously, the posterior variance is calculated to quantify the uncertainty of prediction; The expression for the posterior expectation is: ； in, The total number of particles, For the conditional expectation operator, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle; The expression for the posterior variance is: ； in, For conditional variance operators, For macroscopic response function, For the observed data sequence, For the first The particle in the first Normalized importance weights for each moment. For the first The macroscopic response output corresponding to each particle. For posterior expectation; The posterior expectation curve is used as the stress-strain prediction result, and the posterior variance is used to construct the confidence interval to output the stress-strain relationship prediction product.
8. The Bayesian filtering prediction method for stress-strain relationships in geotechnical materials as described in claim 6, characterized in that, The generation of the initial prior parameter set includes: First, X-ray diffraction analysis was performed on the target rock and soil material to determine the mineral type; Based on mineral category, retrieve the posterior distribution of all previously calibrated materials of the same type from the historical calibration database; A comprehensive transfer prior distribution is constructed by weighting multiple search results; In the initialization phase of the new inversion task, initial parameter samples are generated directly from the integrated priors, rather than being uniformly sampled from a wide physical range; The initial weights are still set to However, the parameter space has been focused on the high-probability region; The inversion process for new types of geotechnical materials can converge in fewer iterations.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the Bayesian filtering prediction method for stress-strain relationships of geotechnical materials as described in any one of claims 1 to 8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the Bayesian filtering prediction method for stress-strain relationships of geotechnical materials as described in any one of claims 1 to 8.