A multi-dimensional cloud agent model assisted high-performance adaptive probabilistic inversion system

Abstract

The application relates to the technical field of safety monitoring and numerical analysis of hydraulic engineering, and discloses a high-performance self-adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model, which comprises finite element modeling, sample generation, cloud agent model construction, self-adaptive inversion and dynamic updating modules. The system calculates cloud digital features such as the expectation, entropy and hyper-entropy of input variables, generates multiple layers of virtual cloud droplets, and constructs a multi-dimensional coupled cloud agent model to replace finite element calculation; a variable step Markov chain Monte Carlo algorithm based on local and global uncertainty indexes is used to perform parameter inversion; time-series monitoring data are processed by combining a state space model and a Bayesian recursive strategy, and continuous correction of the parameter posterior distribution is realized. The application effectively solves the problems of long calculation time, low convergence efficiency and difficulty in processing time-varying characteristics in traditional inversion, and realizes efficient dynamic inversion of dam life cycle parameters and accurate safety state evaluation.

Description

Technical Field

[0001] This invention relates to the field of water conservancy project safety monitoring and numerical analysis technology, specifically a high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud proxy model. Background Technology

[0002] Concrete-faced rockfill dams are a widely used dam type in water conservancy and hydropower projects. Their construction and operational safety are highly dependent on the accurate understanding of the mechanical parameters of the dam materials. Due to the scale effect of indoor tests and the complexity of the construction site environment, the actual mechanical parameters of the dam materials often deviate from the design values. Therefore, displacement back analysis using observation data from the dam prototype has become the main means of obtaining the true calculation parameters.

[0003] However, in existing rockfill dam parameter inversion techniques, the process of establishing the nonlinear mapping relationship between parameters and deformation response typically relies on three-dimensional finite element forward analysis. Given that the inversion algorithm requires numerous iterative calculations, frequent calls to time-consuming finite element programs result in extremely high computational costs, severely limiting inversion efficiency. Although there are studies using surrogate models such as neural networks or support vector machines to replace finite element calculations, conventional surrogate models often require a large amount of sample data for training to ensure accuracy, and most are deterministic mapping models, making it difficult to effectively characterize the inherent randomness and fuzziness of geotechnical parameters. Furthermore, their generalization ability is insufficient when dealing with small-sample and high-dimensional nonlinear coupling problems.

[0004] Furthermore, in probabilistic inversion algorithms, the commonly used Markov chain Monte Carlo method typically employs a fixed step size or a simple random walk strategy when dealing with high-dimensional and complex parameter spaces. This sampling method, lacking an adaptive adjustment mechanism, makes the algorithm slow to search in low probability density regions and prone to getting trapped in local extrema in high probability density regions, leading to difficulties in Markov chain convergence and an inability to efficiently obtain the posterior probability distribution of the parameters within a finite time.

[0005] Meanwhile, rockfill dam materials exhibit time-varying characteristics during long-term operation, with their physical and mechanical parameters evolving over time due to rheology, aging, and other factors. Most existing inversion methods rely on static inversion based on monitoring data at a fixed point in time, assuming constant model parameters. This approach ignores the physical laws governing the evolution of material parameters over time, resulting in inverted parameters that only reflect the state at a specific moment. It fails to dynamically track and update the parameters' lifecycle changes, thus affecting the accuracy of long-term safety assessments of the dam. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud proxy model, which solves the problems of excessively long finite element forward analysis calculation time, low convergence efficiency of inversion algorithms, and difficulty in dynamically reflecting the time-varying characteristics of parameters in traditional dam parameter inversion.

[0007] The high-performance adaptive probabilistic inversion system assisted by the multidimensional cloud proxy model provided by this invention mainly includes a finite element modeling and parameter initialization module, a sample generation and forward analysis module, a multidimensional coupled cloud proxy model construction module, an adaptive probabilistic inversion module, and a dynamic parameter update module.

[0008] The finite element modeling and parameter initialization module is used to construct a three-dimensional finite element model reflecting the dam's geometry. Displacement monitoring points are selected as inversion reference points based on the actual layout of the dam monitoring system, and the physical boundaries and prior probability distribution range of the material parameters to be inverted are determined. The sample generation and forward analysis module is configured to generate statistically representative model parameter samples in the parameter space using the Latin hypercube sampling method, and perform forward analysis calculations through the finite element model to construct an input / output dataset containing parameter samples and deformation response data.

[0009] To address the challenges of high-dimensional parameter nonlinear mapping and small-sample training, the multidimensional coupled cloud surrogate model construction module establishes an alternative model based on cloud theory. This module first standardizes the input and output datasets, calculating the expectation vector, covariance matrix, and entropy and hyperentropy of each dimension of the input variable sample set. The expectation vector represents the parameter distribution center, the covariance matrix measures the coupling correlation between parameters, entropy characterizes the uncertainty of qualitative concepts, and hyperentropy characterizes the uncertainty of entropy. This module utilizes these features to generate multi-layered virtual cloud droplets to represent the multidimensional coupling characteristics and randomness of the parameter space. During virtual cloud droplet generation, hyperentropy is introduced to correct the covariance matrix, simulating different degrees of random perturbation by setting different corrected covariance matrices at different levels. When establishing the mapping relationship, the certainty of each virtual cloud droplet with respect to the surrogate model center is calculated. This certainty is determined based on the squared Mahalanobis distance between the virtual cloud droplet and the surrogate model expectation, as well as the average entropy value of that layer. Finally, weights are assigned based on the certainty, and the prediction results of all levels are weighted and fused. The fused results are then de-standardized, thereby establishing a nonlinear mapping relationship from model parameters to deformed responses.

[0010] The adaptive probability inversion module, based on a Bayesian inference framework, constructs a likelihood function using measured displacement data and the cloud surrogate model's predicted response. To improve the convergence efficiency of Markov chain Monte Carlo sampling, this module is equipped with a variable step-size adjustment mechanism based on cloud features. During sampling, the module calculates the local and global uncertainty indices for the current sampling point in real time. The local uncertainty index is defined as the ratio of the distance between the current sampling point's parameter value and the cloud surrogate model's expected value to the square root of the trace of the covariance matrix; the global uncertainty index is defined as the ratio of hyperentropy to entropy.

[0011] The adaptive probability inversion module adjusts the sampling step size according to a step size hierarchical dynamic adjustment model: when the global uncertainty index shows that hyperentropy dominates, it indicates that there is a large random perturbation in the parameter space, and a step size expansion strategy is executed; when entropy dominates, it indicates that the parameter distribution is relatively stable, and a step size contraction strategy is executed. Simultaneously, the module sets a threshold based on the statistical characteristics of the dispersion of the sampled data. When the local uncertainty index exceeds this threshold, it is identified as a high uncertainty region, and the step size is increased; conversely, the step size is decreased. Furthermore, the module applies a geometric constraint based on Mahalanobis distance to the adjusted step size to prevent the sampling process from deviating excessively from the high probability density region, thereby efficiently obtaining the posterior probability distribution of the parameters to be inverted.

[0012] The dynamic parameter update module establishes a state-space model containing state equations and observation equations to address the performance evolution throughout the entire lifecycle. The state equations describe the evolution of model parameters from the previous time step to the current time step and include process noise. The observation equations describe the mapping relationship between model parameters and observation data, where the observation function is provided by the multidimensional coupled cloud proxy model. This module employs a recursive Bayesian update strategy, using the posterior probability distribution of parameters calculated at the previous time step as the prior information basis for the current time step. It obtains the prior probability distribution at the current moment by advancing the state equations and constructs a likelihood function based on the newly added monitoring data and observation equations at the current moment. This continuously corrects and updates the parameter distribution, outputting a posterior probability distribution sequence reflecting the trajectory of parameter evolution over time.

[0013] This invention provides a high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model. It has the following beneficial effects:

[0014] 1. This invention constructs a multidimensional coupled cloud proxy model, utilizes cloud digital features such as expectation, entropy, and hyperentropy to extract the distribution patterns of small sample data, and enhances the ability of samples to express the randomness and fuzziness of parameter space by generating multi-layer virtual cloud droplets. It effectively solves the problem of excessively long calculation time in traditional dam inversion three-dimensional finite element forward analysis, and ensures the prediction accuracy of the nonlinear mapping relationship between model parameters and deformation response while significantly reducing the calculation cost.

[0015] 2. This invention adopts an adaptive Markov chain Monte Carlo sampling strategy based on cloud features and establishes a variable step size adjustment mechanism that integrates local uncertainty indicators and global hyperentropy features. It can dynamically adjust the search step size in real time according to the complexity of the parameter space. It performs large step size exploration in high uncertainty regions to avoid getting trapped in local extrema, and performs small step size fine search in stable regions, thereby improving the convergence speed and sampling efficiency of the inversion algorithm.

[0016] 3. This invention establishes a dynamic parameter update mechanism based on a state-space model. By using a Bayesian recursive strategy to take the inversion result of the previous time step as the prior information of the current time step, it realizes the temporal transmission of probabilistic information, effectively integrates continuous field monitoring data, continuously corrects the model parameters, accurately reflects the physical characteristics of the evolution of rockfill dam material parameters over time, and meets the needs of safety state assessment of the entire life cycle of the dam. Attached Figure Description

[0017] Figure 1 This is a system structure block diagram of the present invention;

[0018] Figure 2 This is a flowchart illustrating the overall process of the method of the present invention.

[0019] The module includes: 10. Finite element modeling and parameter initialization module; 20. Sample generation and forward analysis module; 30. Multidimensional coupled cloud proxy model construction module; 40. Adaptive probability inversion module; and 50. Dynamic parameter update module. Detailed Implementation

[0020] The technical solutions in 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] See attached document Figure 1 The present invention provides a high-performance adaptive probabilistic inversion system assisted by a multidimensional cloud proxy model. The system includes: a finite element modeling and parameter initialization module 10, a sample generation and forward analysis module 20, a multidimensional coupled cloud proxy model construction module 30, an adaptive probabilistic inversion module 40, and a dynamic parameter update module 50.

[0022] The finite element modeling and parameter initialization module 10 is used to construct the numerical calculation foundation for the face-panel rockfill dam. Based on the design drawings and geological survey data of the face-panel rockfill dam, this module establishes a three-dimensional finite element model reflecting the geometric structure of the dam.

[0023] The finite element modeling and parameter initialization module 10 performs mesh generation and selects displacement monitoring points corresponding to the finite element mesh nodes as inversion reference points based on the actual layout of the dam deformation monitoring system. This module is also used to determine the parameters of the material constitutive model to be inverted and to set the prior probability distribution range and statistical characteristics of each parameter based on the prior engineering information.

[0024] The sample generation and positive analysis module 20, connected to the finite element modeling and parameter initialization module 10, is used to generate training data. The sample generation and positive analysis module 20 is configured to use the Latin hypercube sampling method to sample parameters within a set prior probability distribution range, generating multiple sets of model parameter samples covering the parameter space.

[0025] The sample generation and forward analysis module 20 sequentially inputs the generated model parameter samples into the three-dimensional finite element model for forward analysis calculations, extracting the deformation response data of the reference points corresponding to each parameter sample. The sample generation and forward analysis module 20 then combines the model parameter samples with the corresponding deformation response data to construct the input-output dataset used to train the surrogate model.

[0026] The multidimensional coupled cloud proxy model construction module 30 is configured to receive a dataset from the sample generation and positive analysis module 20. The multidimensional coupled cloud proxy model construction module 30 first standardizes the input and output data, and then calculates cloud digital features such as the expectation, entropy, and hyperentropy of the input variables.

[0027] The multidimensional coupled cloud proxy model construction module 30 utilizes the calculated cloud digital features and covariance matrix to generate multi-layered virtual cloud droplets to characterize the multidimensional coupling characteristics and randomness of the parameter space. The multidimensional coupled cloud proxy model construction module 30 establishes a high-precision nonlinear mapping relationship between model parameters and dam deformation response by calculating the determinism of the cloud droplets and performing weighted fusion operations, thus serving as a substitute model for the finite element model.

[0028] The adaptive probability inversion module 40 interacts with the multidimensional coupled cloud proxy model construction module 30 to perform probabilistic inversion of model parameters. The adaptive probability inversion module 40 receives measured dam displacement monitoring data and constructs a likelihood function by combining it with the predicted response output by the multidimensional coupled cloud proxy model construction module 30.

[0029] The adaptive probability inversion module 40 is equipped with a variable-step Markov chain Monte Carlo sampling algorithm based on cloud features. The adaptive probability inversion module 40 utilizes the local uncertainty index of the cloud proxy model and global cloud feature parameters to dynamically adjust the step size during the sampling process, performing iterative searches within the parameter space to ultimately obtain the posterior probability distribution of the parameters to be inverted.

[0030] The dynamic parameter update module 50 is used to process continuous monitoring data that changes over time. The dynamic parameter update module 50 establishes a state-space model describing the evolution of parameters and uses the posterior distribution of parameters at the previous time step as the prior distribution at the current time step.

[0031] The dynamic parameter update module 50 uses a Bayesian update strategy to integrate newly added monitoring data at the current moment to correct and update the parameter distribution. The dynamic parameter update module 50 repeatedly performs the update operation according to the time series, and outputs a model parameter sequence reflecting the full life cycle performance evolution of the panel rockfill dam.

[0032] See attached document Figure 2 This invention provides a probabilistic inversion method for panel rockfill dam model parameters based on a Bayesian update strategy. The method includes the following steps:

[0033] S100. Establish a finite element model of the panel rockfill dam, determine the parameters to be inverted, and select the constitutive model. In this step, a three-dimensional numerical model reflecting the dam's geometry and foundation conditions is constructed based on the engineering design drawings and geological survey data. Displacement monitoring points corresponding to the finite element mesh node positions are selected as reference points for the inversion analysis based on the actual layout of the dam deformation monitoring system.

[0034] Step S100 also includes selecting a constitutive model based on the mechanical properties of the dam construction materials for the rockfill dam. Using parameter sensitivity analysis, the influence of each model parameter on the dam's deformation response is quantified, and key parameters with sensitivity coefficients higher than a preset threshold are selected as parameters to be inverted.

[0035] S200. Determine the range of parameter probability distributions based on prior information and generate an effective set of model parameters. Based on indoor geotechnical test data, comparative data from similar projects, or expert experience, determine the prior probability distribution type and statistical characteristic values ​​of each parameter to be inverted. Use the Latin hypercube sampling method to randomly sample within the determined prior distribution space, generating a statistically representative sample set of model parameters that covers the parameter space.

[0036] S300. Based on the model parameter set, perform forward analysis using the finite element method to obtain deformation response data. Input each set of parameters from the model parameter sample set generated in step S200 into the finite element model of the panel rockfill dam established in step S100 for numerical calculation. Extract the displacement calculation values ​​at the reference point, combine the model parameter samples with the corresponding displacement response values, and construct the input-output dataset for training the surrogate model.

[0037] S400. Establish a multidimensional coupled cloud surrogate model using model parameter sets and deformation response data. Standardize the input and output datasets obtained in step S300, and calculate cloud digital features such as expectation, entropy, and hyperentropy of the input variables. Based on these features and the covariance matrix between variables, construct a multidimensional coupled cloud surrogate model that can characterize the multidimensional coupling relationship and stochastic uncertainty of the parameters, to replace the finite element model for subsequent response prediction.

[0038] The S500 employs an adaptive Markov chain Monte Carlo method combined with a cloud proxy model for probabilistic inversion, dynamically adjusting the sampling step size to optimize sampling efficiency. A likelihood function is constructed using measured dam displacement monitoring data and the predicted response output by the multidimensional coupled cloud proxy model.

[0039] In step S500, during Markov chain Monte Carlo sampling, the local uncertainty index of the sampling points in the cloud proxy model is calculated, and a variable step size adjustment mechanism is established in conjunction with global cloud feature parameters. The sampling step size is dynamically expanded or contracted according to the uncertainty of the sampling region, and iterative calculation is performed until the Markov chain converges, thereby obtaining the posterior probability distribution of the parameters to be inverted.

[0040] S600: Based on time-series monitoring data, continuous updates of the posterior distribution of parameters are achieved through a probability information transmission strategy. A state-space model describing the evolution of model parameters over time is constructed. The posterior distribution of parameters obtained at the previous monitoring time is used as the prior distribution of parameters at the current monitoring time. Combined with the newly added measured data at the current time, a Bayesian update operation is performed to output the sequence of posterior probability distributions of parameters evolving over time.

[0041] This invention provides a method for constructing a physical model and preparing prior data for a rockfill dam with a concrete panel. The method first establishes a numerical calculation model of the rockfill dam. Based on the dam design drawings, geological survey report, and construction zoning data, the geometric outline of the dam body, the panel structure, and the foundation boundary conditions are determined. A three-dimensional mathematical model is constructed using finite element analysis software, and the model is discretized into a mesh based on the mechanical characteristics of the dam structure. Mesh sizes are set for the rockfill area, panel area, and foundation area of ​​the dam body, and mesh refinement is performed in areas with large stress gradients to ensure calculation accuracy.

[0042] During mesh generation, the coordinates of the displacement monitoring instruments deployed in the actual project are mapped to the nodes of the finite element mesh. Nodes coinciding with or adjacent to the monitoring instrument locations are selected as reference calculation points for the inversion analysis. If the monitoring point location does not fall on a mesh node, a mapping relationship between the monitoring point displacement and the element node displacement is established using shape function interpolation to ensure the consistency between the numerical calculation results and the measured data in spatial location.

[0043] Based on the stress-strain characteristics of the rockfill, a constitutive model that reflects the mechanical behavior of the dam construction materials is selected. In this embodiment, the Duncan-Chang EB model or an elastoplastic model is used to describe the nonlinear deformation characteristics of the rockfill. Parameter sensitivity analysis is performed on the multiple material parameters included in the constitutive model. By applying perturbations within the allowable range of the parameters, the partial derivatives or correlation coefficients of each parameter change with the displacement response at the reference point are calculated to quantify the sensitivity of the parameters to the deformation response. Based on the sensitivity analysis results, minor parameters with sensitivity coefficients below a preset threshold are eliminated, and the remaining key parameters that control the deformation of the dam body are determined as the parameter set to be inverted.

[0044] Based on indoor large-scale triaxial test data, back analysis statistical data of similar panel rockfill dam projects, and expert experience, the prior information of the parameters to be inverted is determined. The prior information includes the probability distribution type and statistical characteristic values ​​of each parameter. The probability distribution type of the parameters is typically set as normal, log-normal, or uniform; the statistical characteristic values ​​include the mean, standard deviation, and upper and lower limits defined by the physical meaning of the parameter.

[0045] The Latin hypercube sampling method is used to generate parameter samples within a defined prior distribution space. The range of values ​​for each parameter to be inverted is divided according to its probability distribution. Each parameter has three equally probable intervals, and a sample value is randomly selected from each interval. By randomly combining the sample values ​​for each parameter dimension without repetition, a sequence is generated containing... The sample set of model parameters. The Latin hypercube sampling method ensures the uniform distribution of samples in the multidimensional parameter space, avoids sample clustering, and ensures that the generated sample set can fully reflect the uncertainty characteristics of the parameter space.

[0046] The generated The model parameter samples are used as input files and sequentially submitted to the finite element analysis engine for forward analysis. After the calculation is completed, the displacement calculation values ​​of each reference calculation point under the corresponding working conditions are extracted. The model parameter samples are mapped one-to-one with their corresponding displacement calculation values ​​to construct a parameter response dataset. This dataset is divided into a training set and a test set. The training set is used for the subsequent construction and parameter calibration of the multidimensional coupled cloud proxy model, while the test set is used to verify the generalization ability and prediction accuracy of the proxy model.

[0047] This invention provides a construction principle for a multidimensional coupled cloud proxy model. This method establishes a nonlinear mapping relationship between input parameters and deformation response based on a parameter-response dataset obtained from finite element forward analysis. First, sample data is read, and the dataset is divided into training and test sets according to a preset ratio. Standardization is then performed on all input variables to ensure each variable has a mean of 0 and a unit variance, thus eliminating the influence of different physical dimensions on model training.

[0048] Assume the training sample set is Each input sample All dimensional vector, i.e. The corresponding output response is Based on this sample set, calculate the expected vector of the samples. As the central location for cloud droplet generation, the calculation formula is:

[0049] ;

[0050] Simultaneously, the covariance matrix CoV of the sample set is calculated to measure the coupling correlation between each input dimension and serves as the distance metric for subsequent virtual cloud droplet generation. The calculation formula is as follows:

[0051] ;

[0052] in, .

[0053] Based on the calculated expectation The covariance matrix CoV is used to extract statistical features of each dimension of the input variable, including entropy. and hyperentropy .entropy It is used to measure the uncertainty of qualitative concepts and is calculated using the following formula:

[0054] ;

[0055] hyperentropy The uncertainty used to measure entropy is calculated using the following formula:

[0056] ;

[0057] Or take it as a proportional function of entropy These cloud features form the basis for virtual cloud droplet sampling and multi-dimensional cloud stitching.

[0058] In a multidimensional input space, hierarchical virtual cloud droplet generation is implemented based on the mean vector and covariance matrix of the training sample set. Assume the... Layer contains Each cloud droplet The generation follows a normal distribution Introducing hyperentropy The covariance matrix is ​​modified to control the overall perturbation amplitude, so that the first... covariance matrix of the layer By setting different perturbation intensities at different levels, and simulating varying degrees of uncertainty, a multi-scale cloud droplet distribution structure is constructed.

[0059] Define a determinism function to characterize the reliability of cloud droplets for the cloud agent model center. For the th The first layer A cloud droplet, its certainty Calculated using the following formula:

[0060] ;

[0061] In the formula, For cloud droplets Expectations with proxy model The squared Mahalanobis distance between them is calculated using the following formula: ,in, Corresponding covariance matrix; Indicates the first The average entropy of the layer, used as an adjustment parameter for determinism calculation, is obtained by the following formula:

[0062] ;

[0063] in, Indicates the first Layer The perturbation entropy of dimension 1. Its calculation formula is:

[0064] ;

[0065] In the formula, Represents the covariance matrix The The diagonal elements are used to represent the variance information of this dimension; These are the standard normally distributed random numbers generated.

[0066] For each of the generated layers, predictions are made on the input samples separately, and a weighted fusion method is used to obtain the final output estimate. Weights are assigned based on the certainty of the prediction results at each layer, and the prediction results from all layers are weighted and summed to obtain the final output result. The calculation formula is:

[0067] ;

[0068] in, These are the weighting coefficients. This corresponds to the response value of the cloud droplet. Through the above multi-layer weighted fusion process, a nonlinear mapping from multi-dimensional model parameters to deformation response is achieved.

[0069] It should be noted that the above calculations yielded... This represents the response value in the standardized space. Before constructing the likelihood function, the mean and variance of the training set output data need to be used to... Perform denormalization to map it back to the original physical space so as to match the measured displacement data. Perform a comparison of quantities with the same dimensions.

[0070] This invention provides an adaptive MCMC inversion strategy based on cloud features. This strategy is implemented through an adaptive probabilistic inversion module 40 to efficiently obtain the posterior distribution of model parameters in a multidimensional parameter space. The adaptive probabilistic inversion module 40 first initializes multiple parallel-running Markov chains and sets the initial proposal distribution to a multivariate normal distribution. The adaptive probabilistic inversion module 40 reads measured dam deformation data, calls a multidimensional coupled cloud surrogate model to calculate the predicted response corresponding to the current parameter sample, and constructs a likelihood function reflecting the deviation between the predicted and measured values.

[0071] Likelihood function It is usually constructed based on the assumption that the observation error follows a Gaussian distribution, and its expression is:

[0072] ;

[0073] In the formula, This is the measured displacement vector; This is the predicted displacement vector output by the cloud agent model; The covariance matrix of the observation error is usually set as a diagonal matrix, with the diagonal elements corresponding to the measurement error variance of each measuring point.

[0074] During the sampling process, the adaptive probability inversion module 40 dynamically adjusts the covariance matrix of the proposal distribution or the sampling step size using a variable step-size strategy based on cloud features. The adaptive probability inversion module 40 also utilizes the statistical characteristics of cloud droplets in the cloud proxy model to calculate the local uncertainty index of the current sampling point in the parameter space. Local uncertainty... Defined as the parameter value of the current sampling point Expectations with cloud agent models The ratio of the distance to the square root of the trace of the covariance matrix is ​​calculated using the following formula:

[0075] ;

[0076] in, This is the trace of the covariance matrix of the cloud agent model.

[0077] The adaptive probability inversion module 40 determines the threshold for dividing the uncertainty region based on the statistical characteristics of the dispersion of the sampled samples. It also calculates the mean of the dispersion of the sampled samples. and standard deviation Set threshold ,in, This is the sensitivity coefficient. It is determined by the local uncertainty at the current sampling point. If the value exceeds the threshold, the region is considered a high-uncertainty region, and the sampling step size needs to be increased to enhance the exploration capability; conversely, if the value is below the threshold, the region is considered a low-uncertainty region, and the step size needs to be decreased for a finer search.

[0078] The adaptive probability inversion module 40 combines the global feature parameters obtained from training the cloud agent model to construct a global uncertainty index. This index is defined as hyperentropy. With entropy The ratio, i.e. .when At this time, it indicates that hyperentropy dominates, and there is a large uncertainty perturbation in the parameter space. The module executes a step-size expansion strategy, with an adjustment coefficient of . ;

[0079] when At this time, it indicates that entropy dominates, the parameter distribution is relatively stable, the module executes a step-size contraction strategy, and the adjustment coefficient is... .

[0080] The adaptive probability inversion module 40 further integrates local uncertainty metrics, global cloud feature parameters, and geometric constraint mechanisms to establish a multi-scale feature fusion sampling step size hierarchical dynamic adjustment model. In each sampling step, the step size is first adjusted by combining local dispersion and global hyperentropy features. Preliminary adjustments are made, and the preliminary adjustment formula is as follows:

[0081] ;

[0082] in, For adjustment coefficients, .

[0083] The adaptive probability inversion module 40 then applies a geometric constraint based on Mahalanobis distance to the initially adjusted step size to prevent the sampling process from deviating excessively from the high probability density region. Final sampling step size. The calculation formula is:

[0084] ;

[0085] in, The squared Mahalanobis distance of the current sample. The squared maximum historical Mahalanobis distance is obtained through sliding window statistics.

[0086] The adaptive probabilistic inversion module 40 generates new candidate samples using a dynamically adjusted step size and decides whether to accept the sample based on the Metropolis-Hastinqs criterion. The adaptive probabilistic inversion module 40 monitors the convergence state of each Markov chain in real time and calculates the potential scale reduction factor using the Gelman-Rubin diagnostic method. .when When the value is less than the preset convergence criterion (e.g., 1.1), the Markov chain is determined to have converged, the sampling process is stopped, and the posterior sample set of the parameters is output.

[0087] This invention provides a method for dynamically updating probabilistic information based on time-series data. This method is executed by a dynamic parameter update module 50 and aims to process time-varying monitoring data throughout the entire life cycle of a panel rockfill dam. The dynamic parameter update module 50 first establishes a state-space model describing the time-varying characteristics of the model parameters. This model includes state equations and observation equations.

[0088] The dynamic parameter update module 50 defines the state equation to describe the parameters from the previous time step. up to the current time step The evolutionary pattern. The state equation is expressed as:

[0089] ;

[0090] in, Indicates time step The model parameter vector; This is the state transition function, defined based on engineering experience or material aging mechanisms; This is process noise, usually set as a random variable that follows a Gaussian distribution, used to characterize random disturbances in the parameter evolution process.

[0091] The dynamic parameter update module 50 defines the observation equation to describe the mapping relationship between model parameters and observation data. The observation equation is expressed as:

[0092] ;

[0093] in, Indicates time step Measured displacement data; The observation function is the cloud proxy model trained by the multidimensional coupled cloud proxy model construction module 30 in this system. The observation noise is set to follow a Gaussian distribution to characterize measurement error and model error.

[0094] The dynamic parameter update module 50 employs a recursive Bayesian update strategy to transmit probability information. The dynamic parameter update module 50 updates the previous time step... The calculated posterior probability distribution of the parameters As the current time step The prior information is based on this. By advancing the parameter distribution over time using the state equation, the prior probability distribution at the current moment is obtained. .

[0095] The dynamic parameter update module 50 receives the current time step. New observation data And construct the likelihood function at the current time by combining the observation equation. The dynamic parameter update module 50, based on Bayes' theorem, multiplies the prior probability distribution at the current time step by the likelihood function and normalizes it to calculate the posterior probability distribution of the parameters at the current time step. .

[0096] The dynamic parameter update module 50 repeatedly executes the above prediction and update steps in time sequence. As monitoring data continues to accumulate, the dynamic parameter update module 50 continuously corrects the probability distribution of model parameters and outputs a probability distribution sequence reflecting the evolution trajectory of the material parameters of the panel rockfill dam over time, providing dynamic parameter basis for the dam safety state assessment.

[0097] This invention provides a specific implementation case, which selects a 200m high concrete-faced rockfill dam project as the application object to verify the actual effectiveness of the aforementioned high-performance adaptive probabilistic inversion system and method assisted by the multidimensional cloud proxy model.

[0098] This embodiment first establishes a three-dimensional finite element model of the rockfill dam using the finite element modeling and parameter initialization module 10. The model is constructed based on the design drawings and includes the rockfill area of ​​the dam body, the concrete face structure, and the bedrock foundation area. The mesh is divided according to the dam body filling zones and construction stages, and the model contains several hexahedral elements. Based on the actual layout of the dam safety monitoring system, the settlement monitoring point located at the maximum cross-section along the dam axis is selected as the reference point for the inversion analysis.

[0099] This embodiment uses an elastoplastic constitutive model to describe the mechanical behavior of the riprap. Through parameter sensitivity analysis, six main model parameters were identified as variables to be inverted: loading modulus coefficient, etc. Unloading modulus coefficient Dry density Loading index Unloading index and bed coefficient The finite element modeling and parameter initialization module 10 sets the prior distribution range and statistical characteristics of each parameter based on engineering analogy experience, for example, setting... It follows a normal distribution with a mean of 1.3. It follows a log-normal distribution with a mean of 1400.

[0100] The sample generation and forward analysis module 20 uses the Latin hypercube sampling method to generate 100 sets of model parameter samples within the aforementioned prior distribution space. The module then calls a finite element method (FEM) program to perform forward analysis on these 100 sets of samples, extracting settlement calculation values ​​at reference points to construct a training dataset containing 100 pairs of parameter settlement data. The multidimensional coupled cloud proxy model construction module 30 reads this dataset, performs standardization and cloud feature extraction, and constructs a 6-input, 1-output multidimensional coupled cloud proxy model.

[0101] The adaptive probability inversion module 40 is configured with four parallel-running Markov chains, and the initial sampling step size is set. The target acceptance rate was set at 0.234. The adaptive probability inversion module 40 reads the measured settlement data of the reference point and initiates the adaptive sampling inversion process in conjunction with the cloud proxy model. During the sampling period, the adaptive probability inversion module 40 uses cloud droplet certainty and overentropy ratio to calculate local and global uncertainty indicators in real time, and dynamically adjusts the sampling step size according to the aforementioned variable step size adjustment mechanism.

[0102] After sampling, the adaptive probability inversion module 40 outputs the posterior distribution statistics of the parameters. The posterior mean was 1.3154, and the standard deviation was 0.0454; parameters The posterior mean was 1400.05, and the standard deviation was 45.7338. The convergence diagnostic index R-hat was less than 1.01, indicating that the Markov chain had reached a stable convergence state. The mean absolute percentage error (MAPE) of the inversion results for each parameter was at a low level. The MAPE value is 0.162%.

[0103] The dynamic parameter update module 50 performs sequential probability inversion based on data from three consecutive monitoring times (t1, t2, t3). The module uses the posterior distribution of the parameters obtained at time t1 as the prior distribution at time t2, and updates the parameter distribution by incorporating newly added monitoring data at time t2. As time progresses, the parameters... The mean value evolved from 1423.05 at time t2 to 1275.88 at time t3, reflecting the attenuation characteristics of the stiffness of the dam material over time; at the same time, the standard deviation of the parameter remained stable, indicating that the uncertainty was effectively controlled.

Claims

1. A high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model, characterized in that, include: The finite element modeling and parameter initialization module is used to construct a three-dimensional finite element model that reflects the geometry of the dam body, select displacement monitoring points as inversion reference points, and determine the parameters to be inverted and the prior probability distribution range of the parameters to be inverted. The sample generation and forward analysis module is used to generate model parameter samples within a set prior probability distribution range, and perform forward analysis calculations through a three-dimensional finite element model to construct an input and output dataset containing parameter samples and deformation response data. The multidimensional coupled cloud proxy model construction module is configured to receive the input and output datasets, calculate the cloud digital features of the input variables, generate multi-layer virtual cloud droplets to characterize the multidimensional coupling characteristics of the parameter space, and establish a mapping relationship between model parameters and deformation response as a substitute model for the finite element model. The adaptive probability inversion module is configured to receive measured displacement monitoring data, perform parameter inversion using a variable step size Markov chain Monte Carlo sampling algorithm based on cloud features, and obtain the posterior probability distribution of the parameters to be inverted. The dynamic parameter update module is used to process time-varying monitoring data, establish a state-space model, and continuously correct and update the parameter distribution by integrating newly added monitoring data through a Bayesian update strategy.

2. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 1, characterized in that, When generating model parameter samples, the sample generation and forward analysis module is configured to use the Latin hypercube sampling method, which divides the value range of each parameter to be inverted into multiple equal probability intervals according to the probability distribution of the parameter to be inverted, randomly selects sampled values ​​in each equal probability interval and performs random non-repeating combination to generate model parameter samples covering the parameter space.

3. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 1, characterized in that, When calculating cloud digital features, the multidimensional coupled cloud proxy model construction module first standardizes the input and output datasets; then it calculates the sample expectation vector as the center position of cloud droplet generation, and calculates the covariance matrix to measure the coupling correlation between input dimensions. Based on the sample expectation vector and covariance matrix, the entropy and hyperentropy of each input variable are extracted, where entropy is used to characterize the uncertainty of qualitative concepts, and hyperentropy is used to characterize the uncertainty of entropy.

4. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 3, characterized in that, When generating multi-layered virtual cloud droplets, the multi-dimensional coupled cloud proxy model construction module is configured to introduce the hyperentropy to modify the covariance matrix based on the sample expectation vector and covariance matrix in order to control the perturbation amplitude. By setting different modified covariance matrices at different levels, hierarchical virtual cloud droplets that follow a normal distribution are generated.

5. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 4, characterized in that, When establishing the mapping relationship, the multidimensional coupled cloud proxy model construction module is configured to calculate the degree of certainty of each virtual cloud droplet with respect to the proxy model center. The degree of certainty is calculated based on the squared Mahalanobis distance between the virtual cloud droplet and the expected value of the proxy model and the average entropy value of the layer. The multidimensional coupled cloud proxy model construction module assigns weights based on the degree of certainty, performs weighted fusion of prediction results at all levels, and performs denormalization on the output results to map them back to the original physical space.

6. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 1, characterized in that, The adaptive probability inversion module is configured to call the alternative model generated by the multidimensional coupled cloud proxy model construction module to calculate the predicted response of the current parameter sample, and construct a likelihood function based on the measured displacement monitoring data and the predicted response; the likelihood function is constructed based on the assumption that the observation error follows a Gaussian distribution, using the deviation between the predicted value and the measured value and the covariance matrix of the observation error.

7. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 6, characterized in that, When performing sampling, the adaptive probability inversion module is configured to calculate the local uncertainty index and the global uncertainty index of the current sampling point. The local uncertainty index is defined as the ratio of the distance between the parameter value of the current sampling point and the expected distance of the cloud agent model to the square root of the trace of the covariance matrix. The global uncertainty index is defined as the ratio of the hyperentropy to the entropy calculated by the multidimensional coupled cloud agent model construction module.

8. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 7, characterized in that, The adaptive probability inversion module is configured with a step size hierarchical dynamic adjustment model. The step size hierarchical dynamic adjustment model first sets a threshold based on the statistical characteristics of the dispersion of the sampled samples. When the local uncertainty index is greater than the threshold, it is determined to be a high uncertainty region and the sampling step size is increased. At the same time, based on the global uncertainty index, it is determined whether it is dominated by hyperentropy or entropy, and the step size expansion or contraction strategy is executed respectively. Finally, a geometric constraint based on Mahalanobis distance is applied to the adjusted step size to generate the final sampling step size.

9. The high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 1, characterized in that, The state-space model established by the dynamic parameter update module includes a state equation and an observation equation. The state equation describes the evolution of model parameters from the previous time step to the current time step and includes process noise. The observation equation describes the mapping relationship between model parameters and observation data, wherein the observation function is a substitute model generated by the multidimensional coupled cloud proxy model construction module.

10. A high-performance adaptive probabilistic inversion system assisted by a multi-dimensional cloud agent model according to claim 9, characterized in that, When performing Bayesian updates, the dynamic parameter update module is configured to use the posterior probability distribution of parameters calculated at the previous time step as the prior information basis for the current time step, advance the state equation to obtain the prior probability distribution at the current moment, and construct a likelihood function by combining the newly added monitoring data at the current moment and the observation equation, and finally calculate the sequence of posterior probability distributions of parameters at the current moment.

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