A Digital Twin Approach for Coal Mine Mining Based on Multi-Level Dynamic Correction and AI Optimization

Abstract

This invention provides a digital twin method for coal mine mining based on multi-level dynamic error correction and AI optimization. The method includes: monitoring data acquisition and dynamic preprocessing, denoising and spatial consistency detection of the data; construction and preprocessing of the coal mine digital twin; generation of a nonlinear deviation field using highly nonlinear variable interpolation and model mapping methods; Kalman filtering error analysis and correction in continuous analysis steps, combined with spatial mutation step marking to optimize model states; staged sliding window long-term fluctuation analysis, classifying and marking regions based on the absolute value of the error and fluctuations; multi-level weighted error optimization based on genetic algorithms to adjust material parameters and boundary conditions; material constitutive error correction based on dynamic Bayesian methods to gradually enhance the model's adaptability and accuracy; and construction of a deep data-driven hybrid network structure AI optimization and prediction model to capture the dynamic changes in material constitutive features and differences in model constitutive characteristics, achieving accurate digital twin simulation of the entire coal mine mining process.

Description

Technical Field

[0001] This invention relates to the field of coal mining engineering technology, specifically to a digital twin method for coal mining based on multi-level dynamic correction and AI optimization. Background Technology

[0002] During coal mining, complex geological conditions, rock strata movement, and stress distribution variations pose significant safety risks. Therefore, simulation and modeling technologies for the mining process play a crucial role in predicting potential geological hazards and guiding mining operations. Current coal mining simulations primarily rely on static processes, built upon prior geological surveys and exploration data, to perform unsupervised simulations of complex mining environments. However, they suffer from the following significant limitations:

[0003] 1. Lack of deep integration with dynamic correction and real-time monitoring data: Existing simulation technologies typically build geological models based on static data before mining to simulate stress distribution and material response. However, during mining, geological conditions and stress fields continuously change with the progress of operations, and existing static models cannot capture and update these changes in a timely manner. Due to the lack of deep integration with real-time monitoring data, the mining process and stress distribution in the model often fail to reflect the actual situation, resulting in low prediction accuracy.

[0004] 2. The application of digital twin technology is still in its early stages: Although digital twin technology has been widely used in industrial manufacturing, urban management and other fields, its application in coal mining is still in its initial stage, especially in the areas of dynamic correction and handling nonlinear stress changes. Existing coal mine simulation technology is limited to limited numerical simulation, lacking real-time feedback on the mining process and refined digital twin process construction, and cannot provide accurate virtual-real mapping to adapt to changes in geological conditions.

[0005] 3. Insufficient dynamic parameter adjustment and multi-level data optimization capabilities: In the coal mining environment, geological abrupt changes at different levels, material hardening effects, and stress concentration phenomena gradually emerge during mining. Existing static simulation models struggle to adjust these parameters in real time and are slow to respond to abnormal signals at monitoring points and sensitive areas of stress concentration. Furthermore, the calculation results of static models are often not optimized in real time for dynamic monitoring data, lacking multi-level parameter correction and anomaly detection mechanisms, resulting in inadequate performance in long-term time-series analysis and dynamic prediction.

[0006] In conclusion, there is still very little research on the deep utilization of digital twin technology for supervised, interactive, and dynamic twin simulation of coal mining. Summary of the Invention

[0007] The applicant of this invention discovered through research that the application of digital twin technology in coal mining can achieve real-time data correction and high-precision simulation prediction, significantly improving the transparency and accuracy of the mining process. However, existing coal mining simulation methods are mostly static simulations, lacking dynamic integration with real-time monitoring data, and offering limited optimization for complex nonlinear material parameters and boundary conditions. To address this technical need, this invention provides a digital twin method for coal mining based on multi-level dynamic correction and AI optimization. This method first dynamically acquires and denoises monitoring data, constructs a geological digital twin model, generates a nonlinear deviation field, and performs precise data mapping. During the simulation, a Kalman filter is used to dynamically correct errors, and a sliding window analysis is used to identify abrupt change regions. For highly volatile regions, material parameters and boundary conditions are further optimized using a genetic algorithm, combined with a dynamic Bayesian method to gradually adjust the material constitutive properties, achieving high-precision fitting under complex geological conditions. Finally, a deep data-driven AI network model is used to dynamically optimize and predict the material constitutive and model constitutive, completing real-time updates of the virtual-real mapping, significantly improving the accuracy and decision support capabilities of the digital twin for coal mining.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization includes the following steps:

[0010] S1. Monitoring data acquisition and dynamic preprocessing: Determine the sensor acquisition frequency and calibrate the timestamp, perform structured settings on the data acquired before processing, set upper and lower limit noise thresholds of mean ± 3 times standard deviation for monitoring points, perform spatial consistency detection, analyze the correlation between the relative positions and stress values ​​of multiple sensors, adaptively adjust the threshold intensity according to fluctuations, and perform smooth interpolation repair on the data of abnormal points.

[0011] S2. Construction and preprocessing of digital twins for coal mines: Using rapid modeling methods for unstructured data from boreholes, exploration, and geophysical surveys, a true three-dimensional state of coal mine geology is constructed. The model undergoes adaptive mesh generation, initial geostress field equilibrium, static boundary condition setting, and material parameter assignment operations to provide a digital foundation for twin simulation.

[0012] S3. High nonlinear variable interpolation and model mapping: For the monitoring data points in step S1, based on the position of the distance from the model grid nodes, a continuous nonlinear deviation field is generated by radial basis function interpolation. The field is aligned according to the model coordinate system space, and the coordinates of each grid node are matched to complete the numerical mapping. Bilinear interpolation is then used to further smooth the transition.

[0013] S4. Kalman Filter Error Analysis and Correction in Continuous Analysis Steps: In each calculation step, the simulation results and monitoring data are subjected to Kalman filter analysis. The Kalman gain is calculated and the state value and covariance matrix are updated. The state value and error of the model are dynamically adjusted through the prediction-correction process. The weights are adaptively adjusted according to the error fluctuations. Spatial analysis is performed on all monitoring point data. The spatial variation coefficient, i.e., the ratio of standard deviation to mean, in the entire monitoring point set is calculated. Spatial mutation steps that exceed the threshold are marked, providing a basis for hierarchical processing for subsequent optimization algorithms.

[0014] S5. Staged sliding window long-term fluctuation analysis: After the length of a working face is completed, a dynamic sliding window is set in the geological structure and stress concentration area where error fluctuations are prone to occur, and the time-series error data within the window is processed by rolling average. The results are classified into anomalies according to the large absolute value of error and the large error fluctuation. For areas with continuous large error or frequent fluctuations within the window, the incremental-decrease threshold detection method is used. For spatial mutation steps marked in step S4 within the error fluctuation area, they will be given higher weight values ​​in subsequent optimization.

[0015] S6. Multi-level weighted error optimization based on genetic algorithm: Taking the degree of error convergence as the fitness target, calculate the mean square error between each monitoring point and interpolation point. Use different combinations of material parameters and boundary conditions to form an initial population. Set weights for the spatial mutation step in step S4, the error with large absolute value in step S5, and the error with large fluctuation. Analyze the long-term dynamic characteristics of the error based on the error time series trend after rolling average. Adjust the local material parameters for the error with large fluctuation and mutation marker areas based on the weights. Fine-tune the boundary conditions for the areas with large absolute error values, maintaining the amplitude at 5% to 10% to maintain convergence stability. Obtain the optimized initial boundary state and material properties for the next step.

[0016] S7. Material constitutive correction based on dynamic Bayes: The results optimized in step S6, geological exploration, historical monitoring data, and known material constitutive model library are used as the initial prior distribution of material constitutive parameters. A likelihood function is constructed based on the differences between simulated stress-strain and monitoring data in multiple steps to reflect the soft and hardening nonlinear response characteristics of materials under different stress states. The posterior distribution is updated in the next working face mining stage based on the combination of the two. As the mining of the working face deepens, the new material constitutive characteristics are used as the prior distribution input to the model for the next stage, gradually enhancing the model's adaptability and accuracy to complex nonlinear and high-stress geological conditions, forming a progressive optimization effect of dynamic feedback and multiple iterations.

[0017] S8. Construct an AI optimization and prediction model based on a hybrid network structure driven by deep data: Using the optimization and monitoring data generated in steps S4 to S7 as input, a recurrent neural network is used to capture the gradual changes of material parameters on the time axis based on the nonlinear relationship between stress and strain; a convolutional neural network is used to extract the spatial distribution features of the boundary and materials, and their time series and spatial features are fused; based on supervised learning and dynamic Bayesian updates, a dynamic material constitutive and model constitutive property update mechanism is constructed to accurately describe the dynamic characteristics of geological changes under mining, and continuously improve the ability to accurately map the dynamic twin virtual and real states of coal mining.

[0018] Furthermore, in step S1, the potential time drift error inside the device is eliminated by comparing and correcting the internal and external clocks of the sensor. The collected raw data is then structured and normalized using a minimum-maximum normalization process. The correlation analysis of the data from each sensor is performed using a combination of Pearson correlation coefficient and mutual information. When the stress value detected by the sensor fluctuates frequently, the threshold is automatically relaxed to accommodate higher dynamic changes, and vice versa. For multi-point anomalies, a regional correlation interpolation method is used to fully consider the stress values ​​of adjacent time and space nodes to ensure the accuracy of anomaly point repair. The end time and start time of each step are set to ensure that the end time of the calculation step is precisely aligned with the acquisition time. A smaller time step is selected by adjusting the time integration step to better capture nonlinear behavior while meeting the acquisition interval frequency.

[0019] Furthermore, in step S3, radial basis function interpolation is used to generate a nonlinear deviation field from the monitoring point to the model node, giving it global continuity and local accuracy. The radial basis function is represented as follows:

[0020]

[0021] Where r represents the coordinates of the target mesh node; r i Represents the coordinates of the monitoring point; ||rr i || represents the Euclidean distance between the grid nodes and the monitoring points; σ is a parameter that controls the smoothness of the radial basis function, which is dynamically adjusted according to the density and spacing of the monitoring points to match the distribution of nonlinear features;

[0022] Next, the deviation field space is aligned according to the model's three-dimensional coordinate system. For each grid node x j The interpolated nonlinear deviation field is mapped to the three-dimensional coordinate space of the model. Assume the value of the monitoring data is f(r). i If the node x is... j The mapping value F(x) at the location j The result is calculated using radial basis function interpolation:

[0023]

[0024] Where, λ i For monitoring point r i The weight of the interpolation effect is determined by the monitoring data and model calibration parameters; N is the total number of monitoring points;

[0025] After mapping, bilinear interpolation is applied to adjacent grid nodes to eliminate numerical abrupt changes. For four adjacent nodes Q in the two-dimensional plane... 11 Q 12 Q 21 Q 22 Interpolate as follows:

[0026]

[0027] Where (x1,y1), (x2,y1), (x1,y2), and (x2,y2) are the coordinates of four adjacent grid nodes, respectively, and f(Q) 11 f(Q) 21 f(Q) 12 f(Q) 22 These represent the values ​​of the four corresponding grid nodes;

[0028] This bilinear interpolation formula can be generalized to three-dimensional meshes, achieving a more accurate and smooth transition of nonlinear deviation fields by calculating eight adjacent nodes in a three-dimensional solid.

[0029] Furthermore, in step S4, a state transition equation is used to predict the next state. And error covariance P k|k-1 :

[0030]

[0031] Among them, F k B is the state transition matrix; k To control the input matrix; u k Q is an external input quantity; k For process noise covariance;

[0032] The calibration phase utilizes monitoring data z k Calculate the residual y k And through Kalman gain K k Balanced observations and observed values:

[0033]

[0034] Among them, H k R is the observation matrix; k To observe the noise covariance matrix;

[0035] State and Error Updates: Final Updated State Estimation And error covariance P k|k for:

[0036]

[0037] P k|k =(IK k H K )P k|k-1

[0038] Where I is the identity matrix.

[0039] Furthermore, in step S5, a dynamic sliding window size W is defined. If a persistently large error is detected, the detection threshold is dynamically increased to focus on the changing region; conversely, it is decreased to avoid repeated optimization back-and-forth. Errors with significantly deviated absolute values ​​from a relatively stable trend, as well as errors with significant short-term fluctuations and high sensitivity under dynamic response, are marked accordingly. The error value e within the sliding window is then... i We can average the values ​​to obtain the average error value within the sliding window.

[0040]

[0041] Where W is the size of the sliding window; i is the current position, representing the center point of the sliding window; j is the specific position within the sliding window, traversing each data point in the window; e j It is the error value at the j-th position;

[0042] Judgment criteria: When the average error When the value exceeds a certain threshold α, the window is marked as a region with a large absolute error.

[0043]

[0044] Among them, α is based on historical monitoring data or a preset empirical threshold, which can be set according to three times the standard deviation of the monitoring data;

[0045] Calculate the standard deviation σ of the error values ​​within the sliding window. e,i This is used to quantify the volatility of error values.

[0046]

[0047] Judgment criterion: When the standard deviation σ within the sliding window... e,i When the fluctuation exceeds the preset fluctuation threshold β, the window is marked as a region with large error fluctuations.

[0048] σ e,i >β

[0049] Here, β is a dynamically adjusted threshold that is set by monitoring the historical fluctuation characteristics of the data.

[0050] Furthermore, in step S6, different levels of weights are set for evaluating fitness during the optimization process. The fitness function is defined by the weighted mean square error. The lower the fitness value, the closer the parameter combination of the individual is to the optimal value. This continuously focuses on the region with significant error, achieving multi-level optimization of boundary conditions and material parameters. The fitness function is calculated as follows:

[0051]

[0052] Where N is the total number of monitoring points; w space These are the weighting coefficients for spatial errors; ∈ space,i w is the spatial error of the i-th monitoring point; absolute These are the weighting coefficients for the absolute error; ∈ absolute,i w is the absolute error of the i-th monitoring point; variance These are the weighting coefficients for variance error; ∈ variance,i w is the variance error of the i-th monitoring point; space w absolute w variance In each iteration of the genetic algorithm, adjustments are made based on error characteristics to ensure improved fitness of the model in error-prone regions. During crossover and mutation processes, the individual parameter update formula is:

[0053] Child param = (1-α)·Parent1 param +α·Parent2 param

[0054] Where α∈[0,1] is the crossover coefficient, ensuring that the new individual is reasonably adjusted based on the parent parameters; Parent1 param These are the parameters for parent individual 1; Parent2 param These are the parameters of parent individual 2.

[0055] Furthermore, in step S7, the prior stability is solidified using optimized parameters, original data, and known nonlinear response multidimensional parameters. A likelihood function is constructed based on the difference in stress-strain data, and the distribution form of the deviation field is defined through the Gamma distribution. After the constitutive parameters are updated, an asymptotic optimization mechanism based on dynamic feedback is constructed. After each working surface is completed, the posterior distribution is updated to the prior distribution of the next stage, gradually converging to the true mechanical properties of the material. The core dynamic Bayesian update formula is as follows:

[0056] p(θ t+1 |D 1:t+1 )∝p(D t+1 |θ t)·p(θ t |D 1:t )

[0057] Where, θ t+1 p(D) represents the updated parameter. t+1 |θ t p(θ) represents the likelihood value of the observed data in the current step. t |D 1:t ) represents the posterior distribution of the previous stage.

[0058] Furthermore, in step S8, the dynamic material constitutive update constructs an initial material constitutive distribution based on historical data, a known library of material constitutive models, and dynamic Bayesian results. It utilizes a recurrent neural network to capture the time-dependent soft hardening trend of the material and a convolutional neural network to acquire spatial features, gradually updating the material's stress-strain curve. The model performs nonlinear strengthening or attenuation on high-stress regions, forming an adaptive adjustment of the constitutive structure. The dynamic material constitutive structure is described by a nonlinear stress-strain relationship, and the AI ​​model constructs a nonlinear constitutive update function for the material through supervised learning and dynamic Bayesian updates.

[0059] σ t+1 =f(σ t ,ε;θ AI )

[0060] Where, σ t+1 The current value is the predicted stress, ε is the strain, and θ is the stress. AI These are model parameters, which are dynamically updated during the learning process;

[0061] In the dynamic model constitutive model, traditional constitutive model parameters are used as initial parameters. AI algorithms are combined to achieve data-driven adaptive correction. By learning historical sequences of stress and strain data to capture material variation trends, the computational residuals are fed back as adjustment factors for parameters φ and c through Bayesian optimization, achieving a posteriori update of the original model parameters. Taking the common Mohr-Coulomb criterion as an example, the update formula is generated using a deep learning model:

[0062] τ=(c+Δc)+σ·tan(φ+Δφ)

[0063] Where Δc and Δφ are the adjusted values ​​at the current time, predicted by the AI ​​model; Adaptive error correction: combining Kalman filtering or Bayesian update methods to generate a new posterior distribution:

[0064] P(c,φ|D 监测 )≈P(c,φ)·L(D 监测 |c,φ)

[0065] Where P(c,φ) represents the joint probability distribution of the material constitutive parameters; L(D 监测|c,φ) represents the difference between the actual data and the constitutive model, and the optimal (c,φ) value is updated through this distribution;

[0066] Starting from the computational essence of material and model constitutive modeling, we gradually overcome strong nonlinear biases through AI-driven deep data analysis, achieving self-optimizing virtual-real dynamic correction and precise twin mapping.

[0067] This invention provides a digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization. It innovatively applies digital twin technology to the real-time monitoring and dynamic simulation of the coal mine mining process. Utilizing high-precision data fusion and adaptive correction strategies, it achieves synchronous mapping and multi-level optimization between virtual and real spaces. Through intelligent algorithm-optimized numerical simulation methods, this invention achieves high-precision dynamic mapping and real-time feedback of the coal mine mining process, overcoming the shortcomings of traditional static numerical simulation. Compared with existing technologies, this invention has the following advantages:

[0068] 1. Interactive and Supervised Twin Simulation: This invention achieves virtual-real synchronization through interactive and supervised twin simulation by dynamically sensing real-time data during the coal mining process. A cyclical feedback mechanism continuously compares and corrects the monitoring data and simulation results, constructing a flexible real-time model correction mechanism that can dynamically capture the changing characteristics of the mining environment and generate high-precision simulation results. Compared with traditional static simulation methods, this invention has significant advantages in virtual-real interaction and dynamic response.

[0069] 2. Multi-level optimization and correction mechanism: This invention employs a multi-level dynamic correction process to adaptively weight and correct simulation deviations at key monitoring points and abrupt change regions. Within this multi-level optimization framework, based on Kalman filtering and sliding window analysis, genetic algorithms and dynamic Bayesian methods are used to optimize and adjust material parameters and boundary conditions. Focus is placed on correcting nonlinear abrupt change points and regions with high error fluctuations, thereby improving the overall convergence speed and accuracy of the simulation model.

[0070] 3. Deep Data-Driven AI Optimization and Prediction: Combining deep learning technology with a complex data-driven algorithm framework, this invention utilizes recurrent neural networks and convolutional neural networks to accurately describe the boundary states and material changes in coal mining in both time and space. Based on dynamic Bayesian updates, an adaptive multi-level feature learning mechanism is constructed, which can effectively identify and predict key stress-strain trends, material constitutive properties, and model constitutive evolution during the mining process. Unlike traditional limited data prediction methods, this invention breaks through the limitations of traditional static simulation, constructing a flexible real-time feedback and dynamic adjustment framework, providing important support for accurate prediction and optimization of complex coal mining processes. Attached Figure Description

[0071] Figure 1This is a schematic diagram of the process of the digital twin method for coal mining based on multi-level dynamic correction and AI optimization provided by the present invention. Detailed Implementation

[0072] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific illustrations.

[0073] Please refer to Figure 1 As shown, this invention provides a digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization, including the following steps:

[0074] S1. Monitoring data acquisition and dynamic preprocessing: Determine the sensor acquisition frequency and calibrate the timestamp, perform structured settings on the data acquired before processing, set upper and lower limit noise thresholds of mean ± 3 times standard deviation for monitoring points, perform spatial consistency detection, analyze the correlation between the relative positions and stress values ​​of multiple sensors, adaptively adjust the threshold intensity according to fluctuations, and perform smooth interpolation repair on the data of abnormal points.

[0075] S2. Construction and preprocessing of digital twins for coal mines: Using rapid modeling methods for unstructured data such as boreholes, exploration, and geophysical exploration, a true three-dimensional state of coal mine geology is constructed. The model is subjected to adaptive mesh generation, initial geostress field equilibrium, static boundary condition setting, and material parameter assignment, providing a digital foundation for twin simulation.

[0076] S3. High Nonlinear Variable Interpolation and Model Mapping: For the monitoring data points in step S1, based on the position of the distance from the model grid nodes, a continuous nonlinear deviation field is generated by interpolation using the Radial Basis Function (RBF). The field is aligned according to the model coordinate system space, and the coordinates of each grid node are matched to complete the numerical mapping. Bilinear interpolation is then used to further smooth the transition.

[0077] S4. Kalman Filter Error Analysis and Correction in Continuous Analysis Steps: In each calculation step, the simulation results and monitoring data are subjected to Kalman filter analysis. The Kalman gain is calculated and the state value and covariance matrix are updated. The state value and error of the model are dynamically adjusted through the prediction-correction process. The weights are adaptively adjusted according to the error fluctuations. Spatial analysis is performed on all monitoring point data. The spatial variation coefficient, i.e., the ratio of standard deviation to mean, in the entire monitoring point set is calculated. Spatial mutation steps that exceed the threshold are marked, providing a basis for hierarchical processing for subsequent optimization algorithms.

[0078] S5. Staged sliding window long-term fluctuation analysis: After the length of a working face is completed, a dynamic sliding window is set in the geological structure (such as faults and folds) and stress concentration area where error fluctuations are prone to occur. The time-series error data within the window is processed by rolling average. The results are classified into anomalies according to the large absolute value of error and the large error fluctuation. For areas with continuous large error or frequent fluctuations within the window, the incremental-decrease threshold detection method is used. For spatial mutation steps marked in step S4 within the error fluctuation area, a higher weight value will be assigned in the subsequent optimization.

[0079] S6. Multi-level weighted error optimization based on genetic algorithm (GA): Taking the degree of error convergence as the fitness objective, the mean square error (MSE) between each monitoring point and interpolation point is calculated. An initial population is formed by different material parameters (elastic modulus, Poisson's ratio, etc.) and boundary conditions. Weights are set for the spatial mutation step in step S4, the error with large absolute value and the error with large fluctuation in step S5. The long-term dynamic characteristics of the error are analyzed based on the error time series trend after rolling average. Based on the weights, the local material parameters are adjusted for the error with large fluctuation and mutation marker areas. The boundary conditions are fine-tuned for the areas with large absolute error, and the amplitude is maintained at 5% to 10% to maintain the stability of convergence. The initial boundary state and material properties of the next step (Step) after optimization are obtained.

[0080] S7. Material constitutive correction based on dynamic Bayes: The results optimized in step S6, geological exploration, historical monitoring data, and known material constitutive model libraries are used as the initial prior distribution of material constitutive parameters. A likelihood function is constructed based on the differences between simulated stress-strain and monitoring data in multiple steps to reflect the nonlinear response characteristics of materials such as softness and hardening under different stress states. The posterior distribution is updated in the next working face mining stage based on the combination of the two. As the mining of the working face deepens (e.g., after mining three or more working face lengths), the new material constitutive properties are used as the prior distribution input model for the next stage, gradually enhancing the model's adaptability and accuracy to complex nonlinear and high-stress geological conditions, forming a progressive optimization effect of dynamic feedback and multiple iterations.

[0081] S8. Construct an AI optimization and prediction model based on a deep data-driven hybrid network structure: Using the optimization and monitoring data generated in steps S4 to S7 as input, a recurrent neural network (RNN) is used to capture the gradual changes of material parameters on the time axis based on the nonlinear relationship between stress and strain; a convolutional neural network (CNN) is used to extract the spatial distribution features of the boundary and materials, and their time series and spatial features are fused; based on supervised learning and dynamic Bayesian updates, a dynamic material constitutive and model constitutive property update mechanism is constructed to accurately describe the dynamic changes of geological characteristics under mining, and continuously improve the ability to accurately map the dynamic twin virtual and real states of coal mining.

[0082] In a specific embodiment, step S1 first eliminates potential time drift errors within the device by comparing and correcting the internal and external clocks of the sensors. The collected raw data is then structured and normalized using a minimum-maximum normalization process. Pearson correlation coefficient and mutual information are combined to perform correlation analysis on the data from each sensor. When the stress value detected by the sensor fluctuates frequently, the threshold is automatically relaxed to accommodate higher dynamic changes; conversely, the threshold is tightened. For multi-point anomalies, regional correlation interpolation is used to fully consider the stress values ​​of adjacent time and space nodes, ensuring the accuracy of anomaly point repair. The end time and initial time of each step are set to ensure precise alignment between the end time of the calculation step and the acquisition time. A smaller time step is selected by adjusting the time integral (increment size) step, better capturing nonlinear behavior while meeting the acquisition interval frequency.

[0083] In a specific embodiment, step S3 utilizes radial basis function (RBF) interpolation to generate a nonlinear deviation field from the monitoring point to the model node, ensuring both global continuity and local accuracy. The radial basis function is represented as follows:

[0084]

[0085] Where r represents the coordinates of the target mesh node; r i Represents the coordinates of the monitoring point; ||rr i || represents the Euclidean distance between the grid nodes and the monitoring points; σ is a parameter that controls the smoothness of the radial basis function, which is dynamically adjusted according to the density and spacing of the monitoring points to match the distribution of nonlinear features;

[0086] Next, the deviation field space is aligned according to the model's three-dimensional coordinate system. For each grid node x j The interpolated nonlinear deviation field is mapped to the three-dimensional coordinate space of the model. Assume the value of the monitoring data is f(r). i If the node x is... j The mapping value F(x) at the location j The result is calculated using radial basis function interpolation:

[0087]

[0088] Where, λ i For monitoring point r i The weight of the interpolation effect is determined by the monitoring data and model calibration parameters; N is the total number of monitoring points;

[0089] After mapping, bilinear interpolation is applied to adjacent grid nodes to eliminate numerical abrupt changes. For four adjacent nodes Q in the two-dimensional plane... 11 Q 12 Q 21 Q 22 Interpolate as follows:

[0090]

[0091] Where (x1,y1), (x2,y1), (x1,y2), and (x2,y2) are the coordinates of four adjacent grid nodes, respectively, and f(Q) 11 f(Q) 21 f(Q) 12 f(Q) 22 These represent the values ​​of the four corresponding grid nodes;

[0092] This bilinear interpolation formula can be generalized to three-dimensional meshes, achieving a more accurate and smooth transition of nonlinear deviation fields by calculating eight adjacent nodes in a three-dimensional solid.

[0093] In a specific embodiment, step S4 uses a state transition equation to predict the next state. And error covariance P k|k-1 :

[0094]

[0095] Among them, F k B is the state transition matrix; k To control the input matrix; u k Q is an external input quantity; k For process noise covariance;

[0096] The calibration phase utilizes monitoring data z k Calculate the residual y k And through Kalman gain K k Balanced observations and observed values:

[0097]

[0098] Among them, H k R is the observation matrix; k To observe the noise covariance matrix;

[0099] State and Error Updates: Final Updated State Estimation And error covariance P k|k for:

[0100]

[0101] P k|k=(IK k H K )P k|k-1

[0102] Where I is the identity matrix.

[0103] In a specific embodiment, step S5 defines a dynamic sliding window size W. If a persistently large error is detected, the detection threshold is dynamically increased to focus on the changing region; conversely, it is decreased to avoid repeated optimization adjustments. Errors with significantly larger absolute values ​​that deviate from a relatively stable trend, as well as errors with significant short-term fluctuations and high sensitivity under dynamic response, are marked accordingly. The error value e within the sliding window is then... i We can average the values ​​to obtain the average error value within the sliding window.

[0104]

[0105] Where W is the size of the sliding window; i is the current position, representing the center point of the sliding window; j is the specific position within the sliding window, traversing each data point in the window; e j It is the error value at the j-th position;

[0106] Judgment criteria: When the average error When the value exceeds a certain threshold α, the window is marked as a region with a large absolute error.

[0107]

[0108] Among them, α is based on historical monitoring data or a preset empirical threshold, which can be set according to three times the standard deviation of the monitoring data;

[0109] Calculate the standard deviation σ of the error values ​​within the sliding window. e,i This is used to quantify the volatility of error values.

[0110]

[0111] Judgment criterion: When the standard deviation σ within the sliding window... e,i When the fluctuation exceeds the preset fluctuation threshold β, the window is marked as a region with large error fluctuations.

[0112] σ e,i >β

[0113] Here, β is a dynamically adjusted threshold that is set by monitoring the historical fluctuation characteristics of the data.

[0114] In a specific embodiment, step S6 sets different levels of weights for evaluating fitness during the optimization process. The fitness function is defined by the weighted mean square error (MSE). The lower the fitness value, the closer the parameter combination of the individual is to the optimal value. This continuously focuses on the region with significant error, achieving multi-level optimization of boundary conditions and material parameters. The fitness function is calculated as follows:

[0115]

[0116] Where N is the total number of monitoring points; w space These are the weighting coefficients for spatial errors; ∈ space,i w is the spatial error of the i-th monitoring point; absolute These are the weighting coefficients for the absolute error; ∈ absolute,i w is the absolute error of the i-th monitoring point; variance These are the weighting coefficients for variance error; ∈ variance,i w is the variance error of the i-th monitoring point; space w absolute w variance In each iteration of the genetic algorithm, adjustments are made based on error characteristics to ensure the model's performance improves in high-error-prone areas. During crossover and mutation, the individual parameter update formula is:

[0117] Child param = (1-α)·Parent1 param +α·Parent2 param

[0118] Where α∈[0,1] is the crossover coefficient, ensuring that the new individual is reasonably adjusted based on the parent parameters; Parent1 param These are the parameters for parent individual 1; Parent2 param These are the parameters of parent individual 2.

[0119] In a specific embodiment, step S7 utilizes multi-dimensional parameters such as optimized parameters, original data, and known nonlinear responses to solidify prior stability. A likelihood function is constructed based on the difference in stress-strain data. The deviation field distribution is defined using the Gamma distribution. After updating the constitutive parameters, a progressive optimization mechanism based on dynamic feedback is constructed. After each working surface is completed, the posterior distribution is updated to the prior distribution for the next stage, gradually converging to the true mechanical properties of the material. The core dynamic Bayesian update formula is as follows:

[0120] p(θ t+1 |D 1:t+1 )∝p(D t+1 |θ t )·p(θ t |D 1:t )

[0121] Where, θ t+1 p(D) represents the updated parameter. t+1 |θ t p(θ) represents the likelihood value of the observed data in the current step. t |D 1:t ) represents the posterior distribution of the previous stage.

[0122] In a specific embodiment, the dynamic material constitutive update in step S8 constructs an initial material constitutive distribution based on historical data, a known library of material constitutive models, and dynamic Bayesian results. It utilizes a recurrent neural network (RNN) to capture the time-dependent soft hardening trend of the material and a convolutional neural network (CNN) to acquire spatial features, gradually updating the material's stress-strain curve. The model performs nonlinear strengthening or attenuation on high-stress regions (such as faults), forming an adaptive adjustment of the constitutive structure. The dynamic material constitutive structure is described by a nonlinear stress-strain relationship, and the AI ​​model constructs a nonlinear constitutive update function for the material through supervised learning and dynamic Bayesian updates.

[0123] σ t+1 =f(σ t ,ε;θ AI )

[0124] Where, σ t+1 The current value is the predicted stress, ε is the strain, and θ is the stress. AI These are model parameters, which are dynamically updated during the learning process;

[0125] In the dynamic model constitutive model, traditional constitutive model parameters are used as initial parameters. AI algorithms are combined to achieve data-driven adaptive correction. By learning historical sequences of stress and strain data to capture material variation trends, the computational residuals are fed back as adjustment factors for parameters φ and c through Bayesian optimization, achieving a posteriori update of the original model parameters. Taking the common Mohr-Coulomb criterion as an example, the update formula is generated using a deep learning model:

[0126] τ=(c+Δc)+σ·tan(φ+Δφ)

[0127] Where Δc and Δφ are the adjusted values ​​at the current time, predicted by the AI ​​model; Adaptive error correction: combining Kalman filtering or Bayesian update methods to generate a new posterior distribution:

[0128] P(c,φ|D 监测 )≈P(c,φ)·L(D 监测 |c,φ)

[0129] Where P(c,φ) represents the joint probability distribution of the material constitutive parameters; L(D 监测|c,φ) represents the difference between the actual data and the constitutive model, and the optimal (c,φ) value is updated through this distribution;

[0130] Starting from the computational essence of material and model constitutive modeling, we gradually overcome strong nonlinear biases through AI-driven deep data analysis, achieving self-optimizing virtual-real dynamic correction and precise twin mapping.

[0131] To better understand the digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization provided by this invention, a detailed description will be provided below with reference to specific embodiments. This embodiment involves field testing at the Shaanxi Coal Mengcun Coal Mine, and the specific steps are as follows:

[0132] S1. Use Python scripts to acquire real-time monitoring data from sensors such as strain gauges and accelerometers installed at the coal mine site. After data acquisition, perform data cleaning using the Pandas library, including removing missing values ​​and noise. Calculate the Pearson correlation coefficient and mutual information between multiple sensors to evaluate the correlation between relative position and stress values. Use SciPy for data smoothing and interpolation to ensure that the acquired monitoring data is free of outliers.

[0133] S2. In Abaqus, use UMAT (User-defined Material Subroutine) to define the material constitutive model, and perform initial static boundary condition settings, stress field equilibrium, and mesh generation.

[0134] S3. Based on the real-time monitoring data collected in step S1, nonlinear deviation field interpolation is performed using the radial basis function (RBF) interpolation method via Python to generate a continuous deviation field based on the model grid. Spatial alignment of the deviation field is achieved using Fortran, mapping the monitoring point interpolation results to the Abaqus grid model, and data smoothing is achieved using the bilinear interpolation method.

[0135] S4. Implement the Kalman filter algorithm using Python and Fortran interface, correct the simulated data and monitoring data obtained in each calculation, calculate the gain, and update the model state. After each iteration, adaptively adjust the weights based on error fluctuations. Use Python to write a sliding window analysis program to perform rolling averages on the time series data within the sliding window and classify them according to "large absolute error value" and "large error fluctuation".

[0136] S5. After each working face is mined, an update is performed. Combining the dynamic Bayesian method, a likelihood function is constructed based on simulation data, monitoring data, and historical data to update the material model. The posterior distribution is calculated using a Fortran and Python interface, and the new material constitutive properties are used as prior inputs for the next stage.

[0137] A deep learning model was built using S6, Python, and TensorFlow. RNNs were used to capture the softening and hardening trends of materials, establishing a nonlinear time-series relationship between stress and strain. Convolutional Neural Networks (CNNs) were used to extract the boundary and material spatial distribution features of the mine. Combining RNNs and CNNs to form a hybrid network structure, network weights were continuously updated through supervised learning to accurately predict geological stress changes and material behavior under different working faces. Based on dynamic Bayesian methods and network outputs, the material constitutive model was progressively optimized, and the new dynamic characteristics were fed back to the next working face. Ultimately, the entire process, from monitoring data collection and processing to dynamic optimization of the digital twin and AI model construction, achieved a closed-loop optimization in coal mining, from model building to dynamic feedback.

[0138] This invention provides a digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization. It innovatively applies digital twin technology to the real-time monitoring and dynamic simulation of the coal mine mining process. Utilizing high-precision data fusion and adaptive correction strategies, it achieves synchronous mapping and multi-level optimization between virtual and real spaces. Through intelligent algorithm-optimized numerical simulation methods, this invention achieves high-precision dynamic mapping and real-time feedback of the coal mine mining process, overcoming the shortcomings of traditional static numerical simulation. Compared with existing technologies, this invention has the following advantages:

[0139] 1. Interactive and Supervised Twin Simulation: This invention achieves virtual-real synchronization through interactive and supervised twin simulation by dynamically sensing real-time data during the coal mining process. A cyclical feedback mechanism continuously compares and corrects the monitoring data and simulation results, constructing a flexible real-time model correction mechanism that can dynamically capture the changing characteristics of the mining environment and generate high-precision simulation results. Compared with traditional static simulation methods, this invention has significant advantages in virtual-real interaction and dynamic response.

[0140] 2. Multi-level optimization and correction mechanism: This invention employs a multi-level dynamic correction process to adaptively weight and correct simulation deviations at key monitoring points and abrupt change regions. Within this multi-level optimization framework, based on Kalman filtering and sliding window analysis, genetic algorithms and dynamic Bayesian methods are used to optimize and adjust material parameters and boundary conditions. Focus is placed on correcting nonlinear abrupt change points and regions with high error fluctuations, thereby improving the overall convergence speed and accuracy of the simulation model.

[0141] 3. Deep Data-Driven AI Optimization and Prediction: Combining deep learning technology with a complex data-driven algorithm framework, this invention utilizes recurrent neural networks and convolutional neural networks to accurately describe the boundary states and material changes in coal mining in both time and space. Based on dynamic Bayesian updates, an adaptive multi-level feature learning mechanism is constructed, which can effectively identify and predict key stress-strain trends, material constitutive properties, and model constitutive evolution during the mining process. Unlike traditional limited data prediction methods, this invention breaks through the limitations of traditional static simulation, constructing a flexible real-time feedback and dynamic adjustment framework, providing important support for accurate prediction and optimization of complex coal mining processes.

[0142] Finally, 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 digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization, characterized in that, Includes the following steps: S1. Monitoring data acquisition and dynamic preprocessing: Determine the sensor acquisition frequency and calibrate the timestamp, perform structured settings on the data acquired before processing, set upper and lower limit noise thresholds of mean ± 3 times standard deviation for monitoring points, perform spatial consistency detection, analyze the correlation between the relative positions and stress values ​​of multiple sensors, adaptively adjust the threshold intensity according to fluctuations, and perform smooth interpolation repair on the data of abnormal points. S2. Construction and preprocessing of digital twins for coal mines: Using rapid modeling methods for unstructured data from boreholes, exploration, and geophysical surveys, a true three-dimensional state of coal mine geology is constructed. The model undergoes adaptive mesh generation, initial geostress field equilibrium, static boundary condition setting, and material parameter assignment operations to provide a digital foundation for twin simulation. S3. High nonlinear variable interpolation and model mapping: For the monitoring data points in step S1, based on the position of the distance from the model grid nodes, a continuous nonlinear deviation field is generated by radial basis function interpolation. The field is aligned according to the model coordinate system space, and the coordinates of each grid node are matched to complete the numerical mapping. Bilinear interpolation is then used to further smooth the transition. S4. Kalman Filter Error Analysis and Correction in Continuous Analysis Steps: In each calculation step, the simulation results and monitoring data are subjected to Kalman filter analysis. The Kalman gain is calculated and the state value and covariance matrix are updated. The state value and error of the model are dynamically adjusted through the prediction-correction process. The weights are adaptively adjusted according to the error fluctuations. Spatial analysis is performed on all monitoring point data. The spatial variation coefficient, i.e., the ratio of standard deviation to mean, in the entire monitoring point set is calculated. Spatial mutation steps that exceed the threshold are marked, providing a basis for hierarchical processing for subsequent optimization algorithms. S5. Staged sliding window long-term fluctuation analysis: After the length of a working face is completed, a dynamic sliding window is set in the geological structure and stress concentration area where error fluctuations are prone to occur, and the time-series error data within the window is processed by rolling average. The results are classified into anomalies according to the large absolute value of error and the large error fluctuation. For areas with continuous large error or frequent fluctuations within the window, the incremental-decrease threshold detection method is used. For spatial mutation steps marked in step S4 within the error fluctuation area, they will be given higher weight values ​​in subsequent optimization. S6. Multi-level weighted error optimization based on genetic algorithm: Taking the degree of error convergence as the fitness target, calculate the mean square error between each monitoring point and interpolation point. Use different combinations of material parameters and boundary conditions to form an initial population. Set weights for the spatial mutation step in step S4, the error with large absolute value in step S5, and the error with large fluctuation. Analyze the long-term dynamic characteristics of the error based on the error time series trend after rolling average. Adjust the local material parameters for the error with large fluctuation and mutation marker areas based on the weights. Fine-tune the boundary conditions for the areas with large absolute error values, maintaining the amplitude at 5% to 10% to maintain convergence stability. Obtain the optimized initial boundary state and material properties for the next step. S7. Material constitutive correction based on dynamic Bayes: The results optimized in step S6, geological exploration, historical monitoring data, and known material constitutive model library are used as the initial prior distribution of material constitutive parameters. A likelihood function is constructed based on the differences between simulated stress-strain and monitoring data in multiple steps to reflect the soft and hardening nonlinear response characteristics of materials under different stress states. The posterior distribution is updated in the next working face mining stage based on the combination of the two. As the mining of the working face deepens, the new material constitutive characteristics are used as the prior distribution input to the model for the next stage, gradually enhancing the model's adaptability and accuracy to complex nonlinear and high-stress geological conditions, forming a progressive optimization effect of dynamic feedback and multiple iterations. S8. Construct an AI optimization and prediction model based on a deep data-driven hybrid network structure: Using the optimization and monitoring data generated in steps S4 to S7 as input, a recurrent neural network is used to capture the gradual changes of material parameters on the time axis based on the nonlinear relationship between stress and strain; a convolutional neural network is used to extract the boundary and material spatial distribution features, and its time series and spatial features are fused. Based on supervised learning and dynamic Bayesian updates, a dynamic material constitutive and model constitutive property update mechanism is constructed to accurately describe the dynamic changes in geological properties under mining, and continuously improve the ability to accurately map the dynamic twin virtual and real states of coal mining.

2. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S1, the potential time drift error inside the device is eliminated by comparing and correcting the internal and external clocks of the sensors. The raw data is then structured and normalized using a minimum-maximum normalization process. Pearson correlation coefficient and mutual information are combined to perform correlation analysis on the data from each sensor. When the stress value detected by the sensor fluctuates frequently, the threshold is automatically relaxed to accommodate higher dynamic changes, and vice versa. For multi-point anomalies, regional correlation interpolation is used to fully consider the stress values ​​of adjacent time and space nodes to ensure the accuracy of anomaly point repair. The end time and start time of each step are set to ensure that the end time of the calculation step is precisely aligned with the acquisition time. A smaller time step is selected by adjusting the time integration step to better capture nonlinear behavior while meeting the acquisition interval frequency.

3. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S3, radial basis function interpolation is used to generate a nonlinear deviation field from the monitoring point to the model node, giving it global continuity and local accuracy. The radial basis function is represented as follows: Where r represents the coordinates of the target mesh node; r i Represents the coordinates of the monitoring point; rr i σ is the Euclidean distance between the grid nodes and the monitoring points; σ is a parameter that controls the smoothness of the radial basis function, which is dynamically adjusted according to the density and spacing of the monitoring points to match the distribution of nonlinear features. Next, the deviation field space is aligned according to the model's three-dimensional coordinate system. For each grid node x j The interpolated nonlinear deviation field is mapped to the three-dimensional coordinate space of the model. Assume the value of the monitoring data is f(r). i If the node x is... j The mapping value F(x) at the location j The result is calculated using radial basis function interpolation: Where, λ i For monitoring point r i The weight of the interpolation effect is determined by the monitoring data and model calibration parameters; N is the total number of monitoring points; After mapping, bilinear interpolation is applied to adjacent grid nodes to eliminate numerical abrupt changes. For four adjacent nodes Q in the two-dimensional plane... 11 Q 12 Q 21 Q 22 Interpolate as follows: Where (x1,y1), (x2,y1), (x1,y2), and (x2,y2) are the coordinates of four adjacent grid nodes, respectively, and f(Q) 11 f(Q) 21 f(Q) 12 f(Q) 22 These represent the values ​​of the four corresponding grid nodes; This bilinear interpolation formula can be generalized to three-dimensional meshes, achieving a more accurate and smooth transition of nonlinear deviation fields by calculating eight adjacent nodes in a three-dimensional solid.

4. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S4, a state transition equation is used to predict the next state. And error covariance P kk-1 : Among them, F k B is the state transition matrix; k To control the input matrix; u k Q is an external input quantity; k For process noise covariance; The calibration phase utilizes monitoring data z k Calculate the residual y k And through Kalman gain K k Balanced observations and observed values: Among them, H k R is the observation matrix; k To observe the noise covariance matrix; State and Error Updates: Final Updated State Estimation And error covariance P kk for: P k|k =(I-K k H K )P k|k-1 Where I is the identity matrix.

5. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S5, a dynamic sliding window size W is defined. If a persistently large error is detected, the detection threshold is dynamically increased to focus on the changing region; conversely, it is decreased to avoid repeated optimization back-and-forth. Errors with significantly deviated absolute values ​​from a relatively stable trend, as well as errors with significant short-term fluctuations and high sensitivity under dynamic response, are marked accordingly. The error value e within the sliding window is then... i We can average the values ​​to obtain the average error value within the sliding window. Where W is the size of the sliding window; i is the current position, representing the center point of the sliding window; j is the specific position within the sliding window, traversing each data point in the window; e j It is the error value at the j-th position; Judgment criteria: When the average error When the value exceeds a certain threshold α, the window is marked as a region with a large absolute error. Among them, α is based on historical monitoring data or a preset empirical threshold, which can be set according to three times the standard deviation of the monitoring data; Calculate the standard deviation σ of the error values ​​within the sliding window. e,i This is used to quantify the volatility of error values. Judgment criterion: When the standard deviation σ within the sliding window... e,i When the fluctuation exceeds the preset fluctuation threshold β, the window is marked as a region with large error fluctuations. s e,i >b Here, β is a dynamically adjusted threshold that is set by monitoring the historical fluctuation characteristics of the data.

6. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S6, different levels of weights are set for evaluating fitness during the optimization process. The fitness function is defined by the weighted mean square error. The lower the fitness value, the closer the parameter combination of the individual is to the optimal value. The system continuously focuses on the region with significant error, achieving multi-level optimization of boundary conditions and material parameters. The fitness function is calculated as follows: Where N is the total number of monitoring points; w space These are the weighting coefficients for spatial errors; ∈ space，i w is the spatial error of the i-th monitoring point; absolute These are the weighting coefficients for the absolute error; ∈ absolute，i w is the absolute error of the i-th monitoring point; variance These are the weighting coefficients for variance error; ∈ variance，i W is the variance error of the i-th monitoring point; space w absolute w variance In each iteration of the genetic algorithm, adjustments are made based on error characteristics to ensure improved fitness of the model in error-prone regions. During crossover and mutation processes, the individual parameter update formula is: Child param <(1-α)·Parentl param +α·Parent2 param Where α∈[0,1] is the crossover coefficient, ensuring that the new individual is reasonably adjusted based on the parent parameters; Parentl param These are the parameters for parent individual 1; Parent2 param These are the parameters of parent individual 2.

7. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S7, the prior stability is solidified using optimized parameters, original data, and known nonlinear response multidimensional parameters. A likelihood function is constructed based on the difference in stress-strain data, and the deviation field distribution is defined through the Gamma distribution. After the constitutive parameters are updated, an asymptotic optimization mechanism based on dynamic feedback is constructed. After each working surface is completed, the posterior distribution is updated to the prior distribution of the next stage, gradually converging to the true mechanical properties of the material. The core dynamic Bayesian update formula is as follows: p(θ t+1 |D 1：t+1 )∝p(D t+1 |θ t )·p(θ t |D 1：t ) Where, θ t+1 p(D) represents the updated parameter. t+1 |θ t p(θ) represents the likelihood value of the observed data in the current step. t |D 1：t ) represents the posterior distribution of the previous stage.

8. The digital twin method for coal mine mining based on multi-level dynamic correction and AI optimization according to claim 1, characterized in that, In step S8, the dynamic material constitutive update constructs an initial material constitutive distribution based on historical data, a known library of material constitutive models, and dynamic Bayesian results. It utilizes a recurrent neural network to capture the time-dependent soft hardening trend of the material and a convolutional neural network to acquire spatial features, gradually updating the material's stress-strain curve. The model performs nonlinear strengthening or attenuation on high-stress regions, resulting in adaptive adjustment of the constitutive structure. The dynamic material constitutive structure is described by a nonlinear stress-strain relationship. The AI ​​model constructs a nonlinear constitutive update function for the material through supervised learning and dynamic Bayesian updates. s t+1 =f(σ t ,e;i AI ) Where, σ t+1 The current value is the predicted stress, ε is the strain, and θ is the stress. AI These are model parameters, which are dynamically updated during the learning process; In the dynamic model constitutive model, traditional constitutive model parameters are used as initial parameters. AI algorithms are combined to achieve data-driven adaptive correction. By learning historical sequences of stress and strain data to capture material variation trends, the computational residuals are fed back as adjustment factors for parameters φ and c through Bayesian optimization, achieving a posteriori update of the original model parameters. Taking the common Mohr-Coulomb criterion as an example, the update formula is generated using a deep learning model: τ=(c+Δc)+σ·tan(φ+Δφ) Where Δc and Δφ are the adjusted values ​​at the current time, predicted by the AI ​​model; Adaptive error correction: combining Kalman filtering or Bayesian update methods to generate a new posterior distribution: P(c,φ|D 监测 )≈P(c,φ)·L(D 监测 |c,φ) Where P(c, φ) represents the joint probability distribution of the material constitutive parameters; L(D 监测 |c, φ) represents the difference between the actual data and the constitutive model, and the optimal (c, φ) value is updated through this distribution; Starting from the computational essence of material and model constitutive modeling, we gradually overcome strong nonlinear biases through AI-driven deep data analysis, achieving self-optimizing virtual-real dynamic correction and precise twin mapping.

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