Earthquake physical model material proportion parameter modeling method based on artificial intelligence

Abstract

The invention discloses a seismic physical model material ratio parameter modeling method based on artificial intelligence. The method comprises the steps of S1, experimental design and data acquisition; s2, performing SVR forward modeling based on a kernel method, and constructing a nonlinear mapping model between a matching matrix of the epoxy resin, the silicone rubber and the talcum powder and physical parameters of the test block based on support vector regression of the kernel method; s3, a data enhancement strategy is carried out, Latin hypercube sampling is carried out in the design space of the material ratio to generate K groups, and K is larger than or equal to 100 new ratio parameters; and S4, performing reverse modeling based on a machine learning method, and constructing an inverse problem solving model for reversely deducing the material ratio parameter X from the target physical parameter Y. The method supports multi-target joint prediction, automatically meets the proportion constraint, has accuracy, robustness and engineering practicability, and provides an efficient and reliable solution for intelligent design of seismic physical simulation materials.

Description

A Modeling Method for Material Proportioning Parameters in Seismic Physics Models Based on Artificial Intelligence Technical Field

[0001] This invention relates to the field of geophysical exploration technology, specifically to an artificial intelligence-based method for modeling material ratio parameters in seismic physical models, applicable to the creation of seismic physical models in scenarios such as oil and gas exploration and geological anomaly exploration. Background Technology

[0002] Seismic physical models are important research tools in fields such as oil and gas exploration and geological anomaly exploration. The accuracy of their parameter preparation directly affects the reliability of forward modeling results. Traditional coal and rock material mix design has the following drawbacks: ① Long experimental cycle: Each model requires sample preparation before construction, including the entire process of material mix design, preparation, curing, and testing, which is time-consuming and costly; ② Strong reliance on experience: Mix adjustment relies on manual trial and error, lacking a systematic parameter optimization method, resulting in repeated trial mixes during the casting of complex models, leading to low research and development efficiency.

[0003] In recent years, although machine learning technology has shown significant advantages in the field of materials science, the strong coupling characteristics of multiple parameters of materials in earthquake physics models (such as the cross-order-of-magnitude correlation between P-wave velocity, S-wave velocity, density, and wave impedance) and the small sample characteristics of experimental data have made traditional single-dimensional modeling methods face serious overfitting risks and difficult to meet accuracy requirements. Summary of the Invention

[0004] To address the shortcomings of existing technologies, a new artificial intelligence-based method for modeling material proportion parameters of earthquake physics models is developed by constructing a dual-model architecture of forward prediction and inverse inversion, combined with physical experiments and data augmentation techniques. This method enables intelligent and rapid prediction of material proportion parameters of earthquake physics models, thus overcoming the dual limitations of efficiency and accuracy of traditional methods.

[0005] To achieve the above objectives, the technical solution adopted by this invention includes: a method for modeling the material proportioning parameters of an earthquake physics model based on artificial intelligence, comprising: S1: experimental design and data acquisition, designing R groups of different material proportioning schemes for the earthquake physics model, where R ≥ 100; the earthquake physics model materials include epoxy resin, silicone rubber, and talc, and the different material proportioning schemes for the earthquake physics model materials are cast into standard three-dimensional test blocks of no less than R groups; obtaining the P-wave velocity Vp, S-wave velocity Vs, and density ρ of the standard three-dimensional test blocks; R is taken as a positive integer; S2: SVR forward modeling based on kernel method, constructing the proportioning matrix of the three materials epoxy resin, silicone rubber, and talc based on support vector regression of the kernel method. With the physical parameters of the test block A nonlinear mapping model between X and X, where X Ha X Ga and X MaThese represent the mass percentages of epoxy resin, silicone rubber, and talc powder in group a, respectively; Vp a Vs a and ρ a These represent the longitudinal wave velocity (m / s), transverse wave velocity (m / s), and density (g / cm³) measured after casting and molding the test block of material group a. 3 Establish a Support Vector Regression (SVR) model in a high-dimensional space H. This enables it to accurately predict Y, that is... S3: Optimize the regularization parameter C of the model through grid search, and evaluate the R² of the model on the training and validation sets respectively; S4: Data augmentation strategy: generate K sets of new proportion parameters (K≥100) by Latin hypercube sampling within the material proportion design space, and then use the above SVR forward model to predict the physical parameters corresponding to these new proportions to obtain K sets of (X,Y) data augmentation datasets; S5: Inverse modeling based on machine learning methods: construct an inverse problem-solving model to deduce the material proportion parameter X from the target physical parameter Y. .

[0006] Optionally, the design space for the material ratio is: epoxy resin XHi: 0%~100%, silicone rubber XGi: 0%~100%, talc powder XMi: 0%~60%, and the total mass fraction is always 100%; epoxy resin and silicone rubber are not simultaneously 0% or 100%; talc powder is not taken as the endpoint value of 0%.

[0007] Optionally, S2 includes: (1) establishing a material proportioning matrix. Physical parameter matrix of test block The vector of input material proportions X forms the input matrix. , where X Ha X Ga and X Ma These represent the epoxy resin content, silicone rubber content, and talc content of the sample in group a, respectively. The physical parameter vectors of the output test block Y constitute the output matrix. Vp a Vs a and ρ a These represent the longitudinal wave velocity, transverse wave velocity, and density measured after the material of group a was cast and molded. (2) Establish a material proportioning matrix With the physical parameters of the test block Nonlinear mapping relationship between , This represents a nonlinear mapping from the original 3D space to a higher-dimensional feature space; based on the Reproducing Kernel Hilbert Space (RKHS) theory, an implicit mapping is constructed: ,in It is a positive definite kernel function that maps data to a potentially infinite-dimensional feature space H; a support vector regression (SVR) model is then built in the high-dimensional space H. This enables it to accurately predict Y, that is... ; (1); where, For kernel functions; Radial basis functions are chosen as the kernel function. ; Let be the bandwidth of the RBF kernel; i and j represent two distinct data points in the dataset; where SVR is a support vector regression model, and a support vector regression SVR model based on the RBF kernel function is constructed in the mapped high-dimensional space H: The model aims to find a linear hyperplane such that the deviation ε between the model's predictions and the true values ​​is controlled within a certain tolerance range; ω represents the normal vector of the regression hyperplane mapped to the high-dimensional feature space; b represents the bias term of the regression hyperplane; ∥ω∥ 2 C is the square of the Euclidean norm of the normal vector, used to control model complexity and improve generalization ability; C>0 is a preset regularization coefficient, used to balance the risk of model structure and the risk of experience; m is the total number of training samples. - Insensitive loss function; The input training dataset, where Let be the input feature vector of the i-th sample. Its corresponding real value label; This is the model's predicted output for the i-th sample. ( ) represents the nonlinear mapping function that maps the original input space to the high-dimensional regenerating kernel Hilbert space; (3) Optimize the regularization parameter C in the SVR model by grid search method, solve the model parameters, and evaluate the determination coefficient R² on the training set and validation set respectively; 1) Solve the regularization parameter C and RBF kernel width parameter γ: Optimize the regularization parameter C by grid search, predefine a discrete set of possible values, and evaluate the model performance corresponding to each candidate C on the validation set; when performing grid search, traverse C and γ at the same time, and the search range and step size need to be set by experience or preliminary experiments.

[0008] 2) Solving for insensitive loss with ε: controlling the model's tolerance to error; 3) Model training and hyperparameter optimization: the loss function tolerates deviations between predicted and true values ​​within ±ε; 4) Using the coefficient of determination R² as a performance evaluation metric: the coefficient of determination R² is the goodness of fit of the optimal model on n-10 training sets. A higher R² value indicates a better fit to the training data; R²_validation: ideally, the best prediction performance of the optimal model on 10 independent validation sets that are not involved in training should be close to R²_training; if it is significantly lower than R²_training, it indicates that the model may be overfitting the training data.

[0009] Optional, the specific training and validation process is as follows: (1) Data splitting: Divide the total sample set into a training set and a validation set, where the training set consists of R-10 sets of data samples; the validation set consists of 10 independent sets of data samples that were not used in the training; (2) Model building: Build the SVR model using the selected kernel function: (3) Model training: On the R-10 training set, train for different combinations of C and suggested γ. On the 10 validation sets, calculate the performance index of the model under each candidate (C,γ) combination. Select the (C,γ) combination that performs best on the validation set, i.e. has the highest R², as the hyperparameter of the final model. (4) Model optimization: Use the training set + validation set or re-integrate all data to retrain the final model with the optimal hyperparameter.

[0010] Optionally, the specific method of S3 is as follows: (1) Sampling constraint: epoxy resin X Ha ∈[0%, 100%]; Silicone rubber X Ga ∈[0%, 100%]; Talc X Ma ∈[20%, 60%], mass conservation constraint: X Ha +X Ga +X Ma =100%; epoxy resin and silicone rubber are not taken as 0% or 100% at the same time; talc powder is not taken as the endpoint value of 0%; (2) Dimension reduction: the 3D design space (X H ,X G ,X M Reduced to a 2D feasible region: fixed talc X M K values ​​X were uniformly sampled within the range of [0%, 60%]. M The remaining mass is R. i =100%-X M The remaining mass of epoxy resin X was allocated. H And silicone rubber X G Generate scaling factor, α i ∈[0,1]; epoxy resin is X H =α i *Ri Silicone rubber is X G =(1-α i )*R i (3) Perform Latin hypercube sampling to generate K sets of matched samples. K≥100 The matrix form is as follows: (4) Data augmentation: based on the positive model Predict the physical parameters Y_pred of K groups of test blocks. The matrix form is as follows: .

[0011] Optional, specific data augmentation strategy process is as follows: a) Input data standardization: Standardize X_new using the same scaler used in the training phase; b) SVR prediction: Input the generated K sets of samples into the trained SVR model; c) Output destandardization: Restore the predicted Vp, Vs, ρ to their original dimensions; d) Construct artificial dataset (X_new, Y_pred).

[0012] Optionally, S4 specifically includes: (1) Data preparation: merging the R sets of original experimental data matrix Y and the K sets of artificial data matrix Y_pred as the input matrix Y for constructing the inverse model. A , ; The original experimental data X and the artificial data X_pred are combined to form the output matrix X of the inverse model. A , ; ; Select a multilayer perceptron neural network for the input Y A Standardize the output X A Normalization is performed; the network structure is as follows: output matching parameter X A The following constraints must be met: Epoxy Resin X H Range 0~100%, silicone rubber X G Range 0~100%, Talc X M The range is 0% to 60%, and the sum of the three is 100%. Epoxy resin and silicone rubber cannot be taken as 0% or 100% simultaneously; talc powder is not taken as the endpoint value of 0%; the output layer is: epoxy resin X H And silicone rubber X G Through a branch, use the sigmoid activation constraint to be between 0 and 1 and multiply by the remaining proportion (1-X). M Talc X M The scaling factor is achieved through another branch, with sigmoid scaling ranging from 0% to 60%; Input layer: 3 nodes Vp, Vs, and ρ; Hidden layers: 3 layers, each with 128 nodes, using the ReLU activation function; Output layer: 3 nodes X HX G and X M For talc X M The output is scaled using the sigmoid function to [0%, 60%]: For epoxy resin X H And silicone rubber X G The remaining proportion 1-X needs to be shared. M The three components of the proportioning parameter (X) H、 X G、 X M The result is converted into two free variables. Since the talc content is between 0% and 60%, the remaining part is between 40% and 100%. The loss function uses mean squared error, outputs three targets, and calculates the MSE of the three targets.

[0013] The advantages of this invention are as follows: The hybrid strategy of "forward model – data augmentation set – inverse modeling" integrates the advantages of physical mechanisms and data-driven approaches. It can ensure the physical interpretability of the predicted parameters such as sound velocity and density through the forward model, and significantly improve the coverage of training samples and the generalization ability of the model by leveraging data augmentation. Thus, it can achieve high-precision and high-efficiency material ratio inversion with limited experimental costs. This method supports multi-objective joint prediction, automatically meets the ratio constraints, and can output material formulations that conform to the physical characteristics of the target strata (such as coal seams and rock strata) in seconds. It combines accuracy, robustness and engineering practicality, and provides an efficient and reliable solution for the intelligent design of earthquake physical simulation materials. Attached Figure Description

[0014] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the following detailed description to explain the present disclosure, but do not constitute a limitation thereof. In the drawings: Figure 1 is a comparison chart of the prediction results for epoxy resin; Figure 2 is a comparison chart of the prediction results for silicone rubber; Figure 3 is a comparison chart of the prediction results for talc. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] This invention deeply integrates physical experimental data with data augmentation technology to construct an artificial intelligence-based method for modeling material proportioning parameters of earthquake physical models, thereby realizing the intelligentization of material proportioning parameters of earthquake physical models and overcoming the dual limitations of traditional methods in terms of efficiency and accuracy. Specifically, an artificial intelligence-based modeling method for earthquake physics model material proportioning parameters is proposed, comprising the following core steps: Step 1: Experimental Design and Data Acquisition. Design different proportion schemes R for earthquake physics model materials, R≥100; earthquake physics model materials include, but are not limited to: epoxy resin, silicone rubber, talc, etc.; the material proportion ranges are epoxy resin (0%~100%), silicone rubber (0%~100%), talc, etc. (0%~60%), with the total mass fraction always being 100%; epoxy resin and silicone rubber are not simultaneously taken as 0% or 100%; talc is not taken as the endpoint value of 0%; through different material proportions, stirring, vacuuming, etc., standard three-dimensional test blocks of 70mm×70mm×70mm with no less than R groups are cast; the longitudinal wave velocity Vp (m / s) and transverse wave velocity Vs (m / s) of the test blocks are obtained using an ultrasonic detector, and the density ρ (g / cm³) is determined by Archimedes' displacement method. 3 ).

[0017] Step 2: SVR Forward Modeling Based on Kernel Method. A proportioning matrix for epoxy resin, silicone rubber, and talc is constructed using Support Vector Regression (SVR) based on the kernel method. With the physical parameters of the test block A nonlinear mapping model between X and X, where X Ha X Ga and X Ma These represent the mass percentages of epoxy resin, silicone rubber, and talc powder in group a, respectively; Vp a Vs a and ρ a The values ​​represent the longitudinal wave velocity, transverse wave velocity, and density measured after the material of group a was cast into a test block.

[0018] 1. Establish a material proportioning matrix Physical parameter matrix of test block Specifically: (1) Input the vector of material proportion X to form the input matrix. , where X Ha X Ga X Ma These represent the epoxy resin content, silicone rubber content, and talc content of the sample in group a, respectively.

[0019] (2) Output the physical parameter vector of the test block Y to form the output matrix. Vp a Vs aρ a The values ​​represent the longitudinal wave velocity, transverse wave velocity, and density measured after the material of group a was cast into a test block.

[0020]

[0021] 2. Establish a material proportioning matrix With the physical parameters of the test block Nonlinear mapping relationship between , It represents a nonlinear mapping from the original 3D space to a higher-dimensional feature space.

[0022] Based on the theory of reproducing kernel Hilbert spaces (RKHS), an implicit mapping is constructed: ,in It is a positive definite kernel function that maps data to a feature space H that may be infinitely dimensional.

[0023] Establish a Support Vector Regression (SVR) model in a high-dimensional space H. This enables it to accurately predict Y, that is... .

[0024] (1) Among them, The kernel function assumes a complex, potentially nonlinear relationship between the input material mix ratio X and the output physical parameters Y of the test specimen. The kernel method implicitly maps the original low-dimensional feature space X to a high-dimensional (or even infinite-dimensional) feature space H using a nonlinear kernel function. In this new high-dimensional space, the originally complex nonlinear relationship may become more linearly separable or easier to fit with a linear model.

[0025] Radial basis functions (RBFs) are selected as the kernel function. ; This is the bandwidth of RBF.

[0026] SVR stands for Support Vector Regression. In the mapped high-dimensional space H, a Support Vector Regression SVR model based on the RBF kernel function is constructed: The model aims to find a linear hyperplane such that the deviation ε between the model's predictions and the true values ​​is controlled within a certain tolerance range; ω represents the normal vector of the regression hyperplane mapped to the high-dimensional feature space; b represents the bias term of the regression hyperplane; ∥ω∥ 2 C is the square of the Euclidean norm of the normal vector, used to control model complexity and improve generalization ability; C>0 is a preset regularization coefficient, used to balance the risk of model structure and the risk of experience; m is the total number of training samples. -Insensitive loss function; The input training dataset, where Let be the input feature vector of the i-th sample. Its corresponding real value label; This is the model's predicted output for the i-th sample. ( ) represents the nonlinear mapping function that maps the original input space to the high-dimensional regenerating kernel Hilbert space (RKHS); 3. The regularization parameter C in the SVR model is optimized by the grid search method, the model parameters are solved, and the coefficient of determination R² is evaluated on the training set and validation set respectively.

[0027] (1) Solving for the regularization parameter C and the RBF kernel width parameter γ: The regularization parameter C balances model complexity (weight size ||w||²) with the tolerance for training data fitting error. A smaller C emphasizes model simplicity (strong regularization), which may lead to underfitting; a larger C reduces the regularization penalty, trying to fit more training points, which may lead to overfitting. This is one of the core hyperparameters for optimization (C=n). Grid search optimization is performed on C. A discrete set of possible values ​​is predefined, and the model performance corresponding to each candidate C is evaluated on the validation set.

[0028] The RBF kernel width parameter γ controls model complexity and local sensitivity in the mapping space. During mesh search, both C and γ are traversed simultaneously. The search range and step size need to be determined empirically or through preliminary experiments.

[0029] (2) Solving with ε-insensitive loss: This controls the model's tolerance to error. The evaluation criteria are usually the mean squared error (MSE) of the validation set or the coefficient of determination (R²). Optimizing without considering γ may lead to suboptimal model performance.

[0030] (3) Model training and hyperparameter optimization: loss function and optimization objective: SVR(ε-SVR) minimizes structural risk (including weight norm ||w||² and empirical loss), and the loss function tolerates samples whose deviation from the predicted value is within ±ε and does not contribute to the penalty.

[0031] (4) Performance evaluation using the coefficient of determination R²: The coefficient of determination R² is the goodness of fit of the optimal model on the R-10 training sets, measuring the model's ability to interpret the training data. A higher R² value indicates a better fit to the training data, but an excessively high value may indicate overfitting. R²_validation: The prediction goodness of the optimal model on 10 independent validation sets that were not used in training. This is a key indicator of the model's generalization ability, reflecting the model's prediction accuracy for new samples. An R²_validation close to and higher than R²_training is ideal; if it is significantly lower than R²_training, it indicates that the model may be overfitting the training data.

[0032] The specific training and validation process is as follows: (1) Data splitting: The total sample set is divided into a training set and a validation set. The training set consists of R-10 sets of data samples (the original total number of samples is R, R≥100); the validation set consists of 10 independent sets of data samples that were not used in the training.

[0033] (2) Modeling: Build the SVR model using the selected kernel function (RBF): .

[0034] (3) Model training: Train the model on the R-10 training sets for different combinations of C and the proposed γ. Calculate the model's performance metrics (such as the R² of the prediction results) for each candidate (C, γ) combination on the 10 validation sets. Select the (C, γ) combination that performs best on the validation set, i.e., has the highest R², as the hyperparameter of the final model.

[0035] (4) Model optimization: Use the training set + validation set or re-integrate all data to retrain the final model with the optimal hyperparameters.

[0036] Step 3: Data Augmentation Strategy (Expanding the Dataset): Established Material Ratios To the physical parameters of the test block Nonlinear mapping model A RBF kernel-based SVR model was developed, with regularization parameter C optimized via grid search (while also optimizing γ), and R² was evaluated on both the training and validation sets.

[0037] Next, Latin hypercube sampling (LHS) is performed within the material proportioning design space to generate K groups (K≥100) of new proportioning parameters. The material proportioning design space is epoxy resin X Hi 0%~100%, silicone rubber X Gi 0%~100%, Talc X Mi The percentage ranges from 0% to 60%, and the total mass fraction is always 100%. Epoxy resin and silicone rubber are not both taken as 0% or 100%. Talc powder is not taken as the endpoint value of 0%.

[0038] Then, the SVR forward model is used to predict the physical parameters corresponding to these new proportions, resulting in K sets of (X,Y) data. These data are used to expand the dataset (measured data + model prediction data) and train an inverse model (the mapping from physical parameter Y to material proportion X).

[0039] The specific methods are as follows: (1) Sampling constraints: epoxy resin (X Hi )∈[0%, 100%]; silicone rubber (X Gi )∈[0%, 100%]; talc, etc. (X Mi X ∈ [0%, 60%], mass conservation constraint: Hi +X Gi +X Mi =100%; epoxy resin and silicone rubber are not taken as 0% or 100% at the same time; talc powder is not taken as the endpoint value of 0%; (2) Dimension reduction: the 3D design space (X H ,X G ,X M Reduced to a 2D feasible region: fixed talc X M K values ​​X were uniformly sampled within the range of [0%, 60%]. M The remaining mass is R. i =100%-X M (∈[40%, 100%]), allocate epoxy resin X by the remaining mass. H And silicone rubber X G Generate scaling factor, α i ∈[0,1] (uniform sampling); epoxy resin is X H =α i *R i Silicone rubber is X G =(1-α i )*R i .

[0040] (3) Perform Latin hypercube sampling to generate K sets of matched samples. K≥100 The matrix form is as follows: (4) Data augmentation: based on the positive model Predict the physical parameters Y_pred of K groups of test blocks. The matrix form is as follows: The specific data augmentation strategy process is as follows: a) Input data standardization: Standardize X_new using the same scaler used in the training phase; b) SVR prediction: Input the generated K sets of samples into the trained SVR model; c) Output destandardization: Restore the predicted Vp, Vs, and ρ to their original dimensions; d) Construct an artificial dataset (X_new, Y_pred).

[0041] Step 4: Construct an inverse problem-solving model based on machine learning methods to deduce the material proportioning parameter X from the target physical parameter Y. .

[0042] The inverse problem is typically ill-posed (the same Y may correspond to multiple Xs) and exhibits non-linear characteristics. We will use machine learning methods to construct the mapping: , where G is the inverse model we require.

[0043] The specific method is as follows: (1) Data preparation: The original experimental data matrix Y of R groups and the artificial data matrix Y_pred of K groups are merged as the input matrix Y for constructing the inverse model. A , ; The original experimental data X and the artificial data X_pred are combined to form the output matrix X of the inverse model. A , ; (2) Model selection: due to the input Y A It is 3D, output X A Since it is 3-dimensional and nonlinear, we choose a multilayer perceptron (MLP) neural network, which can fit complex nonlinear relationships and handle multiple inputs and multiple outputs.

[0044] (3) Data preprocessing: For input Y A Standardize the output X A Normalize.

[0045] (4) Network structure design: Output ratio parameter X A The following constraints must be met: Epoxy Resin X H Range 0-100%, silicone rubber X G Range 0-100%, Talc X M The range is 0% to 60%, and the sum of the three is 100%; epoxy resin and silicone rubber are not taken as 0% or 100% at the same time; talc powder is not taken as the endpoint value of 0%.

[0046] Handling constraints at the output layer is difficult, so while constraints are guaranteed during training data generation, they may be exceeded during model prediction. Therefore, constraints need to be considered before model design, and the output layer should be designed as: epoxy resin X H And silicone rubber X G By taking a branch (using sigmoid activation restricted to 0-1) and multiplying by the remaining proportion (1-X) M ), Talc X M The scaling is achieved through another branch (sigmoid scaling between 0% and 60%), thus ensuring the constraint.

[0047] Input layer: 3 nodes Vp, Vs, ρ; Hidden layer: 3 layers, 128 nodes per layer, using ReLU activation function.

[0048] Output layer: 3 nodes X H X G X M .

[0049] For talc X M The output is scaled using the sigmoid function to [0%, 60%]: X M =0%+60%*sigmoid(output_X M For epoxy resin X H And silicone rubber X G The remaining proportion 1-X needs to be shared. M .

[0050] The three components of the proportioning parameter (X) G、 X G、 X M This is converted into two free variables. Since the talc content is between 0% and 60%, the remaining portion is between 40% and 100%.

[0051] 5. The loss function used is mean squared error (MSE). Note: Output three objectives and calculate the MSE for each objective.

[0052] 6. Training and Validation: Divide the dataset into training and validation sets (80%-20%), and monitor the loss on the validation set. Use early stopping to prevent overfitting.

[0053] 7. Post-processing: The proportions predicted by the model are transformed as described above to obtain the final proportions, which satisfy the constraints.

[0054] 8. Evaluation indicators: In addition to using the prediction accuracy of the proportioning parameters (MAE and RMSE of each component) and the overall constraint satisfaction (sum of 100%, each component within the range) to evaluate the effect.

[0055] Furthermore, since there are multiple solutions (ill-posedness), the physical parameters (R², MSE) of the predicted mix proportions calculated by the forward model can be evaluated to assess how close they are to the target Y.

[0056] This inverse model establishes a stable mapping from physical parameters Y to material proportions X. Through triple safeguards of physical constraint embedding, multi-objective optimization, and consistency verification, the reliability and practicality of inverse problem solving are significantly improved.

[0057] The established inverse prediction model was tested with 100 sets of data for training and 17 sets of data as the test set. The results are shown in Table 1. The errors between the model prediction results and the actual results are as follows: epoxy resin error ≤ 3.84%, silicone rubber error ≤ 3.22%, and talc error ≤ 4.89%.

[0058] Table 1: Comparison of Test Set Predictions and Actual Data

[0059] Figure 1-3 compares the actual data with the predicted data. The blue dots represent the actual data and the predicted data. Most of the blue dots are near the ideal prediction, indicating accurate prediction results. A quantitative evaluation index, R^2, is given; the closer the value is to 1, the better the model's prediction effect. The R^2 values ​​of the model for epoxy resin, silicone rubber, and talc are 0.9501, 0.9700, and 0.9621, respectively, indicating high model prediction reliability.

[0060] Model parameter prediction using this process is not only highly efficient but also has small errors.

[0061] The preferred embodiments of this disclosure have been described in detail above with reference to the accompanying drawings. However, this disclosure is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this disclosure, various simple modifications can be made to the technical solutions of this disclosure, and these simple modifications all fall within the protection scope of this disclosure.

[0062] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, this disclosure will not describe the various possible combinations separately.

[0063] Furthermore, various different embodiments of this disclosure can be combined in any way, as long as they do not violate the spirit of this disclosure, they should also be regarded as the content disclosed in this disclosure.

Claims

1. A method for modeling material proportioning parameters in an earthquake physical model based on artificial intelligence, characterized in that, include: S1: Experimental Design and Data Acquisition. Design R groups of different material mix schemes for the seismic physics model, where R ≥ 100. The seismic physics model materials include epoxy resin, silicone rubber, and talc. At least R groups of standard three-dimensional test blocks are cast using different material mix schemes. Obtain the P-wave velocity Vp, S-wave velocity Vs, and density ρ of the standard three-dimensional test blocks; R is taken as a positive integer. S2: SVR Forward Modeling Based on Kernel Method. Construct the mix matrix of epoxy resin, silicone rubber, and talc based on support vector regression using the kernel method. With the physical parameters of the test block A nonlinear mapping model between X and X, where X Ha X Ga and X Ma These represent the mass percentages of epoxy resin, silicone rubber, and talc powder in group a, respectively; Vp a Vs a and ρ a These represent the longitudinal wave velocity (m / s), transverse wave velocity (m / s), and density (g / cm³) measured after casting and molding the test block of material group a. 3 Establish a Support Vector Regression (SVR) model in a high-dimensional space H. This enables it to accurately predict Y, that is... S3: Optimize the regularization parameter C of the model through grid search, and evaluate the R² of the model on the training and validation sets respectively; S4: Data augmentation strategy: generate K sets of new proportion parameters (K≥100) by Latin hypercube sampling within the material proportion design space, and then use the above SVR forward model to predict the physical parameters corresponding to these new proportions to obtain K sets of (X,Y) data augmentation datasets; S5: Inverse modeling based on machine learning methods: construct an inverse problem-solving model to deduce the material proportion parameter X from the target physical parameter Y. 。 2. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 1, characterized in that, The design space for the material ratio is: epoxy resin XHi: 0%~100%, silicone rubber XGi: 0%~100%, talc powder XMi: 0%~60%, and the total mass fraction is always 100%; epoxy resin and silicone rubber are not taken as 0% or 100% at the same time; talc powder is not taken as the endpoint value of 0%.

3. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 1 or 2, characterized in that, The S2 mentioned above includes: (1) establishing a material proportioning matrix. Physical parameter matrix of test block The vector of input material proportions X forms the input matrix. , where X Ha X Ga and X Ma These represent the epoxy resin content, silicone rubber content, and talc content of the sample in group a, respectively. The physical parameter vectors of the output test block Y constitute the output matrix. Vp a Vs a and ρ a These represent the longitudinal wave velocity, transverse wave velocity, and density measured after the material of group a was cast and molded. (2) Establish a material proportioning matrix With the physical parameters of the test block Nonlinear mapping relationship between ， This represents a nonlinear mapping from the original 3D space to a higher-dimensional feature space; based on the Reproducing Kernel Hilbert Space (RKHS) theory, an implicit mapping is constructed: ,in It is a positive definite kernel function that maps data to a potentially infinite-dimensional feature space H; a support vector regression (SVR) model is then built in the high-dimensional space H. This enables it to accurately predict Y, that is... ； (1); where, For kernel functions; Radial basis functions are chosen as the kernel function. ； Let be the bandwidth of the RBF kernel; i and j represent two distinct data points in the dataset; where SVR is a support vector regression model, and a support vector regression SVR model based on the RBF kernel function is constructed in the mapped high-dimensional space H: The model aims to find a linear hyperplane such that the deviation ε between the model's predictions and the true values ​​is controlled within a certain tolerance range; ω represents the normal vector of the regression hyperplane mapped to the high-dimensional feature space; b represents the bias term of the regression hyperplane; ∥ω∥ 2 C is the square of the Euclidean norm of the normal vector, used to control model complexity and improve generalization ability; C>0 is a preset regularization coefficient, used to balance the risk of model structure and the risk of experience; m is the total number of training samples. - Insensitive loss function; The input training dataset, where Let be the input feature vector of the i-th sample. Its corresponding real value label; This is the model's predicted output for the i-th sample. ( ) represents the nonlinear mapping function that maps the original input space to the high-dimensional regenerating kernel Hilbert space; (3) Optimize the regularization parameter C in the SVR model by grid search method, solve the model parameters, and evaluate the determination coefficient R² on the training set and validation set respectively; 1) Solve the regularization parameter C and RBF kernel width parameter γ: Optimize the regularization parameter C by grid search, predefine a discrete set of possible values, and evaluate the model performance corresponding to each candidate C on the validation set; when performing grid search, traverse C and γ at the same time, and the search range and step size need to be set by experience or preliminary experiments. 2) Solving for insensitive loss with ε: controlling the model's tolerance to error; 3) Model training and hyperparameter optimization: the loss function tolerates deviations between predicted and true values ​​within ±ε; 4) Using the coefficient of determination R² as a performance evaluation metric: the coefficient of determination R² is the goodness of fit of the optimal model on n-10 training sets. A higher R² value indicates a better fit to the training data; R²_validation: ideally, the best prediction performance of the optimal model on 10 independent validation sets that are not involved in training should be close to R²_training; if it is significantly lower than R²_training, it indicates that the model may be overfitting the training data.

4. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 3, characterized in that, The specific training and validation process is as follows: (1) Data splitting: Divide the total sample set into a training set and a validation set, where the training set consists of R-10 sets of data samples; the validation set consists of 10 independent sets of data samples that were not used in the training; (2) Model building: Build the SVR model using the selected kernel function: (3) Model training: On the R-10 training set, train for different combinations of C and suggested γ. On the 10 validation sets, calculate the performance index of the model under each candidate (C,γ) combination. Select the (C,γ) combination that performs best on the validation set, i.e. has the highest R², as the hyperparameter of the final model. (4) Model optimization: Use the training set + validation set or re-integrate all data to retrain the final model with the optimal hyperparameter.

5. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 1 or 2, characterized in that, The specific method of S3 is as follows: (1) Sampling constraint: epoxy resin X Ha ∈[0%, 100%]; Silicone rubber X Ga ∈[0%, 100%]; Talc X Ma ∈[20%, 60%], mass conservation constraint: X Ha +X Ga +X Ma =100%; epoxy resin and silicone rubber are not taken as 0% or 100% at the same time; talc powder is not taken as the endpoint value of 0%; (2) Dimension reduction: the 3D design space (X H ,X G ,X M Reduced to a 2D feasible region: fixed talc X M K values ​​X were uniformly sampled within the range of [0%, 60%]. M The remaining mass is R. i =100%-X M The remaining mass of epoxy resin X was allocated. H And silicone rubber X G Generate scaling factor, α i ∈[0,1]; Epoxy resin is X H =α i *R i Silicone rubber is X G =(1-α i )*R i (3) Perform Latin hypercube sampling to generate K sets of matched samples. ，K≥100， The matrix form is as follows: (4) Data augmentation: based on the positive model Predict the physical parameters Y_pred of K groups of test blocks. The matrix form is as follows: 。 6. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 5, characterized in that, The specific data augmentation strategy process is as follows: a) Input data standardization: Standardize X_new using the same scaler used in the training phase; b) SVR prediction: Input the generated K sets of samples into the trained SVR model; c) Output destandardization: Restore the predicted Vp, Vs, and ρ to their original dimensions; d) Construct an artificial dataset (X_new, Y_pred).

7. The method for modeling material proportioning parameters of an earthquake physical model based on artificial intelligence according to claim 1 or 2, characterized in that, The S4 specifically includes: (1) Data preparation: merging the R sets of original experimental data matrix Y and the K sets of artificial data matrix Y_pred as the input matrix Y for constructing the inverse model. A , ； The original experimental data X and the artificial data X_pred are combined to form the output matrix X of the inverse model. A , ； ; Select a multilayer perceptron neural network for the input Y A Standardize the output X A Normalization is performed; the network structure is as follows: output matching parameter X A The following constraints must be met: Epoxy Resin X H Range 0~100%, silicone rubber X G Range 0~100%, talc X M The range is 0% to 60%, and the sum of the three is 100%. Epoxy resin and silicone rubber cannot be taken as 0% or 100% simultaneously; talc powder is not taken as the endpoint value of 0%; the output layer is: epoxy resin X H And silicone rubber X G Through a branch, use the sigmoid activation constraint to be between 0 and 1 and multiply by the remaining proportion (1-X). M Talc X M The scaling factor is achieved through another branch, with sigmoid scaling ranging from 0% to 60%; Input layer: 3 nodes Vp, Vs, and ρ; Hidden layers: 3 layers, each with 128 nodes, using the ReLU activation function; Output layer: 3 nodes X H X G and X M For talc X M The output is scaled using the sigmoid function to [0%, 60%]: For epoxy resin X H And silicone rubber X G The remaining proportion 1-X needs to be shared. M The three components of the proportioning parameter (X) H、 X G、 X M The result is converted into two free variables. Since the talc content is between 0% and 60%, the remaining part is between 40% and 100%. The loss function uses mean squared error, outputs three targets, and calculates the MSE of the three targets.

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