CN-121980967-A - Rock elastic modulus and poisson ratio field prediction method based on physical constraint

CN121980967ACN 121980967 ACN121980967 ACN 121980967ACN-121980967-A

Abstract

The invention relates to the technical field of rock material elastic modulus field and Poisson's ratio field prediction, in particular to a rock elastic modulus and Poisson's ratio field prediction method based on physical constraint, which comprises the steps of constructing a rock mechanical sample data set, wherein the data set comprises a rock elastic modulus field, a Poisson's ratio field, a strain field, a stress field and space coordinates, constructing a physical information neural network, and constructing an encoder, a decoder and a physical calculation layer, wherein the physical calculation layer is used for calculating a mechanical response strain field; the method comprises the steps of constructing a multi-element composite loss function fused with physical constraints based on a physical information neural network, carrying out iterative training on the physical information neural network based on the multi-element composite loss function, and outputting a high-resolution elastic modulus field and a Poisson ratio field of a target rock test piece.

Inventors

YIN YANCHUN
HU JING
ZHAO TONGBIN
XING MINGLU
LI HUASHAN
WANG ZHUANG
FAN YAN

Assignees

山东科技大学

Dates

Publication Date: 20260505
Application Date: 20260403

Claims (10)

1. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint is characterized by comprising the following steps: constructing a rock mechanical sample data set, wherein the data set comprises a rock elastic modulus field, a poisson ratio field, a strain field, a stress field and space coordinates, and is divided into a training set, a verification set and a test set according to a preset proportion; Constructing a physical information neural network, comprising constructing an encoder, a decoder and a physical calculation layer, wherein the physical calculation layer is used for calculating a mechanical response strain field; constructing a multi-element composite loss function fusing physical constraints based on a physical information neural network, wherein the multi-element composite loss function comprises a data matching loss item and a physical constraint loss item; Performing iterative training on the physical information neural network based on the multi-element composite loss function, and storing optimal network model parameters to obtain an optimal network model; and (3) inputting the sparse measurement point strain data of the target rock test piece into the trained optimal network model, and outputting a high-resolution elastic modulus field and a poisson ratio field of the target rock test piece.
2. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint according to claim 1, wherein the step of constructing the rock mechanical sample data set comprises the steps of generating a heterogeneous elastic modulus field and poisson ratio field of Weibull distribution based on unit space positions, calculating stress and strain responses according to linear elastic constitutive relation, carrying out finite element numerical simulation in combination with boundary conditions, obtaining virtual sample data containing full-field mechanical responses, extracting elastic modulus, poisson ratio, stress, strain and space coordinate data of each discrete unit in the virtual sample, defining space coordinates and strain components with input characteristics of sparse measuring points, and defining output characteristics of full-field elastic modulus field and poisson ratio field.
3. The method for predicting the rock elastic modulus and poisson's ratio field based on physical constraint according to claim 1, wherein the constructing the physical information neural network comprises: The encoder construction comprises the steps of carrying out standardized processing on input sparse measurement point strain data, introducing position codes to reserve space position information, carrying out nonlinear feature extraction and global aggregation through a multi-layer fully connected neural network, and generating a high-dimensional global feature vector; The decoder is constructed by expanding and reconstructing a high-dimensional global feature vector into a low-resolution feature tensor through a full-connection layer, gradually up-sampling the low-resolution feature tensor to a high-resolution latent variable field through multi-layer transposition convolution operation, carrying out feature refinement and channel compression through convolution operation, and finally outputting the high-resolution elastic modulus field and the poisson ratio field; Wherein the position coding is implemented by sine and cosine functions.
4. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint according to claim 3, wherein the construction of the physical calculation layer comprises the steps of constructing the physical calculation layer based on a differentiable line elastic finite element solver, taking the elastic modulus field and poisson ratio field output by the decoder as material parameter field input, combining boundary conditions and stress loads, calculating by solving a mechanical equilibrium equation to obtain a predicted strain field, performing tensor calculation by adopting double-precision floating point numbers to ensure numerical precision in the solving process, regularizing a rigidity matrix to prevent matrix singularity, and performing incremental step-by-step advancing solving by adopting an incremental iteration format.
5. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint according to claim 1, wherein the multi-element composite loss function is formed by weighted combination of a data matching loss term and a physical constraint loss term, wherein the data matching loss term is used for measuring and predicting numerical deviations between an elastic modulus field, a poisson ratio field and a corresponding real parameter field, the physical constraint loss term is used for constraining and predicting the parameter field to meet a linear elastic constitutive equation, weibull statistical distribution rules and a parameter value range allowed by elastic deformation characteristics of a material line, and the expression of the multi-element composite loss function is as follows: ; Wherein, the In order to account for the loss of the modulus of elasticity data, For the poisson's ratio data loss, For the physical loss of the constitutive equation, Physical losses are distributed for Weibull, As a punishment term for the elastic modulus and poisson ratio exceeding the physical value range, 、、、 And Is the weight coefficient of each loss.
6. The method for predicting the elastic modulus and the poisson ratio field of the rock based on the physical constraint according to claim 5, wherein the construction of the data matching loss term comprises the steps of carrying out difference square operation on the elastic modulus predicted value and the poisson ratio predicted value of the full-field discrete unit and the corresponding true value respectively and averaging to obtain the elastic modulus data loss; The calculation formulas of the elastic modulus data loss and the poisson ratio data loss are respectively as follows: ; ; Wherein, the As a total number of grid cells, 、 The elastic modulus and poisson's ratio predicted value of the ith unit, And The modulus of elasticity and poisson's ratio are the true values of the ith cell, respectively.
7. The method for predicting the rock elastic modulus and poisson's ratio field based on the physical constraint according to claim 6, wherein the construction of the physical constraint loss term comprises: Based on generalized Hooke's law, calculating a theoretical strain field by using a predicted elastic modulus field, a Poisson's ratio field and a real stress field, and performing square operation and averaging on the difference between the theoretical strain field and the real strain field to obtain constitutive equation physical loss; ; Calculating a variation coefficient of a predicted elastic modulus field, converting the variation coefficient into Weibull mean degree through a power function fitting relation, and calculating a square difference between the predicted field mean degree and a real field mean degree to obtain Weibull distribution physical loss; The calculation formula of Weibull distribution physical loss is as follows: ; Wherein, the In order to predict the mean value of the elastic modulus field, As the mean value of the true elastic modulus field, The power exponent of the variation coefficient and Weibull mean degree is obtained based on least square fitting; and respectively applying linear punishment to predicted values with the elastic modulus smaller than 0 and the poisson ratio smaller than 0 or larger than 0.5, and averaging to obtain the parameter rationality physical loss: ; Wherein, the In order to predict the mean value of the elastic modulus field, As the mean value of the true elastic modulus field, The power exponent of the variation coefficient and Weibull mean degree is obtained based on least square fitting.
8. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint according to claim 7, wherein the iterative training of the physical information neural network based on the multi-element composite loss function comprises the steps of back-propagating from an output layer to an input layer by utilizing a calculus chain algorithm based on the multi-element composite loss function, calculating gradients of the loss function on the weight matrix, the bias vector and the convolution kernel parameters of each layer of the encoder, and iteratively updating network weights and biases along the opposite direction of the gradients by utilizing a gradient descent optimization algorithm to enable the multi-element composite loss function value to converge to a minimum value, wherein the updating formula of the network weights and the biases is as follows: ; ; Wherein, the In order to update the weights and offsets before they are updated, For the updated weights and offsets to be used, In order for the rate of learning to be high, In order to lose the gradient of the function to the weight, The gradient of the bias for the loss function.
9. The method for predicting the rock elastic modulus and poisson ratio field based on physical constraint according to claim 1, wherein the step of storing the optimal network model parameters to obtain an optimal network model comprises periodically calculating multiple composite losses and each physical constraint component loss on a verification set in an iterative training process, and monitoring and verifying the lumped loss variation trend by adopting an early-stop method; the training process adopts a double-stage termination criterion with physical constraint priority, and when all physical constraint loss items meet a preset convergence threshold and the lumped loss is verified to not generate a new minimum value in a continuous preset round, the training is terminated and the current network state is solidified; storing the network weight, bias, loss item weight coefficient and data preprocessing parameters corresponding to the verified lumped loss minimum value to obtain the optimal network model; the judging formula for each physical constraint loss meeting the preset threshold condition is as follows: ; Wherein, the In order to set the threshold value in advance, The relative convergence factor lost for the constitutive equation, For the physical loss of the current constitutive equation, In order to initiate the physical loss of the constitutive equation, As a relative error coefficient for the loss of mean value, As a relative error coefficient of the total loss, In order to verify the lumped loss, In order to train the lumped loss, Is the relative error coefficient of the modulus of elasticity field variation coefficient, In order to predict the coefficient of variation of the elastic modulus field, The coefficient of variation of the modulus of elasticity field is the true value.
10. The method for predicting the rock elastic modulus and poisson ratio field based on the physical constraint according to claim 1, wherein the outputting the high-resolution elastic modulus field and poisson ratio field of the target rock test piece comprises: loading the data preprocessing parameters determined in the optimal network model and training stage; acquiring sparse measuring point strain data of the surface of a target rock test piece, wherein the data comprise measuring point space coordinates and corresponding strain components; And carrying out standardized preprocessing on the sparse measurement point strain data based on the data preprocessing parameters, inputting the data into a loaded optimal network model, carrying out feature extraction and global aggregation by an encoder to generate a high-dimensional global feature vector, and then carrying out up-sampling reconstruction and channel compression by a decoder to directly output a high-resolution elastic modulus field and a poisson ratio field of the target rock test piece.

Description

Rock elastic modulus and poisson ratio field prediction method based on physical constraint Technical Field The invention relates to the technical field of rock material elastic modulus field and poisson ratio field prediction, in particular to a rock elastic modulus and poisson ratio field prediction method based on physical constraint. Background Rock materials are widely distributed in the geotechnical engineering fields such as mining, underground engineering, tunnel construction, side slope engineering and the like, and the spatial distribution characteristics of the mechanical properties of the rock materials are directly related to the safety and stability of an engineering structure. The elastic modulus and poisson ratio are used as key mechanical parameters for representing rock deformation characteristics, and the heterogeneous distribution rule is a basis for rock mass stress analysis, deformation prediction and stability evaluation, however, the rock mechanical parameters are influenced by factors such as mineral composition, joint cracks, diagenetic environment and the like, and are remarkably random and uneven in space, so that the rock mechanical parameters are difficult to accurately represent by a single test value or a mean value method. In the prior art, the acquisition of a rock mechanical parameter field mainly depends on an indoor test, a field in-situ test and a numerical analysis method based on finite element inversion, although the indoor test and the field test can acquire the real mechanical parameters of local measuring points, the real mechanical parameters are limited by test cost and engineering conditions, the number of the measuring points is extremely limited and is difficult to cover the whole-field distribution, the numerical analysis method based on finite element inversion can be used for optimizing the inversion parameter field through iteration, but depends on dense measurement data or complete boundary conditions, and needs repeated positive and negative analysis iteration, the calculation cost is high, the method is sensitive to initial parameters and is easy to sink into local optimum, and efficient and stable parameter inversion is difficult to realize. Disclosure of Invention The invention provides a rock elastic modulus and Poisson's ratio field prediction method based on physical constraint, which aims to solve the problems that the existing rock mechanical parameter field prediction method depends on intensive measurement data, has high calculation cost and lacks of physical constraint, so that the prediction result has low precision and poor stability. The invention provides a rock elastic modulus and poisson ratio field prediction method based on physical constraint, which adopts the following technical scheme: a rock elastic modulus and Poisson's ratio field prediction method based on physical constraint comprises the following steps: constructing a rock mechanical sample data set, wherein the data set comprises a rock elastic modulus field, a poisson ratio field, a strain field, a stress field and space coordinates, and is divided into a training set, a verification set and a test set according to a preset proportion; Constructing a physical information neural network, comprising constructing an encoder, a decoder and a physical calculation layer, wherein the physical calculation layer is used for calculating a mechanical response strain field; constructing a multi-element composite loss function fusing physical constraints based on a physical information neural network, wherein the multi-element composite loss function comprises a data matching loss item and a physical constraint loss item; Performing iterative training on the physical information neural network based on the multi-element composite loss function, and storing optimal network model parameters to obtain an optimal network model; and (3) inputting the sparse measurement point strain data of the target rock test piece into the trained optimal network model, and outputting a high-resolution elastic modulus field and a poisson ratio field of the target rock test piece. Further, the construction of the rock mechanical sample data set comprises the steps of generating a Weibull distributed heterogeneous elastic modulus field and a Poisson ratio field based on unit space positions, calculating stress and strain response according to linear elastic constitutive relation, carrying out finite element numerical simulation in combination with boundary conditions, obtaining virtual sample data containing full-field mechanical response, extracting elastic modulus, poisson ratio, stress, strain and space coordinate data of each discrete unit in the virtual sample, defining space coordinates and strain components with input characteristics being sparse measuring points, and defining output characteristics being the full-field elastic modulus field and the Poisson ratio field. Further, the constructing a ph