Similar material proportioning optimization method based on double constraints of strength and microseismic signal

Abstract

This invention discloses a method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals. The method includes: conducting variable-angle shear tests at different angles on the original rock and similar materials with different proportions to obtain mechanical parameters and microseismic signal characteristic data; scaling the mechanical parameter data and microseismic signal characteristic data of the original rock to obtain a target set; using the mechanical parameter data, microseismic signal characteristic data, and corresponding raw material mass ratios of similar materials with different proportions as a training set; constructing a Gaussian process surrogate model based on the training set and all similar material sample data to predict the response at various normal stress levels under arbitrary proportions; introducing cosine dissimilarity to ensure the overall shape similarity of the response vector and constructing a comprehensive loss function; using a Bayesian optimization algorithm to optimize the comprehensive loss function to obtain three optimal proportions; and fusing the average values ​​through a convex combination to obtain the final recommended proportion. This method solves the problem of high costs associated with relying on experience-based trial-and-error experiments.

Description

Technical Field

[0001] This invention belongs to the field of similar material ratio optimization technology, and particularly relates to a similar material ratio optimization method based on dual constraints of strength and microseismic signals. Background Technology

[0002] In geomechanical model tests, the preparation of similar materials is a crucial step for the success of the experiment. According to similarity theory, an artificial material needs to be prepared to achieve similar mechanical parameters (such as shear stress). Normal stress Elastic modulus In terms of microseismic response characteristics during the failure process, compared with those based on geometric similarity ratio Density similarity ratio The scaled-down original rock strength remains consistent. Traditional similar material proportioning methods mainly rely on orthogonal experimental design, uniform design, or empirical trial-and-error methods. These methods involve conducting numerous mechanical tests on samples with different proportions to find a proportion that closely approximates the response of the target original rock. However, these methods have the following shortcomings: First, they require a large number of tests and are costly, making it difficult to efficiently optimize within a continuous proportioning space. Second, they only consider single-point mechanical indicators (such as peak strength), neglecting the similarity of the overall shape of the response curve. Third, they do not fully utilize the characteristics of microseismic signals as a criterion for determining failure modes. Fourth, they lack an adaptive optimization mechanism for comprehensive performance under multiple stress levels.

[0003] In recent years, Bayesian optimization algorithms have demonstrated excellent performance in hyperparameter tuning and materials design. Through Gaussian process surrogate models and acquisition function strategies, they can approximate the global optimum with fewer trials. However, existing research mostly applies them to single objectives or simple weighted sums, failing to combine them with similar material mix optimization based on variable angle shear tests, microseismic signal feature fusion, and multi-stress level comprehensive loss functions. Therefore, existing techniques have limitations.

[0004] Similar to the technical problems of optimizing the formulation of materials, such as reliance on experience-based trial and error, high experimental costs, and difficulty in matching multiple stress levels. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a similar material ratio optimization method based on dual constraints of strength and microseismic signals, so as to solve the technical problems of existing technology for similar material ratio optimization, such as reliance on experience trial and error, high experimental costs and difficulty in matching multiple stress levels.

[0006] Technical solution of the present invention:

[0007] A method for optimizing the mix proportions of similar materials based on dual constraints of strength and microseismic signals, the method comprising:

[0008] Step 1: Conduct variable angle shear tests at different angles on the original rock and similar materials with different proportions to obtain mechanical parameters and microseismic signals during the test process; process and analyze the mechanical parameters and microseismic signal characteristics to obtain the shear stress, normal stress, elastic modulus and shear failure microseismic signal characteristic data of each sample of the original rock and similar materials with different proportions.

[0009] Step 2: Scale the mechanical parameter data and microseismic signal feature data of the original rock according to the geometric similarity ratio and density similarity ratio to obtain the scaled target set; use the mechanical parameter data, microseismic signal feature data and corresponding raw material mass ratio of similar materials with different proportions as the training set;

[0010] Step 3: Construct a Gaussian process surrogate model based on the training set using data from all similar material samples to predict the response at various normal stress levels under arbitrary mix proportions;

[0011] Step 4: Using the normal stress at three typical shear angles of 45°, 50° and 55°, and taking the error between the scaled target set and the predicted value of the surrogate model as the target, stress distance fusion weights are introduced to automatically match the stress level, and cosine dissimilarity is introduced to ensure that the overall shape of the response vector is similar, and a comprehensive loss function is constructed.

[0012] Step 5: Using the Bayesian optimization algorithm, the acquisition function is optimized for the comprehensive loss function under three typical normal stresses, and three optimal ratios are obtained independently.

[0013] Step 6: Combine the three optimal ratios by taking the average of the convex combination to obtain the final recommended ratio.

[0014] The method further includes: preparing and casting samples according to the final recommended ratio, conducting variable angle shear tests to verify the results, and obtaining the optimal raw material ratio of similar materials under this similarity ratio.

[0015] The methods for obtaining shear stress, normal stress, elastic modulus, and shear failure microseismic signal characteristic data for each sample of the original rock and similar materials with different mix proportions include:

[0016] Step 1.1, Variable Angle Shear Test:

[0017] Variable angle shear tests were conducted at shear angles of 45°, 50°, and 55°, with each angle corresponding to a normal stress. With shear stress The loading path; the vertical load P applied according to the principle of force balance and the normal stress of the specimen. and shear stress The relationship between them is:

[0018] ;

[0019] ;

[0020] In the formula Normal stress; P is the shear stress; P is the peak load under vertical loading; A is the initial area of ​​the shear failure surface of the specimen. The shearing angle for the variable angle shear test; The internal friction angle of the sample;

[0021] Step 1.2, Mechanical Parameter Analysis:

[0022] Based on the load-displacement curves recorded from the variable angle shear test, the peak load P of each specimen was extracted. max Substitute these equations into equations (1) and (2) to calculate the normal stress of the specimen. and shear stress Simultaneously, the elastic modulus of the specimen is calculated based on the slope of the linear segment of the load-displacement curve. :

[0023] ;

[0024] In the formula, It is the elastic modulus; This represents the stress increment within the linear segment; This corresponds to the axial strain increment;

[0025] For each group of tests, the shear angle A set of results was obtained Data points were used to obtain the cohesion of the sample by linear fitting according to the Mohr-Coulomb criterion. and internal friction angle :

[0026] ;

[0027] In the formula, It is cohesive force; It is the internal friction angle; The slope of the fitted line;

[0028] Step 1.3: Denoise and truncate the microseismic signals collected during each variable angle shear test, and extract the peak frequency, signal energy, centroid frequency, frequency standard deviation and waveform complexity;

[0029] Step 1.4, Data Preparation and Feature Vector Construction:

[0030] For the original rock and similar materials with each ratio, feature vectors are constructed at three shear angles of 45°, 50° and 55° respectively;

[0031] The original rock characteristic vector is denoted as:

[0032] ;

[0033] In the formula, For the original rock at a shear angle of The feature vector at time; For the original rock at a shear angle of Shear stress at that time; For the original rock at a shear angle of Normal stress at time; For the original rock at a shear angle of The elastic modulus at that time; For the original rock at a shear angle of Peak frequency at time; For the original rock at a shear angle of Signal energy at that time; For the original rock at a shear angle of The frequency of the centroid at that time; For the original rock at a shear angle of The standard deviation of the frequency over time; For the original rock at a shear angle of Waveform complexity at that time; The shear angle is [value].

[0034] Methods for constructing proto-rock target sets include:

[0035] Step 2.1, according to geometric similarity ratio And density similarity ratio The mechanical parameters of the original rock at various shear angles are scaled, and similar materials should satisfy the following similarity relationship with the original rock:

[0036] ;

[0037] ;

[0038] ;

[0039] In the formula, , , For similar materials at shear angles The target shear stress, target normal stress, and target elastic modulus are measured. , and The original rock at shear angles of 100° and 200° respectively The shear stress, normal stress, and elastic modulus at that time; It is the geometric similarity ratio; The density similarity ratio;

[0040] For the characteristics of microseismic signals, based on the time similarity ratio in similarity theory... Scaling of frequency-dependent features; scaling of signal energy according to stress similarity ratio; waveform complexity. Dimensionless, similarity ratio of 1; all scaled parameters are concatenated in a fixed order to obtain the original rock target set. :

[0041] ;

[0042] Methods for constructing training sets of similar materials include:

[0043] For M different proportions of similar materials, the three shear angles for each proportion. Experiments were conducted in all ∈{45°, 50°, 55°}, and the first... The proportion of raw materials by weight under the given ratio is as follows:

[0044]

[0045] In the formula, These represent the mass percentages of different raw materials, satisfying... and ;

[0046] No. Under this ratio, the shear angle is The measured response vector at time for:

[0047] ;

[0048] By combining the shear angle, raw material ratio, and response vector, a complete training sample is generated:

[0049] ;

[0050] The training set is formed by merging all samples from all M ratios and 3 shear angles. :

[0051] .

[0052] The method for constructing a Gaussian process surrogate model based on training set data from all similar material specimens to predict the response at various normal stress levels under arbitrary mix proportions includes:

[0053] Step 3.1: Construct the Gaussian process surrogate model:

[0054] For each fixed shear angle Each process is constructed as an independent Gaussian process proxy model, based on the raw material ratio. As input, with response vector Each component is taken as the output. For the k-th component of the response vector, the Gaussian process model is represented as:

[0055] ;

[0056] In the formula, Let x be the predicted value of the k-th response component under the given ratio x; It is a mean function, usually taken as a constant or a linear function; The covariance function (kernel function) measures the similarity between two proportions x and x'.

[0057] Using the quadratic exponential kernel function:

[0058] ;

[0059] In the formula, The signal variance is used to control the scale of the output amplitude. For the first The length scale of each input dimension controls the rate of correlation decay on that dimension. For noise variance, This is the Kronecker delta function; all hyperparameters are optimized by maximizing the marginal log-likelihood.

[0060] Step 3.2, Model Prediction: For any new ratio x*, the Gaussian process model gives the predicted mean and predicted variance of the k-th response component:

[0061] ;

[0062] ;

[0063] In the formula, X is the training set. A matrix composed of all input ratios; This is the observation vector of the k-th response component in the training set; The covariance matrix between training points; This is the covariance vector between the test points and the training points;

[0064] Therefore, regarding the shear angle The predicted value of the complete response vector under any ratio x* is:

[0065] ;

[0066] In the formula, The quantities correspond to each other in turn. .

[0067] Methods for constructing a comprehensive loss function include:

[0068] Step 4.1, Stress Distance Fusion Weighting: For shear angle Define normal stress As an indicator of stress level, a Gaussian kernel function is introduced to automatically calculate the weight based on the difference between the predicted stress and the target stress.

[0069] Step 4.2: Establish cosine dissimilarity:

[0070] ;

[0071] In the formula, is the cosine dissimilarity, with a value range of [0,2]. The smaller the value, the more similar the vector shapes are. This is the response vector predicted in step 3; The target set vector constructed in step 2; · represents the vector dot product; Denotes the Euclidean norm of a vector;

[0072] Step 4.3: Construct a comprehensive loss function consisting of weighted absolute error and cosine dissimilarity;

[0073] ;

[0074] In the formula, To at the shear angle The overall loss value below; and The balance coefficients are set to 0.6 and 0.4 respectively. For stress distance fusion weights; and These are the k-th components of the predicted response vector and the target vector, respectively; It is a very small positive number (take 10⁻). 6 ), to avoid the denominator being zero; Cosine dissimilarity;

[0075] For the three shear angles respectively =45°, =50°, =55°, construct independent integrated loss functions L(45°), L(50°), and L(55°).

[0076] Step 5 describes a method that uses a Bayesian optimization algorithm to optimize the acquisition function of the comprehensive loss function under three typical normal stresses, independently finding the three optimal ratios.

[0077] Step 5.1: Construct a Bayesian optimization framework:

[0078] For each shear angle The comprehensive loss function defined in step 4 Treating the raw material ratio as a black-box objective function to be optimized (satisfy and ) is used as the optimization variable; the optimization objective is:

[0079] ;

[0080] In the formula, Let n be the simplex search space;

[0081] Step 5.2: Generate the initial point dataset:

[0082] In search space Within this process, 50 initial matching points are generated using the Latin hypercube sampling method. For each initial matching point, its response vector is predicted using the Gaussian process surrogate model in step 3, and the corresponding comprehensive loss value is calculated in step 4. This constitutes the initial point dataset:

[0083] ;

[0084] Step 5.3: Construct a probabilistic proxy model:

[0085] Based on the initial point dataset Using Gaussian processes as Proxy model:

[0086] ;

[0087] In the formula, It is a mean function, usually taken as a constant or a linear function; For kernel functions;

[0088] Using the Matern 5 / 2 kernel function:

[0089] ;

[0090] In the formula, The signal variance; For length scale; The distance is the Euclidean distance in the input space; the kernel function hyperparameters are obtained by maximizing the marginal log-likelihood.

[0091] Step 5.5: Define the acquisition function:

[0092] Use Expected Improvement as the acquisition function;

[0093] Step 5.6: Perform iterative optimization to obtain three optimal ratios.

[0094] The method for iterative optimization includes:

[0095] Step 5.5.1: Based on the current Gaussian process surrogate model, search the entire search space. Calculate the EI value for each candidate point;

[0096] Step 5.5.2: Select the point with the largest EI value. As the next evaluation point;

[0097] Step 5.5.3: Predict using a Gaussian process surrogate model The response vector is given, and its actual loss value is calculated in step 4. ;

[0098] Step 5.5.4, Add new points Add to dataset And update the Gaussian process proxy model;

[0099] Step 5.5.5: Repeat steps 5.5.1 to 5.5.4 above until the preset number of iterations is reached, at which point the operation stops.

[0100] Step 5.5.6: Output the dataset at this point. The ratio corresponding to the minimum loss value is taken as the optimal ratio under that shear angle.

[0101] Methods for fusion by taking the mean of overconvex combinations include:

[0102] The three optimal ratios obtained are then combined by averaging using a convex combination to obtain the final recommended ratio:

[0103] ;

[0104] In the formula, The final recommended raw material weight ratio; These are the optimal ratio vectors obtained independently under shear angles of 45°, 50°, and 55°, respectively; due to each All satisfy the condition that the sum is 1 and the mean of the convex combination is also non-negative and sums to 1.

[0105] The methods for conducting variable angle shear tests include:

[0106] According to the final recommended ratio Prepare similar material raw materials, weigh the raw materials according to the proportion, stir and add water to pour standard test samples, and cure them under constant temperature and humidity conditions for 7 days; after curing, perform variable angle shear tests at three shear angles of 45°, 50° and 55° again, and repeat each angle twice.

[0107] After the experiment was completed, the test data were processed according to the mechanical parameter analysis formula and the microseismic signal characteristic analysis formula in step 1 to obtain the verification response vector. :

[0108] ;

[0109] Calculate the verification response and target set The relative error between them:

[0110] ;

[0111] In the formula, For the k-th response component at the shear angle The relative error below; and These are the k-th components of the verification response vector and the target vector, respectively; It is a very small positive number;

[0112] If the relative error of all response components at all shear angles If all values ​​are less than 15%, the final recommended ratio is considered effective. If any response component has a relative error exceeding 15%, the verification test results are added to the training set. Repeat steps 3 to 6 for iterative optimization until the accuracy requirements are met.

[0113] The beneficial effects of this invention are:

[0114] This invention innovatively selects mechanical parameters (shear stress, normal stress, and elastic modulus) and microseismic signal characteristics (peak frequency, signal energy, center of gravity frequency, frequency standard deviation, and waveform complexity) as dual constraint parameters. The mechanical parameters ensure macroscopic static similarity, while the microseismic signal captures the material failure mode and energy release law from the perspective of microscopic damage evolution. This invention achieves a qualitative change from "matching a single static index" to "multidimensional comprehensive matching of static and dynamic indicators" by combining the two. Secondly, for the variable-angle shear test, this invention scientifically selects three typical shear angles of 45°, 50°, and 55°, covering both pure shear and medium-to-high normal stress levels, while using 5° equidistant intervals to balance stress representativeness, test efficiency, and nonlinear response capture capability. Based on this, a comprehensive loss function is constructed, consisting of "stress distance fusion weight" and "cosine dissimilarity." The former automatically focuses on matching accuracy under high stress levels through a Gaussian kernel function, while the latter ensures consistency between the overall shape of the predicted response and the target response from a vector space perspective, overcoming the fundamental deficiency of traditional point-by-point weighted error calculations that ignore the importance of stress level and the similarity of response curve shapes. Simultaneously, a Bayesian optimization algorithm is introduced, utilizing a Gaussian process surrogate model and an expected improvement acquisition function to achieve the desired result while meeting the required ratio. Under nonnegativity and normalization constraints, the global optimum is efficiently approximated with a minimal number of trials, greatly reducing the time and economic cost of mix optimization. Finally, for the optimal mix obtained independently from three perspectives, this invention adopts a fusion strategy of taking the mean of a convex combination, which maintains the closure of the feasible region of the mix space and unbiasedly integrates the local optimum solutions under various stress levels, enhancing the generalization performance of the final recommended mix under different stress conditions. This series of interconnected innovative designs enables this invention to efficiently and accurately obtain the optimal similar material mix that highly matches the overall response of the original rock under multiple stress levels, fundamentally solving the long-standing technical problems of traditional methods such as reliance on experience trial and error, high experimental costs, and difficulty in matching multiple stress levels. Attached Figure Description

[0115] Figure 1 This is a schematic diagram of the process of the present invention;

[0116] Figure 2 This is a schematic diagram illustrating the process of acquiring experimental data, constructing the target set, and constructing the training set in a specific embodiment of the present invention;

[0117] Figure 3 This is a schematic diagram illustrating the proxy model, loss function construction, and optimal allocation calculation process in a specific embodiment of the present invention.

[0118] Figure 4 This is a schematic diagram illustrating the optimal ratio and verification process for a specific embodiment of the present invention. Detailed Implementation

[0119] A method for optimizing the mix proportions of similar materials based on dual constraints of strength and microseismic signals, specifically including:

[0120] Step 1: Conduct variable-angle shear tests at different angles on the original rock and similar materials with different mix proportions, obtain the mechanical parameters and microseismic signals during the test, and process and analyze the characteristics of the mechanical parameters and microseismic signals to obtain the shear stress of each sample of the original rock and similar materials with different mix proportions. Normal stress Elastic modulus And shear failure microseismic signal characteristic data.

[0121] Variable-angle shear tests were conducted at different angles on the original rock and similar materials with different mix proportions. Mechanical parameters and microseismic signals were obtained during the tests. The characteristics of the mechanical parameters and microseismic signals were processed and analyzed to obtain the shear stress of each sample of the original rock and similar materials with different mix proportions. Normal stress Elastic modulus And shear failure microseismic signal characteristic data. Includes the following:

[0122] Step 1.1, Variable Angle Shear Test Design:

[0123] Variable angle shear tests were conducted on original rock samples and similar material samples with different mix proportions at shear angles of 45°, 50°, and 55°. Each angle corresponds to a normal stress. With shear stress The loading path. According to the principle of force balance, the applied vertical load P and the normal stress of the specimen are related. and shear stress The relationship between them is:

[0124]

[0125]

[0126] In the formula, Normal stress; P is the shear stress; P is the peak load under vertical loading; A is the initial area of ​​the shear failure surface of the specimen. The shearing angle for the variable angle shear test; The internal friction angle of the sample is denoted as .

[0127] Step 1.2, Mechanical Parameter Analysis:

[0128] Based on the load-displacement curves recorded from the variable angle shear test, the peak load P of each specimen was extracted. max Substitute these equations into equations (1) and (2) to calculate the normal stress of the specimen. and shear stress Simultaneously, the elastic modulus of the specimen is calculated based on the slope of the linear segment of the load-displacement curve. :

[0129]

[0130] In the formula, It is the elastic modulus; This represents the stress increment within the linear segment; This represents the corresponding axial strain increment.

[0131] For each group of tests, the shear angle A set can be obtained Data points. The cohesion of the specimen was obtained using linear fitting based on the Mohr-Coulomb criterion. and internal friction angle :

[0132]

[0133] In the formula, It is cohesive force; It is the internal friction angle; The slope of the fitted line.

[0134] Step 1.3: Microseismic Signal Feature Analysis

[0135] The microseismic signals collected during each variable-angle shear test were denoised and their waveforms were truncated to extract the following five characteristic parameters:

[0136] (1) Peak frequency ( ):

[0137]

[0138] In the formula, Peak frequency; This is the spectral function of the microseismic signal after fast Fourier transform; Amplitude spectrum; This represents the frequency at which the amplitude reaches its maximum value.

[0139] (2) Signal energy ( ):

[0140]

[0141] In the formula, For signal energy; The time-domain waveform of the microseismic signal; and These represent the start and end times of the microseismic signal.

[0142] (3) Centroid frequency ( ):

[0143]

[0144] In the formula, The centroid frequency; For frequency variables.

[0145] (4) Frequency standard deviation ( ):

[0146]

[0147] In the formula, This represents the standard deviation of the frequency.

[0148] (5) Waveform complexity ( ):

[0149]

[0150] In the formula, Waveform complexity; For the signal at the 1st Amplitude at each sampling point; This represents the total number of sampling points.

[0151] Step 1.4: Data Preparation and Feature Vector Construction

[0152] For the original rock and similar materials with each ratio, feature vectors are constructed at three shear angles of 45°, 50°, and 55°.

[0153] The original rock characteristic vector is denoted as:

[0154]

[0155] In the formula, For the original rock at a shear angle of The feature vector at time; For the original rock at a shear angle of Shear stress at that time; For the original rock at a shear angle of Normal stress at time; For the original rock at a shear angle of The elastic modulus at that time; For the original rock at a shear angle of Peak frequency at time; For the original rock at a shear angle of Signal energy at that time; For the original rock at a shear angle of The frequency of the centroid at that time; For the original rock at a shear angle of The standard deviation of the frequency over time; For the original rock at a shear angle of Waveform complexity at that time; The shear angle is [value].

[0156] For similar materials with different proportions, the first The eigenvectors under the given ratio are denoted as:

[0157]

[0158] In the formula, For the first Similar material ratios at a shear angle of The feature vector at time; For the original rock at a shear angle of Shear stress at that time; For the first Similar material ratios at a shear angle of Normal stress at time; For the first Similar material ratios at a shear angle of The elastic modulus at that time; For the first Similar material ratios at a shear angle of Peak frequency at time; For the first Similar material ratios at a shear angle of Signal energy at that time; For the first Similar material ratios at a shear angle of The frequency of the centroid at that time; For the first Similar material ratios at a shear angle of The standard deviation of the frequency over time; For the first Similar material ratios at a shear angle of Waveform complexity at that time; The shear angle is [value].

[0159] Step 2: Compare the mechanical parameter data and microseismic signal characteristic data of the original rock with geometric similarity ratio. Density similarity ratio The target set is obtained by scaling; the mechanical parameter data, microseismic signal characteristic data, and corresponding mass ratios of various raw materials of similar materials with different proportions are then combined. , ( (Number of raw materials), among which and This serves as the training set; specifically, it includes:

[0160] Step 2.1: Construction of the original rock target set

[0161] According to geometric similarity ratio And density similarity ratio The mechanical parameters of the original rock at various shear angles are scaled. Similar materials should satisfy the following similarity relationship with the original rock:

[0162]

[0163]

[0164]

[0165] In the formula, , , For similar materials at shear angles The target shear stress, target normal stress, and target elastic modulus are measured. , , The original rock at shear angles of 100° and 200° respectively Shear stress, normal stress, and elastic modulus at time; It is the geometric similarity ratio; This represents the density similarity ratio.

[0166] For the characteristics of microseismic signals, based on the time similarity ratio in similarity theory... Scaling the frequency-related features:

[0167]

[0168]

[0169]

[0170] In the formula, , , For similar materials at shear angles The target peak frequency, target centroid frequency, and target frequency standard deviation are as follows; , , The original rock at shear angles of 100° and 200° respectively Peak frequency, centroid frequency, and frequency standard deviation at that time.

[0171] Signal energy scaled according to stress similarity ratio:

[0172]

[0173] In the formula, For similar materials at the shear angle The target signal energy below; For the original rock at a shear angle of The signal energy at that time.

[0174] Waveform complexity Dimensionless, similarity ratio is 1, that is:

[0175]

[0176] In the formula, For similar materials at the shear angle The target waveform complexity is as follows; For the original rock at a shear angle of The waveform complexity at that time.

[0177] All scaled parameters are concatenated in a fixed order to obtain the original rock target set. :

[0178]

[0179] In the formula, The original rock at shear angles of 100° and 200° respectively Shear stress at that time; The original rock at shear angles of 100° and 200° respectively Normal stress at time; The original rock at shear angles of 100° and 200° respectively The elastic modulus at that time; The original rock at shear angles of 100° and 200° respectively Peak frequency at time; For the original rock at a shear angle of Signal energy at that time; The original rock at shear angles of 100° and 200° respectively The frequency of the centroid at that time; The original rock at shear angles of 100° and 200° respectively The standard deviation of the frequency over time; For the original rock at a shear angle of The waveform complexity at that time.

[0180] Step 2.2: Construction of a training set for similar materials

[0181] For M different proportions of similar materials, the three shear angles for each proportion. Experiments were conducted in all ∈{45°, 50°, 55°}. The proportion of raw materials by weight under the given ratio is as follows:

[0182]

[0183] In the formula, These represent the mass percentages of different raw materials, satisfying... and .

[0184] No. Under this ratio, the shear angle is The measured response vector at time for:

[0185]

[0186] In the formula, For the first The shear angle under the following ratio is Shear stress at that time; For the first The shear angle under the following ratio is Normal stress at time; For the first The shear angle under the following ratio is The elastic modulus at that time; For the first The shear angle under the following ratio is Peak frequency at time; For the first The shear angle under the following ratio is Signal energy at that time; For the first The shear angle under the following ratio is The frequency of the centroid at that time; For the first The shear angle under the following ratio is The standard deviation of the frequency over time; For the first The shear angle under the following ratio is The waveform complexity at that time.

[0187] By combining the shear angle, raw material ratio, and response vector, a complete training sample is generated:

[0188]

[0189] All samples from all M ratios and 3 shear angles were merged to form the training set. :

[0190]

[0191] Step 3: Based on the training set, construct a Gaussian process surrogate model using data from all similar material samples to predict the response at various normal stress levels under arbitrary mix proportions.

[0192] In step three, based on the training set, a Gaussian process surrogate model is constructed using data from all similar material samples to predict the response at various shear angles under arbitrary mix proportions. This includes the following:

[0193] Step 3.1, Construction of Gaussian process surrogate model:

[0194] For each fixed shear angle Each process is represented by an independent Gaussian process proxy model. The raw material ratio is used as a reference. As input, with response vector Each component is taken as the output. For the k-th component of the response vector, the Gaussian process model is expressed as:

[0195]

[0196] In the formula, Let x be the predicted value of the k-th response component under the given ratio x; It is a mean function, usually taken as a constant or a linear function; The covariance function (kernel function) measures the similarity between two proportions x and x'.

[0197] Using the quadratic exponential kernel function:

[0198]

[0199] In the formula, The signal variance is used to control the scale of the output amplitude. For the first The length scale of each input dimension controls the rate of correlation decay on that dimension. For noise variance, The function is the Kronecker delta (1 when x=x', 0 otherwise). All hyperparameters are optimized by maximizing the marginal log-likelihood.

[0200] Step 3.2, Model Prediction

[0201] For any new ratio x*, the Gaussian process model gives the predicted mean and predicted variance of the k-th response component:

[0202]

[0203]

[0204] In the formula, X is the training set. A matrix composed of all input ratios; This is the observation vector of the k-th response component in the training set; The covariance matrix between training points; This is the covariance vector between the test points and the training points.

[0205] Therefore, for the shear angle The predicted value of the complete response vector under any ratio x* is:

[0206]

[0207] In the formula, The quantities correspond to each other in turn. .

[0208] Step 4: Fix the normal stress at three typical shear angles of 45°, 50°, and 55°. Using the error between the scaled target set and the surrogate model's predicted value as the objective, introduce stress distance fusion weights to automatically match the stress level, and introduce cosine dissimilarity to ensure the overall shape similarity of the response vectors. Construct a comprehensive loss function, which includes the following:

[0209] Step 4.1, Stress Distance Fusion Weighting

[0210] For shear angle Define normal stress As an indicator of stress level, a Gaussian kernel function is introduced to automatically calculate weights based on the difference between the predicted stress and the target stress.

[0211]

[0212] In the formula, For stress distance fusion weights; The normal stress value predicted by the surrogate model; The scaled target set in step two The target value of normal stress in the middle; The bandwidth parameter is taken as 0.2 times the target stress value range.

[0213] Step 4.2, Cosine Dissimilarity

[0214] To ensure that the shape of similar materials is consistent with the original rock target over the entire response vector, a cosine dissimilarity is introduced:

[0215]

[0216] In the formula, is the cosine dissimilarity, with a value range of [0,2]. The smaller the value, the more similar the vector shapes are. The predicted response vector in step three, i.e. ; The target set vector constructed in step two; · represents the vector dot product; Let Euclidean norm be the vector.

[0217] Step 4.3: The comprehensive loss function consists of two parts: weighted absolute error and cosine dissimilarity.

[0218]

[0219] In the formula, To at the shear angle The overall loss value below; and The balance coefficients are set to 0.6 and 0.4 respectively. For stress distance fusion weights; and These are the k-th components of the predicted response vector and the target vector, respectively; It is a very small positive number (take 10⁻). 6 ), to avoid the denominator being zero; Let be the cosine dissimilarity.

[0220] For the three shear angles respectively =45°, =50°, =55°, construct independent integrated loss functions L(45°), L(50°), L(55°).

[0221] Step 5: Using the Bayesian optimization algorithm, the acquisition function is optimized for the comprehensive loss function under three typical normal stresses, and three optimal ratios are obtained independently.

[0222] In step five, a Bayesian optimization algorithm is used to optimize the acquisition function of the comprehensive loss function under three typical shear angles, independently finding three optimal ratios. This includes the following:

[0223] Step 5.1 Bayesian Optimization Framework

[0224] For each shear angle The comprehensive loss function defined in step four Treating the raw material ratio as a black-box objective function to be optimized (satisfy and ) is used as the optimization variable. The optimization objective is:

[0225]

[0226] In the formula, Let n be the search space of the simplex.

[0227] Step 5.2: Generation of Initial Point Dataset

[0228] In search space Within this process, 50 initial matching points are generated using the Latin hypercube sampling method. For each initial matching point, its response vector is predicted using the Gaussian process surrogate model in step three, and the corresponding comprehensive loss value is calculated in step four. This constitutes the initial point dataset:

[0229]

[0230] Step 5.3: Constructing the Probabilistic Proxy Model

[0231] Based on the initial point dataset Using Gaussian processes as Proxy model:

[0232]

[0233] In the formula, It is a mean function, usually taken as a constant or a linear function; This is the kernel function.

[0234] Using the Matern 5 / 2 kernel function:

[0235]

[0236] In the formula, The signal variance; For length scale; The distance is the Euclidean distance in the input space; the kernel function hyperparameters are obtained by optimizing the marginal log-likelihood.

[0237] Step 5.4, Define the acquisition function

[0238] Using Expected Improvement (EI) as the acquisition function balances exploration and exploitation:

[0239]

[0240]

[0241] In the formula, This represents the best (minimum) loss value observed so far. and These are the mean and standard deviation of the surrogate model's predictions at x, respectively. The cumulative distribution function of the standard normal distribution; It is the probability density function of the standard normal distribution.

[0242] Step 5.5, Iterative Optimization

[0243] ① Based on the current Gaussian process surrogate model, in the entire search space Calculate the EI value for each candidate point;

[0244] ② Select the point with the largest EI value As the next evaluation point;

[0245] ③ Predict using the Gaussian process surrogate model from step three. The response vector is given, and its actual loss value is calculated in step four. ;

[0246] ④ New points Add to dataset And update the Gaussian process proxy model;

[0247] ⑤ Repeat steps ① to ④ above until the preset number of iterations (100 times) is reached, at which point the operation stops;

[0248] ⑥ Output the dataset at this point The ratio corresponding to the minimum loss value is taken as the optimal ratio under that shear angle. .

[0249] To each Performing the above optimization process at angles of 45°, 50°, and 55° yields three optimal proportions: .

[0250] Step 6: Take the average of the three optimal proportions through convex combination to obtain the final recommended proportion, and prepare and cast the sample according to the final recommended proportion, and conduct variable angle shear test to verify it, and obtain the raw material proportion of the optimal similar material under this similarity ratio.

[0251] In step six, the three optimal mix proportions are averaged using a convex combination to obtain the final recommended mix proportion. Based on this final recommended mix proportion, samples are prepared and cast for verification using a variable angle shear test. This includes the following:

[0252] Step 6.1, Optimal ratio fusion

[0253] The three optimal ratios obtained in step five are combined by averaging the results using a convex combination to obtain the final recommended ratio:

[0254]

[0255] In the formula, The final recommended raw material weight ratio; These are the optimal ratio vectors obtained independently under shear angles of 45°, 50°, and 55°, respectively. Because each All satisfy the condition that the sum is 1 and the mean of the convex combination is also non-negative and sums to 1.

[0256] Step 6.2: Verify the test plan

[0257] According to the final recommended ratio Prepare similar material raw materials by weighing them according to the specified proportions, mixing them thoroughly, adding water, and pouring them into standard test specimens. Curing the specimens under constant temperature and humidity conditions for 7 days. After curing, perform variable angle shear tests at three shear angles of 45°, 50°, and 55°, repeating each angle twice.

[0258] Step 6.3, Calculation of Verification Indicators

[0259] After the experiment was completed, the test data were processed according to the mechanical parameter analysis formula and the microseismic signal characteristic analysis formula in step one to obtain the verification response vector. :

[0260]

[0261] Calculate the verification response and target set The relative error between them:

[0262]

[0263] In the formula, For the k-th response component at the shear angle The relative error below; and These are the k-th components of the verification response vector and the target vector, respectively; It is a very small positive number (take 10⁻). 6 ).

[0264] Step 6.4, Determination of the effectiveness of the proportions

[0265] If the relative error of all response components at all shear angles If all values ​​are less than 15%, the final recommended ratio is considered effective, and the output is... As specified and The optimal similar material raw material ratio is determined. If the relative error of any response component exceeds 15%, the verification test results are added to the training set. Repeat steps three through six for iterative optimization until the accuracy requirements are met.

Claims

1. A method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals, characterized in that: The method includes: Step 1: Conduct variable angle shear tests at different angles on the original rock and similar materials with different proportions to obtain mechanical parameters and microseismic signals during the test process; process and analyze the mechanical parameters and microseismic signal characteristics to obtain the shear stress, normal stress, elastic modulus and shear failure microseismic signal characteristic data of each sample of the original rock and similar materials with different proportions. Step 2: Scale the mechanical parameter data and microseismic signal feature data of the original rock according to the geometric similarity ratio and density similarity ratio to obtain the scaled target set; use the mechanical parameter data, microseismic signal feature data and corresponding raw material mass ratio of similar materials with different proportions as the training set; Step 3: Construct a Gaussian process surrogate model based on the training set using data from all similar material samples to predict the response at various normal stress levels under arbitrary mix proportions; Step 4: Using the normal stress at three typical shear angles of 45°, 50° and 55°, and taking the error between the scaled target set and the predicted value of the surrogate model as the target, stress distance fusion weights are introduced to automatically match the stress level, and cosine dissimilarity is introduced to ensure that the overall shape of the response vector is similar, and a comprehensive loss function is constructed. Step 5: Using the Bayesian optimization algorithm, the acquisition function is optimized for the comprehensive loss function under three typical normal stresses, and three optimal ratios are obtained independently. Step 6: Combine the three optimal ratios by taking the average of the convex combination to obtain the final recommended ratio.

2. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: The method further includes: preparing and casting samples according to the final recommended ratio, conducting variable angle shear tests to verify the results, and obtaining the optimal raw material ratio of similar materials under this similarity ratio.

3. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: The methods for obtaining shear stress, normal stress, elastic modulus, and shear failure microseismic signal characteristic data for each sample of the original rock and similar materials with different mix proportions include: Step 1.1, Variable Angle Shear Test: Variable angle shear tests were conducted at shear angles of 45°, 50°, and 55°, with each angle corresponding to a normal stress. With shear stress The loading path; the vertical load P applied according to the principle of force balance and the normal stress of the specimen. and shear stress The relationship between them is: ； ； In the formula Normal stress; P is the shear stress; P is the peak load under vertical loading; A is the initial area of ​​the shear failure surface of the specimen. The shearing angle for the variable angle shear test; The internal friction angle of the sample; Step 1.2, Mechanical Parameter Analysis: Based on the load-displacement curves recorded from the variable angle shear test, the peak load P of each specimen was extracted. max Substitute these equations into equations (1) and (2) to calculate the normal stress of the specimen. and shear stress Simultaneously, the elastic modulus of the specimen is calculated based on the slope of the linear segment of the load-displacement curve. : ； In the formula, It is the elastic modulus; This represents the stress increment within the linear segment; This corresponds to the axial strain increment; For each group of tests, the shear angle A set of Data points were used to obtain the cohesion of the sample by linear fitting according to the Mohr-Coulomb criterion. and internal friction angle : ； In the formula, It is cohesive force; It is the internal friction angle; The slope of the fitted line; Step 1.3: Denoise and truncate the microseismic signals collected during each variable angle shear test, and extract the peak frequency, signal energy, centroid frequency, frequency standard deviation and waveform complexity; Step 1.4, Data Preparation and Feature Vector Construction: For the original rock and similar materials with each ratio, feature vectors are constructed at three shear angles of 45°, 50° and 55° respectively; The original rock eigenvector is denoted as: ； In the formula, For the original rock at a shear angle of The feature vector at time; For the original rock at a shear angle of Shear stress at that time; For the original rock at a shear angle of Normal stress at time; For the original rock at a shear angle of The elastic modulus at that time; For the original rock at a shear angle of Peak frequency at time; For the original rock at a shear angle of Signal energy at that time; For the original rock at a shear angle of The frequency of the centroid at that time; For the original rock at a shear angle of The standard deviation of the frequency over time; For the original rock at a shear angle of Waveform complexity at that time; The shear angle is [value].

4. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: Methods for constructing proto-rock target sets include: Step 2.1, according to geometric similarity ratio And density similarity ratio The mechanical parameters of the original rock at various shear angles are scaled, and similar materials should satisfy the following similarity relationship with the original rock: ； ； ； In the formula, , , For similar materials at shear angles The target shear stress, target normal stress, and target elastic modulus are measured. , and The original rock at shear angles of 100° and 200° respectively The shear stress, normal stress, and elastic modulus at that time; It is the geometric similarity ratio; The density similarity ratio; For the characteristics of microseismic signals, based on the time similarity ratio in similarity theory... Scaling of frequency-dependent features; scaling of signal energy according to stress similarity ratio; waveform complexity. Dimensionless, similarity ratio of 1; all scaled parameters are concatenated in a fixed order to obtain the original rock target set. : ； Methods for constructing training sets of similar materials include: For M different proportions of similar materials, the three shear angles for each proportion. Experiments were conducted in all ∈{45°, 50°, 55°}, and the first... The proportion of raw materials by weight under the given ratio is as follows: ； In the formula, These represent the mass percentages of different raw materials, satisfying... and ; No. Under this ratio, the shear angle is The measured response vector at time for: ； By combining the shear angle, raw material ratio, and response vector, a complete training sample is generated: ； The training set is formed by merging all samples from all M ratios and 3 shear angles. : 。 5. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: The method for constructing a Gaussian process surrogate model based on training set data from all similar material specimens to predict the response at various normal stress levels under arbitrary mix proportions includes: Step 3.1: Construct the Gaussian process surrogate model: For each fixed shear angle Each process is constructed as an independent Gaussian process proxy model, based on the raw material ratio. As input, with response vector Each component is taken as the output. For the k-th component of the response vector, the Gaussian process model is represented as: ； In the formula, Let x be the predicted value of the k-th response component under the given ratio x; It is a mean function, usually taken as a constant or a linear function; The covariance function (kernel function) measures the similarity between two proportions x and x'. Using the quadratic exponential kernel function: ； In the formula, The signal variance is used to control the scale of the output amplitude. For the first The length scale of each input dimension controls the rate of correlation decay on that dimension. For noise variance, This is the Kronecker delta function; all hyperparameters are optimized by maximizing the marginal log-likelihood. Step 3.2, Model Prediction: For any new ratio x*, the Gaussian process model gives the predicted mean and predicted variance of the k-th response component: ； ； In the formula, X is the training set. A matrix composed of all input ratios; This is the observation vector of the k-th response component in the training set; The covariance matrix between training points; This is the covariance vector between the test points and the training points; Therefore, regarding the shear angle The predicted value of the complete response vector under any ratio x* is: ； In the formula, The quantities correspond to each other in turn. .

6. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: Methods for constructing a comprehensive loss function include: Step 4.1, Stress Distance Fusion Weighting: For shear angle Define normal stress As an indicator of stress level, a Gaussian kernel function is introduced to automatically calculate the weight based on the difference between the predicted stress and the target stress. Step 4.2: Establish cosine dissimilarity: ； In the formula, is the cosine dissimilarity, with a value range of [0,2]. The smaller the value, the more similar the vector shapes are. This is the response vector predicted in step 3; The target set vector constructed in step 2; · represents the vector dot product; Denotes the Euclidean norm of a vector; Step 4.3: Construct a comprehensive loss function consisting of weighted absolute error and cosine dissimilarity; ； In the formula, To at the shear angle The overall loss value below; and The balance coefficients are set to 0.6 and 0.4 respectively. For stress distance fusion weights; and These are the k-th components of the predicted response vector and the target vector, respectively; It is a very small positive number (take 10⁻). 6 ), to avoid the denominator being zero; Cosine dissimilarity; For the three shear angles respectively =45°, =50°, =55°, construct independent integrated loss functions L(45°), L(50°), and L(55°).

7. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: Step 5 describes a method that uses a Bayesian optimization algorithm to optimize the acquisition function of the comprehensive loss function under three typical normal stresses, independently finding the three optimal ratios. Step 5.1: Construct a Bayesian optimization framework: For each shear angle The comprehensive loss function defined in step 4 Treating the raw material ratio as a black-box objective function to be optimized (satisfy and ) is used as the optimization variable; the optimization objective is: ； In the formula, Let n be the simplex search space; Step 5.2: Generate the initial point dataset: In search space Within this process, 50 initial matching points are generated using the Latin hypercube sampling method. For each initial matching point, its response vector is predicted using the Gaussian process surrogate model in step 3, and the corresponding comprehensive loss value is calculated in step 4. This constitutes the initial point dataset: ； Step 5.3: Construct a probabilistic proxy model: Based on the initial point dataset Using Gaussian processes as Proxy model: ； In the formula, It is a mean function, usually taken as a constant or a linear function; For kernel functions; Using the Matern 5 / 2 kernel function: ； In the formula, The signal variance; For length scale; The distance is the Euclidean distance in the input space; the kernel function hyperparameters are obtained by maximizing the marginal log-likelihood. Step 5.5: Define the acquisition function: Use Expected Improvement as the acquisition function; Step 5.6: Perform iterative optimization to obtain three optimal ratios.

8. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 7, characterized in that: The method for iterative optimization includes: Step 5.5.1: Based on the current Gaussian process surrogate model, search the entire search space. Calculate the EI value for each candidate point; Step 5.5.2: Select the point with the largest EI value. As the next evaluation point; Step 5.5.3: Predict using a Gaussian process surrogate model The response vector is given, and its actual loss value is calculated in step 4. ; Step 5.5.4, Add new points Add to dataset And update the Gaussian process proxy model; Step 5.5.5: Repeat steps 5.5.1 to 5.5.4 above until the preset number of iterations is reached, at which point the operation stops. Step 5.5.6: Output the dataset at this point. The ratio corresponding to the minimum loss value is taken as the optimal ratio under that shear angle.

9. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 1, characterized in that: Methods for fusion by taking the mean of overconvex combinations include: The three optimal ratios obtained are then combined by averaging using a convex combination to obtain the final recommended ratio: ； In the formula, The final recommended raw material weight ratio; These are the optimal ratio vectors obtained independently under shear angles of 45°, 50°, and 55°, respectively; due to each All satisfy the condition that the sum is 1 and the mean of the convex combination is also non-negative and sums to 1.

10. The method for optimizing the proportion of similar materials based on dual constraints of strength and microseismic signals according to claim 2, characterized in that: The methods for conducting variable angle shear tests include: According to the final recommended ratio Prepare similar material raw materials, weigh the raw materials according to the proportion, stir and add water to pour standard test samples, and cure them under constant temperature and humidity conditions for 7 days; after curing, perform variable angle shear tests at three shear angles of 45°, 50° and 55° again, and repeat each angle twice. After the experiment was completed, the test data were processed according to the mechanical parameter analysis formula and the microseismic signal characteristic analysis formula in step 1 to obtain the verification response vector. : ； Calculate the verification response and target set The relative error between them: ； In the formula, For the k-th response component at the shear angle The relative error below; and These are the k-th components of the verification response vector and the target vector, respectively; It is a very small positive number; If the relative error of all response components at all shear angles If the relative error of any response component is less than 15%, the final recommended ratio is considered effective. If the relative error of any response component exceeds 15%, the verification test results are added to the training set. Repeat steps 3 to 6 for iterative optimization until the accuracy requirements are met.

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