Batch active learning based synchronous grouting material closed-loop proportioning design method for shield tunneling
By employing a batch active learning closed-loop mix design method, combined with a Gaussian process surrogate model and clustering, the problems of low efficiency and information redundancy in the mix design of shield tunnel synchronous grouting material were solved, achieving efficient and accurate optimization of shield tunnel synchronous grouting material mix ratio to meet engineering performance requirements.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2026-04-15
- Publication Date
- 2026-07-14
AI Technical Summary
Existing methods for designing the mix proportions of grouting materials for tunnel boring machines are inefficient and struggle to achieve efficient optimization in high-dimensional nonlinear design spaces with limited number of tests and costs. Furthermore, batch selection of points can lead to information redundancy and insufficient spatial coverage, making it difficult to obtain the optimal mix proportions that meet engineering performance requirements.
A closed-loop matching design method based on batch active learning is adopted. By combining the Gaussian process surrogate model with the expected variance reduction active learning criterion and weighted K-means clustering, high-information subsets are screened and clustered to optimize design variables and performance indicators, thereby achieving efficient matching design.
It can accurately quantify the uncertainty of performance prediction under small sample conditions, significantly reduce the number of experiments, shorten the R&D cycle, improve the efficiency of global exploration and optimization in high-dimensional proportioning space, and recommend formulations that meet engineering performance requirements and adapt to the design needs of solid waste resource-based grouting materials.
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Figure CN122392676A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of civil engineering material design, and in particular to a closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning. Background Technology
[0002] Shield tunneling, due to its advantages such as high automation and minimal ground disturbance, has been widely used in urban underground engineering construction. The gap at the shield tail generated during shield excavation needs to be filled in a timely manner through synchronous grouting to control surface settlement and ensure tunnel stability. Therefore, the mix design of the synchronous grouting material directly affects surface settlement control and tunnel structural stability.
[0003] Currently, the design of synchronous grout mix proportions still mainly relies on traditional "trial and error" methods such as empirical mix design and orthogonal experiments. This method is not only time-consuming, labor-intensive, and costly, but also makes it difficult to efficiently explore the high-dimensional design space composed of multiple proportion parameters. Due to the strong nonlinear coupling relationship between proportion parameters and performance, and the introduction of solid waste resource materials further increases the complexity of the design space, traditional methods are prone to getting trapped in local optima and are difficult to obtain the globally optimal proportion.
[0004] To improve efficiency, statistical methods such as response surface methodology and multiple regression analysis have been introduced. However, these are essentially "passive learning" methods, where the model relies on pre-defined experimental points and cannot adaptively adjust the sampling strategy based on experimental results. While machine learning possesses powerful predictive capabilities, it heavily relies on large-scale, high-quality data, which contradicts the scarcity of experimental data in the grouting material field. Furthermore, existing active learning methods are mostly designed for single-point selection. Simply extending this to batch selection can easily lead to clustering of experimental points, resulting in information redundancy and insufficient spatial coverage. This makes it difficult to balance high information gain and global exploration within a limited number of experiments.
[0005] In summary, there is an urgent need for a closed-loop mix design method for shield tunneling synchronous grouting materials that can solve the above-mentioned technical problems. This method should achieve efficient optimization in a high-dimensional nonlinear design space under the constraints of limited test costs and number of tests, while also taking into account information gain and spatial coverage in batch test scenarios, and quickly obtaining the optimal grouting material mix that meets engineering performance requirements. Summary of the Invention
[0006] This invention aims to provide a closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning, which solves the technical problems of low efficiency, redundancy in batch selection of grouting material mix optimization, and difficulty in efficiently finding the best ratio with a small sample size.
[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention provides a closed-loop mix design method for synchronous grouting materials in tunnel boring machines based on batch active learning, comprising the following steps: S1. Constructing a mix design space for synchronous grouting materials, selecting at least two mix design parameters as design variables, determining the value range of the design variables and discretizing a set of candidate mix design points, and simultaneously setting at least one target performance index and qualification threshold for the synchronous grouting material; S2. Using Latin hypercube sampling, extracting an initial mix design point set from the set of candidate mix design points, preparing and performing performance tests on the initial mix design point set, and establishing an initial sample library; S3. Training a Gaussian process surrogate model based on the initial sample library, and outputting the performance prediction mean and prediction uncertainty of the candidate mix design points through the Gaussian process surrogate model; S4. Based on the trained Gaussian process surrogate model... The following steps are performed: S5. Using the expected variance reduction active learning criterion, the information value of all untested candidate formulations is calculated, and a high-information subset is obtained by filtering according to the information value; S6. The information value of each candidate formulation in the high-information subset is normalized to obtain the corresponding weight coefficient; S7. Based on the weight coefficient, clustering is performed on the high-information subset, and the next batch of test formulations is obtained by filtering according to the single batch test scale; S8. The next batch of test formulations is prepared and its performance is tested, the newly obtained formulations are added to the sample library, and the Gaussian process surrogate model is retrained or incrementally updated; S9. S1-S7 are repeated until the preset iteration termination condition is met; S10. Recommended formulations are output from the candidate formulations that meet the qualified threshold range of the target performance index.
[0008] Furthermore, in S1, the design variables include at least two of the following: water-cement ratio, mortar-cement ratio, swelling-water ratio, powder-ash ratio, and solid waste content; the solid waste content is the volume substitution rate or mass substitution rate of solid waste material for sand; the solid waste material includes at least one of recycled rubber granules, recycled fine aggregate, and mineral solid waste powder.
[0009] Furthermore, in S1, the target performance index includes at least one of fluidity, setting time, density, and early compressive strength; the qualified threshold includes at least one of upper and lower limits of fluidity, upper limit of setting time, upper and lower limits of density, and lower limit of early compressive strength.
[0010] Furthermore, in S2, the number of the initial formula point set is related to the dimension of the synchronous grouting material proportioning design space.
[0011] Furthermore, in S4, the information value screening specifically involves: selecting a preset proportion or a preset number of untested candidate formulations according to their information value from high to low, thus forming the high-information subset.
[0012] Furthermore, in S4, the expected variance reduction active learning criterion is used to quantify the contribution of a single candidate formulation point to reducing the uncertainty of the global model.
[0013] Furthermore, in S6, the clustering process is weighted K-means clustering, which divides the high-information subset into multiple clusters consistent with the scale of a single batch of experiments, and selects representative formulation points from each cluster to form the formulation set for the next batch of experiments.
[0014] Furthermore, the representative recipe point is the recipe point with the highest information value within the cluster; when there are multiple recipe points with the same highest information value, the recipe point closest to the cluster center is selected.
[0015] Furthermore, the Gaussian process surrogate model employs a zero-mean function, selects a radial basis function with automatic correlation determination as the covariance function, and optimizes the model hyperparameters and noise variance by maximizing marginal likelihood.
[0016] Furthermore, the iteration termination condition is any of the following: the average prediction uncertainty of the Gaussian process surrogate model on the set of untested candidate formulations is lower than a first set threshold, and the maximum prediction uncertainty is lower than a second set threshold; the first set threshold and the second set threshold are determined by an upper limit of experimental error or an engineering tolerance; or the cumulative number of tested formulations reaches a set upper limit.
[0017] Compared with the prior art, the present invention has at least the following beneficial effects: This invention employs a Gaussian process surrogate model combined with an expected variance reduction active learning criterion. This allows for the accurate quantification of performance prediction uncertainty under small sample conditions and precise evaluation of the information value of unexperimented candidate points. By guiding the selection of experimental candidate formulations using this criterion, the reliance on large amounts of experimental data is eliminated, significantly reducing the number of experiments, shortening the formulation development cycle, and lowering raw material and labor costs.
[0018] This invention employs a batch selection strategy that combines high-information subset screening with clustering processing. This strategy ensures that the test points have high information gain while avoiding point clustering and information redundancy, resulting in a balanced distribution of batch test points in the design space and improving the efficiency of global exploration and optimization in high-dimensional matching space.
[0019] This invention uses engineering performance indicators and qualification thresholds as optimization targets and screening criteria, and outputs only candidate formulations that meet all qualification thresholds after iteration termination. The recommended formulations can meet the working performance and early strength requirements of shield tunneling synchronous grouting construction. The overall solution fits the actual engineering constraints, has a high degree of intelligence and strong implementability, and is suitable for the efficient design requirements of solid waste resource-based grouting materials. Attached Figure Description
[0020] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0021] Figure 1 A flowchart illustrating the closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning provided in this embodiment; Figure 2 This is a schematic diagram of the distribution of prediction uncertainty (variance) during the batch active learning iteration process in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram showing the comparison between the model's predicted values and the measured values after the iteration in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram illustrating the prediction performance of the final model under different active learning sampling strategies in Embodiment 2 of the present invention. Detailed Implementation
[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.
[0023] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0024] This embodiment provides a complete process for a closed-loop mix design method for shield tunnel synchronous grouting materials based on batch active learning, such as... Figure 1 As shown, it includes the following steps: S1. Construct a design space for the proportioning of synchronous grouting material, select at least two proportioning parameters as design variables, set a lower limit, an upper limit, and a deviation for each proportioning parameter, and discretize the design space to generate a set of candidate formulation points. At the same time, at least one target performance index and its qualified threshold range for synchronous grouting material shall be set.
[0025] S2. Using Latin hypercube sampling, from the set of candidate formulation points... An initial formula point set is extracted, and synchronous grouting material samples are prepared according to a preset preparation process and their performance is tested to establish an initial sample library.
[0026] S3. Train a Gaussian process surrogate model based on the initial sample library, and output the performance prediction mean and prediction uncertainty of the candidate formulation points through the Gaussian process surrogate model.
[0027] Specifically, the prediction uncertainty is the prediction variance or the prediction standard deviation determined by the prediction variance.
[0028] S4. Based on the Gaussian process surrogate model trained in S3, the Active Learning Criterion (ALC) with reduced expectation variance is used to calculate the set of untested candidate formulation points. The information value of each candidate formulation point; and the high-information subset is obtained by filtering according to the information value. .
[0029] Specifically, let This represents the set of tested formulation points corresponding to the current sample library. The set of tested formulation points includes the initial formulation point set obtained in S2, and the formulation points added in subsequent iterations that have completed preparation and performance testing. The set of untested candidate formulation points... Defined as the set of candidate formulation points With the set of tested formulation points The difference set, i.e. .
[0030] S5. Normalize the information value of each candidate formulation point in the high-information subset to obtain the weight coefficient corresponding to each candidate formulation point.
[0031] Specifically, the normalization process preferably employs a minimum-maximum scaling method. For high-information subsets... any candidate formulation point Its normalized weight coefficients The calculation formula is:
[0032] in, For the formula point Information value and High information subsets The minimum and maximum values of information about all candidate recipe points.
[0033] After this normalization process, each weight coefficient is linearly mapped to the [0,1] interval, which is used to characterize the relative importance of each candidate recipe point in the clustering process. This allows the candidate recipe point with greater information value in the active learning criterion to have a higher weight coefficient, thereby giving it a greater influence in the subsequent clustering process.
[0034] S6. Perform clustering processing on the high-information subset based on the weight coefficients, and select the next batch of test formulas according to the single batch test size.
[0035] S7. For each formula point in the next batch of test formula sets, prepare synchronous grouting material samples according to the same preparation process as in S2, and conduct performance tests. Add the newly obtained formula points and their corresponding performance test data to the sample library to update the sample library. Based on the updated sample library, retrain the Gaussian process surrogate model, or incrementally update it based on the original model to improve the prediction accuracy of the model's ratio-performance mapping relationship. The updated model will be used for information value calculation in the next iteration.
[0036] S8. Repeat S4-S7 until the preset iteration termination condition is met.
[0037] S9. Output a recommended formula from all candidate formulas that meet the qualified threshold range of the target performance index, as the final synchronous grouting material proportioning scheme.
[0038] This scheme organically combines Gaussian process models, expected variance reduction active learning criteria, and clustering processing to form a closed-loop iteration of "experimentation-modeling-point selection-re-experimentation". By normalizing the information value and using it for batch point selection in clustering, it balances information content and spatial coverage. It can achieve efficient optimization in high-dimensional matching space without a large number of experiments, reducing the number of experiments and shortening the design cycle. Compared with traditional empirical matching and orthogonal experiments, it has higher efficiency and stronger optimization capabilities.
[0039] In this embodiment, the design variables are further defined to include at least two of the following: water-cement ratio, mortar-cement ratio, water-swelling ratio, powder-ash ratio, and solid waste content; the solid waste content is the volume substitution rate or mass substitution rate of solid waste material for sand; the solid waste material includes one or more of the following: recycled rubber granules, recycled fine aggregate, and mineral solid waste powder.
[0040] Specifically, based on literature and engineering case studies, the following key proportioning parameters were selected: fly ash ratio (mass ratio of fly ash to cement), water-cement ratio (mass ratio of water to cementitious materials), swelling ratio (mass ratio of bentonite to water), mortar ratio (mass ratio of cementitious materials to sand), and solid waste content.
[0041] This scheme ensures that the design space covers the key proportioning parameters of the shield tunnel synchronous grouting material, thus guaranteeing the integrity of the design space. In particular, the introduction of solid waste admixture enables this method to meet the needs of solid waste resource utilization in green construction, making the method widely applicable to the design of green grouting materials and improving the applicability and environmental benefits of the project.
[0042] In this embodiment, the target performance indicators are further defined as at least one of fluidity, setting time, density and early compressive strength; the qualified thresholds include at least one of upper and lower limits of fluidity, upper limit of setting time, upper and lower limits of density and lower limit of early compressive strength.
[0043] This scheme, guided by the core performance of the project, clearly defines the optimization objectives and ensures that the recommended formula can meet the engineering requirements of shield tunneling synchronous grouting for pumpability (flowability), stability (setting time, density) and early bearing capacity (such as 3-day strength). It enhances the practicality and feasibility of the method and makes the final formula directly applicable to on-site grouting.
[0044] In this embodiment, the number of initial formula point sets is further limited to the dimension of the synchronous grouting material proportioning design space.
[0045] Specifically, the dimension of the design space for the proportioning of synchronous grouting material is set as The initial number of recipe points is set to to ( ≥3, ≤10, and , (as preset coefficients), for example, when designing spatial dimensions When the formula value is 5, the initial number of formula points can be 30. This range ensures that the Gaussian process surrogate model has sufficient training data in the initial stage, avoiding underfitting due to insufficient samples; at the same time, it controls the initial experimental cost to be too high, achieving a reasonable balance between model initialization accuracy and experimental resource consumption.
[0046] In this embodiment, the specific requirements for information value screening are clarified: information values are selected from the set of untested candidate formulations in descending order of value. The candidate recipes with the highest information value, either by a predetermined proportion or a predetermined number, are selected to form a high-information subset. .
[0047] For example, the preset ratio is 10% to 15%. This range ensures that a sufficient number of high-value points are selected while effectively controlling the data scale of subsequent clustering processing. In another specific embodiment, the preset number is set to the same size as the single-batch trial size. A value that is directly proportional, for example, taking 2. Or 3 This ensures that the size of the highly informative subset is sufficient to support subsequent weighted K-means clustering analysis. The specific size can be flexibly set based on the design space and experimental resources.
[0048] In this embodiment, the expected variance reduction active learning criterion is further defined to quantify the contribution of a single candidate formulation point to the reduction of model uncertainty.
[0049] Specifically, for any candidate formulation point The formula for calculating its information value is:
[0050] in, This represents the set of reference points used to evaluate the variance reduction effect. This set is derived from the set of untested candidate formulation points obtained through random sampling or Latin hypercube sampling methods. The reference points are selected to approximate global prediction of uncertainty. The size of the reference point set can be set according to the design space scale, for example, 100 to 500 points. The covariance function of a Gaussian process is used to measure the correlation between two sample points. This is the covariance matrix calculated based on all tested formulation points in the current sample library; This refers to all tested formulation points and reference points in the current sample library. The covariance vector between them; For all tested formulation points and candidate formulation points in the current sample library The covariance vector between them; The noise variance in the Gaussian process model represents the random error in the observed data. It is an identity matrix.
[0051] That is, by calculating the candidate formulation points After adding to the sample library, the reference point set The average reduction in the predicted variance at each point is used to approximate the contribution of the candidate formulation point to reducing the uncertainty of the global model.
[0052] In this embodiment, the clustering process is further defined as weighted K-means clustering, which divides the high-information subset into multiple clusters consistent with the scale of a single batch of experiments, and selects representative formulation points from each cluster to form the next batch of experimental formulation sets.
[0053] Specifically, the weighted K-means clustering uses the weight coefficients of each candidate formulation point as sample weights, and aims to minimize the sum of weighted squared errors to determine the division of each cluster and the cluster centers, thus defining the high-information subset. Divided into batches consistent with the size of a single-batch test For each cluster, the center of each cluster is iteratively updated during the clustering process using a weighted average method. The calculation formula is as follows:
[0054] In the formula, The number of clusters is the preset number, and it is equal to the size of a single batch of experiments (i.e., the number of formulation points to be selected in each batch). Indicates the first One cluster, For the first The center of each cluster, Candidate formulation point Normalized weight coefficients. During iterative optimization, each cluster center is updated using the following formula:
[0055] This weighted update method ensures that candidate formula points with higher weight coefficients dominate the determination of cluster centers, thereby guaranteeing the guiding role of high-information-value regions in the clustering results.
[0056] This scheme uses weighted K-means clustering to give higher information value points greater influence within clusters, ensuring that cluster centers are biased towards information-rich areas; it also selects representative formula points from each cluster, ensuring that the selected points in the same batch have a greater influence. Each formula point is both a "representative of information value" within its own high-information area and dispersed across different areas of the design space, combining the advantages of high information gain and spatial coverage. This solves the problems of easy clustering and information redundancy in batch active learning.
[0057] In this embodiment, the representative recipe point is the recipe point with the highest information value within the cluster; when there are multiple recipe points with the same highest information value, the recipe point closest to the cluster center is selected.
[0058] This scheme ensures that the selected recipe points for each cluster are the candidate recipe points with the highest information value within that cluster, guaranteeing the information quality of the selected recipe points. When information value is equal, selecting the point closest to the cluster center helps maintain the representativeness of the selected recipe points for the region within the cluster, avoiding the selection of extreme outliers, and making the selection results more stable. This rule is simple and effective, requiring no additional computational cost, and forms a complete batch selection mechanism with clustering processing, further improving the rationality and robustness of batch selection.
[0059] In this embodiment, the Gaussian process surrogate model is further defined to use a zero-mean function as the prior mean and a radial basis function with automatic correlation determination as the covariance function. During the model training process, the model hyperparameters and noise variance are optimized by maximizing the marginal likelihood.
[0060] Specifically, the covariance function assigns an independent length scale parameter to each input dimension in the synchronous grout mix design space, and the calculation formula is as follows:
[0061] in, For any two recipe points (i.e., input vectors) in the design space; The dimensions of the design space, i.e., the number of proportioning parameters; , They are respectively and In the Values in each dimension; For the first The length scale parameter of each input dimension controls the model's sensitivity in that dimension: the smaller the length scale, the more significant the impact of changes in that dimension on output performance. The signal variance characterizes the overall variation of the model's predicted output.
[0062] By assigning an independent length scale parameter to each input dimension, the covariance function can automatically learn the importance of each matching parameter to the prediction of target performance, thereby effectively improving the model's fitting ability and interpretability in high-dimensional design space.
[0063] The hyperparameters and noise variance are optimized by maximizing the marginal likelihood. The hyperparameters to be optimized include the logarithms of the length scale parameters in each dimension. Logarithm of signal variance The process of maximizing marginal likelihood enables the model to adaptively learn the complex mapping relationship between proportion and performance from the data under limited sample conditions, avoiding the subjectivity of manual parameter tuning and enhancing the model's generalization ability.
[0064] In this embodiment, the iteration termination condition is specified as either of the following two cases: The iteration terminates when the average prediction uncertainty of the Gaussian process surrogate model on the set of untested candidate formulations falls below a first preset threshold, and the maximum prediction uncertainty falls below a second preset threshold. The first and second preset thresholds are determined by an upper limit for experimental error or an engineering tolerance; for example, in a specific embodiment, the average prediction uncertainty threshold can be set to 0.5 MPa, and the maximum prediction uncertainty threshold can be set to 2 MPa. This condition indicates that the model's prediction accuracy meets the requirements of engineering applications, and further experimentation is unnecessary.
[0065] Alternatively, the iteration can terminate when the cumulative number of tested formulation points reaches a set upper limit. This condition serves as a constraint on experimental costs, ensuring that the method converges within a limited budget.
[0066] That is, the iteration stops when any one of the conditions is met, thus ensuring the accuracy of the model while making reasonable use of experimental resources.
[0067] The present invention will be further explained below with reference to specific embodiments: Example 1 The shield tunneling synchronous grouting material closed-loop mix design method based on batch active learning described in this embodiment includes the following steps: S1: Constructing the design space for the proportioning of synchronous grouting material Based on literature review and engineering case studies, the following parameters were selected: fly ash to cement ratio (mass ratio of fly ash to cement), water-cement ratio (mass ratio of water to cementitious materials), swelling ratio (mass ratio of bentonite to water), mortar-cement ratio (mass ratio of cementitious materials to sand), and solid waste content. Specifically, the solid waste content refers to the volumetric substitution rate of the solid waste material for sand; the solid waste material is recycled rubber granules, and the solid waste content represents the rubber granule substitution rate. express.
[0068] For each proportioning parameter, a lower limit, an upper limit, and a deviation range are set, and the design space is discretized to generate a set of candidate formulation points. The design spatial dimensions and grid division are shown in Table 1. After discretization, the set of candidate recipe points is... The CCP includes 20,580 formula points.
[0069] Table 1. Dimensions and grid division of the design space in Example 1
[0070] In this embodiment, the 3-day compressive strength is used as the target performance index. At the same time, the upper and lower limits of fluidity, the upper and lower limits of setting time, the density range and other qualified threshold ranges can be set according to specific engineering requirements, and used as screening conditions when outputting recommended formulas in the future.
[0071] S2: Initial Sampling and Sample Library Construction Latin hypercube sampling was used to select candidate formulation points from the set. An initial formula point set is extracted from the data. In this embodiment, the spatial dimension is designed. =5, the total number of initial formula point samples is 30 (5 dimensions × 6). For the selected initial formula points, synchronous grouting material samples are prepared according to the preset preparation process, and performance tests are carried out (the compressive strength is tested after 3 days in this embodiment), thereby establishing an initial sample library.
[0072] The materials used are as follows: cement is P·O 42.5 ordinary Portland cement, fly ash is Grade II fly ash, bentonite is sodium-based bentonite, sand is standard sand, and solid waste material is recycled rubber granules made from crushed waste tires and passed through a 60-mesh sieve.
[0073] The maintenance conditions are: standard maintenance conditions (20℃±2℃, RH>90%).
[0074] The performance test adopted the cement mortar compressive strength test, and the performance index was the 3-day compressive strength.
[0075] The set of formulation points that have completed the experiment and been included in the sample library is denoted as . In the initial stage, That is, the set of tested formulation points corresponding to the initial sample library.
[0076] S3: Training the Gaussian process surrogate model A Gaussian process surrogate model is trained based on the aforementioned sample library. Specifically, the following steps are included: S31: Data Preprocessing. Standardize the matching parameters to eliminate the influence of different units on model training.
[0077] S32: Model Specification and Training. The Gaussian model uses a zero-mean function as the prior mean and selects an automatically correlated radial basis function as the covariance function. This kernel function assigns an independent length scale parameter to each input dimension in the design space; the calculation formula is as follows:
[0078] in, For signal variance, For the first The length scale parameter of each input dimension is used. The hyperparameters are optimized by maximizing the marginal likelihood. and noise variance .
[0079] S33: Uncertainty quantification. For any point in the candidate formulation set... The trained Gaussian process model outputs its performance prediction mean. With prediction variance The prediction variance serves as a measure of the model's prediction uncertainty at that point.
[0080] S4: Definition of the set of untested candidate formulations, calculation of the information value of active learning criteria, and construction of high-information subsets. The set of untested candidate formulation points is defined as the difference between the set of constructed candidate formulation points and the set of tested formulation points, i.e.:
[0081] Using the trained Gaussian process model, calculate the set The information value of the active learning criterion for each candidate formulation point. In this embodiment, the information value is the expected variance reduction active learning criterion (ALC), used to quantify the expected reduction in the uncertainty of the global model prediction after adding a candidate formulation point to the sample library. For candidate formulation points Its value Calculated using the following formula:
[0082] In the formula, The set of reference points used to evaluate variance reduction is obtained through random sampling or Latin hypercube sampling; Let covariance function be the Gaussian process function. The covariance matrix is based on the current sample database; For the current sample library and reference point The covariance vector between them For the current sample library and candidate formulation points The covariance vector between them; This represents the noise variance.
[0083] In descending order of information value, the set of candidate formulations that have never been tested... The candidate recipe points with the highest information value are selected from a predetermined proportion or a predetermined number to form a high-information-value subset. In this embodiment, the top 15% of recipe points in terms of information value are selected to form the high-information-value subset. .
[0084] S5: Normalization Processing high information value subset The information value of each candidate formulation point is normalized to obtain the weight coefficient corresponding to each point. The normalization process uses a min-max scaling method to subdivide the subset. Each point in The ALC value is linearly mapped to the [0,1] interval, and the calculation formula is as follows:
[0085] in, and High information subsets The minimum and maximum values of internal information value. These are the normalized weighting coefficients.
[0086] S6: Clustering process, selecting representative formulation points Based on the obtained normalized weight coefficients, the high-information subset We performed weighted K-means clustering analysis. The goal of this clustering method is to cluster highly informative subsets. Divided into There are several clusters, and the center of each cluster is determined by minimizing the following weighted sum of squared errors function. :
[0087] in, Indicates the first One cluster, For the first The center of each cluster, Candidate formulation point The normalized weight coefficients. During clustering, the cluster centers... Iterative updates are performed using the following formula:
[0088] In this embodiment, the scale of a single batch of trials is taken as... =5, meaning 5 formulation samples are selected per batch, thus creating a high-information subset. It is divided into 5 clusters.
[0089] One representative formulation point is selected from each cluster, and all selected representative formulation points are combined to form the next batch of experimental formulation sets. In this embodiment, the selection rule for representative formulation points is as follows: the formulation point with the highest information value within the cluster is selected first; if multiple candidate formulation points within the same cluster have the same highest information value, the formulation point closest to the cluster center is selected as the representative formulation point.
[0090] S7: Experimentation, Data Updates, and Model Retraining The next batch of experimental formulations will be prepared and its performance tested. The new sample data obtained will be added to the sample library to update the sample library, and the set of experimental formulation points will be updated simultaneously. ,in, This is the set of formulation points newly added and tested in this batch. Subsequently, the Gaussian process surrogate model is retrained based on the updated sample library, or incremental updates are performed on the original model.
[0091] S8: Repeat steps S4 to S7 until the iteration termination condition is met.
[0092] The termination condition selected in this embodiment is: the number of formulation points reaches 60, or the average prediction variance of the Gaussian process model on the set of untested candidate formulation points is lower than a first set threshold (0.5 MPa in this embodiment). 2 Furthermore, the maximum prediction variance is lower than the second set threshold (2 MPa in this embodiment). 2 The threshold can be determined by the upper limit of experimental error or the allowable deviation in engineering.
[0093] S9: After the iteration terminates, output a recommended formula from all formulas that meet the acceptable threshold range of the target performance index. In this embodiment, the 3-day compressive strength is used as the target index; if acceptable thresholds for performance indices such as fluidity / setting time / density are also set, they are included as screening conditions in the output.
[0094] Iteration results and verification like Figure 2 The diagram shows the distribution of prediction uncertainty (variance) during the batch active learning iteration process. The model reaches the set termination condition in the third iteration, at which point the average prediction variance is 0.234 MPa. 2 The maximum prediction variance is 3.63 MPa. 2 The three-round iterative cycle adds 5 new samples to the initial sample pool of 30 samples each time, for a total of 15 new samples, and the total number of samples at the end of the iteration is 45.
[0095] like Figure 3 The diagram shown illustrates the comparison between model predictions and measured values after the iteration. Five formulations were randomly selected from the untested candidate set for preparation and 3-day compressive strength testing. These five formulations are detailed in Table 2.
[0096] Table 2. Recipes used for model testing and validation after iterative training.
[0097] All measured values fall within the 95% confidence interval predicted by the model. For test formulations 1, 4, and 5, the error between the predicted and measured values is within 0.25 MPa. For test formulation 2, the predicted and measured values show good agreement. The experimental results demonstrate that the method proposed in this invention has good prediction accuracy and stability.
[0098] Example 2 This embodiment aims to compare the performance differences between the active learning strategy in the closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning described in this invention, and the conventional random sampling strategy and the ordinary K-means clustering sampling strategy.
[0099] For ease of quantitative comparison, the regression equation obtained from the orthogonal experiment is assumed to be the true mapping function of the grout setting time in high-dimensional space, and the calculation method is as follows:
[0100] in, Indicates the setting time of the synchronous grouting material. , , and These are the water-to-binder ratio, powder-to-ash ratio, water-swelling ratio, and binder-to-mortar ratio, respectively. To simulate measurement noise in real experiments, random Gaussian noise is added to the above true function values, and the relative standard deviation of the noise is set to 10%.
[0101] In this embodiment, the design spatial dimensions and grid division are shown in Table 3. After discretization, the candidate recipe point set is... The CCP includes 7,605 formula points.
[0102] Table 3. Dimensions and grid division of the design space in Example 2
[0103] From the set of candidate formulation points Twenty formulation points were randomly selected, and their setting times were calculated using the true setting time function to construct an initial sample library. A Gaussian process surrogate model was trained based on this initial sample library. This model uses a zero-mean function and selects radial basis functions with automatic correlation determination as the covariance function.
[0104] During the active learning iteration process, this embodiment compares the active learning strategy proposed in this invention with the following two comparative strategies: Conventional random sampling strategy: Randomly select a preset number of untested candidate formulations for each batch.
[0105] Ordinary K-means clustering sampling strategy: Using the prediction variance output by the Gaussian process model as the uncertainty measure, only the top 10% of samples with the highest uncertainty (prediction variance) are subjected to ordinary (unweighted) K-means clustering, which divides them into 5 clusters consistent with the size of a single batch of experiments. The formulation point closest to the cluster center in each cluster is selected as the formulation for the next batch of experiments.
[0106] In this embodiment, five formulation points are selected for each batch of experiments. The formulation point and the measured value of the condensation time calculated by the true function of condensation time are added to the sample library to complete the data update, and the Gaussian process model is retrained. The above process is repeated until the set upper limit of the number of iterations (5 times) is reached.
[0107] Iteration results After the iteration, the total number of samples in the final sample library under each active learning sampling strategy was 40, and the number of unlabeled samples in the design space was 7560. For example... Figure 4 The comparison of the final prediction performance of the model under different active learning sampling strategies is shown: the coefficient of determination R for condensation time prediction of the final model under the conventional random sampling strategy and the ordinary K-means clustering sampling strategy. 2 The values are 0.9710 and 0.9780 respectively; while under the active learning strategy proposed in this invention, the final model's R... 2The accuracy reached 0.9884, significantly outperforming the comparison strategy.
[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning, characterized in that, Includes the following steps: S1. Construct a design space for the proportion of synchronous grouting material, select at least two proportioning parameters as design variables, determine the value range of the design variables and generate a set of candidate formulation points discretely, and set at least one target performance index and qualified threshold for synchronous grouting material. S2. Using Latin hypercube sampling, an initial formulation point set is extracted from the candidate formulation point set, and the initial formulation point set is prepared and its performance is tested to establish an initial sample library; S3. Train a Gaussian process surrogate model based on the initial sample library, and output the performance prediction mean and prediction uncertainty of the candidate formulation points through the Gaussian process surrogate model; S4. Based on the trained Gaussian process surrogate model, the expected variance reduction active learning criterion is adopted to calculate the information value of all untested candidate formulations, and a high-information subset is obtained according to the information value. S5. Normalize the information value of each candidate recipe point in the high-information subset to obtain the corresponding weight coefficient; S6. Perform clustering processing on the high-information subset based on the weighting coefficients, and select the next batch of test formulas according to the single batch test size; S7. Prepare and perform performance testing on the next batch of experimental formula sets, add the newly obtained formula points to the sample library, and retrain or incrementally update the Gaussian process proxy model; S8. Repeat S4-S7 until the preset iteration termination condition is met; S9. Output a recommended formulation from the candidate formulations that meet the acceptable threshold range of the target performance indicators.
2. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S1, the design variables include at least two of the following: water-cement ratio, mortar ratio, swelling ratio, powder-ash ratio, and solid waste content. The solid waste content refers to the volume or mass substitution rate of the solid waste material for the sand. The solid waste material includes at least one of recycled rubber granules, recycled fine aggregates, and mineral solid waste powder.
3. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S1, the target performance index includes at least one of fluidity, setting time, density and early compressive strength; the qualified threshold includes at least one of upper and lower limits of fluidity, upper limit of setting time, upper and lower limits of density and lower limit of early compressive strength.
4. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S2, the number of initial formula point sets is related to the dimension of the synchronous grouting material proportioning design space.
5. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S4, the information value filtering specifically refers to: Based on information value from high to low, a preset proportion or a preset number of untested candidate formulations are selected to form the high-information subset.
6. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S4, the expected variance reduction active learning criterion is used to quantify the contribution of a single candidate formulation point to reducing the uncertainty of the global model.
7. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, In S6, the clustering process is weighted K-means clustering, which divides the high-information subset into multiple clusters consistent with the scale of a single batch of experiments, and selects representative formulation points from each cluster to form the formulation set for the next batch of experiments.
8. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 7, characterized in that, The representative recipe point is the recipe point with the highest information value within the cluster; When there are multiple recipe points with the highest information value, select the recipe point that is closest to the cluster center.
9. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, The Gaussian process surrogate model uses a zero-mean function, selects a radial basis function with automatic correlation determination as the covariance function, and optimizes the model hyperparameters and noise variance by maximizing marginal likelihood.
10. The closed-loop mix design method for shield tunnel synchronous grouting material based on batch active learning according to claim 1, characterized in that, The iteration termination condition is any one of the following: The average prediction uncertainty of the Gaussian process surrogate model on the set of untested candidate formulations is lower than a first set threshold, and the maximum prediction uncertainty is lower than a second set threshold; the first set threshold and the second set threshold are determined by the upper limit of experimental error or the engineering tolerance. Or the cumulative number of tested formula points has reached the set limit.