A probabilistic constraint-based reverse design method for ultra-high performance concrete mix proportion

Abstract

The application relates to the technical field of intelligent design of building materials, and discloses a reverse design method for mix proportion of ultra-high performance concrete based on probability constraint, which comprises the following steps: constructing a comprehensive data set of the ultra-high performance concrete; processing the data set to obtain a high-value feature subset; taking the high-value feature subset as input, taking toughness, compressive strength and fluidity as output, and constructing a multi-target performance prediction proxy model; performing explainability analysis on the proxy model by adopting a SHAP method to obtain key features influencing reverse optimization of the mix proportion; constructing a reverse design optimization model of the mix proportion under probability constraint; solving the reverse design optimization model of the mix proportion, selecting a candidate mix proportion by a limited expected improvement function, obtaining a candidate mix proportion solution set satisfying the probability constraint condition, and determining a recommended mix proportion scheme from the candidate mix proportion solution set. In this way, the reverse precise design of the ultra-high performance concrete with toughness improvement as the core and multi-dimensional engineering indexes controlled can be realized.

Description

Technical Field

[0001] This application relates to the field of intelligent design technology for building materials, such as a reverse design method for ultra-high performance concrete mix proportions based on probability constraints. Background Technology

[0002] Ultra-high performance concrete (UHPC), with its dense microstructure and outstanding macroscopic mechanical properties, has become a key material in the construction of modern major projects such as cross-sea bridges, high-rise buildings, and offshore wind turbines. However, behind its excellent performance lies an extremely complex nonlinear coupling between a highly complex cementitious material system, aggregate gradation, and multi-scale hybrid fibers. In practical engineering applications, the mix design of UHPC not only needs to meet ultimate mechanical standards (such as fracture toughness and compressive strength), but also must take into account demanding workability requirements (such as flowability) and increasingly stringent economic and low-carbon environmental protection indicators. This high-dimensional, highly coupled multi-objective synergy constitutes a major challenge in the field of materials science.

[0003] However, current UHPC mix design generally relies on empirical trial mixing, orthogonal experiments, or semi-empirical close-packing theory. These traditional methods not only have long trial-and-error cycles and high physical experimental costs, but also have insurmountable theoretical limitations: due to the extremely large multi-component synergistic design space, traditional trial-and-error methods can often only find compromise solutions that "barely meet the basic requirements" in a very small local range, and are simply unable to accurately locate the optimal solution that maximizes comprehensive benefits in the global feature space.

[0004] In recent years, with the introduction of machine learning technology into the development of UHPC, although data-driven models have improved the fitting ability of nonlinear material relationships to some extent, existing machine learning-aided design solutions still reveal the following core pain points in deep engineering applications: First, the design paradigm is limited, lacking the ability to "reverse decode" driven by objectives. Currently, most applications in this field are fixed in a "forward prediction" mode (i.e., passively inputting the formula to obtain performance prediction values). This method fails to fundamentally reverse the nature of "trial and error," lacking a reverse design mechanism that actively maps physical formula parameters back to the target performance indicators. Second, the shallow nature of feature engineering and the severe "black box" effect of data. When constructing existing machine learning models, raw material components are often simply piled up as independent numerical features, failing to effectively characterize composite features with clear physical meanings, such as water-cement ratio, mineral admixture substitution rate, fiber reinforcement index, and fiber-matrix coupling relationship. This easily leads to feature redundancy and spurious correlations, resulting in insufficient generalization ability and interpretability of prediction results, and reducing the physical rationality and engineering reliability of recommended mix proportions. Third, highly complex integrated models or neural networks lack interpretability mechanisms, making it impossible for engineers to discover the synergistic gains between the fiber system and the matrix, resulting in a lack of transparency and engineering trust in the model-recommended mix proportions.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0007] This disclosure provides a reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints, so as to achieve precise reverse design of ultra-high performance concrete with toughness improvement as the core and multi-dimensional engineering indicators under control.

[0008] In some embodiments, the reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints includes: S10, acquiring matrix material parameters, hybrid fiber parameters, performance test parameters, material cost parameters, and carbon emission parameters to construct a comprehensive dataset for ultra-high performance concrete; S20, performing data preprocessing and feature dimensionality reduction on the comprehensive dataset sequentially to obtain a high-value feature subset; S30, using the high-value feature subset as input and toughness, compressive strength, and fluidity as output, establishing multi-objective performance prediction surrogate models using the XGBoost model; wherein, the surrogate models include: a toughness prediction surrogate model, a compressive strength prediction surrogate model, and a fluidity prediction surrogate model; S40, using the SHAP method to perform interpretability analysis on the surrogate models, obtaining the contribution of each input feature to the prediction results of toughness, compressive strength, and fluidity, and determining the influence based on the contribution. The key features of the mix proportion inverse optimization, the contribution direction of the key features, and the reasonable value range of the key features; S50, based on the key features, the contribution direction of the key features, and the reasonable value range of the key features, determine the mix proportion parameters to be optimized and their variable boundaries, take maximizing toughness performance as the optimization objective, and construct a mix proportion inverse design optimization model under probabilistic constraints with compressive strength, flowability, material cost, and carbon emissions as constraints; S60, within the design space defined by the key features and their variable boundaries, establish a Gaussian process model of the objective function and a Gaussian process model of the constraint function using a constraint-based Bayesian optimization algorithm; solve the mix proportion inverse design optimization model using the objective function Gaussian process model and the constraint function Gaussian process model, select candidate mix proportions through a constrained expected improvement function, obtain a set of candidate mix proportion solutions that satisfy the probabilistic constraints, and determine the recommended mix proportion scheme from the set of candidate mix proportion solutions.

[0009] The present disclosure provides a reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints, which can achieve the following technical effects: 1. Data preprocessing and feature dimensionality reduction of comprehensive datasets can effectively reduce the impact of data noise, sample imbalance and variable collinearity on model training, and improve the stability and expressive power of high-value feature subsets; 2. Using a subset of high-value features as model input, XGBoost models are used to establish toughness prediction surrogate models, compressive strength prediction surrogate models, and fluidity prediction surrogate models, respectively, so as to characterize the nonlinear mapping relationship between multi-component mix proportion parameters and multi-objective performance of ultra-high performance concrete; 3. Further, the SHAP interpretability analysis method is introduced to identify the contribution direction of matrix material parameters, hybrid fiber parameters and composite characteristic variables to the prediction results of toughness, compressive strength and flowability, thereby enhancing the transparency and engineering credibility of the model recommendation results; 4. With maximizing toughness performance as the optimization objective, compressive strength, flowability, material cost, and carbon emission requirements are incorporated into a probabilistically constrained mix design optimization model. A constraint-based Bayesian optimization algorithm is used to search for candidate mix proportions. The uncertainties of the objective function and constraint function are estimated using a Gaussian process model, and a constrained expectation improvement function is used to select candidate mix proportions in the design space that have both toughness enhancement potential and constraint satisfaction probability. This effectively reduces the risk of engineering constraint breach caused by model prediction errors, experimental discreteness, and sample perturbation. 5. Based on the comprehensive toughness target value, compressive strength satisfaction probability, flowability satisfaction probability, material cost, and carbon emission level of the candidate mix proportions, the recommended mix proportion scheme that meets the requirements of engineering applications is determined from multiple dimensions, making the scheme more accurate; 6. It can reduce the number of trial mixes and material consumption, improve the efficiency of high-toughness ultra-high performance concrete mix design, and achieve targeted improvement of toughness performance while meeting the requirements of compressive strength, fluidity, cost and carbon emission, thereby improving the reliability, interpretability and engineering applicability of the recommended mix design.

[0010] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0011] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein: Figure 1 This is a schematic diagram of a reverse design method for ultra-high performance concrete mix proportion based on probability constraints provided in an embodiment of this disclosure; Figure 2 This is a schematic diagram of the comprehensive dataset construction, data preprocessing, and feature dimensionality reduction process provided in this embodiment of the disclosure; Figure 3 This is a schematic diagram of the training and evaluation process of the XGBoost multi-objective performance prediction proxy model provided in this embodiment of the disclosure; Figure 4 This is a schematic diagram of the SHAP interpretability analysis results of the resilience prediction surrogate model provided in the embodiments of this disclosure; Figure 5 This is a schematic diagram of the SHAP interpretability analysis results of the compressive strength prediction proxy model provided in this embodiment of the present disclosure; Figure 6 This is a schematic diagram of the SHAP interpretability analysis results of the liquidity prediction proxy model provided in this embodiment of the present disclosure; Figure 7This is a schematic diagram of the principle of inverse optimization based on constraint Bayesian optimization under probabilistic constraints provided in the embodiments of this disclosure; Figure 8 This is a comparison chart of the experimental test results of the recommended mix ratio provided in this embodiment with the preset target index; Figure 9 This is a comparison chart of the actual calculated results of the recommended mix proportion material cost and carbon emissions provided in this embodiment with the preset upper limit. Detailed Implementation

[0012] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0013] The terms "first," "second," etc., used in the specification and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0014] Unless otherwise stated, the term "multiple" means two or more.

[0015] In this embodiment of the disclosure, the character " / " indicates that the preceding and following objects are in an "or" relationship. For example, A / B means: A or B, and in mathematical expressions, ratios of physical quantities, and units of measurement, it represents division or the meaning of "per". For example, W / B represents the water-cement ratio, L f / D f This indicates the fiber aspect ratio.

[0016] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0017] The term "correspondence" can refer to an association or binding relationship. The correspondence between A and B means that there is an association or binding relationship between A and B.

[0018] Combination Figure 1 As shown, this disclosure provides a reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints, including: S10: Obtain matrix material parameters, hybrid fiber parameters, performance test parameters, material cost parameters, and carbon emission parameters to construct a comprehensive dataset for ultra-high performance concrete. This includes the following steps: S11 involves collecting historical mix design data, laboratory test data, and publicly available literature data for ultra-high performance concrete (UHVPC) to construct a comprehensive dataset. Each sample set corresponds to a set of UHVPC mix designs. The sample data includes input parameters and output parameters. Input parameters include matrix material parameters, hybrid fiber parameters, material cost parameters, and carbon emission parameters. Output parameters include toughness target parameters and constraint target parameters.

[0019] The mix proportion parameters include, but are not limited to: cement content C, silica fume content SF, fly ash content FA, slag powder content SL, metakaolin content MK, precipitated beads content CS, quartz powder content, fine aggregate content S, average particle size of fine aggregate, water-cement ratio W / B, and water-reducing agent content SP. Among the above components, the water-cement ratio and water-reducing agent dosage can be expressed in dimensionless form, while the units for other components can be uniformly expressed as kg / m³.

[0020] Fiber parameters include, but are not limited to: fiber type, fiber length L f Fiber diameter D f Fiber aspect ratio L f / D f Fiber volume content V f The parameters include fiber elastic modulus, fiber tensile strength, and whether it is a single fiber or a hybrid fiber system. For different fiber types such as steel fiber, polyvinyl alcohol fiber, polypropylene fiber, and basalt fiber, numerical encoding can be used to represent them, allowing them to be used as input variables in subsequent calculations.

[0021] Material cost parameters include: the unit price of each raw material, transportation costs, processing costs, or total material costs.

[0022] Environmental parameters include the unit mass carbon emission factor for cement, silica fume, fly ash, slag powder, fiber, aggregate, and admixtures. For each mix design sample, the unit volume material cost (Cost(x)) can be calculated based on the raw material usage and unit price, and the unit volume carbon emission (Carbon(x)) can be calculated based on the raw material usage and carbon emission factor.

[0023] The output parameters include: toughness target parameters and constraint target parameters. The toughness target parameters include: fracture toughness K. IC Fracture energy G w And flexural strength. Constraint target parameters include: compressive strength and slump spread. For data from different sources, when there are differences in the name of the toughness index or the test method, they can be uniformly converted into the normalized toughness index T.

[0024] To enhance the ability of machine learning models to express the underlying physical mechanisms of materials, composite feature variables are constructed based on the original variables. These composite feature variables include, but are not limited to: total cementitious material content (B) and mineral admixture substitution rate (R). m Water-cement ratio (W / B), water-reducing agent-cement ratio (SP / B), sand-cement ratio (S / B), fiber reinforcement index (FI), and the product of fiber aspect ratio and volume fraction (V). f ·L f / D f The interaction term V between fiber volume fraction and water-cement ratio f / (W / B), the interaction term SF / (W / B) between silica fume content and water-cement ratio, the slurry surplus coefficient related to the total amount of cementitious materials and fluidity, and the fiber-matrix coupling index reflecting the synergistic effect of fiber-matrix.

[0025] The fiber reinforcement index FI is calculated according to the following formula: , Among them, V f L is the fiber volume fraction. f D represents the fiber length. f The fiber diameter is the reference value. This indicator can simultaneously reflect the effects of fiber content and fiber morphology on bridging, crack propagation inhibition, and toughness improvement.

[0026] The matrix densification index MI is constructed, and its expression is as follows: , Wherein, SF represents the amount of silica fume, SL represents the amount of slag powder, MK represents the amount of metakaolin, B represents the total amount of cementitious materials, and W / B represents the water-cement ratio, where W is the water content per unit volume of concrete and B is the total amount of cementitious materials. This index is used to characterize the combined contribution of the mineral admixture filling effect, pozzolanic reaction, and low water-cement ratio to matrix densification.

[0027] S20 involves performing data preprocessing and feature dimensionality reduction on the comprehensive dataset sequentially to obtain a high-value feature subset. Specifically, this includes the following steps: like Figure 2 As shown, the comprehensive dataset is first preprocessed, specifically including: S21 standardizes the variable names, units of measurement, and test ages for samples from different sources. Material usage is standardized to kg / m³, compressive strength to MPa, slump spread to mm, and toughness indices are organized according to the same test standards and ages.

[0028] S22 handles missing values, duplicate samples, obviously erroneous samples, and unit outlier samples. For data in the input variables where the missing proportion is lower than the preset proportion, the median imputation method is used to complete the data; for samples with missing target performance parameters, they are removed from the training sample library; for duplicate samples, the set with more complete test conditions is retained; for samples that obviously violate the physical laws of materials, they are corrected according to the original data source, and deleted if they cannot be confirmed.

[0029] S23 employs the Isolation Forest algorithm to identify anomalous samples in the multivariate feature space. Samples with missing values ​​processed are input into the Isolation Forest model, and anomaly scores are calculated for each sample. Samples with anomaly scores higher than a preset score are marked as anomalous. Anomalous samples caused by input errors, unit errors, or test condition errors are removed; truly existing extreme values ​​of high toughness, high strength, and high flowability are retained and identified to avoid mistakenly deleting extremely superior mix proportions with engineering value.

[0030] S24. To alleviate the shortage of high-toughness, high-strength, and high-flowability samples, the SMOTE method is used for sample enhancement. Specifically, high-toughness, high-strength, and high-flowability samples are treated as a scarce sample set. The nearest neighbor samples of each scarce sample are found in the feature space, and linear interpolation is performed between the scarce sample and its nearest neighbor samples to generate enhanced samples. The continuous mix proportion parameters in the enhanced samples are kept within the physically feasible range, and the fiber type remains consistent with the original scarce samples.

[0031] S25, perform dimensionless processing on the input variables using the Min-Max method, the calculation formula is as follows: , Where x is the original variable, x min and x max , respectively, are the minimum and maximum values ​​of the variable in the training set, and x' is the normalized variable.

[0032] Then, feature dimensionality reduction is performed on the preprocessed data, specifically including: S26. Calculate the Pearson correlation coefficient between the input variables and the target variable, and screen variables that are significantly correlated with toughness, compressive strength and flowability.

[0033] S27. Calculate the correlation matrix between the input variables. If there is a high degree of collinearity between two input variables, retain the variable with a clearer physical meaning or a higher contribution to the target variable.

[0034] S28 can calculate the variance inflation factor. When the variance inflation factor of a certain variable is higher than a preset threshold, it can be deleted, merged or transformed.

[0035] S29, After the above processing, the high-value feature subset X is obtained. s The high-value feature subset includes both original features such as water-cement ratio, silica fume content, fiber volume content, and fiber aspect ratio, as well as composite features such as fiber reinforcement index, matrix densification index, mineral admixture replacement rate, water-reducing agent-cement ratio, and fiber-matrix coupling index.

[0036] In this way, by using S20 data preprocessing and feature dimensionality reduction, we can avoid simply piling up material components as numerical values, thereby improving the model's ability to learn the physical laws of materials.

[0037] S30 uses a subset of high-value features as input and toughness, compressive strength, and flowability as outputs. An XGBoost model is used to establish multi-objective performance prediction surrogate models. These surrogate models include: a toughness prediction surrogate model, a compressive strength prediction surrogate model, and a flowability prediction surrogate model. The specific steps are as follows: S31, such as Figure 3 As shown, the high-value feature subset X obtained in S20 s As input to the XGBoost model, toughness, compressive strength, and flowability are used as outputs. A toughness prediction surrogate model f is established separately. T (x), compressive strength prediction surrogate model f c (x) and the liquidity prediction surrogate model f F (x).

[0038] S32 divides the comprehensive dataset into training, validation, and test sets at a ratio of 80%, 10%, and 10%, respectively. The training set is used for learning model parameters, the validation set is used for tuning model parameters, and the test set is used to evaluate the model's final generalization ability.

[0039] S33. To improve the stability of model evaluation under small sample conditions, a five-fold cross-validation method is used to train and evaluate the XGBoost model.

[0040] The S34 XGBoost model fits the nonlinear mapping relationship between a subset of high-value features and the target performance through an additive ensemble of multiple regression trees. Its objective function is as follows: , Where Obj is the training objective function value of the XGBoost model; n is the number of samples; The training loss function that measures the difference between the predicted value and the true target value; y i Let i be the true target value of the i-th sample; Let f be the target value for the i-th sample; K is the number of decision trees; f kLet be the prediction function corresponding to the k-th regression tree; This is the regularization term for the k-th tree, used to control the model complexity.

[0041] The expansion of the regularization term is as follows: , Among them, T k This represents the number of leaf nodes; y is the leaf node weight vector; γ and λ are regularization coefficients.

[0042] In this way, by introducing a regularization term, the XGBoost model can improve its fitting ability while suppressing overfitting, thereby enhancing its generalization ability to samples with unknown combination ratios.

[0043] S35. During model training, hyperparameters such as learning rate, maximum tree depth, subsampling ratio, column sampling ratio, minimum leaf node weight, regularization coefficient, and number of regression trees are set. The model parameters are adjusted based on the prediction results of the validation set to achieve a balance between the model's data fitting ability and generalization ability.

[0044] S36. The root mean square error (RMSE), coefficient of determination (R²), and mean absolute percentage error (MAPE) are used to evaluate the model performance. The expressions for each evaluation index are as follows: , , , Where n is the number of samples. The mean of the true values, y i Let i be the true target value of the i-th sample. Let be the predicted target value for the i-th sample. RMSE measures the model's sensitivity to high-error samples, R² measures the overall model's fit, and MAPE measures the proportion of prediction error to the true value.

[0045] S37: When the toughness prediction surrogate model, compressive strength prediction surrogate model, and flowability prediction surrogate model all meet the preset accuracy requirements on both the validation and test sets, the corresponding model will be used as the surrogate model for subsequent probabilistic constraint modeling and inverse optimization. If the model does not meet the preset accuracy, return to S10 and S20, supplement sample data, adjust the composite feature construction method, and retrain the XGBoost model.

[0046] This approach enables the establishment of a nonlinear mapping relationship between a subset of high-value features and toughness, compressive strength, and flowability, achieving rapid prediction of multiple properties of candidate mix proportions. Simultaneously, through cross-validation, regularization constraints, and model accuracy evaluation, the stability and generalization ability of the predictive surrogate model are improved, providing a reliable performance evaluation basis for subsequent interpretability analysis, probabilistic constraint modeling, and inverse optimization solutions, while reducing the number of mix proportion trials and experimental costs.

[0047] S40. The SHAP method is used to perform interpretability analysis on the surrogate model, obtaining the contribution of each input feature to the prediction results of toughness, compressive strength, and flowability. Based on the contribution, the key features affecting the inverse optimization of the mix proportion, the contribution direction of the key features, and the reasonable value range are determined. Specifically, this includes the following steps: S41, For any predicted target, the model output can be expressed as follows: , in, This represents the prediction result of the surrogate model for the i-th sample; Output as the model baseline; The SHAP contribution value of the j-th feature to the prediction result of the i-th sample; m is the number of input features, when When the value is positive, it indicates that the j-th input feature improves the prediction result of the sample relative to the baseline output; when... When the value is negative, it indicates that the j-th input feature causes the prediction result of the sample to decrease relative to the benchmark output.

[0048] S42, the high-value feature subset X obtained from S20 s As the object of SHAP analysis, the contribution of each input feature in each sample to the prediction results of toughness, compressive strength and flowability is calculated.

[0049] For the i-th sample and the j-th feature, its SHAP value is denoted as To obtain the global feature importance, the average absolute contribution of each feature across all samples is calculated: , in, The j-th feature is the average absolute contribution of the j-th feature in all samples; N is the total number of samples. The SHAP contribution value of the j-th feature in the i-th sample.

[0050] S43, according to The magnitude of all input features is sorted to obtain a set of key features affecting toughness, compressive strength, and flowability. For the toughness prediction surrogate model, the focus is on identifying fiber volumetric doping V. f Fiber aspect ratio Lf / D f The contributions of fiber reinforcement index (FI) and matrix densification index (MI) to toughness prediction results.

[0051] like Figure 4 As shown, in the toughness prediction surrogate model, features such as fiber volumetric content, fiber type, fiber aspect ratio, water-cement ratio, and fiber reinforcement index have high mean absolute SHAP values. Specifically, within the sample range of this embodiment, fiber volumetric content and fiber aspect ratio generally show positive contributions, while water-cement ratio generally shows a negative contribution. This indicates that appropriately increasing fiber volumetric content and fiber aspect ratio is beneficial for enhancing fiber bridging and crack propagation inhibition, while an excessively high water-cement ratio reduces matrix density, thereby weakening the toughness of ultra-high performance concrete.

[0052] like Figure 5 As shown, in the surrogate model for predicting compressive strength, features such as water-cement ratio, silica fume content, cement content, mortar-cement ratio, and water-reducing agent content have high average absolute SHAP values. Specifically, within the sample range of this embodiment, the water-cement ratio generally shows a negative contribution, while silica fume and cement content generally show positive contributions. This indicates that reducing the water-cement ratio and increasing the silica fume and cement content within a reasonable range is beneficial for improving the density of the matrix and the reaction level of the cementitious materials, thereby increasing the compressive strength.

[0053] like Figure 6 As shown, in the flowability prediction surrogate model, features such as water-reducing agent dosage, sand-to-binder ratio, fiber volume content, water-to-binder ratio, and fine aggregate dosage have high average absolute SHAP values. Within the sample range of this embodiment, water-reducing agent dosage and sand-to-binder ratio generally show positive contributions, while fiber volume content generally shows a negative contribution. This indicates that appropriately increasing the water-reducing agent dosage and reasonably adjusting the sand-to-binder ratio is beneficial to improving the flowability of the mixture, while excessive fiber volume content will increase the resistance between fibers and between fibers and the matrix, thereby reducing the flowability of the mixture.

[0054] S44, combined Figures 4 to 6 The SHAP swarm diagram shown further analyzes the contribution direction of each feature to the prediction results of toughness, compressive strength, and flowability within different value ranges after obtaining the global feature importance. Specifically, the distribution of SHAP values ​​for the same feature in different value intervals is statistically analyzed to determine whether the feature improves or reduces the target performance. For example, when the fiber volume fraction V... fWhen within the preset range, the SHAP value usually makes a positive contribution to the toughness index, indicating that an appropriate amount of fiber can improve the toughness of the material through bridging and crack propagation inhibition. When the fiber volume content exceeds the preset range, the SHAP value may decrease, indicating that excessive fiber content will cause fiber agglomeration, decreased fluidity and uneven dispersion, thereby weakening the toughness gain.

[0055] S45, to further reveal the nonlinear interaction between fiber parameters and matrix material parameters, for any two input features x q and x p The interaction contribution value of SHAP in each sample is analyzed and denoted as . Significant interaction feature combinations are identified based on the average absolute interaction contribution (SHAP). The contribution direction and favorable joint value range of significant interaction feature combinations are determined based on the distribution of interaction contribution values ​​in the SHAP. It should be noted that identifying significant interaction feature combinations and determining their contribution direction and favorable joint value range are existing technologies and will not be elaborated upon here.

[0056] S46. Through the above interactive analysis, the following material design information can be obtained: fiber volume content and fiber aspect ratio jointly determine crack bridging ability; water-cement ratio and silica fume content jointly affect matrix densification degree; water-reducing agent-cement ratio and fine aggregate content jointly affect the fluidity of the mixture; there is a synergistic relationship between fiber reinforcement index and matrix densification index, which can jointly affect the fracture toughness and flexural strength of high-toughness ultra-high performance concrete.

[0057] S47. Finally, the SHAP analysis results are fed back into the subsequent inverse optimization process of the mix proportions. For features that contribute significantly and have a positive effect on toughness, their reasonable range of variation is retained during the optimization process; for features that have a significant negative impact on flowability or compressive strength, they are restricted by constraint thresholds and variable boundaries in the subsequent probabilistic constraint modeling. This allows the XGBoost model not only to output performance predictions but also to explain the main driving factors of the prediction results, providing an interpretable basis for subsequent probabilistic constraint optimization.

[0058] Thus, by performing SHAP interpretability analysis on the XGBoost model obtained in step S30 through S40, the SHAP method decomposes the model output into the sum of the contributions of each input feature, thereby quantitatively evaluating the impact of different mix proportion parameters on the predicted results of toughness, compressive strength and flowability, which can improve the transparency and engineering credibility of the model's recommended mix proportion.

[0059] S50, based on the key features, their contribution direction, and reasonable value range, determine the mix proportion parameters to be optimized and their variable boundaries. With maximizing toughness as the optimization objective and compressive strength, flowability, material cost, and carbon emissions as constraints, construct a probabilistic constraint-based reverse design optimization model for the mix proportion. Specifically, this includes the following steps: S51, after obtaining the predictive surrogate models for toughness, compressive strength, and flowability, a reverse design optimization model for mix proportions under probabilistic constraints is constructed. Let the mix proportion parameter vector to be optimized be: , Where C represents cement content; SF represents silica fume content; FA represents fly ash content; SL represents slag powder content; MK represents metakaolin content; CS represents dissolved perlite content; S represents fine aggregate content; W / B represents water-cement ratio; SP represents water-reducing agent content; FiberType represents fiber type; L f / D f V is the fiber aspect ratio; f This refers to the fiber volume content.

[0060] S52, to ensure the engineering feasibility of candidate mix proportions, upper and lower limits are set for each design variable. For example, the dosage of each cementitious material should meet the range of engineering experience and specification requirements, the water-cement ratio should be within the workable range, the water-reducing agent dosage should not exceed the recommended material limit, and the fiber volume content should not exceed the upper limit that would cause severe agglomeration or mixing difficulties. The variable boundaries can be expressed as follows: , Where, x min and x max These are the lower and upper limits of the mixing ratio parameters, respectively.

[0061] In one embodiment, the design variable boundaries are set as follows: cement dosage 600 kg / m³ to 850 kg / m³, silica fume dosage 100 kg / m³ to 250 kg / m³, fly ash dosage 0–150 kg / m³, slag powder dosage 0 to 200 kg / m³, fine aggregate dosage 900 kg / m³ to 1200 kg / m³, water-cement ratio 0.15 to 0.22, water-reducing agent dosage 1.0% to 3.0% of the cementitious material mass, fiber aspect ratio 40 to 90, and fiber volume fraction 1.0% to 3%.

[0062] S53 prioritizes maximizing toughness as its highest optimization objective. If fracture toughness K is also considered... IC Fracture energy G w When considering flexural strength, the three factors can be normalized to construct the comprehensive toughness target T(x), as shown in the following formula: , Among them, KIC ' (x), G w '(x) and BT'(x) are the normalized fracture toughness, fracture energy, and flexural strength indices, respectively, with α1, α2, and α3 being weighting coefficients, and α... 1+ α2+α3=1.

[0063] It should be noted that if only a single resilience indicator is considered, then that indicator can be directly used as the optimization target.

[0064] S54, simultaneously, compressive strength, flowability, cost, and carbon emissions are used as constraints. Due to model errors and data perturbations in XGBoost predictions, using only deterministic predictions as constraints may lead to the recommended mix proportions failing to consistently meet engineering requirements in actual experiments. Therefore, the compressive strength and flowability constraints are transformed into probabilistic constraints.

[0065] S541, for compressive strength, the probabilistic constraint is: , Among them, f c (x) represents the predicted compressive strength; f c,min ε1 represents the lower limit threshold for compressive strength; ε2 represents the probability of failure allowed by the compressive strength constraint. In this embodiment, ε1 is set to 0.05, meaning that the probability that the candidate mix proportion meets the lower limit requirement for compressive strength is not less than 95%.

[0066] S542, for fluidity, the probabilistic constraint is: , Where Flow(x) is the predicted flowability value; Flow min ε1 represents the lower limit threshold for fluidity; ε2 represents the allowed probability of breach of fluidity constraints. In this embodiment, ε2 is set to 0.05, meaning that the probability that the candidate mix proportions meet the lower limit requirement for fluidity is not less than 95%.

[0067] S543, regarding the cost constraint, its expression is: , in, Cost is the material cost per unit volume. max This is the highest budget constraint.

[0068] S544, regarding carbon emission constraints, has the following expression: , in, Carbon emissions per unit volume; max This serves as a constraint on carbon emission limits.

[0069] S55, for any constraint function The probability that it satisfies is denoted as: , Among them, g m (x) represents the m-th constraint function; ε is the total allowed default probability of the system. In this embodiment, the allowed default probability is set to 0.05 for both the compressive strength constraint and the flowability constraint; therefore, the satisfaction probability threshold for the corresponding individual constraint is 0.95. For situations where multiple probability constraints exist simultaneously, adjustments can be made according to the engineering safety level. The value of .

[0070] S56, by combining the above multiple constraints into the optimization process, we obtain the mix ratio reverse design optimization model under probabilistic constraints: maxT(x).

[0071] The optimization model requires that the above-mentioned probabilistic constraints on compressive strength, probabilistic constraints on fluidity, and variable boundaries for cost and carbon emissions be satisfied.

[0072] In this way, the S50 transforms the traditional forward prediction method of "input mix proportion - predict performance" into a reverse design method of "given target performance and engineering constraints - reverse search for mix proportions." Driven by the need to improve toughness performance, it actively searches for candidate mix proportions that meet the constraints within the preset mix proportion parameters, avoiding the blind trial mixing and local search problems caused by repeated manual adjustments of mix proportion parameters in the traditional forward prediction process. At the same time, by setting the compressive strength and flowability requirements as probabilistic constraints, it can comprehensively consider the impact of surrogate model prediction errors and experimental dispersion on the performance judgment results, thereby improving the search efficiency, constraint satisfaction reliability, and engineering applicability of mix proportion reverse design.

[0073] S60, within the design space defined by the key features and their variable boundaries, a constraint-based Bayesian optimization algorithm is used to establish a Gaussian process model for the objective function and a Gaussian process model for the constraint function; the Gaussian process model for the objective function and the Gaussian process model for the constraint function are used to solve the inverse design optimization model for the mix proportion; candidate mix proportions are selected through a constrained expectation improvement function to obtain a set of candidate mix proportion solutions that satisfy the probabilistic constraints; and the recommended mix proportion scheme is determined from the set of candidate mix proportion solutions. Figure 7 As shown, the specific steps include: S61, to ensure the initial samples are uniformly distributed in the design space, a Latin hypercube sampling method is adopted at the variable boundaries. Generate an initial set of candidate points: , in, is the initial candidate mix designation set; n is the number of initial candidate points.

[0074] S62, for each initial candidate point The XGBoost model established in step S30 is used to calculate the predicted values ​​of toughness, compressive strength, and flowability. The material cost per unit volume and carbon emissions per unit volume are also calculated based on the raw material usage. This yields the initial observation dataset. , Where g1(x) is the compressive strength constraint function; g2(x) is the flowability constraint function; g3(x) is the material cost constraint function; g4(x) is the carbon emission constraint function; and m is the constraint function number.

[0075] S63, with the initial observation dataset Based on this, Gaussian process models for the comprehensive resilience target and each constraint are established respectively.

[0076] S64. For the resilience maximization problem, let the currently obtained optimal feasible resilience target value be T. best Then the unconstrained expected improvement function of the resilience target is expressed as: , in, This represents the unconstrained expected improvement in resilience targets; ; It is the standard normal distribution function; μ is the probability density function of the standard normal distribution. T (x) represents the predicted mean of the Gaussian process model output; σ T (x) represents the prediction standard deviation of the Gaussian process model output.

[0077] S65, for the m-th constraint function g m If (x)≤0, the probability that the constraint is satisfied is expressed as: , in, Let be the predicted mean of the m-th constraint function output by the Gaussian process model; Let be the prediction standard deviation of the m-th constraint function output by the Gaussian process model.

[0078] S66. Multiply the expected improvement value of the objective function by the probability of satisfying all constraints to construct the constrained expected improvement function cEI(x), as shown in the following equation: , in, P[g] represents the constrained expected improvement value; EI(x) represents the unconstrained expected improvement value of the resilience target; P[g] represents the unconstrained expected improvement value of the resilience target. m[x)≤ 0] is the probability of satisfying the m-th constraint; M is the number of constraints.

[0079] S67 uses the maximization of the constrained expected improvement function as the search criterion and iteratively solves the mix proportion reverse design optimization model by maximizing cEI(x). This allows for the priority selection of candidate mix proportions that may improve toughness performance and have a high probability of satisfying constraints.

[0080] S68, in the t-th round of optimization iteration, within the design space satisfying the upper and lower bound constraints of the variables, the mix proportion parameter vector with the largest constrained expected improvement value is determined by maximizing the constrained expected improvement function, and is used as the candidate mix proportion for the next round: , Where X represents the design space that satisfies the upper and lower limits of the variables. For candidate points that do not meet the variable boundaries or material physical feasibility, boundary correction and feasibility repair are performed to bring them back to the feasible mix proportion range.

[0081] S69, obtaining candidate matching ratio x t+1 Then, the XGBoost model is called to calculate the predicted values ​​of toughness, compressive strength, and fluidity of the candidate mix proportion, and the material cost and carbon emissions are calculated based on the amount of raw materials used.

[0082] S610, then the candidate coordination ratio x t+1 The corresponding objective function values ​​and constraint function values ​​are added to the observation dataset, and the objective function Gaussian process model and the constraint function Gaussian process model are retrained based on the updated observation dataset: .

[0083] S611, repeat the iterative process described above: "Gaussian process model update—constrained expectation improvement function calculation—candidate mix ratio selection—objective and constraint evaluation—dataset update" until the stopping conditions are met. The stopping conditions include reaching the maximum number of iterations, the improvement of the optimal resilience target value being lower than a preset threshold for several consecutive rounds, and the probability of satisfying the candidate mix ratio constraint being consistently higher than a preset threshold.

[0084] After the iteration is completed, the candidate mix design set is obtained: , Each candidate mix proportion satisfies the probability constraints of compressive strength, flowability, cost, carbon emission, and variable boundary constraints.

[0085] S612, comprehensively screen the candidate mix proportions. First, eliminate those with a compressive strength requirement probability below the first probability threshold (1-ε1), a flowability requirement probability below the second probability threshold (1-ε2), and a cost exceeding the maximum budget constraint.max Or carbon emissions exceed the carbon emission ceiling constraint. max Candidate solutions.

[0086] S613, Next, the remaining candidate schemes are sorted from high to low according to the comprehensive resilience target T(x), and the highest comprehensive resilience target value among the candidate schemes is determined based on the sorting results.

[0087] S614, the candidate schemes whose relative difference between the comprehensive toughness target value and the highest comprehensive toughness target value is less than or equal to a preset ratio threshold are determined as preferred candidate schemes.

[0088] S615, sort all the preferred candidate schemes according to material cost and carbon emissions, and eliminate the preferred candidate schemes whose contribution direction or value range of key features does not conform to the SHAP analysis results, to obtain the set of preferred candidate mix proportions.

[0089] S616 Finally, from the set of preferred candidate mix proportions, the preferred candidate mix proportion with the highest probability of satisfying the compressive strength requirement (greater than or equal to the first probability threshold), the highest probability of satisfying the flowability requirement (greater than or equal to the second probability threshold), and the highest overall toughness target value is selected as the recommended mix proportion scheme. When there are multiple preferred candidate mix proportions with the same overall toughness target value, the candidate mix proportion with lower material cost and lower carbon emissions is preferred. It should be noted that the preset proportion threshold, the first probability threshold, and the second probability threshold can be selected according to actual needs, and this embodiment does not specifically limit them.

[0090] Thus, through S60, after obtaining the inverse design optimization model of the mix proportion under probabilistic constraints, a constraint-based Bayesian optimization algorithm is used for inverse optimization. This algorithm, under a finite number of candidate mix proportion evaluations, uses a Gaussian process model to characterize the uncertainties of the objective function and constraint functions, and selects the most valuable candidate mix proportion for the next round through a constrained expected improvement function.

[0091] In summary, the reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints provided in this embodiment can achieve the following technical effects: 1. Data preprocessing and feature dimensionality reduction of comprehensive datasets can effectively reduce the impact of data noise, sample imbalance and variable collinearity on model training, and improve the stability and expressive power of high-value feature subsets; 2. Using a subset of high-value features as model input, XGBoost models are used to establish toughness prediction surrogate models, compressive strength prediction surrogate models, and fluidity prediction surrogate models, respectively, so as to characterize the nonlinear mapping relationship between multi-component mix proportion parameters and multi-objective performance of ultra-high performance concrete; 3. Further, the SHAP interpretability analysis method is introduced to identify the contribution direction of matrix material parameters, hybrid fiber parameters and composite characteristic variables to the prediction results of toughness, compressive strength and flowability, thereby enhancing the transparency and engineering credibility of the model recommendation results; 4. With maximizing toughness performance as the optimization objective, compressive strength, flowability, material cost, and carbon emission requirements are incorporated into a probabilistically constrained mix design optimization model. A constraint-based Bayesian optimization algorithm is used to search for candidate mix proportions. The uncertainties of the objective function and constraint function are estimated using a Gaussian process model, and a constrained expectation improvement function is used to select candidate mix proportions in the design space that have both toughness enhancement potential and constraint satisfaction probability. This effectively reduces the risk of engineering constraint breach caused by model prediction errors, experimental discreteness, and sample perturbation. 5. Based on the comprehensive toughness target value, compressive strength satisfaction probability, flowability satisfaction probability, material cost, and carbon emission level of the candidate mix proportions, the recommended mix proportion scheme that meets the requirements of engineering applications is determined from multiple dimensions, making the scheme more accurate; 6. It can reduce the number of trial mixes and material consumption, improve the efficiency of high-toughness ultra-high performance concrete mix design, and achieve targeted improvement of toughness performance while meeting the requirements of compressive strength, fluidity, cost and carbon emission, thereby improving the reliability, interpretability and engineering applicability of the recommended mix design.

[0092] Comprehensive performance analysis To verify whether the recommended mix proportion scheme provided in this embodiment can meet the preset target indicators, experimental mixing and performance testing were conducted on the recommended mix proportion, and the preset target indicators, model prediction results and experimental test results were compared.

[0093] As shown in Table 1, in one embodiment, the recommended mix proportion output by the constraint-based Bayesian optimization algorithm is as follows: cement dosage 720 kg / m³, silica fume dosage 180 kg / m³, fly ash dosage 80 kg / m³, slag powder dosage 100 kg / m³, fine aggregate dosage 1050 kg / m³, water-cement ratio 0.18, water-reducing agent dosage 2.0% of cementitious material mass, fiber type steel fiber, steel fiber aspect ratio 65, and steel fiber volume content 2.0%. This recommended mix proportion also provides the material cost per unit volume and carbon emissions per unit volume for subsequent economic and low-carbon constraint determination.

[0094] Raw materials were weighed, mixed, molded, and cured according to the recommended mix proportions shown in Table 1. During the trial mixing process, cement, silica fume, fly ash, slag powder, and fine aggregate were first dry-mixed to ensure uniform mixing of the powder materials and fine aggregates; then water and water-reducing agent were added for wet mixing; after the slurry reached a homogeneous state, steel fibers were added in batches and mixing continued to ensure uniform dispersion of the steel fibers in the matrix, resulting in an ultra-high performance concrete mixture.

[0095] Table 1 Recommended mix proportion parameters based on the output of step S60

[0096] The slump flow of the ultra-high performance concrete mixture was tested, and the compressive strength, flexural strength, fracture toughness, and fracture energy of the cured specimens were tested. Table 2 shows that the recommended mix proportion has a comprehensive toughness index of 1.08, a compressive strength of 156.2 MPa, a slump flow of 670 mm, and a fracture toughness of 6.86 MPa·m. 1 / 2 The fracture energy is 30.40 kJ·m. -2 The flexural strength is 25.30 MPa, and the material cost per unit volume is 2150 yuan / m³. 3 The carbon emission per unit volume is 800 kg CO2 / m³. 3 The above experimental test results all meet the corresponding preset target indicators.

[0097] Table 2 Comparison of Preset Target Indicators, Model Predictions, and Experimental or Actual Calculation Results

[0098] Furthermore, such as Figure 8 and Figure 9 As shown, the recommended mix proportion exhibits compressive strength, slump spread, fracture toughness, fracture energy, flexural strength, and overall toughness all exceeding their respective preset lower limits; while the material cost per unit volume and carbon emissions per unit volume are both less than or equal to their respective preset upper limits. This demonstrates that the recommended mix proportion, under actual preparation and testing conditions, can simultaneously meet the requirements of high toughness, strength, flowability, economy, and low carbon emissions.

[0099] Summary Table 2 Figure 8 and Figure 9The comparison results show that the model prediction results and experimental test results have good consistency, and the experimental test results all meet the preset target indicators. Therefore, it is determined that the recommended mix proportion meets the design requirements of high-toughness ultra-high-performance concrete set in this embodiment and can be used as the final recommended mix proportion output. If any performance indicator fails to meet the preset target in subsequent experiments, or if the deviation between the experimental test results and the model prediction results exceeds the preset allowable range, the mix proportion and its experimental test results will be fed back to the comprehensive dataset to update the XGBoost predictive surrogate model, the SHAP interpretability analysis results, and the constraint-based Bayesian optimization process.

[0100] Based on the above, Table 1, Table 2, Figure 8 and Figure 9 The experimental verification process in this embodiment forms a closed-loop verification mechanism of "preset target index - model reverse recommendation of mix ratio - experimental testing - target index comparison - data feedback update". This mechanism can verify whether the recommended mix ratio meets the preset target requirements, and can use the experimental results to continuously correct the subsequent model training and reverse optimization process, thereby improving the reliability and engineering applicability of the recommended mix ratio scheme.

[0101] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0102] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints, characterized in that, include: S10: Obtain matrix material parameters, hybrid fiber parameters, performance test parameters, material cost parameters, and carbon emission parameters to construct a comprehensive dataset for ultra-high performance concrete. S20, perform data preprocessing and feature dimensionality reduction on the comprehensive dataset in sequence to obtain a high-value feature subset; S30, using the high-value feature subset as input and toughness, compressive strength, and flowability as output, a multi-objective performance prediction proxy model is established using the XGBoost model; wherein, the proxy model includes: a toughness prediction proxy model, a compressive strength prediction proxy model, and a flowability prediction proxy model; S40, The SHAP method is used to perform interpretability analysis on the surrogate model to obtain the contribution of each input feature to the prediction results of toughness, compressive strength and flowability, and the key features affecting the reverse optimization of the mix proportion, the contribution direction of the key features and the reasonable value range are determined according to the contribution. S50. Based on the key features, the contribution direction of the key features and the reasonable value range, determine the mix proportion parameters to be optimized and their variable boundaries. With the maximization of toughness performance as the optimization objective and compressive strength, fluidity, material cost and carbon emissions as constraints, construct a mix proportion reverse design optimization model under probabilistic constraints. S60, within the design space defined by the key features and their variable boundaries, a constraint-based Bayesian optimization algorithm is used to establish a Gaussian process model for the objective function and a Gaussian process model for the constraint function; the Gaussian process model for the objective function and the Gaussian process model for the constraint function are used to solve the reverse design optimization model for the mix proportion; candidate mix proportions are selected through a constrained expectation improvement function to obtain a set of candidate mix proportion solutions that satisfy the probability constraints; and a recommended mix proportion scheme is determined from the set of candidate mix proportion solutions.

2. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 1, characterized in that, In S20, The data preprocessing includes: Standardize the variable names, units of measurement, and testing ages in samples from different sources; Handling missing values, duplicate samples, erroneous samples, and single outlier samples; The isolated forest algorithm is used to identify anomalous samples in a multivariate feature space, and the SMOTE method is used for sample augmentation. Perform Min-Max dimensionless processing on the input variables; The feature dimensionality reduction includes: Calculate the Pearson correlation coefficient between the input variables and the target variable, and screen variables that are significantly correlated with toughness, compressive strength and flowability; Calculate the correlation matrix between the input variables. If there is a high degree of collinearity between two input variables, retain the variable with a clearer physical meaning or a higher contribution to the target variable. Calculate the variance inflation factor. When the variance inflation factor is higher than a preset threshold, delete, merge, or transform the corresponding variables.

3. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 1, characterized in that, In S30 The objective function of the XGBoost model is expressed as follows: ， Where Obj is the training objective function value of the XGBoost model; n is the number of samples; The training loss function that measures the difference between the predicted value and the true target value; y i Let i be the true target value of the i-th sample; Let f be the target value for the i-th sample; K is the number of decision trees; f k Let be the prediction function corresponding to the k-th regression tree; Let be the regularization term for the k-th tree; The expanded form of the regularization term is expressed as: ， Among them, T k The number of leaf nodes; y is the leaf node weight vector; γ and λ are regularization coefficients.

4. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 3, characterized in that, In step S40, the interpretability analysis of the surrogate model using the SHAP method is performed to obtain the contribution of each input feature to the prediction results of toughness, compressive strength, and flowability, including: ， in, The proxy model's prediction result for the i-th sample; Output as the model baseline; Let m be the SHAP contribution value of the j-th feature to the prediction result of the i-th sample; when When the value is positive, it indicates that the j-th input feature improves the prediction result of the sample relative to the baseline output; when... When the value is negative, it indicates that the j-th input feature causes the prediction result of the sample to decrease relative to the benchmark output.

5. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 1, characterized in that, In step S40, determining the key features affecting the reverse optimization of the mix ratio, the contribution direction of the key features, and the reasonable value range based on the contribution degree includes: Calculate the average absolute contribution of each feature across all samples: ， in, is the average absolute contribution of the j-th feature in all samples, and N is the total number of samples; Let m be the SHAP contribution value of the j-th feature to the prediction result of the i-th sample; when When the value is positive, it indicates that the j-th input feature improves the prediction result of the sample relative to the baseline output; when... When the value is negative, it indicates that the j-th input feature causes the prediction result of the sample to decrease relative to the benchmark output; according to The size of all input features is sorted to obtain a set of key features that affect toughness, compressive strength and flowability; Analyze the contribution direction of each feature to the model output; Analyze any two input features x q and x p The interaction contribution value of SHAP in each sample Significant interaction feature combinations are identified based on the average absolute interaction contribution, and the contribution direction and favorable joint value range of the significant interaction feature combinations are determined based on the distribution of the interaction contribution values ​​of the SHAP.

6. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 1, characterized in that, In S50, The probabilistic constraint that the compressive strength satisfies is: ， Where x is the mix proportion parameter vector; f c (x) represents the predicted compressive strength; f c,min ε1 represents the lower limit threshold of the compressive strength constraint and the probability of default allowed by the compressive strength constraint. The probabilistic constraints that the mobility must satisfy are: ， Where Flow(x) is the predicted flow rate; Flow min ε is the lower limit threshold for liquidity; ε2 is the allowed default probability of the liquidity constraint; Material cost constraints are: ， in, Cost is the material cost per unit volume. max Subject to the highest budget constraint; Carbon emission constraints are: ， in, Carbon emissions per unit volume; max As a constraint on carbon emission limits; Variable boundaries are represented as: ， Where, x min and x max These are the lower and upper limits of the mixing ratio parameters, respectively.

7. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 6, characterized in that, In step S50, the construction of the reverse design optimization model for mix proportions under probabilistic constraints includes: Let the vector of mix proportion parameters to be optimized be: ， Where C represents cement content; SF represents silica fume content; FA represents fly ash content; SL represents slag powder content; MK represents metakaolin content; CS represents granulated bead content; and S represents fine aggregate content. Water-cement ratio; SP is the amount of water-reducing agent; FiberType is the fiber type; L f / D f V is the fiber aspect ratio; f This refers to the fiber volume content; The overall resilience target T(x) is: ， Among them, K IC ' (x), G w '(x) and BT'(x) are the normalized fracture toughness, fracture energy, and flexural strength indices, respectively; α1, α2, and α3 are weighting coefficients, and α 1+ α² + α³ = 1; The reverse design optimization model for mix proportions under probability constraints is as follows: maxT(x).

8. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 7, characterized in that, In step S60, the step of establishing the objective function Gaussian process model and the constraint function Gaussian process model using a constraint-based Bayesian optimization algorithm includes: Using the Latin hypercube sampling method, at the variable boundary... Internal generation of an initial candidate mix design set: ， in, Let n be the initial candidate mix design set; n is the number of initial candidate points. For each initial candidate point The XGBoost model was used to calculate the predicted values ​​of toughness, compressive strength, and fluidity. Based on the raw material usage, the material cost per unit volume and carbon emissions per unit volume were calculated to obtain the initial observation dataset. ， Where g1(x) is the compressive strength constraint function; g2(x) is the flowability constraint function; g3(x) is the material cost constraint function; g4(x) is the carbon emission constraint function; and m is the constraint function number. With the initial observation dataset Based on this, Gaussian process models for the comprehensive resilience target and each constraint are established respectively; For the resilience maximization problem, let the currently obtained optimal feasible resilience target value be T. best Then the unconstrained expected improvement value EI(x) of the mix proportion parameter vector x is expressed as: ， Where, μ T (x) represents the predicted mean of the Gaussian process model output; σ T (x) represents the prediction standard deviation of the Gaussian process model output; ， It is the standard normal distribution function; It is the probability density function of the standard normal distribution; For the m-th constraint function g m If (x)≤0, the probability that the constraint is satisfied is expressed as: ， in, Let be the predicted mean of the m-th constraint function output by the Gaussian process model; Let be the prediction standard deviation of the m-th constraint function output by the Gaussian process model.

9. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 8, characterized in that, In step S60, solving the mix design optimization model using the objective function Gaussian process model and the constraint function Gaussian process model, and selecting candidate mix ratios through the constrained expectation improvement function to obtain a set of candidate mix ratio solutions that satisfy the probability constraints, includes: The unconstrained expected improvement value of the resilience target is determined based on the Gaussian process model of the objective function. The probability of satisfying each constraint condition is determined based on the Gaussian process model of the constraint function. The constrained expected improvement function is then constructed as follows: ， in, This represents a limited expected improvement value; This represents the unconstrained expected improvement in resilience targets; Let M be the probability of satisfying the m-th constraint; M is the number of constraints. The reverse design optimization model for the mix proportion is iteratively solved using the maximization of the constrained expected improvement function as the search criterion. In the t-th round of optimization iteration, the mix proportion parameter vector that maximizes the constrained expected improvement value within the design space that satisfies the upper and lower bound constraints of the variables is determined as the candidate mix proportion for the next round: ， Where X is the design space that satisfies the upper and lower bound constraints of the variables; The XGBoost model was used to calculate the predicted values ​​of toughness, compressive strength, and fluidity of the candidate mix proportions, and the material cost and carbon emissions were calculated based on the amount of raw materials used. The candidate combination ratio x t+1 The corresponding objective function values ​​and constraint function values ​​are added to the observation dataset, and the objective function Gaussian process model and the constraint function Gaussian process model are retrained based on the updated observation dataset; Repeat the iterative process until the stopping condition is met to obtain the candidate mix designation solution set: ， Each candidate mix design satisfies the probability constraints of compressive strength, probability constraints of fluidity, cost constraints, carbon emission constraints, and variable boundary constraints.

10. The reverse design method for ultra-high performance concrete mix proportions based on probabilistic constraints according to claim 1, characterized in that, include: In step S60, determining the recommended mix design from the candidate mix design solution set includes: Candidates with a compressive strength requirement that is less than the first probability threshold, a flowability requirement that is less than the second probability threshold, a cost that exceeds the maximum budget constraint, or a carbon emission requirement that exceeds the carbon emission ceiling constraint will be eliminated. The remaining candidate solutions are sorted from high to low according to the comprehensive resilience target T(x), and the highest comprehensive resilience target value among the candidate solutions is determined. Candidate solutions whose relative difference between the comprehensive resilience target value and the highest comprehensive resilience target value is less than or equal to a preset proportion threshold are determined as preferred candidate solutions; The preferred candidate solutions are ranked according to material cost and carbon emissions, and preferred candidate solutions whose contribution direction or value range of key features does not conform to the SHAP analysis results are eliminated. From the retained preferred candidate schemes, the preferred candidate mix ratio with the highest comprehensive toughness target value, the probability of satisfying the compressive strength is greater than or equal to the first probability threshold, and the probability of satisfying the flowability is greater than or equal to the second probability threshold is selected as the recommended mix ratio scheme.

Images