BN-based UHPC mix proportion data analysis method and strength prediction system

Abstract

The invention relates to the technical field of data processing, in particular to a BN-based UHPC mix proportion data analysis method and a strength prediction system.The intelligent level of ultra-high performance concrete mix proportion design is improved by introducing a Bayesian network model and a multi-objective optimization algorithm, and the method comprises the steps that firstly, an enhanced feature set is generated through feature engineering; a nonlinear relationship and a cross-level interaction effect among material parameters are fully excavated, and the characterization capability of the model on a complex material system is enhanced; secondly, the Bayesian network model is combined with causal reasoning and a hierarchical regularization strategy, so that the overfitting risk is reduced while the compressive strength prediction precision is ensured; in the multi-objective optimization link, through dynamic weight adjustment and Pareto frontier search, carbon emission and strength requirements are effectively balanced, and candidate schemes with low carbon and excellent mechanical properties are output; and finally, dynamic evaluation and risk analysis are carried out to further screen out a mix proportion with high stability and strong feasibility, and a reliable decision basis is provided for engineering practice.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and more specifically, to a BN-based UHPC mix proportion data analysis method and intensity prediction system. Background Technology

[0002] Currently, the mix design of ultra-high performance concrete (UHPC) faces a dual technical bottleneck.

[0003] On the one hand, traditional design methods rely excessively on empirical trial and error and static packing models, making it difficult to quantify the dynamic influence of multi-scale factors such as hydration reaction and particle size distribution on mechanical properties of cementitious materials. For example, while optimizing pore structure through rheological property range constraints and the densest packing model can improve compressive strength, it does not establish an explicit causal relationship between raw material proportioning parameters and microstructure evolution, resulting in a lack of physical mechanism guidance for mix proportion adjustments.

[0004] On the other hand, while existing intelligent methods employ deep learning to construct multi-scale performance prediction models, reducing trial-and-error costs, their black-box modeling cannot trace the key causal paths of strength formation and lacks integration of carbon emission constraints, making it difficult to achieve low-carbon design goals. A more prominent contradiction lies in the fact that while existing machine learning models can capture the nonlinear relationship between material parameters and macroscopic properties, their ability to characterize cross-level interactive features such as the oxide composition, particle size distribution, and synergistic effects of activators in cementitious materials is insufficient. Furthermore, the weighting strategy for curing performance and environmental indicators during optimization easily leads to candidate solutions getting trapped in local optima. Simultaneously, existing carbon emission assessments mostly employ static calculation rules, failing to form a closed-loop feedback with dynamic mix design optimization, making it difficult to simultaneously achieve low-carbon goals and strength requirements.

[0005] Therefore, the aforementioned shortcomings make it difficult for the existing UHPC design system to meet the dual requirements of high performance and low carbon emissions. It is urgent to develop a UHPC design system that combines physical interpretability and multi-objective dynamic optimization capabilities, which is a technical problem that needs to be solved at present. Summary of the Invention

[0006] In order to at least improve the above-mentioned deficiencies in the prior art, one of the objectives of the present invention is to provide a BN-based UHPC mix proportion data analysis method and strength prediction system.

[0007] A first aspect of this invention provides a BN-based UHPC mix proportion data analysis method, the method being executed through a strength prediction system. The method includes: acquiring a material parameter sample set for ultra-high performance concrete, the material parameter sample set comprising multiple material parameter combinations, each material parameter combination including cementitious particle oxide composition, cementitious particle size distribution, water-cement ratio, water-reducing agent dosage, chemical activator dosage, mortar-cement ratio, aggregate particle size distribution, and steel fiber content; performing feature processing on the material parameter sample set to generate an enhanced feature set containing nonlinear derived features and cross-level interaction features; and further... For the enhanced feature set, a Bayesian network model is invoked to predict compressive strength, obtaining the predicted strength value for each material parameter combination. The Bayesian network model determines its network structure through an initial causal network topology and multi-algorithm collaborative search optimization, and employs a hierarchical regularization strategy for parameter optimization. Based on preset carbon emission calculation rules and the predicted strength values, a Pareto front search is performed on the material parameter combinations using a multi-objective optimization algorithm to generate candidate mix proportion schemes that satisfy dual-objective constraints. Dynamic weight evaluation and risk confidence analysis are performed on the candidate mix proportion schemes to output the optimal low-carbon mix proportion result set.

[0008] This invention significantly improves the intelligence level of ultra-high performance concrete (UHPC) mix design by introducing a Bayesian network model and a multi-objective optimization algorithm. It visualizes the causal relationships affecting UHPC performance, achieving a breakthrough in the interpretability of machine learning models from a mechanistic perspective. First, enhanced feature sets are generated through feature engineering to fully explore the nonlinear relationships and cross-level interaction effects between material parameters, enhancing the model's ability to characterize complex material systems. Second, the Bayesian network model, combined with causal inference and hierarchical regularization strategies, reduces the risk of overfitting while ensuring the accuracy of compressive strength prediction. The multi-objective optimization stage effectively balances carbon emissions and strength requirements through dynamic weight adjustment and Pareto front search, outputting candidate solutions that are low-carbon and possess excellent mechanical properties. Finally, dynamic evaluation and risk analysis further screen for mix proportions with high stability and feasibility, providing a reliable decision-making basis for engineering practice.

[0009] A second aspect of the present invention provides an intensity prediction system, including a processor and a memory and a bus connected to the processor; wherein the processor and the memory communicate with each other through the bus; the processor is used to call program instructions in the memory to execute the above-described BN-based UHPC mix proportion data analysis method. Attached Figure Description

[0010] Figure 1 This is a flowchart of a BN-based UHPC mix proportion data analysis method provided in an embodiment of the present invention.

[0011] Figure 2 This is the initial topology of the Bayesian network provided in the embodiment of the present invention.

[0012] Figure 3 This is a multi-scale causal network topology diagram provided in an embodiment of the present invention.

[0013] Figure 4 This is an example diagram of a Bayesian network model provided in an embodiment of the present invention.

[0014] Figure 5 This is a block diagram of an intensity prediction system provided in an embodiment of the present invention. Detailed Implementation

[0015] Please see Figure 1 The flowchart below illustrates a BN-based UHPC mix proportion data analysis method according to an optional embodiment of the present invention. This method can be applied to an intensity prediction system. In this embodiment, the intensity prediction system can be a computer, tablet, or other computer device capable of data analysis and processing, and is not limited thereto. Optionally, the method includes steps 110-150:

[0016] Step 110: The strength prediction system obtains a sample set of material parameters for ultra-high performance concrete. The sample set of material parameters includes multiple combinations of material parameters. Each combination of material parameters includes the oxide composition of cementitious particles, particle size distribution of cementitious particles, water-cement ratio, water-reducing agent dosage, chemical activator dosage, mortar-cement ratio, aggregate particle size distribution, and steel fiber content.

[0017] In this embodiment, the strength prediction system constructs a sample set of material parameters for ultra-high performance concrete through systematic data collection and standardization. Specifically, the strength prediction system uses the Web of Science core database as a foundation and employs the compound search query "((TL=(UHPC))AND AB=(CO2 OR'carbon emission'OR GWP))" to search for literature from September 30, 2000 to September 30, 2023, initially obtaining 40 relevant studies.

[0018] Understandably, the process involved four stages of rigorous screening: first, three duplicate articles were eliminated; then, nine irrelevant studies (such as structural component analysis and studies without mix proportion data) were excluded based on their titles and abstracts; then, 14 articles (including two review articles) were excluded after a thorough reading of the full text; and finally, 15 valid articles were retained.

[0019] For each document, the strength prediction system extracts six core parameters: the particle size distribution of cementitious materials (e.g., CaO content of 52.3±3.8% and SiO2 content of 28.7±2.5% in cement), the particle size distribution of cementitious materials (measured using a laser particle size analyzer: D10 = 2.1μm, D50 = 15.3μm, D90 = 48.7μm), the water-cement ratio (range 0.14-0.22), and the dosage of water-reducing agent (calculated based on solid content as 4.2-12.6 kg / m³). 3 The following parameters are considered: dosage of chemical activator (e.g., sodium hydroxide to cementitious material mass ratio 0.03-0.10), cement-sand ratio (1.0-1.3:1), aggregate particle size distribution (the gradation curve of manufactured sand conforms to Fuller equation n = 0.45 ± 0.05), and steel fiber content (0-2.5% volume fraction).

[0020] For example, a literature sample records a belite cement usage of 315 kg / m³. 3 Silica fume 214kg / m 3 425 kg / m³ of basalt powder 3 The reactive index X0 of the cementitious material was calculated to be 0.87 by the benchmark cement comparison method, the active CaO / SiO2 molar ratio Y1 = 1.82, the active SO3 / Al2O3 molar ratio Y2 = 0.41, the particle packing density Y3 calculated based on the improved CPM model was 0.79, and the compressive strength reached 143.6 MPa after 28 days under curing temperature of 60℃.

[0021] Step 120: The strength prediction system performs feature processing on the material parameter sample set to generate an enhanced feature set containing nonlinear derived features and cross-level interactive features.

[0022] In this step, the intensity prediction system performs multi-dimensional feature engineering to construct an enhanced feature set. The system first constructs nonlinear features based on a Taylor expansion of a third-order polynomial, for example, expanding the water-cement ratio X1 to X1. 2 X1 3 The reactivity X0 of the cementitious material was logarithmically transformed using ln(X0+1). Cross-level interaction features were constructed using a mechanism-driven approach, for example, by designing (Y1×Y3) / (X2+0.1) to characterize the synergistic effect between hydration activity and packing density, where Y1 is the molar ratio of active CaO / SiO2, Y3 is the initial particle packing density, and X2 is the amount of activator. In the feature selection stage, an elastic net regularization model was used for variable screening, with the objective function defined as:

[0023] min_{β}left{frac{1}{2n}sum_{i=1}^{n}(Z1_i-β^Tφ(x_i))^2+λ(α|β|_1+(1-α)|β|_2^2)right}.

[0024] The regularization parameters α = 0.95 and λ = 0.032 (determined through 10-fold cross-validation) retain the characteristic that the absolute value of the standardized coefficient is greater than 0.01. In actual calculations, the cubic term X1 of the water-to-glue ratio... 3 The elasticity coefficient is 0.023, and the coefficient of the interaction term (Y1×Y3) is 0.156. Both of them passed the threshold screening and entered the feature set.

[0025] The intensity prediction system further employs Bootstrap resampling 1000 times to calculate feature stability. For example, the active CaO / SiO2 molar ratio Y1 was selected in 987 samples, with a selection probability of 98.7%; while the quadratic term of the activator dosage X2 appeared only 312 times, and was removed with a probability of 31.2%. The final feature set contains 8 original variables and 15 derived features, and principal component analysis verified that the multicollinearity (VIF) values ​​were all below 4.0.

[0026] Step 130: Based on the enhanced feature set, the strength prediction system calls the Bayesian network model to predict the compressive strength and obtain the strength prediction value for each material parameter combination; wherein, the Bayesian network model determines the network structure through an initial causal network topology and multi-algorithm collaborative search optimization, and adopts a hierarchical regularization strategy for parameter optimization.

[0027] In this embodiment, the strength prediction system constructs a Bayesian network prediction model based on a hybrid constraint learning framework. The network topology consists of three layers: the root node layer includes the reactivity of the cementitious material X0 (K value range 0.72-1.15), the water-cement ratio X1 (0.14-0.22), the activator dosage X2 (0-94.2 kg / m3), the mortar-cement ratio X3 (1.0-1.3), and the steel fiber content X4 (0-2.5% vol); the intermediate node layer includes the molar ratio of active oxides Y1 (1.2-2.3), Y2 (0.3-0.7), and the initial particle packing density Y3 (0.68-0.85); the leaf node layer is the 28-day compressive strength Z1 (75-243 MPa). During the structure learning phase, a combination of tabu search (weight 0.6), hill climbing algorithm (weight 0.3), and MMHC algorithm (weight 0.1) is used for optimization, and edge stability is verified by 100 Bootstrap resampling iterations. For example, the probability of the causal relationship between steel fiber content X4 and compressive strength Z1 is 93.2%, and the probability of the causal relationship between packing density Y3 and Z1 is 87.5%, both exceeding the 80% confidence threshold. Parameter learning employs a hierarchical regularization strategy, implementing Bayesian ridge regression on the core variable Z1.

[0028] hat{β}=argmin_{β}left{sum_{i=1}^{n}(y_i-β^Tx_i)^2+λ|β|_2^2right}.

[0029] The dynamic regularization coefficient is adjusted according to λ(t) = 0.1 × exp(-0.01 × ESS(t)), where the effective sample size ESS(t) is calculated based on Cook distance weighting. When the inputs are X0 = 0.85, X1 = 0.16, Y1 = 1.78, and Y3 = 0.81, the model output Z1 = 138.6 MPa, with a 95% confidence interval of [132.4, 144.8] MPa. Model validation shows that the mean RMSE = 9.3 MPa, MAE = 7.1 MPa, and R² = 0.872. The residual distribution is confirmed to be normal by the KS test (p = 0.213).

[0030] Step 140: The intensity prediction system performs Pareto front search on the material parameter combination using a multi-objective optimization algorithm based on the preset carbon emission calculation rules and the intensity prediction value, and generates candidate mix proportion schemes that satisfy the dual objective constraints.

[0031] In this embodiment, the strength prediction system establishes a dual-objective optimization model of compressive strength and carbon emissions. Carbon emissions are calculated according to the formula:

[0032] E_{UHPC}=sumM_i*E_i+E_p+E_c+E_t*2.

[0033] Among them, the carbon emission factors for cement are E_i = 0.82 kg / kg, silica fume E_i = 0.12 kg / kg, basalt powder E_i = 0.06 kg / kg, and the transportation distance is calculated as 100 km, E_t = 0.012 kg / kg·km. The strength prediction system calls the NSGA-II algorithm to perform Pareto front search, setting the population size to 200, crossover probability to 0.85, mutation probability to 0.02, and generation number to 100. In the standardization stage, the compressive strength is normalized according to fnorm = (Z1-75) / (243-75), and the carbon emission is inversely normalized according to Enorm = 1-(E-622) / (1200-622). A certain volume solution corresponds to a mix ratio of 30% cement, 1.8% steel fiber, and a water-cement ratio of 0.17, with a predicted strength Z1 = 142.3 MPa (fnorm = 0.87) and carbon emission E = 712 kg / m. 3 (Enorm = 0.79), the overall score is Score = 0.87 × 0.6 + 0.79 × 0.4 = 0.838. After 100 generations of evolution, the system generates a Pareto front containing 85 non-dominated solutions. Three-dimensional visualization shows the optimal solution set at compressive strength of 140-160 MPa and carbon emissions of 650-750 kg / m³. 3The interval forms a convex distribution, confirming a significant negative correlation between intensity and carbon emissions (Pearson's r = -0.793).

[0034] Step 150: The intensity prediction system performs dynamic weight evaluation and risk confidence analysis on the candidate mix proportion schemes, and outputs the optimal low-carbon mix proportion result set.

[0035] In this embodiment, the intensity prediction system implements multi-criteria decision analysis. First, the target weights are calculated using the entropy weight method. Based on the coefficient of variation of compressive strength (0.18) and carbon emission (0.23), the final weights are determined to be wf = 0.62 and wE = 0.38. The risk analysis module evaluates the stability of the proposed scheme through 10,000 Monte Carlo simulations. For example, if a candidate scheme predicts an intensity Z1 = 135.4 MPa, the probability of it being below 120 MPa is 3.2%, and the carbon emission exceeds 800 kg / m³. 3 The probability is 1.7%. The system ultimately outputs 5 optimal low-carbon mix proportions, with a typical scheme including 350kg / m³ of Belite cement. 3 Silica fume 214kg / m 3 2.0% vol steel fiber, measured strength 128.7 MPa (predicted value 132.5 MPa), carbon emissions 689 kg / m³ 3 The flowability was 225 mm, and the flexural strength ratio was 0.24. All schemes were tested using a t-test, which confirmed that the prediction error was not statistically significant (p>0.05), verifying the engineering applicability of the strength prediction system. The final technical report generated by the system includes material cost analysis, process feasibility assessment, and sensitivity analysis, providing complete decision support for the industrial production of low-carbon ultra-high performance concrete.

[0036] In one optional implementation, the step of obtaining the material parameter combination further includes:

[0037] Step 111: Obtain quantitative data of cementitious materials; wherein, the quantitative data of cementitious materials includes the amount of cementitious materials used or the mixing ratio.

[0038] In step 111, the strength prediction system obtains quantitative data on cementitious materials through literature data collection and standardization transformation. Specifically, the system (strength prediction system) extracts cementitious material composition information from the literature database; for example, a literature document states that the mix proportion of UHPC is 315 kg / m³ of Belite silicate cement. 3 Silica fume 214kg / m 3 425 kg / m³ of basalt powder 3 The dosage of each component is uniformly converted into a standard dosage per unit volume.

[0039] The system automatically identifies the types of cementitious materials in the mix proportions, including pozzolanic materials and industrial by-products, and establishes a structured storage matrix. Each row corresponds to a mix proportion sample, and the column vectors record the cement dosage (0-1251.2 kg / m³). 3 ), silica fume usage (0-1242.7kg / m³) 3 Slag usage (0-1058.2 kg / m³) 3 Precise values ​​such as ) are provided. For the steel fiber volume fraction parameter, the system converts the 1.8% volume fraction reported in the literature to 19.6 kg / m³. 3 (Steel fiber density 7800 kg / m³) 3 Ensure that all parameters conform to the International System of Units (SI).

[0040] Step 112: Based on the preset particle compaction model, process the oxide composition of the cementitious material particles, the particle size distribution of the cementitious material particles, and the quantitative data of the cementitious material to obtain the initial particle packing density index that reflects the particle packing effect.

[0041] In step 112, the strength prediction system calculates the initial particle packing density index based on an improved continuous particle size distribution model (CPM model). Specifically, the system inputs the particle size distribution data of a sample of cementitious materials: cement D10 = 2.1 μm, D50 = 15.3 μm, D90 = 48.7 μm, silica fume D50 = 0.8 μm, and basalt powder D50 = 12.5 μm. When the system performs the close packing simulation calculation, it first discretizes the particles of each component, dividing them into 100 particle size intervals, and uses an iterative optimization algorithm to solve for the optimal packing ratio. The calculated initial particle packing density Y3 of the sample is 0.79, corresponding to a porosity of 21%. For steel fiber-containing mix proportions, the system treats the fiber as a rigid cylinder (0.2 mm in diameter and 13 mm in length) and uses an improved MAA model to calculate its influence factor on the packing system. When the volume content of steel fiber reaches 2%, the system automatically deducts the volume occupied by the fiber and recalculates the density of the aggregate-cement system.

[0042] Step 113: Based on the reactivity of the cementitious material, the oxide composition of the cementitious material particles, and the quantitative data of the cementitious material, obtain the corrected molar ratio index of the hydration effect of the reactive cementitious material; wherein, the corrected molar ratio index includes the CaO / SiO2 molar ratio index and the SO3 / Al2O3 molar ratio index.

[0043] In step 113, the strength prediction system calculates the corrected molar ratio index based on the oxide composition of the cementitious material. First, it analyzes the chemical composition of a sample cementitious material: Belite cement contains 52.3% CaO and 28.7% SiO2, silica fume contains 94.5% SiO2, and basalt powder contains 18.2% Al2O3 and 2.1% SO3. The system applies the active oxide correction formula to calculate the total active CaO content by weighting each component according to its mass ratio: (315×0.523)+(214×0)+(425×0.032)=168.7kg / m³ 3 The active SiO2 content is: (315×0.287)+(214×0.945)+(425×0.381)=387.6kg / m³ 3 Therefore, the corrected active CaO / SiO2 molar ratio Y1 = (168.7 / 56) / (387.6 / 60) = 1.82 is obtained. At the same time, the active SO3 / Al2O3 molar ratio Y2 = (425 × 0.021 / 80) / (425 × 0.182 / 102) = 0.41 is calculated. The system automatically verifies whether the molar ratio calculation results are within a reasonable range (Y1 ∈ [1.2, 2.3], Y2 ∈ [0.3, 0.7]) and initiates the data review process for outliers.

[0044] Step 114: Generate a combination of material parameters using the initial particle packing density index and the corrected molar ratio index.

[0045] In step 114, the strength prediction system integrates multi-dimensional parameters to generate a complete combination of material parameters. The processing results from steps 111-113 are matrix-concatenated to form a feature vector containing 12 dimensions. For example, a sample feature vector might be: X0 = 0.87 (cementing material reactivity), X1 = 0.16 (water-cement ratio), X2 = 0.05 (activator dosage), X3 = 1.1 (mortar-cement ratio), X4 = 1.8% (steel fiber content), Y1 = 1.82, Y2 = 0.41, Y3 = 0.79, and also includes auxiliary parameters such as aggregate gradation parameters (manufactured sand D50 = 0.45mm) and curing temperature of 60℃. The system establishes a parameter correlation verification mechanism. When a water-cement ratio X1 = 0.22 is detected, the system automatically correlates and verifies whether the water-reducing agent dosage is ≥12kg / m³, ensuring the physical rationality of the parameter combination.

[0046] In one alternative implementation, step 120, which involves performing feature processing on the material parameter sample set to generate an enhanced feature set containing nonlinear derived features and cross-level interaction features, includes:

[0047] Step 121: Extract original feature variables from the material parameter sample set. The original feature variables include: cementitious material particle oxide composition, cementitious material particle size distribution, water-cement ratio, water-reducing agent dosage, chemical activator dosage, mortar-cement ratio, aggregate particle size distribution, steel fiber content, initial particle packing density index of reactive particle packing effect, and corrected molar ratio index of reactive cementitious material hydration effect.

[0048] In step 121, the strength prediction system extracts original feature variables from the combination of material parameters. For example, a 16-dimensional original feature vector can be constructed, which includes the amount of cementitious material (cement 315 kg / m³). 3 Silica fume 214kg / m 3 The system records parameters such as particle size (cement D50 = 15.3 μm), chemical composition (CaO 52.3%), and process parameters (water-cement ratio 0.16). For aggregate particle size distribution, the system uses a Fuller curve fitting parameter n = 0.45 as the characteristic value, and also records morphological parameters such as the steel fiber aspect ratio (65:1). The system performs data integrity checks; for missing activator dosage fields, it interpolates using the average value of similar materials (0.03) and adds a data missing marker.

[0049] Step 122: Perform a nonlinear transformation on the original feature variables using the third-order Taylor expansion approximation method to generate the first type of derived features.

[0050] In step 122, the intensity prediction system uses the third-order Taylor expansion approximation method to generate nonlinear derived features. Taking a water-cement ratio of X1 = 0.16 as an example, the system calculates its quadratic term X1. 2 =0.0256, cubic term X1 3 =0.0041, and the logarithmic transformation of the cementitious material reactivity X0 = 0.87 yields ln(X0+1) = 0.642. For the corrected molar ratio index Y1 = 1.82, the system constructs a (Y1-μ) / σ normalized feature, where μ = 1.65 and σ = 0.23, resulting in a normalized value of 0.739. The system also generates interaction term features, such as X1×Y3 = 0.16×0.79 = 0.126, which are recorded in the derived feature matrix.

[0051] Step 123: Based on the cross-level interaction between gelation hydration activity and gelation material stacking effect, construct the second type of derived feature.

[0052] In step 123, the intensity prediction system constructs cross-level interactive features to characterize the hydration-accumulation synergistic effect. Based on the hydration activity parameter Y1 = 1.82 and the packing density Y3 = 0.79, a nonlinear interaction term (Y1 × Y3) / (X2 + 0.1) = (1.82 × 0.79) / (0.05 + 0.1) = 9.63 is constructed. Simultaneously, mechanism-driven features such as (Y1 2 ×Y3) / (X1+0.01)=(1.82 2 (×0.79) / (0.16+0.01)=14.2, capturing the nonlinear relationship between hydration reaction and particle packing. The system verifies the physical meaning of the interaction term and ensures that its numerical range meets expectations (e.g., 0-20).

[0053] Step 124: Standardize and concatenate the original feature variables, the first type of derived features, and the second type of derived features to obtain an initial enhanced feature set.

[0054] In step 124, the intensity prediction system performs feature standardization and concatenation to form an initial enhanced feature set. Z-score standardization is applied to both the original and derived features; for example, the water-glue ratio X1 = 0.16 is converted to (0.16 - 0.18) / 0.03 = -0.67. For the interaction term feature (Y1 × Y3) = 1.44, the standardized value is (1.44 - 1.25) / 0.35 = 0.54. The system ultimately generates an enhancement matrix containing 31 dimensions: 8 original features, 15 nonlinear features, and 8 interaction features, ensuring consistent dimensions across all features.

[0055] Step 125: Call the elastic network regularization model to perform sparse filtering on the initial enhanced feature set, retaining features in the initial enhanced feature set whose absolute value of the normalized coefficient is higher than a preset threshold, and generate the final enhanced feature set.

[0056] In one alternative embodiment, sparse filtering of the resilient network regularization model includes:

[0057] Step 1250: Set the elastic network mixing parameter α to be biased towards L1 regularization to enhance feature sparsity; determine the optimal value of the regularization strength λ through multi-fold cross-validation; calculate the selection frequency of each feature under Bootstrap resampling, and retain features with frequencies higher than a set proportion; perform multicollinearity test on the selected features, and remove features with variance inflation factors greater than a preset value to obtain the final enhanced feature set; wherein, the final enhanced feature set is used to map to the input layer of the Bayesian network model.

[0058] In step 1250, the intensity prediction system implements elastic network regularization feature screening. Specifically, the mixing parameter α = 0.95 and the regularization intensity λ = 0.032 (determined through 10-fold cross-validation) can be set, and the objective function can be applied: min_β{1 / (2×136)Σ(Z1_i-β^TΦ(x_i)) 2 +0.032×(0.95|β|1+0.05|β|2 2 After iterative solution, the cubic term X1 of the water-cement ratio is obtained. 3 The coefficient β = 0.023, and the β of the interaction term (Y1×Y3) = 0.156, both exceed the threshold of 0.01 and are retained. The system performs 1000 Bootstrap resampling cycles and calculates the selection frequency of each feature. For example, Y1 is selected in 987 samples (98.7%), and X2... 2 Only 312 instances (31.2%) were removed. The final 18 retained features all had a VIF score <4.0, ensuring the validity and independence of the feature set.

[0059] In one exemplary implementation, the limiting edges of the initial causal network topology include: cementitious material hydration effect index → ​​compressive strength; cementitious material particle packing effect index → ​​compressive strength; water-cement ratio, mortar ratio, water-reducing agent dosage, chemical activator dosage, and steel fiber content → compressive strength; wherein, the compressive strength is a unique leaf node. Based on this, the step 130 of calling the Bayesian network model to predict the compressive strength includes:

[0060] Step 131: Based on prior knowledge or causal relationship analysis strategies, construct the initial structure of the Bayesian network and restrict the directed edges of the initial structure of the Bayesian network. The initial structure of the Bayesian network includes a material parameter layer, a reaction mechanism layer, and a compressive strength layer. The nodes of the material parameter layer are forced to point to the nodes of the reaction mechanism layer, and the nodes of the reaction mechanism layer are forced to point to the nodes of the compressive strength layer.

[0061] In step 131, the strength prediction system constructs an initial Bayesian network structure based on the multi-level causal relationship of material-mechanism-performance, dividing the nodes into three levels: material parameter layer, reaction mechanism layer, and compressive strength layer. The material parameter layer includes root nodes such as cementitious material reactivity X0 = 0.87, water-cement ratio X1 = 0.16, activator dosage X2 = 0.05, mortar-cement ratio X3 = 1.1, and steel fiber content X4 = 1.8%. The reaction mechanism layer includes intermediate nodes such as active CaO / SiO2 molar ratio Y1 = 1.82, active SO3 / Al2O3 molar ratio Y2 = 0.41, and initial particle packing density Y3 = 0.79. The compressive strength layer is the only leaf node Z1 = 143.6 MPa. The system enforces causal relationships between material parameter layer nodes and reaction mechanism layer nodes. For example, the reactivity X0 of cementitious materials directly affects the active CaO / SiO2 molar ratio Y1 through the oxide composition of cementitious materials, while the water-cement ratio X1 affects the active SO3 / Al2O3 molar ratio Y2 through the regulation of the hydration environment. Simultaneously, the system applies blacklist constraints to prohibit reverse causality, such as prohibiting the compressive strength Z1 from inversely affecting the steel fiber content X4, ensuring that the network topology conforms to the mechanisms of materials science.

[0062] Step 132: The initial structure of the Bayesian network is optimized using a hybrid constraint learning algorithm to obtain the optimized Bayesian network structure; wherein, the whitelist constrains the path from the authorized material parameter layer to the compressive strength layer, and the blacklist constrains the prohibition of reverse causal relationships.

[0063] In step 132, the strength prediction system uses a hybrid constraint learning algorithm to optimize the network structure. The whitelist authorizes potential paths from the material parameter layer to the compressive strength layer, for example, allowing steel fiber content X4 to directly point to Z1 (path probability initially set to 0.8). The blacklist isolates reverse causality between layers, for example, prohibiting compressive strength Z1 from pointing to mortar ratio X3. The system uses Kendall's tau test (significance level α = 0.01) to verify edge validity. For a sample of data, the tau of steel fiber content X4 and compressive strength Z1 is calculated to be 0.326 (p = 0.003), confirming that the edge is retained. The parent node number penalty term is calculated according to the formula Penalty(G) = Σexp(|Pa(v_i)|). When the number of parent nodes of a node exceeds 5, the penalty factor reaches exp(5) = 148.4, forcibly triggering pruning. After optimization, the number of network edges was reduced from the initial 48 to 22, and the critical paths included X0→Y1, X1→Y2, Y3→Z1, etc.

[0064] Step 133: By integrating the Bootstrap resampling hill-climbing algorithm, the tabu search algorithm, and the minimax hill-climbing algorithm, the Bayesian network optimization structure is searched using a multi-algorithm collaborative search. The Bayesian network parameters are dynamically adjusted based on a hierarchical regularization strategy to obtain the Bayesian network model. In the Bayesian network model, the core compressive strength node adopts Bayesian ridge regression, and the auxiliary nodes adopt maximum likelihood estimation.

[0065] In step 133, the intensity prediction system performs multi-algorithm collaborative search and hierarchical regularization parameter optimization. Specifically, it can integrate tabu search (weight 0.6), hill-climbing algorithm (weight 0.3), and maximum-minimum hill-climbing algorithm (weight 0.1) for structure search, and use the BGe scoring function to evaluate network quality. In the BGe scoring formula, the posterior covariance matrix S_i of node Z1 is 9.28, the degrees of freedom ν is 8, and the score P(D|G) is calculated as 3.2 × 10⁻⁶. -5 During the parameter learning phase, Bayesian ridge regression was used for the compressive strength node Z1, with its conditional probability distribution being N(β0+β1Y1+β2Y3, σ 2 The regularization coefficient λ = 0.1 × exp(-0.01 × ESS), and the effective sample size ESS = 136 × (1 / (1+0.32)) = 103. Auxiliary nodes such as Y1 are modeled using maximum likelihood estimation, with the conditional distribution modeled as Y1 = 0.87X0 + 0.12X2 + ε, where ε ~ N(0, 1.5). 2 After 100 Bootstrap resampling cycles, the probability of the existence of the critical edge Y3→Z1 reached 93.2%, confirming the stability of the network structure.

[0066] Step 134: Input the enhanced feature set into the Bayesian network model and output the intensity prediction value and the confidence interval of the intensity prediction value for each material parameter combination.

[0067] In step 134, the intensity prediction system inputs the enhanced feature set into the trained Bayesian network model to predict the intensity. For a sample feature vector [X0 = 0.85, X1 = 0.18, Y1 = 1.78, Y3 = 0.81], the model calculates the expected value of Z1 as 138.6 MPa, with a 95% confidence interval of [132.4, 144.8] MPa. The system simultaneously outputs the contribution of each parent node, where the partial regression coefficient β of Y3 = 0.81 on Z1 is 15.3, indicating that each increase of 0.01 in packing density can increase the intensity by 0.153 MPa. Model validation shows that the average RMSE on 136 training data sets is 9.3 MPa, and the MAE on the test set is 7.1 MPa. 2 =0.872, confirming that the prediction accuracy meets engineering requirements.

[0068] In a preferred embodiment, the dynamic adjustment step of the hierarchical regularization strategy includes:

[0069] Step 1331: Set the number of parent nodes of the compressive strength node as the core parameter, and use an exponential penalty term to control the network complexity.

[0070] In step 1331, the strength prediction system sets a penalty term for the number of parent nodes of the compressive strength node to control the model complexity. For example, according to the formula Penalty(G)=exp(|Pa(Z1)|), when the number of parent nodes of Z1 increases from 3 to 4, the penalty term increases from exp(3)=20.1 to exp(4)=54.6. The system forcibly limits the maximum number of parent nodes of Z1 to 5. When Pa(Z1)=6 is detected in a certain iteration, the edge with the lowest significance is automatically deleted (such as Y2→Z1, whose conditional probability coefficient β=0.08). Through this mechanism, in the final network structure, Z1 retains three parent nodes: Y1, Y3, and X4, balancing the model's expressive power and generalization performance.

[0071] Step 1332: Dynamically decay the regularization coefficient based on the effective sample size; where the decay rate is negatively correlated with the sample confidence level.

[0072] In step 1332, the intensity prediction system implements a dynamic regularization coefficient decay strategy. The initial regularization coefficient λ0 = 0.1 is set. When the effective sample size ESS(t) = 10³, λ(t) = 0.1 × exp(-0.01 × 10³) = 0.036 is calculated. This mechanism reduces the regularization strength when the data quality is high (high ESS), thus enhancing the model's fitting ability. For the Bayesian ridge regression of the compressive strength node Z1, when ESS = 120 in a certain iteration, λ is automatically adjusted to 0.1 × exp(-0.01 × 120) = 0.030, corresponding to a decrease in the standard deviation of the β estimate from ±2.1 MPa to ±1.8 MPa.

[0073] Step 1333: Apply a fixed regularization coefficient to the auxiliary nodes. The fixed regularization coefficient is used to suppress overfitting and maintain computational efficiency.

[0074] In step 1333, the intensity prediction system uses a fixed regularization coefficient for auxiliary nodes to improve computational efficiency. For example, the conditional probability modeling of node Y1 in the reaction mechanism layer uses maximum likelihood estimation, and a fixed L2 regularization coefficient λ = 0.01 is set. This value was determined through preliminary experiments. In 100 random samples, the mean square error of node Y1 stabilized between 0.22 and 0.25, and the computation time decreased from 8.7 seconds / time to 3.2 seconds / time. At the same time, the system monitors the risk of overfitting. When the ratio of training error to validation error of node Y1 exceeds 1.5, a λ value doubling mechanism is triggered, adjusting it up to a maximum of λ = 0.05.

[0075] Step 1334: Diagnose anomalous samples using Cook distance and reduce the weight of the anomalous samples to optimize parameter estimation.

[0076] In step 1334, the intensity prediction system diagnoses anomalous samples and adjusts their weights using Cook distance. For example, if the Cook distance D_i of a sample i is calculated to be 0.32, exceeding the threshold of 0.2, it is determined to be a point with strong influence. The system adjusts its weight to w_i = 1 / (1+0.32) = 0.75, reducing its impact on parameter estimation. In 1000 iterations, a total of 12 anomalous samples (8.8%) were identified. After adjustment, the model RMSE decreased by 1.2 MPa, and the p-value of the residual distribution KS test increased from 0.032 to 0.152, confirming the normality assumption.

[0077] Step 1335: Update the Bayesian network parameters based on a set period and verify the generalization ability of the Bayesian network model.

[0078] In step 1335, the strength prediction system performs periodic parameter updates and generalization capability verification. This means that after every 50 parameter iterations, the system calculates the generalization error metric on the retained 20% validation set. An early stop mechanism is triggered when the validation error increases by more than 5% over three consecutive cycles. For example, in a training iteration, if the validation RMSE in round 150 is 10.1 MPa, a 3.1% increase from 9.8 MPa in round 100, the system continues training; however, if the RMSE in round 200 is 10.7 MPa (a 9.2% increase), training is terminated and the system rolls back to the parameter state in round 180. The final model achieves an RMSE of 9.9 MPa on the independent test set, confirming that the generalization performance meets the target.

[0079] In one optional implementation, step 140, which involves performing a Pareto front search on the material parameter combination using a multi-objective optimization algorithm based on preset carbon emission calculation rules and the predicted intensity value, to generate candidate mix proportion schemes that satisfy dual-objective constraints, includes:

[0080] Step 141: Calculate the carbon emission value per unit volume of concrete based on the predicted strength value and the combination of material parameters, and generate a strength-carbon emission dual-objective dataset.

[0081] In step 141, the strength prediction system calculates the carbon emissions per unit volume of concrete based on the combination of material parameters and the strength prediction values ​​output by the Bayesian network. Specifically, the system invokes preset carbon emission calculation rules: for a given sample mix proportion, the cement content is 315 kg / m³. 3 (Carbon emission factor 0.82 kg / kg), silica ash 214 kg / m³ 3 (0.12kg / kg), basalt powder 425kg / m 3(0.06kg / kg), steel fiber 19.6kg / m 3 (2.34 kg / kg), calculate the carbon emissions from the raw materials: E_m = 315 × 0.82 + 214 × 0.12 + 425 × 0.06 + 19.6 × 2.34 = 386.2 kg / m 3 The carbon emissions from the combined preparation process, E_p, are 45 kg / m³. 3 (Stirring energy consumption), curing carbon emissions E_c = 32kg / m 3 (Standard maintenance), transportation carbon emissions E_t=0.012×100×2.5=3.0kg / m 3 (Distance 100km, transport coefficient 2.5), total carbon emissions E_UHPC=386.2+45+32+3.0=466.2kg / m 3 The system compares the predicted intensity value Z1 = 143.6 MPa with E_UHPC = 466.2 kg / m³. 3 The data is stored in association to form a dual-objective dataset of strength and carbon emissions, containing 200 candidate solutions. The compressive strength ranges from 121.5 to 158.7 MPa, and the carbon emissions range from 432.1 to 892.6 kg / m³. 3 ].

[0082] Step 142: Perform range normalization on the intensity-carbon emission dual-objective dataset to make the compressive strength and carbon emission values ​​in the same dimension space.

[0083] In step 142, the intensity prediction system performs range normalization on the dual-objective dataset to identify the global compressive strength maximum value f_max = 158.7 MPa and minimum value f_min = 121.5 MPa. The normalized value f_norm for a sample Z1 = 143.6 MPa is (143.6 - 121.5) / (158.7 - 121.5) = 0.594. The maximum carbon emission value E_max = 892.6 kg / m³. 3 Minimum value E_min = 432.1 kg / m 3 The corresponding sample E = 466.2 kg / m³ 3 The normalized value E_norm = 1 - (466.2 - 432.1) / (892.6 - 432.1) = 0.926. The system verifies the normalization result to ensure that f_norm ∈ [0, 1] and E_norm ∈ [0, 1], and establishes a mapping relationship matrix, where the data vector in the i-th row is [f_norm_i, E_norm_i, X0_i, X1_i, ..., Y3_i].

[0084] Step 143: Use the NSGA-II algorithm to filter the non-dominated solution set of the normalized intensity-carbon emission dual-objective dataset and generate the initial Pareto front.

[0085] In step 143, the intensity prediction system calls the Non-Dominated Sort Genetic Algorithm Type II (NSGA-II) to perform Pareto front search. Specifically, the population size is set to 200, the number of generations to 100, the crossover probability to 0.85, and the mutation probability to 0.02. The initial population is injected with candidate solutions generated by the Bayesian network. For example, an individual's gene encoding is [X0 = 0.85, X1 = 0.17, X4 = 1.8%, Y1 = 1.78, Y3 = 0.81], corresponding to target values ​​f_norm = 0.62 and E_norm = 0.89. The algorithm performs non-dominated sorting and calculates the dominance level of individuals: when individual A's f_norm = 0.62 ≥ individual B's 0.58 and E_norm = 0.89 ≥ individual B's 0.85, A is determined to dominate B. The first generation of the population generated 200 non-dominated solutions. Crowding calculations showed that the distribution density of the frontier solutions in the interval f_norm = 0.6-0.7 was 15 solutions / 0.1 interval.

[0086] Step 144: Iteratively optimize the initial Pareto front based on a dynamic weight adjustment strategy; wherein, the weight coefficients in the dynamic weight adjustment strategy change dynamically with the sample validity and carbon emission threshold.

[0087] In step 144, the intensity prediction system implements a dynamic weight adjustment strategy to optimize the Pareto front, setting initial weight coefficients w_f = 0.6 and w_E = 0.4. When carbon emissions in the population exceed 800 kg / m³, the system proceeds. 3 When the proportion of individuals exceeding 30% triggers the weight adjustment rule: w_E = min(0.6, 0.4 + 0.05 × N_violate / N_total), where N_violate = 65 individuals exceeding the standard, and N_total = 200, the calculated w_E = 0.4 + 0.05 × 65 / 200 = 0.416. The comprehensive score formula is then updated synchronously to Score = 0.584 × f_norm + 0.416 × E_norm, tilting the optimization direction towards low-carbon. After every 20 iterations, the system verifies the compressive strength constraint satisfaction rate. When the proportion of individuals with strength ≥ 120 MPa is below 95%, w_f = 0.6 + 0.1 × (1 - η), where η = 0.92, and the adjusted w_f = 0.608.

[0088] Step 145: Visualize the compressive strength, carbon emission value and comprehensive evaluation index through three-dimensional spatial mapping, output the final Pareto optimal solution set, and use the final Pareto optimal solution set to generate candidate mix proportion schemes that satisfy the dual objective constraints.

[0089] In step 145, the strength prediction system constructs a three-dimensional visualization spatial mapping Pareto optimal solution set, setting the coordinate system with the X-axis representing compressive strength (range 120-160 MPa) and the Y-axis representing carbon emissions (430-900 kg / m³). 3 The Z-axis represents the overall score (0-1). The spatial coordinates corresponding to a certain Pareto solution are (142.3MPa, 689kg / m²). 3 The system uses MATLAB's `scatter3` function to generate a scatter plot, marking leading-edge solutions as red cubes and non-dominated solutions as blue dots. Among the five optimal solutions output, solution B1 has coordinates (135.4 MPa, 622 kg / m²). 3 The value (0.812) is located at the inflection point of the leading edge curve, representing the optimal balance point between intensity and carbon emissions. The system exports a CSV file to record detailed parameters for each solution, such as the cement content of 30%, steel fiber content of 2.0%, and water-cement ratio of 0.17 for solution B1, and provides an interactive rotating view of the 3D graph.

[0090] In a preferred implementation, the iterative optimization of the NSGA-II algorithm includes:

[0091] Step 210: Inject candidate solutions generated by the Bayesian network during population initialization to accelerate the convergence process.

[0092] In step 210, the intensity prediction system injects high-quality candidate solutions generated by the Bayesian network during the NSGA-II initialization phase. From the 200 sets of prediction results output by the Bayesian network, the top 50 solutions with the highest comprehensive scores are selected as 50% of the initial seeds. For example, the genetic code of a certain seed individual is [X0 = 0.87, X1 = 0.16, X4 = 2.0%, Y1 = 1.82, Y3 = 0.79], corresponding to an intensity prediction value Z1 = 143.6 MPa and carbon emission E = 702 kg / m³. 3 This mechanism increases the proportion of high-intensity (Z1≥140MPa) individuals in the initial population from 12% to 38% of the randomly generated individuals, and reduces the number of generations for algorithm convergence from the original 120 generations to 80 generations, achieving an acceleration rate of 33.3%.

[0093] Step 220: Generate offspring population using simulated binary crossover and polynomial mutation operators.

[0094] In step 220, the intensity prediction system uses simulated binary crossover and polynomial mutation operators to generate offspring. For parent individuals P1 [X0 = 0.85, X1 = 0.17] and P2 [X0 = 0.88, X1 = 0.15], the crossover operator generates offspring C1 [X0 = 0.863, X1 = 0.161] with η_c = 20, calculated as β = ((2u)^(1 / (η_c+1)))|u ≤ 0.5; β = (1 / (2(1-u)))^(1 / (η_c+1))|u > 0.5, where u = 0.32. The mutation operator applies a perturbation to X4 = 1.8% with a probability of 0.02, generating a mutation amount of Δ = 0.15%, resulting in a new individual X4 = 1.95%. 100 offspring are generated per generation, merged with the parent individuals, and then subjected to non-dominated sorting.

[0095] Step 230: Sort the non-dominated solutions based on the crowding comparison operator and retain the individual with the best diversity.

[0096] In step 230, the intensity prediction system uses a crowding comparison operator to maintain population diversity. For example, it calculates the crowding distance of an individual in the target space: when its adjacent solutions differ by Δf = 3.2 MPa on the compressive strength axis and ΔE = 28 kg / m on the carbon emission axis. 3 At that time, the crowding distance L = √(3.2) 2 +28 2 = 28.2. The algorithm prioritizes retaining individuals with large crowding distances to ensure that the frontier solutions are uniformly distributed within the intensity axis range of 130-150 MPa. After 100 generations of evolution, the intensity standard deviation of the frontier solutions decreased from the initial 18.7 MPa to 9.3 MPa, and the carbon emission standard deviation decreased from 156 kg / m³. 3 Reduced to 74kg / m 3 This proves that the diversity preservation mechanism is effective.

[0097] Step 240: Set the number of iterations and adjust the weight coefficients once to meet the compressive strength constraint.

[0098] In step 240, the intensity prediction system periodically adjusts the weight coefficients to strengthen constraint satisfaction. This can be understood as follows: after every 20 generations, the proportion η of individuals in the population with a compressive strength ≥120 MPa is statistically analyzed. When η = 92%, the intensity weight coefficient Δw_f = 0.1 × (1 - 0.92) = 0.008 is increased according to the rules, raising w_f from 0.6 to 0.608. Simultaneously, the target standardization interval is dynamically updated. For example, when a new generation exhibits f_max = 162.3 MPa, f_norm = (Z1 - 121.5) / (162.3 - 121.5) is recalculated to ensure that the normalized value correctly reflects the population's evolutionary state. This strategy results in a constraint satisfaction rate of 98.5% in the final population, an improvement of 6.2 percentage points compared to the baseline algorithm.

[0099] Step 250: Output the Pareto front solution set and label the overall score ranking of each Pareto front solution.

[0100] In step 250, the strength prediction system outputs the Pareto front solution set with a comprehensive score. The 85 non-dominated solutions are sorted in descending order by Score = 0.6f_norm + 0.4E_norm, with the top 5 solutions having a Score ∈ [0.812-0.838]. The system generates an Excel report detailing the mix proportion parameters, predicted strength, carbon emissions, and ranking for each solution. For example, the solution ranked 1st is labeled as follows: cement content 32%, steel fiber 2.1%, water-cement ratio 0.165, predicted strength 145.2 MPa (+1.8%), carbon emissions 689 kg / m³. 3 (-3.2%), overall score 0.838. The strength-carbon emission tradeoff between solutions is also output; for example, an increase of 1 MPa in strength requires an additional 12.6 kg / m³ of carbon emissions. 3 This provides a quantitative basis for engineering decisions.

[0101] In one optional implementation, step 150, which involves performing dynamic weight evaluation and risk confidence analysis on the candidate mix design, includes:

[0102] Step 151: Construct a comprehensive evaluation index function, which integrates the weighted scores of normalized compressive strength and carbon emission value.

[0103] In step 151, the strength prediction system constructs a comprehensive evaluation index function to quantify the merits of the scheme. For example, the entropy weight method can be used to determine the target weights, calculated based on the coefficients of variation of 200 Pareto solutions: compressive strength coefficient of variation 0.18, carbon emission coefficient of variation 0.23, corresponding to weights w_f = 0.62 and w_E = 0.38. For a certain scheme, the normalized compressive strength f_norm = 0.87 (Z1 = 145.2 MPa), and the normalized carbon emission E_norm = 0.79 (E = 689 kg / m³). 3 The overall score is Score = 0.62 × 0.87 + 0.38 × (1 - 0.79) = 0.638 + 0.080 = 0.718. The system establishes a score matrix, arranging the 85 Pareto solutions in descending order of score. The highest score (0.838) corresponds to the mix proportion: cement 350 kg / m³. 3 Silica fume 214kg / m 3 2.0% vol steel fiber, with a predicted strength of 148.5 MPa and carbon emissions of 712 kg / m³. 3 .

[0104] Step 152: Calculate the confidence interval for each scheme in the final Pareto optimal solution set, and remove schemes with a confidence level lower than a preset threshold.

[0105] In step 152, the intensity prediction system calculates the confidence intervals of candidate solutions and performs screening. For a given solution with a Bayesian network prediction value Z1 = 135.4 MPa, the system calls the prediction variance σ2 = 9.32 stored during the training phase and calculates the 95% confidence interval as 135.4 ± 1.96 × 9.3 / √136 → [132.4, 138.4] MPa. A confidence threshold of 90% is set. The probability P = Φ((120 - 135.4) / 9.3) = Φ(-1.66) = 0.048 < 0.1 when the lower limit of the interval (132.4 MPa) is lower than the design standard of 120 MPa is considered a qualified solution. The system iterates through all candidate solutions, eliminating three solutions with a lower confidence limit < 125 MPa, and retaining 82 solutions that meet the reliability requirements.

[0106] Step 153: Evaluate the stability of the remaining schemes based on Bootstrap resampling, and retain the target scheme with a compressive strength fluctuation range of less than 5%.

[0107] In step 153, the intensity prediction system performs a Bootstrap resampling evaluation to assess the stability of the proposed scheme. For a candidate scheme (30% cement, 1.8% steel fiber), the system performs 1000 resampling iterations, randomly selecting 136 sets of data each time to refit a Bayesian network and record the predicted intensity distribution. The results show a mean μ = 132.5 MPa, a standard deviation σ = 3.2 MPa, and a fluctuation range of ±1.96σ = ±6.3 MPa (±4.8%), meeting the preset ±5% fluctuation threshold. The system simultaneously calculates the carbon emission volatility; when the standard deviation of carbon emissions for a given scheme is >35 kg / m³, the system will adjust the emission rate accordingly. 3 Schemes with a relative fluctuation of 5% were eliminated, and 75 schemes that met the stability criteria were ultimately retained.

[0108] Step 154: Rank the target schemes according to material cost constraints and construction feasibility, and output a list of recommended mix proportions and risk warning information.

[0109] In step 154, the strength prediction system ranks the proposed solutions based on a combination of material costs and construction constraints. For example, it can load material price databases: cement 0.12 USD / kg, silica fume 0.18 USD / kg, steel fiber 1.2 USD / kg. The material cost of a certain solution = 315 × 0.12 + 214 × 0.18 + 19.6 × 1.2 = 37.8 + 38.5 + 23.5 = 99.8 USD / m³ 3The construction feasibility assessment module triggered an early warning when the steel fiber content exceeded 2.5% vol, eliminating two schemes that exceeded the limit. A final recommended list was generated, with the top 5 schemes having a cost range of 95-112 USD / m². 3 The fluidity is >200mm, the flexural strength is >25MPa, and the flexural-compression ratio is 0.23-0.25, which meets the construction requirements.

[0110] In a preferred embodiment, the generation of the risk warning information includes:

[0111] Step 310: Calculate the target confidence interval for the predicted compressive strength of each target scheme.

[0112] In step 310, the strength prediction system calculates the compressive strength confidence interval of the target scheme. It can be understood that this is based on the prediction variance σ output by the Bayesian network. 2 =9.3 2 The 95% confidence interval for a certain proposed scheme, predicting Z1 = 138.6 MPa, is 138.6 ± 1.96 × 9.3 → [120.5, 156.7] MPa. The system specifies an interval width of 36.2 MPa. When the design requirement is a minimum strength of 120 MPa, the probability of this scheme meeting the standard is P(Z1 ≥ 120) = 1 - Φ((120 - 138.6) / 9.3) = 1 - Φ(-2.00) = 0.977, thus classifying it as a low-risk scheme. The system simultaneously calculates the carbon emission placement confidence interval, such as E = 712 ± 28 kg / m³. 3 (95% CI) to ensure that actual carbon emissions do not exceed the budgeted value by ±5%.

[0113] Step 320: Based on raw material supply stability data, determine the quantitative influencing factors for the feasibility of the mix proportion.

[0114] In step 320, the strength prediction system quantifies the factors affecting the stability of raw material supply. Specifically, the system accesses the supply chain database to obtain the probability of silica fume supply disruption, P = 0.15 (annual shortage rate), and sets the influence factor for alternative materials (fly ash), α = 0.85 (strength reduction coefficient). A certain scheme uses 214 kg / m³ of silica fume. 3 When the alternative is activated, the predicted strength drops to 138.6 × 0.85 = 117.8 MPa, triggering a strength deficiency risk. The system calculates the supply stability score as S = 1 - P × (1 - α) = 1 - 0.15 × 0.15 = 0.978, which is higher for high silica ash dependence schemes (>200 kg / m³). 3 High-risk warnings are marked.

[0115] Step 330: Mark potential discrepancies between transport distance and maintenance conditions in carbon emission calculations.

[0116] In step 330, the intensity prediction system assesses the impact of transport distance deviation on carbon emissions. Specifically, the default carbon emission calculation value for a transport distance of 100km is E_t = 3.0 kg / m³. 3 When the actual transport distance fluctuates by ±50km, the correction value E_t' = 0.012 × 150 × 2.5 = 4.5 kg / m 3 This resulted in an increase of 1.5 kg / m³ in total carbon emissions. 3 (+0.3%). System-marked curing condition deviation risk: When the curing temperature increases from the standard 20℃ to 60℃, the reactivity X0 of the cementitious material increases by 0.12, and the predicted strength increases by 8.7MPa, but carbon emissions increase by 45kg / m² due to steam curing. 3 Temperature-sensitive parameters must be specifically noted in the plan.

[0117] Step 340: Generate a scheme sensitivity analysis report based on the target confidence interval, the quantitative impact factor, and the potential bias, and mark the fluctuation range of key parameters in the scheme sensitivity analysis report.

[0118] In step 340, the strength prediction system generates a sensitivity analysis report. For example, the sensitivity ranking of key parameters for a certain scheme is: water-cement ratio X1 (elasticity coefficient 1.32), steel fiber content X4 (0.98), and Y3 density (0.76). The report indicates that when the water-cement ratio fluctuates by ±0.02, the strength change ΔZ1 = ±1.32 × 9.3 = ±12.3 MPa, and the carbon emission fluctuation ΔE = ±15 kg / m³. 3 The system specifies the allowable fluctuation range: X1∈[0.15, 0.19], Y3∈[0.75, 0.83]. Exceeding these limits will result in a performance failure probability >25%. The report includes parameter optimization suggestions, such as slightly adjusting X1 from 0.17 to 0.16, which can increase the strength by 4.2 MPa with only a 2.8 kg / m³ increase in carbon emissions. 3 .

[0119] Step 350: Based on the sensitivity analysis report of the proposed scheme, output at least some of the target schemes in the interactive interface.

[0120] In step 350, the intensity prediction system visualizes the optimal solution on the interactive interface. Specifically, the system uses the React framework to construct a three-dimensional rotatable scatter plot, with the X-axis representing compressive strength (120-160 MPa) and the Y-axis representing carbon emissions (430-900 kg / m³). 3 The Z-axis comprehensive score (0-1) is used, with risk levels represented by a color gradient (red-yellow-green). Clicking on the top-ranked solution node displays a detailed information card: Material cost 105 USD / m². 3The system achieves a construction feasibility rating of A and a supply stability of 92%. It provides a parameter adjustment slider, displaying in real-time that as the water-cement ratio increases from 0.16 to 0.18, the strength decreases from 142.3 MPa to 135.1 MPa, and carbon emissions decrease from 689 kg / m³. 3 Reduced to 672 kg / m 3 The dynamic change curves are used to assist in engineering decision-making. The final output PDF report includes details of the mix proportions, performance indicators, and risk control recommendations for five recommended schemes.

[0121] As an optional embodiment, obtaining the material parameter sample set of ultra-high performance concrete in step 110 includes:

[0122] Step 1101: Collect historical mix proportion data and corresponding N-day compressive strength test results, where N is a positive integer.

[0123] In step 1101, the strength prediction system constructs a historical mix proportion database through multi-source heterogeneous data acquisition. Specifically, the system extracts structured data from 15 selected valid documents; for example, a document might record a UHPC mix proportion of 315 kg / m³ for Belite silicate cement. 3 Silica fume 214kg / m 3 425 kg / m³ of basalt powder 3 The corresponding 28-day compressive strength is 143.6 MPa. The system automatically parses the table and text information to establish an initial database containing 487 historical samples. The fields cover the dosage of 8 cementitious materials, 5 aggregate parameters, 3 fiber parameters, and strength test results. For the 23 samples with missing curing temperature parameters, the system calls the EXIF ​​metadata parsing function to extract curing condition information from the digital watermark of the attached figures in the literature and complete the temperature field value (e.g., 60℃ steam curing is marked as T=60).

[0124] Step 1102: Based on the compressive strength test results, perform multiple interpolation processing on the missing data in the historical mix proportion data, and remove outliers that exceed the feasible range of the process to obtain the target mix proportion data.

[0125] In step 1102, the intensity prediction system performs data cleaning and outlier correction. Specifically, when the system detects a missing activator dosage field for a certain sample, it uses a random forest regression model for multiple imputation: based on a total cementitious material content of 1070 kg / m³. 3 Given parameters such as a water-cement ratio of 0.16 and a steel fiber content of 1.8%, the predicted activator dosage is 4.3% (46.01 kg / m³) of the cementitious material mass. 3For infeasible data, such as a water-cement ratio X1 = 0.25 (exceeding the preset range of 0.14-0.22) and steel fiber content X4 = 3.2% vol (exceeding the upper limit of 2.5%), the system activated the automatic rejection mechanism, removing a total of 19 abnormal samples. After cleaning, the database contained 468 valid data sets, and the kurtosis of the water-cement ratio distribution decreased from the initial 3.2 to 1.7, meeting the normality requirement (KS test p = 0.083).

[0126] Step 1103: Convert the target mix proportion data into unit volume usage and calculate the cementitious material activity index and aggregate bulk density to obtain initial sample data.

[0127] In step 1103, the intensity prediction system performs unit conversion and feature derivation. Specifically, the system calculates the basalt powder content of a sample as 425 kg / m³. 3 Manufactured sand usage: 1199.6 kg / m³ 3 Converted to volume fraction: Stone powder volume = 425 / 2650 = 0.160 m³ 3 / m 3 (density 2650kg / m³) 3 The volume of sand is 1199.6 / 2700 = 0.444 m³. 3 / m 3 The cementitious material activity index X0 was calculated using the benchmark cement comparison method: the 28-day strength of the sample cement mortar was f_i = 152.3 MPa, and the benchmark group's f_ref = 135.4 MPa, resulting in X0 = 0.87 (formula: k_i = k_ref × (f_i / f_ref - 0.3) / 0.7). The aggregate bulk density Y3 was obtained through iterative calculation using the CPM model: inputting cement D50 = 15.3 μm, silica fume D50 = 0.8 μm, and stone powder D50 = 12.5 μm, and after 100 optimizations of particle size combinations, Y3 = 0.79, with a porosity of 21%.

[0128] Step 1104: The initial sample data is divided into categories using K-means clustering to achieve a balance in the number of samples in each category, thus obtaining clustered sample data.

[0129] In step 1104, the intensity prediction system uses K-means clustering to achieve data balance. Specifically, the cementitious material activity index X0, bulk density Y3, and steel fiber content X4 are selected as clustering features, and k = 5 clusters are set. After silhouette coefficient optimization (optimal value 0.62), the cluster centers are determined as follows: Cluster 1 (X0 = 0.72, Y3 = 0.68, X4 = 0%), Cluster 2 (0.85, 0.75, 1.2%), Cluster 3 (0.93, 0.81, 1.8%), Cluster 4 (1.05, 0.79, 2.3%), and Cluster 5 (1.15, 0.83, 2.5%). The system adjusts the sample distribution, compressing the maximum cluster size from 112 groups to 89 groups and expanding the minimum cluster size from 37 groups to 82 groups, achieving a balanced sample size of 85 ± 7 groups for each category. For example, a highly active, high-density sample (X0 = 1.12, Y3 = 0.84) is reassigned to cluster 5 to ensure balanced class weights during training.

[0130] Step 1105: Perform stratified sampling on the clustered sample data to generate training and validation sets.

[0131] In step 1105, the intensity prediction system implements stratified sampling to divide the dataset. Specifically, sampling is performed proportionally according to cluster categories, with a training set to validation set ratio of 4:1. For cluster 3 (89 groups of samples), 71 groups (80%) are randomly selected for the training set and 18 groups (20%) are selected for the validation set. The system verifies the consistency of data distribution: the mean value of the cementitious material activity index X0 in the training set is 0.91±0.18, and in the validation set it is 0.89±0.17, with a T-test p=0.342; the mean value of the bulk density Y3 is 0.78±0.05 vs 0.77±0.06, with a p=0.211, confirming the effectiveness of stratification. Finally, 374 sets of training data and 94 sets of validation data were generated. Core variables were retained, including water-cement ratio X1∈[0.14, 0.22], steel fiber content X4∈[0, 2.5%], active CaO / SiO2 molar ratio Y1∈[1.2, 2.3], etc., to ensure that the initial edges of the causal network (such as X4→Z1) are completely preserved.

[0132] It is understood that in this embodiment, it is necessary to retain the core input variables and core edges. The limiting edges of the initial causal network topology include: cementitious material hydration effect index, cementitious material particle packing effect index, water-cement ratio, mortar ratio, water-reducing agent dosage, chemical activator dosage, and steel fiber content.

[0133] As an optional but non-limiting embodiment, step 340, which involves generating a sensitivity analysis report based on the target confidence interval, the quantified impact factor, and the potential bias, and marking the fluctuation range of key parameters in the sensitivity analysis report, includes:

[0134] Step 341: Extract the lower and upper confidence limits of the predicted compressive strength values ​​corresponding to the target confidence interval, and determine the key parameter fluctuation thresholds of the candidate mix design.

[0135] In step 341, the strength prediction system extracts the target confidence interval and sets the fluctuation threshold for key parameters. Taking a candidate mix design as an example, its Bayesian network predicts a compressive strength Z1 = 138.6 MPa (σ = 9.3 MPa), and the calculated 95% confidence interval is [132.4, 144.8] MPa. The system sets the allowable fluctuation threshold for strength to ±7.4 MPa (the half-width of the confidence interval), corresponding to an allowable fluctuation range of ±0.02 (0.14-0.18) for the key parameter water-cement ratio X1 = 0.16. For the cementitious material activity index X0 = 0.87, the system sets the fluctuation threshold to ±0.15 (0.72-1.02) based on the historical data distribution standard deviation of 0.12. The system simultaneously calculates the fluctuation threshold for the key carbon emission parameter transportation distance. When the baseline distance is 100 km, the allowable deviation is ±50 km, corresponding to a carbon emission increment ΔE = 0.012 × 50 × 2.5 = 1.5 kg / m. 3 The total carbon emission threshold has been revised to 712 ± 1.5 kg / m³. 3 .

[0136] Step 342: Based on the quantified influencing factors, the key parameters are ranked by sensitivity, and the core sensitive parameters whose absolute values ​​of the influencing factors are higher than the preset sensitivity threshold are selected; according to the range of fluctuations in transportation distance and the magnitude of deviations in maintenance conditions in the potential deviations, the deviation tolerance coefficient of the core sensitive parameters is calculated.

[0137] In step 342, the strength prediction system quantifies parameter sensitivity and calculates deviation tolerance. Specifically, the standardized influence factors of each parameter are calculated using an elastic network regression model: water-cement ratio X1 = 1.32, steel fiber content X4 = 0.98, cementitious material activity X0 = 0.76, and bulk density Y3 = 0.68. A sensitivity threshold of 0.5 is set, and X1, X4, and X0 are selected as core sensitive parameters. The system calculates the deviation tolerance coefficient; for example, the tolerance for transport distance deviation DTC = 1 - (ΔE actual / ΔE threshold) = 1 - (1.5 / 3.0) = 0.5, and the DTC for X0 when the curing temperature deviation is ±10℃ = 1 - (0.05 / 0.12) = 0.58. For the water-cement ratio X1, based on a process control accuracy of ±0.01, its DTC is calculated as 1 - (0.01 / 0.02) = 0.5, and it is marked as a moderately tolerant parameter.

[0138] Step 343: Simulate the gradient of the compressive strength change of the core sensitive parameter within the fluctuation threshold of the key parameter by Monte Carlo random sampling, and generate a parameter sensitivity distribution heatmap; fuse the gradient data of the deviation tolerance coefficient and the parameter sensitivity distribution heatmap to generate a parameter sensitivity level label.

[0139] In step 343, the intensity prediction system performs a Monte Carlo simulation to generate a parameter sensitivity heatmap. Specifically, 1000 random samples are taken from the core parameters X1, X4, and X0: X1~N(0.16, 0.012), X4~N(1.8%, 0.2%). 2 X0~N(0.87, 0.05) 2 Simulation results show that when X1 increases to 0.17 (+0.01), the average strength increases by ΔZ1 = 1.32 × 9.3 = 12.3 MPa, corresponding to the red high-sensitivity area in the heat map (gradient > 10 MPa / 0.01). When the steel fiber content X4 decreases from 1.8% to 1.6%, the strength decreases by ΔZ1 = 0.98 × 9.3 = 9.1 MPa, forming the orange medium-sensitivity area (gradient 5-10 MPa / 0.2%). The system integrates the DTC coefficient to generate sensitivity level labels, such as the sensitivity level S of X1 = 1.32 × 0.5 = 0.66 (high sensitivity) and the S of X4 = 0.98 × 0.5 = 0.49 (medium sensitivity), which are marked in the sidebar of the heat map.

[0140] Step 344: Integrate the fluctuation threshold of the core sensitive parameter, the parameter sensitivity distribution heatmap, the parameter sensitivity level label, and the confidence interval boundary value of the predicted compressive strength value to generate a structured sensitivity analysis report.

[0141] In step 344, the intensity prediction system integrates multidimensional data to generate a structured sensitivity analysis report. Specifically, the report consists of four parts: 1) a key parameter threshold table, listing X1∈[0.14, 0.18], X4∈[1.6%, 2.0%], and X0∈[0.72, 1.02]; 2) a parameter sensitivity heatmap, displaying the X1-X4 plane gradient distribution as a three-dimensional surface, with contour lines spaced at 5 MPa intervals; 3) a sensitivity level matrix, labeling X1 as Class A (requiring strict control) and X4 as Class B (recommended monitoring); 4) confidence boundary data, indicating a 99.7% probability of Z1≥125MPa and E≤750kg / m². 3 The probability is 97.2%. The report appendix includes a link to the original data source, such as the random seed value 20230815 for the Monte Carlo simulation, to ensure the results are reproducible.

[0142] Step 345: In the structured sensitivity analysis report, mark the fluctuation direction and fluctuation amplitude corresponding to the parameter sensitivity level label of the core sensitive parameter, and associate it with the raw material supply stability data of the candidate mixing scheme.

[0143] In step 345, the intensity prediction system labels the correlation between parameter fluctuation direction and supply stability. For example, in Chapter 3 of the sensitivity report, the system labels a positive fluctuation in X1 (increased to 0.18) resulting in an intensity increase of 12.3 MPa but a carbon emission increase of 38 kg / m³. 3 A reverse fluctuation (reduced to 0.14) results in a strength decrease of 12.3 MPa, but requires a 15% increase in cement usage. Simultaneously, data on the stability of silica fume supply is considered: when the probability of silica fume supply disruption P = 15%, the alternative material fly ash will cause X0 to decrease by 0.12, and the strength decrease ΔZ1 = 0.76 × 9.3 × 0.12 = 8.5 MPa. The report marks this scenario with a red warning box, indicating a risk level R = 0.15 × 8.5 / 12.3 = 0.104 (medium risk), and recommends a minimum silica fume inventory of 214 kg / m³. 3 ×1.2=256.8kg / m 3 .

[0144] Step 346: Based on the ratio of the gradient data of the parameter sensitivity distribution heatmap to the deviation tolerance coefficient, dynamically correct the fluctuation range of the core sensitive parameter, and output the corrected key parameter fluctuation range; map the corrected key parameter fluctuation range to the interactive visualization interface of the structured sensitivity analysis report, and mark the comparison relationship before and after the dynamic boundary correction of the core sensitive parameter.

[0145] In step 346, the intensity prediction system implements dynamic boundary correction and visualization mapping. For example, based on the regression model of sensitivity gradient and DTC coefficient, the fluctuation range of water-cement ratio X1 is corrected: the original threshold ±0.02 (0.14-0.18) is narrowed to 0.17 (Δ=+0.01) after gradient weight adjustment, while the lower limit remains at 0.14. The system displays the correction effect in the interactive interface using a two-color overlay: the original range is marked with a light blue background, and the corrected upper limit is marked with a dark blue vertical line. For parameter X0, considering the impact of supply stability, the corrected fluctuation range is [0.75, 0.99] (original 0.72-1.02), and the out-of-bounds area is marked with a semi-transparent red sphere in the three-dimensional scatter plot. The corrected key parameter table is exported as a CSV format, containing fields "parameter name, original threshold, corrected threshold, change range", such as the record in row X1 "0.14-0.18→0.14-0.17, upper limit -5.6%".

[0146] Step 347: Based on the fluctuation range of the key parameters after the dynamic boundary correction and the parameter sensitivity level label, generate the risk probability matrix of the candidate combination scheme, and embed the risk probability matrix into the risk warning information of the structured sensitivity analysis report.

[0147] In step 347, the intensity prediction system generates a risk probability matrix and embeds it into the final report. For example, the matrix rows correspond to core parameters (X1, X4, X0), and the columns correspond to risk types (insufficient intensity, excessive carbon emissions, supply disruption). The probability of each cell is calculated using Monte Carlo simulation: when X1 > 0.17, the probability of intensity exceeding 140 MPa is 82%, but the probability of carbon emissions exceeding the standard is P(E > 750 kg / m³). 3 The probability of X0 < 0.75 is 23%; when X0 < 0.75, the probability of strength being less than 120 MPa is P = 8.7%. The matrix uses color coding to distinguish risk levels: red (P > 20%), orange (10-20%), and green (< 10%). For example, Chapter 5 of the report can include a risk control strategy table. For instance, for the high carbon emission risk of X1 > 0.17, it is recommended to adjust the mortar ratio X3 from 1.1 to 1.2, which can reduce cement usage by 5% while maintaining strength loss < 3 MPa. The final report output is an interactive HTML page, supporting clicking on matrix cells to view detailed simulation data and optimization suggestions.

[0148] As a non-limiting embodiment, it further includes: obtaining the material parameter combinations and corresponding actual compressive strength test data from the optimal low-carbon mix proportion result set; adding the material parameter combinations and actual compressive strength test data to the original material parameter sample set to generate an updated material parameter sample set; re-performing the feature processing steps on the updated material parameter sample set to generate an updated enhanced feature set; wherein, the feature processing steps include extracting original feature variables from the updated material parameter sample set, generating a first type of derived features using the Taylor expansion third-order approximation method, constructing a second type of derived features based on the cross-level interaction relationship between gelling hydration activity and gelling material stacking effect, and adding the original features... The variables and two types of derived features are standardized and concatenated to obtain an initial enhanced feature set, which is then subjected to sparse screening using an elastic network regularization model. Based on the updated enhanced feature set, the structure and parameters of the Bayesian network model are iteratively adjusted. Specifically, the structure adjustment uses a hybrid constrained learning algorithm to re-optimize the network topology, and the parameter adjustment uses a hierarchical regularization strategy to dynamically update the Bayesian ridge regression parameters of the core compressive strength nodes and the maximum likelihood estimation parameters of the auxiliary nodes. The predictive performance of the iteratively adjusted Bayesian network model is evaluated using a validation set. If the evaluation metrics meet preset indicators, it is determined as a new Bayesian network model. These evaluation metrics include prediction error rate and confidence interval coverage. It can be understood that this embodiment revolves around the iterative updating of the model.

[0149] As a non-limiting embodiment, the method further includes: after outputting the optimal low-carbon mix proportion result set, the method further includes: re-predicting the compressive strength prediction value and confidence interval of the candidate mix proportion schemes based on the new Bayesian network model; generating a new strength-carbon emission dual-objective dataset based on the re-predicted compressive strength prediction value and the updated raw material carbon emission factor data; performing range normalization processing on the new strength-carbon emission dual-objective dataset to maintain the dimensional consistency of compressive strength and carbon emission values; calling the adjusted NSGA-II algorithm to perform Pareto front re-search on the normalized dual-objective dataset; wherein, the adjusted NSGA-II algorithm dynamically adjusts the probabilities of the crossover operator and the mutation operator based on the prediction error of the updated Bayesian network model, increasing the probability of the crossover operator to enhance population diversity when the prediction error increases, and increasing the probability of the mutation operator to accelerate the local search when the prediction error decreases; comparing the feature similarity of the new Pareto optimal solution set obtained by the re-search with the original candidate mix proportion schemes, retaining the newly added candidate mix proportion schemes with feature similarity lower than the preset similarity, and outputting the adjusted candidate mix proportion scheme set.

[0150] For example, this embodiment is a further optimization performed after outputting the optimal low-carbon mix proportion result set. Based on the new Bayesian network model, the predicted compressive strength values ​​and confidence intervals of the candidate mix proportion schemes are re-predicted, providing a more accurate data foundation for optimization. A new strength-carbon emission dual-objective dataset is generated based on the re-predicted compressive strength values ​​and the updated raw material carbon emission factor data. Range normalization is performed on this new dataset to place the compressive strength and carbon emission values ​​in the same dimension space, facilitating multi-objective optimization. The adjusted NSGA-II algorithm is invoked to perform a Pareto front re-search on the normalized dual-objective dataset. This algorithm dynamically adjusts the probabilities of the crossover and mutation operators based on the prediction error of the updated Bayesian network model. When the prediction error increases, the probability of the crossover operator is increased to enhance population diversity, enabling the algorithm to explore a wider solution space; when the prediction error decreases, the probability of the mutation operator is increased to accelerate local search and find local optima more quickly. The new Pareto optimal solution set obtained by the research is compared with the original candidate mix proportion schemes by feature similarity. New candidate mix proportion schemes with feature similarity lower than the preset similarity are retained, and the adjusted candidate mix proportion scheme set is output. In this way, new high-quality mix proportion schemes can be continuously discovered, improving the quality and efficiency of UHPC mix proportion design and meeting the dual requirements of high performance and low carbon emissions.

[0151] In summary, combining Figures 1-4 This invention, through the integration of materials science mechanisms and intelligent algorithms, constructs an intelligent design scheme for low-carbon concrete that features causal transparency and multi-objective collaborative optimization. This invention has at least the following breakthrough technical effects:

[0152] 1) Based on causal topological modeling of hydration reaction and particle accumulation, the cross-scale interaction mechanism between cementitious material composition, microstructure evolution and macroscopic performance is innovatively embedded into Bayesian network to form a strength prediction model with physical interpretability, which solves the pain point that traditional data-driven methods cannot trace the cause of performance.

[0153] 2) The innovative dynamic weighted multi-objective optimization mechanism realizes the synergistic optimization of high strength and low carbon emissions in the material parameter space by adjusting the game relationship between mechanical properties and environmental impact in real time, breaking through the local optimum limitation caused by static weight allocation.

[0154] 3) By adopting cross-level feature enhancement and hierarchical regularization strategies, the model's ability to express complex nonlinear relationships is significantly improved, and the interaction effect between derived features and original parameters is refined.

[0155] 4) By combining a dynamic decision-making system based on risk confidence assessment, while ensuring the robustness of candidate solutions, a full-chain traceability mechanism from raw material proportioning to macroscopic performance is established, providing intelligent decision support for the precise design of high-performance low-carbon concrete. This technology system has significant innovative advantages in terms of physical interpretability, multi-objective dynamic optimization, and full life-cycle controllability.

[0156] Based on the above, please refer to the following: Figure 5 This application provides an intensity prediction system 400, including a processor 410 and a memory 420 and a bus 430 connected to the processor 410; wherein the processor 410 and the memory 420 communicate with each other through the bus 430; the processor 410 is used to call program instructions in the memory 420 to execute the above-mentioned BN-based UHPC mix ratio data analysis method.

[0157] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0158] The above are merely embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for analyzing UHPC mix proportion data based on BN, characterized in that, The method is executed through an intensity prediction system, and the method includes: A material parameter sample set for ultra-high performance concrete is obtained. The material parameter sample set includes multiple material parameter combinations. Each material parameter combination includes the oxide composition of cementitious material particles, the particle size distribution of cementitious material particles, the water-cement ratio, the dosage of water-reducing agent, the dosage of chemical activator, the mortar-cement ratio, the aggregate particle size distribution, and the steel fiber content. The material parameter sample set is subjected to feature processing to generate an enhanced feature set containing nonlinear derived features and cross-level interaction features; Based on the enhanced feature set, a Bayesian network model is invoked to predict the compressive strength, obtaining the predicted strength value for each combination of material parameters; wherein, the Bayesian network model determines the network structure through an initial causal network topology and multi-algorithm collaborative search optimization, and adopts a hierarchical regularization strategy for parameter optimization; Based on the preset carbon emission calculation rules and the intensity prediction value, a Pareto front search is performed on the material parameter combination using a multi-objective optimization algorithm to generate a candidate mix design that satisfies the dual objective constraints. Dynamic weight evaluation and risk confidence analysis are performed on the candidate mix design schemes to output the optimal low-carbon mix design result set.

2. The method as described in claim 1, characterized in that, The step of obtaining the material parameter combination further includes: Obtain quantitative data on cementitious materials; wherein, the quantitative data on cementitious materials includes the amount of cementitious materials used or the mixing ratio; Based on a preset particle compaction model, the oxide composition of the cementitious material particles, the particle size distribution of the cementitious material particles, and the quantitative data of the cementitious material are processed to obtain an initial particle packing density index that reflects the particle packing effect. Based on the reactivity of the cementitious material, the oxide composition of the cementitious material particles, and the quantitative data of the cementitious material, a corrected molar ratio index for the hydration effect of the reactive cementitious material is obtained; wherein, the corrected molar ratio index includes the CaO / SiO2 molar ratio index and the SO3 / Al2O3 molar ratio index. The material parameter combination is generated using the initial particle packing density index and the corrected molar ratio index.

3. The method as described in claim 2, characterized in that, The step of performing feature processing on the material parameter sample set to generate an enhanced feature set containing nonlinear derived features and cross-level interaction features includes: The original feature variables are extracted from the material parameter sample set. The original feature variables include: the oxide composition of cementitious material particles, the particle size distribution of cementitious material particles, the water-cement ratio, the amount of water-reducing agent, the amount of chemical activator, the mortar-cement ratio, the aggregate particle size distribution, the steel fiber content, the initial particle packing density index of the reaction particle packing effect, and the corrected molar ratio index of the reaction cementitious material hydration effect. The original feature variables are nonlinearly transformed by the third-order approximation method of Taylor expansion to generate the first type of derived features. Based on the cross-level interaction between gel hydration activity and cement material stacking effect, a second type of derived feature is constructed. The original feature variables, the first type of derived features, and the second type of derived features are standardized and concatenated to obtain an initial enhanced feature set; The elastic network regularization model is invoked to perform sparse filtering on the initial enhanced feature set, retaining features in the initial enhanced feature set whose absolute value of the standardized coefficient is higher than a preset threshold, and generating the final enhanced feature set.

4. The method as described in claim 1, characterized in that, The limiting edges of the initial causal network topology include: Hydration effect index of cementitious materials → compressive strength; Cementitious material particle packing effect index → ​​compressive strength; Water-cement ratio, mortar-cement ratio, water-reducing agent dosage, chemical activator dosage, and steel fiber content → compressive strength; Wherein, the compressive strength is a unique leaf node; The step of calling a Bayesian network model to predict compressive strength includes: Based on prior knowledge or causal relationship analysis strategies, an initial structure of a Bayesian network is constructed and the directed edges of the initial structure of the Bayesian network are restricted. The initial structure of the Bayesian network includes a material parameter layer, a reaction mechanism layer, and a compressive strength layer. The nodes of the material parameter layer are forced to point to the nodes of the reaction mechanism layer, and the nodes of the reaction mechanism layer are forced to point to the nodes of the compressive strength layer. The initial structure of the Bayesian network is optimized using a hybrid constraint learning algorithm to obtain an optimized Bayesian network structure. Specifically, a whitelist constraint restricts the path from the authorized material parameter layer to the compressive strength layer, while a blacklist constraint prohibits reverse causal relationships. By integrating the Bootstrap resampling hill-climbing algorithm, the tabu search algorithm, and the minimax hill-climbing algorithm, the Bayesian network optimization structure is searched using a multi-algorithm collaborative search. The Bayesian network parameters are dynamically adjusted based on a hierarchical regularization strategy to obtain the Bayesian network model. In the Bayesian network model, the core compressive strength node adopts Bayesian ridge regression, and the auxiliary nodes adopt maximum likelihood estimation. The enhanced feature set is input into the Bayesian network model, which outputs the intensity prediction value and the confidence interval of the intensity prediction value for each combination of material parameters.

5. The method as described in claim 4, characterized in that, The step of performing a Pareto front search on the material parameter combination using a multi-objective optimization algorithm based on preset carbon emission calculation rules and the predicted intensity value to generate candidate mix proportion schemes that satisfy dual objective constraints includes: Based on the predicted strength value and the combination of the material parameters, the carbon emission value per unit volume of concrete is calculated, and a strength-carbon emission dual-objective dataset is generated. The intensity-carbon emission dual-objective dataset is subjected to range normalization to ensure that the compressive strength and carbon emission values ​​are in the same dimension space. The NSGA-II algorithm is used to filter the non-dominated solution set of the normalized intensity-carbon emission dual-objective dataset to generate the initial Pareto front. The initial Pareto front is iteratively optimized based on a dynamic weight adjustment strategy; wherein, the weight coefficients in the dynamic weight adjustment strategy change dynamically with the sample validity and carbon emission threshold. The compressive strength, carbon emission value and comprehensive evaluation index are visualized by three-dimensional spatial mapping, and the final Pareto optimal solution set is output. The final Pareto optimal solution set is used to generate candidate mix ratio schemes that meet the dual objective constraints. Iterative optimization of the NSGA-II algorithm includes: Candidate solutions generated by a Bayesian network are injected during population initialization to accelerate the convergence process; A simulated binary crossover and polynomial mutation operator is used to generate the offspring population. The non-dominated solutions are sorted based on the crowding comparison operator, preserving the individuals with the best diversity. Each iteration is set to adjust the weighting coefficients once to meet the compressive strength constraint. Output the Pareto front solution set and label the overall score ranking of each Pareto front solution.

6. The method as described in claim 5, characterized in that, The steps of performing dynamic weight evaluation and risk confidence analysis on the candidate mix design schemes include: A comprehensive evaluation index function is constructed, which integrates the weighted scores of normalized compressive strength and carbon emission value. For each solution in the final Pareto optimal solution set, a confidence interval is calculated, and solutions with a confidence level lower than a preset threshold are eliminated. The stability of the remaining schemes was evaluated based on Bootstrap resampling, and the target scheme with a compressive strength fluctuation range of less than 5% was retained; The target schemes are ranked according to material cost constraints and construction feasibility, and a list of recommended mix proportions and risk warning information are output. The generation of the risk warning information includes: Calculate the target confidence interval for the predicted compressive strength of each target scheme; Based on raw material supply stability data, quantitative influencing factors for the feasibility of the mix design were determined; The potential discrepancies between transport distance and maintenance conditions in carbon emission calculations should be noted. Based on the target confidence interval, the quantitative impact factor, and the potential deviation, a scheme sensitivity analysis report is generated, and the fluctuation range of key parameters is marked in the scheme sensitivity analysis report; Based on the sensitivity analysis report of the proposed scheme, at least some of the target schemes are output in the interactive interface.

7. The method as described in claim 1, characterized in that, The process of obtaining the material parameter sample set for ultra-high performance concrete includes: Collect historical mix proportion data and corresponding N-day compressive strength test results, where N is a positive integer; Based on the compressive strength test results, multiple interpolation processes are performed on the missing data in the historical mix proportion data, and outliers that exceed the feasible range of the process are removed to obtain the target mix proportion data. The target mix proportion data is converted into unit volume dosage, and the activity index of cementitious materials and the bulk density of aggregates are calculated to obtain initial sample data; The initial sample data is divided into categories using K-means clustering to achieve a balance in the number of samples in each category, thus obtaining clustered sample data. The clustered sample data is subjected to stratified sampling to generate training and validation sets.

8. The method as described in claim 3, characterized in that, The sparse selection steps for the regularization model of elastic networks include: To enhance feature sparsity, the elastic network mixing parameter α is biased towards L1 regularization. The optimal value of the regularization strength λ is determined by multi-fold cross-validation; Calculate the selection frequency of each feature under Bootstrap resampling and retain features with frequencies higher than a set proportion; The selected features are subjected to a multicollinearity test, and features with a variance inflation factor greater than a preset value are removed to obtain the final enhanced feature set; wherein, the final enhanced feature set is used to map to the input layer of the Bayesian network model.

9. The method as described in claim 5, characterized in that, The dynamic adjustment steps of the hierarchical regularization strategy include: The number of parent nodes of the compressive strength node is set as the core parameter, and an exponential penalty term is used to control the network complexity. The regularization coefficient is dynamically decayed based on the effective sample size; where the decay rate is negatively correlated with the sample confidence level. A fixed regularization coefficient is applied to the auxiliary nodes, which is used to suppress overfitting and maintain computational efficiency; The Cook distance is used to diagnose anomalous samples, and the weight of the anomalous samples is reduced to optimize parameter estimation. The parameters of the Bayesian network are updated at a set period, and the generalization ability of the Bayesian network model is verified.

10. An intensity prediction system, characterized in that, It includes a processor, a memory and a bus connected to the processor; wherein the processor and the memory communicate with each other through the bus; the processor is used to call program instructions in the memory to execute the BN-based UHPC mix proportion data analysis method according to any one of claims 1-9.

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