Optimization method for lightweight aggregate concrete proportioning based on response surface intelligent analysis

Abstract

The present application relates to the technical field of neural network intelligent optimization, and particularly relates to a lightweight aggregate concrete proportioning optimization method based on response surface intelligent analysis. The method comprises the following steps: obtaining proportioning test data and electron microscope image data, performing response surface factor interaction analysis and electron microscope image feature extraction, obtaining response surface interaction data and electron microscope image feature data; splicing the two tensors into multi-modal proportioning representation data; based on the data, performing graph neural network training and material science priori physical constraint modeling to generate proportioning relationship graph data and aggregate constraint data; using the aggregate constraint data to update the interlayer weight of the proportioning relationship graph data to form a neural network proxy model; obtaining a proportioning solution space proxy model through hyperparameter collaborative training, and outputting proportioning parameter network data through front evolution optimization, thereby improving the lightweight aggregate concrete proportioning prediction accuracy and applicability.

Description

Technical Field

[0001] This invention relates to the field of neural network intelligent optimization technology, and in particular to a method for optimizing the mix proportion of lightweight aggregate concrete based on response surface intelligent analysis. Background Technology

[0002] Lightweight aggregate concrete, due to its light weight, good thermal insulation properties, and strong heat insulation capacity, has high application value in building envelopes, energy-saving building components, and green building materials. The introduction of materials such as volcanic slag lightweight aggregate and recycled aggregate can reduce the consumption of natural aggregates to a certain extent and improve the thermal performance of concrete. However, the performance of lightweight aggregate concrete is influenced by multiple factors, including the water-cement ratio, lightweight aggregate replacement rate, aggregate gradation, cementitious material ratio, pore structure, and the state of the interfacial transition zone. Significant nonlinear coupling relationships exist between these factors.

[0003] Traditionally, lightweight aggregate concrete mix design relies on manual trial mixing, empirical adjustments, or conventional response surface methodology (RSM). While RSM can fit the relationship between mix design factors and performance indicators under limited experimental conditions, it typically uses second-order polynomial models, which struggle to fully express the complex nonlinear relationships between lightweight aggregate replacement rate, water-cement ratio, pore structure, thermal conductivity, compressive strength, and splitting tensile strength. When the number of mix design variables increases, or when simultaneously considering strength, thermal insulation performance, workability, and pore structure stability, RSM becomes limited by the number of experimental samples, factor level settings, and empirical boundaries, leading to local optima, insufficient generalization ability, and poor engineering adaptability in the mix design results. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method for optimizing the mix proportion of lightweight aggregate concrete based on intelligent response surface methodology, thereby resolving at least one of the aforementioned technical issues.

[0005] This application provides a method for optimizing the mix proportion of lightweight aggregate concrete based on response surface intelligent analysis, including the following steps: S1. Obtain the mixing ratio test data and electron microscope image data; perform response surface factor interaction analysis based on the mixing ratio test data to obtain response surface interaction data; extract electron microscope image features based on the electron microscope image data to obtain electron microscope image feature data; and perform tensor stitching on the response surface interaction data and electron microscope image feature data to obtain multimodal mixing ratio characterization data. S2. Based on the multimodal proportioning characterization data, graph neural network training and materials science prior physical constraints are performed to obtain proportioning relationship graph data and aggregate constraint data, respectively. S3. Update the interlayer weights of the mix proportion diagram data based on the aggregate constraint data to obtain the neural network surrogate model; S4. Perform hyperparameter co-training on the neural network surrogate model to obtain the matching solution space surrogate model; S5. Perform frontier evolution optimization on the surrogate model of the matching solution space to obtain the matching parameter network data.

[0006] This invention employs a collaborative processing approach, combining mix proportioning test data with electron microscopy image data. First, response surface methodology is used to extract the initial coupling relationships between lightweight aggregate content, water-cement ratio, pore structure, and mechanical properties. Then, electron microscopy image features are incorporated into multimodal mix proportioning characterization. This allows the model to not only fit macroscopic experimental results but also absorb material mechanism information reflected by aggregate interfaces, pore connectivity, and microstructural changes. A mix proportioning relationship graph is constructed using graph neural network training, and aggregate constraint data is generated by combining prior physical constraints from materials science. This suppresses propagation paths that do not meet strength, thermal conductivity, porosity, or aggregate substitution rate boundaries during network propagation, while strengthening mix proportioning paths that meet material performance requirements. This improves the physical consistency and interpretability of mix proportioning predictions. By using hyperparameter co-training and frontier evolution optimization, the neural network surrogate model can quickly screen candidate mix proportions that combine strength, thermal insulation performance, workability, and pore structure stability within a large mix proportion solution space. This reduces the dependence of traditional response surface methodology on finite orthogonal experiments and second-order polynomial fitting, reduces the number of repeated mix design trials, and improves the accuracy, stability, and engineering applicability of lightweight aggregate concrete mix proportion optimization.

[0007] Preferably, the response surface interaction analysis in S1 specifically includes: Factor variables were extracted from the proportioning experiment data to obtain proportioning factor data; response values ​​were aligned with the proportioning factor data to obtain proportioning response matrix data; interaction terms were constructed based on the proportioning factor data to obtain response surface interaction term data; response surface fitting was performed based on the response surface interaction term data and the proportioning response matrix data to obtain response surface coefficient data; interaction contribution was filtered based on the response surface coefficient data to obtain response surface interaction data.

[0008] This invention, through the aforementioned response surface methodology interaction analysis steps, transforms the discrete and scattered original experimental results in mix design test data into structured analytical data with clear factor relationships and response orientations. The system first extracts mix design factors such as water-cement ratio, lightweight aggregate replacement rate, and cementitious material ratio, then aligns them with response values ​​such as slump, thermal conductivity, compressive strength, and splitting tensile strength, avoiding model input deviations caused by missing or inconsistent index sequences between different test batches. Further, through interaction term construction and response surface fitting, it can not only identify the impact of single factors on performance but also represent the coupling effects between different mix design factors, such as the law by which lightweight aggregate replacement rate and water-cement ratio jointly influence pore structure and strength development. By filtering response surface coefficients and interaction contributions, weakly correlated or randomly fluctuating terms can be eliminated, retaining key interaction combinations that substantially affect the target performance.

[0009] Preferably, the electron microscope image feature extraction in S1 specifically involves: Phase region segmentation is performed on electron microscope image data to obtain phase region segmentation data; boundary region identification is performed on phase region segmentation data to obtain interface transition region data; pore morphology analysis is performed on interface transition region data to obtain pore structure feature data; and microscopic feature vector encapsulation is performed on interface transition region data and pore structure feature data to obtain electron microscope image feature data.

[0010] This invention employs phase region segmentation in electron microscopy images to distinguish between aggregate, paste, and porous phases, providing a clear regional foundation. Based on the phase region segmentation data, the interface transition zone between aggregate and paste is identified, enabling the model to capture key areas in lightweight aggregate concrete that influence strength development and interfacial bonding performance. Pore morphology analysis of the interface transition zone extracts structural features such as pore distribution, pore size variation, connectivity, and morphological uniformity, reflecting the microscopic impact of lightweight aggregate content and water-cement ratio variations on the material's internal structure. Encapsulating the interface transition zone data and pore structure feature data into a microscopic feature vector allows for the fusion of electron microscopy image information with response surface interaction data, improving the accuracy and interpretability of mix design predictions.

[0011] Preferably, the training of the graph neural network in S2 is specifically as follows: Node attribute mapping is performed on the multimodal matching representation data to obtain matching node data; node association relationships are constructed based on response surface interaction data and electron microscopy image feature data to obtain edge connection data; adjacency matrix is ​​generated based on the matching node data and edge connection data to obtain matching graph structure data; gating state update training is performed based on the matching graph structure data to obtain node embedding feature data and edge weight update data; graph structure correction is performed based on the node embedding feature data and edge weight update data to obtain matching relationship graph data.

[0012] This invention transforms multimodal mix design data from ordinary vector input into a structured mix design graph with nodes, edges, and propagation weights. The system first maps water-cement ratio, lightweight aggregate replacement rate, pore structure characteristics, interface transition zone characteristics, and macroscopic performance indicators to different types of mix design nodes, providing a unified basis for expressing the originally dispersed mix design variables, microscopic features, and performance responses. Then, it utilizes response surface interaction data and electron microscopy image feature data to construct node relationships, ensuring that edge connections are not merely simple data correlations but simultaneously reflect the interaction of mix design factors and the influence of material microstructure. Through adjacency matrix generation and gated state update training, the model can dynamically retain stable correlation paths that have a stable impact on properties such as strength, thermal conductivity, and porosity during node propagation, while weakening noisy features or weakly correlated paths. Graph structure correction through node embedding features and edge weight update data improves the ability of the mix design graph to express nonlinear coupling relationships, thereby enhancing the stability of lightweight aggregate concrete mix design prediction and optimization results.

[0013] Preferably, the prior physical constraints in materials science in S2 are as follows: Based on the multimodal mix design data, aggregate composition boundaries were identified and mechanical property boundaries were set, resulting in aggregate replacement rate constraint data and strength constraint data. Based on the electron microscopy image feature data in the multimodal mix design data, pore structure boundary analysis was performed to obtain pore structure constraint data. Based on the multimodal mix design data and pore structure constraint data, thermal performance boundaries were set to obtain thermal conductivity constraint data. The aggregate replacement rate constraint data, pore structure constraint data, strength constraint data, and thermal conductivity constraint data were then encapsulated to obtain aggregate constraint data.

[0014] In this invention, through the aforementioned material science prior physical constraint steps, the engineering boundaries that must be satisfied during the optimization of lightweight aggregate concrete mix proportions can be transformed into constraint data that can be recognized and invoked by the model. The system identifies aggregate composition boundaries and mechanical property boundaries based on multimodal mix proportion characterization data, limiting the reasonable variation range of volcanic slag lightweight aggregate replacement rate, water-cement ratio, and strength indicators, avoiding the generation of mathematically feasible but engineeringally difficult or insufficiently strong mix proportions. Combining electron microscopy image features for pore structure boundary analysis allows the introduction of microstructural information such as porosity, pore size distribution, pore connectivity, and interface transition zone states into the constraint system, enabling subsequent optimization to not only focus on macroscopic strength results but also represent the influence of the material's internal structure on performance. By linking pore structure constraints with thermal performance boundaries to set thermal conductivity constraint data, the relationship between thermal insulation performance and pore structure can be constrained more accurately, avoiding strength degradation caused by simply reducing thermal conductivity. Encapsulating aggregate replacement rate, pore structure, strength, and thermal conductivity constraints into aggregate constraint data improves the reliability, interpretability, and engineering applicability of the mix proportion optimization results.

[0015] Preferably, S3 specifically comprises: The initial graph neural network model is obtained by initializing the graph neural network based on the mix proportion graph data; the constraint factor is encoded based on the aggregate constraint data to obtain the aggregate constraint vector; the constraint weight mapping data is obtained by performing constraint matching on the initial graph neural network model based on the aggregate constraint vector; the constraint weight mapping data is used to re-balance the graph convolution propagation path of the initial graph neural network model to obtain the constraint update network model; and the neural network surrogate model is trained by backpropagation of errors based on the multimodal mix proportion characterization data to obtain the neural network surrogate model.

[0016] In this invention, a graph neural network is initialized based on mix proportion graph data, enabling mix proportion variables, microstructural features, and macroscopic performance indicators to propagate through nodes within a unified graph structure. Aggregate replacement rate, pore structure, strength boundary, and thermal conductivity boundary are then encoded as aggregate constraint vectors, transforming material science priors from empirical judgments into constraint expressions that can participate in model training. Through constraint matching and graph convolution propagation path rebalancing, propagation paths that do not meet the lower strength limit, upper thermal conductivity limit, or reasonable porosity range are suppressed, while node-edge relationships that conform to the evolution of material properties are enhanced, thereby reducing the model's sensitivity to abnormal test points or weakly correlated features. Error backpropagation training is performed using multimodal mix proportion characterization data, ensuring the model maintains data fitting ability while possessing physical consistency and engineering interpretability, enabling a more accurate representation of the nonlinear mapping relationship between lightweight aggregate concrete mix proportions, microstructure, and comprehensive performance.

[0017] Preferably, the graph convolution propagation path re-trade is specifically as follows: The graph propagation path is extracted from the initial graph neural network model to obtain graph propagation path data. The constraint association is calibrated on the graph propagation path data based on the constraint weight mapping data to obtain path constraint association data. Material boundary propagation is re-estimated on the path constraint association data to obtain path contribution weight data. The weights of the initial graph neural network model are redistributed based on the path contribution weight data to obtain re-balanced graph convolution parameter data. The parameters of the initial graph neural network model are solidified based on the re-balanced graph convolution parameter data to obtain the constraint update network model.

[0018] In this invention, graph convolutional propagation paths between proportion variable nodes, microstructure nodes, and macroscopic performance nodes are extracted from the initial graph neural network model. Constraint weight mapping data is then used to perform constraint correlation calibration on each propagation path, making the material boundary meanings corresponding to different paths clearer. Through material boundary propagation re-estimation, it is possible to identify which propagation paths lead to a decrease in strength, an increase in thermal conductivity, or a deviation of the pore structure from a reasonable range, and their path contribution weights are reduced accordingly. For propagation paths that can simultaneously meet the requirements of strength, thermal insulation, and pore structure, their weight proportions are increased. Through weight redistribution and parameter solidification, the initial graph neural network model is transformed from a general data-driven model into a constraint-updated network model constrained by the material physical boundaries. This reduces the interference of abnormal samples, weakly correlated features, and unreasonable proportion combinations on model training, improving the model's ability to express the nonlinear relationship between lightweight aggregate concrete proportions, microstructure, and macroscopic performance, and enhancing its engineering interpretability.

[0019] Preferably, the material boundary propagation recalculation specifically includes: The path constraint association data is aggregated by constraint type to obtain path constraint type data; material boundary deviation is identified based on the path constraint type data to obtain path boundary deviation data; propagation penalty coefficient is generated from the path boundary deviation data to obtain path inhibition coefficient data; effective propagation potential is re-estimated based on the path constraint type data and path inhibition coefficient data to obtain path propagation potential data; and standard weight transformation is performed on the path propagation potential data to obtain path contribution weight data.

[0020] This invention first categorizes the path constraint data by constraint type, ensuring that different constraints such as aggregate replacement rate, pore structure, lower strength limit, and upper thermal conductivity limit no longer act concurrently on the network propagation process, but are instead assigned to specific path constraint types. Subsequently, by identifying material boundary deviations, it can determine whether each propagation path carries the risk of insufficient strength, increased thermal conductivity, porosity imbalance, or excessive aggregate replacement rate, and generate propagation penalty coefficients to apply stronger suppression to paths with significant deviations. Through effective propagation potential reestimation, the influence of paths that do not conform to the physical laws of materials can be weakened during graph convolution propagation, while retaining or enhancing effective propagation paths that meet the requirements of strength, thermal insulation, and pore structure. Path contribution weight data is generated through standard weight transformation, providing a clear material boundary basis for subsequent weight redistribution, thereby improving the physical consistency, noise resistance, and reliability of proportion prediction in the neural network surrogate model.

[0021] Preferably, S4 specifically comprises: The hyperparameter search space is constructed based on the neural network surrogate model to obtain hyperparameter space data; a joint training objective is constructed based on multimodal proportioning characterization data and aggregate constraint data to obtain collaborative training loss data; the neural network surrogate model is iteratively trained based on the hyperparameter space data and collaborative training loss data to obtain surrogate model data; the validation error of the surrogate model data is evaluated to obtain optimal hyperparameter combination data; and the solution space is mapped based on the optimal hyperparameter combination data to obtain the proportioning solution space surrogate model.

[0022] This invention first constructs a hyperparameter search space, incorporating parameters such as the number of graph convolutional layers, hidden dimensions, learning rate, constraint loss weights, and training iterations into a unified adjustment range, avoiding reliance on single empirical parameter settings for model training. A joint training objective is constructed by combining multimodal mix design data and aggregate constraint data, enabling the model to reduce prediction errors while considering aggregate replacement rate boundaries, strength boundaries, pore structure boundaries, and thermal conductivity boundaries, avoiding model results that only perform well in data fitting but do not conform to the laws of materials engineering. Through iterative training and validation error assessment, optimal hyperparameter combinations with good generalization ability and small deviations from physical constraints can be selected, improving the model's predictive stability for untested mix designs. Solution space mapping is performed based on the optimal hyperparameter combinations, enabling the neural network surrogate model to quickly map candidate mix design parameters into performance response prediction results and feasible solution ranges.

[0023] Preferably, S5 specifically includes: The search boundary for the matching variables is set according to the matching solution space surrogate model to obtain the matching search space data; the initial matching population is generated according to the matching search space data to obtain the initial matching population data; the initial matching population data is input into the matching solution space surrogate model for performance response prediction to obtain the matching performance prediction data; fitness is evaluated according to the matching performance prediction data to obtain the frontier matching data; constraint feasibility is screened according to the frontier matching data to obtain the matching parameter network data.

[0024] In this invention, a search boundary for proportioning variables is first set based on a proportioning solution space proxy model. This restricts candidate variables such as water-cement ratio, lightweight aggregate replacement rate, and cementitious material ratio to a range with engineering feasibility, preventing invalid proportions from entering the subsequent optimization process. By generating an initial proportioning population, a set of differentiated candidate schemes can be formed within the proportioning space, improving the coverage of potential optimal regions during the optimization process. After inputting the initial proportioning population into the proportioning solution space proxy model for performance response prediction, predictions of strength, thermal conductivity, slump, and porosity can be obtained without conducting physical tests on each proportion, thereby reducing testing costs and the screening cycle. Fitness assessment determines the balance between mechanical, thermal, and construction performance of different proportioning schemes, forming frontier proportioning data. Constrained feasibility screening eliminates schemes that do not meet the lower strength limit, upper thermal conductivity limit, or aggregate boundary, retaining proportioning parameter network data that better meets material performance requirements and engineering application conditions, thereby improving the feasibility, stability, and performance coordination of the proportioning optimization results.

[0025] The beneficial effects of this invention are as follows: The system extracts the interaction relationships between factors such as water-cement ratio, lightweight aggregate replacement rate, and cementitious material ratio from the mix proportion test data, and performs tensor splicing with the pore structure, interface transition zone, and aggregate morphology features reflected in electron microscopy images, so that the model input simultaneously includes macroscopic experimental response and microscopic structural mechanism information. By training a graph neural network to construct a mix proportion relationship graph, the nonlinear coupling relationship between mix proportion variables, microstructure, and performance indicators such as strength, thermal conductivity, and porosity can be expressed in the form of nodes and edge weights, avoiding the problem of insufficient expression of material relationships by simple tabular data modeling. Combining aggregate constraint data for interlayer weight updates allows the inclusion of aggregate replacement rate boundaries, lower strength limits, upper thermal conductivity limits, and pore structure boundaries into the network propagation process, suppressing association paths that do not conform to the physical laws of materials and strengthening propagation paths that meet engineering performance requirements, thereby improving the physical consistency and interpretability of the surrogate model. By using hyperparameter collaborative training and frontier evolution optimization, candidate mix proportions that combine mechanical properties, thermal properties, workability, and pore structure stability can be quickly screened within a large mix proportion solution space. This reduces the number of repeated experiments, improves mix proportion optimization efficiency, and enhances the stability and feasibility of lightweight aggregate concrete mix proportions in actual engineering preparation. Attached Figure Description

[0026] Other features, objects, and advantages of this application will become more apparent from the following detailed description of the non-limiting embodiments, taken with reference to the accompanying drawings: Figure 1 A flowchart illustrating the steps of a lightweight aggregate concrete mix design optimization method based on response surface intelligent analysis is shown in one embodiment. Figure 2A flowchart illustrating the steps of a response surface methodology interaction analysis method according to one embodiment is shown. Figure 3 A flowchart illustrating the steps of a graph neural network training method according to an embodiment is shown. Figure 4 A flowchart illustrating the steps of an inter-layer weight update method according to an embodiment is shown. Figure 5 A flowchart illustrating the steps of a hyperparameter co-training method according to one embodiment is shown. Figure 6 A flowchart illustrating the steps of a frontier evolution optimization method according to one embodiment is shown. Detailed Implementation

[0027] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0028] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0029] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0030] Using volcanic slag lightweight aggregate concrete as the optimization target, the system collected 96 sets of mix design test data and corresponding 192 electron microscopy images. Mix design factors included water-cement ratio, volcanic slag fine aggregate replacement rate, volcanic slag coarse aggregate replacement rate, cementitious material dosage, and admixture dosage. The water-cement ratio was set to 0.25–0.55, the volcanic slag fine aggregate replacement rate to 0%–50%, and the volcanic slag coarse aggregate replacement rate to 0%–60%. Test response values ​​included slump, 28-day compressive strength, splitting tensile strength, thermal conductivity, and thermal insulation performance.

[0031] The system first performed response surface methodology (RSM) analysis on 96 sets of mix design data, identifying a high level of interaction contribution between the water-cement ratio and the replacement rate of coarse volcanic slag aggregate, and between the replacement rate of fine volcanic slag aggregate and the amount of cementitious materials. The normalized interaction contribution values ​​were 0.18 and 0.13, respectively, both higher than the interaction contribution screening threshold of 0.05. The system then performed phase region segmentation and interface transition zone identification on the electron microscopy images, extracting features such as porosity, average pore size, pore roundness, pore connectivity density, and average thickness of the interface transition zone. For example, a mix design with a porosity of 0.146, an average pore size of 18.3 μm, and an average interface transition zone thickness of 24.6 μm was encapsulated as electron microscopy image feature data.

[0032] The system stitches response surface interaction data with electron microscopy image feature data to form multimodal proportioning characterization data and constructs a proportioning relationship diagram. The system sets a minimum compressive strength threshold. Minimum splitting tensile strength threshold Upper limit of thermal conductivity Porosity limit Maximum thickness of the interface transition area After correcting the propagation path of the graph neural network using aggregate constraint data, the system obtains a neural network surrogate model. Validation set testing shows that this surrogate model has an average prediction error of 3.8% for compressive strength and 4.6% for thermal conductivity, significantly lower than the 8.9% and 10.7% errors achieved using only the quadratic response surface model.

[0033] During the frontier evolution optimization process, the system screened the optimal mix proportions from the solution space: a water-cement ratio of 0.36, a volcanic slag fine aggregate replacement rate of 35%, a volcanic slag coarse aggregate replacement rate of 45%, a cementitious material dosage of 410 kg / m³, and an admixture dosage of 1.1%. After prediction by a surrogate model and verification by experiments, this mix proportion showed a slump of 182 mm, a 28-day compressive strength of 36.5 MPa, a splitting tensile strength of 3.12 MPa, and a thermal conductivity of 0.52 W / (m·K), resulting in a 13.4% improvement in thermal insulation performance compared to ordinary lightweight aggregate concrete.

[0034] Compared with manual experience-based mix proportions, the optimized mix proportions in this embodiment, while meeting the requirements for slump and strength during construction, reduce the thermal conductivity from 0.68 W / (m·K) to 0.52 W / (m·K), a reduction of approximately 23.5%; increase the 28-day compressive strength from 33.1 MPa to 36.5 MPa, an increase of approximately 10.3%; and reduce the number of verification test groups required from 36 to 12, a reduction of approximately 66.7%. This demonstrates that this method can achieve a synergistic optimization among the replacement rate of volcanic slag lightweight aggregate, pore structure, interface transition zone, and thermal performance, not only reducing the workload of trial mixes but also avoiding the problems of excessive porosity and strength reduction caused by simply pursuing low thermal conductivity.

[0035] Please see Figures 1 to 6 This application provides a method for optimizing the mix proportion of lightweight aggregate concrete based on response surface intelligent analysis, including the following steps: S1. Obtain the mixing ratio test data and electron microscope image data; perform response surface factor interaction analysis based on the mixing ratio test data to obtain response surface interaction data; extract electron microscope image features based on the electron microscope image data to obtain electron microscope image feature data; and perform tensor stitching on the response surface interaction data and electron microscope image feature data to obtain multimodal mixing ratio characterization data. Specifically, the system first establishes a mix proportion test data table, using a single group of specimens as the smallest recording unit, and records the mix proportion test data of the i-th group of specimens as follows: ,in It can indicate the water-to-glue ratio. It can represent the replacement rate of volcanic slag fine aggregate. This can represent the replacement rate of volcanic slag coarse aggregate. It can indicate the amount of cementitious materials or the amount of admixtures; This indicates the test response values ​​for slump, compressive strength, splitting tensile strength, thermal conductivity, and thermal insulation performance measured under this mix proportion, for example... Slump For compressive strength, To improve thermal insulation performance, the system normalizes each factor to obtain a standardized factor matrix. , This represents the original value of the first proportioning factor in the i-th proportioning specimen. For the i-th proportioned specimen, the first... The original values ​​of each matching factor. The system targets each type of performance response. Constructing a quadratic response surface model: ,in This represents the predicted value of the j-th type of performance response for the i-th mix design specimen, such as predicted slump, compressive strength, splitting tensile strength, thermal conductivity, and thermal insulation performance. Let be the coefficient of the constant term in the j-th type of performance response. The total number of matching factors participating in the response surface analysis, where a and b are the matching factor numbers and , Let be the linear effect coefficient of the a-th matching factor on the j-th type of performance response, also known as the main effect of the factor. This is the quadratic influence coefficient of the a-th proportioning factor on the j-th type of performance response, also known as the curvature effect coefficient. Let a be the standardized variable value of the a-th proportioning factor in the i-th group of specimens. Let b be the standardized variable value of the proportioning factor in the i-th group of specimens. This represents the interaction coefficient between the a-th and b-th matching factors on the j-th type of performance response, also known as the pairwise interaction strength. The system extracts all linear, quadratic, and interaction coefficients and calculates the interaction contribution term: , It is a variance operation function. This is the standardized value of the a-th proportioning factor, such as the standardized water-cement ratio. The standardized value of the b-th proportioning factor, such as the standardized replacement rate of volcanic slag fine aggregate, is used to form response surface interaction data. It includes at least the main effect of the factor, the second curvature effect, the pairwise interaction strength of the factors, and the prediction bias of the corresponding performance response.

[0036] For electron microscopy image data, the system binds the electron microscopy images of each group of specimens with the proportioning test data according to specimen number, magnification, and sampling area, and records them as follows: The system first reads the scale information from the electron microscope image and establishes a pixel-to-size conversion coefficient according to the correspondence between the pixel length of the scale and the actual micrometer length. For example, it converts 1 pixel to the corresponding μm scale to obtain a scale calibration image. The color or pseudo-color image is then uniformly converted to grayscale, and histogram equalization is performed on the grayscale values ​​to widen the grayscale differences between the aggregate region, slurry region, and pore region. For speckle noise and local bright spots in the image, the system uses median filtering or small-window Gaussian filtering for smoothing, preserving aggregate boundaries and pore contours.

[0037] During phase region segmentation, the system first uses a grayscale threshold. , Make preliminary divisions, =55, =155: If pixel grayscale If so, they are initially marked as candidate pixels for apertures; if If so, they are initially marked as candidate pixels for highlighting minerals / aggregates; if If the pixel is initially marked as a candidate pixel for slurry, then for the aggregate candidate region, the system calculates the local gray-level variance within a 7×7 pixel window. ,when and When this area is identified as the aggregate zone, then... and At that time, the area was identified as a slurry region. The system uses the Sobel operator to calculate the horizontal gradient. and vertical gradient And obtain the gradient magnitude: ,when When pixels are continuously connected to form an edge connected region, and the length of this connected region is not less than 30 pixels and the break interval is not more than 3 pixels, it is identified as the phase region boundary. The system uses this boundary to perform closure correction on the contours of the pore region and aggregate region, avoiding misidentification of a single dark spot or bright spot as an independent phase region. For overlapping regions with gray levels between 100 and 155, the system calculates the gray-level co-occurrence matrix contrast. .when And when the local variance is ≥180, it is classified into the aggregate zone; when Furthermore, regions with a local variance ≤ 80 are classified as slurry regions; other regions are merged according to the area ratio of adjacent connected regions. The system deletes isolated regions with an area less than 25 pixels, fills internal holes with an area less than 40 pixels, and merges adjacent connected regions of the same type to obtain phase region segmentation data for aggregate region, slurry region, and pore region.

[0038] The system uses phase region segmentation data as a basis to calculate the sum of the pixel areas marked as pore regions. And statistically analyze the effective field of view area. Calculate porosity The system marks the connected components in the pore region to obtain the connected components of each pore. Calculate their areas respectively. ,perimeter and equivalent aperture Then, the average pore diameter is obtained by averaging the equivalent pore diameters of all connected pore regions. For each pore connected domain, the system according to Calculate the roundness and take the average value as the pore roundness. The system counts the number of connected domains that are close to or connected to adjacent pores, and uses the number of connected relationships per unit area as the pore connectivity density. After obtaining the phase region segmentation data of the aggregate region, slurry region, and pore region, the system first extracts the outer contour boundary of the aggregate region, denoted as... This boundary marks the point of contact between the volcanic slag lightweight aggregate and the cement paste. The system uses the aggregate boundary as a reference. Starting from the aggregate, extend towards the slurry zone along the outer normal direction. Each pixel, such as 60 pixels, yields a candidate band for the interface. This candidate band can be represented as: ,in, Indicates the aggregate area. This indicates the outward expansion of the aggregate zone. The area after one pixel =60, Indicates the slurry region. This represents the interface transition zone. For the interface transition zone, the system calculates the average width of the region in multiple normal directions based on the candidate interface band formed by the extension of the aggregate boundary towards the slurry side, thus obtaining the average thickness of the interface transition zone. The system also calculates the mean or magnitude distribution of the gray-level gradient in the interface transition zone and the pore neighborhood to obtain the gray-level gradient characteristics. Texture features are calculated based on the contrast, energy, or entropy values ​​of the gray-level co-occurrence matrix. The specimens were packaged into electron microscopy image feature data according to their specimen numbers. .

[0039] The system uses the specimen number For indexing, the response surface interaction data and electron microscopy image feature data are aligned at the sample level. If multiple electron microscopy images exist for a particular specimen, the mean, range, or quantile statistics of the image features under the same specimen are first taken to form a unified image feature vector. The system then concatenates the two into: The data are stacked according to sample dimensions to form multimodal matching characterization data. , This is the multimodal mix design characterization vector for the first group of mix design specimens. This is the multimodal mix design characterization vector for the second group of mix design specimens. Let be the multimodal proportioning characterization vector of the nth proportioned specimen.

[0040] S2. Based on the multimodal proportioning characterization data, graph neural network training and materials science prior physical constraints are performed to obtain proportioning relationship graph data and aggregate constraint data, respectively. Specifically, the system uses the obtained multimodal matching data to characterize the data. For input, where , The main effects and interaction effects of factors such as water-cement ratio, replacement rate of fine aggregate with volcanic slag, replacement rate of coarse aggregate with volcanic slag, and dosage of cementitious materials are included. Microscopic features include porosity, average pore size, thickness of the interface transition zone, grayscale gradient, and texture characteristics. These are the original proportioning factors. The system first constructs a proportioning sample diagram. Each proportioning specimen is treated as a sample node. The initial features of the nodes are represented as follows: ,in This indicates that multimodal features are standardized. The system establishes node edges based on the similarity of matching factors, response surface interaction similarity, and electron microscopy image microstructure similarity. For any two sample nodes... and Calculate the difference in their proportions: And calculate the differences in microstructure: ,in The difference in matching factors between the i-th and k-th matched samples is called the Euclidean distance of the matching factors. Number the matching factors. This represents the total number of matching factors involved in the variance calculation. Let be the standardized value of the a-th matching factor in the i-th matching sample. Let a be the standardized value of the a-th matching factor in the k-th matching sample. Let be the porosity of the i-th sample. Let be the porosity of the k-th sample. Let be the average pore size of the i-th proportioned sample. Let be the average pore size of the k-th proportioned sample. Let be the average thickness of the interface transition zone for the i-th proportion sample. Let be the average thickness of the interface transition zone for the k-th mix design sample. Porosity Let be the average pore size, and t be the thickness of the interface transition zone. If... and , =0.25, =0.20, This is the threshold for determining the difference in matching factors, also known as the similarity distance threshold for matching factors. The threshold for determining differences in electron microscopic microstructures, also known as the distance threshold for microscopic structural similarity, is then set at the node. and Establish related edges between If two samples show a gradient change only in one key proportion factor, such as only the replacement rate of volcanic slag coarse aggregate differs, while the differences in other factors do not exceed the preset error. , =0.03, also establish directional edges to express the propagation relationship of single-factor changes on performance. The edge attributes of each edge are denoted as: ,in The difference in matching factors, For the difference in response surface interaction terms, This represents the difference in microscopic features observed under electron microscopy.

[0041] The system learns relationships based on a graph neural network. The update of the l-th layer node can be represented as: ,in For the first Layer nodes The updated node features, also known as updated node embedding features. For nodes in layer l The current node features, also known as the current layer node embedding features, Number the adjacent nodes. The weight matrix is ​​mapped to the node's own features. The neighborhood message mapping weight matrix, For nodes The set of adjacent nodes, The activation function is nonlinear. The training objective is to predict experimental response values ​​such as slump, compressive strength, splitting tensile strength, thermal conductivity, and thermal insulation performance based on the node representations, enabling the graph network to learn the correlation and propagation laws between proportioning factors, microstructure, and macroscopic performance. After training, the system outputs a node embedding matrix. The adjacency matrix A and the edge attribute set E are encapsulated into a proportioning graph data. The system establishes aggregate constraint data based on prior knowledge in materials science. Extract the proportion vector: ,in For water consumption, This refers to the amount of cementitious material used. This refers to the amount of fine aggregate used. This refers to the amount of coarse aggregate used. The replacement rate of volcanic slag, This refers to the dosage of admixtures. The system is set with water-cement ratio constraints. Volcanic slag aggregate replacement rate constraint , Maximum allowable replacement rate for volcanic slag aggregate, volume balance constraint: ,in This represents the percentage of water used by volume. This represents the volume percentage of the cementitious material. This refers to the volume percentage of fine aggregate. This represents the volume percentage of coarse aggregate. To design the pore volume fraction.

[0042] S3. Update the interlayer weights of the mix proportion diagram data based on the aggregate constraint data to obtain the neural network surrogate model; Specifically, the system uses the obtained proportioning relationship diagram data G=(V,A,E,H) and aggregate constraint data Let V be the set of matching sample nodes, A be the adjacency matrix, and E be the set of edge attributes. Features embedded in nodes; aggregate constraint data This includes at least the water-cement ratio range, the volcanic slag replacement rate range, the volume balance relationship, the porosity threshold, and the interface transition zone thickness threshold. The system uses preset parameters or expert knowledge for each node. Generate constraint state vector: ,in, , The preset lower limit for the water-to-binder ratio is set to 0.25. The preset upper limit for the water-to-glue ratio is set to 0.55. This indicates whether the volcanic slag replacement rate exceeds the limit. Indicates whether volume balance is satisfied. Porosity Does it exceed , The upper limit of porosity is preset and set according to engineering requirements. Indicates the thickness of the interface transition area Does it exceed , The maximum thickness of the preset interface transition zone is set to 30μm. When any of the above constraints is 0, the system marks the node as a constraint deviation node; when all are 0, it is marked as a constraint stable node.

[0043] The system corrects the edge propagation in the matching graph based on the constraint state. For the edge... If node and If all nodes are constrained and stable, then the original edge attributes are preserved. If any node has excessive porosity or excessive thickness in the interface transition zone, the edge is marked as a micro-weakening propagation edge; if there is an abnormal water-cement ratio or volume balance, the edge is marked as a proportion imbalance propagation edge. In each layer of the graph neural network, the system executes different update rules based on the edge labels: stable edges participate in normal neighborhood aggregation, micro-weakening propagation edges only transmit porosity, interface, and texture-related features, and proportion imbalance propagation edges do not participate in main effect propagation, only retaining abnormal constraint labels for error correction.

[0044] The update of the l-th layer node is represented as: ,in For the first Layer nodes The updated node features, also known as updated node embedding features. For nodes in layer l The current node features, also known as the current layer node embedding features, For adjacent nodes in layer l The adjacent node embedding features, Number the adjacent nodes. It is a non-linear activation function. This is the set of effective neighborhood nodes after aggregate constraint screening. For the first Layer node weight matrix, The edge feature mapping matrix, This represents the constraint state vector of adjacent nodes. The system uses measured values ​​of slump, compressive strength, splitting tensile strength, thermal conductivity, or thermal insulation performance as supervision labels to establish a prediction error term: , Let be the error term for predicting the experimental response, where i is the sample number, n is the total number of sample numbers, j is the experimental response index number, and q is the total number of experimental response indices. Let be the predicted value of the test response of the i-th matching sample corresponding to the j-th type. For the measured values ​​of the test response of type j corresponding to the i-th mix designation sample, establish constraint deviation terms: The overall training objective is: The system updates the inter-layer weights according to the gradient descent rule: ,in For learning rate, This refers to the deviation of the water-to-binder ratio. The deviation of the volcanic slag replacement rate. This is the deviation from volume balance. This represents the deviation in porosity. This represents the thickness deviation of the interface transition zone. This is the updated network weight matrix for layer l. Let be the current network weight matrix of layer l. Let be the gradient of the total training loss with respect to the weight matrix of the l-th layer. The system constructs a performance prediction output function based on the above parameter set. , which is the neural network surrogate prediction function formed by graph convolution propagation, constraint weight correction, and output layer mapping. After training, the system updates the inter-layer weight set. Adjacency relationships after constraint filtering Node representation and performance prediction output function Encapsulate to obtain a neural network proxy model.

[0045] S4. Perform hyperparameter co-training on the neural network surrogate model to obtain the matching solution space surrogate model; Specifically, the system uses the obtained neural network surrogate model For the initial model, where This is the performance prediction function after aggregate constraint correction. To constrain the filtered adjacency relationships. For node representation, the system divides the samples corresponding to the multimodal proportioning representation data into training set, validation set, and solution space verification set, for example, in a 7:2:1 ratio, ensuring that samples from different volcanic slag replacement rate ranges and different water-cement ratio ranges are included in each set. The system constructs a hyperparameter combination vector: ,in This indicates the number of layers in a graph neural network. Indicates the hidden feature dimension. This indicates the number of neighboring nodes that each node participates in the aggregation. Indicates the learning rate. Indicates the number of samples in the batch. Indicates the proportion of random inactivation. Indicates the maximum number of training rounds. This indicates the threshold for early stopping. The system does not optimize individual hyperparameters in isolation, but rather... Conduct collaborative experiments as part of the overall training configuration; for example, when Synchronization limit when increasing Not lower than the preset lower limit to prevent overfitting caused by deep aggregation; when During the increase, check synchronously. Check whether adjacent edges satisfy aggregate constraints to avoid incorrectly including nodes with excessive porosity or abnormal interface transition zones in normal propagation. For any candidate hyperparameter combination... The system re-instantiates the proxy model: ,in For the i-th proportion sample, the single-test response prediction value is... The neural network surrogate prediction function under the s-th group of hyperparameter configurations is composed of a graph convolutional propagation layer, a material constraint mapping layer, and an experimental response output layer. For multimodal proportion characterization data, This is aggregate-constrained data. During training, the system uses measured values ​​of compressive strength, splitting tensile strength, thermal conductivity, or thermal insulation performance. Calculate the verification error for the label: , Let be the validation error corresponding to the s-th candidate hyperparameter combination, used to evaluate the prediction accuracy of the surrogate model trained with the s-th hyperparameter combination on the validation set, where m is the total number of matched samples in the validation set, and i is the matched sample number in the validation set. This is the predicted test response output for the i-th validation sample. Let be the measured value of the experimental response corresponding to the i-th verification sample.

[0046] At the same time, check whether the prediction results violate the material science boundaries, such as whether the water-cement ratio corresponding to the predicted optimal ratio falls within the range. Does the volcanic slag replacement rate fall into the range? Does the porosity not exceed Does the thickness of the interface transition area not exceed , This is the lower limit of the water-to-binder ratio, for example, 0.25. This is the upper limit of the water-to-binder ratio, for example, 0.55. This refers to the maximum allowable replacement rate or the upper limit of the replacement rate of volcanic slag aggregate. This represents the upper limit or maximum allowable porosity, with a value of 0.18. This represents the upper limit of the average thickness of the interface transition zone or the maximum allowable thickness of the interface transition zone, and is set to 30 μm. If a combination has a small error but generates a large number of unconstrained proportions, then that combination will not be included in the candidate retention set.

[0047] The system updates the hyperparameter combination according to the requirement that the verification error decreases and the number of non-compliant samples does not increase; if the verification error changes by less than 0.001 for 10 consecutive rounds, early stopping is triggered, and the current optimal combination is retained. The system will The model is embedded into a neural network surrogate model, and candidate matching points are generated within the allowed range of matching variables. ,in The replacement rate of volcanic slag fine aggregate, denoted as volcanic slag coarse aggregate replacement rate, c as cementitious material dosage, and a as admixture dosage. To conform to aggregate constraint data, the system uses an optimized surrogate model to perform batch predictions on candidate mix proportions, obtaining predicted values ​​for strength, thermal conductivity, and thermal insulation performance for each mix proportion point. The system then encapsulates the candidate mix proportion point, predicted performance, constraint state, and adjacency relationship into a mix proportion solution space surrogate model.

[0048] S5. Perform frontier evolution optimization on the surrogate model of the matching solution space to obtain the matching parameter network data.

[0049] Specifically, the system uses the obtained sizing solution space proxy model. For input, where To meet the candidate mix designation points that satisfy aggregate constraints, The performance data, such as strength, thermal conductivity, and thermal insulation performance, are predicted by the surrogate model. In the state of aggregate constraint, This establishes the correlation between candidate matchups. The system defines each candidate matchup point as an evolutionary individual: ,in This refers to the water-to-glue ratio. The replacement rate of volcanic slag fine aggregate, denoted as volcanic slag coarse aggregate replacement rate, c as cementitious material dosage, and a as admixture dosage; Indicates the predicted intensity. Indicates the predicted thermal conductivity. This indicates predicted energy-saving or thermal insulation performance; if expressed numerically, a higher number indicates better performance. This indicates whether the mix proportions meet aggregate constraints.

[0050] The system's frontier optimization direction is set as follows: the strength is not lower than the design threshold. , Based on the pre-set requirements of the test task or engineering application, the thermal conductivity should be minimized as much as possible, the energy-saving performance should be maximized, and the candidate points should continuously meet the requirements. For any two individuals and If the following conditions are met: And at least one indicator is strictly better than Then determine Dominate , Let j be the j-th candidate mix design, also known as the j-th candidate solution. It includes the mix design parameters of the j-th group of lightweight aggregate concrete and the corresponding predicted performance indices. The m-th candidate allocation scheme, also known as the m-th candidate solution, is used for multi-objective performance comparison with the j-th candidate allocation scheme. Let j be the predicted value for the j-th performance objective. Let m be the predicted intensity value of the m-th candidate mix. Let J be the predicted thermal conductivity of the j-th candidate mix proportion. Let be the predicted thermal conductivity of the m-th candidate mix proportion. Let j be the predicted thermal insulation performance index value of the j-th candidate mix proportion. Let m be the predicted thermal insulation performance index value for the m-th candidate mix ratio. The system iterates through all candidate mix ratios and counts the number of times each candidate mix ratio is dominated by other mix ratios. .like =0 indicates that there are currently no other candidate allocations that are non-inferior across all objectives and superior in at least one objective; therefore, this allocation is included in the first frontier set. .get Then, the system will The proportions in the candidate set are temporarily removed, and the dominance count of the remaining proportions is recounted; proportions whose dominance count becomes 0 are then added to the second frontier set. Continue repeating the above process to obtain the following results sequentially. , The process continues at the leading level until all candidate allocations are assigned to a level.

[0051] In each evolutionary round, the system prioritizes selecting parent mix proportions from individuals at the first or second leading edge level that satisfy aggregate constraints. Local perturbations are applied to the parent mix proportions to generate offspring mixes; for example, the replacement rate of volcanic slag fine aggregate is adjusted without disrupting volume equilibrium. , To update the replacement rate of volcanic slag fine aggregate, The replacement rate of volcanic slag fine aggregate before the update. For the adjustment of the volcanic slag fine aggregate replacement rate, such as 0.05, the amount of ordinary fine aggregate is reduced by an equal volume. When fine-tuning the water-cement ratio, the amount of water or cementitious material is adjusted simultaneously to ensure that the w / c ratio remains within the constraint range. If the disturbed mix proportion causes the predicted porosity to exceed... Or the thickness of the interface transition area exceeds If the offspring is not selected, it will be directly removed and will not be included in the next round of frontier sorting.

[0052] The system will re-input the retained offspring into the matching solution space surrogate model to obtain updated prediction performance data, and then merge and sort it with the previous round's leading individuals. If the first leading set is used for several consecutive rounds... If the boundary change of the index is less than 0.005, or if the maximum evolutionary cycle is reached, the optimization process stops. The system uses the leading edge ratio point as a node and the relationship between two ratios—where a perturbation of one ratio generates another ratio or where only a single factor's gradient changes—as edges, forming a ratio parameter network: ,in Storage of optimal ratio parameters and predictive performance, Storage ratio evolution relationship, Storage non-dominated hierarchy, constraint states, and performance boundaries.

[0053] Preferably, the response surface interaction analysis in S1 specifically includes: S11. Extract factor variables from the proportioning experiment data to obtain proportioning factor data; Specifically, the system uses single-group specimen numbering. As an index, extract the water-cement ratio from the mixing test data. Volcanic slag fine aggregate replacement rate Volcanic slag coarse aggregate replacement rate Dosage of cementitious materials Additive dosage Factors such as these form the matching factor data. , Let i be the water-cement ratio of the i-th sample. The amount of additive in the i-th sample ratio is denoted as .

[0054] S12. Align the response values ​​of the proportioning test data with the proportioning factor data to obtain the proportioning response matrix data; Specifically, the system follows Align the proportioning factor data with the response values ​​of compressive strength, splitting tensile strength, thermal conductivity, and thermal insulation coefficient; samples with missing response values ​​are not included in the fitting, thus obtaining the proportioning response matrix. , Let be the measured slump value of the i-th mix design sample. is the measured value of the test response of the i-th sample with the q-th ratio.

[0055] S13. Construct interaction items based on the ratio factor data to obtain response surface interaction item data; Specifically, the system for Perform a second expansion to generate a first-order term. Square terms and pairwise interaction items This forms the response surface interaction item data: , This is the value of the a-th matching factor, also known as the linear term or main effect term of the a-th matching factor. This is the interaction term between the a-th and b-th matching factors, also known as the two-factor interaction term.

[0056] S14. Based on the response surface interaction term data and the ratio response matrix data, perform response surface fitting to obtain response surface coefficient data; Specifically, the system uses For independent variable, Perform least squares fitting for the dependent variable: , The response surface regression design matrix is ​​composed of the response surface design vectors of all proportioned samples. Arranged in rows, the response surface coefficient data are obtained. , These are the intercept coefficients or constant term coefficients of the response surface model. Let be the regression coefficient of the first-order term of the a-th matching factor. This is the quadratic regression coefficient of the a-th matching factor, also known as the curvature effect coefficient of the a-th matching factor. It is the regression coefficient of the interaction term between the a-th and b-th matching factors, also known as the two-factor interaction coefficient.

[0057] S15. Based on the response surface coefficient data, perform interaction contribution filtering to obtain response surface interaction data.

[0058] Specifically, the system extracts interaction coefficients. And calculate the interaction contribution: , The interaction contribution value between the a-th matching factor and the b-th matching factor. The sample variance of the two-factor interaction term. For the interaction term between the a-th matching factor and the b-th matching factor, Standardize to obtain , Let be the standardized interaction contribution of the a-th matching factor and the b-th matching factor, representing the proportion of the interaction contribution of this factor pair to the total interaction contribution of all two-factor pairs; Factors with a value higher than 0.05 are retained, and the response surface interaction data is output.

[0059] Preferably, the electron microscope image feature extraction in S1 specifically involves: S16. Perform phase region segmentation based on electron microscope image data to obtain phase region segmentation data; Specifically, the system processes electron microscope images Perform scale calibration, grayscale equalization, and median filtering, based on grayscale threshold. Edge gradient G(x,y) and texture response divide pixels into aggregate region, slurry region and porosity region, generating a phase region label matrix. The phase segmentation data is obtained; the specific process is described in the aforementioned embodiment.

[0060] S17. Identify the boundary region based on the phase region segmentation data to obtain the interface transition region data; Specifically, the system extracts the boundaries of the aggregate zone. Extending 30 μm towards the slurry side in the boundary normal direction, a candidate interface zone is formed; then, pore connectivity fracture regions are eliminated, retaining those that satisfy the gray-scale gradient abrupt change. The area is used to obtain interface transition area data. .

[0061] S18. Based on the interface transition zone data, perform pore morphology analysis to obtain pore structure characteristic data; Specifically, the system in Identify pore connectivity regions within and adjacent slurry areas, and calculate pore area. ,perimeter Equivalent aperture Roundness and porosity , The pore area within the interface transition zone. The effective analysis area of ​​the interface transition zone is determined; based on the above, the pore structure characteristic data are obtained.

[0062] S19. Microscopic feature vector encapsulation is performed based on the interface transition zone data and pore structure feature data to obtain electron microscope image feature data.

[0063] Specifically, the system will adjust the average thickness of the interface transition area. Mean grayscale gradient Porosity Average aperture Average roundness and the number of connected pores Packaged into vectors according to specimen number We obtained electron microscope image feature data.

[0064] Preferably, the training of the graph neural network in S2 is specifically as follows: S21. Map the node attributes of the multimodal proportioning characterization data to obtain the proportioning node data; Specifically, the system uses the obtained multimodal matching data to characterize the data. Input, and use the specimen number. As a node index, the i-th mix design specimen is mapped to a node. .in This includes response surface main effects, squared terms, and interaction terms data. This includes the thickness of the interface transition zone, porosity, average pore size, roundness, and number of connected pores. The system normalizes each dimension of the feature to obtain the node attributes: ,in Output the proportioning node data for the original proportioning factors such as water-cement ratio, volcanic slag replacement rate, and amount of cementitious materials.

[0065] S22. Construct node association relationships based on response surface interaction data and electron microscope image feature data to obtain edge connection data; Specifically, the system constructs node edges based on response surface interaction data and electron microscopy image feature data. For two nodes... , If the differences in their interaction items satisfy: Furthermore, the differences in porosity and interfacial transition zone thickness satisfy the following: Then establish an edge , The difference value contributed by the two-way interaction between the i-th and j-th matched samples is... Let be the interaction contribution value between the a-th and b-th matching factors in the i-th matching sample. Let be the interaction contribution value between the a-th and b-th matching factors in the j-th matching sample. This represents the porosity difference between the i-th and j-th sample ratios. Let be the porosity of the i-th sample. Let be the porosity of the j-th sample. Let be the difference in thickness of the interface transition zone between the i-th and j-th proportion samples. Let be the average thickness of the interface transition zone for the i-th proportion sample. Let be the average thickness of the interface transition zone for the j-th mix design sample. If the two nodes exhibit a single-factor gradient change only in the replacement rate of fine aggregate or coarse aggregate in the volcanic slag, and the differences in other factors are less than 1... Edges are also created to represent the paths of ratio changes. Edge attributes are denoted as: Obtain edge connection data. Contribute difference values ​​to response surface interactions. This represents the porosity difference value. This represents the thickness difference value of the interface transition zone. This is the vector of differences in matching factors.

[0066] S23. Generate an adjacency matrix based on the matching node data and edge connection data to obtain the matching graph structure data; Specifically, the system generates an adjacency matrix A based on the matching node data and edge connection data. If an edge exists... Then let Otherwise and set Preserve node self-loop information. The system synchronously generates a degree matrix D, where... , Let be the degree value of the i-th matching sample node. Let the adjacency matrix elements between the i-th matching sample node and the j-th matching sample node be used, and let the node attribute matrix be used as the adjacency matrix elements. The adjacency matrix A and the edge attribute set E are encapsulated into matching graph structure data. , The initial node embedding features are used for the first matching sample node. The initial node embedding features are used for the nth matching sample node.

[0067] S24. Perform gating state update training based on the matching diagram structure data to obtain node embedding feature data and edge weight update data. Specifically, the system performs gated state update training on the matching graph structure data. In layer l, the nodes... First, aggregate neighborhood information: Then generate the gating coefficients: And update the node status: , ,in Let N(i) be the neighborhood aggregation message of the i-th matching sample node in layer l, where i is the number of the i-th matching sample node, j is the number of the j-th matching sample node, l is the layer number of the graph neural network, and N(i) is the set of adjacent nodes. Let be the adjacency matrix element between the i-th matching sample node and the j-th matching sample node. The neighborhood message mapping weight matrix, The current node embedding features for the j-th matching sample node in the l-th layer. Let i be the edge attribute data between the i-th matching sample node and the j-th matching sample node. Let be the gating coefficient for the i-th matching sample node in the l-th layer. , , The training parameters are initialized to preset values. The system is trained using measured values ​​of compressive strength, thermal conductivity, or energy-saving performance as supervised labels, and the edge weights are updated synchronously. , Let be the edge weight between the i-th and j-th matched sample nodes in the (l+1)-th layer. The updated node embedding features are for the i-th matched sample node in the (l+1)-th layer. The updated node embedding features are for the j-th matching sample node in the (l+1)-th layer. Generate a weight matrix for the edge weights, with initial values ​​set to preset values; output node embedded feature data. and edge weight update data .

[0068] S25. Based on the node embedding feature data and edge weight update data, perform graph structure correction to obtain the matching relationship graph data.

[0069] Specifically, the system performs graph structure correction based on the trained node embedding features and edge weights. If the edge weights... If the predicted performance change direction of two nodes is opposite to the interaction direction of the response surface, then delete the corresponding edge; if the embedding distance between two nodes is: , Let be the node embedding feature of the i-th matching sample node. If the node embedding feature of the j-th matching sample node is less than 0.12 and both satisfy the porosity and interface transition zone thickness constraints, then a potential edge is added. This forms the corrected set of nodes, adjacency matrix, edge attributes, and edge weights, resulting in the matching relationship graph data.

[0070] Preferably, the prior physical constraints in materials science in S2 are as follows: S26. Based on the multimodal proportioning characterization data, the aggregate composition boundary is identified and the mechanical property boundary is set to obtain aggregate replacement rate constraint data and strength constraint data respectively. Specifically, the system characterizes data using a multimodal matching approach. As input, and trace back the original proportions of the components. ,in For the response surface interaction data of the i-th ratio sample, For the electron microscopy image feature data of the i-th matching sample, This refers to the water-to-glue ratio. The replacement rate of volcanic slag fine aggregate, denoted as volcanic slag coarse aggregate replacement rate, c as cementitious material dosage, and a as admixture dosage. The system first statistically analyzes the effective coverage range of the volcanic slag replacement rate in the experimental design, and then sets the material mixability boundary accordingly: , =0, =0.5, =0, =0.6, if a certain ratio satisfies volume balance: ,in This represents the percentage of water used by volume. This represents the volume percentage of the cementitious material. This refers to the volume percentage of fine aggregate. This represents the volume percentage of coarse aggregate. To design the pore volume fraction, and , If all samples fall within the above range, they are marked as feasible aggregate composition samples, forming aggregate replacement rate constraint data. The system simultaneously... Extracting compressive strength from the corresponding response value Splitting tensile strength ,set up: ,in , The minimum mechanical performance requirements set for the target design level or test task are used to obtain strength constraint data.

[0071] S27. Based on the electron microscopy image feature data in the multimodal proportioning characterization data, perform pore structure boundary analysis to obtain pore structure constraint data; Specifically, the system extracts electron microscopy image feature data from multimodal ratio characterization data. Extract the thickness of the interface transition area Porosity Average aperture pore roundness and the number of connected pores The system uses samples that satisfy the strength constraints as the stable sample set. Within this set, the permissible boundaries of the pore structure are determined: ,in, , , , Take the upper quantile value of the corresponding index in the stable sample set or the engineering-set threshold. If a sample exceeds the limits for porosity, pore size, or interface transition zone, it is marked as a sample with unstable pore structure, and the pore structure constraint data is output.

[0072] S28. Based on the multimodal proportioning characterization data and pore structure constraint data, thermal performance boundaries are set to obtain thermal conductivity constraint data; Specifically, the system extracts the thermal conductivity based on the thermal response values ​​or surrogate prediction values ​​in the multimodal proportioning characterization data. or thermal resistance The thermal performance boundaries are set based on the obtained pore structure constraint data. The system specifies that the candidate mix proportions must meet the following requirements: , The upper limit of thermal conductivity is taken as 0.65 W / (m·K). The lower limit of thermal resistance is taken as 0.30m. 2 ·K / W, and when porosity Or the thickness of the interface transition area Even at that time The sample with low thermal conductivity is not directly classified as a thermally optimal sample, but rather marked as a sample with low thermal conductivity but structural risk. This represents the upper limit of porosity, such as 0.18. This is the upper limit of the thickness of the interface transition zone, such as 30 μm; only when Furthermore, effective thermal conductivity constraint data is only generated when the pore structure constraint is true. This avoids introducing too many pores in pursuit of low thermal conductivity, which could lead to strength degradation.

[0073] S29. Encapsulate the aggregate replacement rate constraint data, pore structure constraint data, strength constraint data, and thermal conductivity constraint data to obtain aggregate constraint data.

[0074] Specifically, the system will use aggregate replacement rate constraint data. Pore ​​structure constraint data Strength constraint data and thermal constraint data According to specimen number Package: If all four types of constraints are satisfied, then If any constraint is not satisfied, the corresponding failure type is recorded.

[0075] Preferably, S3 specifically comprises: S31. Initialize the graph neural network based on the matching relationship graph data to obtain the initial graph neural network model; Specifically, the system uses the obtained proportioning relationship data The input is V, where V is the matched sample node and A is the adjacency matrix. For edge attributes, These are the initial attributes of the nodes. The system classifies them according to node feature dimensions. Target Embedding Dimension and output performance dimension Initialize graph neural network parameters and set node mapping matrix Edge mapping matrix Parameters of convolutional layers and output layer parameters , For the reason OK, Let the matrix space of the columns of real numbers be: , The initial node embedding features of the i-th matching sample node are used to obtain the initial graph neural network model. .

[0076] S32. Encode the constraint factors based on the aggregate constraint data to obtain the aggregate constraint vector; Specifically, the system uses the obtained aggregate constraint data As input, each type of constraint is transformed into a constraint factor that can participate in network propagation. This represents the constraint state of the aggregate replacement rate for the i-th mix design sample. This represents the pore structure constraint state of the i-th mix design sample. Let i be the strength constraint state of the i-th matching sample. Let represent the thermal conductivity constraint state for the i-th sample. If the i-th sample satisfies the volcanic slag replacement rate boundary, then... =1, otherwise =0; satisfying the pore structure boundary condition =1, otherwise 0; if the strength boundary condition is satisfied, then... =1; if the thermal conductivity boundary condition is satisfied, then... =1. Simultaneously record the deviation: By concatenating the two, we obtain the aggregate constraint vector: Output aggregate constraint vector , This represents the constraint state of the aggregate replacement rate for the i-th mix design sample. This represents the pore structure constraint state of the i-th mix design sample. Let i be the strength constraint state of the i-th matching sample. This represents the thermal conductivity constraint state for the i-th sample ratio. Let be the overall constraint deviation of the i-th matching sample. This is the aggregate constraint vector for the first mix design sample. This is the aggregate constraint vector for the nth mix design sample.

[0077] S33. Perform constraint matching on the initial graph neural network model based on the aggregate constraint vector to obtain constraint weight mapping data; Specifically, the system will use aggregate constraint vectors Compared with the node states in the initial graph neural network model Perform a corresponding match. For any edge... The system compares the constraint states of the two endpoints. If and If all four types of constraints are met, the edge is marked as a valid propagation edge; if any end has excessive porosity or abnormal thermal conductivity, it is marked as a structural risk propagation edge; if the strength is insufficient, it is marked as a mechanical weakening propagation edge. System formation constraint matching coefficient: ,in For constraint mapping parameters, Representing an edge The degree of preservation in subsequent graph convolution propagation, output constraint weight mapping data. .

[0078] S34. Based on the constraint weight mapping data, the initial graph neural network model is re-balanced by graph convolution propagation path to obtain the constraint update network model. Specifically, the system re-evaluates the propagation path of the initial graph neural network model based on the constraint weight mapping data. For nodes... The propagation of the l-th layer neighborhood is based on the original adjacency relationship. Revised to: And perform graph convolution update: ,in The propagation strength after aggregate constraint correction. These are the parameters for the neighborhood message mapping. If a certain edge corresponds to... Below the threshold If the value is 0.3, the system does not delete the edge but only retains its anomaly marker. This edge does not participate in normal performance propagation, preventing unstable samples from misleading the feasible allocation region. This leads to the constrained update network model. .

[0079] S35. Based on the multimodal matching data, the constraint update network model is trained by backpropagation to obtain the neural network surrogate model.

[0080] Specifically, the system characterizes data using a multimodal matching approach. The corresponding measured performance response As a supervisory label, This represents the measured compressive strength of the i-th mix design sample. This represents the measured splitting tensile strength of the i-th mix design sample. Let be the measured value of the thermal conductivity of the i-th sample. Let be the measured value of the thermal insulation performance index of the i-th sample ratio. Proportioning diagram The aggregate constraint vector Q is input to constrain and update the network model to obtain the predicted output: , To constrain the prediction function of the updated network model, This is the multimodal matching characteristic data for the i-th matching sample. This is the adjacency matrix of the mix proportions after material constraint correction. The edge attribute data of the matching relationship graph. Given the set of aggregate constraint vectors, the system calculates the prediction error: And construct the training objective by combining the constraint deviation: , The constraint deviation of the i-th matching sample is then updated according to the backpropagation rule. Training stops when the validation error changes by less than 0.001 for 10 consecutive rounds or when the maximum number of training rounds is reached. The network parameters are then encapsulated, and the adjacency matrix is ​​adjusted according to constraints. Node embedding and prediction function This yields a neural network proxy model.

[0081] Preferably, the graph convolution propagation path re-trade is specifically as follows: Graph propagation path data is obtained by extracting the graph convolution propagation path based on the initial graph neural network model. Specifically, the system is based on the initial graph neural network model. Extract the graph convolution propagation path. For the proportioning relationship diagram, The adjacency matrix is ​​the matching relationship graph. The edge attribute data of the matching relationship graph. Embed the feature matrix for the initial node. Let A be the current network weight matrix for layer l. For graph convolution in layer l, the system reads the weights from the adjacency matrix A that satisfy... The edge with =1, and the target node Centered on the target node, the propagation path is formed by tracing outwards to neighboring nodes within a maximum of one hop. , For the j-th matching sample node, Let be the edge between the j-th matching sample node and the a-th matching sample node. For the a-th matching sample node, Let be the edge between the b-th matching sample node and the i-th matching sample node. Let be the i-th matching sample node. If duplicate nodes appear in the path, the system only retains the shortest acyclic path; if the edge attribute... If a path is missing, it will not be included in subsequent calculations. This yields the graph propagation path data. It records the path's starting point, ending point, level, traversed edges, and original adjacency relationships.

[0082] Based on the constraint weight mapping data, constraint association calibration is performed on the graph propagation path data to obtain path constraint association data; Specifically, the system maps data according to constraint weights. Constraint association and labeling are performed on the graph propagation path data. For any path The system reads the constraint matching coefficients of each edge on the path. And read the aggregate constraint vector corresponding to the node. If all nodes in the path meet the requirements for aggregate replacement rate, pore structure, strength, and thermal conductivity boundaries, it is marked as a feasible propagation path. If there are nodes in the path with excessive porosity, excessive interface transition zone thickness, or insufficient strength, it is marked as a risk propagation path, and the failure type is recorded. This yields path constraint association data. For propagation path type, For the propagation path, Let be the aggregate constraint vector for the u-th mix design sample node. Let be the constraint matching coefficient between the u-th matching sample node and the v-th matching sample node, where u is the number of the u-th matching sample node.

[0083] Material boundary propagation re-estimation is performed on path constraint correlation data to obtain path contribution weight data; Specifically, the system performs material boundary propagation reestimation on the path constraint association data. For path P, the system calculates path constraint consistency: And check the material boundary status of the nodes in the path. If And it does not exist in the path. , , , In cases where the hard boundary exceeds the limit, the path is retained as a normal contribution path; if any of the above hard boundary limits are exceeded, the path contribution is marked as a restricted contribution; if both strength and pore structure exceed the limit, the path is marked as a prohibited performance propagation path, retaining only the abnormal label. The system then generates path contribution weight data accordingly. .

[0084] The initial graph neural network model is weighted and redistributed based on the path contribution weight data to obtain the reweighted graph convolution parameter data. Specifically, the system reallocates weights to the initial graph neural network model based on path contribution weight data. For any side... The system summarizes the contributions of all paths containing that edge: , , , Let be the path contribution coefficient between the i-th and j-th matched sample nodes. Let be the set of propagation paths between the i-th and j-th matching sample nodes. For the number of propagation paths, For the propagation path, Let i be the set of propagation paths pointing to the i-th matching sample node. For another propagation path in the set of propagation paths, The overall contribution value of the transmission path, The overall contribution value of another propagation path, For the propagation path constraint matching value, For path P to target node Path contribution weight, The path inhibition coefficient is calculated based on boundary deviations such as excessive water-cement ratio, excessive volcanic slag replacement rate, excessive porosity, excessive interfacial transition zone thickness, insufficient strength, or abnormal thermal conductivity along the path. The original adjacent propagation relationship is then corrected as follows: ,Graph convolution update from the original The transmission was adjusted to spread: The reweighted graph convolution parameter data is obtained, including the corrected adjacency matrix. Path contribution weight , Side-level propagation coefficient and the corresponding graph convolution parameters , .

[0085] The parameters of the initial graph neural network model are solidified based on the reweighted graph convolution parameter data to obtain the constrained update network model.

[0086] Specifically, Replacing A in the initial model will result in values ​​below the threshold. The path is set to the error message path instead of the normal aggregation path. =0.05, and fix the propagation parameter set of the current layer: As a constraint update network model, This is the neural network surrogate model updated with material constraints. For the proportioning relationship diagram, This is the adjacency matrix of the matching graph after path contribution redistribution. The edge attribute data of the matching relationship graph. Embed the feature matrix for the initial node. Let be the current network weight matrix of layer l. The neighborhood message mapping weight matrix, It is the path contribution coefficient between the i-th matching sample node and the j-th matching sample node.

[0087] Preferably, the material boundary propagation recalculation specifically includes: The constraint types of the path constraint associated data are grouped to obtain path constraint type data; Specifically, the system uses path constraints to associate data. For input, where The propagation path consists of nodes and edges. Nodes in the path aggregate constraint vector, The edge constraint matching coefficient is used. The system reads the constraint state of each node in the path one by one and assigns it to the aggregate replacement rate constraint. Pore ​​structure constraints Strength constraints Thermal confinement Four categories. If any node in the path has a porosity exceeding the limit, the path record... =1; if there is an intensity below the threshold, then record it. =1. This forms path constraint type data: , where each term represents the type of material boundary involved in the propagation path.

[0088] Material boundary deviation is identified based on path constraint type data to obtain path boundary deviation data; Specifically, the system according to The actual material parameters of each node in the readback path, including the slag replacement rate. Porosity Thickness of the interface transition area Compressive strength thermal conductivity Calculate the boundary deviations separately: , , , , If the deviation is 0, it means the node is within the corresponding material boundary; if it is greater than 0, it indicates a risk of exceeding the boundary. The system summarizes the deviations of all nodes within the path to obtain the path boundary deviation data: ,in For the propagation path The deviation of the aggregate replacement rate For the propagation path The porosity deviation, For the propagation path The thickness deviation of the interface transition area. For the propagation path The intensity deviation, For the propagation path The deviation of thermal conductivity, These represent the maximum or average deviation at the path level, respectively.

[0089] The path inhibition coefficient data is obtained by generating a propagation penalty coefficient from the path boundary deviation data. Specifically, the system determines the deviation data based on the path boundary. Generate a path suppression coefficient. If the path has no boundary deviations, set the suppression coefficient. This indicates that the path participates normally in graph convolution propagation; if there is a single boundary deviation, a decay coefficient is generated based on the deviation magnitude. If both pore structure deviation and strength deviation exist simultaneously, for example and Then mark the path as a strongly suppressed path and make Not higher than the preset upper limit , =0.20. This yields the path inhibition coefficient data.

[0090] The effective propagation potential is re-estimated based on the path constraint type data and the path inhibition coefficient data to obtain the path propagation potential data. Specifically, the system reads the constraint matching coefficients of each edge on the path. Calculate the consistency of the original propagation: Then, the effective propagation potential is generated by combining the path inhibition coefficient: ,in This indicates the extent to which the path can still be used for performance information propagation under the condition that the material boundary conditions are met. If If only the thermal conductivity constraint deviates while the strength and pore structure are satisfied, the path is retained as the thermal risk warning path; if If both the pore structure and strength constraint deviation exist simultaneously, then... Set it to 0 or close to 0 so that it does not participate in normal performance aggregation.

[0091] The path propagation potential data is transformed using standard weights to obtain path contribution weight data.

[0092] Specifically, the system will target the same node The set of all incident propagation paths is denoted as The propagation potential of each path is standardized: ,in, To prevent extremely small constants with a denominator of 0. If a certain path , =0.05, then this path is not considered a normal graph convolution propagation path; only its anomaly type and boundary deviation record are retained. If the path contribution weight is not specified, it will be considered a valid path and participate in the subsequent edge propagation weight aggregation. Output path contribution weight data. .

[0093] Preferably, S4 specifically comprises: S41. Construct the hyperparameter search space based on the neural network surrogate model to obtain hyperparameter space data; Specifically, the system uses the obtained neural network surrogate model Based on, To constrain the prediction function of the updated network model, This is the adjacency matrix of the matching graph after path contribution redistribution. The edge attribute data of the matching relationship graph. Embed the feature matrix into the nodes after updating the material constraints. Given the set of network weight parameters, we read adjustable parameters such as the number of model layers, hidden dimension, learning rate, number of neighborhood samples, batch size, inactivation rate, number of training epochs, and constraint thresholds to construct a hyperparameter search space. Where L is the number of graph convolutional layers, Embed dimensions for nodes. For learning rate, Let B be the number of neighborhoods participating in the aggregation for each node, B be the number of samples in the batch, p be the random inactivation rate, and T be the maximum number of training rounds. A threshold value of 0.3 is reserved for the constrained edges. A path contribution threshold of 0.05 is set. The system generates candidate combinations based on preset discrete or continuous intervals. This yields hyperparameter space data.

[0094] S42. Construct a joint training objective based on multimodal proportioning characterization data and aggregate constraint data to obtain collaborative training loss data; Specifically, the system characterizes data using a multimodal matching approach. Aggregate constraint data and measured response As input, construct a joint training objective. The measured compressive strength of the i-th mix design specimen is... The measured splitting tensile strength of the i-th mix design specimen is... Let be the measured thermal conductivity of the i-th mix design specimen. This represents the measured energy-saving performance index or thermal insulation performance index of the i-th mix design specimen. This index can be derived from thermal insulation tests, heat transfer coefficient conversion results, or building energy consumption simulation results. If expressed as a percentage, it can be the energy-saving rate or the improvement rate of thermal insulation performance. The model output is: The prediction error term is: , Let be the predicted experimental response vector for the i-th proportion sample. Let be the constrained update network model prediction function under the s-th candidate hyperparameter combination. This is the multimodal matching characteristic data for the i-th matching sample. This is the adjacency matrix of the matching graph after path contribution redistribution. For the aggregate constraint data of the i-th mix design sample, The supervision label for the i-th mix design sample is used, and constraint deviation terms are generated based on aggregate replacement rate, pore structure, strength, and thermal conductivity boundary. The deviations originate from the aggregate constraint vector. The system will... and Encapsulated as collaborative training loss data: .

[0095] S43. Iteratively train the neural network surrogate model based on the hyperparameter space data and the co-training loss data to obtain surrogate model data; Specifically, the system selects candidate combinations one by one from the hyperparameter space data. This is then written into the neural network proxy model to form the current training model. During training, the system reads data in batches. , E and Perform forward prediction and calculate Then, according to: Update model parameters. To update the training parameters of the network model after the constraints of the (t+1)th iteration, To update the network model training parameters for the constraints at the t-th iteration, Let be the learning rate corresponding to the s-th candidate hyperparameter combination. Let be the gradient of the joint training loss with respect to the training parameters at iteration t. If the constraint deviation term continues to increase during training, even if the prediction error decreases, the iteration of this combination will be paused; if the loss changes less than 1 / 2 for several consecutive iterations... If the condition is not met, the process should be stopped early. After training each candidate combination, the model parameters, loss curve, number of constraint violation samples, and prediction output are saved to obtain the surrogate model data.

[0096] S44. Validate and evaluate the proxy model data to obtain the optimal hyperparameter combination data; Specifically, the system inputs the proxy model data into the validation set and calculates the validation error: The number of samples that violated aggregate replacement rate, porosity, interfacial transition zone thickness, lower strength limit, and upper thermal conductivity limit was statistically analyzed. The system's filtering rule is: prioritize retaining... Fewer combinations; when the number of violations is the same, choose Smaller combinations are preferred; if the errors are similar, combinations with fewer layers and smaller parameter sizes are selected to reduce overfitting. Optimal hyperparameter combination data are obtained: , For the optimal combination of hyperparameters, To determine the optimal number of convolutional layers for the graph, Embed the feature dimension for the optimal hidden node. To achieve the optimal learning rate, The optimal number of neighboring nodes. To determine the optimal batch size, The optimal random inactivation ratio. To achieve the optimal maximum number of training rounds, To retain the threshold for the optimal constraint edge, The threshold is used to contribute to the optimal path.

[0097] S45. Based on the optimized hyperparameter combination data, the neural network surrogate model is mapped to the solution space to obtain the ratio solution space surrogate model.

[0098] Specifically, the system will optimize the combination of hyperparameters. By embedding the model into a neural network surrogate, a stable prediction function is obtained. Generate candidate mix design solutions within the allowable range of aggregate constraints: ,in, , , And satisfy the volume equilibrium condition. This is the lower limit of the water-to-binder ratio, such as 0.25. This represents the upper limit of the water-to-binder ratio, such as 0.55. This represents the lower limit of the replacement rate of volcanic slag fine aggregate, such as 0. This represents the upper limit of the replacement rate of volcanic slag fine aggregate, such as 0.50. This represents the lower limit of the replacement rate of volcanic slag coarse aggregate, such as 0. This represents the upper limit of the replacement rate of volcanic slag coarse aggregate, such as 0.6. The system inputs the solution for each candidate mix design. Predict its strength, thermal conductivity, and energy-saving performance: , The network model prediction function is updated under the constraints of optimal training parameters, and the candidate matching ratio, prediction performance, constraint state, and graph association are then encapsulated as follows: The surrogate model of the matching solution space is obtained. Let j be the matching factor vector for the j-th candidate matching ratio. Let j be the experimental response prediction vector for the j-th candidate mix. For aggregate constraint data set, The graph association corresponding to the j-th candidate allocation after path contribution redistribution.

[0099] Preferably, S5 specifically includes: S51. Set the search boundary for the matching variables based on the matching solution space proxy model to obtain the matching search space data; Specifically, the system uses the obtained sizing solution space proxy model. As input, read the candidate matching variables. Aggregate constraint data And the range of variables allowed by the proxy model. The system sets the water-glue ratio boundary as: The boundary value for the replacement rate of volcanic slag fine aggregate is set as follows: The boundary value for the replacement rate of coarse aggregate from volcanic slag is set as follows: The system limits the amount of cementitious material (c) and admixture (a) to fall within the acceptable mixing range of the test. Simultaneously, the system uses volume equilibrium as a hard constraint. Only the proportioning regions that satisfy the above variable boundaries and volume balance relationships are retained to obtain the proportioning search space data. .

[0100] S52. Generate the initial matching population based on the matching search space data to obtain the initial matching population data; Specifically, the system searches the matching space data. An initial population with matching ratios is generated internally. Each individual in the population is represented as: ,in The water-cement ratio for the m-th candidate formulation is... Let m be the replacement rate of volcanic slag fine aggregate in the m-th candidate mix. Let m be the replacement rate of volcanic slag coarse aggregate in the m-th candidate mix. Let m be the amount of cementitious material used in the m-th candidate mix proportion. Let m be the admixture dosage for the m-th candidate mix design, where m is the individual population number. The system first performs uniform sampling or Latin hypercube sampling within the boundaries of each variable to generate candidate individuals. For each candidate individual, a volume balance check is performed. If changes in the volcanic slag replacement rate cause a mismatch in the volume of ordinary aggregate, the dosage of ordinary fine aggregate or ordinary coarse aggregate is adjusted according to the equal volume replacement rule. If the boundary is still not met after adjustment, the individual is removed. N individuals that satisfy the basic mix design boundaries are retained to form the initial mix design population data. , This is the first candidate formulation. This is the second candidate formulation. This is the Nth candidate ratio scheme.

[0101] S53. Input the initial ratio population data into the ratio solution space surrogate model to predict the performance response and obtain the ratio performance prediction data; Specifically, the system will use the initial population data. Input the matching solution space surrogate model. For the m-th matching individual... The system calls the fixed proxy prediction function: The predicted performance response value corresponding to this ratio is obtained: ,in , , , , These represent the predicted slump, predicted compressive strength, predicted splitting tensile strength, predicted thermal conductivity, and predicted thermal insulation performance for the m-th mix proportion individual, respectively. These predicted values ​​collectively constitute the mix proportion performance prediction data. The system binds each mix proportion individual to its predicted performance to obtain the mix proportion performance prediction data:

[0102] S54. Based on the performance prediction data of the proportioning, conduct fitness assessment to obtain the frontier proportioning data; Specifically, the system performs a fitness assessment based on the predicted performance data of the mix proportions. The system evaluation criteria are: compressive strength and splitting tensile strength should not be lower than the design thresholds, such as 30 MPa and 2.5 MPa, respectively; lower thermal conductivity is better; and higher energy-saving performance is better. For any two individual mix proportions... and If the following conditions are met: , Let m be the predicted compressive strength value of the m-th candidate mix proportion. The predicted compressive strength value for the nth candidate mix proportion. Let m be the predicted splitting tensile strength of the m-th candidate mix. The predicted splitting tensile strength value for the nth candidate mix proportion. Let m be the predicted thermal conductivity value for the m-th candidate mix proportion. The predicted thermal conductivity value for the nth candidate mix proportion. Let m be the predicted value of the thermal insulation performance index for the m-th candidate mix proportion. The predicted thermal insulation performance index of the nth candidate formulation is given, and at least one performance index is strictly better than that of the nth candidate formulation. Then determine Dominate The system then performs a non-dominated ranking of all individuals, forming the first frontier set. Second Frontier Set The system prioritizes retaining individuals from the first frontier set; if the number of individuals in the first frontier set is insufficient, it supplements the frontier set with individuals whose predictive performance is similar and whose variable distribution is dispersed, thus obtaining frontier matching data.

[0103] S55. Based on the frontier ratio data, perform constraint feasibility screening to obtain the ratio parameter network data.

[0104] Specifically, the system performs constraint feasibility screening on the frontier ratio data. For each frontier ratio... The system reads back the aggregate constraint data. Each item is judged to determine whether it meets the constraint of volcanic slag replacement rate. Pore ​​structure constraints Strength constraints and thermal confinement If the following conditions are met: The value is If the constraints are met, the mix designation is marked as a feasible frontier mix designation; if there are issues such as excessive porosity, excessive thickness of the interface transition zone, or insufficient strength, it is discarded or marked as a risk mix designation. The system uses feasible frontier mix designs as nodes. The single-factor variation relationship between the two proportions is used as the boundary. For example, only or Connection edges are established when gradient differences exist and differences in other variables are less than 0.03. Node attributes store matching parameters and prediction performance, while edge attributes store the direction of variable changes and performance change trends, forming: ,in The set of nodes for candidate allocation schemes. Let the set of edges between the nodes of the candidate allocation scheme be . Record the non-dominated hierarchy, constraint state, and performance boundary information to obtain the matching parameter network data.

[0105] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended application documents rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the application documents be incorporated into the invention.

[0106] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A method for optimizing the mix proportion of lightweight aggregate concrete based on response surface methodology, characterized in that, Includes the following steps: S1. Obtain the mixing ratio test data and electron microscope image data; perform response surface factor interaction analysis based on the mixing ratio test data to obtain response surface interaction data; extract electron microscope image features based on the electron microscope image data to obtain electron microscope image feature data; and perform tensor stitching on the response surface interaction data and electron microscope image feature data to obtain multimodal mixing ratio characterization data. S2. Based on the multimodal proportioning characterization data, graph neural network training and materials science prior physical constraints are performed to obtain proportioning relationship graph data and aggregate constraint data, respectively. S3. Update the interlayer weights of the mix proportion diagram data based on the aggregate constraint data to obtain the neural network surrogate model; S4. Perform hyperparameter co-training on the neural network surrogate model to obtain the matching solution space surrogate model; S5. Perform frontier evolution optimization on the surrogate model of the matching solution space to obtain the matching parameter network data.

2. The method according to claim 1, characterized in that, The specific interaction analysis of response surface factors in S1 is as follows: Factor variables were extracted from the mix proportioning experiment data to obtain mix proportioning factor data; response values ​​were aligned with the mix proportioning experiment data based on the mix proportioning factor data to obtain mix proportioning response matrix data; interaction terms were constructed based on the mix proportioning factor data to obtain response surface interaction term data. Response surface coefficient data are obtained by fitting the response surface interaction term data and the ratio response matrix data. The interaction contribution is filtered based on the response surface coefficient data to obtain the response surface interaction data.

3. The method according to claim 1, characterized in that, The specific feature extraction of electron microscopy images in S1 is as follows: Phase region segmentation is performed based on electron microscope image data to obtain phase region segmentation data; boundary region identification is performed based on phase region segmentation data to obtain interface transition region data; pore morphology analysis is performed based on interface transition region data to obtain pore structure feature data. Microscopic feature vectors are encapsulated based on interface transition zone data and pore structure feature data to obtain electron microscopy image feature data.

4. The method according to claim 1, characterized in that, The specific training of the neural network in S2 is as follows: Node attribute mapping is performed on the multimodal proportion characterization data to obtain proportion node data; node association relationships are constructed based on response surface interaction data and electron microscopy image feature data to obtain edge connection data; An adjacency matrix is ​​generated based on the matching node data and edge connection data to obtain the matching graph structure data; Gated state update training is performed based on the matching graph structure data to obtain node embedding feature data and edge weight update data; graph structure correction is performed based on the node embedding feature data and edge weight update data to obtain matching relationship graph data.

5. The method according to claim 1, characterized in that, The specific a priori physical constraints in materials science in S2 are: Based on the multimodal mix design data, aggregate composition boundaries were identified and mechanical property boundaries were set, resulting in aggregate replacement rate constraint data and strength constraint data. Based on the electron microscopy image feature data in the multimodal mix design data, pore structure boundary analysis was performed to obtain pore structure constraint data. Based on the multimodal mix design data and pore structure constraint data, thermal performance boundaries were set to obtain thermal conductivity constraint data. The aggregate replacement rate constraint data, pore structure constraint data, strength constraint data, and thermal conductivity constraint data were then encapsulated to obtain aggregate constraint data.

6. The method according to claim 1, characterized in that, S3 specifically refers to: The initial graph neural network model is obtained by initializing the graph neural network based on the mix proportion graph data; the constraint factor is encoded based on the aggregate constraint data to obtain the aggregate constraint vector; the constraint weight mapping data is obtained by performing constraint matching on the initial graph neural network model based on the aggregate constraint vector; the constraint weight mapping data is used to re-balance the graph convolution propagation path of the initial graph neural network model to obtain the constraint update network model; and the neural network surrogate model is trained by backpropagation of errors based on the multimodal mix proportion characterization data to obtain the neural network surrogate model.

7. The method according to claim 6, characterized in that, The specific trade-off of graph convolution propagation path rebalancing is as follows: The graph propagation path is extracted from the initial graph neural network model to obtain graph propagation path data. The constraint association is calibrated on the graph propagation path data based on the constraint weight mapping data to obtain path constraint association data. Material boundary propagation is re-estimated on the path constraint association data to obtain path contribution weight data. The weights of the initial graph neural network model are redistributed based on the path contribution weight data to obtain re-balanced graph convolution parameter data. The parameters of the initial graph neural network model are solidified based on the re-balanced graph convolution parameter data to obtain the constraint update network model.

8. The method according to claim 7, characterized in that, The material boundary propagation reassessment specifically includes: The path constraint association data is aggregated by constraint type to obtain path constraint type data; material boundary deviation is identified based on the path constraint type data to obtain path boundary deviation data; propagation penalty coefficient is generated from the path boundary deviation data to obtain path inhibition coefficient data; effective propagation potential is re-estimated based on the path constraint type data and path inhibition coefficient data to obtain path propagation potential data; and standard weight transformation is performed on the path propagation potential data to obtain path contribution weight data.

9. The method according to claim 1, characterized in that, S4 specifically refers to: The hyperparameter search space is constructed based on the neural network surrogate model to obtain hyperparameter space data; a joint training objective is constructed based on multimodal proportioning characterization data and aggregate constraint data to obtain collaborative training loss data; the neural network surrogate model is iteratively trained based on the hyperparameter space data and collaborative training loss data to obtain surrogate model data; the validation error of the surrogate model data is evaluated to obtain optimal hyperparameter combination data; and the solution space is mapped based on the optimal hyperparameter combination data to obtain the proportioning solution space surrogate model.

10. The method according to claim 1, characterized in that, S5 specifically refers to: The search boundary for the matching variables is set according to the matching solution space surrogate model to obtain the matching search space data; the initial matching population is generated according to the matching search space data to obtain the initial matching population data; the initial matching population data is input into the matching solution space surrogate model for performance response prediction to obtain the matching performance prediction data; fitness is evaluated according to the matching performance prediction data to obtain the frontier matching data; constraint feasibility is screened according to the frontier matching data to obtain the matching parameter network data.

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