Partial combinatorial part selection (pcsp) aided design method based on combinatorial degree prediction

Abstract

The application discloses a partial combination PCSP aided design method based on combination degree prediction, relates to the field of computer-aided architectural design, and realizes rapid prediction of combination degree by taking wallboard design parameters as input, taking a first combination degree based on initial stiffness and a second combination degree based on bearing capacity as output, and through a pre-trained machine learning agent model; further, the trained agent model is explained after the event through an explainability analysis method, the contribution analysis result of each design parameter to the combination degree prediction result is quantified, and the deviation between an engineering response index and a combination degree design threshold is combined to generate a parameter adjustment direction suggestion based on the contribution analysis result, so that the combination degree prediction, the explainability analysis and the parameter optimization suggestion are integrated into an integrated aided design process, and the design efficiency is significantly improved and an explainable design decision basis is provided.

Description

Technical Field

[0001] This application belongs to the field of computer-aided architectural design, and in particular relates to a partially combined PCSP-aided design method based on combination degree prediction. Background Technology

[0002] Precast concrete sandwich insulated wall panels (PCSPs) are high-performance building components that integrate load-bearing, enclosure, and insulation functions, and their application in prefabricated building systems has become increasingly widespread in recent years. A typical PCSP consists of an inner concrete leaf panel, an outer concrete leaf panel, and an intermediate insulation layer. Ties pass through the insulation layer, allowing the two leaf panels to work together. Based on shear force transfer efficiency and the degree of cooperation between the inner and outer leaf panels, PCSPs are generally classified into three categories according to their mechanical properties: non-composite, fully composite, and partially composite. In non-composite wall panels, the shear resistance provided by the ties is limited and cannot effectively restrain the longitudinal relative slippage between the two leaf panels. Therefore, the inner and outer leaf panels mainly bear the load independently, resulting in reduced section stiffness and load-bearing capacity, and insufficient material utilization efficiency. Fully composite wall panels require sufficiently stiff and densely arranged ties to ensure that the two leaf panels form a unified load-bearing structure. While this design achieves higher cross-sectional stiffness and load-bearing capacity, it places stricter requirements on the tie members, making it difficult to fully implement in engineering. Furthermore, the strong shear connections can create significant thermal bridges, weakening the wall panel's insulation performance. In contrast, some composite wall panels, by employing tie members with appropriate shear stiffness and a rational arrangement, can achieve a more favorable balance between structural and insulation performance, thus possessing broader engineering application prospects.

[0003] The design theory and methods for partially composite wall panels are far more complex than those for non-composite and fully composite wall panels. Classical section analysis methods based on the plane section assumption are difficult to accurately describe the actual mechanical response of partially composite wall panels because their stiffness and load-bearing capacity depend on the degree of cooperation between the inner and outer concrete blades.

[0004] Currently, research on the mechanical properties of some composite wall panels mainly relies on three types of methods. The first type is simplified analytical models. These methods are computationally efficient, but usually require many idealized assumptions, making it difficult to fully consider the complex influences of material properties, geometric dimensions, and boundary conditions in actual engineering. The second type is refined finite element simulation. This method can accurately capture the slippage of tie members and material nonlinearity, but the modeling workload and computational cost are high, and the calibration of constitutive model parameters remains challenging. The third type is full-scale or scaled-down testing. The test results are usually reliable, but the testing costs are high and the cycle is long.

[0005] In summary, there are still shortcomings in the current analysis of the mechanical properties of some composite wall panels. Summary of the Invention

[0006] This application provides a partially combinatorial PCSP-aided design method based on combinatorial degree prediction to solve the problem that it is difficult to balance computational efficiency and the accuracy requirements of actual engineering modeling in traditional partially combinatorial PCSP design.

[0007] This application provides a partial combinatorial PCSP-aided design method based on combinatorial degree prediction, including:

[0008] Obtain a machine learning agent model trained based on a training sample set. Each part of the combined PCSP sample in the training sample set includes wall panel design parameters in at least three dimensions: geometric parameters, material parameters, and tie-in parameters.

[0009] The machine learning proxy model is analyzed based on the interpretability analysis method, and the contribution analysis results of each wall panel design parameter to the prediction results output by the machine learning proxy model are obtained.

[0010] Receive wall panel design parameters input by the user;

[0011] The wall panel design parameters are input into the machine learning surrogate model, and the predicted first combination degree and the predicted second combination degree are output. The first combination degree is the combination degree based on the initial stiffness, and the second combination degree is the combination degree based on the bearing capacity.

[0012] Based on the predicted first combination degree and the predicted second combination degree, calculate at least one engineering response index for the partial combination PCSP to be designed.

[0013] Based on the contribution analysis results of each wall panel design parameter, parameter adjustment direction suggestions are generated. These suggestions are used to guide users in adjusting the wall panel design parameters so that the deviations of the engineering response index from the preset index threshold, the deviations of the predicted first combination degree from the first combination degree design threshold, and the deviations of the predicted second combination degree from the second combination degree design threshold meet their respective preset allowable deviation range requirements.

[0014] The partially combinatorial PCSP-assisted design method based on combinatorial degree prediction provided in this application has at least the following beneficial effects:

[0015] By acquiring a machine learning surrogate model trained on a training sample set, and using wall panel design parameters as input and a first combination degree based on initial stiffness and a second combination degree based on bearing capacity as output, the combination degree evaluation in the design stage is transformed from time-consuming finite element solution to rapid inference of the surrogate model, enabling rapid prediction of the combination degree. Furthermore, the trained surrogate model is interpreted ex-post through interpretability analysis methods, quantifying the contribution analysis results of each design parameter to the combination degree prediction results. Combining the deviations between the engineering response index and preset index thresholds, the deviations between the predicted first combination degree and the first combination degree design threshold, and the deviations between the predicted second combination degree and the second combination degree design threshold, parameter adjustment suggestions with clear directions are generated based on the contribution analysis results. Thus, combination degree prediction, interpretability analysis, and parameter optimization suggestions are integrated into a unified auxiliary design process, significantly improving design efficiency and providing technical support for the auxiliary design of some combined PCSPs. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a partially combinatorial PCSP-aided design method based on combinatorial degree prediction provided in an embodiment of this application.

[0017] Figure 2 This is a partial finite element model of the combined PCSP provided in the embodiments of this application;

[0018] Figure 3 This is a uniaxial stress-strain curve of concrete provided in the embodiments of this application;

[0019] Figure 4 This is the stress-strain curve of the reinforcing steel provided in the embodiments of this application;

[0020] Figure 5 This is the shear force-relative slip constitutive model of the GFRP plate tie member provided in the embodiments of this application.

[0021] Figure 6 This is a schematic diagram of the feature importance analysis results provided in the embodiments of this application;

[0022] Figure 7 This is the model application process provided in the embodiments of this application. Detailed Implementation

[0023] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0024] like Figure 1As shown in the embodiments of this application, the partially combinatorial PCSP-aided design method based on combinatorial degree prediction includes:

[0025] S10, Obtain the machine learning agent model trained based on the training sample set. Each part of the combined PCSP sample in the training sample set includes wall panel design parameters in three dimensions: geometric parameters, material parameters, and tie-in parameters.

[0026] S20, The machine learning proxy model is analyzed based on the interpretability analysis method to obtain the contribution analysis results of each wall panel design parameter to the prediction results output by the machine learning proxy model.

[0027] S30 receives wall panel design parameters input by the user.

[0028] Among them, the wall panel design parameters include at least three dimensions: geometric parameters, material parameters, and tie-in parameters;

[0029] S40, input the wall panel design parameters into the machine learning surrogate model, and output the predicted first combination degree and the predicted second combination degree. The first combination degree is the combination degree based on the initial stiffness, and the second combination degree is the combination degree based on the bearing capacity.

[0030] S50, calculate at least one engineering response index of the partial combination PCSP to be designed based on the predicted first combination degree and the predicted second combination degree;

[0031] S60, based on the contribution analysis results of each wall panel design parameter, generate parameter adjustment direction suggestions. The parameter adjustment direction suggestions are used to guide users to adjust the wall panel design parameters so that the deviation of the engineering response index from the preset index threshold, the deviation of the predicted first combination degree from the first combination degree design threshold, and the deviation of the predicted second combination degree from the second combination degree design threshold meet their respective preset allowable deviation range requirements.

[0032] In this application, the combination degree is divided into a combination degree based on the initial stiffness. That is, the first degree of combination, and the degree of combination based on bearing capacity. This refers to the second combination degree, which is used for stiffness evaluation and bearing capacity evaluation, respectively. Among them;

[0033] (1),

[0034] In the formula, The elastic modulus of concrete; The moment of inertia of a portion of the composite wall panel section; The moment of inertia of the fully composite wall panel section; is the moment of inertia of the non-composite wall panel section.

[0035] Under simply supported four-point bending conditions, the moment of inertia of the cross section It can be calculated using the following formula:

[0036] (2);

[0037] In the formula, For the span of the specimen; The distance from the support to the loading point; To apply a load; This refers to the mid-span deflection.

[0038] To reduce the influence of initial contact effect, tie member response, and numerical dispersion, the least squares method is used to fit the load-deflection data within the linear elastic range to obtain the equivalent slope. This is used to characterize the equivalent bending stiffness of the specimen.

[0039] (3).

[0040] Substituting equation (3) into equation (2), we get:

[0041] (4).

[0042] Substituting equation (4) into equation (1), we get:

[0043] (5);

[0044] In the formula, This represents the equivalent bending stiffness of a portion of the composite wall panels. The equivalent bending stiffness of the fully assembled wall panel; This represents the equivalent bending stiffness of the non-composite wall panel.

[0045] The peak load is determined using the formula derived from the load method, and is defined as follows:

[0046] (6);

[0047] In the formula, This represents the peak load-bearing capacity of a portion of the composite wall panels; The peak load-bearing capacity of the fully assembled wall panel; This represents the peak load-bearing capacity of the non-composite wall panel.

[0048] Before performing combinatorial prediction, a surrogate model is first selected for combinatorial prediction. Before obtaining the machine learning surrogate model trained on the training sample set, the following steps are also included:

[0049] Establish a finite element model of a partial combined PCSP;

[0050] Based on the finite element model, a training sample set is generated in the multidimensional wall panel design parameter space using the Latin hypercube sampling method. The multidimensional wall panel design parameter space includes at least geometric parameters, material parameters, and tie-in parameters. Finite element analysis is performed on each sample in the training sample set to obtain the corresponding first combination degree and second combination degree. Based on the wall panel design parameters and the corresponding first combination degree and second combination degree, a parameter-response dataset is constructed.

[0051] Using a parameter-response dataset, multiple candidate machine learning models were trained, and the candidate machine learning model with the best performance was selected as the machine learning surrogate model.

[0052] As an example, a simplified two-dimensional finite element model for PCSP is built using ABAQUS. The overall structure of the finite element model is as follows: Figure 2 As shown, the specific construction will be explained in detail in the specific examples provided later. Wall panel design parameters may include wall panel width (W), concrete leaf thickness (C), insulation layer thickness (I), and concrete axial compressive strength (f). c ), reinforcement ratio (R), tie spacing (S), initial stiffness of tie (K), and bearing capacity of tie (F).

[0053] Candidate machine learning models can employ decision trees, random forests, extreme random trees, GBRT, XGBoost, LightGBM, CatBoost, and Stacking, etc., and this application does not limit them. By incorporating candidate models with various algorithmic architectures, covering multiple machine learning paradigms such as single-tree models, Bagging ensemble models, Boosting ensemble models, and Stacking models, the adaptability of different algorithms to the combination degree prediction task can be fully compared during the model selection stage. This avoids prediction performance bottlenecks caused by the selection of a single model and improves the generalization ability and prediction accuracy of the final surrogate model.

[0054] Before inputting the training sample set into the model, the input features can be Z-score standardized to eliminate the dimensional differences between different variables and improve the training stability of scale-sensitive models. The performance of each candidate machine learning model can then be tested using a test set, with the coefficient of determination (COP) being a suitable performance metric. It includes at least one of the following indicators: mean absolute error (MAE), root mean square error (RMSE), etc.

[0055] Optionally, given the high sensitivity of machine learning model performance to hyperparameter configuration, a system hyperparameter optimization strategy is introduced before model training. As an example, during the training of multiple candidate machine learning models, an automatic hyperparameter optimization strategy based on Tree-structured Parzen Estimator (TPE) is used to search for hyperparameters for the candidate machine learning models.

[0056] After completing model training and performance analysis, the model with the best performance is selected as the machine learning proxy model to participate in the wall panel design optimization of the user's subsequent combined PCSP. Furthermore, to verify the rationality of the structural design and whether the laws learned by the model conform to mechanical mechanisms, this application introduces the SHAP interpretability analysis method to quantitatively analyze the contribution of each wall panel design parameter to the prediction results output by the machine learning proxy model, obtaining the contribution analysis results.

[0057] It is important to note that SHAP interpretability analysis is a post-hoc interpretive analysis performed after the machine learning surrogate model has been trained and its parameters have been fixed. During this analysis, the model parameters are not updated, and the model's structure and weights are not altered. It only quantifies the contribution of each input parameter to the prediction result by traversing and statistically analyzing the internal structure of the trained model. Therefore, SHAP interpretability analysis and the training process of the machine learning surrogate model are temporally independent and technically uncoupled.

[0058] By introducing the SHAP interpretability analysis method, the machine learning surrogate model is transformed from a "black box" into an "interpretable tool." This allows engineering designers not only to obtain the predicted results of the combination degree but also to understand the magnitude and direction of the contribution of each design parameter to the predicted results, thereby enhancing their confidence in the model's predictions. Simultaneously, by verifying whether the parameter influence patterns learned by the model conform to structural mechanics mechanisms (e.g., the positive contribution of tie member stiffness to the combination degree based on initial stiffness, and the positive contribution of tie member bearing capacity to the combination degree based on bearing capacity), the reliability of the surrogate model can be verified in reverse, avoiding erroneous design recommendations due to model overfitting or data bias. The post-hoc interpretation analysis architecture completely decouples the model training and interpretation stages, ensuring that the predictive performance of the surrogate model is not affected while providing an interpretable theoretical basis for subsequent parameter optimization recommendations.

[0059] Optionally, the contribution analysis results shall at least include the ranking and direction of the parameter influence intensity, and the ranking and direction of the parameter influence intensity shall be determined by the following steps:

[0060] For each sample in the parameter-response dataset, calculate the marginal contribution (SHAP value) of each wall panel design parameter to the first combination degree prediction value and the second combination degree prediction value.

[0061] Based on the statistical aggregation of marginal contribution values, the global importance index of each wall panel design parameter to the first combination degree and the second combination degree is determined, and the parameter influence intensity is ranked according to the global importance index.

[0062] Based on the positive and negative distribution of marginal contribution values, the rising and falling trends of the changes in the design parameters of each wall panel on the first and second combination degrees are determined, and the direction of influence of each wall panel design parameter on the first and second combination degrees is obtained.

[0063] It should be noted that the "first combination degree prediction value," "second combination degree prediction value," "predicted first combination degree," and "predicted second combination degree" in this application are technically identical. Both are combination degree prediction results output by the model based on the input wall panel design parameters, and their physical definitions, generation logic, and quantification dimensions are completely consistent. The two types of expressions are merely distinguishing markers for the technical stage in the text.

[0064] "First combination degree prediction value / Second combination degree prediction value" corresponds to the model interpretability analysis stage, specifically referring to the combination degree results output by the model when conducting ex post-training interpretation analysis on the machine learning agent model, which is used to calculate the contribution and interaction effects of each wall panel design parameter;

[0065] "Predicted first combination degree / predicted second combination degree" corresponds to the actual design application reasoning stage. Specifically, it refers to the combination degree prediction result output by the model after receiving the current input parameters of the wall panel to be designed by the user. It is used for deviation calculation and parameter adjustment and optimization.

[0066] As an example, the calculation method for the global importance index and direction of influence of each wall panel design parameter on the first combination degree / second combination degree is as follows:

[0067] Take the marginal contribution value of the corresponding wall panel design parameter to the predicted value of the first combination degree / second combination degree from all samples, take the absolute value and then average it to obtain the global importance index of the wall panel design parameter to the first combination degree / second combination degree. Then, arrange the global importance index of each wall panel design parameter to the first combination degree / second combination degree in descending order to obtain the parameter influence intensity ranking of the first combination degree / second combination degree.

[0068] Based on the positive and negative distribution of the marginal contribution values ​​of each wall panel design parameter, the direction of influence of each wall panel design parameter on the first combination degree / second combination degree is determined. The direction of influence represents the trend of increasing or decreasing the influence of a certain wall panel design parameter on the first combination degree / second combination degree.

[0069] By averaging the absolute values ​​of the marginal contributions, the problem of positive and negative contributions of the same parameter canceling each other out in different samples is eliminated. This ensures that the global importance index truly reflects the overall impact of the parameter on the prediction results, rather than just its net contribution within a specific sample interval. This approach guarantees that even if a parameter contributes positively in some samples and negatively in others (i.e., exhibits a nonlinear effect), its global importance index can still accurately reflect the overall strength of its influence.

[0070] Furthermore, the wall panel design parameter with the highest global importance to the first combination degree can be identified as the first dominant design parameter, and the wall panel design parameter with the highest global importance to the second combination degree can be identified as the second dominant design parameter. By identifying the first and second dominant design parameters, the key parameters with the greatest influence on the first combination degree (based on initial stiffness) and the second combination degree (based on bearing capacity) are clarified, providing a priority basis for subsequent parameter adjustment suggestions. When it is necessary to improve the combination degree, prioritizing the adjustment of the dominant design parameters can achieve the greatest improvement effect on the combination degree with the smallest parameter change, thus improving the efficiency of parameter optimization. At the same time, the first and second dominant design parameters may be different (for example, the first dominant design parameter may be the initial stiffness of the tie member, and the second dominant design parameter may be the ultimate bearing capacity of the tie member). This differential identification reflects the essential difference in the mechanical mechanism between the two combinations degree, providing targeted optimization directions for engineering designers.

[0071] Optionally, the contribution analysis results also include the interaction contribution values ​​between any two wall panel design parameters on the first combination degree and the second combination degree, respectively, which are determined as follows:

[0072] For any two wall panel design parameters, calculate the marginal contribution of the interaction between the two wall panel design parameters to the first combination degree and the second combination degree based on the Shapley interaction index;

[0073] Based on the magnitude and sign of the interaction marginal contribution value, determine whether there is an interaction effect between the two wall panel design parameters, and whether the interaction effect is positive or negative. A positive interaction effect means that when the two wall panel design parameters change simultaneously, the impact on the degree of combination is greater than the sum of their independent effects. A negative interaction effect means that when the two wall panel design parameters change simultaneously, the impact on the degree of combination is less than the sum of their independent effects.

[0074] By quantifying the interaction effects between parameters, the coupling relationships between design parameters are revealed. When a positive interaction effect is identified, it suggests that engineers can achieve a synergistic gain of "1+1>2" by simultaneously adjusting these two parameters, thus achieving the design goal with a smaller parameter adjustment range. When a negative interaction effect is identified, it suggests that engineers can avoid adjusting these two parameters simultaneously, as this may produce mutually canceling effects, or a more refined parameter ratio should be required. This analysis provides a theoretical basis for multi-parameter joint optimization, avoiding optimization failures or inefficiencies caused by ignoring the coupling effects between parameters during parameter adjustment.

[0075] Finally, based on the contribution analysis results of each wall panel design parameter, suggestions for parameter adjustment directions are generated, including:

[0076] By combining at least one of the following: the influence direction of each wall panel design parameter on the first combination degree and the second combination degree, the ranking of parameter influence intensity, and the interaction contribution value of any two wall panel design parameters on the first combination degree and the second combination degree, a parameter adjustment direction suggestion is generated. This suggestion ensures that the deviation of the predicted first combination degree from the first combination degree design threshold, the deviation of the predicted second combination degree from the second combination degree design threshold, and the deviation of the engineering response index from the preset index threshold, as well as the deviation of the wall panel design parameters adjusted based on the parameter adjustment direction suggestion and input into the machine learning agent model, respectively, meet their respective preset allowable deviation range requirements.

[0077] Engineering response indicators may include at least one of equivalent flexural stiffness, deflection, and ultimate load. The preset threshold values ​​for different engineering response indicators may vary. When the deviation of each engineering response indicator from its corresponding preset threshold value, the deviation of the predicted first combination degree from the first combination degree design threshold value, and the deviation of the predicted second combination degree from the second combination degree design threshold value all meet their respective preset allowable deviation range requirements, the currently input wall panel design parameters are deemed valid, and wall panel design is performed based on these parameters.

[0078] Optionally, after generating parameter adjustment suggestions, the wall panel design parameters adjusted based on the parameter adjustment direction suggestions are re-input into the machine learning proxy model for iterative prediction, and the predicted first combination degree and predicted second combination degree corresponding to the current iteration number are output. Based on the predicted first combination degree and predicted second combination degree corresponding to the current iteration number, at least one engineering response index corresponding to the current iteration number is calculated. If the deviation of the predicted first combination degree from the first combination degree design threshold, the deviation of the predicted second combination degree from the second combination degree design threshold, and the deviation of the engineering response index from the preset index threshold respectively meet their respective preset allowable deviation range requirements, then the final design scheme is output. If any one of the deviations between the predicted first combination degree and the first combination degree design threshold, the predicted second combination degree and the second combination degree design threshold, and the deviation between the engineering response index and the preset index threshold corresponding to the current iteration number does not fall within the corresponding preset allowable deviation range, then the step of generating parameter adjustment direction suggestions continues.

[0079] By constructing a closed-loop iterative mechanism of "prediction → verification → adjustment → re-prediction," the parameter optimization process can automatically converge to a feasible solution that satisfies all design constraints. Compared to methods that output results after a single adjustment, the iterative optimization mechanism can handle under-adjustment or over-adjustment problems caused by excessively large or small parameter adjustment ranges. Through multiple rounds of iteration, it gradually approaches the optimal design scheme, improving the reliability and accuracy of the design scheme. Furthermore, since the prediction process in each iteration is completed by a computationally efficient machine learning surrogate model (rather than a finite element model), the time cost of the iteration process is extremely low, enabling multiple rounds of optimization to be completed within seconds.

[0080] Optionally, if the deviations of the predicted first combination degree from the first combination degree design threshold, the predicted second combination degree from the second combination degree design threshold, and the engineering response index from the preset index threshold corresponding to the current iteration number meet their respective preset allowable deviation range requirements, then the wall panel design parameters after parameter adjustment are input into the finite element model as candidate design schemes for finite element analysis to obtain the first combination degree verification value and the second combination degree verification value corresponding to the candidate design scheme; the first combination degree verification value and the predicted first combination degree are compared, and the second combination degree verification value and the predicted second combination degree are compared. When the deviations between the first combination degree verification value and the predicted first combination degree, and the deviations between the second combination degree verification value and the predicted second combination degree are both within the preset tolerance range, the candidate design scheme is confirmed as valid and is adopted as the final design scheme; when the deviations between the first combination degree verification value and the predicted first combination degree, or the deviations between the second combination degree verification value and the predicted second combination degree, exceed the preset tolerance range, a model prediction deviation warning is issued.

[0081] By introducing a finite element method (FEM) verification step before the final design output, the prediction results of the machine learning surrogate model are independently validated, effectively preventing unqualified design schemes from being output due to prediction biases in the marginal regions of the parameter space. FEM verification acts as a "safety valve" mechanism, ensuring that the final output design scheme is confirmed by high-fidelity numerical simulation, compensating for the surrogate model's insufficient generalization in sparse training data regions. The warning issued when the verification value deviates significantly from the predicted value also prompts engineers to pay attention to the model's reliability in that parameter region, providing guidance for subsequent supplementation of training samples and improvement of the surrogate model's prediction accuracy in that region.

[0082] The following is a specific example.

[0083] First, establish a system using ABAQUS such as Figure 2 The PCSP simplified two-dimensional finite element model shown has the global coordinate system defined as the horizontal direction as the X-axis and the vertical direction as the Y-axis. The concrete blade, insulation board, and loading pad are simulated using the four-node reduced integral plane strain element CPE4R, and the reinforcing steel is simulated using the truss element T2D2. The insulation board and concrete blade are in surface-to-surface contact (e.g., ...). Figure 2 The left-hand magnified view shows the "contact" area, assuming no tangential friction; the reinforcing bars are embedded in the concrete leaf plate through embedded constraints. The axial response of the tie rod is simulated using the axial spring element SPRINGA, and the tangential response is simulated using the two-node two-dimensional connection element CONN2D2. Figure 2 The right-hand side shows a magnified view of the "spring" and "connector." The model is supported at both ends by "supports": the left support is subject to simply supported boundary conditions, constraining both horizontal and vertical displacements (UX=UY=0); the right support only constrains vertical displacement (UY=0) to allow free expansion and contraction of the beam ends along the X-direction. Vertical loads are applied at the two top "loading" positions via displacement-controlled loading pads. All elements use a uniform 10mm mesh size.

[0084] Concrete materials were simulated using the ABAQUS concrete damage plasticity (CDP) model, with a Poisson's ratio of 0.2. The elastic modulus of concrete and the nonlinear uniaxial tensile and compressive constitutive relations were determined according to GB / T 50010—2010, and representative curves are shown in [reference needed]. Figure 3 In the CDP plasticity parameters, the expansion angle is taken as 30°, the flow potential eccentricity is taken as 0.1, the ratio of initial biaxial compressive yield stress to initial uniaxial compressive yield stress f_b0 / fc0 is taken as 1.16, the CDP yield surface shape parameter K is taken as 0.667, and the viscosity parameter is taken as 0.0001. The reinforcing steel adopts an elastic-ideal plastic bilinear model, such as... Figure 4 As shown; the insulation board adopts a linear elastic material model.

[0085] A simplified constitutive model for the GFRP plate tie member is established. The axial response of the tie member is assumed to be linearly elastic, and the shear force-relative slip relationship is defined as a four-segment piecewise model, as follows: Figure 5 As shown, the model consists of an initial elastic segment, a nonlinear strengthening segment, an approximate plateau segment in the limit stage, and a descending segment. This simplified model is used to characterize the mechanical response dominated by shear deformation of the tie member, without explicitly considering interface failure or anchorage failure.

[0086] The tie-joint model described above is used in a partially combined finite element model. The fully combined reference model is given a sufficiently large tie-joint stiffness to approximate the rigid interaction between the two concrete blades; the non-combined reference model is given a sufficiently small tie-joint stiffness to minimize shear force transmission.

[0087] Four specimens (P-300-S-10, P-300-S-12, SP-1-1, and SP-1-2) were selected to verify the finite element model. The quantitative comparison between the load-deflection curves obtained from the finite element simulation and the experimental results is listed in Table 1. The bending loading process of the specimens can be roughly divided into four stages: initial loading to cracking, cracking to yielding, yielding to peak load, and peak load to failure. The comparison results show that the simulated curves and the experimental curves agree well in terms of overall response trends. Based on the TEST / FE ratio listed in Table 1, the average deviation between the finite element results and the experimental results is 1.0% for initial stiffness and 2.2% for peak bearing capacity. Therefore, the established finite element model can reasonably reproduce the nonlinear bending performance of the specimens.

[0088] Table 1 Comparison of experimental and finite element analysis results

[0089] To systematically evaluate the DCA of different machine learning algorithms for PCSP s and DCA c To assess the predictive performance, 10 representative models were selected for comparative analysis, covering various typical algorithms. Single-tree models employed decision trees; ensemble models based on bagging and randomized trees included Random Forest and Extra Trees; gradient tree models based on boosting included GBRT, XGBoost, LightGBM, and CatBoost; kernel methods employed Support Vector Regression (SVR); and neural network models used Artificial Neural Networks (ANNs). Furthermore, Stacking was employed as a stacked ensemble model. This model framework systematically compares the applicability and performance differences of different algorithms in predicting combinatorial degrees under engineering simulation data conditions from the perspectives of single learners, ensemble learners, kernel methods, neural networks, and stacked ensemble frameworks.

[0090] This example constructs a dataset containing 591 samples to train and test a machine learning prediction model for the two combinatorial indices of PCSP. The dataset includes 8 input variables and 2 output variables. The input variables are wall panel width (W), concrete leaf thickness (C), insulation layer thickness (I), and concrete axial compressive strength (f). c The parameters include: reinforcement ratio (R), tie spacing (S), initial stiffness of tie (K), and bearing capacity of tie (F); the output variable is the degree of combination based on the initial stiffness. That is, the first degree of combination and the degree of combination based on bearing capacity. This is the second degree of cohesion. The statistical characteristics of the dataset are summarized in Table 2. The mean and median reflect the central tendency of the variables, while the standard deviation, minimum, and maximum represent their dispersion.

[0091] Table 2 Statistical range of PCSP dataset parameters

[0092] The machine learning workflow is implemented using Python 3.12.6. Data processing and matrix operations are performed using NumPy 2.1.1 and Pandas 2.2.2, while scientific computing uses SciPy 1.15.3. Scikit-learn 1.7.0 provides a unified framework for preprocessing, cross-validation, and regression model evaluation. XGBoost 3.0.2, LightGBM 4.6.0, and CatBoost 1.2.8 are used to implement gradient boosting models. Neural network training is performed using PyTorch 2.5.1, and hyperparameter optimization is performed using Optuna 4.5.0.

[0093] In the data preprocessing stage, the dataset is divided according to the distribution of the output variables using a stratified sampling strategy

[58] . Samples are randomly assigned within each stratum to obtain training and test sets accounting for 80% and 20% of the dataset, respectively. Subsequently, the input features are Z-score standardized to eliminate the differences in scale between different variables and improve the training stability of the scale-sensitive model. The mean and standard deviation required for standardization are calculated only from the training set, and the same transformation is applied to the training and test sets to avoid data leakage. The standardization formula is as follows:

[0094]

[0095] In the formula, For the first The first sample The original values ​​of each feature; For the first The first sample The value after standardizing the features; and These are the mean and standard deviation of the feature in the training set, respectively.

[0096] To evaluate the predictive performance of the regression model from different perspectives, the coefficient of determination (COP) is used. Commonly used regression indicators include mean absolute error (MAE) and root mean square error (RMSE). The Model for Estimating Prediction Error (MAE) measures the goodness of fit; a higher MAE value indicates that the model can explain a larger proportion of the data variance. MAE directly quantifies the average magnitude of the absolute prediction error, providing a direct reflection of the overall prediction accuracy. Relative Probability of Error (RMSE) assigns higher weight to larger errors, making it suitable for evaluating the impact of larger biases. Furthermore, RMSE has the same dimensions as the target variable, allowing it to characterize the model's overall prediction error. The corresponding calculation formulas are as follows:

[0097] ;

[0098] ;

[0099] ;

[0100] In the formula, The actual value; This is a predicted value; The mean of the sample; The total number of samples.

[0101] a20 is used as a tolerance-based accuracy metric. A prediction is considered acceptable when the ratio of the predicted value to the actual value is between 0.80 and 1.20, i.e., the relative error does not exceed 20%. a20 is defined as follows:

[0102]

[0103] In the formula, I() is an indicator function, which takes the value of 1 if the condition is met, and 0 otherwise; This is the relative error threshold.

[0104] The final evaluation of a machine learning model should also include metrics sensitive to the direction of error. Mean Bias Error (MBE) quantifies the model's overall tendency to overestimate or underestimate by averaging the differences between predicted and measured values. An MBE close to 0 indicates a small average directional bias; a positive or negative MBE indicates average overestimation or underestimation, respectively.

[0105]

[0106] Given the high sensitivity of machine learning model performance to hyperparameter configuration, a systematic hyperparameter optimization strategy is introduced before model training to avoid subjective biases caused by manually setting parameters, fully leverage the predictive potential of each model on a given dataset, and ensure the robustness and repeatability of the prediction framework. Existing research shows that reasonable hyperparameter configuration significantly affects the generalization performance of a model, especially for small sample sizes or highly nonlinear problems. This example uses the Optuna framework based on the Tree-structured Parzen Estimator (TPE) for hyperparameter optimization. The TPE algorithm models both potentially good and poor regions in the hyperparameter space and balances exploration and utilization during the search process, thereby approximating the near-optimal hyperparameter configuration within a limited number of trials. Hyperparameter optimization is performed only on the training set; the test set is not involved in the search process to avoid the risk of data leakage.

[0107] Hyperparameter optimization was performed solely on the training set. Each optimization trial used the mean of the coefficients of determination (R²) obtained from five-fold cross-validation within the training set as the objective function. For each model, a search space was constructed based on its key hyperparameters, such as the maximum tree depth, number of estimators, and learning rate for tree models or boosting models, and the hidden layer size and learning rate for neural network models. To ensure fair comparison, all models used the same training set partitioning and cross-validation strategy, and each model underwent 1000 independent optimization trials.

[0108] After hyperparameter optimization, each model is trained using its optimal configuration. Five-fold cross-validation is performed on the training set to compare prediction accuracy and stability across folds. Each fold is calculated... The mean, MAE, and RMSE are expressed as mean and standard deviation, respectively. The mean reflects the overall predictive performance, while the standard deviation reflects the model's sensitivity to the training-validation set split.

[0109] for CatBoost and GBRT had the highest mean R² (rounded) of 0.996, with CatBoost having the lowest MAE (1.9 × 10⁻³) and RMSE (0.003). The leading models all had relatively small standard deviations, indicating limited fluctuations across different folds of the training data. The prediction task is more difficult: CatBoost ranks first with R²=0.889±0.011, MAE=0.056±0.0026, RMSE=0.078±0.0038, followed closely by GBRT. The low R² and large error indicate that the input-output mapping near the limit state is more complex compared to the stiffness response. Overall, the boosting-based model leads in both output tasks. All models are then evaluated on independent test sets; CatBoost is retained only as a unified algorithmic basis for SHAP interpretation to compare the two combinatorial metrics within the same model family, while prediction performance is still compared separately for each output.

[0110] After optimization, each model is refitted on the complete training set and evaluated on an independent test set that did not participate in hyperparameter optimization and model fitting, thus obtaining the generalization performance estimate on the reserved samples. In addition to R², MAE, and RMSE, a20 is used to quantify the prediction proportion that meets the 20% relative error criterion, and MBE is used to identify systematic overestimation or underestimation.

[0111] CatBoost achieves the best performance for DCAs. / MAE / RMSE performance, among which =0.998, MAE=0.002, RMSE=0.002, a20=0.983, MBE=0.000414. Stacking and GBRT follow closely behind, both with R²=0.997, MAE=0.002, and a20 reaching the maximum value of 1.000. LightGBM, ANN, and XGBoost all have an a20 of 0.992, while the remaining models are no higher than 0.958. The MBE of the nine models is a small positive value, while DecisionTree has a small negative MBE value, indicating that the average directional bias is limited. Therefore, when R², MAE, and RMSE are prioritized, CatBoost is preferable; when the 20% relative error hit rate is the main evaluation criterion, Stacking or GBRT is preferable.

[0112] for Stacking achieves the best / MAE / RMSE performance, among which =0.901, MAE=0.053, RMSE=0.074, a20=0.807, MBE=−0.000541. CatBoost ranks second in these three metrics: R²=0.896, MAE=0.055, RMSE=0.076, but its a20 is the highest at 0.849. GBRT and ANN have the next best relative tolerance, with a20 values ​​of 0.824 and 0.815 respectively; XGBoost, LightGBM, and Stacking have the same a20 value of 0.807. Except for ANN, the MBE values ​​of the other models are all negative, and the absolute value of the MBE does not exceed 0.015. Therefore, model selection depends on the evaluation metrics: when R², MAE, and RMSE are prioritized, Stacking is preferable; when a 20% relative error hit rate is prioritized, CatBoost is preferable.

[0113] Based on the combined results of cross-validation and independent testing, three conclusions can be drawn. First, The prediction accuracy is higher than The best R² values ​​for both on the test set are 0.998 and 0.901, respectively, with corresponding RMSEs of 0.002 and 0.074. This difference is related to... The elastic stage mapping represented is relatively stable, and This aligns with the characteristic of stronger coupling between material, tie rods, and damage near the ultimate load. Second, the ensemble method ranks highly in both output tasks, indicating its applicability to the multi-parameter nonlinear relationships embodied in the finite metadata set presented in this paper. Third, the optimal prediction model depends on both output metrics and evaluation priorities. When prioritizing R², MAE, and RMSE, CatBoost and DCAc are recommended to use Stacking; when prioritizing a20-index, Stacking or GBRT is recommended. CatBoost is recommended because it is the best performing common model overall in the reported cross-validation results, and it is also the best in terms of R², MAE, and RMSE on the independent test set. The model is therefore also used as the unified algorithmic basis for SHAP interpretation.

[0114] The CatBoost model is explained using SHAP. Global importance is quantified by the mean absolute SHAP value, and the signed SHAP value is used to determine whether a feature level improves or decreases the predictive combination degree relative to the model baseline. Figure 6 The bee colony graph and global importance graph are given, and Table 3 lists the signed SHAP mean values ​​corresponding to the discrete parameter levels.

[0115] Table 3 and Average SHAP value of input parameters

[0116] for , Figure 6 The global importance values, from highest to lowest, are K (0.03036), W (0.02156), I (0.01260), S (0.01135), C (0.00827), and f. c (0.00111), F (0.00095), and R (0.00021). Therefore, K is the dominant predictive feature, while f c The contributions of F and R are relatively small. The signed means in Table 3 show that the contribution of K monotonically changes with the value: the average SHAP value increases from −0.06838 at 2000 N / mm and −0.04012 at 5000 N / mm to 0.00442 at 10000 N / mm and 0.04368 at 15000 N / mm. This trend is consistent with the fact that increasing K can enhance the constraint on the relative slip of the two blades. W shows the opposite trend, with its average SHAP value decreasing from 0.03245 at 300 mm to −0.00607 at 450 mm and −0.02546 at 600 mm; while the contribution of I increases from −0.01339 at 30 mm and −0.00598 at 50 mm to 0.01805 at 80 mm. The dependency plot further shows that the beneficial contributions of K and I vary with the corresponding minor feature level. The positive effect corresponding to the increase of I may stem from the increase of the internal lever arm, but whether this effect can be fully realized seems to depend on whether the tie member has sufficient shear force transmission stiffness. These patterns are correlations learned by the model from the combination of sampled parameters, rather than independent causal effects.

[0117] Different control patterns emerge. The global importance, from highest to lowest, is as follows: F (0.11224), W (0.07779), S (0.07329), K (0.06548), R (0.03733), C (0.03523), f... c(0.03284) and I (0.02040). F contributes the most, with its average SHAP value increasing from −0.17752 at 5000 N and −0.02090 at 10000 N to 0.08362, 0.14354, and 0.17629 at 15000 N, 20000 N, and 25000 N, respectively. K also shows a similar change, increasing from −0.13047 and −0.08963 at 2000 N / mm and 5000 N / mm to 0.02953 and 0.07359 at 10000 N / mm and 15000 N / mm, respectively. The dependency plot shows that when K is also high, the positive contribution of high F is more significant. From a mechanical point of view, this is consistent with F controlling the available ultimate shear transfer capacity and K affecting the degree of mobilization of this bearing capacity before failure. W and S predict This also has a significant impact. The average SHAP value of W decreased from 0.11664 at 300 mm to −0.01116 at 450 mm and −0.10078 at 600 mm; while S decreased from 0.12882 at 300 mm to −0.02010 at 450 mm and −0.08599 at 600 mm. Therefore, within the parameter level studied in this paper, an increase in either W or S is associated with the predicted The correlation diagram also shows that when S=300mm, the positive contribution of high F is more significant; while when S=600mm, even if F reaches 20000-25000N, many samples are still in the negative contribution region. This pattern is consistent with the decrease in the density of tie members and the interface shear force transfer capacity caused by increasing S, indicating that increasing the load-bearing capacity of a single tie member cannot completely compensate for the effect of sparse arrangement. R, C, f c The global impact of I is relatively limited. In summary, the SHAP results indicate that DCA... s It is mainly controlled by K and geometric deformation coordination, while DCA c The relationship with F, W, S, and K is closer. The above explanation applies only to the fitted CatBoost model, the dataset generated by the finite element method, and the discrete parameter levels considered in this example.

[0118] To facilitate the application of the combination degree prediction model to PCSP-aided design, a system was established. Figure 7 The model application process is shown below. To implement this process, a Python-based graphical user interface for auxiliary design was developed. This tool integrates functions such as model selection, parameter input, combination degree prediction, engineering response calculation, applicability verification, and result visualization. Users first define design requirements: deflection, ultimate load, and DCA. s Design thresholds and DCA c Design thresholds, etc.; then input design parameters: W, C, f c R, I, S, K, F; the graphical interface responds to user input of W, C, fc After designing parameters such as R, I, S, K, and F, a pre-trained machine learning model is called to predict DCA. s The process involves DCA (Distributed Dynamic Analysis); then, based on the predicted combination degree, engineering response indices are calculated, including initial stiffness, service load deflection, ultimate load, ultimate bending moment, and other design indices. The engineering response indices are used to determine if the design requirements are met. If not, the "SHAP-based parameter adjustment" step is executed, and the process returns to the parameter input stage for re-prediction. If the requirements are met, "finite element verification" continues, and the process is checked for compliance. If not, the process returns to the "SHAP-based parameter adjustment" step for iteration. After both levels of verification pass, the "PCSP-aided design recommended parameter scheme" is output. This forms an integrated auxiliary design process, from design requirement definition, parameter input, combined performance prediction, engineering response calculation to applicability verification and finite element verification, creating a closed loop.

[0119] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0120] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A partially combinatorial PCSP-aided design method based on combinatorial degree prediction, characterized in that, include: Obtain a machine learning agent model trained based on a training sample set. Each part of the combined PCSP sample in the training sample set includes wall panel design parameters in at least three dimensions: geometric parameters, material parameters, and tie-in parameters. The machine learning proxy model is analyzed based on the interpretability analysis method, and the contribution analysis results of each wall panel design parameter to the prediction results output by the machine learning proxy model are obtained. Receive wall panel design parameters input by the user; The wall panel design parameters are input into the machine learning surrogate model, and the predicted first combination degree and the predicted second combination degree are output. The first combination degree is the combination degree based on the initial stiffness, and the second combination degree is the combination degree based on the bearing capacity. Based on the predicted first combination degree and the predicted second combination degree, calculate at least one engineering response index for the partial combination PCSP to be designed. Based on the contribution analysis results of each wall panel design parameter, parameter adjustment direction suggestions are generated. These suggestions are used to guide users in adjusting the wall panel design parameters so that the deviations of the engineering response index from the preset index threshold, the deviations of the predicted first combination degree from the first combination degree design threshold, and the deviations of the predicted second combination degree from the second combination degree design threshold meet their respective preset allowable deviation range requirements.

2. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 1, characterized in that, Before obtaining the machine learning agent model trained on the training sample set, the following steps are also included: Establish a finite element model of a partial combined PCSP; Based on the finite element model, a training sample set is generated in the multidimensional wall panel design parameter space using the Latin hypercube sampling method. The multidimensional wall panel design parameter space includes at least geometric parameters, material parameters, and tie-in parameters. Finite element analysis is performed on each sample in the training sample set to obtain the corresponding first combination degree and second combination degree. Based on the wall panel design parameters and the corresponding first combination degree and second combination degree, a parameter-response dataset is constructed. Using a parameter-response dataset, multiple candidate machine learning models were trained, and the candidate machine learning model with the best performance was selected as the machine learning surrogate model.

3. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 2, characterized in that, The method further includes: The performance of each candidate machine learning model is measured by at least one of the following metrics: coefficient of determination, mean absolute error, and root mean square error.

4. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 2, characterized in that, The contribution analysis results include at least the ranking of parameter influence intensity and the direction of influence. The analysis of the machine learning proxy model based on interpretability analysis methods yields the contribution analysis results of each wall panel design parameter to the prediction results output by the machine learning proxy model, including: For each sample in the training sample set, calculate the marginal contribution of each wall panel design parameter to the predicted values ​​of the first and second combination degrees. Based on the statistical aggregation of marginal contribution values, the global importance index of each wall panel design parameter to the first combination degree and the second combination degree is determined, and the parameter influence intensity is ranked according to the global importance index. Based on the positive and negative distribution of marginal contribution values, the rising and falling trends of the changes in the design parameters of each wall panel on the first and second combination degrees are determined, and the direction of influence of each wall panel design parameter on the first and second combination degrees is obtained.

5. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 4, characterized in that, The contribution analysis results also include the interaction contribution values ​​between any two wall panel design parameters on the first combination degree and the second combination degree, respectively; the method also includes: For any two wall panel design parameters, based on the decomposition of marginal contribution values, calculate the interactive marginal contribution values ​​of the two wall panel design parameters to the first combination degree and the second combination degree, respectively. Based on the magnitude and sign of the interaction marginal contribution value, determine whether there is an interaction effect between the two wall panel design parameters, and whether the interaction effect is positive or negative. A positive interaction effect means that when the two wall panel design parameters change simultaneously, the impact on the degree of combination is greater than the sum of their independent effects. A negative interaction effect means that when the two wall panel design parameters change simultaneously, the impact on the degree of combination is less than the sum of their independent effects.

6. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 5, characterized in that, The parameter adjustment direction suggestions generated based on the contribution analysis results of each wall panel design parameter include: Based on at least one of the following: the influence direction of each wall panel design parameter on the first combination degree and the second combination degree, the ranking of parameter influence intensity, and the interaction contribution values ​​of any two wall panel design parameters on the first combination degree and the second combination degree, parameter adjustment direction suggestions are generated. This ensures that the deviation of the predicted first combination degree from the first combination degree design threshold, the deviation of the predicted second combination degree from the second combination degree design threshold, and the deviation of the engineering response index from the preset index threshold, as well as the deviation of the wall panel design parameters adjusted based on the parameter adjustment direction suggestions and input into the machine learning agent model, respectively, meet their respective preset allowable deviation range requirements.

7. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 1, characterized in that, The method further includes: The wall panel design parameters, adjusted based on the parameter adjustment direction suggestion, are re-input into the machine learning agent model for iterative prediction, and the first combination degree and the second combination degree of the prediction corresponding to the current iteration number are output. Based on the predicted first combination degree and the predicted second combination degree corresponding to the current iteration number, at least one engineering response index corresponding to the current iteration number is calculated. If the deviation of the predicted first combination degree from the first combination degree design threshold, the deviation of the predicted second combination degree from the second combination degree design threshold, and the deviation of the engineering response index from the preset index threshold corresponding to the current iteration number meet their respective preset allowable deviation range requirements, then the final design scheme is output. If any of the following deviations—the deviation between the predicted first combination degree and the first combination degree design threshold, the deviation between the predicted second combination degree and the second combination degree design threshold, or the deviation between the engineering response index and the preset index threshold—does not fall within the corresponding preset allowable deviation range, then the step of generating parameter adjustment direction suggestions will continue.

8. The partially combinatorial PCSP-aided design method based on combinatorial degree prediction as described in claim 7, characterized in that, If the deviations of the predicted first combination degree from the first combination degree design threshold, the predicted second combination degree from the second combination degree design threshold, and the engineering response index from the preset index threshold corresponding to the current iteration number respectively meet their respective preset allowable deviation range requirements, then the final design scheme is output, including: If the deviation of the predicted first combination degree from the first combination degree design threshold, the deviation of the predicted second combination degree from the second combination degree design threshold, and the deviation of the engineering response index from the preset index threshold corresponding to the current iteration number meet their respective preset allowable deviation range requirements, then the wall panel design parameters adjusted based on the parameter adjustment direction suggestion will be used as candidate design schemes and input into the finite element model for finite element analysis to obtain the first combination degree verification value and the second combination degree verification value corresponding to the candidate design scheme. The first combination degree verification value and the predicted first combination degree are compared with the second combination degree verification value and the predicted second combination degree. When the deviation between the first combination degree verification value and the predicted first combination degree, and the deviation between the second combination degree verification value and the predicted second combination degree are both within the preset tolerance range, the candidate design scheme is confirmed to be valid and the candidate design scheme is taken as the final design scheme. When the deviation between the first combination degree verification value and the predicted first combination degree, or the deviation between the second combination degree verification value and the predicted second combination degree, exceeds the preset tolerance range, a model prediction deviation warning is issued.

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