Fly ash composite roadbed structure parameter strategy optimization method fusing experimental data

Abstract

The invention discloses a fly ash composite roadbed structure parameter strategy optimization method fusing experimental data, and relates to the technical field of data processing, and the method comprises the steps: 1, coding a fly ash composite roadbed structure parameter strategy into a vector, and setting a data structure; step 2, constructing and training a physical information neural network model PINN; 3, executing core iterative optimization by adopting the physical information neural network model PINN constructed and trained in the step 2, an active learning module and a grey wolf genetic hybrid optimization algorithm GWGA; and step 4, outputting a final fly ash composite roadbed structure parameter strategy after core iterative optimization convergence. Unification of data driving and physical constraint is realized, so that the model has continuous learning and self-correction capabilities; in the aspect of optimization efficiency, the convergence speed and the global search precision are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of data processing and analysis technology, and in particular to a method for optimizing the structural parameters of fly ash composite roadbed by integrating experimental data. Background Technology

[0002] In recent years, the reuse of fly ash as an industrial byproduct in transportation infrastructure construction has received widespread attention, especially in highway and railway subgrade engineering, where fly ash is used to improve soil strength, reduce deformation, and enhance durability. However, the multi-layered coupling characteristics of fly ash composite subgrade structures significantly increase the complexity of structural parameter design. Traditional subgrade design often relies on empirical parameters or linear regression models to determine key parameters such as admixture ratio, layer thickness, and compaction standards. These methods are often unstable when initial experimental data is limited or environmental conditions change, leading to discrepancies between calculation results and actual engineering performance. Existing numerical simulation methods, such as finite element analysis and constitutive model calculations, can accurately reflect stress-strain distribution, but they are highly dependent on material parameters, and model calibration usually requires a large amount of field experimental data. They lack adaptive learning and model updating capabilities, making real-time optimization under different construction conditions difficult.

[0003] In recent years, some studies have attempted to introduce data-driven optimization approaches, using machine learning algorithms or neural network models to predict the structural response of fly ash composite roadbeds. For example, prediction methods based on multilayer perceptrons or convolutional neural networks have been used to estimate the strength or settlement performance under different mix proportions. The advantage of these methods is that they can utilize existing experimental data to construct high-dimensional mapping relationships, but their disadvantage is that they do not fully consider material physical constraints. The model prediction results may violate fundamental engineering principles such as stress balance or boundary continuity, leading to model distortion during extrapolation. Furthermore, traditional neural network models typically require a complete training dataset to obtain stable outputs. However, in actual engineering scenarios involving fly ash composite roadbeds, experimental data often exhibits heterogeneity and incompleteness, making model training prone to overfitting or prediction bias. For the parameter search problem in the optimization process, existing technologies often employ swarm intelligence optimization methods such as genetic algorithms, particle swarm optimization, or ant colony optimization to find the optimal combination of performance in a multi-parameter space. However, these algorithms often face problems such as slow convergence speed, obvious local optimum traps, and insufficient search accuracy in high-dimensional, nonlinear, and multi-objective engineering optimization problems. Some studies have improved search performance through hybrid algorithms, such as combining genetic algorithms with particle swarm optimization to enhance global exploration capabilities. However, these methods usually lack dynamic learning mechanisms for engineering scenarios, meaning they cannot proactively select new experimental data for supplementary optimization based on the uncertainty of model predictions, thus limiting the model's adaptability in complex environments. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the structural parameters of fly ash composite roadbed by integrating experimental data. By combining a physical information neural network model, an active learning mechanism, and a gray wolf genetic hybrid optimization algorithm, adaptive optimization and dynamic adjustment of fly ash composite roadbed structures can be achieved.

[0005] To address the aforementioned technical problems, this invention provides a method for optimizing the structural parameters of fly ash composite roadbeds by integrating experimental data. This method includes: Step 1: Encode the fly ash composite roadbed structure parameter strategy into a vector and set the data structure; Step 2: Construct and train the Physical Information Neural Network (PINN) model; Step 3: The physical information neural network model PINN constructed and trained in Step 2, the active learning module, and the gray wolf genetic hybrid optimization algorithm GWGA are used to perform core iterative optimization. The core iterative optimization includes: using the gray wolf genetic hybrid optimization algorithm GWGA to generate candidate fly ash composite subgrade structure parameter strategies, using the physical information neural network model PINN to evaluate the target values ​​of the candidate fly ash composite subgrade structure parameter strategies, and using the active learning module to trigger sample collection based on the uncertainty measure of the physical information neural network model PINN to obtain new experimental data and incrementally update the physical information neural network model PINN constructed and trained in Step 2. Step 4: After the core iterative optimization converges, output the final fly ash composite roadbed structure parameter strategy.

[0006] Furthermore, in step 1, the structural parameter strategy is encoded as an ordered vector of length 6, which consists of the following values ​​in sequence: admixture level, layer thickness level, moisture content control level, compaction level, reinforcement structure type, and construction temperature level. The admixture level is an integer from 1 to 9, the layer thickness level is an integer from 1 to 8, the moisture content control level is an integer from 1 to 5, the compaction level is an integer from 1 to 5, the reinforcement structure type is an integer from 1 to 4, and the construction temperature level is an integer from 1 to 4. The six discrete fields are then linearly scaled to the range of 0 to 1 according to their respective maximum levels.

[0007] Furthermore, in step 2, the training objectives of the Physical Information Neural Network (PINN) model are constructed. The training objectives include data error, balance error, and boundary error. The data error is the sum of the absolute differences between the observed output and the network output at the depth points where observations are made. The balance error is the sum of the absolute values ​​of the differences in horizontal stress and vertical stress at adjacent depth points over all adjacent pairs. The boundary error includes the absolute value of the vertical displacement at depth 0.00 and the absolute value of the difference between the vertical stress and the target load level at depth 1.00. The target load level is obtained by mapping the construction temperature level.

[0008] Furthermore, in step 2, the construction and training of the physical information neural network model PINN are repeatedly performed on the same structure and data with 5 different random seeds to obtain 5 independent physical information neural network models PINN, which are used for uncertainty assessment in the core iterative optimization.

[0009] Furthermore, in the core iterative optimization, the target values ​​for evaluating the structural parameter strategies of candidate fly ash composite roadbeds include calculating three target values: the maximum vertical displacement, the maximum bending tensile response index, and the minimum structural safety index. Among them, the bending tensile response index is defined as the absolute difference between horizontal stress and vertical stress, and the structural safety index is defined as the minimum value of the absolute difference between vertical stress and horizontal stress at 21 depth points.

[0010] Furthermore, the steps of the strategy for generating candidate fly ash composite roadbed structure parameters using the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) include: performing a Grey Wolf-guided update process: selecting three leader individuals based on non-dominated sorting and crowding distance; for the remaining individuals, taking the median of the scaling values ​​of the three leader individuals in the field as a reference value, generating a uniform random ratio of 0.2 to 0.8, and shifting the current field value of the individual towards the reference value by the distance of the generated uniform random ratio; if the field is a discrete field, rounding the update result to the adjacent level; and subsequently performing a genetic operation process: performing tournament selection on the temporary population guided by Grey Wolves, performing two-point crossover on the selected parent pairs, with the crossover position fixed at the 2nd and 5th fields, and performing a transformation operation on the offspring.

[0011] Furthermore, the step of triggering sample collection using the uncertainty metric of the Physical Information Neural Network (PINN) model based on the active learning module includes: after every 40 generations of evolution, inputting five independent PINN models into the first 48 individuals of the non-dominant frontier, calculating the difference between the maximum and minimum values ​​of the three target values ​​on the five models, and taking the maximum value as the uncertainty metric of the individual; selecting the top 12 individuals with uncertainty metrics greater than 0.12 in descending order of metric value to form a candidate collection set; and generating a sample collection instruction for each individual in the candidate collection set, which includes the individual's six level fields, the set of depth coordinates to be measured, and the three output values ​​to be recorded.

[0012] Furthermore, the incremental update steps for the physical information neural network model PINN include: after adding the new records obtained from the sample collection command to the training sample set, additionally training each of the five independent physical information neural network models PINN for 2000 rounds, using the Adam optimizer, with a learning rate of 0.0005, a batch size of 64, and setting the early stopping threshold to a decrease of less than 0.00005 for 300 consecutive rounds.

[0013] Furthermore, the core iterative optimization convergence criterion is to calculate two convergence quantification indicators in the outer loop: one is the average of the optimal values ​​of the maximum vertical displacement, the maximum bending-tensile response index, and the minimum structural safety index on the non-dominated frontier in the last 5 generations; the other is the average of the diversity index of the non-dominated frontier. When the average improvement is less than 3.0% and the average of the diversity index of the non-dominated frontier is less than 2.0%, the current outer loop is considered to have converged.

[0014] Furthermore, in step 4, after the 6th outer loop is completed or after any outer loop meets the convergence criterion, the 10 fly ash composite roadbed structural parameter strategies with the largest congestion distance in the non-dominated front are output as the final result.

[0015] The fly ash composite roadbed structural parameter optimization method of this invention, which integrates experimental data, has the following beneficial effects: It achieves adaptive optimization and dynamic learning of fly ash composite roadbed structural parameters, forming a stable balance between performance, cost, and safety. This method has wide applicability under different construction environments and material conditions. Compared with traditional methods that rely solely on empirical parameters or fixed regression models, this invention introduces stress-strain balance constraints through a physical information neural network model, enabling the model to maintain mechanical consistency while fitting experimental data, avoiding the problem of prediction results deviating from the actual engineering laws, thereby improving the accuracy and stability of responses to complex multi-layered structures. The introduction of the Grey Wolf Genetic Hybrid Optimization Algorithm allows the search process to consider both global exploration and local refinement, enabling rapid convergence to the non-dominated front solution set in high-dimensional nonlinear design spaces, effectively reducing the probability of getting trapped in local optima. Simultaneously, the active learning mechanism enables the model to identify high uncertainty regions during the optimization process and actively trigger new data acquisition and incremental updates of the physical information neural network model, significantly improving data utilization efficiency and model generalization ability. Through this self-feedback cyclic optimization, the model can not only continuously correct prediction errors but also continuously expand its applicable range. The core technical solution achieves an organic integration of data-driven approaches, physical constraints, and intelligent search, ensuring that each model training and parameter search is physically interpretable and optimization-oriented. The final output set of structural parameter strategies can cover various engineering scenarios, providing diverse and directly implementable design solutions. This invention achieves breakthroughs in the automation, intelligence, and high reliability of fly ash composite roadbed design, significantly reducing design cycles, improving construction adaptability and operational safety, and providing a new systematic solution for the comprehensive utilization of materials and structural optimization in the field of transportation infrastructure. Attached Figure Description

[0016] Figure 1 A schematic diagram of the depth-direction response prediction of the Physical Information Neural Network (PINN) provided in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the calculation principle of uncertainty measurement for the multi-PINN model provided in an embodiment of the present invention. Figure 3 The diagram illustrates the principle of crossover and transformation operations in the genetic algorithm provided in this embodiment of the invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] A method for optimizing the structural parameters of fly ash composite roadbeds by integrating experimental data, the method comprising: Step 1: Encode the fly ash composite roadbed structure parameter strategy into a vector and set the data structure.

[0019] In one embodiment, the fly ash composite subgrade structural parameter strategy optimization method integrating experimental data first uniformly encodes the fly ash composite subgrade structural parameter strategy and sets a data structure that matches the subsequent calculation process. This allows the structural parameter strategy to be directly used as the input unit for the subsequent physical information neural network model and the gray wolf genetic hybrid optimization algorithm, avoiding search failures and training instability caused by unclear parameter meanings or inconsistent value ranges. In this embodiment, the fly ash composite subgrade structural parameter strategy is defined as an ordered vector of length 6. The field order of the vector is fixed as: admixture level, layer thickness level, moisture content control level, compaction level, reinforcement structure type, and construction temperature level. By fixing the field order, the value at the same position corresponds to a unique meaning at any stage, facilitating direct indexing and calculation.

[0020] refer to Figure 1The left side of the figure shows the depth profile of the fly ash composite roadbed. This profile is represented using normalized depth coordinates, with depths ranging from 0.00 to 1.00, where depth 0.00 corresponds to the road surface and depth 1.00 corresponds to the bottom of the roadbed. In the vertical direction of the normalized depth coordinates, the roadbed profile is divided into four functional zones from top to bottom: the upper load-bearing zone, the fly ash blending layer, the middle transition zone, and the bottom constraint zone. The upper load-bearing zone, located at depths of 0.00 to approximately 0.20, primarily bears the loads from the road surface; the fly ash blending layer, located at depths of 0.20 to approximately 0.40, is the main layer for implementing the blending strategy; the middle transition zone, located at depths of 0.40 to approximately 0.80, serves as a stress transfer and transition zone; and the bottom constraint zone, located at depths of 0.80 to 1.00, provides support and constraint for the superstructure. On this depth profile structure, 21 depth sampling points are evenly distributed along the depth direction. The depth coordinates of these 21 sampling points are 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, and 1.00, respectively, with a depth interval of 0.05 between adjacent sampling points. These sampling points are marked with solid black circles in the figure, representing the computation nodes where the PINN model performs response prediction at these depth locations. By setting 21 evenly distributed depth sampling points, the response variation trend from the road surface to the roadbed can be fully characterized without increasing the computational load excessively.

[0021] The right side of the figure shows three depth-direction response distribution curves predicted by the PINN model. This part is represented by a two-dimensional coordinate system, with the vertical axis representing the depth coordinates, ranging from 0.00 to 1.00, corresponding to the depth coordinates of the roadbed profile on the left; the horizontal axis represents the numerical values ​​of the response parameters. Grid lines are drawn within the coordinate system to facilitate reading the response values ​​corresponding to each depth location. The first curve is the vertical displacement distribution curve, which starts at the left side of the coordinate system at depth 0.00, indicating that the vertical displacement at the road surface location is close to zero. As the depth increases, the curve gradually extends to the right, indicating that the vertical displacement gradually increases. The curve shows a relatively rapid growth trend in the depth range of 0.00 to 0.50, reflecting the more significant vertical deformation in the upper and middle regions under load; in the depth range of 0.50 to 1.00, the growth rate of the curve gradually slows down and tends to stabilize, indicating that the growth of vertical displacement in the bottom region is limited by the underlying layer. The shape of the first curve conforms to the stress characteristics of the roadbed structure under vertical load, which is transmitted layer by layer from the road surface to the depth, resulting in cumulative deformation. The second curve is the vertical stress distribution curve, which starts on the right side of the coordinate system at a depth of 0.00, indicating that the road surface is subjected to greater vertical stress. As the depth increases, the curve gradually extends to the left, indicating that the vertical stress gradually decreases along the depth direction. The curve shows a faster attenuation trend in the depth range of 0.00 to 0.40, reflecting the dispersion and transmission effect of the upper load-bearing zone and fly ash admixture layer on the vertical stress; in the depth range of 0.40 to 1.00, the attenuation rate of the curve gradually slows down, and finally maintains a certain stress level at the bottom of the roadbed. The shape of this curve conforms to the mechanical law of vertical stress transmission from the road surface to the depth and gradual diffusion and attenuation in a layered roadbed structure. The third curve is the horizontal stress distribution curve, which starts at the middle position of the coordinate system at a depth of 0.00, indicating that the horizontal stress at the road surface is relatively small. As the depth increases, the curve first extends to the right and then returns to the left. The curve gradually extends to the right in the depth range of 0.00 to 0.50, indicating that the horizontal stress increases with depth. This is due to the lateral expansion of the subgrade material during vertical compression, leading to the accumulation of horizontal stress. In the depth range of 0.50 to 1.00, the curve gradually returns to the left, indicating that the horizontal stress gradually decreases due to lateral constraint in the deeper region. The curve reaches its peak at a depth of approximately 0.50, reflecting the maximum interaction between horizontal and vertical stresses at this depth. The shape of the curve conforms to the distribution characteristic of horizontal stress in the subgrade structure under three-dimensional stress conditions, which first increases and then decreases along the depth direction. Several hollow circles are marked on the three response distribution curves, corresponding to five specific depth coordinates: 0.10, 0.30, 0.50, 0.70, and 0.90, representing the actual response data points obtained through experimental observation.Each of the three curves at each depth location is marked with a corresponding hollow circle, indicating that experimental observations of vertical displacement, vertical stress, and horizontal stress were simultaneously collected at these depth locations. These experimental observation data points were used to train and validate the prediction accuracy of the PINN model. It can be observed that all three prediction curves pass well through their corresponding experimental observation data points, indicating that the PINN model can reasonably predict the response at other unobserved depth locations while fitting known experimental data, thus forming a complete and continuous depth-direction response distribution curve.

[0022] Blending levels are used to characterize the variation in fly ash content or fly ash-related material combinations. Blending levels are set as integers from 1 to 9, for a total of 9 levels. For example, blending level 1 corresponds to a lower blending range, blending level 9 corresponds to a higher blending range, and the levels increase progressively according to the amount or performance, forming 9 consecutive engineering-feasible levels. By merging consecutive blending schemes into 9 levels, the granularity of the search space can be constrained, making the optimization process more focused on the engineering-feasible range, while retaining sufficient resolution to distinguish the performance differences of different fly ash combinations.

[0023] Thickness levels are used to characterize the design thickness range of fly ash composite road base layers or related structural layers. Thickness levels are set to integers from 1 to 8. For example, in a specific application, level 1 can correspond to a thinner thickness range, level 8 to a thicker thickness range, and intermediate levels can be divided according to fixed thickness increments. By setting eight thickness levels, the range of conventional structural thicknesses is covered, while controlling the number of combinations of structural parameter strategies. This makes it easier for the Grey Wolf Genetic Hybrid Optimization Algorithm to converge to a solution with engineering value in finite feasible designs. Moisture content control levels are used to represent the moisture content control objectives during construction and use. Moisture content control levels are set to integers from 1 to 5, representing five executable levels from low to high moisture content control. For example, level 3 can correspond to the conventional recommended control range, while levels 1 and 5 can correspond to control strategies on the safer side. By discretizing into five levels, moisture content control decisions can be introduced into the optimization process without requiring complex searches within a continuous moisture content range, thus simplifying implementation and assisting the physical information neural network model in learning stable response patterns.

[0024] The compaction grade is used to characterize the compaction quality control standard. The compaction grade is set to an integer from 1 to 5, corresponding to five levels from standard to higher standards. In practical applications, different grades can be mapped to different testing index requirements, such as different compaction targets or combinations of testing methods. Consolidating compaction control into five grades facilitates the direct integration of construction quality control strategies into the structural parameter strategy vector, enabling subsequent optimization to balance structural performance and construction requirements simultaneously. The reinforcement structure type represents the structural reinforcement scheme used in conjunction with fly ash composite subgrade. The reinforcement structure type is set to an integer from 1 to 4, corresponding to four preset engineering reinforcement methods, such as no reinforcement, single-layer reinforcement, multi-layer reinforcement, and combined drainage and reinforcement structures. By limiting it to four types, different structural systems can be explicitly distinguished in the coding, allowing the physical information neural network model to learn the impact of different construction schemes on the response, while also enabling the Grey Wolf genetic hybrid optimization algorithm to select and combine structural types.

[0025] The construction temperature rating represents the ambient temperature range during construction. The construction temperature rating is set to an integer from 1 to 4, corresponding to four temperature ranges: low temperature, low-to-medium temperature, high-to-medium temperature, and high temperature. The construction temperature rating participates in the subsequent mapping of load rating target values ​​to constrain the consistency between boundary conditions and material operating conditions. By introducing the construction temperature rating, environmental factors can be incorporated into the structural parameter strategy encoding in a discrete form, ensuring that the optimized structural parameter strategy matches the expected construction environment.

[0026] In this implementation, to enable the above six fields to be directly input into the physical information neural network model and participate in the continuous space search in the Grey Wolf genetic hybrid optimization algorithm, the integer levels of each field are linearly mapped to values ​​in the range of 0 to 1. Specifically, for the blending level, level 1 is mapped to 0.111, level 9 is mapped to 1.000, and intermediate levels are mapped at equal intervals; for the layer thickness level, level 1 is mapped to 0.125, and level 8 is mapped to 1.000; for the water content control level, level 1 is mapped to 0.200, and level 5 is mapped to 1.000; for the compaction level, level 1 is mapped to 0.200, and level 5 is mapped to 1.000; for the reinforcement structure type, type 1 is mapped to 0.250, and type 4 is mapped to 1.000; for the construction temperature level, level 1 is mapped to 0.250, and level 4 is mapped to 1.000. This linear mapping ensures that all fields behave within the same numerical range, preventing any single field from having a dominant effect during the training of the physical information neural network model due to an excessively large numerical range. At the same time, it enables the Grey Wolf Genetic Hybrid Optimization Algorithm to perform position updates, crossovers, and transformations on a uniform scale, improving the controllability of the search step size and search direction.

[0027] After encoding, the structural parameter strategy vector is stored as a fixed-length array, with each element containing the scaling value for the corresponding field. For example, six consecutive storage units are used to sequentially store the scaling values ​​for blending level, layer thickness level, moisture content control level, compaction level, reinforcement structure type, and construction temperature level. In implementation, this can be achieved by sequentially arranging six floating-point numbers in memory to form a single record, or by storing multiple structural parameter strategies as fixed-length records in persistent storage, facilitating fast indexing and batch reading. All subsequent calculations are read and written in this order to avoid parsing ambiguity.

[0028] In one optional implementation, to balance the readability of the integer level with the computability of the scaled values, the original integer level and the scaled values ​​can be stored simultaneously in the same record. For example, the first six storage units store the integer level, and the last six storage units store the corresponding scaled values. The physical information neural network model and the gray wolf genetic hybrid optimization algorithm only use the scaled values ​​in the calculation, and engineers read the integer level when reviewing and issuing construction plans. In this way, results that conform to engineering expression habits can be directly generated without changing the input structure of the optimization algorithm.

[0029] Step 2: Construct and train the physical information neural network model PINN.

[0030] In one embodiment, the process of constructing and training the Physical Information Neural Network (PINN) model is based on the fly ash composite subgrade structural parameter strategy encoding formed in step 1. Combined with a clear depth discretization method, response output definition, and constraint construction method, the experimental data and knowledge of the subgrade stress continuity are unified into a numerically executable training objective. This allows the PINN model to not only provide response predictions along continuous depth directions for a given fly ash composite subgrade structural parameter strategy, but also to be forced during training to approximate stress distribution and boundary states consistent with engineering understanding. In this embodiment, a depth coordinate discretization scheme is first set based on the stress characteristics of the fly ash composite subgrade. The thickness of the roadbed structure is mapped to a depth range of 0.00 to 1.00 using a normalized form. Within this range, 21 depth coordinates are selected, namely 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, and 1.00. Twenty-one points are chosen because the uniform division with an interval of 0.05 can characterize the response change trend from the road surface to the roadbed without increasing the computational load excessively. This reflects the differences between the upper loaded region, the middle transition region, and the bottom constrained region, enabling the Physical Information Neural Network (PINN) model to continuously recognize gradient changes during training, avoiding unsmooth response curves or local abrupt changes caused by predicting only at a few depth locations.

[0031] For each set of fly ash composite roadbed structural parameter strategies, the six scaled values ​​obtained in step 1 are combined one by one with the aforementioned 21 depth coordinates. Specifically, the same fly ash composite roadbed structural parameter strategy is combined with depth coordinate 0.00 to form one input record, then combined with depth coordinate 0.05 to form the next input record, and so on, until it is combined with depth coordinate 1.00 to form the 21st input record. Each input record contains six scaled fly ash composite roadbed structural parameter strategy fields and one depth coordinate, for a total of seven values. This unfolding method allows the Physical Information Neural Network (PINN) model to simultaneously perceive the overall configuration of the structural parameter strategy and the current depth position when receiving input, thereby outputting a continuous distribution result related to depth during prediction, without needing to manually stitch together predictions of discrete points outside the network.

[0032] For each input record, the Physical Information Neural Network (PINN) model outputs three values: the estimated vertical displacement, the estimated vertical stress, and the estimated horizontal stress at the corresponding depth. These three outputs collectively describe the critical response state at the corresponding depth under the corresponding fly ash composite subgrade structural parameter strategy, and are used for subsequent target value calculation and physical constraint verification. By simultaneously predicting vertical displacement, vertical stress, and horizontal stress at each depth point, information related to settlement control, bearing capacity, and stress coordination can be obtained from the same network, reducing inconsistencies between multiple independent models.

[0033] In terms of training data construction, in one specific implementation, 40 to 80 representative fly ash composite subgrade structural parameter strategies can be selected. Vertical displacement, vertical stress, and horizontal stress observations at some depth points are obtained through indoor layered loading tests or field loading verification tests. For ease of direct implementation, observation data can be collected at depth coordinates of 0.10, 0.30, 0.50, 0.70, and 0.90, ensuring that each fly ash composite subgrade structural parameter strategy corresponds to at least 5 actual response records at depth points. When forming the training dataset, the actual measured vertical displacement, vertical stress, and horizontal stress are retained for depth points with observations. For other depth points, observation values ​​are not forcibly assigned; instead, they are constrained during training through balancing errors and boundary errors, enabling the Physical Information Neural Network (PINN) model to automatically generate prediction curves that conform to the continuity of force between known and unknown points.

[0034] In this implementation, the Physical Information Neural Network (PINN) model adopts a feedforward fully connected network structure. The input layer has a dimension of 7, corresponding to 6 scaled fly ash composite subgrade structural parameter strategy fields and 1 depth coordinate. The network contains 8 hidden layers, each with 128 neural units. The activation function uses a smooth nonlinear function to enhance the expressive power of complex mapping relationships. The output layer has a dimension of 3, corresponding to the vertical displacement estimate, vertical stress estimate, and horizontal stress estimate. The reason for using 8 layers with 128 units per layer is to provide sufficient expressive power under controllable numerical scale, for simultaneously fitting complex response distributions of multiple structural parameter strategies and multiple depth points, without relying on manually set piecewise empirical formulas.

[0035] The training objective of the Physical Information Neural Network (PINN) consists of three parts: data error, balance error, and boundary error. Data error ensures that at depths with actual observations, the PINN's predictions are as close as possible to the actual responses. Specifically, for each input record containing actual observations, the network outputs the estimated vertical displacement, vertical stress, and horizontal stress, subtracting the corresponding observed values. The absolute value of these differences is then summed across the three outputs for the same record, and finally accumulated across all records with observations. This method of accumulating absolute differences ensures that each observation point directly impacts the training and that the bias participates in optimization linearly, avoiding the obscuring of adjustment space at other locations due to the squared amplification of extreme samples.

[0036] The equilibrium error is used to shape the continuity of stress variation and the layer-by-layer transmission relationship in the depth direction. Specifically, in the prediction results of 21 depth points corresponding to the same fly ash composite subgrade structural parameter strategy, for each pair of adjacent depth points, the absolute values ​​of the differences in horizontal and vertical stress estimates are calculated and added together to represent the degree of stress jump within that interval. This value is then accumulated for all adjacent depth pairs to obtain the equilibrium error. By controlling the stress difference between adjacent depth points, unreasonable local fluctuations in the network can be suppressed, making the network tend to give a stress distribution that changes smoothly layer by layer. This type of distribution is consistent with the continuous variation characteristics of load transmission in layered media, and is closer to the actual engineering state. This equilibrium error constructed based on the difference between adjacent points is simple to implement and computationally stable. The Physical Information Neural Network (PINN) model can spontaneously generate solutions that satisfy mechanical intuition on conventional depth profiles.

[0037] Boundary errors are used to guide the Physical Information Neural Network (PINN) model to meet the expected boundary conditions at both ends of the depth interval. In this implementation, at depth coordinate 0.00, the absolute value of the vertical displacement estimate is included as part of the boundary error to constrain the vertical displacement of the road surface location to be close to zero or remain at a small order of magnitude, thereby reflecting the limitation of the road surface rigid structure on vertical displacement. At depth coordinate 1.00, the absolute value of the difference between the vertical stress estimate and the target load level is included in the boundary error. The target load level is mapped through the construction temperature level; for example, construction temperature level 1 corresponds to a target load level of 0.25, construction temperature level 2 corresponds to 0.50, construction temperature level 3 corresponds to 0.75, and construction temperature level 4 corresponds to 1.00. The reason for this setting is that by introducing a target stress level associated with the construction temperature level at the bottom depth position, the PINN model can incorporate the bearing requirements corresponding to the environmental conditions into the overall stress distribution, so that the prediction results automatically match the stress state of the fly ash composite roadbed structure parameter strategy at the bottom position.

[0038] During training, data error, balancing error, and boundary error are accumulated and used as the overall optimization objective for the Physical Information Neural Network (PINN) model. The network's internal parameters are gradually adjusted through backpropagation and numerical optimization. In one specific implementation, an adaptive learning rate optimization algorithm is first used for pre-training, for example, setting the learning rate to 0.001, the batch size to 64, and the training epochs to 9000, to quickly approximate the reasonable domain of understanding with a large update step size. Subsequently, a quasi-Newton optimization algorithm is used for fine-tuning, adding approximately 3000 more training epochs to make the error convergence more stable. To avoid drastic gradient oscillations during training, the gradient of each parameter update can be pruned, for example, limiting the norm of a single update to within 1.0, thereby ensuring smooth progress in the training process.

[0039] To support sample collection triggering based on uncertainty measurement in subsequent active learning, this implementation constructs five independent Physical Information Neural Network (PINN) models under the same data structure and training objective. Specifically, different random initialization seeds are used for each of the five networks during parameter initialization, and the same training process is executed for each. The five PINN models obtained in this way exhibit similar overall trends and data / physical constraints, but quantifiable differences exist in local predictions. During subsequent iterative optimization, uncertainty can be assessed by comparing the prediction differences of the five PINN models for the same fly ash composite roadbed structure parameter strategy, providing a clear triggering basis for the active learning module.

[0040] In one alternative implementation, the number of depth points can be increased, for example, by using 41 depth coordinates divided at 0.025 intervals, to enhance the ability to characterize subtle stress gradient changes. In another alternative implementation, the number of hidden layers and the number of neurons per layer can be adjusted, for example, by using a 6-layer structure with 64 neurons per layer, to adapt to scenarios with limited computing resources.

[0041] Step 3: The physical information neural network model PINN constructed and trained in Step 2, the active learning module, and the gray wolf genetic hybrid optimization algorithm GWGA are used to perform core iterative optimization. The core iterative optimization includes: using the gray wolf genetic hybrid optimization algorithm GWGA to generate candidate fly ash composite subgrade structure parameter strategies, using the physical information neural network model PINN to evaluate the target values ​​of the candidate fly ash composite subgrade structure parameter strategies, and using the active learning module to trigger sample collection based on the uncertainty measure of the physical information neural network model PINN to obtain new experimental data and incrementally update the physical information neural network model PINN constructed and trained in Step 2.

[0042] In one embodiment, when the physical information neural network model PINN, the active learning module, and the gray wolf genetic hybrid optimization algorithm GWGA, constructed and trained in step 2, are used to perform core iterative optimization, the multi-objective performance search, stress response prediction, and introduction of new experimental data of the fly ash composite subgrade structural parameter strategy are unified in a clear and executable loop, so that the generation, evaluation, and correction of each candidate fly ash composite subgrade structural parameter strategy have a clear calculation path and judgment basis.

[0043] The core iterative optimization is based on the fly ash composite subgrade structural parameter strategy vector of length 6 determined in step 1 and the physical information neural network model PINN trained in step 2. First, an initial candidate set is constructed. Specifically, a population size of 96 can be selected, treating each fly ash composite subgrade structural parameter strategy as an individual. An initial set of individuals is generated using a uniform random method within each level range. For example, the blending level is selected with equal probability from 1 to 9, the layer thickness level with equal probability from 1 to 8, and the moisture content control level, compaction level, reinforcement structure type, and construction temperature level are selected within their respective defined ranges. Each level is linearly scaled to a value within the range of 0 to 1, forming a 6-dimensional vector conforming to the order specified in step 1. To ensure the diversity of the initial search space, duplicates can be checked when generating 96 individuals. Duplicate individuals are re-extracted until 96 distinct fly ash composite subgrade structural parameter strategies are obtained.

[0044] For each fly ash composite subgrade structural parameter strategy in the initial population, its response in the depth direction is calculated using the Physical Information Neural Network (PINN) model obtained in step 2. During calculation, the six scaling values ​​of the fly ash composite subgrade structural parameter strategy are combined one by one with 21 depth coordinates to form 21 input records, which are then input into the PINN model to obtain estimated vertical displacement, vertical stress, and horizontal stress values ​​at the 21 depth locations. Based on these prediction results, three target values ​​are calculated for each fly ash composite subgrade structural parameter strategy. The first objective is the maximum value of the vertical displacement estimate across the entire depth range, reflecting the adverse effects of the structural parameter strategy on settlement control. The second objective is the maximum value of the flexural-tensile response index across the entire depth range, where the flexural-tensile response index is represented by the absolute value of the difference between the horizontal stress estimate and the vertical stress estimate at each depth location, reflecting the cracking risk that may be caused by localized stress unevenness. The third objective is the minimum value of the structural safety index across the entire depth range, where the structural safety index is taken as the absolute value of the difference between the vertical stress estimate and the horizontal stress estimate at each depth location, measuring the degree of stress coordination; the larger the minimum value, the safer the overall stress state. This evaluation method simultaneously constrains three directions: the vertical displacement target encourages reduced settlement, the flexural-tensile response target encourages reduced tensile stress concentration, and the structural safety index encourages maintaining stress coordination at each depth location, thereby guiding the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) to converge towards a fly ash composite subgrade structural parameter strategy with balanced comprehensive performance.

[0045] Based on the three objective values ​​mentioned above, a multi-objective non-dominated ranking strategy is implemented for the fly ash composite roadbed structural parameters in the population. In practical implementation, any two individuals are compared. When one individual is not inferior to the other in all objective values ​​and is superior to the other in at least one objective value, the former is considered to have a dominant relationship with the latter. After completing the overall comparison, individuals not dominated by any other individual are formed into the first front layer. This process is then repeated from the remaining individuals to form the second front layer, the third front layer, and so on. Within the same front layer, to avoid individuals concentrating in local areas, a crowding distance is calculated for each individual based on the distribution density in each objective dimension. This distance measures the sparsity of the solutions around the individual; individuals with larger crowding distances are more conducive to maintaining the diversity of the solution set. Through non-dominated ranking and crowding distance, multi-objective performance can be comprehensively ranked and filtered without manually setting objective weights.

[0046] In each generation of population updates, the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) is used to perform a guided search on the current set of fly ash composite subgrade structural parameter strategies. Specifically, three best-performing fly ash composite subgrade structural parameter strategies are first selected from the current population based on non-dominated sorting results and crowding distance, designated as leader individuals: Leader 1, Leader 2, and Leader 3. These three leader individuals are considered as references guiding the search direction in the current iteration because they simultaneously possess relatively low maximum vertical displacement, low maximum bending-tensile response index, and high minimum structural safety index, and are relatively dispersed in the solution space. Using them as references guides other individuals to concentrate in areas with better performance while maintaining a certain distribution breadth.

[0047] For each individual other than the leader individual, for each field in the vector, the scaling values ​​of the three leader individuals for that field are read, and the median value of these three scaling values ​​is calculated. This median value is used as the reference position for that field. The reason for using the median value instead of simply selecting a single leader individual is that the median value is located between the three excellent solutions and can be regarded as the representative position of the current excellent solution region. This can reduce the excessive concentration caused by the search process being pulled by a single individual when guiding the update. Subsequently, a random ratio between 0.2 and 0.8 is generated for this field. This ratio is used to control the distance that the current field value of the individual moves towards the reference position, so that some individuals quickly move closer to the excellent region, while retaining a certain deviation to explore the neighborhood around the reference position. For the six fields of blending level, layer thickness level, moisture content control level, compaction level, reinforcement structure type, and construction temperature level, when the updated scaling value needs to be returned to the level expression, the scaling value is rounded to the corresponding level and mapped back to a specific level. This ensures that after each update, an effective fly ash composite subgrade structure parameter strategy that meets the constraints of step 1 is still obtained. This process generates a temporary population that is updated under the guidance of gray wolves, causing most individuals to converge toward the high-performance region represented by the leader individual, while maintaining diversity under random perturbations of the scaling factor.

[0048] After obtaining the temporary population updated under the guidance of gray wolves, a genetic operation is performed to further increase the combinatorial diversity and local refinement capability of candidate solutions. Specifically, a tournament selection method is used to select parent individuals from the temporary population. In each round, individuals with higher non-dominance levels and greater crowding distances are selected from four randomly selected individuals as parents. A two-point crossover operation is performed on the selected parents, using the second and fifth fields of the fly ash composite subgrade structural parameter strategy vector as the crossover positions. Fields between these two positions are swapped, generating two offspring. This fixed-position two-point crossover method can reorganize some field combinations while maintaining the stability of some fields, allowing for new combinations of reinforcement structure types with key fields such as layer thickness or blending levels, exploring the impact of different design element combinations on overall performance. After the crossover, a transformation operation is performed on each field of the offspring, with each field triggering a transformation with a probability of 0.08. For the field that triggers the transformation, if it is a scaling representation, a random perturbation between -0.05 and 0.05 is added to the current value, and then the result is truncated to the interval between 0 and 1. If it is a level representation, one of the allowed neighboring levels is randomly selected to replace the current level. Introducing a small perturbation in this way helps to escape local optima while avoiding the generation of extreme solutions that are completely unrelated to the current high-performance solution.

[0049] refer to Figure 3In this embodiment, a two-point crossover method is used to reorganize the structural parameter strategy vectors of fly ash composite subgrade. Specifically, it is assumed that two parent individuals are selected from the temporary population. The structural parameter strategy vector of parent 1 is [0.556, 0.500, 0.600, 0.800, 0.750, 0.500], and the structural parameter strategy vector of parent 2 is [0.778, 0.750, 0.400, 0.600, 0.500, 0.750]. Both vectors are ordered vectors of length 6, corresponding to the scaling values ​​of admixture grade, layer thickness grade, moisture content control grade, compaction grade, reinforcement structure type, and construction temperature grade, respectively. When performing the crossover operation, the second and fifth fields are used as fixed crossover positions. These two locations were chosen because they contain three key fields: water content control level, compaction level, and reinforcement structure type. By exchanging the field combinations in this section, new combinations of reinforcement structure type with key fields such as layer thickness or admixture level can be created, thereby exploring the impact of different design element combinations on overall performance. The specific crossover process is as follows: Keeping fields 0 and 1 of parent generation 1 unchanged, and keeping field 5 unchanged, fields 2 through 4 are replaced with the corresponding fields of parent generation 2, thus generating child generation 1. Simultaneously, keeping fields 0 and 1 of parent generation 2 unchanged, and keeping field 5 unchanged, fields 2 through 4 are replaced with the corresponding fields of parent generation 1, thus generating child generation 2. Through this process, the structure parameter strategy vector of offspring 1 is [0.556, 0.500, 0.400, 0.600, 0.500, 0.500], and the structure parameter strategy vector of offspring 2 is [0.778, 0.750, 0.600, 0.800, 0.750, 0.750]. After the crossover operation is completed, a transformation operation is performed on each field of the generated offspring individuals. In this implementation, each field triggers the transformation with a probability of 0.08. This probability value has been experimentally verified to achieve a balance between maintaining population stability and exploring new areas. When a field triggers a transformation, a random perturbation between -0.05 and 0.05 is added to the current scaling value, and the result is then truncated to the valid interval of 0 to 1. For example, in the vector of offspring 1, suppose the third field (compaction level scaling value) triggers the transformation operation, and its original value is 0.600. After adding the perturbation, the value may become 0.650. This small perturbation helps the search process escape local optima while avoiding extreme solutions completely unrelated to the current high-performance solution. For fields that need to be expressed as integer levels, the scaling value is rounded to map back to a specific level, ensuring that each update still yields an effective fly ash composite subgrade structure parameter strategy that meets the constraints of step 1.By combining the above crossover and transformation operations, the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) can maintain the fast convergence characteristic of the Grey Wolf algorithm while utilizing the global search capability of the genetic algorithm to effectively avoid getting trapped in local optima and increase the probability of finding a solution with better overall performance.

[0050] The offspring individuals obtained through gray wolf-guided genetic operations are merged with the best-performing individuals from the previous generation. The Physical Information Neural Network (PINN) model is then used to recalculate three target values. Non-dominated sorting and crowding distance calculations are performed, and the population size is truncated to 96, resulting in a new generation of fly ash composite roadbed structure parameter strategy set. By repeating this process, the Gray Wolf Genetic Hybrid Optimization Algorithm (GWGA), guided by the PINN model, gradually pushes candidate solutions towards regions with higher overall performance and a more reasonable distribution.

[0051] In the core iterative optimization, active learning is introduced to identify regions where the predictions of the Physical Information Neural Network (PINN) model are unstable, and the model's reliability is improved by adding new experimental data. Specifically, after every 40 generations of the Gray Wolf Genetic Hybrid Optimization Algorithm (GWGA), 48 well-performing fly ash composite subgrade structural parameter strategies from the current generation's non-dominated frontier are selected as key evaluation targets. For these 48 fly ash composite subgrade structural parameter strategies, the five independent PINN models constructed in step 2 are input. For each strategy, the maximum vertical displacement, maximum bending-tensile response index, and minimum structural safety index outputs of the five models are recorded. For each target value, the difference between the maximum and minimum values ​​among the five model outputs is calculated, and the larger of the three differences is used as the uncertainty measure of the fly ash composite subgrade structural parameter strategy. This uncertainty measure reflects the consistency of different PINN models around the structural parameter strategy; a large value indicates that the existing training data is insufficient to constrain the response prediction in that region.

[0052] refer to Figure 2In this embodiment, for a candidate fly ash composite subgrade structural parameter strategy in the core iterative optimization process, its six scaled parameter values ​​are combined with 21 depth coordinates one by one to form 21 input records, which are then input into five independent Physical Information Neural Network (PINN) models. These five PINN models are trained separately using different random initialization seeds in step 2, so they are generally similar in terms of data and physical constraints, but exhibit quantifiable differences in local predictions. Each PINN model outputs three target values ​​for this strategy: the maximum value of the vertical displacement estimate across the entire depth range (Target 1), the maximum value of the bending-tensile response index across the entire depth range (Target 2), and the minimum value of the structural safety index across the entire depth range (Target 3). In this embodiment, for a candidate fly ash composite subgrade structural parameter strategy in the core iterative optimization process, its six scaled parameter values ​​are combined with 21 depth coordinates one by one to form 21 input records, which are then input into five independent Physical Information Neural Network (PINN) models. These five PINN models were trained separately using different random initialization seeds in step 2. Therefore, they are similar in overall trend and have similar data and physical constraints, but exhibit quantifiable differences in local predictions. Each PINN model outputs three target values ​​for the strategy: the maximum value of the vertical displacement estimate across the entire depth range (Target 1), the maximum value of the bending-tensile response index across the entire depth range (Target 2), and the minimum value of the structural safety index across the entire depth range (Target 3). After calculating the uncertainty measure of each of the three target values, the largest of these three measures is taken as the comprehensive uncertainty measure of the fly ash composite subgrade structural parameter strategy. In this example, the comprehensive uncertainty measure is max(0.7, 0.7, 0.9) = 0.9. The maximum value is used instead of the average value or other statistics because it is necessary to be vigilant about high uncertainty on any target to ensure that active learning can capture areas that need supplementary training data in a timely manner. When the comprehensive uncertainty measure is greater than a preset threshold (e.g., 0.12), the fly ash composite subgrade structural parameter strategy is determined to be a high uncertainty candidate and is included in the active learning sample collection candidate set. This mechanism can identify regions where the PINN (Physical Information Neural Network) prediction is unstable, and the reliability of the model in these regions can be improved by adding new experimental data, making the search direction of the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) more reliable in subsequent iterations.In one specific implementation, after every 40 generations of evolution, 48 fly ash composite roadbed structural parameter strategies with good performance are selected from the non-dominant frontier of the current generation. The uncertainty metric calculation is performed on these 48 strategies, and the strategies with a metric value greater than 0.12 are sorted from largest to smallest. The top 12 are selected to form a candidate acquisition set. Then, the real response data corresponding to these strategies are obtained through standard indoor loading tests or field loading tests, which are used to incrementally update the 5 independent physical information neural network PINN models.

[0053] In one specific implementation, fly ash composite subgrade structural parameter strategies with an uncertainty metric greater than 0.12 are designated as high-uncertainty candidates, and sorted by uncertainty metric from largest to smallest, with the top 12 selected to form a candidate acquisition set. For each fly ash composite subgrade structural parameter strategy in the candidate acquisition set, a sample acquisition instruction is generated. The instruction includes six level fields of the fly ash composite subgrade structural parameter strategy, as well as vertical displacement, vertical stress, and horizontal stress data to be acquired at depth coordinates of 0.10, 0.30, 0.50, 0.70, and 0.90. After implementing the sample acquisition instruction, the corresponding real response can be obtained through standard indoor loading tests or field loading tests, and this new data is appended to the dataset used to train the Physical Information Neural Network (PINN) model.

[0054] After acquiring new data, incremental training is performed on five independent Physical Information Neural Network (PINN) models. For example, each model can be trained for an additional 2000 epochs using an adaptive optimization algorithm with a learning rate of 0.0005 and a batch size of 64. Incremental training is stopped when the overall error decreases by less than 0.00005 over 300 consecutive epochs. By introducing real observations and performing targeted updates in high-uncertainty regions, the prediction results of the five PINN models in these regions are made more consistent, thereby reducing the risk of misjudgment in these regions by the Gray Wolf Genetic Hybrid Optimization (GWGA) algorithm in subsequent iterations and making the search direction more reliable. After the update, the latest PINN model is used as the evaluation basis, and the cycle of candidate generation, target value calculation, multi-target ranking, Gray Wolf guided update, genetic operations, and active learning triggering and incremental update is repeated.

[0055] Step 4: After the core iterative optimization converges, output the final fly ash composite roadbed structure parameter strategy.

[0056] In one embodiment, after completing the core iterative optimization using the Physical Information Neural Network (PINN) model, active learning, and the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA), the final set of fly ash composite subgrade structural parameter strategies is output through a clear convergence determination process and candidate set screening process. In this embodiment, the core iterative optimization is organized in the form of outer loops. Each outer loop contains a fixed number of evolutionary generations, for example, 80 to 120 generations. During the execution of each outer loop, the Grey Wolf Genetic Hybrid Optimization Algorithm (GWGA) generates multiple fly ash composite subgrade structural parameter strategies according to step 3. For each generation of the population, the maximum vertical displacement, the maximum bending tensile response index, and the minimum structural safety index are calculated using the Physical Information Neural Network (PINN) model, and non-dominated sorting and congestion distance calculation are completed. Based on this, the convergence status of each outer loop is measured to determine whether to continue with a new outer loop or proceed to the final result output stage.

[0057] To perform executable convergence checks, the non-dominated front information of the most recent five generations is recorded in each outer loop. For each of these five generations, the individual with the smallest maximum vertical displacement, the smallest maximum bending-tensile response index, and the largest minimum structural safety index is selected from its non-dominated front, and these are recorded as the best performance of that generation on the three objectives. Then, the best performances of the first and fifth generations are compared in chronological order, and the improvement margin for each objective is calculated. The improvement margin is expressed as a percentage, i.e., the ratio of the difference between the best value of the first generation and the best value of the fifth generation to the best value of the first generation. When the best values ​​of the maximum vertical displacement and the maximum bending-tensile response index gradually decrease with each generation, and the best value of the minimum structural safety index gradually increases with each generation, the improvement margin is positive, indicating that the core iterative optimization is still searching for a better solution. When the improvement margins of the three objectives tend to be very small, for example, if the average improvement margin of the three objectives is less than 3.0, it can be considered that the performance improvement of the non-dominated front in the most recent five generations has been very limited, and further expanding the population size or the number of iterations will only lead to greater computational costs and make it difficult to obtain significant benefits.

[0058] While calculating the performance improvement, the diversity of the non-dominated front is measured. In a specific implementation, 10 pairs of fly ash composite subgrade structural parameter strategies can be randomly selected within the non-dominated front of the same generation. For each pair, the differences in the values ​​of its six fields are compared, the number of different fields is counted, and the average of the number of different fields in the 10 pairs of samples is calculated to obtain the diversity index for that generation. This diversity index reflects the distribution of solutions in the structural parameter space within the non-dominated front. When the index value is large, it indicates that there are significant differences among candidate solutions in multiple combinations of admixture levels, layer thickness levels, moisture control levels, compaction levels, reinforcement structure types, and construction temperature levels, and the design space coverage is relatively wide. When the index drops to a smaller value, it indicates that most solutions within the non-dominated front have shrunk to near similar parameter combinations, and the search space has been effectively compressed. In convergence determination, the average value of the diversity index in the most recent 5 generations can be calculated. When the average value is below 2.0, it indicates that the convergence degree of the non-dominated front on the structural parameter combination is already relatively high.

[0059] In this implementation, the performance improvement magnitude and the diversity index are used in combination: when the average performance improvement magnitude over the last 5 generations is less than 3.0 and the average non-dominated front diversity index over the last 5 generations is less than 2.0, the current outer loop is considered to have reached convergence. This is because, on the one hand, the performance improvement magnitude limits invalid repetitive computations, preventing large-scale evolution when the target is already relatively stable; on the other hand, the diversity index ensures that the algorithm does not stop prematurely due to getting stuck in a local solution, but rather that the candidate solution's performance tends to stabilize while its structural parameter combinations have concentrated in a finite and representative region, reflecting that the algorithm has completed an effective search overall.

[0060] Regarding the upper limit control of the entire process, the maximum number of executions of the outer loop can be set to 6. If the convergence conditions of performance improvement and diversity indicators are not met simultaneously after the 6th outer loop, the core iterative optimization process still ends, and the final result selection stage begins. This approach gives the algorithm clear time and resource boundaries, making it suitable for deployment in engineering design scenarios and avoiding delays in engineering decisions caused by unlimited iteration.

[0061] After completing the above convergence determination, the non-dominated front is extracted from the final generation of the last effective outer cycle population as the final candidate set. Each individual in the non-dominated front is a high-quality scheme selected based on a comprehensive screening of three objectives: maximum vertical displacement, maximum flexural response index, and minimum structural safety index. No other individual is superior in all three objectives simultaneously. Based on this candidate set, the individuals are ranked by congestion distance, and 10 fly ash composite subgrade structural parameter strategies are selected as the final output schemes.

[0062] The calculation of congestion distance can be performed as follows in a specific implementation: For the set of individuals within the non-dominated front, for each of the three objectives—maximum vertical displacement, maximum flexural response index, and minimum structural safety index—all individuals are individually sorted in ascending or descending order according to the objective value. For each objective, the individuals at the top and bottom of the sorting result are assigned larger boundary distance values ​​to encourage the retention of extreme solutions at both ends of the objective space. For each individual in the middle position, the objective values ​​of the two individuals immediately before and after it are read, and the sum of the objective differences between the current individual and the individuals before and after it is used as the local spacing metric for that individual on that objective. The local spacing metrics obtained for the three objectives are summed to obtain the congestion distance for each individual. The larger the congestion distance value, the more sparse the individual is in the objective space, representing a compromise relationship that is significantly different from other solutions. By prioritizing individuals with larger congestion distances, it can be ensured that the final output of the 10 fly ash composite subgrade structural parameter strategies not only approaches the high-quality solution of the non-dominated front in performance but also has different balance methods among different objectives, providing designers with diverse options.

[0063] Therefore, in this implementation, the final output is triggered when one of the following two conditions is met: first, any outer loop meets the convergence condition that the average performance improvement is less than 3.0 and the average non-dominated front diversity index is less than 2.0; second, the outer loop is executed 6 times. When the output is triggered, the top 10 fly ash composite roadbed structural parameter strategies are selected from the corresponding final non-dominated fronts, sorted by congestion distance from largest to smallest. The integer values ​​of their 6 level fields are directly output, and the maximum vertical displacement, maximum bending tensile response index, and minimum structural safety index corresponding to each scheme can be given simultaneously as the basis for subsequent engineering comparison, design finalization, and construction technical condition preparation.

[0064] In one optional implementation, the number of fly ash composite roadbed structure parameter strategies output can be adjusted to 5, 15, or 20, depending on the specific project's requirements for the number and distribution range of schemes, while maintaining the non-dominant front screening and congestion distance sorting methods unchanged. In another optional implementation, screening conditions can be added to some schemes during output, such as removing individuals whose maximum vertical displacement exceeds a preset threshold or whose minimum structural safety index is below a preset threshold, making the final result more closely aligned with the specifications of the specific project.

[0065] The present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for optimizing the parameter strategy of fly ash composite subgrade structure by fusing experimental data, characterized in that, The method comprises: Step 1: encode the fly ash composite roadbed structure parameter strategy into a vector and set a data structure; Step 2: build and train a physical information neural network model PINN; Step 3: perform core iterative optimization by using the physical information neural network model PINN built and trained in step 2, an active learning module and a grey wolf genetic hybrid optimization algorithm GWGA, which comprises: generating a candidate fly ash composite roadbed structure parameter strategy by using the grey wolf genetic hybrid optimization algorithm GWGA, evaluating the target value of the candidate fly ash composite roadbed structure parameter strategy by using the physical information neural network model PINN, and triggering sample collection based on the uncertainty measurement of the physical information neural network model PINN by using the active learning module to obtain new experimental data and incrementally update the physical information neural network model PINN built and trained in step 2; Step 4: output the final fly ash composite roadbed structure parameter strategy after the core iterative optimization converges.

2. The method of claim 1, wherein, In step 1, the structure parameter strategy is encoded into an ordered vector with a length of 6, which is in turn a mixing level, a layer thickness level, a water content control level, a compaction level, a reinforcement structure type and a construction temperature level; the mixing level takes an integer from 1 to 9, the layer thickness level takes an integer from 1 to 8, the water content control level takes an integer from 1 to 5, the compaction level takes an integer from 1 to 5, the reinforcement structure type takes an integer from 1 to 4, and the construction temperature level takes an integer from 1 to 4; and the six discrete fields are linearly scaled to the range of 0 to 1 according to their maximum levels.

3. The method of claim 1, wherein, In step 2, the training target of the physical information neural network model PINN is built, which includes data error, balance error and boundary error; the data error is the absolute difference between the observed output and the network output summed at the depth points with observations; the balance error is the sum of the absolute values of the horizontal stress difference and the absolute values of the vertical stress difference at adjacent depth points summed at all adjacent pairs; the boundary error is the absolute value of the vertical displacement at depth 0.00, and the absolute value of the difference between the vertical stress and the load level target value at depth 1.00, which is mapped from the construction temperature level.

4. The method of claim 1, wherein, In step 2, the construction and training of the physical information neural network model PINN are repeatedly performed with 5 different random seeds on the same structure and data to obtain 5 independent physical information neural network models PINN for uncertainty evaluation in the core iterative optimization.

5. The method of claim 1, wherein, In the core iterative optimization, the evaluation of the target value of the candidate fly ash composite roadbed structure parameter strategy comprises calculating three target values: the maximum vertical displacement, the maximum bending and tensile response index and the minimum structure safety index; wherein the bending and tensile response index is defined as the absolute difference between the horizontal stress and the vertical stress, and the structure safety index is defined as the minimum value of the absolute difference between the vertical stress and the horizontal stress at 21 depth points.

6. The method of claim 1, wherein, The steps of generating candidate fly ash composite roadbed structure parameter strategies by using the grey wolf genetic hybrid optimization algorithm GWGA include: performing a grey wolf guided updating process: selecting three leader individuals according to non-dominated sorting and crowding distance; taking the median of the scaling values of the three leader individuals in the fields as the reference value, generating a uniform random ratio of 0.2 to 0.8, and generating a uniform random ratio of the distance between the current field value of the individual and the reference value, and rounding the updated result to the adjacent level if the field is a discrete field; and then performing a genetic operation process: performing tournament selection on the temporary population guided by the grey wolf, performing two-point crossover on the selected parent pairs, and fixing the crossover positions at the second and fifth fields, and performing transformation operation on the offspring.

7. The method of claim 1, wherein, The steps of triggering sample collection based on the uncertainty measurement of the physical information neural network model PINN by using the active learning module include: after completing 40 generations of evolution, inputting the first 48 individuals in the non-dominated front into five independent physical information neural network models PINN respectively, calculating the difference between the maximum and minimum values of the three target values on the five models, and taking the maximum value among the three as the uncertainty measurement of the individual; taking the first 12 individuals in the descending order of the measurement values as the candidate collection set; for each individual in the candidate collection set, generating a sample collection instruction, and the sample collection instruction includes the six level fields of the individual, the depth coordinate set to be measured and the three output values to be recorded.

8. The method of claim 7, wherein, The steps of incrementally updating the physical information neural network model PINN include: after adding the new records obtained by collecting the sample collection instructions to the training sample set, appending 2000 rounds of training to the five independent physical information neural network models PINN respectively, using the Adam optimizer, the learning rate is 0.0005, the batch size is 64, and the early stopping threshold is set to less than 0.00005 for 300 consecutive rounds of decline.

9. The method of claim 1, wherein, The convergence judgment condition of the core iterative optimization is that in the outer loop, two convergence quantification indicators are calculated: one is the average of the optimal value improvement amplitude of the maximum vertical displacement, the maximum bending and tensile response index and the minimum structure safety index on the non-dominated front in the last 5 generations, and the other is the average of the non-dominated front diversity index; when the average of the improvement amplitude is less than 3.0% and the average of the non-dominated front diversity index is less than 2.0%, it is determined that the current outer loop converges.

10. The method of claim 1, wherein, In step 4, after the completion of the 6th outer loop or after any outer loop meets the convergence judgment condition, the 10 fly ash composite roadbed structure parameter strategies with the largest crowding distance in the non-dominated front are output as the final result.

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