A pavement structure layer modulus back calculation method, device, equipment and medium

Abstract

This invention provides a method, apparatus, equipment, and medium for back-calculating the modulus of a pavement structure layer. It relates to the field of road engineering technology and addresses the problem of low iterative efficiency caused by traditional modulus back-calculation relying on theoretical forward calculations. The method includes: collecting measured deflection basin data; obtaining the current modulus combination during iteration and inputting it into a preset database to obtain a set of adjacent benchmark modulus nodes; then processing this node set using a dimensionality-reduction multidimensional interpolation strategy to obtain the theoretical deflection basin; updating the modulus based on the error until convergence and outputting the result; wherein the database is constructed from benchmark modulus combinations generated based on a logarithmic interval strategy, and the interpolation strategy sequentially performs one-dimensional interpolation along each dimension to achieve dimensionality reduction query. By synergistically combining logarithmic interval and dimensionality-reduction interpolation, forward calculations are avoided, improving back-calculation efficiency while ensuring accuracy.

Description

Technical Field

[0001] This invention relates to the field of road engineering technology, and in particular to a method, apparatus, equipment and medium for back-calculating the modulus of pavement structure layers. Background Technology

[0002] The pavement structure modulus is a core mechanical parameter for evaluating the bearing capacity and remaining service life of a pavement structure. In non-destructive testing of road engineering, equipment such as falling weight deflectometers typically collect deflection basin data from a massive number of measuring points along the longitudinal direction of the road at fixed intervals. Due to spatial variability caused by material properties, construction quality, and service conditions, each measuring point must undergo independent and complete modulus back-calculation, making it impossible to simplify or share calculation results in batches. This creates a real engineering challenge: "huge number of measuring points—independent back-calculation for each measuring point—extremely high total computational load."

[0003] Current mainstream modulus back-calculation techniques generally adopt a baseline scheme of iterative optimization + theoretical forward calculation: first, an initial modulus combination is given, and then forward calculation is performed through elastic layered system theory or finite element method to obtain the corresponding theoretical deflection basin; the theoretical deflection basin is compared with the measured deflection basin, and the modulus is iteratively updated with the goal of minimizing the error until convergence. Under this mechanism, each iteration must fully call the theoretical forward calculation. Forward calculation involves complex numerical integration such as Hankel integral and Burmister solution in semi-infinite space, or solving large-scale mesh equations in finite element method, which has high computational complexity and is time-consuming. Due to this mechanism, the total back-calculation time for a single measurement point is long. When facing a large number of measurement points with dense vertical acquisition in engineering, the total time increases with the number of measurement points, ultimately resulting in low overall computational efficiency, which is difficult to meet the actual needs of rapid detection, real-time evaluation, batch processing, and timely maintenance decision-making in engineering sites. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, equipment, and medium for back-calculating the modulus of pavement structure layers to address the aforementioned technical problems.

[0005] The following technical solution is adopted in this specification: This specification provides a method for back-calculating the modulus of pavement structure layers, including: Collect measured deflection basin data of the target road surface; In the iterative back calculation of the modulus of the target pavement structural layer, the current modulus combination is obtained based on the preset initial modulus value of each structural layer and its iterative update result. The current modulus combination is input into a preset database to obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination. The adjacent reference modulus node set is then interpolated using a preset dimensionality reduction and multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination. The preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy. The dimensionality reduction and multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction queries. Obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, update the current modulus combination based on the error using a preset optimization algorithm strategy, and output the back calculation result when the preset convergence condition is met.

[0006] Further, the step of updating the current modulus combination based on the error using a preset optimization algorithm strategy includes: The fitness value is obtained based on the error, and the fitness value is input into a preset optimization algorithm to generate a new combination of moduli. The optimization algorithm includes at least one of genetic algorithm, particle swarm optimization algorithm or Levenberg-Marquardt algorithm.

[0007] Furthermore, the preset database is constructed using a baseline modulus combination generated based on a logarithmic interval strategy, including: Obtain the preset upper and lower limits of the modulus of each structural layer; Multiple reference modulus values ​​are extracted between the preset upper limit and the preset lower limit according to the logarithmic interval rule, so that the reference modulus value density in the low modulus range is greater than the reference modulus value density in the high modulus range. By combining the reference modulus values ​​of all structural layers, several reference modulus combinations are obtained. Obtain the deflection basin response corresponding to several reference modulus combinations, associate and store the reference modulus combinations with the corresponding deflection basins, and obtain a database.

[0008] Furthermore, the deflection basin response corresponding to several reference modulus combinations is obtained by using the elastic layered system theory method or the finite element method to obtain the deflection basin response corresponding to each reference modulus combination.

[0009] Furthermore, the one-dimensional interpolation operation in the dimension-wise dimensionality reduction multidimensional interpolation strategy employs at least one of linear interpolation, nearest neighbor interpolation, Hermitian interpolation, or cubic spline interpolation.

[0010] Furthermore, the preset convergence conditions include: the error between the measured deflection basin data and the theoretical deflection basin is less than a preset threshold, or the number of iterations reaches the preset maximum number of iterations.

[0011] Furthermore, it also includes: evaluating the preset database and the dimensionality reduction multidimensional interpolation strategy, including: Construct a test dataset containing several combinations of validation moduli; Based on the verification modulus combination input to the preset database, the corresponding estimated deflection response is obtained through the dimension-by-dimensional reduction multidimensional interpolation strategy; The root mean square error between the estimated deflection response and the accurate theoretical deflection response obtained through forward mechanics calculation is calculated. The root mean square error is the square root of the average of the sum of squares of the differences in deflection values ​​at each sensor location. Based on the variation trend of the root mean square error under different database sizes and interpolation method configurations, the target database size and target interpolation method are determined.

[0012] This specification provides a device for back-calculating the modulus of a road surface structure layer, comprising: The data acquisition module is used to collect measured deflection basin data of the target road surface; The state determination module is used to obtain the current modulus combination based on the preset initial modulus values ​​of each structural layer and its iterative update results in the iterative back calculation of the modulus of the target pavement structural layer. The interpolation query module is used to input the current modulus combination into a preset database, obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination, and perform interpolation processing on the adjacent reference modulus node set through a preset dimensionality reduction multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination; the preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy; the dimensionality reduction multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction query; The modulus inverse calculation module is used to obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, and to update the current modulus combination based on the error through a preset optimization algorithm strategy until the preset convergence condition is met, and then output the inverse calculation result.

[0013] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for inverse calculation of the modulus of road structure layers.

[0014] This specification provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described method for back-calculating the modulus of the pavement structure layer.

[0015] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: This invention constructs a database using a benchmark modulus combination generated based on a logarithmic interval strategy. This results in a higher density of benchmark nodes in the low-modulus range, where the deflection basin is more sensitive to modulus changes, effectively avoiding interpolation distortion caused by sparse nodes. Simultaneously, by employing a multi-dimensional interpolation strategy of dimensionality reduction, complex high-dimensional queries are decomposed into one-dimensional interpolations performed sequentially along each modulus dimension. This allows for accurate fitting of the order-of-magnitude nonlinear response of the deflection basin as the modulus changes. This mechanism eliminates the need for the algorithm to repeatedly call complex mechanical formulas during iterations. Instead, it uses lightweight mathematical interpolation to directly and quickly reconstruct the theoretical deflection basin, which highly matches the current modulus combination, using pre-calculated benchmark physical nodes. This ensures inverse calculation accuracy while completely solving the problem of low computational efficiency in traditional methods. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is one of the flowcharts illustrating a method for back-calculating the modulus of a pavement structure layer provided in this specification; Figure 2 This is a schematic diagram illustrating the logarithmic interval values ​​of a reference modulus provided in this specification; Figure 3 This is the second flowchart illustrating a method for back-calculating the modulus of a pavement structure layer, as provided in this specification. Figure 4 This document provides a schematic diagram of a three-tier database structure. Figure 5 This is a diagram illustrating the accuracy comparison of different interpolation methods provided in this specification; Figure 6 This document provides a schematic diagram illustrating the relationship between database size, RMSE, and generation time. Figure 7 This is a schematic diagram of a pavement structure layer modulus back-calculation device provided in this specification; Figure 8 This is a schematic diagram of a computer device provided for this specification. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0018] The technical solution provided by this invention can be applied to non-destructive testing and pavement structure evaluation in road engineering. The pavement structure layer modulus is a key parameter for evaluating the bearing capacity and remaining service life of the pavement structure. Back-calculating the modulus of each structural layer based on FWD (Falling Weight Deflectometer) deflection basin data is a core step in pavement structure evaluation. Traditional modulus back-calculation methods are based on iterative optimization, requiring forward calculations using elastic layered system theory or finite element methods in each iteration. This involves numerical solutions of Hankel integrals or Burmister solutions in a semi-infinite space, resulting in a large computational load and a significant computational efficiency bottleneck when dealing with massive FWD measurement data. Existing improvements, such as intelligent optimization algorithms, reduce the number of iterations but do not reduce the single-step computation time. Artificial neural networks suffer from insufficient generalization ability and high training costs. While database methods offer pre-calculation and query approaches, they suffer from shortcomings such as a lack of systematic database construction strategies, a single interpolation method, and an unquantified assessment of the balance between database size and accuracy. Therefore, it is necessary to propose a systematic method for rapid back-calculation of pavement structure layer modulus based on an interpolation database. This method aims to significantly improve computational efficiency while ensuring back-calculation accuracy, thus meeting the needs of rapid processing of large amounts of data in engineering practice. To address the above issues, this application provides a method for rapid back-calculation of pavement structure layer modulus based on an interpolation database. By employing a logarithmic interval strategy to generate a baseline modulus combination, and using elastic layered system theory or the finite element method for forward calculation to construct a deflection basin database, database interpolation is used to replace theoretical forward calculation to obtain the deflection basin during the modulus back-calculation iteration process. This significantly shortens the calculation time for a single iteration while ensuring back-calculation accuracy.

[0019] The method for back-calculating the modulus of the road structure layer of the present invention is described below with reference to the accompanying drawings.

[0020] Figure 1 This is one of the flowcharts illustrating a method for back-calculating the modulus of a pavement structure layer, as provided in this specification. Figure 1 As shown, the method includes the following: S101. Collect measured deflection basin data of the target road surface.

[0021] For example, in the embodiments of this application, when collecting measured deflection basin data of the target road surface, there may be a variety of acquisition methods. For example, the measured deflection basin data of the target road surface can be received from an airborne falling weight deflectometer device, or the measured deflection basin data of the target road surface can be obtained from local storage. Of course, the measured deflection basin data of the target road surface can also be obtained from a third-party road detection database, etc. The specific settings can be made according to actual needs.

[0022] S102. In the iterative back calculation of the modulus of the target pavement structure layer, the current modulus combination is obtained based on the preset initial value of the modulus of each structure layer and its iterative update results.

[0023] In this embodiment, for a typical three-layer pavement structure, a set of initial modulus values ​​can be randomly generated within the range of modulus values ​​for each layer. For example, the initial value of the surface layer modulus is set to 3000 MPa, the initial value of the base layer modulus is set to 10000 MPa, and the initial value of the subgrade modulus is set to 100 MPa. In subsequent iterations, the modulus values ​​are corrected according to the calculation error each time, and the corrected set of modulus values ​​is used as the current modulus combination. The purpose of this is to clarify the initial physical state and dynamic evolution path of the iterative back-calculation, thereby providing a data foundation for the subsequent acquisition of the theoretical deflection basin.

[0024] S103. Input the current modulus combination into a preset database to obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination. Perform interpolation processing on the set of adjacent reference modulus nodes through a preset dimensionality reduction multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination. The preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy. The dimensionality reduction multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction query.

[0025] In this embodiment, a pre-constructed multidimensional array database is used for query matching to find discrete nodes surrounding the current modulus combination. When inputting the current modulus combination into the database to obtain the set of adjacent reference modulus nodes, for the modulus value of each structural layer, the interval in the preset logarithmic interval reference modulus sequence of that layer is searched. If the modulus value is exactly equal to a certain reference modulus value, the reference node is directly taken; if the modulus value exceeds the preset upper and lower limits, a truncation strategy is adopted, and the upper and lower limit endpoints are taken as adjacent nodes to form the set of adjacent reference modulus nodes surrounding the current modulus combination. Then, the set of adjacent reference modulus nodes is interpolated using a preset dimensionality reduction multidimensional interpolation strategy (i.e., the conventional multidimensional interpolation method based on tensor integral solutions in the art). The purpose of this is to bypass the time-consuming theoretical forward numerical integration calculation and directly obtain the deflection basin response through data mapping, thereby providing an execution basis for subsequent error calculation and modulus update.

[0026] S104. Obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, and update the current modulus combination based on the error using a preset optimization algorithm strategy until the preset convergence condition is met, and then output the back calculation result.

[0027] In this embodiment, the theoretical value is compared with the measured value to calculate the difference, and the next generation of modulus assignment states are generated using the rules of the optimization algorithm. The process stops and the final result is output when the difference is sufficiently small or the loop reaches its upper limit. The purpose of this is to continuously approximate the real pavement physical modulus parameters through a closed-loop feedback mechanism, thereby providing a data foundation for the final pavement structure evaluation.

[0028] Based on the above Figure 1 In the embodiment shown, when the preset database is constructed using a benchmark modulus combination generated based on a logarithmic interval strategy in S103, this application provides a possible implementation: First, determine the pavement structure parameters and the range of modulus values. Based on the structural composition of the pavement to be evaluated, determine the number of structural layers n (n is an integer from 1 to 5), as well as known parameters such as the thickness and Poisson's ratio of each structural layer. For each structural layer, determine the upper limit of the modulus of that layer based on the material type and engineering experience. and lower limit ,in Subsequently, a baseline modulus combination is generated based on the logarithmic interval. For the ... Layered structure layer, at its upper limit of modulus and lower limit Take values ​​at logarithmic intervals to generate One baseline modulus value. The formula for the logarithmic interval is: ; in For the first The first layer Each layer has a baseline modulus value. The baseline modulus values ​​of all layers are then combined to obtain the total. A set of baseline moduli. The reason for using logarithmic intervals instead of equal intervals is that the modulus of pavement materials typically varies across one or more orders of magnitude. Figure 2 This is a schematic diagram illustrating the logarithmic interval values ​​of a reference modulus provided in this specification, such as... Figure 2 As shown, logarithmic intervals provide denser value points in regions with lower moduli, thus better capturing the sensitivity of the deflection basin to modulus changes. Next, the deflection basin responses corresponding to several benchmark modulus combinations are obtained. The deflection basin responses for each benchmark modulus combination are then obtained using the elastic layered system theory or finite element method. For example, the Burmister solution in the elastic layered system theory is used for numerical integration with Bessel functions. The deflection basin consists of deflection values ​​at each sensor location of the FWD, typically containing 7 to 9 deflection values. All benchmark modulus combinations and their corresponding deflection basins are stored together to form a database. The database data structure can be represented as a set. ,in For the first A combination of baseline moduli, For the corresponding deflection basin, Total database size This represents the number of sensors.

[0029] When obtaining the theoretical deflection basin, a mechanism for high-dimensional dimensionality reduction queries is achieved by sequentially performing one-dimensional interpolation operations along each modulus dimension using a pre-defined dimensionality reduction multidimensional interpolation strategy. Specifically, one or more of linear interpolation, nearest neighbor interpolation, Hermitian interpolation, and cubic spline interpolation are selected as the interpolation method for database queries. Linear interpolation involves linear interpolation between adjacent reference modulus points, which is computationally simple but only has first-order continuity. Nearest neighbor interpolation directly takes the deflection value corresponding to the nearest reference modulus point, which has the least computational cost but the lowest accuracy. Hermitian interpolation uses function values ​​and their derivative information to construct piecewise polynomials, ensuring that the interpolation function has first-order derivative continuity at the nodes, thus better preserving the morphological characteristics of the deflection basin curve. Cubic spline interpolation constructs cubic polynomials to ensure that the interpolation function has second-order derivative continuity at the nodes, resulting in a smooth interpolation curve and high accuracy in regions with gradual modulus changes. For multi-layer structures, a multi-dimensional interpolation strategy is adopted, that is, one-dimensional interpolation is performed sequentially along each modulus dimension to finally obtain the estimated value of the deflection basin corresponding to the target modulus combination. S103 establishes a deflection basin database in advance before the back-calculation iteration and replaces the theoretical forward calculation with database interpolation during the iteration process. The calculation time of each iteration is reduced from milliseconds or even seconds to microseconds, which significantly improves the overall efficiency of modulus back-calculation and is particularly suitable for the rapid processing of large batches of measurement point data. A logarithmic interval strategy is employed to generate a baseline modulus combination, fully considering the order-of-magnitude variation in pavement material modulus. This results in a higher resolution database within the modulus-sensitive region, thereby improving interpolation accuracy. By executing S103, high-resolution baseline nodes can be provided in the low modulus-sensitive region, and the deflection basin curve shape can be preserved using dimensionality-reduced interpolation, thus providing a high-precision data foundation for subsequent error calculations.

[0030] Based on the above Figure 1 In the embodiment shown, when updating the current modulus combination based on the error using a preset optimization algorithm strategy in S104, this application embodiment provides a possible implementation method: First, a set of initial modulus values ​​is randomly generated or given based on experience. ; in the In the next iteration, the current modulus combination Input the data into the database and quickly obtain the corresponding theoretical deflection basin using interpolation methods. This eliminates the need to invoke the theory of elastic layered systems or the finite element method for forward calculation; it also allows for the calculation of theoretical deflection basins. Compared with the measured deflection basin The algorithm calculates the error between the measured and measured modulus values; updates the modulus combination according to the optimization algorithm's strategy, and proceeds to the next iteration; when the error meets the convergence criterion or reaches the maximum number of iterations, the iteration terminates, and the final modulus back-calculation result is output. This optimization algorithm includes, but is not limited to, genetic algorithms, particle swarm optimization algorithms, and Levenberg-Marquardt algorithms. When using the Levenberg-Marquardt algorithm, the Jacobian matrix is ​​approximated using the central difference method: a small perturbation is applied to a certain layer of the modulus in the current modulus combination, and the perturbed theoretical deflection basin is obtained again through database interpolation. The approximate gradient of that dimension is obtained by dividing the difference between the deflection basins before and after the perturbation by the perturbation. For genetic algorithms and particle swarm optimization algorithms, the reciprocal of the sum of squared errors between the theoretical and measured deflection basins is directly used as the fitness value for population iteration updates. By executing S104, the global search capability of the intelligent optimization algorithm can be used to avoid getting trapped in local optima, and the iteration is stably terminated when preset conditions are met, thus providing an execution basis for the final output result.

[0031] Based on the above Figure 1 The embodiments shown in this application provide a possible implementation method for evaluating the preset database and the dimensionality reduction multidimensional interpolation strategy: A test dataset containing several combinations of verification moduli is constructed. Based on these verification moduli combinations, the preset database is used to obtain the corresponding estimated deflection response through the dimensionality-reduction multidimensional interpolation strategy. The root mean square error (RMSE) between the estimated deflection response and the accurate theoretical deflection response obtained through forward mechanics calculation is calculated. The RMS error is the square root of the average of the sum of squares of the differences in deflection values ​​at each sensor location, calculated using the following formula: ; in, The number of sensors, where The first obtained by database interpolation method Deflection values ​​at each sensor location The first one obtained by forward calculation of theory Deflection values ​​at each sensor location. Calculated over a large number of randomly generated modulus combinations. The mean and distribution of the interpolation values ​​are used to comprehensively evaluate the accuracy of database methods. This is achieved by comparing different interpolation methods on the same database size. Values, and the same interpolation method under different database sizes. Value, taking into account both database generation time and other factors. The value determines the optimal combination of database size and interpolation method.

[0032] In one specific embodiment, taking a typical three-layer pavement structure as an example, the implementation process of the method of the present invention is described in detail. The three-layer structure consists of a surface layer, a base layer, and a subgrade, with the subgrade being an elastic semi-infinite foundation. Figure 3 This is the second flowchart illustrating a method for back-calculating the modulus of a pavement structure layer, as provided in this specification. Figure 3 As shown, the method includes: Step 1: Determine the range of pavement structure parameters and modulus values.

[0033] The structural parameters of the pavement to be evaluated are as follows: surface layer thickness is 18cm, Poisson's ratio is 0.25; base layer thickness is 30cm, Poisson's ratio is 0.25; subgrade Poisson's ratio is 0.40. The FWD load parameters are: load radius 15cm, load pressure 0.7MPa. Nine deflection sensors are installed, with offsets from the load center of 0, 20, 30, 45, 60, 90, 120, 150, and 180cm, respectively. Based on engineering experience with asphalt mixture as the surface layer material, the surface layer modulus is determined to range from 500MPa to 20000MPa; the base layer material is cement-stabilized crushed stone, with the base layer modulus range from 1000MPa to 50000MPa; and the subgrade modulus range from 20MPa to 300MPa.

[0034] Step 2: Generate a baseline modulus combination based on logarithmic intervals.

[0035] The modulus of the surface layer was taken at logarithmic intervals between 500 MPa and 20000 MPa. Taking the first point as an example, the... The baseline modulus values ​​are: ; This yields the following surface layer reference modulus sequence: 500, 604, 730, 883, 1067, 1290, 1560, 1886, 2280, 2757, 3334, 4032, 4875, 5894, 7126, 8616, 10418, 12596, 15229, 18413 (all units are in MPa, rounded to the nearest integer). It can be seen that the values ​​are more densely packed in the low modulus range and more sparsely packed in the high modulus range, which is consistent with the physical characteristic that the deflection basin is more sensitive to the low modulus region. Similarly, the base layer modulus is... =20 logarithmic intervals, for the subgrade modulus. =15 logarithmic intervals. The three-layer modulus is fully combined to obtain the total. A combination of baseline moduli.

[0036] Step 3: Establish a deflection basin database through forward calculation.

[0037] For the aforementioned 6000 reference modulus combinations, forward calculations were performed using the theory of elastic layered systems. The core of the theory of elastic layered systems is to solve the displacement response of the Burmister multilayer elastic system under a circular uniformly distributed load, which involves numerical integration of integral expressions containing Bessel functions. Figure 4 This document provides a schematic diagram of a three-tier database architecture. Figure 4 As shown, for each reference modulus combination, deflection values ​​at nine sensor locations are calculated, forming a deflection basin curve. The 6000 modulus combinations and their corresponding deflection basins are stored in a database. On a modern computer, using an optimized numerical integration algorithm, the total time for 6000 forward calculations is approximately several minutes, representing a one-time initial investment. The database storage structure adopts a multidimensional array format. Specifically, the database can be represented as a... A four-dimensional array (for a three-layer structure) is used, where the first three dimensions correspond to the indices of the surface layer, base layer, and subgrade modulus, respectively, and the last dimension corresponds to the sensor number. This regular grid structure facilitates subsequent multi-dimensional interpolation operations.

[0038] Step 4: Select the interpolation method.

[0039] During the inverse calculation iteration, a set of modulus combinations to be queried is given. The corresponding deflection basin needs to be obtained through database interpolation. Since the database is built on a regular logarithmic grid, multidimensional interpolation can be achieved by sequentially performing one-dimensional interpolation along each dimension. Taking linear interpolation as an example, for the surface modulus value to be queried... First, find the one that satisfies the reference modulus sequence of the surface layer. Calculate the interpolation weights for adjacent reference points. Then, linear interpolation is performed along this dimension. The above operation is repeated along the base course and subgrade modulus dimensions to finally obtain the estimated deflection basin value corresponding to the target modulus combination.

[0040] For the specific implementation of multidimensional interpolation, a step-by-step interpolation strategy is adopted. Taking three-dimensional interpolation as an example, firstly, one-dimensional interpolation is performed on all involved data points along the first dimension (surface layer modulus), reducing the three-dimensional interpolation problem to a two-dimensional interpolation problem; then, one-dimensional interpolation is performed along the second dimension (base layer modulus), reducing the two-dimensional problem to a one-dimensional problem; finally, one-dimensional interpolation is performed along the third dimension (subgrade modulus) to obtain the final result. This strategy decomposes high-dimensional interpolation into a series of one-dimensional interpolation operations, maintaining accuracy while reducing implementation complexity.

[0041] The four interpolation methods considered in this invention are as follows: Linear interpolation: Interpolation is performed by constructing a linear polynomial between two adjacent reference points. Let the adjacent reference points be... and The corresponding function value is and For The interpolation result is Linear interpolation is easy to calculate, but the interpolation function only has zero-order continuity at the nodes, and its derivative is discontinuous.

[0042] Nearest neighbor interpolation: For a given query point, the function value corresponding to the nearest reference point is directly taken as the interpolation result. Let the query point be... x Then find the satisfying Minimum reference point Output Nearest neighbor interpolation has the least computational cost, but the result is a step-like piecewise constant function, and its accuracy is usually the lowest.

[0043] Hermite interpolation: This method constructs a cubic polynomial using the function values ​​and derivatives at the nodes, ensuring the continuity of the first derivative of the interpolation function at the nodes. In practice, the derivative values ​​at the nodes are approximated by the difference between the function values ​​of adjacent nodes. Specifically, a piecewise cubic Hermite interpolation polynomial is used. This method maintains the monotonicity of the data and avoids overshoot and oscillations.

[0044] Cubic spline interpolation: Constructs a cubic polynomial over each adjacent node interval, requiring the function values, first derivative, and second derivative to be continuous at all internal nodes, while applying boundary conditions (natural boundary conditions or non-node boundary conditions) at the two endpoints. Cubic spline interpolation produces the smoothest curves, but oscillations may occur in regions of rapid data variation.

[0045] Step 5: Obtain the deflection basin through output interpolation.

[0046] The specific steps of the inverse calculation iteration process are as follows: I. Input measured deflection basin data .

[0047] II. Randomly generate initial modulus combinations within the range of modulus values ​​for each layer. Optionally, an empirical formula based on the characteristics of the deflection basin can be used for initial value estimation to accelerate convergence.

[0048] III. In the In the next iteration, the current modulus combination Input the data into the database and quickly obtain the theoretical deflection basin using the selected interpolation method. .

[0049] IV. Calculate the objective function value. The objective function is the sum of squared relative errors between the measured deflection basin and the theoretical deflection basin: ; V. Determine the convergence condition. If the objective function value Less than the preset convergence threshold Or the number of iterations reaches the preset maximum value. If the iteration terminates, the current modulus combination is output. As the result of the inverse calculation.

[0050] VI. If the convergence condition is not met, a new modulus combination is generated according to the update strategy of the optimization algorithm. Then return to step III to continue the iteration. During the iteration process, each solution for the deflection basin is completed through database interpolation, avoiding the need to call the theoretical forward calculation module, thereby significantly shortening the calculation time for a single iteration.

[0051] Step 6: Accuracy assessment and parameter optimization.

[0052] To systematically evaluate the accuracy of the database method, a large number (10,000 in this case) of modulus combinations were randomly generated within the range of modulus values ​​for each layer as a validation set. For each modulus combination in the validation set, the deflection basin was obtained using both database interpolation and theoretical forward calculation methods, and the RMSE value between the two methods was calculated. Parameter scan experiments were conducted for different database sizes and interpolation methods. The database size was adjusted by varying the number of reference modulus values ​​for each layer. To regulate, for example, to The values ​​were set to 5, 10, 15, 20, 25, 30, 40, and 50, respectively. For each size setting, four interpolation methods were used to calculate the average RMSE value and database generation time on the validation set.

[0053] Figure 5 This is a diagram illustrating the accuracy comparison of different interpolation methods provided in this specification; for example... Figure 5 As shown, the RMSE value decreases with increasing database size, but the rate of decrease gradually slows down, exhibiting a clear diminishing marginal effect. Once the database size reaches a certain point, further increasing the number of baseline modulus points has very limited effect on improving accuracy, while database generation time and storage space increase linearly. Therefore, there exists an optimal database size that achieves a good balance between accuracy and efficiency.

[0054] Figure 6 This document provides a schematic diagram illustrating the relationship between database size, RMSE, and generation time. Figure 6As shown, for interpolation methods, cubic spline interpolation and Hermitian interpolation outperform linear interpolation and nearest neighbor interpolation in most cases. The advantages of higher-order interpolation methods are particularly pronounced when the database size is small, as they can better utilize limited reference point information to fit the nonlinear relationship between the deflection basin and the modulus. As the database size increases, the accuracy of linear interpolation gradually approaches that of higher-order methods. Although nearest neighbor interpolation performs the worst in terms of accuracy, it offers the fastest query speed and can be used in rapid screening scenarios where high accuracy is not required.

[0055] Considering both database generation time and RMSE accuracy, the recommended parameter selection strategy is as follows: for a three-layer structure, use 20 to 30 log-interval baseline modulus values ​​for each layer, and employ cubic spline interpolation or Hermitian interpolation as the interpolation method. With this configuration, the database generation time is on the order of minutes, while the single deflection basin query time in the back-calculation iteration is reduced to the order of microseconds, representing a speedup of approximately two orders of magnitude compared to theoretical methods. This invention systematically compares four methods: linear interpolation, nearest neighbor interpolation, Hermitian interpolation, and cubic spline interpolation, and uses RMSE as a quantitative indicator to evaluate the accuracy of each method. By comprehensively considering the balance between database generation time and accuracy, it provides a clear basis for parameter selection in engineering applications.

[0056] The pavement structure layer modulus inverse calculation device provided by the present invention is described below. The pavement structure layer modulus inverse calculation device described below and the pavement structure layer modulus inverse calculation method described above can be referred to in correspondence.

[0057] Figure 7 This is a schematic diagram of a pavement structure layer modulus back-calculation device provided by the present invention. For example, please refer to [link to schematic diagram]. Figure 7 As shown, the pavement structure layer modulus back-calculation device may include: The data acquisition module is used to collect measured deflection basin data of the target road surface.

[0058] The state determination module is used to obtain the current modulus combination based on the preset initial modulus values ​​of each structural layer and its iterative update results in the iterative back calculation of the modulus of the target pavement structural layer.

[0059] The interpolation query module is used to input the current modulus combination into a preset database, obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination, and perform interpolation processing on the set of adjacent reference modulus nodes through a preset dimensionality reduction multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination; the preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy; the dimensionality reduction multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction query.

[0060] The modulus inverse calculation module is used to obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, and to update the current modulus combination based on the error through a preset optimization algorithm strategy until the preset convergence condition is met, and then output the inverse calculation result.

[0061] Specific limitations regarding the pavement structure layer modulus inverse calculation device can be found in the limitations on pavement structure layer modulus inverse calculation above, and will not be repeated here. Each module in the aforementioned pavement structure layer modulus inverse calculation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0062] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A method for back-calculating the modulus of pavement structure layers is provided.

[0063] This instruction manual also provides Figure 8 The schematic diagram of the computer device shown is as follows: Figure 8 At the hardware level, the computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 A method for back-calculating the modulus of pavement structure layers is provided.

[0064] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0065] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for back-calculating the modulus of a pavement structure layer, characterized in that, include: Collect measured deflection basin data of the target road surface; In the iterative back calculation of the modulus of the target pavement structural layer, the current modulus combination is obtained based on the preset initial modulus value of each structural layer and its iterative update result. The current modulus combination is input into a preset database to obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination. The adjacent reference modulus node set is then interpolated using a preset dimensionality reduction and multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination. The preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy. The dimensionality reduction and multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction queries. Obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, update the current modulus combination based on the error using a preset optimization algorithm strategy, and output the back calculation result when the preset convergence condition is met.

2. The method for back-calculating the modulus of pavement structure layers according to claim 1, characterized in that, The step of updating the current modulus combination based on the error using a preset optimization algorithm strategy includes: The fitness value is obtained based on the error, and the fitness value is input into a preset optimization algorithm to generate a new combination of moduli. The optimization algorithm includes at least one of genetic algorithm, particle swarm optimization algorithm or Levenberg-Marquardt algorithm.

3. The method for back-calculating the modulus of pavement structure layers according to claim 1, characterized in that, The preset database is constructed using a baseline modulus combination generated based on a logarithmic interval strategy, including: Obtain the preset upper and lower limits of the modulus of each structural layer; Multiple reference modulus values ​​are extracted between the preset upper limit and the preset lower limit according to the logarithmic interval rule, so that the reference modulus value density in the low modulus range is greater than the reference modulus value density in the high modulus range. By combining the reference modulus values ​​of all structural layers, several reference modulus combinations are obtained. Obtain the deflection basin response corresponding to several reference modulus combinations, associate and store the reference modulus combinations with the corresponding deflection basins, and obtain a database.

4. The method for back-calculating the modulus of pavement structure layers according to claim 3, characterized in that, The deflection basin response corresponding to several reference modulus combinations is obtained by using the elastic layered system theory method or the finite element method to obtain the deflection basin response corresponding to each reference modulus combination.

5. The method for back-calculating the modulus of pavement structure layers according to claim 1, characterized in that, The one-dimensional interpolation operation in the dimensionality reduction multidimensional interpolation strategy adopts at least one of linear interpolation, nearest neighbor interpolation, Hermitian interpolation, or cubic spline interpolation.

6. The method for back-calculating the modulus of pavement structure layers according to claim 1, characterized in that, The preset convergence conditions include: the error between the measured deflection basin data and the theoretical deflection basin is less than a preset threshold, or the number of iterations reaches the preset maximum number of iterations.

7. The method for back-calculating the modulus of pavement structure layers according to claim 1, characterized in that, Also includes: The evaluation of the preset database and the dimensionality reduction multidimensional interpolation strategy includes: Construct a test dataset containing several combinations of validation moduli; Based on the verification modulus combination input to the preset database, the corresponding estimated deflection response is obtained through the dimension-by-dimensional reduction multidimensional interpolation strategy; The root mean square error between the estimated deflection response and the accurate theoretical deflection response obtained through forward mechanics calculation is calculated. The root mean square error is the square root of the average of the sum of squares of the differences in deflection values ​​at each sensor location. Based on the variation trend of the root mean square error under different database sizes and interpolation method configurations, the target database size and target interpolation method are determined.

8. A device for back-calculating the modulus of a road surface structure layer, characterized in that, include: The data acquisition module is used to collect measured deflection basin data of the target road surface; The state determination module is used to obtain the current modulus combination based on the preset initial modulus values ​​of each structural layer and its iterative update results in the iterative back calculation of the modulus of the target pavement structural layer. The interpolation query module is used to input the current modulus combination into a preset database, obtain the set of adjacent reference modulus nodes corresponding to the current modulus combination, and perform interpolation processing on the adjacent reference modulus node set through a preset dimensionality reduction multidimensional interpolation strategy to obtain the theoretical deflection basin corresponding to the current modulus combination; the preset database is constructed using reference modulus combinations generated based on a logarithmic interval strategy; the dimensionality reduction multidimensional interpolation strategy is a mechanism that performs one-dimensional interpolation operations sequentially along each modulus dimension to achieve high-dimensional dimensionality reduction query; The modulus inverse calculation module is used to obtain the error between the theoretical deflection basin and the measured deflection basin data corresponding to the current modulus combination, and to update the current modulus combination based on the error through a preset optimization algorithm strategy until the preset convergence condition is met, and then output the inverse calculation result.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method for back-calculating the modulus of the pavement structure layer as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for back-calculating the modulus of the pavement structure layer as described in any one of claims 1 to 7.

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