Asphalt pavement modulus back calculation method and system based on detection data of traffic speed deflectometer

Abstract

The invention discloses an asphalt pavement modulus back calculation method and system based on detection data of a traffic speed deflectometer, and relates to the technical field of road engineering nondestructive testing, and the method comprises the following steps: introducing an inertia point theory into a TSD dynamic loading scene, and constructing a TSD finite element mechanical response model based on a multilayer elasticity theory and a double-wheel rolling loading characteristic; by simulating working conditions of different combinations, a direct physical relationship between deflection and the thickness of the soil matrix and the thickness of the superstructure is constructed to determine a unique soil matrix modulus, and by taking the unique soil matrix modulus as a physical boundary condition, a simulated annealing-particle swarm optimization matching method is introduced to realize dynamic modulus back calculation of the superstructure, so that the dynamic modulus of the superstructure is calculated. Therefore, an inverse calculation system based on coupling of a physical rule and intelligent optimization is constructed. According to the method, the back calculation precision and stability can be remarkably improved, the sensitivity to an initial value is reduced, the multi-working-condition adaptability is enhanced, and reliable technical support is provided for application of the TSD in road network level structure evaluation and intelligent maintenance.

Description

Technical Field

[0001] This invention relates to the fields of road engineering and non-destructive testing technology, and more specifically to a method and system for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer test data. Background Technology

[0002] Dynamic modulus is a core parameter for scientifically assessing the bearing capacity and damage development patterns of asphalt pavements. Currently, the main method for obtaining this parameter in engineering is to back-calculate the structural layer modulus based on the pavement mechanical response measured in the field. The falling weight deflectometer (FWD), as the most commonly used field response testing device, has advantages such as high testing accuracy and ease of operation. However, it suffers from susceptibility to traffic and weather conditions, low testing efficiency, and limited operational safety. To meet the needs of rapid assessment at the road network level, the Traffic Speed ​​Deflectometer (TSD) has emerged. This device continuously collects the longitudinal deformation velocity of the pavement at normal driving speeds using a Doppler laser sensor. It boasts advantages such as high efficiency, low interference, and high automation, demonstrating great potential in road asset management and intelligent maintenance.

[0003] In recent years, modulus inversion methods based on TSD test data have been continuously developing, mainly including trial-and-error methods, matching methods, and empirical formula methods. Among them, compared with trial-and-error methods and empirical formula methods, matching methods are more widely used due to their flexible modeling and strong applicability, and can be further subdivided into iterative optimization methods, database search methods, and artificial neural network matching methods. The above matching methods have significant differences: 1) Iterative method: By calculating the theoretical deformation response of the pavement in real time and combining it with optimization algorithms to gradually adjust structural parameters, the difference between theoretical and measured values ​​is minimized. Iterative methods can also be combined with various optimization algorithms, such as genetic algorithms (GA), particle swarm optimization (PSO), simulated annealing (SA), and ant colony algorithms (ACA). These methods are relatively mature in modulus inversion based on FWD data, but their application to TSD is still in the exploratory stage. Iterative methods are characterized by high inversion accuracy and good physical consistency, but their convergence process is highly dependent on initial parameters. They also suffer from non-unique solutions and high computational costs, thus limiting their effectiveness in large-scale, multi-condition rapid inversion. 2) Database search method: This method sets reasonable ranges for structural parameters before inversion and pre-constructs a structural parameter-pavement response database based on theoretical calculations or numerical simulations. During inversion, the optimal solution is quickly located by looking up tables or interpolation. This method has advantages such as high stability and simple implementation, making it suitable for rapid analysis of a large number of conditions. However, the inversion accuracy and solution uniqueness are highly dependent on the database coverage and parameter granularity, and the predictive ability significantly decreases when facing new conditions exceeding the preset range. 3) Artificial Neural Network (ANN) matching method: Similar to the database search method, it also requires pre-generating multi-condition response samples. However, the inversion stage no longer relies on physical calculations but instead establishes a nonlinear mapping relationship between mechanical response and structural parameters by training a neural network. This method has advantages such as fast inverse calculation speed and ability to handle complex nonlinear relationships, but the prediction accuracy depends on the diversity and quality of the training samples, and the uniqueness of the solution cannot be guaranteed.

[0004] Therefore, it can be seen that although the matching method shows good adaptability under different working conditions, its core limitation lies in the non-uniqueness of the solution, which is particularly prominent in practical applications. To address this issue, the academic community has proposed a physical law-driven inversion approach in the field of FWD: the Deflection-Basin Regularity (DBR) method. Although this method mainly serves the inversion of FWD data, its advantages in improving inversion stability and uniqueness are also of significant reference value for the inversion of TSD data. The core idea of ​​the regularity method is to extract feature points with clear physical meaning from the pavement response to establish the analytical relationship of the structural modulus. This method posits that for FWD test data, the sensitivity of deflection at different measuring points to the surface modulus and foundation modulus varies significantly, and there exists an inertial point that is insensitive to the panel modulus. Utilizing this point can effectively alleviate the non-uniqueness problem in modulus inversion. In recent years, many scholars have verified the stability and physical consistency of this method. However, since FWD is a single-point impact load and TSD is a continuous dynamic load, there are significant differences between the two in terms of loading method, influence depth and inertial characteristics, making it difficult to directly apply this method to TSD.

[0005] Therefore, how to propose a method and system for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer detection data, and overcome the shortcomings of existing technologies, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data. This method offers an efficient, unique, and highly accurate modulus back-calculation method that is adaptable to the dynamic response characteristics of TSD (Transient Speed ​​Deflectometer) dual-wheel moving loads and maintains stable and reliable back-calculation performance under various working conditions. It is particularly effective for the load and response characteristics of TSD and can adapt to multiple working conditions. To achieve the above objectives, the present invention adopts the following technical solution: A method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data includes: Data was collected using a traffic speed deflectometer, and mechanical response characteristic parameters were extracted. Construct an analytical relationship between the soil modulus and mechanical response characteristic parameters, and perform soil modulus inversion; Under the constraint of known subgrade modulus, an optimization model for minimizing the error between measured response and theoretical response is constructed, and the base course modulus and surface course modulus are inverted using the SA-PSO algorithm.

[0007] Optionally, the mechanical response characteristic parameters include: structural layer parameters, structural layer modulus and initial range, TSD load parameters and TSD test data.

[0008] Optionally, the inversion of the subgrade modulus includes: Given the soil modulus and the total thickness of the superstructure, determine the corresponding TSD inert point parameters; At the offset distance, the theoretically calculated deflection is compared with the measured deflection based on the TSD inert point parameters, and convergence is determined. If the convergence condition is met, the soil modulus corresponding to the current inertial point is accepted as the unique solution.

[0009] Optionally, determining the corresponding TSD inert point parameters includes: Given the subgrade modulus Es and the total thickness H of the superstructure, based on multilayer elasticity theory and finite element simulation model, the dynamic deflection response of the pavement under TSD dual-wheel moving load is calculated, and the results are obtained. Theoretical deflection basin data for L groups of superstructures and load conditions under combined load conditions. ; For each measuring point offset distance i, first calculate the average value of the deflection under all working conditions at that location. Then, the root mean square error at that position is calculated to obtain discrete data of RMSE as a function of offset distance i. Finally, spline interpolation is used to smooth the RMSE(i) curve. Search for the first local minimum point on the smoothed RMSE(i) curve, and denote the corresponding offset distance as . ,Right now( The horizontal position of the inertial point under the combination; At the same offset position Take the average deflection , denoted as the inertial point deflection value To obtain the inertial point parameters ( , ).

[0010] Optionally, the step of comparing the theoretically calculated deflection with the measured deflection based on the TSD inertia point parameters at the offset distance and determining convergence includes: S11: At offset distance At this point, the theoretically calculated inertial point deflection value will be... Compared with the measured deflection Compare; S12: If the convergence condition is met, that is, when When, accept the current lazy point position. Soil modulus corresponding to the location It is a unique solution; If the convergence condition is not met, that is, when hour: a. If Then, the initial modulus Too small; ; Repeat S1 until the convergence condition is met. b. If Then, the initial modulus Too large; ; Repeat S1 until the convergence condition is met.

[0011] Optionally, the inversion of the base layer modulus and surface layer modulus using the SA-PSO algorithm includes: S21: Within a given search interval , and soil modulus Under the conditions: a. Generate the initial particle swarm positions and velocities, and denote the two-dimensional position of each particle as ( ). ); b. Set the particle number N and the learning factor. , initial temperature Annealing coefficient α, maximum number of iterations M, iteration index k; S22: In each iteration, for a given ( Theoretical deflection at each measuring point based on multilayer elasticity theory or finite element model Calculate the objective function F; S23: For each particle in the current particle swarm ( Calculate the objective function value F and use it as the particle fitness to perform optimal updates for individuals and the population. S24: Update the velocity and position of each particle according to the standard PSO update formula; S25: For the new solution after PSO update, avoid local optima by using simulated annealing SA criterion; S26: Perform iterations based on preset conditions. After the iterations are complete, output the optimal position of the population. These are the surface layer modulus and base layer modulus obtained from the final inversion.

[0012] Optionally, the objective function is: .

[0013] Optionally, avoiding local optima through simulated annealing (SA) criteria includes: For the new solution after PSO update, calculate the change in the objective function. ; a. If ΔF≤0, then the new solution is accepted unconditionally; b. If ΔF > 0, then accept the worse solution with probability p, thus escaping the local optimum: ; ; Where p is the acceptance probability. The change in the objective function Let be the temperature of the k-th iteration. The initial temperature. This is the cooling coefficient.

[0014] Optionally, after the iteration is completed, the corresponding RMSE is output as a matching accuracy index.

[0015] Optionally, an asphalt pavement modulus back-calculation system based on traffic speed deflectometer detection data includes: a data acquisition module for acquiring data through a traffic speed deflectometer and extracting mechanical response characteristic parameters; Soil modulus inversion module: used to construct the analytical relationship between soil modulus and mechanical response characteristic parameters, and to perform soil modulus inversion; Identification module: Used to construct an optimization model that minimizes the error between the measured response and the theoretical response under the constraint of known subgrade modulus, and to invert the base layer modulus and surface layer modulus using the SA-PSO algorithm.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer detection data, which has the following beneficial effects: (1) By introducing a constraint mechanism based on inertial points, the problem of non-uniqueness of solutions in traditional inversion methods is effectively eliminated, ensuring the uniqueness and stability of the subgrade modulus. (2) By uniquely determining the subgrade modulus, the optimization dimension is reduced, and the SA-PSO hybrid algorithm is further adopted, which significantly improves the computational efficiency while ensuring high accuracy. It can meet the needs of large-scale road network-level inversion tasks, can process a large amount of road segment data and shorten the computation time, and is suitable for complex road network evaluation. (3) Based on physical laws, it has good versatility and adaptability. It can efficiently adapt to different temperature, load speed and structural thickness conditions under both flexible pavement and semi-rigid pavement structures, showing excellent working condition adaptability and suitable for various practical engineering applications. (4) By combining measured TSD detection road segment data for inversion verification, the practical feasibility and stability of this invention in engineering are further proved. It can effectively control errors, provide accurate decision support for intelligent transportation and road maintenance, and has broad application prospects. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the inert point method provided by the present invention.

[0019] Figure 2 This is a schematic diagram illustrating the determination of inertia point parameters provided by the present invention.

[0020] Figure 3 This invention provides a schematic flowchart of a method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data.

[0021] Figure 4 This is a schematic diagram of the calculation model under dual-wheel load provided by the present invention.

[0022] Figure 5 This is a schematic diagram of the rigid underlayer provided by the present invention.

[0023] Figure 6 This is a schematic diagram of the fitting results of the inert point position Rc and deflection Dc provided by the present invention.

[0024] Figure 7 This is a schematic diagram illustrating the inverse modulus calculation of flexible pavement provided by the present invention.

[0025] Figure 8 This is a schematic diagram of the inverse modulus calculation of semi-rigid pavement provided by the present invention.

[0026] Figure 9 A schematic diagram comparing the back-calculation results of the subgrade modulus under flexible and semi-rigid pavement structures using different inversion methods provided by this invention.

[0027] Figure 10 This diagram illustrates the inversion accuracy of the base modulus under flexible and semi-rigid pavement structures using different inversion methods provided by this invention.

[0028] Figure 11 This is a schematic diagram comparing the accuracy of surface modulus inversion using different inversion methods provided by this invention under flexible and semi-rigid pavement structures.

[0029] Figure 12 This diagram illustrates the comparison of the average relative errors of different inversion methods provided by this invention in flexible and semi-rigid pavements. Detailed Implementation

[0030] 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, and 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.

[0031] This invention discloses a method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data, comprising: Data was collected using a traffic speed deflectometer, and mechanical response characteristic parameters were extracted. Construct an analytical relationship between the soil modulus and mechanical response characteristic parameters, and perform soil modulus inversion; Under the constraint of known subgrade modulus, an optimization model for minimizing the error between measured response and theoretical response is constructed, and the base course modulus and surface course modulus are inverted using the SA-PSO algorithm.

[0032] In its specific implementation, this invention proposes a method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data (hereinafter referred to as DBR-guided SA-PSO). This method aims to combine the characteristics of TSD dual-wheel rolling loading with mechanical response to overcome the problems of non-unique inversion solutions, unstable convergence, and low computational efficiency in existing technologies. Specifically, the DBR-guided SA-PSO inversion method follows a step-by-step calculation strategy: The first step is to construct an analytical relationship between the subgrade modulus and the characteristic parameters of the TSD mechanical response based on the deflection law, so as to achieve a unique inversion of the subgrade modulus; The second step involves constructing an optimization model that minimizes the error between the measured and theoretical responses of the TSD under the constraint of known subgrade modulus, and identifying the base and surface moduli using the SA-PSO algorithm.

[0033] The inversion principle between the subgrade modulus and the superstructure modulus is as follows: (1) Principle of soil modulus inversion 1) Under the same load, geometry, and boundary conditions, for the same soil modulus E s For asphalt pavements with a total superstructure thickness H, changes in the superstructure and environmental parameters (such as surface layer modulus, base layer modulus, driving speed, and temperature) will result in a stable and monotonous variation in the shape of the pavement surface deflection basin: a larger surface layer modulus leads to a flatter deflection basin, while a smaller surface layer modulus results in a steeper deflection basin. In other words, under the same conditions... E sUnder conditions H, multiple sets of deflection basins obtained by different combinations of superstructure parameters will inevitably intersect at a certain offset position. The deflection value corresponding to this intersection point is basically insensitive to the superstructure modulus, driving speed, and temperature, and is only related to the total thickness H of the surface layer and base layer and the subgrade modulus. E s Regarding this, the intersection point is defined as an inert point, such as... Figure 1 As shown, the inertial point mainly consists of two parameters: the horizontal position of the inertial point. and corresponding deflection value Therefore, lazy point parameters can be established ( , ) and soil modulus E s The relationship is shown in formula (1): (1); in, This indicates the horizontal offset distance of the inert point relative to the center of the load; This indicates the road surface deflection value corresponding to that point; H is the total thickness of the surface layer and base layer. E s This refers to the soil modulus.

[0034] 2) In order to use formula (1) in the soil inversion calculation, it is necessary to first analyze different soil types. E s Inert point parameters in combination with H ( , The calculation is performed using the method of minimizing the root mean square error (RMSEmin). The determination of the inertia point parameters is primarily based on the criterion of minimizing the root mean square error (RMSEmin), such as... Figure 2 As shown, the process can be summarized as follows: For a given E s Using multilayer elasticity theory and finite element (FE) simulation, considering various working conditions (including different surface layer moduli, base layer moduli, vehicle speed, temperature, etc.), the corresponding TSD dynamic response was calculated, yielding multiple sets of theoretical deflection or deflection slope data. Assuming that under a given... E s In case H, there are L different combinations of operating conditions, using This represents the theoretical deflection of the x-th combination; Let denot be the average value of all combined deflections. Then, the corresponding root mean square error (RMSE) can be defined as shown in the following formula (2).

[0035] (2); Where RMSEi is the root mean square error at offset distance i; L is the number of different working condition combinations; The theoretical deflection of the x-th modulus combination at offset distance i is expressed in mm. The mean deflection at offset distance i is expressed in mm.

[0036] Therefore, the offset distance and deflection corresponding to RMSEmin are the inertia points. and See formula (3): ; (3).

[0037] (2) Principle of Modulus Inversion between Base Layer and Surface Layer

[0038] After knowing the subgrade modulus, the simulated annealing-particle swarm optimization (SA-PSO) algorithm is used to invert the modulus of the base course and surface course. Among them, particle swarm optimization (PSO) achieves parameter optimization through group collaborative search and has good convergence efficiency, but it is easy to get trapped in local optima. Simulated annealing (SA) is based on a probabilistic jump mechanism, which can improve the ability to jump out of local optima. The SA-PSO algorithm, which combines the two algorithms, can effectively jump out of local optima during the search process by introducing the probabilistic acceptance mechanism of the SA algorithm, while maintaining the high efficiency of the PSO algorithm. Its goal is to optimize the matching degree between theoretical deflection and measured deflection, so as to invert the modulus parameters of each structural layer of asphalt pavement. The objective function is defined as shown in the following formula (4): (4); in, This represents the theoretically calculated deflection, Di represents the measured deflection, and n represents the number of sensors. The first term in this formula controls for larger global errors, while the second term controls for local deviations.

[0039] In a specific implementation, a method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data is provided, such as... Figure 3 As shown, a framework for back-calculating the modulus of asphalt pavement based on TSD test data is proposed, using measured TSD values ​​and theoretical values ​​from finite element (FE) simulations. The back-calculation process consists of three main functional modules: an input module, a back-calculation module, and an output module. The overall process can be divided into the following steps: (1) Input module 1) Structural layer parameters: thickness of surface layer, base layer, subgrade, and rigid underlying layer ( h a , h b , h s , h r ); Poisson's ratio of each structural layer ( μ a , μb , μ s , μ r ).

[0040] 2) Structural layer modulus and initial range: Initial value and range of subgrade modulus: E s0 [E] s，min E s，max Initial value and range of base modulus: E b0 [E] b，min E b，max Initial values ​​and range of surface layer modulus: E a0 [E] a，min E a，max ].

[0041] 3) TSD load parameters: applied load P, equivalent contact radius R 1 and R 2.

[0042] 4) TSD test data: number of measuring points m, number of sensors n, offset distance i, measured deflection D i or deflection slope DS i .

[0043] (2) Soil Subgrade Modulus Back Calculation Module

[0044] 1) Calculation of TSD inert point parameters

[0045] Given the soil modulus E s Given the total thickness H of the superstructure, this step is used to determine the TSD inert point parameters corresponding to this combination, specifically including the following process: a. Multi-condition dynamic response calculation Based on multilayer elasticity theory and finite element (FE) simulation model, and considering various combinations of working conditions such as different surface layer modulus, base layer modulus, vehicle speed, and temperature, the dynamic deflection (or deflection slope) response of the pavement under TSD dual-wheel moving load is calculated, and the results are obtained. E s Theoretical deflection basin data for L groups of superstructures and load conditions under combination H) , where x=1~L is the xth working condition, and i is the offset distance of the i-th measuring point.

[0046] b. Root Mean Square Error Calculation

[0047] For each measuring point offset distance i, first calculate the average value of the deflection under all working conditions at that location. Then, the root mean square error at that position is calculated according to formula (2). After obtaining the discrete data of RMSE as a function of offset distance i, spline interpolation is used to smooth the RMSE(i) curve to improve the stability of inert point identification.

[0048] c. Lazy point parameter identification

[0049] Search for the first local minimum point on the smoothed RMSE(i) curve, and denote the corresponding offset distance as . That is, the ( E s The horizontal position of the inertial point under the combination of H); then at the same offset position Take the average deflection , denoted as the inertial point deflection value Therefore, the inertia point parameters consistent with formula (1) can be obtained. , This data serves as the foundation for subsequent soil modulus inversion and regression relationship modeling.

[0050] 2) Inertial point deflection comparison

[0051] offset distance At this point, the theoretically calculated deflection Compared with the measured deflection D c Compare them.

[0052] 3) Convergence criterion

[0053] If the convergence condition is met, that is, when When, accept the current lazy point position. Soil modulus corresponding to the location E s It is the only solution.

[0054] If the convergence condition is not met, that is, when At that time, there are two possibilities: a. If This indicates that the initial modulus Es0 is too small and needs to be increased; So, E s，min = E s ; E s = ( E s + E s，max ) / 2; then repeat step 2) until the convergence condition is met.

[0055] b. If This indicates that the initial modulus Es0 is too large and needs to be reduced. So, E s，max = E s ; E s = ( E s + E s，min ) / 2. Then repeat step 2) until the convergence condition is met.

[0056] 4) Output parameter I

[0057] To obtain a unique and stable soil modulus .

[0058] (3) Base and surface modulus inverse calculation module

[0059] In soil modulus Given that the base modulus has been uniquely determined by the inert point method, the simulated annealing-particle swarm optimization (SA-PSO) algorithm is used to determine the base modulus. E b With surface modulus E a Perform the inversion. The basic steps are as follows: 1) Parameter initialization In a given search interval [ E b，min , E b，max ]、[ E a，min , E a，max and soil modulus Under the conditions: a. Generate the initial particle swarm positions and velocities, and denote the two-dimensional position of each particle as ( ). E a , E b ); b. Set the number of particles N and the learning factor. c 1, c 2. Initial temperature T 0, annealing coefficient α, maximum number of iterations M, iteration index k.

[0060] 2) Objective function (minimization)

[0061] In each iteration, for a given ( E a , E b , Theoretical deflection at each measuring point based on multilayer elasticity theory or finite element model Substitute into formula (5) to calculate the objective function F: (5); 3) Fitness calculation and optimal update of individuals / groups For each particle in the current particle swarm ( E a , E b Calculate the objective function value F and use it as the particle fitness; a. If the fitness of a particle is better than its historical best value, then update the individual best position p of that particle; b. If a particle's fitness is better than the current best position in the population, then update the best position g in the population.

[0062] 4) Particle position and velocity update

[0063] The velocity and position of each particle are updated according to the standard PSO update formula. For example, assuming the population size is m and the current position and velocity are X, respectively. k and V k，在 During the iteration process, the velocity and position of each particle are updated according to the standard PSO update formula, as shown in formula (6): ; (6); in, , The random number is a number in the interval [0, 1] and is randomly generated in each iteration. It is used to introduce random perturbation between individual optimality and group optimality, thereby enhancing the global search capability of the algorithm and preventing premature convergence.

[0064] 5) Simulated annealing (SA) criterion to avoid local optima.

[0065] For the new solution after PSO update, calculate the change Δ in the objective function. F=F new - F old .

[0066] a. If ΔF≤0, then the new solution is accepted unconditionally; b. If ΔF>0, then accept the worse solution with probability to escape the local optimum, as shown in formula (7): ; (7); Where p is the acceptance probability; ΔF is the change in the objective function; Tk The temperature at the k-th iteration; T 0 represents the initial temperature; α This is the cooling coefficient.

[0067] 6) Termination Criteria

[0068] The iteration stops if any of the following conditions are met: a. The current optimal objective function value of the population, F< ε ; b. If the number of iterations k > M; otherwise, let k = k + 1 and return to step 3) to continue iterating.

[0069] 7) Output parameter II

[0070] After the iteration, the optimal position of the group ( , The final inversion results in the surface modulus and base modulus, and the corresponding RMSE is output as the matching accuracy index.

[0071] In a specific implementation, an asphalt pavement modulus back-calculation system based on traffic speed deflectometer detection data includes: a data acquisition module for acquiring data through a traffic speed deflectometer and extracting mechanical response characteristic parameters; Soil modulus inversion module: used to construct the analytical relationship between soil modulus and mechanical response characteristic parameters, and to perform soil modulus inversion; Identification module: Used to construct an optimization model that minimizes the error between the measured response and the theoretical response under the constraint of known subgrade modulus, and to invert the base layer modulus and surface layer modulus using the SA-PSO algorithm.

[0072] In a specific embodiment, experimental verification is conducted, and the specific steps are as follows: (1) Establishing the TSD finite element mechanical model 1) Load parameters To improve the accuracy of the back-calculation results, this embodiment improves upon the traditional FWD single-circle load mechanical model in the calculation theory of multi-layer elastic systems, proposing a TSD dual-wheel load model: the load area at each tire contact point can be equivalent to a uniformly distributed circular load, calculated through the effective ground contact area. The equivalent circle radius R is obtained from the formula... The results show that, based on calculations, R is taken as 10.52 cm, the uniformly distributed load P as 0.7 MPa, and the distance between the two wheels S as 34.3 cm. The calculation model under the double-wheel load is as follows: Figure 4 As shown.

[0073] 2) Rigid subfloor setup

[0074] like Figure 5As shown, the specific settings for the rigid underlayer are as follows: the depth of the rigid underlayer is 731.2 cm from the road surface, the modulus is 6894.76 MPa, and the Poisson's ratio is 0.2.

[0075] 3) Structural parameters and operating condition combinations

[0076] To determine the inertia point parametric equations, different combinations of total pavement thickness and modulus need to be simulated. The influence of different working conditions on the inertia point parameters was studied. The surface layer modulus was calculated from the dynamic modulus master curve according to different velocity and temperature combinations, totaling 15... Five groups. The base modulus intervals are 200 MPa (flexible) and 1500 MPa (semi-rigid), and the subgrade modulus interval is 10 MPa. Other structural parameters are shown in Table 1.

[0077] Table 1. Combinations of different thickness and modulus values

[0078] (2) Parameter calculation

[0079] 1) Inertial point parametric equations

[0080] Calculations yielded 393,750 inertial point parameters for the flexible pavement structure and 511,875 for the semi-rigid pavement structure. Tablecurve regression analysis was performed on the inertial point parameters of both pavement structures to select the model with better regression performance. R 2 Filter out R 2 The formula with a value of 0.99983 characterizes the location of the inertia point. The relationship between the soil modulus and the thickness of the structural layers. R 2 The formula with a value of 0.99975 characterizes the location of the inertia point. The relationship between the soil modulus and the thickness of the structural layers. That is, the location of the inertia point. and bending The regression model is shown in Equations (8) and (9): (8); (9); Where H is the thickness of the pavement structure layer (the sum of the thicknesses of the surface layer and the base layer), and the unit is cm; E s This refers to the soil modulus, expressed in MPa. r 1, r 2, ..., r 10 and d 1, d 2, ...,d 1 represents each regression coefficient, and the fitting results are as follows: Figure 6 As shown, (a) is the position of the inert point Rc, and (b) is the position of the inert point Dc.

[0081] After determining the form of the regression model, regression analysis was performed using Matlab software to obtain the regression coefficients of the inertial point parameters of flexible and semi-rigid asphalt pavement structures. The specific results are shown in Tables 2 and 3, respectively. When back-calculating the subgrade modulus, different regression coefficients can be selected and substituted into the calculation according to different pavement types.

[0082] Table 2 Regression coefficients of Rc for inertia point locations

[0083] Among them, flexible R 2 =0.99982633; semi-rigid R 2 =0.9999472.

[0084] Table 3 Regression coefficients of inert point deflection Dc

[0085] Among them, flexible R 2 =0.9997524; semi-rigid R 2 =0.9999230.

[0086] 2) Other inversion parameters

[0087] The SA-PSO optimization algorithm used for the superstructure mainly involves the following six key variables: particle number N (representing the number of particles in the population, determining the coverage of the search space); learning factor; and learning factor. s 1 , s 2 (in, s 1 Controlling the degree to which a particle depends on its historical best value, and s 2 (Controlling the learning intensity of particles on the population's historical best value); annealing coefficient α (Characterizing the temperature decay rate during the controlled simulated annealing process); maximum number of iterations M (characterizing the maximum number of search steps for the algorithm); and problem dimension D (reflecting the number of variables in the optimization problem). Through trial calculations, the final values ​​of each parameter are shown in Table 4 below: Table 4 Parameter values ​​for the SA-PSO algorithm

[0088] (3) Inversion results based on simulated values

[0089] To evaluate the effectiveness of the proposed DBR-guided SA-PSO method, finite element simulations were performed on ten flexible pavement cases (Tables 5-6) and sixteen semi-rigid pavement cases (Tables 7-8) as validation scenarios. For each case, the modulus back-calculation results were compared with the corresponding theoretical values.

[0090] Table 5 Structural parameters of flexible asphalt pavement

[0091] Table 6 Deflection of Flexible Asphalt Pavement Structure (mm)

[0092] Table 7 Structural parameters of semi-rigid asphalt pavement

[0093] Table 8 Deflection of Semi-rigid Asphalt Pavement Structures

[0094] like Figure 7 As shown, (a) represents the surface layer modulus; (b) represents the base layer modulus; (c) represents the subgrade modulus; and (d) represents the relative error. The proposed DBR-guided SA-PSO method exhibits high back-calculation accuracy in flexible pavement structures. The relative errors of the back-calculated surface layer and base layer moduli are typically within 15%, while the average deviation of the base layer modulus is less than 3%. The overall RMSE remains below 1.5%, indicating a high degree of consistency between the back-calculation results and the theoretical values, thus verifying the applicability of this method in flexible pavement applications.

[0095] For semi-rigid pavement structures, such as Figure 8 As shown, (a) represents the surface layer modulus; (b) represents the base course modulus; (c) represents the subgrade modulus; and (d) represents the relative error. This method maintains good adaptability. The error in most surface layer moduli is below 20%, the error in base course modulus is mostly controlled within 25%, and the deviation in base course modulus is generally controlled within 10%. Although there are local deviations in individual cases (such as B12-B14), the overall RMSE remains below 2.0%, indicating that this method can robustly adapt to the relatively rigid response characteristics of semi-rigid pavements.

[0096] The above results demonstrate that the DBR-guided SA-PSO strategy can achieve stable back-calculation performance across different pavement types, providing a reliable foundation for subsequent verification using field TSD measurement data.

[0097] (4) Evaluation of inversion accuracy based on simulated values

[0098] To evaluate the superiority of the proposed coupling strategy over traditional methods, the DBR method, SA-PSO matching algorithm, and DBR-guided SA-PSO coupling method were used to further analyze the surface layer, base course, and subgrade moduli of all pavement cases in (3). By calculating the relative error between the back-calculated modulus and the theoretical value, the comparison results are as follows: Figures 9-11 As shown.

[0099] 1) Subgrade

[0100] like Figure 9 As shown, (a) is the subgrade modulus of the flexible pavement; (b) is the relative error of the flexible pavement; (c) is the subgrade modulus of the semi-rigid pavement; and (d) is the relative error of the semi-rigid pavement. The comparative analysis of the subgrade modulus inversion under the three methods shows that both the flexible and semi-rigid pavement systems exhibit a consistent trend, thus verifying the reliability and stability of the proposed method. (1) In the case of flexible pavement, such as Figure 9 As shown in (a) and (b), both the DBR and DBR-guided SA-PSO methods employ inertial point estimation methods to achieve highly accurate results, with relative errors generally controlled within 3%, showing excellent consistency with theoretical values. The SA-PSO matching algorithm also achieves acceptable accuracy, with most results remaining within 5%; however, its performance fluctuates slightly, mainly due to its sensitivity to initial parameter settings and nonlinear search characteristics. 2) In semi-rigid structures, such as Figure 9 As shown in (c) and (d), the inertial point estimation method used in the DBR and DBR-guided methods maintained good reliability, with errors controlled within 10% in most cases. In contrast, the SA-PSO method showed greater fluctuations in several specimens, with the relative error of the subgrade modulus occasionally exceeding 50%. However, due to the low absolute value of the subgrade modulus, its actual impact on structural performance was limited.

[0101] 2) Grassroots

[0102] like Figure 10 As shown, (a) represents the relative error of the flexible pavement; (b) represents the base modulus of the flexible pavement; (c) represents the relative error of the semi-rigid pavement; and (d) represents the base modulus of the semi-rigid pavement. The base modulus inversion results show that the three methods exhibit significantly different performance characteristics in flexible and semi-rigid pavement structures. (1) In the case of flexible pavement, such as Figure 10As shown in (a) and (b), all three methods achieve good agreement with the theoretical base modulus, confirming their reliable convergence under flexible conditions. The DBR method has the highest accuracy, with a maximum relative error of about 10%; the errors of the SA-PSO method and the DBR-guided SA-PSO method are both controlled within 15%. This indicates that for flexible pavements, all three methods can stably restore the base stiffness without significant deviation. (2) In semi-rigid structures, such as Figure 10 As shown in (c) and (d), significant differences exist among the methods. The DBR method has limited applicability, and its feature point estimation occasionally produces unreasonable results (such as B1-B3), causing the inverted elastic modulus to exceed the upper tolerance limit. This overestimation mainly stems from the narrow search range of the elastic modulus, the sensitivity of feature points to the accuracy of local deflection, and the lack of optimization feedback. The SA-PSO method exhibits more stable inversion behavior, with smaller fluctuations and closer to the theoretical value, but still has some large deviations (such as B15), which may be due to the upward propagation of the cumulative error of the subgrade modulus. The DBR-guided SA-PSO method provides the most balanced and robust results, controlling the relative error of the base course within 25%, and exhibits strong adaptability to the nonlinear response of semi-rigid structures.

[0103] 3) Surface layer

[0104] like Figure 11 As shown, (a) represents the relative error of the flexible pavement; (b) represents the surface modulus of the flexible pavement; (c) represents the relative error of the semi-rigid pavement; and (d) represents the surface modulus of the semi-rigid pavement. The comparison of the surface modulus inversion results reveals the significant differences between the flexible and semi-rigid pavement structures, further verifying the robustness of the proposed method. (1) In the case of flexible pavement, as shown in the example, Figure 11 As shown in (a) and (b), all three inversion methods achieve good agreement with the theoretical surface modulus. The DBR method has the smallest deviation, with the relative error controlled within 10%; the SA-PSO method and the DBR-guided SA-PSO method have comparable accuracy, with most results having an error of no more than 15%. These results indicate that under flexible pavement conditions, all three methods can accurately invert the surface stiffness, and are convergent, stable, and have low sensitivity to initialization parameters. (2) In semi-rigid structures, such as Figure 11 As shown in (c) and (d), the performance differences among the three methods are more significant. The DBR method has limited applicability because its estimated values ​​for the modulus of multiple surface layers are below the lower tolerance limit (e.g., B1–B3, B5, B8, B11, B12). This underestimation mainly stems from the high stiffness contrast between layers, the method's sensitivity to small displacement changes, and the lack of global optimization feedback. In contrast, although the SA-PSO matching algorithm occasionally exhibits local overcorrection, its overall results are more stable and agree better with theoretical values. The proposed DBR matching method effectively overcomes these shortcomings, controlling the relative error within 20%, achieving the best balance between accuracy and robustness.

[0105] 4) Comprehensive Analysis

[0106] Overall, for flexible pavements, all three back-calculation methods can accurately estimate the modulus of each layer, but there are slight differences in accuracy between different structural layers. In contrast, for semi-rigid pavements, the DBR method exhibits significant instability, while the DBR-guided SA-PSO method demonstrates superior adaptability and robustness, achieving reliable inversion accuracy even under complex stiffness contrast conditions. These findings further confirm that the DBR-guided SA-PSO method can integrate the physical regularity of the DBR method with the optimization capability of the SA-PSO algorithm, thereby ensuring consistent performance across various pavement configurations. Figure 12 The average relative error of the three methods is summarized, (a) is the average relative error of the flexible pavement case, and (b) is the average relative error of the semi-rigid pavement case.

[0107] like Figure 12 As shown in (a), all three inversion strategies can provide acceptable accuracy for flexible pavement structures, but their performance varies across different layers. The DBR method exhibits the best accuracy, with average relative errors of 2.93%, 4.39%, and 1.41% for the surface layer, base layer, and subgrade layer, respectively, demonstrating excellent reliability and consistency under smooth elastic modulus transition conditions. The SA-PSO method has larger deviations, at 7.50%, 9.25%, and 3.70% for the three layers, respectively. Although it maintains good adaptability to stress gradient effects, its accuracy is somewhat reduced. The proposed DBR-guided SA-PSO method shows balanced performance, with errors of 9.43%, 7.24%, and 1.41% for the pavement layer, base layer, and subgrade layer, respectively. All layer errors are below 10%, indicating that this method has stable and balanced performance in flexible pavements.

[0108] In addition, semi-rigid pavement structures, such as Figure 12A more significant deviation was observed in (b): the DBR method, which performs well on flexible pavements, exhibited marked instability here. Although its surface layer error remained at a low level of 2.59%, its accuracy dropped significantly in the higher stiffness base and subgrade layers, with average relative errors reaching 43.53% and 47.97%, respectively. These large deviations indicate that the regression-based formula cannot converge correctly when there are abrupt changes in stiffness and modulus between adjacent layers. The SA-PSO method achieved a moderate improvement, reducing the base and subgrade errors to 22.68% and 30.02%, respectively, but its sensitivity to the dominant surface gradient and susceptibility to local optimization traps led to a surface layer error of 21.38%. In contrast, the proposed DBR-guided SA-PSO method demonstrated significantly enhanced robustness and overall consistency. This method reduced the average errors of the surface, base, and subgrade layers to 2.59%, 6.14%, and 12.18%, respectively, without divergence or boundary saturation, confirming its excellent adaptability under high stiffness gradient conditions.

[0109] Overall, for flexible structures, all three methods meet the engineering accuracy requirements, with a performance ranking as follows: DBR > DBR-guided SA-PSO method > SA-PSO method. In the field of semi-rigid pavements, this method outperforms the two traditional methods, achieving the best balance between inversion accuracy and robustness. Therefore, this method is considered the preferred solution for modulus inversion in layered systems with large modulus contrast or significant dynamic response effects. Its field applicability will be further verified below using TSD measurement data.

[0110] (5) Evaluation of inversion accuracy based on measured values

[0111] To further verify the engineering applicability of the proposed DBR matching inversion method, field validation was conducted using TSD data collected from an existing semi-rigid asphalt pavement section. This validation aimed to assess the robustness and accuracy of the method under field measurement conditions, thereby determining its suitability for large-scale pavement monitoring based on TSD. The process included acquiring and preprocessing TSD velocity-settlement data, implementing an inversion framework to estimate the modulus of each layer, and evaluating the inversion performance based on field conditions.

[0112] A 1.5-kilometer semi-rigid asphalt pavement section was selected for testing. The first 300 meters were used for acceleration, followed by a constant speed data collection zone of 500-1000 meters, and the last 200 meters were used for deceleration. The pavement structure consisted of: a 12cm double-layer asphalt surface layer (4cm AC-13 + 8cm AC-25), a 36cm cement-stabilized base course, and a 15cm graded crushed stone base course.

[0113] The test followed the TSD calibration procedure specified by JTG and the Australian Road Association. The test was repeated three times along the marked rut track at a speed of 40 km / h. Outliers were removed using statistical filtering, and the deformation velocity was converted to settlement slope using formula (10): (10) in, V y，i Let i be the vertical velocity measured at the offset. V h This refers to the vehicle's speed.

[0114] Table 9 summarizes representative TSD deflection data at different speeds, which will serve as input parameters for subsequent elastic modulus inversion calculations.

[0115] Table 9. On-site measured deflection of the Haixi Road test section

[0116] To verify the applicability of the proposed coupled inversion framework under actual working conditions, the TSD settlement data measured in the field of the Haixi Road test section were processed using the DBR-guided SA-PSO method. The inversion process followed the same computational framework as the simulation analysis, including subgrade modulus estimation based on inert points and SA-PSO-assisted optimization of the superstructure. Table 10 summarizes the calculated moduli of the pavement layer, base course, and subgrade at ten representative measurement points.

[0117] To further verify the feasibility and stability of the proposed coupled inversion framework under actual working conditions, the DBR-guided SA-PSO method was used to process the TSD settlement data measured on-site in the Haixi Road test section.

[0118] Table 10 summarizes the calculated layer modulus and corresponding internal root mean square error values ​​for ten representative test points within a 1.5 km road section. This error value is defined as the root mean square deviation between the measured and fitted subsidence basins, and is generally below 10%, indicating that the model convergence and data fitting consistency are both satisfactory.

[0119] Table 10 Results of inversion using the DBR-guided SA-PSO method based on field measured data.

[0120] As shown in Table 10, the field inversion results exhibit a numerical range consistent with reality and a physically consistent distribution. The average subgrade modulus is approximately 110 MPa, with a coefficient of variation of 11.96%, indicating that the estimation based on the inertial point formula has stability and consistency. The base course modulus ranges from 2100 to 4100 MPa, with an average of 2910 MPa and a coefficient of variation of 25.9%, indicating its sensitivity to local stiffness variations and construction heterogeneity. The average surface course modulus is approximately 6000 MPa, consistent with the characteristics of a typical semi-rigid asphalt pavement under moderate traffic loads and temperatures.

[0121] Despite the lack of a direct reference modulus for absolute accuracy assessment, the inversion framework exhibits stable convergence at all test points and maintains a physically consistent modulus hierarchy (Ea>Eb>>Es). This structural model, combined with a low root mean square error, validates the robustness and practicality of the method under field conditions.

[0122] In summary, this invention (1) introduces the inertial point theory into the TSD dynamic loading scenario for the first time. Based on multi-layer elasticity theory and the characteristics of dual-wheel rolling loading, a finite element mechanical response model suitable for TSD load conditions is constructed. By simulating different combinations of working conditions (such as surface layer modulus, base layer modulus, driving speed, temperature, etc.), the location of the inertial point based on the TSD deformation response is established. With corresponding deflection value The parameterized model realizes the accurate calculation of the inertia point of asphalt pavement under TSD load, providing reliable theoretical support and methodological guarantee for the accurate calculation of subgrade modulus Es.

[0123] (2) By utilizing the physical properties of inert points being insensitive to the superstructure modulus and highly sensitive to the subgrade modulus, this invention proposes a subgrade modulus inversion mechanism that does not depend on initial values ​​and can avoid multiple solutions. This is achieved by establishing TSD inert point parameters (…). , The one-to-one correspondence between the soil modulus Es and the soil modulus successfully realizes the uniqueness and stability of the soil modulus solution, solves the common problems of multiple solutions and uncertainty in traditional inversion methods, and greatly improves the accuracy and reliability of the inversion results.

[0124] (3) Based on the uniquely determined subgrade modulus Es obtained in (2), this invention further constructs an inversion model for the surface layer and base layer modulus based on TSD measurement data. The objective function is composed of local error and global deflection error. Combining simulated annealing (SA) and particle swarm optimization (PSO) algorithms, the PSO algorithm quickly approaches the optimal region, while SA escapes the local optimum, ensuring the efficiency of the calculation process and global stable convergence. This process significantly improves the search efficiency of the parameter space and achieves high-precision inversion of the base layer modulus Eb, surface layer modulus Ea, and inversion error RMSE, providing a scientific solution for the dynamic evaluation of complex pavement structures.

[0125] (4) The inverse calculation method based on the coupling of physical laws and intelligent optimization proposed in this invention (DBR-guided SA-PSO) was systematically compared with the traditional deflection basin law method (DBR) and the existing SA-PSO optimization inverse method. The results show that the present invention has significant advantages in the following aspects: it ensures the uniqueness of the soil modulus solution and solves the non-uniqueness problem in the traditional method; the DBR-guided SA-PSO method greatly improves the stability of the base course and surface course modulus inverse process and enhances the adaptability of the method under multiple working conditions and temperature changes; in terms of computational efficiency, the method of the present invention can meet the requirements of road network-level TSD evaluation, especially in large-scale data processing and real-time evaluation.

[0126] (5) Based on the inversion results of actual TSD-detected road sections, the modulus calculated in this invention was verified in engineering. By comparing measured data, the applicability and stability of the inversion method of this invention were evaluated. The verification results show that this invention can provide high-precision modulus inversion results under complex road conditions and dynamic load conditions, and has excellent engineering applicability and reliability, providing solid technical support for intelligent maintenance and road health monitoring. The proposed DBR-guided SA-PSO method effectively alleviates the common instability and non-uniqueness problems of TSD-based inversion calculations. The modulus distribution curve generated by this method is reasonable and changes smoothly, which is consistent with the expected pavement behavior, confirming its applicability to TSD structure evaluation at a large-scale network level.

[0127] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0128] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data, characterized in that, include: Data was collected using a traffic speed deflectometer, and mechanical response characteristic parameters were extracted. Construct an analytical relationship between the soil modulus and mechanical response characteristic parameters, and perform soil modulus inversion; Under the constraint of known subgrade modulus, an optimization model for minimizing the error between measured response and theoretical response is constructed, and the base course modulus and surface course modulus are inverted using the SA-PSO algorithm.

2. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data as described in claim 1, characterized in that, The mechanical response characteristic parameters include: structural layer parameters, structural layer modulus and initial range, TSD load parameters and TSD test data.

3. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data as described in claim 1, characterized in that, The inversion of soil modulus includes: Given the soil modulus and the total thickness of the superstructure, determine the corresponding TSD inert point parameters; At the offset distance, the theoretically calculated deflection is compared with the measured deflection based on the TSD inert point parameters, and convergence is determined. If the convergence condition is met, the soil modulus corresponding to the current inertial point is accepted as the unique solution.

4. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data as described in claim 3, characterized in that, The determination of the corresponding TSD inert point parameters includes: Given the subgrade modulus Es and the total thickness H of the superstructure, based on multilayer elasticity theory and finite element simulation model, the dynamic deflection response of the pavement under TSD dual-wheel moving load is calculated, and the results are obtained. Theoretical deflection basin data for L groups of superstructures and load conditions under combined load conditions. ; For each measuring point offset distance i, first calculate the average value of the deflection under all working conditions at that location. Then, the root mean square error at that position is calculated to obtain discrete data of RMSE as a function of offset distance i. Finally, spline interpolation is used to smooth the RMSE(i) curve. Search for the first local minimum point on the smoothed RMSE(i) curve, and denote the corresponding offset distance as . ,Right now( The horizontal position of the inertial point under the combination; At the same offset position Take the average deflection , denoted as the inertial point deflection value To obtain the inertial point parameters ( , ).

5. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data according to claim 4, characterized in that, The step of comparing the theoretically calculated deflection with the measured deflection based on the TSD inertia point parameters at the offset distance, and determining convergence, includes: S11: At offset distance At this point, the theoretically calculated inertial point deflection value will be... Compared with the measured deflection Compare; S12: If the convergence condition is met, that is, when When, accept the current lazy point position. Soil modulus corresponding to the location It is a unique solution; If the convergence condition is not met, that is, when hour: a. If Then, the initial modulus Too small; ; Repeat S1 until the convergence condition is met. b. If Then, the initial modulus Too large; ; Repeat S1 until the convergence condition is met.

6. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data according to claim 1, characterized in that, The inversion of the base layer modulus and surface layer modulus using the SA-PSO algorithm includes: S21: Within a given search interval , and soil modulus Under the conditions: a. Generate the initial particle swarm positions and velocities, and denote the two-dimensional position of each particle as ( ). ); b. Set the particle number N and the learning factor. , initial temperature Annealing coefficient α, maximum number of iterations M, iteration index k; S22: In each iteration, for a given ( Theoretical deflection at each measuring point based on multilayer elasticity theory or finite element model Calculate the objective function F; S23: For each particle in the current particle swarm ( Calculate the objective function value F and use it as the particle fitness to perform optimal updates for individuals and the population. S24: Update the velocity and position of each particle according to the standard PSO update formula; S25: For the new solution after PSO update, avoid local optima by using simulated annealing SA criterion; S26: Perform iterations based on preset conditions. After the iterations are complete, output the optimal position of the population. These are the surface layer modulus and base layer modulus obtained from the final inversion.

7. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data according to claim 6, characterized in that, The objective function is: 。 8. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data according to claim 6, characterized in that, The method of avoiding local optima through simulated annealing (SA) includes: For the new solution after PSO update, calculate the change in the objective function. ; a. If ΔF≤0, then the new solution is accepted unconditionally; b. If ΔF > 0, then accept the worse solution with probability p, thus escaping the local optimum: ； ； Where p is the acceptance probability. The change in the objective function Let be the temperature of the k-th iteration. The initial temperature, This is the cooling coefficient.

9. The method for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data according to claim 6, characterized in that, After the iteration is completed, the corresponding RMSE is output as a matching accuracy index.

10. A system for back-calculating the modulus of asphalt pavement based on traffic speed deflectometer data, characterized in that, Includes: Acquisition module: used to collect data using a traffic speed deflectometer and extract mechanical response characteristic parameters; Soil modulus inversion module: used to construct the analytical relationship between soil modulus and mechanical response characteristic parameters, and to perform soil modulus inversion; Identification module: Used to construct an optimization model that minimizes the error between the measured response and the theoretical response under the constraint of known subgrade modulus, and to invert the base layer modulus and surface layer modulus using the SA-PSO algorithm.

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