A pavement structure modulus back-calculation method considering different modulus characteristics in tension and compression

Abstract

The application is suitable for the technical field of road engineering and relates to a pavement structure modulus back-calculation method considering different modulus characteristics of tension and compression, comprising the following steps: S10, data acquisition and verification; S20, parameter and constraint setting; S30, initial value generation; S40, axisymmetric forward calculation and NR iteration; S50, target function construction; S60, gradient / Jacobian evaluation; S70, SLSQP with constraint optimization; S80, result checking and uncertainty evaluation; and S90, archiving and report generation. The application has simple process and convenient operation, greatly improves the material constitutive reality, calculation efficiency, numerical stability and engineering data robustness of pavement structure modulus identification.

Description

Technical Field

[0001] This invention belongs to the field of road engineering technology, and in particular relates to a method for back-calculating the modulus of pavement structure considering different tensile and compressive modulus characteristics. Background Technology

[0002] Accurate identification of pavement structural modulus is a crucial step in design evaluation, overlay design, life prediction, and segmented repair. Falling weight deflectometer (FWD) tests induce deflection response through controlled impact loads, and inverse calculation algorithms are used to obtain the equivalent elastic parameters of each material layer and the subgrade response values. Current engineering practices are mostly based on the assumption of layered linear elastic single modulus (tensile-compression equivalent), employing finite element / layered elastic analytical or semi-analytical algorithms for forward calculations, and using least squares or empirical regression methods for parameter inversion. This paradigm has advantages in terms of workload and implementation complexity, but it has significant limitations in areas such as material asymmetry (different tensile and compressive moduli), half-space far-field processing, numerical stability, and identifiability. For example, simplified material characterization does not match actual mechanical behavior, errors exist in the boundary and internal compatibility handling of the calculation model, the numerical stability of the ill-conditioned inversion process is poor, and there is a lack of robustness in handling engineering data noise.

[0003] Patent CN108660880B discloses a method for determining the optimal modulus combination of asphalt pavement structural layers. First, the upper, middle, and lower layers are considered as a whole. Based on the requirements of the elastic modulus range in the specifications, the median modulus is used as the uniform modulus of the surface layer, and n sets of base-to-surface layer modulus ratios are selected. Then, the surface layer modulus, the n sets of base-to-surface layer modulus ratios, and the thickness of each structural layer are input into finite element software to obtain the mechanical response influence of the asphalt pavement on the design indicators under different base-to-surface layer modulus ratios, thus determining the optimal base-to-surface layer modulus ratio. Finally, based on the requirements of the specifications for the elastic modulus range of inorganic binder-stabilized materials, while ensuring that the average of the upper, middle, and lower surface layers is the median of the entire surface layer modulus, the modulus gradient of the upper and lower layers is changed to adjust the modulus of the upper and lower layers, resulting in m combinations of the upper, middle, and lower surface layer modulus groups. This patent also uses finite element analysis for modulus analysis, and thus suffers from the same defects as existing technologies.

[0004] Therefore, how to provide a method for back-calculating the pavement structure modulus that can simultaneously take into account the constitutive authenticity of materials, computational efficiency, numerical stability, and robustness to engineering data is a problem that urgently needs to be solved by researchers in this field. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for back-calculating the modulus of pavement structures that considers the different modulus characteristics of tension and compression, so as to solve the problem that the identification of pavement structure modulus in existing technologies cannot simultaneously take into account the authenticity of material constitutives, computational efficiency, numerical stability and robustness of engineering data.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] This invention provides a method for back-calculating the modulus of a pavement structure considering different tensile and compressive moduli, comprising the following steps:

[0008] S10. Data acquisition and verification: Obtain the magnitude of the impact load and the contact radius or equivalent contact pressure from the falling weight deflectometer, and at the same time read the pavement structure layer thickness information, sensor radius sequence and corresponding deflection observation value.

[0009] S20, Parameter and Constraint Settings: The compressive elastic modulus of each material layer is denoted as... The compression ratio is denoted as The tensile parameters are determined based on the principle of flexibility conservation, and boundary and inequality constraints are applied to all parameters.

[0010] S30, Initial value generation: Under the premise of satisfying the constraints in S20, the initial compressive modulus and compressive-tensile ratio are given for each layer of material;

[0011] S40, Axisymmetric Forward Calculation and NR Iteration: Given a parameter vector, calculate the theoretical deflection corresponding to the observation radius. After assembly, use the NR method to solve the displacement field. During the iteration process, update the tangent stiffness and material state simultaneously until the residual norm and displacement increment meet the preset convergence threshold.

[0012] S50. Objective function construction: After the forward solution converges, a weighted least squares objective function is constructed based on the deviation between the theoretical deflection and the observed deflection.

[0013] S60, Gradient / Jacobi Evaluation: Evaluate the gradient of the objective function with respect to the parameter vector or the Jacobian of the response vector with respect to the parameters;

[0014] S70, SLSQP constrained optimization: The SLSQP algorithm is called to construct a quadratic approximation near the current point and solve the subproblem with boundary and general inequality constraints. The step size that satisfies sufficient descent is selected through line search, and the updated parameters are kept in the feasible region. When the preset tolerance is met, the optimization is terminated and the optimal parameters are output; otherwise, return to S40.

[0015] S80. Result verification and uncertainty assessment: After the algorithm converges, the theoretical deflection and the observed deflection are compared and verified, and the parameter covariance and sensitivity are estimated based on the Jacobian matrix to give the confidence interval, correlation and identification stability evaluation of the optimal solution.

[0016] S90. Archiving and Report Generation: The optimal parameters, residual statistics, sensitivity and confidence intervals, iteration logs, and key graphs are archived in a unified manner to generate one-page or multi-page reports for engineering applications. At the same time, the data version number, random seed, and software version information are saved to ensure that the results are traceable and recalculated.

[0017] Furthermore, in S10, the original data is first standardized in terms of units and dimensions, time windows are aligned, and steady-state segments of repeatedly loaded records are extracted. Statistical methods are used to remove obvious outliers, and initial weights are set for each observation point according to the confidence level and spatial distribution of the measurement points to form a standardized data package, which serves as the unified input for subsequent processes.

[0018] Furthermore, the sensor radius sequence includes 0mm, 200mm, 300mm, 450mm, 600mm, 900mm, 1200mm, 1300mm and 1350mm, corresponding to a deflection value of 0.01mm.

[0019] Furthermore, in S20, the constraints include the upper and lower bounds of the elastic modulus, the Poisson's ratio being in the (0, 0.5) interval, and the hierarchical order constraint. When the proportional relationship causes the tensile Poisson's ratio to exceed the limit, it is kept within the feasible region by parameter contraction or projection.

[0020] Furthermore, in S30, Latin hypercube sampling is used to generate several sets of candidate initial values ​​in the feasible region. First, the relative merits of the objective function are evaluated by fast forward solving with reduced accuracy. Then, 1 to 3 sets are selected as the formal starting point. After the initial values ​​are determined, they are uniformly mapped to the scaled variable space for optimization.

[0021] Furthermore, in S40, the governing equations and stress-strain relationships are constructed in axisymmetric coordinates, and the computational domain is divided into a combination of near-field finite blocks and far-field infinite blocks. The blocks are unified to the standard parent domain through isoparametric mapping to achieve consistent processing of shape function interpolation and numerical integration. Displacement and traction compatibility conditions are applied to the common edges between blocks, and the resultant force balance is satisfied at the corner points. Interface coupling is achieved using Lagrange multipliers or penalty methods. The principal stress is determined at the Gaussian point level, and the compression or tension parameters are selected according to the stress sign, thereby assembling the axisymmetric equivalent stiffness matrix.

[0022] Furthermore, in S50, the weights are adjusted according to the confidence level of the measurement point and its distance from the loading center. When there are a few suspected abnormal observations, it is allowed to switch to a robust loss form. In multi-condition or multi-segment applications, the targets of each condition are superimposed according to the weights to form a joint target, so as to simultaneously identify shared or associated layer parameters.

[0023] Furthermore, in S60, a differential approximation with relative perturbation is adopted, and the decomposition results of the forward solution are reused to improve the gradient quality with quasi-Newton update or adjoint approximation. After the evaluation is completed, the gradient or Jacobian and the weight matrix are passed into S70.

[0024] Furthermore, in S70, when constraint switching is frequent or the boundary is activated, the feasibility is maintained stably by means of active set or projection, and the outer iteration uses KKT conditions, constraint violation degree, step size and target value change as joint stopping criteria.

[0025] Furthermore, in S90, the iteration log includes the starting point, constraint activation state, and line search record, and the key graphs include a black-and-white deflection comparison graph and a residual scatter plot.

[0026] The method for back-calculating the modulus of pavement structures considering different tensile and compressive moduli provided by this invention has at least the following advantages compared with the prior art:

[0027] Existing technologies for identifying pavement structure modulus cannot simultaneously consider material constitutive accuracy, computational efficiency, numerical stability, and robustness to engineering data. This invention offers a simple and convenient process, focusing on "compression modulus..." +compression ratio The minimum parameterization characterizes the tensile and compressive modulus properties, and within an axisymmetric half-space framework, it directly eliminates systematic errors caused by finite domain truncation and boundary reflection through "near-field finite block - far-field infinite block" discretization and numerical realization of interface displacement / traction compatibility and corner mechanical equilibrium. Combined with principal stress-driven differentiable tensile / compressive switching and Newton-Raphson (NR) iteration, it ensures the symmetry / positive definiteness of the stiffness matrix and iteration continuity, thereby simultaneously improving the physical accuracy and numerical stability of the inverse calculation, significantly improving the overall fitting quality of the near-field to mid-field of the deflection basin. At the inverse level, weighted least squares is used as the objective, and sequential least squares quadratic programming (SLSQP) is employed to apply parameter boundaries, hierarchical and physical feasible region constraints. This is integrated through multi-condition / multi-segment joint identification, weight and robust loss processing, and uncertainty assessment of the Gauss-Newton approximation, forming an engineering closed loop of "forward solution - evaluation - optimization." The process automatically degenerates into a single-modulus flow, facilitating seamless integration with existing systems. Therefore, this invention significantly improves the material constitutive accuracy, computational efficiency, numerical stability, and robustness of engineering data in pavement structure modulus identification, making it more suitable for engineering scenarios such as high loads, soft soil foundations, and high-precision assessments. Attached Figure Description

[0028] To more clearly illustrate the solution of the present invention, a brief introduction will be given to the drawings used in the description of the embodiments below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0029] Figure 1 This is a flowchart illustrating a method for back-calculating the modulus of a road structure considering different tensile and compressive moduli, provided as an embodiment of the present invention. Detailed Implementation

[0030] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0031] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0032] This invention provides a method for back-calculating the pavement structure modulus considering different tensile and compressive modulus characteristics. Applied to the identification of pavement structure modulus, the method includes the following steps:

[0033] S10. Obtain the impact load magnitude and contact radius or equivalent contact pressure from the falling weight deflectometer. Simultaneously, read the pavement structure layer thickness information, sensor radius sequence (radial distance sequence from FWD points to the loading center, determining the sampling location and weighting strategy of the objective function), and corresponding deflection observations; S20. Record the compressive elastic modulus of each layer of material as... The compression ratio is denoted as The tensile parameters are determined based on the principle of flexibility conservation, and boundary and inequality constraints are applied to all parameters; S30, under the premise of satisfying the constraints in S20, the initial compressive modulus and compressive-tensile ratio are given for each layer of material; S40, with the given parameter vector as a condition, the theoretical deflection corresponding to the observation radius is calculated. After assembly, the displacement field is solved using the NR method. During the iteration process, the tangent stiffness and material state are updated synchronously until the residual norm and displacement increment meet the preset convergence threshold; S50, after the forward solution converges, a weighted least squares objective function is constructed based on the deviation between the theoretical deflection and the observed deflection; S60, the gradient of the objective function with respect to the parameter vector or the Jacobian of the response vector with respect to the parameters is evaluated; S70, the SLSQP algorithm is called in the current... A quadratic approximation is constructed near the previous point, and a subproblem with boundary and general inequality constraints is solved. A sufficient descent step size is selected through line search, while keeping the updated parameters within the feasible region. Optimization terminates and the optimal parameters are output when the preset tolerance is met; otherwise, the process returns to step S40. In step S80, after the algorithm converges, the theoretical deflection and observed deflection are compared and verified. The parameter covariance and sensitivity are estimated based on the Jacobian matrix to provide the confidence interval, correlation, and identification stability evaluation of the optimal solution. In step S90, the optimal parameters, residual statistics, sensitivity and confidence interval, iteration log, and key maps are archived together to generate a one- or multi-page report for engineering applications. The data version number, random seed, and software version information are also saved to ensure the traceability and recalculation of the results.

[0034] The present invention has a simple process and is easy to operate, which greatly improves the material constitutive authenticity, calculation efficiency, numerical stability and engineering data robustness of pavement structure modulus identification.

[0035] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0036] This invention provides a method for back-calculating the pavement structure modulus considering the different tensile and compressive moduli. This method is applied to the identification of the pavement structure modulus. The different tensile and compressive moduli refer to the objective characteristic that the equivalent elastic modulus of a material differs under tensile and compressive conditions. In this embodiment, the "compressive modulus" is used as the term. +compression ratio "To minimize the parameterization, the tensile modulus is derived from this." (The same applies to Poisson's ratio if necessary), making the inverse calculation both simple and accurately describing the asymmetry of forces. Compression modulus. It is the equivalent elastic modulus of the material under compression, and is one of the core decision variables for each layer, obtained through back calculation. Tensile modulus. It is the equivalent elastic modulus of a material under tension, and is not directly identified separately; it is determined by... This linkage reduces the dimensionality of variables and improves identifiability. The tension-to-compression ratio k is a dimensionless coefficient representing the ratio of the tension / compression parameter, typically... , is the second core decision variable in each layer, and Together they characterize the bimodulus. Poisson's ratio is the ratio of transverse strain to axial strain within the linear elastic range; the compressive Poisson's ratio... It can be given or set as to be identified; the Lapoisson ratio can be proportional. Alternatively, the same-domain constraints can be determined to ensure the physically feasible region. .

[0037] like Figure 1 As shown, in this embodiment, the method for back-calculating the modulus of pavement structures considering different tensile and compressive moduli is self-consistent and closed-loop. Data quality control provides reliable input for parameterization and constraints. Parameterization and constraints ensure that forward solving and optimization are performed within the physically feasible domain. Axisymmetric (circular loading and layered structures are symmetric about the axis, and physical quantities are independent of circumferential coordinates) forward solutions and NR iterations provide stable response evaluation. Gradient / Jacobi guarantees the effective search of SLSQP, and the joint stopping criterion ensures timely termination while meeting accuracy requirements. Finally, uncertainty assessment and archiving reports complete the closed loop from data to parameter identification and engineering conclusions. Specifically, it includes the following steps:

[0038] S10. Data Acquisition and Verification: During implementation, the magnitude of the impact load and the contact radius or equivalent contact pressure are obtained from the falling weight deflectometer (FWD, a field test device that excites road deflection by impact load and records the response at multiple radii, providing load, contact radius, sensor radius-deflection data as back-calculation input). At the same time, the pavement structure layer thickness information, sensor radius sequence and corresponding deflection observation values ​​are read.

[0039] Specifically, in this embodiment, to ensure the robustness of subsequent back-calculation, the original data is first standardized in terms of units and dimensions, time windows are aligned, and steady-state segments of repeatedly loaded records are extracted. Based on this, statistical methods are used to remove obvious outliers, and initial weights are set for each observation point according to the confidence level and spatial distribution of the measurement points. After processing, a standardized data package is formed, which serves as the unified input for subsequent processes. Typical sensor radius sequences (in mm) can be: 0, 200, 300, 450, 600, 900, 1200, 1300, 1350; and the corresponding deflection values ​​(0.01 mm) are given.

[0040] S20, Parameter and Constraint Settings: The compressive elastic modulus of each material layer is denoted as... The compression ratio is denoted as And the tensile parameters are determined based on the principle of flexibility conservation (e.g.) (Poisson's ratio can also be determined by proportionality), and boundary and inequality constraints are applied to all parameters.

[0041] Specifically, in this embodiment, to ensure physical feasibility and engineering rationality, boundary and inequality constraints are applied to all parameters during implementation. These constraints include at least upper and lower bounds on the elastic modulus, a Poisson's ratio within the (0, 0.5) interval, and, if necessary, hierarchical order constraints. When the proportional relationship may cause the stretched Poisson's ratio to exceed the limit, parameter shrinkage or projection is used to keep it within the feasible region. To avoid numerical ill-conditioning caused by different dimensions, the parameter vector is scaled and fixed to the standard variable space for subsequent optimization.

[0042] S30, Initial value generation: Under the premise of satisfying the constraints in S20, the initial compressive modulus and compressive-tensile ratio are given for each layer of material.

[0043] Specifically, in this embodiment, to improve the global convergence probability, in a preferred implementation, Latin hypercube sampling is used to generate several sets of candidate initial values ​​within the feasible region. The relative merits of the objective function are first evaluated using a fast forward solution with reduced precision, and then 1 to 3 sets are selected as the formal starting point. After the initial values ​​are determined, they are uniformly mapped to a scaled variable space for optimization.

[0044] S40, Axisymmetric Forward Calculation and NR Iteration: Given a parameter vector, calculate the theoretical deflection corresponding to the observation radius. After assembly, use the NR method to solve the displacement field. During the iteration process, update the tangent stiffness and material state simultaneously until the residual norm and displacement increment meet the preset convergence threshold.

[0045] Specifically, in this embodiment, the governing equations and stress-strain relationships are first constructed in axisymmetric coordinates, and the computational domain is divided into a combination of near-field finite blocks and far-field infinite blocks. Through isoparametric mapping, each block is unified to a standard parent domain (mapping any block to a unified parameter domain for integration and interpolation), achieving consistency in shape function interpolation and numerical integration. Displacement and traction compatibility conditions are applied to the common edges between blocks (displacement and corresponding traction force are continuous on the common edges of adjacent blocks / layers), and resultant force balance is satisfied at corner points (resultant force / moment balance at the intersection of multiple blocks, improving the physical consistency and numerical stability of the forward solution at geometric inflection points). Interface coupling is achieved using Lagrange multipliers or penalty methods. Subsequently, principal stress (the eigenvalue of the stress tensor at that point) is determined at the Gaussian point level, and compression or tension parameters are selected based on the stress sign, thereby assembling the axisymmetric equivalent stiffness matrix (the stiffness matrix of the axisymmetric stress-strain relationship).

[0046] Furthermore, in this embodiment, to reduce numerical jitter when the principal stress crosses zero, a smooth sign function is used to achieve continuous processing of parameter switching. If convergence difficulties occur during iteration, appropriate damping can be introduced or the process can be rolled back to the previous stable state before proceeding.

[0047] In other embodiments, the finite block method (FBM, a numerical discretization method using blocks as basic units, which can be regarded as a unified framework for stitching together higher-order units / subdomains) can be equivalent to higher-order finite element / spectral element method, boundary element method (BEM / DBEM), radial basis function / meshless method (RBF, RPIM), hybrid boundary-domain method, as long as it can realize the response calculation of layered half-space (covered by multiple layers of material, connected to a foundation soil that can be regarded as infinitely deep); far-field infinite blocks can be equivalent to infinite elements (units / blocks "extending to infinity" embedded in the discrete layer, satisfying far-field displacement / stress attenuation), mapping / absorbing boundary (PML / ABC), semi-analytical kernel (Hankel / ring-loaded kernel) or Kelvin fundamental solution superposition; Lagrange multipliers can be equivalent to Nitsch e. Penalty function method, (dual) mortar / double-mortar or continuous contact element; principal stress symbol can be replaced by principal strain (the characteristic value of the strain tensor at that point), volumetric strain / compressive stress or tensile / compressive energy density symbol; NR can be replaced by trust region Newton / LM (Levenberg–Marquardt), quasi-Newton (BFGS / L-BFGS), continuation / homotopy or pseudo-transient damping advance; NR can be replaced by trust region Newton / LM (Levenberg–Marquardt), quasi-Newton (BFGS / L-BFGS), continuation / homotopy or pseudo-transient damping advance.

[0048] S50. Objective function construction: After the forward solution converges, a weighted least squares objective function is constructed based on the deviation between the theoretical deflection and the observed deflection.

[0049] Specifically, to make the theoretical deflection basin Compared with the measured deflection To minimize the difference, construct the objective function as follows:

[0050]

[0051] Where m is the number of deflection measurement points (FWD typically has 7 to 9 sensors). The distance from the sensor to the center of the load (e.g., r=0, 200, 300, 450, 600, 900, 1200, 1500, 1800mm). This represents the measured deflection value. This represents the theoretical deflection value calculated based on the bimodulus theoretical model, where p is the inverse calculation variable. , Weighting coefficients (optional, can take into account the weights of different sensor locations) (To emphasize central deflection). To ensure physical rationality and numerical stability, boundary constraints are introduced for each layer:

[0052] , ;

[0053] in, This is the lower limit of the inverse modulus. This is used to calculate the upper limit of the modulus, in order to avoid negative values ​​or unrealistically large values. The upper limit for the ratio of compression to tension modulus is generally taken as 2.0 to 2.5. In summary, this inverse calculation problem can be reduced to nonlinear least squares optimization with boundary constraints.

[0054] In this embodiment, the weights can be adjusted according to the confidence level of the measurement points and their distance from the loading center. When there are a few suspected anomalous observations, a robust loss form can be switched to reduce the impact of anomalous points on the overall target. In multi-condition or multi-segment applications, the targets of each condition can be superimposed according to their weights to form a joint target, so as to simultaneously identify shared or associated layer parameters.

[0055] In other embodiments, in addition to weighted L2, M-estimation such as L1, Huber, Cauchy, and Tukey may be used.

[0056] S60. Gradient / Jacobi Evaluation: To improve the approximation quality of constrained quadratic programming subproblems, the gradient of the objective function with respect to the parameter vector or the Jacobian of the response vector with respect to the parameters is evaluated.

[0057] Specifically, in this embodiment, the objective function is calculated. gradient:

[0058]

[0059] in, The residual is Jacobian (m×N); This is the residual vector (m×1), representing the difference between the theoretical deflection and the measured deflection. The constraint function is also calculated. gradient matrix (p×N, where p is the number of constraints).

[0060] In this embodiment, a difference approximation with relative perturbation is employed, and the decomposition results of the forward solution are reused where possible to reduce computational overhead; quasi-Newton updates or adjoint approximations are used to improve gradient quality. After evaluation, the gradient or Jacobian and the weight matrix are passed together to the optimizer in the next step.

[0061] In other embodiments, the difference can be replaced by the complex step size method, automatic differentiation (AD), adjoint method, or stochastic approximation (SPSA); in high dimensions, it can be combined with column block / low rank approximation.

[0062] S70 and SLSQP Constrained Optimization: Hessian Matrix Approximation in the SLSQP Algorithm This is the core of the algorithm, used to capture second-order information (i.e., curvature) of the objective function and constraints, thereby improving the accuracy of the search direction. It is used to obtain new iteration points. Updated later This allows for full utilization of the differences between the two points. For the least squares dual-modulus inverse calculation model, the second derivative of the objective function f... It can be approximated as (Ignoring higher-order terms), but directly recalculating the complete Hessian algorithm is computationally expensive; SLSQP uses BFGS low-rank updates to progressively improve this approximation while maintaining the positive definiteness of the matrix, ensuring the subproblem is convex and directionally stable. The update formula is:

[0063]

[0064] in, Let be the updated Hessian approximation matrix (an N×N symmetric positive definite matrix), representing the Lagrange function. The second derivative approximation is used for the curvature term of subsequent QP subproblems. It is the Hessian approximation matrix of the current iteration, inherited from the previous update. It is the Lagrange gradient difference vector (N×1), defined as It captures the gradient change from the old point to the new point, reflecting the actual curvature of the function; It is a Lagrange gradient; The step vector (N×1) is defined as follows: This represents the change in modulus from the current point to the next point (which can be initialized with a small perturbation before the first iteration). Furthermore, the formula... The first item A correction based on the actual gradient change is added, and the second term subtracts the projection of the old approximation in the s direction to maintain consistency and positive definiteness.

[0065] At the current iteration point A first-order / second-order approximation model is constructed, and the search vector is obtained using a QP solver. This approach reduces the objective function while satisfying the linearization of constraints. In the bimodulus-deflection inverse problem, this approach adjusts the decision variables (compression modulus to tensile modulus ratio) to minimize deflection error. Therefore:

[0066]

[0067]

[0068] in, This indicates minimizing the variable d, where d is the search vector (N×1) and represents the increment of the modulus or compressive / tensile modulus ratio update. Expand the Taylor series to the quadratic term. Expand a term using Taylor series; This is the current constraint value vector. To constrain the projection of the gradient onto direction d, we obtain... and the corresponding Lagrange multipliers Then, it is used to update the work function and check the Karush-Kuhn-Tucker (KKT) conditions.

[0069] In summary, the SLSQP algorithm is invoked to construct a quadratic approximation near the current point and solve the subproblem with boundary and general inequality constraints. A sufficient descent step size is selected through line search, and the updated parameters are kept within the feasible region. The optimization is terminated and the optimal parameters are output when the preset tolerance is met; otherwise, the process returns to step S40.

[0070] Specifically, in this embodiment, when constraints switch frequently or boundaries are activated, feasibility is maintained stably by active set or projection. The outer iteration uses KKT conditions (necessary optimality conditions for constrained optimization problems, which, together with step size / feasibility tolerance, serve as stopping criteria), constraint violation degree, and changes in step size and target value as joint stopping criteria.

[0071] In some other embodiments, SLSQP can be replaced by trust-constr / interior point (IPOPT class) / Augmented-Lagrangian / filtering; L-BFGS-B is used when only boundaries are considered.

[0072] In some other embodiments, a global coarse search can be performed first using CMA-ES / PSO / genetic algorithm / simulated annealing, and then switched to local differentiable optimization (SLSQP / LM / BFGS).

[0073] S80. Structural Verification and Uncertainty Assessment: After the algorithm converges, the theoretical deflection and the observed deflection are compared and verified to check whether there is a systematic deviation in the distribution of the residuals on the radius. Under the Gauss-Newton approximation, the parameter covariance and sensitivity are estimated based on the Jacobian matrix to give the confidence interval, correlation and identification stability evaluation of the optimal solution. At the same time, it is verified whether the parameters of each layer meet the requirements of engineering experience range and physical feasible region.

[0074] S90. Archiving and Report Generation: The optimal parameters, residual statistics, sensitivity and confidence intervals, iteration logs (including start point, constraint activation status and line search records), and key graphs (black and white deflection comparison graph and residual scatter plot) are archived in a unified manner to generate a one-page or multi-page report for engineering applications; at the same time, the data version number, random seed and software version information are saved to ensure the traceability and recalculation of the results.

[0075] The pavement structure modulus back-calculation method considering different tensile and compressive modulus characteristics described in the above embodiments, compared with the prior art, cannot simultaneously consider the material constitutive authenticity, computational efficiency, numerical stability, and robustness to engineering data in pavement structure modulus identification. The present invention has a simple process and is easy to operate, focusing on "compressive modulus..." +compression ratio The minimum parameterization characterizes the tensile and compressive modulus properties, and within an axisymmetric half-space framework, it directly eliminates systematic errors caused by finite domain truncation and boundary reflection through "near-field finite block - far-field infinite block" discretization and numerical realization of interface displacement / traction compatibility and corner mechanical equilibrium. Combined with principal stress-driven differentiable tensile / compressive switching and Newton-Raphson (NR) iteration, it ensures the symmetry / positive definiteness of the stiffness matrix and iteration continuity, thereby simultaneously improving the physical accuracy and numerical stability of the inverse calculation, significantly improving the overall fitting quality of the near-field to mid-field of the deflection basin. At the inverse level, weighted least squares is used as the objective, and sequential least squares quadratic programming (SLSQP) is employed to apply parameter boundaries, hierarchical and physical feasible region constraints. This is integrated through multi-condition / multi-segment joint identification, weight and robust loss processing, and uncertainty assessment of the Gauss-Newton approximation, forming an engineering closed loop of "forward solution - evaluation - optimization." The process automatically degenerates into a single-modulus flow, facilitating seamless integration with existing systems. Therefore, this invention significantly improves the material constitutive accuracy, computational efficiency, numerical stability, and robustness of engineering data in pavement structure modulus identification, making it more suitable for engineering scenarios such as high loads, soft soil foundations, and high-precision assessments.

[0076] Obviously, the embodiments described above are merely preferred embodiments of the present invention, and not all embodiments. The accompanying drawings illustrate preferred embodiments of the present invention, but do not limit the scope of the patent. The present invention can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of patent protection of this invention.

Claims

1. A pavement structure modulus back-calculation method considering tension-compression different modulus characteristics, characterized in that, The method comprises the following steps: S10, obtaining the impact load size and contact radius or equivalent contact pressure from the falling weight deflectometer, and reading the layer thickness information of the pavement structure, the sensor radius sequence and the corresponding deflection observation value; S20, the compressive elastic modulus of each layer of material is recorded as The compressive-tensile ratio is recorded as The tensile parameters are determined based on the principle of compliance conservation, and boundary and inequality constraints are imposed on all parameters; S30, under the premise of meeting the constraint condition in S20, giving the initial compression modulus and compression-tension ratio for each layer material; S40, calculating the theoretical deflection corresponding to the observation radius with the given parameter vector as the condition, assembling and completing, and then using the NR method to solve the displacement field, and synchronously updating the tangent stiffness and material state in the iteration process until the residual norm and displacement increment meet the preset convergence threshold; S50, after the forward solution converges, constructing a weighted least squares objective function based on the deviation between the theoretical deflection and the observed deflection; S60, evaluating the gradient of the objective function with respect to the parameter vector or the Jacobian of the response vector with respect to the parameter; S70, calling the SLSQP algorithm to construct a quadratic approximation near the current point and solve the sub-problem with boundary and general inequality constraints, selecting a step length that meets the sufficient descent through line search, and keeping the updated parameters in the feasible region, and terminating the optimization and outputting the optimal parameters when the preset tolerance is met, otherwise returning to S40; S80, after the algorithm converges, comparing and checking the theoretical deflection and the observed deflection, and estimating the parameter covariance and sensitivity based on the Jacobian matrix to give the confidence interval, correlation and identification stability evaluation of the optimal solution; S90, archiving the optimal parameters, residual statistics, sensitivity and confidence interval, iteration log and key drawings, generating one or more pages of reports for engineering applications, and saving the data version number, random seed and software version information to ensure the results are traceable and recalculable.

2. The method according to claim 1, wherein, In S10, the original data are first unified in units and dimensions, time windows are aligned, and the steady-state section of repeated loading records is extracted, obvious outliers are removed using statistical methods, and initial weights are set for each observation point according to the confidence and spatial distribution of the measurement points to form a standardized data package as the unified input for the subsequent process.

3. The method according to claim 2, wherein, The sensor radius sequence includes 0 mm, 200 mm, 300 mm, 450 mm, 600 mm, 900 mm, 1200 mm, 1300 mm and 1350 mm, and the corresponding deflection values are 0.01 mm.

4. The method according to claim 1, wherein, In S20, the constraints include the upper and lower bounds of the elastic modulus, the Poisson's ratio in the interval (0, 0.5), and the layer sequence order constraint. When the proportional relationship causes the tensile Poisson's ratio to possibly exceed the interval, the parameter is contracted or projected to keep it within the feasible region.

5. The method according to claim 1, wherein, In S30, Latin hypercube sampling is used to generate several groups of candidate initial values in the feasible region. The relative merits of the objective function are evaluated by fast forward solution with descending precision, and 1-3 groups are selected as the formal starting point. After the initial value is determined, it is mapped to the scaled variable space for optimization.

6. The method according to claim 1, wherein, In the S40, the control equation and stress-strain relationship are constructed under the axisymmetric coordinates, the calculation domain is divided into a combination of near-field finite blocks and far-field infinite blocks, each block is unified to a standard parent domain through isoparametric mapping, the consistent treatment of shape function interpolation and numerical integration is realized, displacement and traction compatibility conditions are applied on the common edges between blocks, the force balance is met at the corner points, the interface coupling is realized through Lagrange multiplier or penalty method, the principal stress discrimination is completed at the Gauss point level, the compression or tension parameters are selected according to the stress sign, and thus the axisymmetric equivalent stiffness matrix is assembled.

7. The method according to claim 1, wherein, In the S50, the weight is adjusted according to the confidence of the measuring point and the distance from the loading center, when there are a small number of suspected abnormal observations, the loss form with robustness is allowed to be switched, in the application of multiple working conditions or multiple measuring sections, the joint target is formed by superimposing each working condition target according to the weight, so as to identify the shared or associated layer parameters at the same time.

8. The method according to claim 1, wherein, In the S60, the differential approximation of relative disturbance is adopted, the decomposition result of forward solving is reused, the gradient quality is improved through quasi-Newton update or adjoint approximation, after the evaluation is completed, the gradient or Jacobian and the weight matrix are transmitted into the S70.

9. The method according to claim 1, wherein, In the S70, in the case that the constraint switching is frequent or the boundary is activated, the feasibility is stably maintained in an active set or projection manner, the outer iteration takes the KKT condition, the constraint violation degree, the step length and the target value change as the joint stop criterion.

10. The method according to claim 1, wherein, In the S90, the iteration log includes the starting point, the constraint activation state and the line search record, and the key drawings include the black and white deflection contrast chart and the residual scatter chart.

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