A method, equipment, and medium for correcting the analytical model of dynamic response of pile foundations.

Abstract

This application discloses a method, device, and medium for correcting an analytical model of dynamic response of pile foundations, relating to the fields of non-destructive testing in geotechnical engineering, computational mechanics, and artificial intelligence. The method includes: acquiring geological survey parameters of the target pile foundation and collecting measured velocity response data; constructing an analytical model of dynamic response based on the geological survey parameters using Rayleigh-Love member theory, solving the model to obtain an initial analytical solution; constructing a physical information neural network to obtain a high-fidelity dynamic response field; differentiating the high-fidelity dynamic response field from the initial analytical solution to extract systematic deviations and constructing an explicit mathematical compensation operator; coupling the operator to the analytical model of dynamic response to form an augmented analytical model and generating a defect-free response baseline curve; and differentiating the measured velocity response data from the defect-free response baseline curve to obtain the defect reflection wave component.

Description

Technical Field

[0001] This application relates to the fields of non-destructive testing in geotechnical engineering, computational mechanics and artificial intelligence, and in particular to a method, equipment and medium for correcting an analytical model of dynamic response of pile foundations. Background Technology

[0002] As the underlying load-bearing structure of large infrastructure projects, the response characteristics of pile foundations under dynamic loads are crucial for evaluating pile integrity and bearing capacity. Current testing practices primarily rely on elastic wave theory, using velocity-time history curves after pile top excitation to deduce the pile's structural state. However, in actual engineering environments, pile foundations are not situated in a single medium but rather form a coupled system with highly nonlinear and damping-inhomogeneous soil and rock masses. Especially with the widespread adoption of large-diameter piles, geometric dispersion phenomena caused by three-dimensional lateral inertial effects, such as… Figure 1 As shown, the complex wave field scattering effect at local defects causes the dynamic flow field of the pile foundation to exhibit extremely strong nonlinear characteristics. There is a significant systematic deviation between traditional theoretical models and actual engineering conditions, posing a major challenge to accurate defect identification and quantitative evaluation.

[0003] Currently, there are two main approaches to predicting and correcting the dynamic response of pile foundations. One approach is based on idealized physical assumptions and forward analytical and numerical simulation methods. This focuses on solving the wave equation using analytical derivation or numerical simulation methods (such as the finite element method and finite difference method) starting from the mechanical mechanism. Essentially, this approach forcibly covers model structural defects with parameter uncertainties. When faced with errors dominated by nonlinear mechanisms, it often has extremely low convergence efficiency and is prone to multiple solutions, losing its explanatory power regarding physical mechanisms. The other approach is a data-driven prediction method based on deep learning mapping. This treats the dynamic response system as a black box, using the nonlinear activation function of neurons to fit the functional relationship between input and output, thereby achieving rapid end-to-end inference. Purely data-driven methods, lacking fundamental physical constraints, are prone to overfitting when processing sparse data, and the output results often violate physical logic, failing to provide highly confident feature support for subsequent semantic recognition and defect localization. Summary of the Invention

[0004] This application provides a method, device, and medium for correcting the analytical model of pile foundation dynamic response, in order to solve the following technical problems: the analytical theory in existing pile foundation dynamic response analysis is too idealistic, the numerical simulation is inefficient, and the pure data-driven model lacks physical logic.

[0005] In a first aspect, embodiments of this application provide a method for correcting an analytical model of the dynamic response of a pile foundation. The method includes: acquiring geological survey parameters of the target pile foundation and collecting measured velocity response data under low-strain excitation at the pile top; constructing an analytical model of the dynamic response based on the geological survey parameters using Rayleigh-Love member theory, and solving the analytical model to obtain an initial analytical solution of the target pile foundation under the current working condition; constructing a physical information neural network, wherein the governing equations and boundary conditions of the analytical model of the dynamic response are used as physical constraints, and the measured velocity response data are used as data constraints, to construct a multinomial coupling loss function corresponding to the physical information neural network; and based on the multinomial coupling loss function... The loss function is used to train the physical information neural network to obtain a trained physical information neural network. Based on the physical information neural network, a high-fidelity dynamic response field corresponding to the target pile foundation is obtained. The high-fidelity dynamic response field is differiated from the initial analytical solution to extract systematic deviations, and an explicit mathematical compensation operator is constructed. The explicit mathematical compensation operator is coupled to the dynamic response analytical model to form an augmented analytical model, and a defect-free response reference curve under the current working condition is generated based on the augmented analytical model. The measured velocity response data is differiated from the defect-free response reference curve to obtain the defect reflection wave component, wherein the defect reflection wave component is used to characterize the local impedance mutation characteristics of the target pile foundation.

[0006] Secondly, embodiments of this application also provide a pile foundation dynamic response analytical model correction device, the device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a pile foundation dynamic response analytical model correction method as described in the first aspect above.

[0007] Thirdly, embodiments of this application also provide a computer storage medium storing computer-executable instructions, which, when executed, implement a pile foundation dynamic response analytical model correction method as described in the first aspect above.

[0008] The method, equipment, and medium for correcting the analytical model of dynamic response of pile foundations provided in this application have the following beneficial effects: A deep learning architecture integrating classical mechanics mechanisms is constructed using Physical Information Neural Networks (PINNs) to achieve forward calculation of dynamic response under the constraints of physical laws. Subsequently, by introducing sparse field measured data as dynamic driving terms, the nonlinear approximation capability of PINNs is utilized to capture complex dynamic characteristics (such as nonlinear damping of soil and high-frequency dispersion distortion) that are difficult to cover by traditional analytical theories, outputting a high-fidelity response field with high confidence and physical consistency. Finally, by extracting the nonlinear deviation component between the high-fidelity output value and the initial analytical solution, a mathematical compensation term is explicitly constructed, thereby upgrading the traditional closed-loop analytical model to an analytical augmented model. In this way, the problem of directly solving complex nonlinear partial differential equations is cleverly avoided, realizing a reverse closed loop from theoretical prediction to measured-driven correction, significantly improving the discrimination accuracy and physical interpretability of pile foundation dynamic testing under complex working conditions. Attached Figure Description

[0009] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 A schematic diagram of the three-dimensional lateral inertial effect of a large-diameter pile; Figure 2 A flowchart illustrating a method for correcting an analytical model of dynamic response of a pile foundation, provided in an embodiment of this application; Figure 3 A simplified mechanical model diagram of pile-soil coupling provided in this application embodiment; Figure 4 A schematic diagram of theoretical analytical response and high-fidelity speed response waveforms provided for embodiments of this application; Figure 5 A schematic diagram of a signal decoupling and defect identification principle based on a dual-drive correction model of physics and data provided in this application embodiment; Figure 6 A schematic diagram of a physical and data-driven dual-drive correction and defect assessment framework for a pile foundation dynamic response analytical model provided in this application embodiment; Figure 7 This application provides a schematic diagram of a field implementation of low-strain dynamic testing for pile foundations. Figure 8 This is a schematic diagram of the internal structure of a pile foundation dynamic response analytical model correction device provided in an embodiment of this application. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] Currently, there are two main approaches to predicting and refining the dynamic response of pile foundations: Existing technology 1: Forward analytical and numerical simulation method based on idealized physical assumptions This type of technology focuses on solving wave equations from a mechanical perspective, using analytical derivation methods or numerical simulation methods (such as the finite element method and the finite difference method). While analytical methods offer high efficiency through closed-loop calculations, their underlying assumptions are often overly idealistic, failing to encompass the nonlinear damping evolution of soil and the slippage effect at contact interfaces. Numerical simulation methods, while improving modeling flexibility, are highly dependent on the setting of artificial boundary conditions and fine mesh generation. When dealing with discrepancies between theory and reality, these approaches typically employ an inverse approach of iterative parameter optimization, approximating the measured waveform by continuously adjusting macroscopic parameters such as material modulus and damping coefficients. This approach essentially uses parameter uncertainties to forcibly cover structural defects in the model; when faced with errors dominated by nonlinear mechanisms, it often exhibits extremely low convergence efficiency and is prone to multiple solutions, thus losing its explanatory power regarding physical mechanisms.

[0012] Existing technology 2: Data-driven prediction method based on deep learning mapping To avoid the cumbersome process of physical modeling, some existing technologies have begun to explore purely data-driven paths for predicting dynamic responses. This approach establishes complex nonlinear mappings between large amounts of sample data by constructing convolutional neural networks (CNNs) or recurrent neural networks (RNNs). The core logic of this technology is to treat the dynamic response system as a black box and use the nonlinear activation functions of neurons to fit the functional relationship between input and output, thereby achieving rapid end-to-end inference. However, in pile foundation engineering sites, measured data often exhibit significant sparsity and strong noise characteristics. Purely data-driven methods, lacking fundamental physical constraints, are prone to overfitting when processing such sparse data, and the output results often violate physical logic, failing to provide highly confident feature support for subsequent semantic recognition and defect localization.

[0013] In recent years, to address the limitations of purely data-driven models in terms of physical consistency and extrapolation generalization capabilities, the field has begun to explore a higher-order solution paradigm—hybrid-driven modeling techniques (such as Physical Information Neural Networks, PINNs). This approach no longer treats neural networks as purely "black-box" fitting tools, but rather introduces classical mechanics mechanisms into the deep learning framework, achieving synergistic constraints between data patterns and physical laws, thus providing a new path for solving complex dynamic problems.

[0014] The implementation path of this technical solution mainly includes the following key steps: (1) Construction of a loss function based on physical constraints. Unlike traditional deep learning, which relies solely on label errors for training, this method focuses on constructing a multinomial coupled loss function. In addition to the mean squared error term that includes the fitted observation data, it also utilizes automatic differentiation to transform the pile wave equation, boundary conditions, and initial conditions into residual terms that are embedded into the loss function. This mechanism ensures that the network, during optimization, not only approximates known sample points but is also subject to stringent constraints from the underlying physical mechanisms.

[0015] (2) Physically Guided Feature Mapping. Deep neural networks are used as approximators for continuous functions to establish a mapping relationship from spatiotemporal coordinates to physical field quantities. Within this framework, physical laws are treated as a special regularization operator, guiding the network to search for the optimal solution that conforms to the propagation characteristics of stress waves in the multidimensional parameter space. Thus, even with small samples or even unlabeled data, it is still possible to accurately approximate the dynamic flow field of stress waves by minimizing the physical residuals.

[0016] (3) Dynamic inference of physical consistency. In the model inference stage, since the network parameters have captured the implicit characteristics of the dynamic equations, their output results naturally satisfy the physical conservation law of pile foundation vibration. Compared with traditional methods, this scheme does not require explicit iterative integration, and can continuously provide the physical field distribution in the entire time domain. Moreover, it exhibits stronger robustness and physical robustness when facing working conditions outside the training set.

[0017] This technical solution effectively solves the problem of scale limitation of traditional numerical simulation under complex computing power by constructing a hybrid modeling paradigm that deeply couples mechanism and data, and corrects the distortion defects in physical logic of pure data-driven models. Thus, while ensuring physical consistency, it achieves high-precision and rapid inversion of the full-time and space-time evolution trajectory of stress waves.

[0018] Although the aforementioned existing technologies have promoted the development of pile foundation testing theory to some extent, the following technical defects and application bottlenecks still objectively exist regarding the core logic of analytical model correction and physical data-driven collaboration: 1. Limitations of parameter compensation in numerical simulation and conventional inversion methods (the aforementioned prior art) when dealing with model structure biases. Numerical simulation methods, when dealing with deviations between theoretical predictions and measured responses, primarily rely on manually adjusting macroscopic parameters such as material modulus or damping coefficients to approximate the measured waveforms. This approach essentially uses parameter uncertainties to forcibly cover structural flaws in the theoretical model. Since the geometric dispersion of large-diameter piles and the strong nonlinear mechanisms of soil in actual working conditions are not represented in the underlying analytical operators, simple parameter inversion cannot eliminate the systematic biases inherent in the model itself. Furthermore, when dealing with semi-infinite space wave problems, this method heavily relies on the setting of artificial boundary conditions and fine mesh generation, resulting in enormous computational resource consumption and failing to meet the timeliness requirements of real-time interpretation in engineering projects. The root cause of this deficiency lies in the lack of explicit extraction methods for nonlinear deviation components during stress wave propagation. Because it is impossible to quantitatively deconstruct theoretical blind spots (such as high-frequency dispersion and complex damping evolution) at the analytical level, the correction process often degenerates into numerical fitting lacking physical mechanism support, resulting in extremely low convergence efficiency, easy generation of multiple solutions, and loss of physical consistency of the corrected analytical model.

[0019] 2. The shortcomings of pure data-driven prediction methods (the aforementioned prior art 2) in terms of physical and logical constraints and adaptability to sparse data. Pure data-driven prediction methods attempt to circumvent complex physical modeling processes by constructing neural networks to establish a nonlinear mapping between pile-soil parameters and dynamic responses. However, in pile foundation engineering sites, measured data generally exhibit strong sparsity and environmental noise. Lacking the mandatory constraints of an analytical model as a physical benchmark, this approach is highly susceptible to severe overfitting when processing such data, leading to output waveforms that often violate the laws of momentum or energy conservation. This distortion of physical logic severely limits its application potential in the field of pile foundation integrity assessment, where safety requirements are extremely high. The core reason for this problem lies in the fact that traditional deep learning architectures are essentially a pure data fitting mode based on statistical correlation, rather than a physical solution system based on causal relationships. The loss function optimization process of the network model is driven solely by data bias. Because the dynamic equations of stress wave propagation are not embedded into the underlying model, the model searches for approximate solutions in a high-dimensional solution space unconstrained by physical laws, failing to provide a feature benchmark with high confidence and mechanical logic support for subsequent defect localization and quantitative evaluation.

[0020] 3. Bottlenecks of hybrid-driven modeling techniques (similar to the above-mentioned techniques) in terms of analytical model enhancement and bias explicitness. While hybrid-driven modeling techniques, exemplified by PINNs, introduce physical equation residuals into the loss function, from the perspective of analytical model correction, the results are still implicitly mapped in the form of weights and biases of deep neural networks. This implicit mapping mechanism leads to the inherent systematic biases of the theoretical model (such as three-dimensional inertial effects) being highly coupled with the actual physical defects of the pile body within the neuron parameters, making it impossible to explicitly decouple the two at the physical level. Furthermore, these approaches focus on using the network to fully replace the formula solution rather than providing targeted enhancements to the analytical model, making it difficult to form a hybrid architecture with rigorous analytical principal terms and explicit data-driven compensation. The core reason for this problem is that existing hybrid-driven architectures lack an augmented modeling logic, namely, the inability to identify and quantify structural deficiencies in analytical formulas at specific feature frequency bands or spatial scales. This substitution rather than correction approach prevents the extraction of analytically expressible mathematical compensation operators from the trained model, limiting the model's ability to make targeted corrections when dealing with theoretical blind spots such as highly nonlinear mechanisms. It also prevents the correction results from directly participating as explicit algebraic operators in the automatic evaluation of upper-level intelligent inference systems.

[0021] In summary, the key bottleneck in the field of pile foundation dynamic testing is to break away from the traditional mindset of optimizing underlying parameters and replacing them with black boxes, and to use physical laws as constraints and benchmarks. This involves the explicit extraction and analytical compensation of nonlinear deviation components to construct an augmented analytical model that combines theoretical rigor with high-fidelity experimental results.

[0022] To address the aforementioned problems, this application provides a method for correcting the analytical model of pile foundation dynamic response based on a dual-driven approach of physics and data. The technical solution proposed in this application will be described in detail below with reference to the accompanying drawings.

[0023] Figure 2 A flowchart illustrating a method for correcting an analytical model of dynamic response of a pile foundation, as provided in an embodiment of this application. Figure 2 As shown in the embodiment of this application, a method for correcting the analytical model of dynamic response of pile foundations specifically includes the following steps: Step 201: Obtain the geological survey parameters of the target pile foundation and collect the measured velocity response data under low strain excitation at the pile top.

[0024] Step 202: Based on the geological survey parameters, construct a dynamic response analytical model using Rayleigh-Love member theory, and solve the dynamic response analytical model to obtain the initial analytical solution of the target pile foundation under the ideal state in the current working condition.

[0025] In one possible implementation, solving the dynamic response analytical model to obtain the initial analytical solution of the target pile foundation under the ideal state in the current working condition includes: The control equations and boundary conditions in the dynamic response analytical model are subjected to Laplace transformation, which transforms the partial differential equations into ordinary differential equations with respect to depth z, and the general solution in the Laplace domain is obtained by solving the general solution. Using the impedance function recursion method, combined with the boundary conditions at the top and bottom of the pile, the undetermined coefficients are determined to obtain the velocity response in the Laplace domain. The initial velocity response curve in the time domain is obtained through inverse Laplace transform or numerical inversion.

[0026] In practical applications, large-diameter floating piles can be simplified to, for example... Figure 3 The simplified mechanical model of pile-soil coupling shown is as follows: Figure 3 middle, r p For the radius of large-diameter floating piles, H p , H fp These refer to the lengths of the semi-embedded large-diameter floating bearing piles and the diffused loose soil piles, respectively. θ For the diffusion angle of the loose soil pile, k s , c s These are the stiffness coefficient of the spring and the viscous damping coefficient of the damper, respectively. P ( t ) represents the simple harmonic load applied to the top of the pile. r Radial coordinates, z The vertical coordinates are... o The origin of the coordinate system is used. The longitudinal vibration of the pile is described using Rayleigh-Love rod theory, which considers lateral inertial effects. The soil along the pile can be equivalently represented as a continuously distributed spring-damped system along the pile. The soil at the pile tip can be modeled using a variable cross-section virtual soil pile to simulate the equivalent impedance effect of stress diffusion from the pile tip to the surrounding soil along the diffusion angle. The bottom of the pile is designed as a rigid support. A harmonic load can be applied to the pile top for excitation. P ( t ), to simulate the excitation input in low strain detection.

[0027] To accurately characterize the longitudinal vibration of large-diameter piles, the Rayleigh-Love bar theory, which considers lateral inertial effects, can be used. The constructed partial differential equation governing the pile is as follows: (1) In the formula, , , , , , These are the elastic modulus, cross-sectional area, density, Poisson's ratio, radius, and displacement of the solid pile. Let be the stiffness coefficient of the spring. is the viscous damping coefficient.

[0028] In the above formula, It is a time t A changing function can represent a certain depth of the pile. z At a certain moment t The longitudinal displacement (i.e., the axial displacement along the pile length).

[0029] The formula for calculating the elastic modulus of a solid pile is as follows: .

[0030] in, This represents the elastic longitudinal wave velocity.

[0031] Based on the low-strain testing conditions for pile foundations, and assuming that the displacement and velocity of all mass points in the pile are zero at t=0, the initial conditions can be expressed as follows: (2) (3) in, It indicates the displacement at a fixed time t=0 (the starting time).

[0032] For large-diameter piles, the incident wave in low-strain testing is often input as a local excitation, with the applied excitation being a simple harmonic load, expressed as: (4) in, This represents the peak amplitude of the excitation force. Let be the pulse duration. The above formula can be used as the boundary condition for the pile top.

[0033] In practical applications, the pile bottom in the loose soil can be assumed to be a rigid support. In the longitudinal direction, the boundary conditions of the pile (the force boundary at the top and the displacement boundary at the bottom of the pile during longitudinal vibration) can be expressed as: (5) (6) in ， Representative moment t The displacement at the coordinates of the bottom of the pile (i.e., the bottom of the loose soil pile). , These represent the lengths of the semi-embedded large-diameter floating bearing pile and the diffused loose soil pile, respectively. The sum of the two represents the total equivalent distance of stress wave propagation in the pile body. When the wave propagates to this depth coordinate, it is considered to have reached the bottom boundary of the pile.

[0034] In the radial direction, the relationship between the pile and the soil it contacts can be expressed as pile-soil displacement continuity and pile-soil stress continuity, which can be represented as follows: (7) (8) In pile-soil coupled systems, the pile body and soil are usually considered as two different solution domains, and different subscripts are used to distinguish their displacements. u1 represents the axial displacement function of the pile body, and u2 represents the axial displacement function of the soil at the pile tip (i.e., the virtual soil pile). The meaning of the above formula (7) is that in At this point, the displacement (u1) of the pile body must be equal to the displacement (u2) of the surrounding soil. This ensures that the pile-soil interface does not slip or separate, demonstrating geometric continuity.

[0035] The equivalent elastic modulus of the virtual soil pile, This represents the equivalent cross-sectional area of ​​the virtual soil pile. The above formula (8) indicates that at the contact surface at the bottom of the pile, the axial force squeezed by the left pile body must be equal to the reaction force borne by the virtual soil pile on the right.

[0036] The analytical solution obtained based on the Laplace transform and impedance function recursion method is as follows: (9) in, The term "dimensional velocity response" refers to the dimensionless velocity response at the pile top. It is a purely numerical waveform derived from the frequency response function and the integral of the impulse characteristic. It is used to accurately characterize the waveform profile, phase change, and time evolution of the velocity response at the mathematical level, and it does not have physical units. It is a dimensional physical velocity response at the pile top, representing the actual vibration velocity time history at the pile top (unit: m / s). To apply the maximum excitation force to the top of the pile, The density of the pile material, Let be the cross-sectional area of ​​the pile. The longitudinal wave velocity is the velocity of the pile material.

[0037] (10) in, It is a dimensionless velocity response. The complex frequency domain velocity admittance (transfer function) of the pile-soil system. T The dimensionless pulse width of the excitation force. ω The angular frequency is t. It should be noted that in the formula jwt on the right, t is the time delay of the stress wave traveling back and forth at the pile bottom or pile defect, and j is the imaginary unit.

[0038] (11) in, For the complex frequency domain velocity admittance of the pile-soil system, , The dimensionless radius of the pile body. The radius of the pile body, l n Where is the wavelength, and j is the imaginary unit. It is a dimensionless frequency parameter. ; The equivalent shear deformation coefficient of the soil along the pile shaft represents the damping contribution of the soil along the pile shaft to the vibration of the pile shaft. The elastic modulus of the pile body; These are the characteristic time parameters of the pile body; The equivalent shear stiffness provided by the soil along the pile to the pile body. This is the normalized wavenumber parameter for the soil impedance at the pile tip; The normalized phase angle is the soil impedance at the pile tip.

[0039] Thus, by performing a Laplace transform on the governing equation (1) and the boundary conditions (2)-(8), the partial differential equation is transformed into an ordinary differential equation with respect to depth z, the general solution of which has the form of a superposition of a downward wave and an upward wave. Using the impedance function recursion method, combined with the pile top boundary conditions and the pile bottom impedance boundary conditions, the undetermined coefficients are determined, and the velocity response expression in the Laplace domain is obtained. Then, through the inverse Laplace transform (analytical or numerical inversion), the initial velocity response curve in the time domain is obtained, which serves as the initial analytical benchmark for subsequent model correction.

[0040] In practical applications, the initial analytical solution described above is a theoretical benchmark response derived from the model based on geological survey parameters, under the assumptions of defect-free geometry, linear viscoelastic soil reaction force, and idealized boundary conditions. This benchmark response has a clear physical meaning and a closed mathematical form, but it does not yet include complex factors such as nonlinear damping, parameter spatial variability, and local defect scattering in the actual pile-soil system. Therefore, it can serve as a reference and correction object for PINN learning in subsequent steps, rather than a precise description of the actual response.

[0041] Step 203: Construct a physical information neural network.

[0042] Specifically, the control equations and boundary conditions of the dynamic response analytical model are used as physical constraints, and the measured velocity response data are used as data constraints, in order to construct the multinomial coupling loss function corresponding to the physical information neural network.

[0043] In one possible implementation, the multiple coupling loss function includes: The physical residual term is used to constrain the output of the physical information neural network to satisfy the control equation. Boundary condition terms are used to constrain the output of the physical information neural network to satisfy the boundary condition; A data fitting term is used to constrain the output of the physical information neural network to approximate the measured velocity response data.

[0044] It should be noted that the above-mentioned pile foundation wave equation involves multiple physical quantities with vastly different dimensions and magnitudes. If the original physical quantity (z,t) is directly used as the network input, the automatic differential chain rule can repeatedly multiply and divide these vastly different coefficients, resulting in inconsistent magnitudes of the terms in the PDE residuals, the loss function being dominated by the maximum term, the gradient update direction being distorted, and gradient explosion or diffusion occurring. The training may appear to be decreasing, but the physical residuals can never converge to a reasonable level.

[0045] Therefore, considering the large range of parameters in pile foundation engineering, the first step is to implement dimensionless transformation techniques to eliminate the risk of gradient explosion. This is achieved by setting dimensionless variables. , , (in, ), Substituting these dimensionless variables into the original governing equations and boundary conditions allows the governing equations to be mapped to a safe computational domain of [-1, 1]. The residual terms are numerically weighted fairly, laying a numerically stable foundation for subsequent training. In the above formula, This represents the elastic longitudinal wave velocity.

[0046] Subsequently, a fully connected feedforward neural network was constructed, using tanh, which has high-order continuous derivative properties, as the activation function to ensure that the calculated flow field is infinitely differentiable with respect to spatiotemporal coordinates. tanh is a C∞ smooth function, and its automatic differentiation allows for infinite-order differentiation. The output range of tanh is (…). 1,1), which is beneficial for numerical stability and has a good fitting ability for the oscillatory solution of the wave problem. The practical meaning of infinite order differentiability in the context of PINNs is that the response field of the network output is a smooth differentiable function in the sense of automatic differentiation, and its partial derivatives of all orders can be stably calculated. Thus, the PDE residual can faithfully reflect the degree to which the wave equation is violated at a certain point.

[0047] Subsequently, multiple coupling loss functions can be constructed: (12) in, The physical residuals are calculated by substituting the network output into the dimensionless Rayleigh-Love equation using automatic differentiation techniques. , Constrained boundary excitation and initial static state; The mean square error between the sparse measured velocity points on site and the network prediction values ​​is then used to dynamically incorporate the actual observation patterns into the optimization objective. , , , These correspond to adjustment coefficients (weights) for the four errors mentioned above, used to balance the importance of different error terms.

[0048] This architecture not only subjectes the neural network to the rigid constraints of physical laws but also endows it with the data-driven force to converge to real-world working conditions. Thus, through joint optimization, the physical information neural network, under the rigid constraints of physical laws, possesses the data-driven force to converge to real-world pile foundation working conditions, thereby outputting a high-fidelity dynamic response field that is both conserved and comparable to actual measurements.

[0049] Step 204: Train the physical information neural network based on the multiple coupling loss functions to obtain the trained physical information neural network, and obtain the high-fidelity dynamic response field corresponding to the target pile foundation based on the physical information neural network.

[0050] In one possible implementation, training the physical information neural network based on the multiple coupling loss functions to obtain the trained physical information neural network includes: Based on the aforementioned multiple coupling loss functions, the weight parameters of the physical information neural network are updated through an optimization algorithm until the multiple coupling loss functions converge to a preset threshold, thereby obtaining the trained physical information neural network. The optimization algorithm includes: using the Adam optimizer for coarse-tuning training, and switching to the L-BFGS optimizer for fine-tuning training when the gradient norm of the multiple coupling loss functions is less than a preset gradient norm threshold. During the training process of the physical information neural network, a Latin hypercube sampling strategy is used to arrange the points of the physical equations in the dimensionless spatiotemporal solution domain, which together with the measured velocity response data constitute the training sample space.

[0051] In one possible implementation, the training of the physical information neural network is performed in one of the following ways: Perform a complete training process for the target pile foundation from its initial state; Based on the pre-trained model, transfer learning or parameter fine-tuning is performed using the measured velocity response data of the target pile foundation to be tested.

[0052] In practical applications, the generated augmented analytical model or defect-free response baseline curve can also be directly called based on the calibrated model of the same site or similar pile type.

[0053] In practical applications, physical laws and observational data are used to jointly optimize neural network parameters, thereby obtaining a dynamic response field that approximates the real working conditions. Before training, collocation points are first set up in the dimensionless spatiotemporal solution domain. A Latin hypercube sampling strategy is used to generate uniformly distributed collocation points for the physical equations, and sparse measured data points collected on-site are simultaneously loaded to construct a training sample space with global mechanism constraints and local data guidance.

[0054] The training process employs a phased collaborative optimization technique to ensure high-precision convergence of the model. In the coarse-tuning phase, the Adam optimizer is used for initial iterations. Through its adaptive first-order and second-order momentum prediction mechanisms, it achieves rapid gradient descent on the loss function surface, which exhibits highly nonlinear characteristics. This algorithm leverages the momentum gradient properties to effectively traverse noisy regions within the loss function, rapidly searching for a globally suboptimal solution in a broad, high-dimensional parameter space, quickly reducing the loss to a preset initial threshold.

[0055] When the loss function's descent becomes gradual and the gradient norm enters a low-sensitivity region—for example, when the loss function's descent within a preset number of consecutive steps is less than a preset descent threshold, or when the gradient norm of the loss function is less than a preset gradient norm threshold—the algorithm switching mechanism can be automatically triggered to enter the fine-tuning stage. In this stage, the L-BFGS algorithm is introduced, utilizing historical gradient information to construct an approximation of the inverse Hessian matrix, achieving convergence optimization at the second derivative level. Since PINNs have extremely high requirements for the accuracy of the partial differential equation residuals, L-BFGS, through a precise line search strategy, can further converge the control equation residuals to an extremely low order of magnitude, ensuring that the displacement and velocity fields output by the network not only closely match the measured data but also possess stringent physical consistency.

[0056] After the model converges and the weights and bias parameters are fixed, a high-fidelity velocity response curve covering the entire time and space can be output by giving the pile top coordinates in the input layer and performing continuous-time inference. Based on physical mechanism constraints, this curve explicitly characterizes the geometric dispersion distortion caused by the large diameter effect of the pile foundation by adaptively capturing the energy attenuation and phase shift characteristics in the measured data, and implicitly absorbs the nonlinear damping evolution law exhibited by the soil around the pile due to strong disturbance. Compared with the initial analytical solution, the response flow field obtained in the above steps realizes dynamic compensation for the blind zone of the analytical theory, and constitutes a high-confidence target field for subsequent extraction of explicit compensation operators and completion of the augmentation and correction of the analytical model.

[0057] Step 205: Difference the high-fidelity dynamic response field with the initial analytical solution to extract systematic deviations and construct an explicit mathematical compensation operator.

[0058] In one possible implementation, the step of differencing the high-fidelity dynamic response field with the initial analytical solution to extract systematic deviations includes: The high-fidelity dynamic response field and the initial analytical solution are subtracted by vector at the same time node to obtain the time-domain deviation vector, thereby obtaining the systematic deviation. The systematic deviation includes at least one of the following: phase lag and waveform broadening caused by the geometric dispersion effect induced by three-dimensional lateral inertia; and amplitude attenuation rate deviation caused by the nonlinear damping evolution of the pile-soil contact interface.

[0059] In practical applications, differential stripping is first performed to obtain the high-fidelity speed response curve output by the trained physical information neural network under defect-free operating conditions. The initial analytical solution obtained above Perform timeline alignment, such as Figure 4 As shown, point-to-point vector subtraction is performed using the same discrete clock array to extract the nonlinear residual components that are neglected due to the overly idealistic nature of traditional analytical theory. The calculation formula is as follows:

[0060] The time-domain bias vector obtained here Physically, this corresponds to systematic deviations in the dynamic response of large-diameter pile foundations that are not covered by classical theory. These mainly include: the geometric dispersion effect caused by three-dimensional lateral inertia, i.e., the difference in phase velocity of different frequency components caused by radial expansion and contraction of large-diameter cross sections, which manifests as waveform broadening and phase tailing; and the nonlinear damping evolution of the pile-soil contact interface, i.e., the local slippage and hysteretic energy dissipation of soil under strong dynamic loads cause the equivalent damping to deviate from the linear assumption, which manifests as a deviation in the amplitude attenuation rate.

[0061] In one possible implementation, the explicit mathematical compensation operator is a damped oscillation function, as shown in the following formula:

[0062] in, This is the initial amplitude deviation correction coefficient, used to correct the energy transfer deviation between the dynamic response analytical model and the actual dynamic input at the moment of transient excitation; The nonlinear damping dissipation rate is used to characterize the energy decay rate caused by shear slippage of the soil and rock mass along the pile and the viscoelasticity of the material. This is a high-frequency coupling correction frequency used to compensate for energy coupling loss between the lateral inertial fluctuations and the longitudinal principal stress waves of the pile. The phase lag angle of the three-dimensional effect is used to quantify the degree of phase tailing and waveform distortion caused by geometric dispersion during the propagation of stress waves in large-diameter piles.

[0063] In one possible implementation, the parameters of the explicit mathematical compensation operator are used to identify the optimal solution for each physical parameter by minimizing the approximation residual between the explicit mathematical compensation operator and the systematic deviation in the time domain.

[0064] In practical applications, to overcome the technical bottleneck that traditional neural network prediction results cannot be directly used for analytical formula correction due to their black-box nature, nonlinear function fitting and symbolic regression techniques can be introduced to transform the discrete residual signals. Reconstructed into a continuous explicit mathematical compensation operator with a clear physical mechanism. The specific mathematical compensation operator is fitted to a damped oscillation form, and its expression is: .

[0065] In this compensation operator, This is the initial amplitude deviation correction coefficient, used to correct the energy transfer deviation between the dynamic response analytical model and the actual dynamic input at the instant of the transient excitation. The nonlinear damping dissipation rate explicitly characterizes the energy decay rate caused by shear slippage of the soil and rock mass along the pile and the viscoelasticity of the material. This is a high-frequency coupling correction frequency used to compensate for energy coupling loss between the lateral inertial fluctuations and the longitudinal principal stress waves of the pile. The phase lag angle of the three-dimensional effect explicitly quantifies the degree of phase tailing and waveform distortion caused by geometric dispersion during the propagation of stress waves in large-diameter piles.

[0066] Finally, by minimizing in the time domain and By approximating the residuals, the optimal solutions for each physical parameter are identified, thus completing the key transformation from implicit network prediction to white-box analytical operators.

[0067] By employing differential stripping operations, the bias information, originally scattered across tens of thousands of weight parameters in a neural network, is explicitly extracted into a time-domain bias curve. This releases the theoretically unrepresented portion from the black box into a visible and analyzable signal. Secondly, by introducing a damped oscillation function with a physical skeleton to parametrically fit this bias curve, the complex waveform differences are compressed into a few parameters with clear mechanical significance, including correction coefficients, nonlinear damping rates, frequency, and phase lag angle. This translates the implicitly learned experience of the neural network into physical quantities that engineers can understand, verify, and adjust. Finally, this compensation function exists independently in a closed analytical form, no longer dependent on any neural network framework or weight file, thus enabling explicit augmentation and correction of the response model. This transformation process overcomes the technical bottlenecks of traditional deep learning methods, such as uninterpretable models and the inability to embed results into analytical formulas, enabling data-driven compensation of theoretical models to leap from theoretical model compensation to white-box enhancement.

[0068] Step 206: Couple the explicit mathematical compensation operator to the dynamic response analytical model to form an augmented analytical model, and generate the defect-free response baseline curve under the current working condition based on the augmented analytical model.

[0069] In one possible implementation, the explicit mathematical compensation operator is coupled to the dynamic response analytical model to form an augmented analytical model, including: The explicit mathematical compensation operator is fed back into the dynamic response analytical model in the form of algebraic superposition to form an augmented analytical model; The augmented analytical model includes a mechanistic principal term and an explicit compensation term. The mechanistic principal term is the initial analytical solution, which provides the physical framework and conservation law constraints for stress wave propagation. The explicit compensation term is the damped oscillation function, which is used to embed specific site damping and dispersion characteristics.

[0070] In practical applications, the mathematical compensation operator described above, which is explicitly constructed and has its parameters identified, can be used. Feedback is injected into the initial analytical model in the form of algebraic superposition to construct an augmented analytical model that incorporates the complex dynamic characteristics of the field. Its calculation formula is expressed as follows: .

[0071] The result obtained here This is the constructed augmented analytical model. Because this model not only retains the rigorous wave equation mechanism principal terms in the traditional analytical solution, but also incorporates explicit compensation terms that include specific site damping and dispersion characteristics, it can more closely approximate the complex boundaries of actual engineering sites.

[0072] Subsequently, a site benchmark is generated. Using this augmented analytical model, forward fluctuation calculations are performed to output a high-confidence defect-free response benchmark curve for the current working condition. This benchmark curve pre-filters out geometric dispersion clutter caused by the three-dimensional lateral inertia of large-diameter piles, as well as high-frequency signal distortion caused by soil nonlinearity, thus providing a highly physically consistent defect-free benchmark line. This provides a high-fidelity reference for accurately identifying and removing actual physical defects in the pile body amidst complex background noise. The aforementioned defect-free response benchmark curve is actually a corrected / augmented version of the initial analytical model, more closely resembling the true defect-free response pattern under the current working condition. Therefore, it can provide a physically consistent reference for subsequent differential defect extraction.

[0073] In practical applications, high-precision quantitative identification of pile defects can be achieved based on augmented analytical benchmarks. First, a time-domain signal decoupling process is performed to convert the actual measured curves containing defects collected on-site. The augmented baseline curve of the defect-free state generated above Perform timeline alignment and differential subtraction, the calculation formula of which is expressed as follows: .

[0074] This differential operation effectively filters out and cancels out pseudo-defect clutter caused by three-dimensional geometric dispersion effects and complex pile-soil nonlinear background interference in the measured signal, thereby extracting the defect reflection wave component caused only by local impedance abrupt change in the pile body. . Figure 5 This diagram illustrates the signal decoupling and defect identification principle based on a dual-drive correction model using both physical and data principles, as provided in this application embodiment. The physical principle of this differential operation lies in the fact that the augmented reference curve has been pre-incorporated with normal background features under defect-free conditions, such as geometric dispersion waveform broadening, phase tailing, and nonlinear damping attenuation of the soil, through explicit compensation terms. Therefore, the aforementioned background components in the measured curve cancel each other out after subtraction with the reference curve, while the additional reflection disturbance caused by local impedance abrupt changes (defects) in the measured curve is retained, forming a pure defect reflection wave component.

[0075] Step 207: Difference the measured velocity response data with the defect-free response reference curve to obtain the defect reflection wave component.

[0076] The defect reflected wave component is used to characterize the local impedance abrupt change characteristics of the target pile foundation.

[0077] The aforementioned defect reflection wave components can be used to evaluate the quality of the target pile foundation.

[0078] In one possible implementation, after obtaining the defect-reflected wave component, the method further includes: Based on the defect reflection wave components, the arrival time of the defect reflection wave is generated; Based on the arrival time of the defective reflected wave and the designed pile length, calculate the corrected wave velocity under the current working condition; The defect depth is calculated based on the corrected wave velocity and the arrival time of the defect reflected wave. Determine the nature of the defect based on the relationship between the polarity of the reflected wave and the direction of the incident wave; Based on the absolute amplitude of the main peak of the defect reflection wave, and combined with the formula for the one-dimensional stress wave reflection coefficient, the percentage change in cross-sectional area at the defect is obtained by inversion.

[0079] Subsequently, defect feature extraction and quantitative evaluation were performed. Wave velocity self-calibration was conducted using the pile bottom reflection signal from the same pile. This was achieved by identifying the decoupled... The starting point of the significant abrupt change pulse in the curve is used to determine the arrival time of the defect-reflected wave. Utilizing the pile bottom reflection time and the known design pile length First, calculate the corrected wave velocity under the current operating conditions. , This method avoids the errors that may be introduced by using theoretical or empirical wave velocities, and makes the wave velocity value match the actual dispersion characteristics of the current pile-soil system.

[0080] Furthermore, based on the principle of time-domain reflection, the specific depth of the defect can be obtained. .

[0081] Based on this, both qualitative and quantitative discrimination can be performed: In qualitative polarity discrimination, if the main peak direction of the defect reflection pulse is consistent with the direction of the excitation pulse at the pile top, according to the one-dimensional wave transmission and reflection law, it is determined that a decrease in pile impedance has occurred at that depth, and it is diagnosed as a defect such as diameter reduction, segregation, or pile breakage; if the main peak direction of the reflection pulse is opposite to the direction of the excitation pulse, it is diagnosed as diameter expansion. In quantitative amplitude analysis, the absolute amplitude of the main peak of the defect reflection wave is extracted, and combined with the one-dimensional stress wave reflection coefficient calculation formula, the percentage reduction or expansion of the cross-sectional area at the defect is calculated, ultimately achieving a quantitative evaluation of the location, nature, and severity of local defects in large-diameter pile foundations.

[0082] In this embodiment, a deep learning architecture integrating classical mechanics mechanisms is constructed using Physical Information Neural Networks (PINNs) to achieve forward calculation of dynamic response under the constraints of physical laws. Subsequently, by introducing sparse field measured data as dynamic driving terms, the nonlinear approximation capability of PINNs is used to capture complex dynamic characteristics (such as nonlinear damping of soil and high-frequency dispersion distortion) that are difficult to cover by traditional analytical theories, outputting a high-fidelity response field with high confidence and physical consistency. Finally, by extracting the nonlinear deviation component between the high-fidelity output value and the initial analytical solution, a mathematical compensation term is explicitly constructed, thereby upgrading the traditional closed-loop analytical model to an analytical augmented model. In this way, the problem of directly solving complex nonlinear partial differential equations is cleverly avoided, realizing a reverse closed loop from theoretical prediction to measured-driven correction, significantly improving the discrimination accuracy and physical interpretability of pile foundation dynamic detection under complex working conditions.

[0083] Figure 6This paper presents a framework diagram for a dual-driven correction and defect assessment of a pile foundation dynamic response analytical model, which can be divided into three logical layers: a data acquisition layer, a core calculation layer, and a correction and decoupling application layer. First, in the data acquisition layer, both field hammer test data and the pile body analytical solution based on the wave equation are simultaneously inputted, serving as the foundational input for subsequent analysis. In the core calculation layer, an initial analytical baseline curve is generated based on the above inputs, and error diagnosis is initiated by calculating the total missing function between theoretical and measured values. During this process, the algorithm constructs a multi-source loss function including physical constraint equation loss, initial boundary condition loss, and measured data matching loss, and iteratively solves it using the Adam and L-BFGS collaborative optimization algorithms to minimize the total loss, ultimately outputting a high-fidelity dynamic response field. Subsequently, the application layer for correction and decoupling is entered. The high-fidelity dynamic response field is differentiated from the initial analytical solution. An explicit mathematical compensation operator is constructed through mathematical fitting and coupled back to the original model, forming a more accurate augmented analytical model. Finally, this model is used to forward calculate the waveform of the defect-free pile foundation under the current working conditions. By performing a difference operation with the measured signal, background interference is accurately removed, thereby achieving a quantitative assessment of the depth, properties, and degree of pile defects. This method, by embedding physical laws into the neural network training process, effectively solves the problems of insufficient accuracy and inconsistency with physical properties in traditional detection, significantly improving the accuracy and reliability of defect diagnosis.

[0084] The pile foundation dynamic response analytical model correction method in this application embodiment is mainly applied to the integrity detection and evaluation of complex working conditions such as large-diameter cast-in-place piles and ultra-long piles in actual engineering. The implementation process of the above method is described in detail below with reference to the accompanying drawings and specific implementation examples.

[0085] 1. Engineering application scenario setup This embodiment uses a large-diameter, deep-cast-in-place pile in the foundation engineering of a major bridge as an application scenario. The pile foundation has a diameter D of 2.5 meters and a pile length L of 60 meters. Due to the huge pile diameter, the geometric dispersion phenomenon caused by lateral inertia is very serious during low-strain reflected wave detection, resulting in a large amount of clutter in the shallow part of the pile body in the measured curve, which can easily mask the true defect signal.

[0086] At the implementation site, a high-sensitivity velocity sensor was first installed at the top of the pile, and the velocity-time history curve at the top of the pile was obtained by vibration with a force hammer. Figure 7 This is a schematic diagram of a field implementation of low-strain dynamic testing for pile foundations. Due to the complex field environment and limited measurement points, the acquired measured data exhibits significant sparsity and environmental noise characteristics, serving as the driving factor for subsequent PINNs in the field.

[0087] 2. Construct the initial analytical baseline model First, based on preliminary geological survey parameters (such as soil properties and concrete wave velocity), technicians used Rayleigh-Love rod theory and variable cross-section virtual soil pile theory to construct a dynamic analytical model of the pile-soil coupling system.

[0088] Implementation method: Through analytical derivation, the initial theoretical velocity curve of the ideal state (ignoring nonlinear damping and dispersion loss) under this working condition is calculated.

[0089] Current situation description: The initial analytical curve at this time serves as a physical benchmark. Although it has a rigorous logic, its waveform trend deviates significantly from the measured curve in terms of phase and amplitude attenuation due to overly ideal assumptions.

[0090] 3. Perform PINNs calculus driven by both physics and experimental data. The partial differential equations (PDEs) in the initial analytical model are used as rigid constraints, and the sparse measured data collected on-site are used as guiding constraints. Both are input into the physical information neural network processing system.

[0091] Computational logic: During training, the neural network ensures that the output results satisfy the laws of the wave equation through automatic differentiation; at the same time, by minimizing the error between the model and the measured data points, it forces the model to move closer to the real working conditions.

[0092] Output: The aforementioned physical information neural network ultimately outputs a high-fidelity dynamic response field. This response field not only conforms to the wave evolution law but also accurately captures the phase lag and nonlinear damping characteristics of the soil caused by the large diameter effect in the field.

[0093] 4. Explicit extraction of bias components from analytical models Implementation method: Compare the high-fidelity response curve output by the above PINNs with the above initial analytical solution using differential comparison.

[0094] Extraction content: Through differential stripping, the residual components between the two are explicitly extracted. This residual represents the structural deficiencies of the initial analytical model when dealing with specific engineering environments (such as frequency-related damping losses and phase deviations).

[0095] 5. Construct an augmented analytical model and upgrade the analytical model. Operational details: The extracted deviation components are transformed into an explicit mathematical compensation operator through function fitting.

[0096] Correction result: The compensation operator is fed back and superimposed into the initial analytical model formula, thereby constructing an augmented analytical model. This model not only retains the framework of the original analytical theory, but also incorporates complex field environment characteristics through the compensation term, achieving an upgrade from a general analytical solution to an engineering adaptive analytical solution.

[0097] 6. Engineering solutions and signal decoupling applications The modified augmented analytical model was directly applied to the pile foundation quality evaluation of this batch of projects: (1) Geometric interference removal: A reference waveform in a defect-free state is generated using an augmented analytical model. This reference waveform is then superimposed in phase with the field measured signal and the difference is calculated.

[0098] (2) Precise Judgment: By performing subtraction, false defect signals caused by large-diameter geometric effects in the measured signal are precisely eliminated. Engineers only need to analyze the pure residual signal after elimination. If there is an abnormal reflected wave at a specific location in the residual signal, the actual location of the diameter reduction, segregation, or fracture can be determined based on the arrival time, polarity, and amplitude of the reflected wave.

[0099] 7. Implementation Results Description This implementation method clearly restores the signals of large-diameter piles that were previously uninterpretable due to three-dimensional geometric dispersion. This method not only solves the problem of discrepancies between analytical models and actual working conditions in traditional methods, but also achieves precise stripping of complex dynamic characteristics through an explicit compensation mechanism, significantly improving the accuracy and confidence level of pile foundation integrity detection.

[0100] The above are embodiments of the method proposed in this application. Based on the same inventive concept, embodiments of this application also provide a pile foundation dynamic response analytical model correction device, the structure of which is as follows: Figure 8 As shown.

[0101] Figure 8 This is a schematic diagram of the internal structure of a pile foundation dynamic response analytical model correction device provided in an embodiment of this application. Figure 8 As shown, the device includes: At least one processor 801; And a memory 802 that is communicatively connected to at least one processor; The memory 802 stores instructions that can be executed by at least one processor. The instructions are executed by at least one processor 801 so that at least one processor 801 can: execute the above-described pile foundation dynamic response analytical model correction method.

[0102] Some embodiments of this application provide corresponding to Figure 1 A non-volatile computer storage medium stores computer-executable instructions, which are configured to execute the above-mentioned pile foundation dynamic response analytical model correction method.

[0103] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments for IoT devices and media are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0104] Those skilled in the art will understand that embodiments of this application can be provided as methods or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0105] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0108] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0109] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0110] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0111] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0112] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the scope of the claims of this application.

Claims

1. A pile foundation dynamic response analytical model correction method, characterized in that, The method includes: Obtain the geological survey parameters of the target pile foundation and collect the measured velocity response data under low strain excitation at the pile top; Based on the geological survey parameters, a dynamic response analytical model is constructed using Rayleigh-Love member theory, and the dynamic response analytical model is solved to obtain the initial analytical solution of the target pile foundation under the current working conditions. A physical information neural network is constructed, wherein the control equations and boundary conditions of the dynamic response analytical model are used as physical constraints, and the measured velocity response data are used as data constraints, so as to construct the multinomial coupling loss function corresponding to the physical information neural network. The physical information neural network is trained based on the multiple coupling loss functions to obtain the trained physical information neural network, and a high-fidelity dynamic response field corresponding to the target pile foundation is obtained based on the physical information neural network. The high-fidelity dynamic response field is differentially divided with the initial analytical solution to extract systematic deviations and construct explicit mathematical compensation operators. The explicit mathematical compensation operator is coupled to the dynamic response analytical model to form an augmented analytical model, and a defect-free response baseline curve under the current working condition is generated based on the augmented analytical model. The measured velocity response data is differentially analyzed with the defect-free response baseline curve to obtain the defect reflection wave component, wherein the defect reflection wave component is used to characterize the local impedance abrupt change characteristics of the target pile foundation.

2. The method of claim 1, wherein, Solving the dynamic response analytical model to obtain the initial analytical solution of the target pile foundation under the ideal state in the current working condition includes: The control equations and boundary conditions in the dynamic response analytical model are subjected to Laplace transformation, which transforms the partial differential equations into ordinary differential equations with respect to depth z, and the general solution in the Laplace domain is obtained by solving the general solution. Using the impedance function recursion method, combined with the boundary conditions at the top and bottom of the pile, the undetermined coefficients are determined to obtain the velocity response in the Laplace domain. The initial velocity response curve in the time domain is obtained through inverse Laplace transform or numerical inversion.

3. The method of claim 1, wherein, The multiple coupling loss functions include: The physical residual term is used to constrain the output of the physical information neural network to satisfy the control equation. Boundary condition terms are used to constrain the output of the physical information neural network to satisfy the boundary condition; A data fitting term is used to constrain the output of the physical information neural network to approximate the measured velocity response data.

4. The method according to claim 1, characterized in that, The step of training the physical information neural network based on the multiple coupling loss functions to obtain the trained physical information neural network includes: Based on the aforementioned multiple coupling loss functions, the weight parameters of the physical information neural network are updated through an optimization algorithm until the multiple coupling loss functions converge to a preset threshold, thereby obtaining the trained physical information neural network. The optimization algorithm includes: using the Adam optimizer for coarse-tuning training, and switching to the L-BFGS optimizer for fine-tuning training when the gradient norm of the multiple coupling loss functions is less than a preset gradient norm threshold. During the training process of the physical information neural network, a Latin hypercube sampling strategy is used to arrange the points of the physical equations in the dimensionless spatiotemporal solution domain, which together with the measured velocity response data constitute the training sample space.

5. The method according to claim 1, characterized in that, The step of differentiating the high-fidelity dynamic response field from the initial analytical solution to extract systematic bias includes: The high-fidelity dynamic response field and the initial analytical solution are subtracted by vector at the same time node to obtain the time-domain deviation vector, thereby obtaining the systematic deviation. The systematic deviation includes at least one of the following: phase lag and waveform broadening caused by the geometric dispersion effect induced by three-dimensional lateral inertia; and amplitude attenuation rate deviation caused by the nonlinear damping evolution of the pile-soil contact interface.

6. The method according to claim 1, characterized in that, The explicit mathematical compensation operator is a damped oscillation function, and the formula is as follows: in, This is the initial amplitude deviation correction coefficient, used to correct the energy transfer deviation between the dynamic response analytical model and the actual dynamic input at the moment of transient excitation; The nonlinear damping dissipation rate is used to characterize the energy decay rate caused by shear slippage of the soil and rock mass along the pile and the viscoelasticity of the material. This is a high-frequency coupling correction frequency used to compensate for energy coupling loss between the lateral inertial fluctuations and the longitudinal principal stress waves of the pile. The phase lag angle of the three-dimensional effect is used to quantify the degree of phase tailing and waveform distortion caused by geometric dispersion during the propagation of stress waves in large-diameter piles.

7. The method according to claim 6, characterized in that, The explicit mathematical compensation operator is coupled to the dynamic response analytical model to form an augmented analytical model, including: The explicit mathematical compensation operator is fed back into the dynamic response analytical model in the form of algebraic superposition to form an augmented analytical model; The augmented analytical model includes a mechanistic principal term and an explicit compensation term. The mechanistic principal term is the initial analytical solution, which provides the physical framework and conservation law constraints for stress wave propagation. The explicit compensation term is the damped oscillation function, which is used to embed specific site damping and dispersion characteristics.

8. The method according to claim 1, characterized in that, After obtaining the defect-reflected wave component, the method further includes: Based on the defect reflection wave components, the arrival time of the defect reflection wave is generated; Based on the arrival time of the defective reflected wave and the designed pile length, calculate the corrected wave velocity under the current working condition; The defect depth is calculated based on the corrected wave velocity and the arrival time of the defect reflected wave. Determine the nature of the defect based on the relationship between the polarity of the reflected wave and the direction of the incident wave; Based on the absolute amplitude of the main peak of the defect reflection wave, and combined with the formula for the one-dimensional stress wave reflection coefficient, the percentage change in cross-sectional area at the defect is obtained by inversion.

9. A device for correcting an analytical model of dynamic response of a pile foundation, characterized in that, The device includes: At least one processor; And, a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform a pile foundation dynamic response analytical model correction method as described in any one of claims 1-8.

10. A computer storage medium storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed, they implement the pile foundation dynamic response analytical model correction method as described in any one of claims 1-8.

Images