A method, device and medium for analyzing longitudinal vibration response of a large-diameter floating pile

Abstract

The application discloses a longitudinal vibration response analysis method, equipment and medium of a large-diameter floating pile, and relates to the technical field of engineering construction. The method comprises the following steps: constructing a pile-soil coupling dynamics model by simplifying and continuously correcting the soil around the pile; performing dimensionless processing on the pile-soil coupling dynamics model; constructing a physical information neural network architecture; calculating the partial derivatives of the network output data corresponding to the network input data to determine a model loss function; training the physical information neural network to model convergence through importance sampling and phased collaborative optimization to obtain a physical information neural model; calculating a predicted velocity curve of the pile top of the large-diameter floating pile; and calculating the residual waveform between the predicted velocity curve of the pile top and the real-time pile top velocity signal to obtain the longitudinal vibration response analysis result of the large-diameter floating pile. The application solves the technical problems of low analysis efficiency, poor robustness and inability to meet the timeliness requirement of the large-diameter floating pile vibration response analysis through the above method.

Description

Technical Field

[0001] This application relates to the field of engineering construction technology, and in particular to a method, equipment and medium for longitudinal vibration response analysis of large-diameter floating piles. Background Technology

[0002] As the most critical concealed load-bearing component in modern large-scale infrastructure, the structural integrity of pile foundations directly affects the safety and stability of the superstructure. In current engineering practice, the low-strain reflected wave method has become the mainstream method for pile foundation integrity testing due to its speed, non-destructive nature, and economy. Existing technologies for analyzing and solving pile-soil coupled vibration problems are mainly divided into two categories: numerical simulation methods and analytical derivation methods.

[0003] With the continuous development of artificial intelligence technology, deep neural networks are being used as approximate models of complex physical systems. By constructing deep network structures, nonlinear mapping relationships are established between multidimensional inputs and outputs to improve the analysis efficiency of the vibration response of floating piles. In existing technologies, numerical simulation methods, when solving semi-infinite space wave problems, lack rigorous analytical derivation of viscoelastic artificial boundary or transmission boundary parameters, relying heavily on empirical formulas. Furthermore, these methods are highly sensitive to wave field frequencies, making it difficult to achieve ideal energy absorption effects across the entire frequency domain, resulting in high computational resource consumption and low analysis efficiency. Analytical derivation methods rely on Laplace transforms or Fourier transforms to map time-domain problems to the transform domain for solution. However, due to the approximation defects of integral transforms for discontinuous functions, the analysis results are easily distorted. For methods such as deep neural networks, the loss function optimization process of the network model is only driven by data bias and lacks rigid constraints from physical control equations. When facing complex operating conditions outside the training set distribution, it is difficult to guarantee the reliability and physical consistency of extrapolation predictions. Summary of the Invention

[0004] This application provides a method, equipment, and medium for longitudinal vibration response analysis of large-diameter floating piles, which solves the technical problems of low efficiency, poor robustness, and inability to meet timeliness requirements in the vibration response analysis of large-diameter floating piles in the prior art.

[0005] In a first aspect, embodiments of this application provide a method for analyzing the longitudinal vibration response of a large-diameter floating pile. The method comprises: constructing a pile-soil coupled dynamic model corresponding to the large-diameter floating pile based on a preset Winkler model, through simplification of the soil around the pile and continuous variable cross-section correction; performing dimensionless processing on the pile-soil coupled dynamic model to obtain a standardized pile-soil coupled dynamic model; constructing a physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model; acquiring the network input data and network output data of the physical information neural network architecture, and calculating the partial derivatives of each order of the network input data corresponding to the network output data to determine the model loss function of the physical information neural network architecture; training the physical information neural network until the model converges based on the model loss function through importance sampling and phased collaborative optimization to obtain a physical information neural model; calculating the predicted velocity curve at the pile top of the large-diameter floating pile according to the physical information neural model; acquiring real-time pile top velocity signals, and calculating the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal to obtain the longitudinal vibration response analysis results of the large-diameter floating pile.

[0006] In one embodiment, based on a pre-defined Winkler model, a pile-soil coupled dynamic model corresponding to a large-diameter floating pile is constructed through pile perimeter soil simplification and continuous variable cross-section correction. Specifically, this includes: based on the Winkler model, performing longitudinal and lateral inertia analysis on the pile resistance of the pile side soil of the large-diameter floating pile to determine the Rayleigh-Love rod wave equation corresponding to the large-diameter floating pile; using a pre-defined variable cross-section diffusion virtual soil pile model, continuously modifying the pile bottom soil of the large-diameter floating pile to obtain the governing equation of the stress wave spherical diffusion effect; and constructing the pile-soil coupled dynamic model by setting boundaries based on the Rayleigh-Love rod wave equation and the governing equation.

[0007] In one embodiment, the pile-soil coupled dynamics model is dimensionlessly processed to obtain a standardized pile-soil coupled dynamics model. Specifically, this includes: selecting characteristic quantities with dimensional terms in the pile-soil coupled dynamics model and defining dimensionless variables corresponding to the characteristic quantities; and reconstructing each dimensional term in the pile-soil coupled dynamics model into a dimensionless form based on the dimensionless variables to obtain the standardized pile-soil coupled dynamics model.

[0008] In one embodiment, the physical information neural network architecture includes: an input layer, a hidden layer, an activation function, and an output layer; the physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model is constructed by: receiving dimensionless spatiotemporal coordinates through the input layer, and connecting the input layer to the hidden layer; connecting the hidden layer to the output layer, and setting the activation function corresponding to the hidden layer to the hyperbolic tangent function; and outputting dimensionless longitudinal displacement prediction values ​​through the output layer.

[0009] In one embodiment, calculating the partial derivatives of the network output data corresponding to the network input data of each order to determine the model loss function of the physical information neural network architecture specifically includes: calculating the partial derivatives of the network output data corresponding to the network input data of each order, and calculating the mean square error of the corresponding control equation based on the partial derivatives of each order to obtain the first model loss function term; setting the condition parameters of the large-diameter floating pile, and constructing the second model loss function term corresponding to the condition parameters; wherein, the condition parameters include: initial conditions and boundary conditions; configuring the loss function weights corresponding to each condition term of the first model loss function term and the second model loss function term to determine the model loss function.

[0010] In one embodiment, based on the model loss function, a physical information neural network is trained until the model converges through importance sampling and phased collaborative optimization to obtain a physical information neural model. Specifically, this includes: randomly generating training collocations in the spatiotemporal solution domain of the model and distributing the training collocations at a predetermined ratio in the high-frequency period of the excitation pulse and the corresponding neighborhood to determine the physical information neural model to be trained; performing a first-stage training of the physical information neural model to be trained using the Adam optimizer; and performing a second-stage training of the model after the first-stage training using the L-BFGS optimizer and Hessian matrix information, training the model loss function to converge to a predetermined order of magnitude to obtain the physical information neural model.

[0011] In one embodiment, the calculation of the predicted velocity curve at the top of a large-diameter floating pile based on the physical information neural model specifically includes: calculating the displacement response prediction data of the large-diameter floating pile in the full solution domain based on the physical information neural model; performing dimensional restoration on the displacement response prediction data; and reconstructing the dimensional restored displacement response prediction data into the predicted velocity curve at the top of the pile.

[0012] In one embodiment, the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal is calculated to obtain the longitudinal vibration response analysis results of the large-diameter floating bearing pile. Specifically, this includes: aligning the peaks of the predicted pile top velocity curve and the real-time pile top velocity signal, and normalizing the amplitude of the peak-aligned predicted pile top velocity curve and the real-time pile top velocity signal to obtain a set of waveforms to be processed; performing time-domain difference processing on the set of waveforms to be processed to obtain the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal; and obtaining the longitudinal vibration response analysis results based on the residual waveform and the qualitative analysis of actual defects.

[0013] Secondly, embodiments of this application also provide a longitudinal vibration response analysis device for large-diameter floating piles, characterized in that the device includes: 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 implement a longitudinal vibration response analysis method for large-diameter floating piles.

[0014] Thirdly, embodiments of this application also provide a non-volatile computer storage medium for longitudinal vibration response analysis of large-diameter floating piles, storing computer-executable instructions, characterized in that the computer-executable instructions are configured to implement a longitudinal vibration response analysis method for large-diameter floating piles when executed.

[0015] This application provides a method, equipment, and medium for analyzing the longitudinal vibration response of large-diameter floating piles. By establishing a pile-soil coupled dynamic model that considers lateral inertial effects and pile end diffusion effects and training the corresponding Physical Information Neural Network (PINNs) architecture, it solves the technical problems of low efficiency, poor robustness, and inability to meet timeliness requirements in the vibration response analysis of large-diameter floating piles in the prior art. It achieves high-precision and high-efficiency solution of the longitudinal vibration wave field of large-diameter floating piles without the need for mesh generation, complex integral transformation, and reliance on a large amount of measured label data, and improves the generalization adaptability of the analysis method for large-diameter floating piles to extrapolated working conditions in engineering construction. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0017] Figure 1 A flowchart illustrating a longitudinal vibration response analysis method for large-diameter floating piles provided in this application embodiment;

[0018] Figure 2 A simplified mechanical model diagram of pile-soil coupling provided in this application embodiment;

[0019] Figure 3 A schematic diagram of the overall architecture for solving the PDE equations of pile-soil coupling using PINNs, provided in an embodiment of this application;

[0020] Figure 4 This application provides a schematic diagram comparing PINNs with the analysis results in an embodiment of the present application.

[0021] Figure 5 This is a schematic diagram of the internal structure of a longitudinal vibration response analysis device for a large-diameter floating pile, provided as an embodiment of this application. Detailed Implementation

[0022] 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.

[0023] This application provides a method, equipment, and medium for analyzing the longitudinal vibration response of large-diameter floating piles. By establishing a pile-soil coupled dynamic model that considers lateral inertial effects and pile end diffusion effects and training the corresponding Physical Information Neural Network (PINNs) architecture, it solves the technical problems of low efficiency, poor robustness, and inability to meet timeliness requirements in the vibration response analysis of large-diameter floating piles in the prior art. It achieves high-precision and high-efficiency solution of the longitudinal vibration wave field of large-diameter floating piles without the need for mesh generation, complex integral transformation, and reliance on a large amount of measured label data, and improves the generalization adaptability of the analysis method for large-diameter floating piles to extrapolated working conditions in engineering construction.

[0024] The technical solutions proposed in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0025] Figure 1 A flowchart illustrating a longitudinal vibration response analysis method for large-diameter floating piles provided in this application embodiment. Figure 1 As shown in the embodiment of this application, a longitudinal vibration response analysis method for a large-diameter floating pile is provided, which specifically includes the following steps:

[0026] Step 101: Based on the preset Winkler model, construct the pile-soil coupled dynamic model corresponding to the large-diameter floating pile by simplifying the soil around the pile and correcting the continuous variable cross section.

[0027] For example, to study the feasibility of applying physical information neural networks to analyze pile-soil coupling problems, this application adopts a diffused virtual soil pile model to represent the supporting effect of the soil at the pile bottom on the pile; the soil at the pile tip is assumed to be a viscoelastic rod model similar to the pile, while considering the stress diffusion effect. Although the plane strain model proposed by Novak in the prior art can accurately describe the fluctuation effect of soil layers in the frequency domain, its stiffness and damping are expressed through Bessel functions and have frequency dependence, making it difficult to directly apply to solving nonlinear partial differential equations in the time domain. Due to the effectiveness of the PINNs method in handling variable cross sections and lateral inertial effects, and the fact that the Winkler model has been widely proven to have sufficient engineering accuracy in the time domain analysis of pile foundation dynamics, this application adopts the Winkler foundation model to simplify the soil around the pile into a system of linear elastic springs and viscous dampers distributed along the pile body, thus constructing a pile-soil coupling dynamic model.

[0028] Specifically, based on the pre-set Winkler model, a pile-soil coupled dynamic model corresponding to large-diameter floating piles is constructed through pile perimeter soil simplification and continuous variable cross-section correction. This includes: based on the Winkler model, longitudinal and lateral inertia analyses are performed on the pile resistance of the pile side soil of large-diameter floating piles to determine the Rayleigh-Love rod wave equation corresponding to large-diameter floating piles; through a pre-set variable cross-section diffusion virtual soil pile model, continuous variable cross-section correction is performed on the pile bottom soil of large-diameter floating piles to obtain the governing equation of stress wave spherical diffusion effect; and based on the Rayleigh-Love rod wave equation and the governing equation, a pile-soil coupled dynamic model is constructed through boundary setting.

[0029] Figure 2 A simplified mechanical model diagram of pile-soil coupling provided for an embodiment of this application.

[0030] In one embodiment, the simplified mechanical model is first set as follows: the upper surface of the soil layer is a free boundary, and the bottom of the virtual soil pile is a rigid support; the soil around the pile is a viscoelastic isotropic body, and there are no principal stresses or shear stresses on the ground surface; at infinity, the strain wave in the soil will completely attenuate; the incident signal excited at the pile top is a half-sine harmonic load, and the site is not affected by other external loads at the same time; the solid pile and the soil beside the pile are considered to be in complete continuous contact; the force and displacement at the interface between the pile tip and the virtual soil pile, as well as at the interface between each unit of the pile (including the virtual soil pile), are continuous.

[0031] Based on the above assumptions, the resistance of the soil along the pile to the pile (virtual soil pile) It can be represented as:

[0032] (1)

[0033] in, , These are the stiffness coefficient of the spring and the viscous damping coefficient of the damper, respectively.

[0034] Based on the dynamic equilibrium analysis of the infinitesimal element, considering the transverse Poisson effect of the material, in addition to the conventional longitudinal inertial force... In addition, a lateral inertial term derived from radial motion kinetic energy is introduced simultaneously. .

[0035] Furthermore, based on the Winkler pile-side soil model, a Rayleigh-Love rod wave equation containing a fourth-order mixed derivative term was established, which is explained by the following formula.

[0036] (2)

[0037] in, , , , , , , These are the elastic modulus, elastic longitudinal wave velocity, cross-sectional area, density, Poisson's ratio, radius, and displacement of the solid pile. .

[0038] When dealing with the dynamic response of a diffused fictions soil pile, the traditional transfer matrix method usually discretizes it into several cylindrical layers with equal cross-sections for approximate solution.

[0039] This application, based on the PINNs framework, modifies the continuously variable cross-section Rayleigh-Love rod model by directly introducing a cross-sectional radius that varies continuously at depth z. and cross-sectional area The governing equations, which include geometric coefficient terms, were established:

[0040] (3)

[0041] in, , , , , , , These are the elastic modulus, elastic longitudinal wave velocity, cross-sectional area, density, Poisson's ratio, radius, and displacement of the virtual soil pile.

[0042] , , The diffusion angle is [value].

[0043] Compared with the traditional transfer matrix method, the method adopted in this application can avoid the geometric errors caused by step discretization and more accurately describe the propagation behavior of stress waves in diffused virtual soil piles.

[0044] Based on the low-strain testing conditions of pile foundations, and assuming that the displacement and velocity of all particles in the pile body are zero at t=0, the initial conditions can be expressed as follows:

[0045] (4)

[0046] (5)

[0047] For large-diameter piles, the incident wave in low-strain testing is often input in the form of local excitation. The excitation applied in this application is a simple harmonic load, which is explained by the following formula.

[0048] (6)

[0049] in, This represents the peak amplitude of the excitation force. The duration of the pulse.

[0050] Furthermore, assuming the pile bottom is rigidly supported in the loose soil, the longitudinal boundary conditions of the pile can be expressed as follows:

[0051] (7)

[0052] (8)

[0053] 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:

[0054] (9)

[0055] (10)

[0056] Step 102: Perform dimensionless processing on the pile-soil coupled dynamic model to obtain a standardized pile-soil coupled dynamic model.

[0057] For example, pile-soil interaction systems involve complex physical and mechanical processes, with physical parameters such as geometric dimensions, time scales, and material properties in their governing equations spanning multiple orders of magnitude. If governing equations and constraints containing original dimensions are directly embedded into a physical information neural network, the vast differences in parameter scales can lead to extreme imbalances in the curvature of the network's loss function space across different dimensions. This can induce "ill-conditioned gradients" during backpropagation, where terms with large numerical magnitudes dominate gradient updates, easily masking smaller but equally crucial physical constraints. This can cause the model to fall into local optima, converge slowly, or even diverge. To address these technical problems, this application performs dimensionless processing on the pile-soil coupled dynamics model to obtain a standardized pile-soil coupled dynamics model. This achieves the dimensionless transformation of the pile-soil coupled dynamics model, eliminating the interference of the huge order-of-magnitude differences between different physical parameters on the gradient descent process of the neural network.

[0058] Specifically, the pile-soil coupled dynamics model is dimensionless to obtain a standardized pile-soil coupled dynamics model. This includes: selecting characteristic quantities with dimensional terms in the pile-soil coupled dynamics model and defining dimensionless variables corresponding to the characteristic quantities; and reconstructing each dimensional term in the pile-soil coupled dynamics model into a dimensionless form based on the dimensionless variables to obtain the standardized pile-soil coupled dynamics model.

[0059] In one embodiment, to solve the aforementioned technical problem, it is necessary to introduce a characteristic scale to perform rigorous dimensionless processing on the governing equations, uniformly mapping various physical variables to... The scaling interval in the vicinity effectively compresses the dynamic range of the parameters, significantly improves the condition number of the system's Hessian matrix from the algorithm's underlying level, and ensures that the gradient scale of each physical constraint in the loss function is balanced.

[0060] Therefore, dimensionless processing is a key prerequisite for eliminating dimensional differences, ensuring that deep learning models achieve balanced convergence across multiple physical terms, and thus improving the efficiency of algorithm optimization, solution accuracy, and model generalization ability.

[0061] To eliminate the interference of huge differences in physical parameters between different orders of magnitude on the gradient descent process of neural networks, this application constructs a loss function in a dimensionless space.

[0062] Taking the governing equations as an example, based on , , (in, ), The dimensionless definition is used to treat the control equations of solid piles (Equation 2) and diffused virtual soil piles (Equation 3) as dimensionless, resulting in the following dimensionless control equations:

[0063] (11)

[0064] (12)

[0065] in, , , , , , ;

[0066] , They are respectively , Displacement of the pile.

[0067] Step 103: Construct the physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model;

[0068] Specifically, the physical information neural network architecture includes: an input layer, a hidden layer, an activation function, and an output layer; the physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model includes: receiving dimensionless spatiotemporal coordinates through the input layer, connecting the input layer to the hidden layer; connecting the hidden layer to the output layer, with the activation function of the hidden layer set as the hyperbolic tangent function; and outputting dimensionless longitudinal displacement prediction values ​​through the output layer.

[0069] Figure 3 This is a schematic diagram of the overall architecture for solving the PDE equations of pile-soil coupling using PINNs, as provided in an embodiment of this application.

[0070] In one embodiment, a fully connected feedforward neural network (FNN) is constructed, comprising: an input layer, a hidden layer, an activation function, and an output layer.

[0071] Input layer: Two neurons are set up to receive dimensionless spatiotemporal coordinates.

[0072] Hidden layers: set to 4 layers, each containing 64 neurons.

[0073] Activation function: In order to meet the calculation requirements of the fourth derivative in the governing equation, all hidden layers use the Tanh function as the activation function. This function has infinite differentiability and the output is centrally symmetric, which is beneficial to accelerate convergence.

[0074] Output layer: Set up 1 neuron to output dimensionless longitudinal displacement prediction value.

[0075] This application establishes an automatic differentiation module, which is faster and more accurate than traditional differentiation methods, playing a crucial role, especially in gradient calculation when solving optimization problems. The basic idea of ​​automatic differentiation is to use a computer program to differentiate complex mathematical functions and then automatically obtain the function's derivative or gradient.

[0076] First, the function is symbolically differentiated, followed by numerical computation, with intermediate results preserved. Finally, the chain rule is used to apply all intermediate results to the entire function, yielding its derivative at a specific point. Then, automatic differentiation is employed to calculate the derivative of the function with respect to time and space at each time step and coordinate. Backpropagation is used to update the network parameters to minimize the loss function. Finally, as the loss function approaches zero, the predicted value of the neural network model approaches the true value.

[0077] Step 104: Obtain the network input data and network output data of the physical information neural network architecture, and calculate the partial derivatives of each order of the network output data corresponding to the network input data, so as to determine the model loss function of the physical information neural network architecture.

[0078] For example, the core idea of ​​PINNs is to integrate physical knowledge into the architecture and training of the neural network to solve problems related to physical systems. Therefore, the loss function becomes the link between prior physical knowledge and the neural network. Constructing a suitable loss function based on the governing equations and constraints is the key to PINNs solving the vibration problem of elastically supported piles considering lateral inertial effects and pile end diffusion effects.

[0079] Specifically, the partial derivatives of the network output data corresponding to the network input data are calculated to determine the model loss function of the physical information neural network architecture. This includes: calculating the partial derivatives of the network output data corresponding to the network input data, and calculating the mean square error of the corresponding control equation based on the partial derivatives to obtain the first model loss function term; setting the condition parameters of the large-diameter floating pile, and constructing the second model loss function term corresponding to the condition parameters; wherein the condition parameters include: initial conditions and boundary conditions; configuring the loss function weights corresponding to each condition term of the first model loss function term and the second model loss function term to determine the model loss function.

[0080] In one embodiment, referring to the loss function design widely adopted in the current PINNs field, this application uses mean squared error (MSE) to characterize the fitting error of the network output to the dynamic equation, and the construction of the loss function corresponding to the control equation is explained by the following formula.

[0081] (13)

[0082] (14)

[0083] (15)

[0084] in, It is the loss function of the control equations constructed by the model based on equations (11) and (12) on the control equations. This represents the number of random sampling points within the domain.

[0085] Furthermore, the initial and boundary conditions of the elastically supported piles are explained by the following formula for constructing the corresponding loss function.

[0086] (16)

[0087] (17)

[0088] (18)

[0089] (19)

[0090] (20)

[0091] (twenty one)

[0092] in, It is the loss function constructed by the model after dimensionless transformation according to equations (4) and (5) on the boundary conditions. , These are the loss functions constructed by the model after dimensionless transformation according to equations (7) and (8) under the boundary conditions. It is the loss function constructed by the model after dimensionless transformation according to equations (9) and (10) on the boundary conditions. It is the boundary loss function defined by the model under the boundary conditions; , , , These represent the initial time, the pile top, the pile (virtual soil pile) bottom, and the number of random sampling points at the pile-soil contact surface.

[0093] The model loss function is:

[0094] (twenty two)

[0095] in, , , These are the weights of the control equation loss function, boundary loss function, and initial loss function, respectively.

[0096] After multiple trials and optimizations, this application sets weights. , , Take values ​​of 1, 100, and 100 respectively.

[0097] Step 105: Based on the model loss function, train the physical information neural network until the model converges through importance sampling and phased collaborative optimization to obtain the physical information neural model.

[0098] For example, Physical Information Neural Networks (PINNs) differ fundamentally from traditional neural networks that rely on large amounts of labeled data for feature extraction. They employ a physically constrained unsupervised learning paradigm. For the forced vibration problem of elastically supported piles, PINNs do not require prior acquisition of real observations; instead, they directly solve the problem within a specific spatiotemporal domain. The training set is constructed by randomly collocation points, and then the spatiotemporal coordinates are mapped into the network. The residual norm of the governing equation and other constraints are used as loss functions to drive weight updates, so as to achieve a high-precision approximation of the target physical field.

[0099] Specifically, based on the model loss function, the physical information neural network is trained until the model converges through importance sampling and phased collaborative optimization to obtain the physical information neural model. This includes: randomly generating training points in the spatiotemporal solution domain of the model and distributing a preset proportion of training points in the high-frequency period of the excitation pulse and its corresponding neighborhood to determine the physical information neural model to be trained; performing the first stage of training on the physical information neural model to be trained using the Adam optimizer; and performing the second stage of training on the model after the first stage of training using the L-BFGS optimizer and Hessian matrix information, training the model loss function to converge to a preset order of magnitude to obtain the physical information neural model.

[0100] In one embodiment, the density strategy of the sampling points is a key adjustment part in the training process of PINNs. Although high-density sampling can usually strengthen physical constraints and improve the accuracy of approximate solutions, the resulting computational load and convergence difficulty will also increase significantly.

[0101] To strike a balance between computational efficiency and solution accuracy, this application employs a hybrid collocation strategy combining temporal progression and importance sampling to accurately capture transient dynamic responses. Network training utilizes a phased temporal growth strategy, dividing the training process into three continuously expanding time windows, with the next stage only proceeding after convergence in the current time window. Based on this, a phased collaborative optimization strategy using the Adam optimizer and the L-BFGS optimizer is employed to train the physical information neural network. In the initial stage, the Adam optimizer performs global optimization, quickly converging to a reasonable parameter range; in the later stage, the L-BFGS optimizer performs local fine-tuning, improving model convergence accuracy and physical consistency. These two stages of optimization balance global search and local convergence performance, effectively improving the accuracy and stability of the PINN solution.

[0102] In the initial training based on the Adam optimizer, a dynamic random resampling mechanism is used within the computational domain. In each iteration, 2000 uniformly distributed points are sampled in both the solid pile and virtual soil pile domains. For boundary conditions and initial conditions, the model sets independent sampling sets. In each iteration, 1000 points are randomly sampled for each of the initial conditions, pile top, pile bottom, and pile-soil interface. The initial condition sampling points are... The points are uniformly distributed along the pile body at all times, while the points at the interface and the bottom of the pile are randomly sampled uniformly within the current time window.

[0103] Furthermore, to address the high-frequency characteristics of pulsed loads, the pile top force boundary adopted time-dimensional importance sampling: that is, 30% of the collocation points were forcibly concentrated in the excitation period and its neighborhood, while the remaining 70% were distributed throughout the entire period.

[0104] During the later stages of training, when entering the second-order optimization phase of the L-BFGS optimizer, the collocation strategy is changed from dynamic random sampling to static fixed sampling to meet the deterministic requirement of the objective function in the quasi-Newton method. At this point, to compensate for potential insufficient local coverage due to the cessation of resampling, this invention significantly increases the number of collocations used per iteration: the number of collocations within the computational domain is increased from 2000 to 6000, and the number of collocations for various boundary conditions is increased from 1500 to 5000. This high-density fixed collocation set remains unchanged throughout the entire L-BFGS optimizer optimization process.

[0105] Furthermore, although this application has dimensionlessly processed the governing equations and their constraints, it was found in the actual training process that, despite the dimensionless processing balancing the numerical range of each variable, the characteristics of different loss terms in the optimization space still have significant differences.

[0106] The loss term in the governing equations involves the fourth-order mixed partial derivatives of displacement with respect to time and space. In backpropagation calculations, the PDE loss is prone to generating high-frequency noise, making optimization difficult. In contrast, initial and boundary conditions only involve function values ​​or first derivatives, making them easier for neural networks to fit. If all loss terms are given the same weight, the optimizer tends to reduce the PDE loss first while ignoring the initial and boundary condition losses, causing the model to converge to an incorrect solution that does not conform to physical facts.

[0107] To alleviate this "gradient ill-conditioning" problem and force the neural network to strictly follow the boundary conditions, a multi-objective loss weighting strategy is adopted to construct the total loss function. By assigning large penalty weights to the boundary conditions and initial conditions, the model is forced to prioritize matching the physical boundary in the early stage of training, and then approximate the exact solution of the control equation in the spatiotemporal domain.

[0108] Step 106: Calculate the predicted velocity curve at the top of the large-diameter floating bearing pile based on the physical information neural model.

[0109] For example, this application uses a trained and converged physical information neural model to perform forward prediction of the dynamic response and reconstruction of the theoretical time history curve of a large-diameter floating bearing pile, thereby improving the stability and accuracy of the predicted velocity curve at the pile top.

[0110] Specifically, based on the physical information neural model, the predicted velocity curve at the top of the large-diameter floating bearing pile is calculated, including: calculating the displacement response prediction data of the large-diameter floating bearing pile in the full solution domain based on the physical information neural model; restoring the dimensions of the displacement response prediction data; and reconstructing the dimension-restored displacement response prediction data into the predicted velocity curve at the top of the pile.

[0111] Figure 4 This is a schematic diagram showing the comparison between PINNs and the analysis results provided in an embodiment of this application.

[0112] In one embodiment, firstly, a high-density predicted coordinate lattice is discretized and generated within a continuous spatiotemporal solution domain, strictly according to the sampling frequency and effective observation time window set by the actual engineering testing equipment. This lattice is then fed into an optimized neural network as an input variable to obtain the corresponding dimensionless displacement response field within the entire solution domain. Subsequently, a physical reference scale is introduced to perform a reverse mapping on the dimensionless results output by the neural network. That is, using characteristic parameters such as the actual pile length, reference wave velocity, and reference displacement, the dimensionless spatiotemporal coordinates and displacement scalars are restored to a physical field with actual mechanical dimensions.

[0113] Furthermore, considering the objective reality that field measurements typically focus on pile top velocity signals, this study utilizes automatic differentiation techniques to calculate the partial derivative of the longitudinal displacement of the pile top surface with respect to time, thereby reconstructing a physically accurate theoretical pile top velocity time history curve. This theoretical curve essentially characterizes the reference response signal of a complete, defect-free pile. Internally, it naturally couples the dispersion distortion and high-frequency oscillation characteristics caused by the lateral inertia of the pile body, dominated by Rayleigh-Love member theory, with the geometric damping and amplitude attenuation characteristics caused by the semi-infinite spherical diffusion at the pile tip, as described by the variable cross-section virtual soil pile theory. This establishes a rigorous theoretical reference system for the subsequent refined calibration of measured signals.

[0114] Furthermore, to verify the effectiveness of this embodiment, the following typical working condition parameters were selected for simulation verification: pile length. ,radius ,density wave speed Poisson's ratio ; diffusion angle of loose soil pile .

[0115] Depend on Figure 4 As can be seen, the waveform calculated in this application is not only smooth and oscillatory, but also clearly shows the geometric dispersion characteristics caused by lateral inertia. Compared with the analytical solution based on Laplace transform, the two have a very high degree of agreement, and the fitting of the method of this invention at the abrupt change of the wavefront is smoother, verifying the accuracy and advantages of this method.

[0116] Step 107: Acquire real-time pile top velocity signal and calculate the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal to obtain the longitudinal vibration response analysis results of the large-diameter floating bearing pile.

[0117] For example, the reconstructed theoretical pile top velocity time history curve is used as a benchmark for high-precision assessment of the integrity of foundation piles in engineering sites. By constructing a multi-dimensional comparison mechanism to decouple and remove geometric dispersion interference, the quantitative classification and high reliability assessment of the structural integrity of large-diameter floating piles can be achieved.

[0118] Specifically, the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal is calculated to obtain the longitudinal vibration response analysis results of the large-diameter floating bearing pile. This includes: aligning the peaks of the predicted pile top velocity curve and the real-time pile top velocity signal, and normalizing the amplitude of the aligned predicted pile top velocity curve and the real-time pile top velocity signal to obtain the waveform group to be processed; performing time-domain difference processing on the waveform group to be processed to obtain the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal; and obtaining the longitudinal vibration response analysis results based on the residual waveform and the qualitative analysis of actual defects.

[0119] In one embodiment, the low-strain reflected wave method is first used to apply transient excitation to the large-diameter floating bearing pile to be tested on site, the response signal is collected and preprocessed through low-pass filtering, baseline correction and integration, etc., to obtain the pile top velocity time history curve measured on site.

[0120] Then, the measured curves and theoretical curves are mapped to the same time coordinate system. Using the first arrival peak of the initial incident wave as the synchronization matching reference, the two sets of time-series signals are calibrated by time axis translation and amplitude normalization. Addressing the engineering challenge of large-diameter solid piles easily inducing local waveform oscillations and phase lag in the shallow section due to strong lateral inertial effects, a time-domain difference method is introduced to calculate the residual time series of the measured and theoretical waveforms. Since the theoretical curves fully characterize the geometric effects of large diameter piles and contain no defect scattering information, the above residual extraction operation can effectively counteract high-frequency lateral inertial interference and normal pile-soil system energy attenuation at the mathematical level, thereby completely eliminating the "pseudo-defect" characteristics induced by abrupt changes in geometric dimensions.

[0121] Finally, focusing on the pure residual waveform after removing background interference, the true impedance abrupt change source is diagnosed strictly according to the one-dimensional elastic stress wave reflection theory: if a reflection peak in phase with the incident wave appears in the residual waveform evolution, the corresponding depth range is identified as having impedance attenuation defects such as diameter reduction, slag inclusion, or concrete segregation; if a reflection trough in opposite phase appears, it is determined to be an impedance surge phenomenon such as diameter expansion. Combining the time delay difference between the peaks (or troughs) and the corrected one-dimensional longitudinal wave propagation velocity, the physical depth of the impedance abrupt change interface is accurately inverted, and the relative amplitude characteristics of the defect reflection wave are comprehensively considered to finally achieve quantitative classification and high reliability assessment of the structural integrity of large-diameter floating piles.

[0122] The above are embodiments of the method proposed in this application. Based on the same inventive concept, embodiments of this application also provide a longitudinal vibration response analysis device for large-diameter floating piles, the structure of which is as follows: Figure 5 As shown.

[0123] Figure 5 This is a schematic diagram of the internal structure of a longitudinal vibration response analysis device for a large-diameter floating pile, provided as an embodiment of this application. Figure 5 As shown, the device includes:

[0124] At least one processor 501;

[0125] And a memory 502 that is communicatively connected to at least one processor;

[0126] The memory 502 stores instructions that can be executed by at least one processor. The instructions are executed by at least one processor 501 to enable at least one processor 501 to implement a longitudinal vibration response analysis method for a large-diameter floating pile.

[0127] Some embodiments of this application provide corresponding to Figure 1 A non-volatile computer storage medium for longitudinal vibration response analysis of large-diameter floating piles is provided, which stores computer-executable instructions. When executed, these computer-executable instructions enable the implementation of a longitudinal vibration response analysis method for large-diameter floating piles.

[0128] 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.

[0129] The systems, media, and methods provided in this application are one-to-one correspondences. Therefore, the systems and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the systems and media will not be repeated here.

[0130] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, 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.

[0131] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), 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.

[0132] 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 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0133] 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.

[0134] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0135] 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.

[0136] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using 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 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.

[0137] 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 process, method, article, or apparatus. Unless otherwise specified, 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 that element.

[0138] The above are merely embodiments of this application and are not intended to limit the scope of 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 principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for analyzing the longitudinal vibration response of large-diameter floating piles, characterized in that, The method includes: Based on the pre-set Winkler model, a pile-soil coupled dynamic model corresponding to large-diameter floating piles is constructed by simplifying the soil around the pile and correcting for continuous variable cross-section. The pile-soil coupled dynamic model is dimensionless to obtain a standardized pile-soil coupled dynamic model. Construct the physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model; Obtain the network input data and network output data of the physical information neural network architecture, and calculate the partial derivatives of each order of the network output data corresponding to the network input data to determine the model loss function of the physical information neural network architecture; Based on the model loss function, the physical information neural network is trained until the model converges through importance sampling and phased collaborative optimization, thus obtaining the physical information neural model. Based on the physical information neural model, the predicted velocity curve at the top of the large-diameter floating bearing pile is calculated; Real-time pile top velocity signals are acquired, and the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal is calculated to obtain the longitudinal vibration response analysis results of the large-diameter floating pile. Based on the model loss function, the physical information neural network is trained until the model converges through importance sampling and phased collaborative optimization, resulting in a physical information neural model, which specifically includes: Training points are randomly generated within the spatiotemporal solution domain of the model, and a predetermined proportion of training points are distributed in the high-frequency period of the excitation pulse and the corresponding neighborhood to determine the physical information neural model to be trained. The first stage of training of the physical information neural model to be trained is performed using the Adam optimizer. The model trained in the first stage is trained in the second stage using the L-BFGS optimizer and Hessian matrix information, and the model loss function is trained to converge to a preset order of magnitude to obtain the physical information neural model.

2. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, Based on the pre-defined Winkler model, a pile-soil coupled dynamic model for large-diameter floating piles is constructed through pile perimeter soil simplification and continuous variable cross-section correction. Specifically, this includes: Based on the Winkler model, longitudinal and lateral inertia analyses are performed on the pile resistance of the soil sidewall of the large-diameter floating pile to determine the Rayleigh-Love rod wave equation corresponding to the large-diameter floating pile. By using a pre-defined variable cross-section diffusion virtual soil pile model, the soil at the bottom of the large-diameter floating bearing pile is continuously modified with variable cross-section to obtain the control equation of the stress wave spherical diffusion effect. Based on the Rayleigh-Love bar wave equation and the control equation, the pile-soil coupled dynamic model is constructed by setting boundaries.

3. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, The pile-soil coupled dynamic model is dimensionlessly processed to obtain a standardized pile-soil coupled dynamic model, specifically including: Select the dimensionless variables corresponding to the dimensionless variables in the pile-soil coupled dynamic model. Based on the dimensionless variables, each dimensional term in the pile-soil coupled dynamics model is reconstructed into a dimensionless form to obtain the standardized pile-soil coupled dynamics model.

4. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, The physical information neural network architecture includes: an input layer, a hidden layer, an activation function, and an output layer; The physical information neural network architecture corresponding to the standardized pile-soil coupled dynamic model is constructed, specifically including: The input layer receives dimensionless spatiotemporal coordinates, and the input layer is connected to the hidden layer. The hidden layer is connected to the output layer, and the activation function corresponding to the hidden layer is set to the hyperbolic tangent function; The output layer outputs dimensionless longitudinal displacement prediction values.

5. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, Calculating the partial derivatives of the network output data with respect to the network input data to determine the model loss function of the physical information neural network architecture specifically includes: Calculate the partial derivatives of the network output data corresponding to the network input data of each order, and calculate the mean square error of the corresponding control equation based on the partial derivatives of each order, so as to obtain the first model loss function term; The conditional parameters of the large-diameter floating pile are set, and the second model loss function term corresponding to the conditional parameters is constructed; wherein, the conditional parameters include: initial conditions and boundary conditions; Configure the loss function weights corresponding to each condition term of the first model loss function term and the second model loss function term to determine the model loss function.

6. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, Based on the physical information neural model, the predicted velocity curve at the top of the large-diameter floating pile is calculated, specifically including: Based on the physical information neural model, the displacement response prediction data corresponding to the large-diameter floating bearing pile in the full solution domain is calculated; The displacement response prediction data is restored to its original dimensions, and the restored displacement response prediction data is reconstructed into the predicted velocity curve at the top of the pile.

7. The longitudinal vibration response analysis method for a large-diameter floating pile according to claim 1, characterized in that, Calculate the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal to obtain the longitudinal vibration response analysis results of the large-diameter floating pile, specifically including: Align the peaks of the predicted velocity curve at the top of the pile with the peaks of the real-time velocity signal at the top of the pile, and normalize the amplitudes of the predicted velocity curve at the top of the pile and the real-time velocity signal at the top of the pile after peak alignment to obtain the waveform group to be processed. The waveform group to be processed is subjected to time-domain difference processing to obtain the residual waveform between the predicted pile top velocity curve and the real-time pile top velocity signal; Based on the residual waveform, the longitudinal vibration response analysis results are obtained through qualitative analysis of the actual defect.

8. A longitudinal vibration response analysis device for large-diameter floating piles, 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 implement the longitudinal vibration response analysis method for large-diameter floating piles as described in any one of claims 1-7.

9. A non-volatile computer storage medium for longitudinal vibration response analysis of large-diameter floating piles, storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed, they are configured to implement a longitudinal vibration response analysis method for large-diameter floating piles as described in any one of claims 1-7.

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