Method and device for co-controlling bidirectional load of pile foundation in geotechnical centrifugal model test

Abstract

The application discloses a kind of geotechnical centrifugal model test pile foundation bidirectional load collaborative control method and device.It includes: real-time acquisition of the pile body rotation angle of pile under load in centrifugal test, actual vertical load of loading point and actual horizontal position of vertical actuator;Pile body rotation angle and dynamically updated deformation mode coefficient estimate actual horizontal displacement of pile top;The deviation between actual horizontal displacement of pile top and actual horizontal position generates horizontal motion instruction, and drives vertical actuator to carry out horizontal following;Based on the deviation between target vertical load and actual vertical load, generate vertical fine-tuning instruction, compensate the vertical load disturbance caused by horizontal following.This application introduces double closed-loop decoupling collaborative control and multistage dynamic coefficient correction mechanism, suppresses the loading force distortion caused by mechanical motion coupling, avoids the problem of pile body damage caused by eccentric load.

Description

Technical Field

[0001] This invention relates to the field of geotechnical centrifuge model testing technology, specifically to a method and device for coordinated control of bidirectional loads on pile foundations in geotechnical centrifuge model testing. Background Technology

[0002] In geotechnical centrifuge model tests, a centrifugal force with n times the gravitational acceleration is applied to provide a hypergravity field with the same stress level as the prototype, so that the test model and the prototype have similar mechanical performance. When simulating the mechanical response of pile foundations under actual stress, achieving bidirectional loading in both vertical and horizontal directions helps to accurately reproduce and reveal the bearing mechanism, deformation evolution law, and nonlinear interaction characteristics of piles under complex environments.

[0003] Currently, centrifugal model bidirectional loading schemes rely on independent loading mechanisms. During testing, a horizontal actuator applies a horizontal thrust to the test model from the side, causing horizontal displacement or deflection. Simultaneously, a vertical loading device maintains a constant downward load. In this type of scheme, the loading device cannot automatically sense and follow the model's movement, or it relies on rigid linkage for passive dragging and following.

[0004] However, existing technologies face technical challenges in implementing loading, including distortion of displacement estimation models and cross-dimensional coupling interference between load and displacement. Therefore, further research and innovation are needed to address these issues in existing technologies. Summary of the Invention

[0005] Purpose of the invention: In view of the above-mentioned problems in the prior art, this application provides a method and device for coordinated control of bidirectional loads on pile foundations in geotechnical centrifugal model tests.

[0006] Technical solution: Firstly, a method for coordinated control of bidirectional loads on pile foundations using geotechnical centrifuge model tests, including:

[0007] Real-time acquisition of the pile rotation angle of the loaded pile, the actual vertical load at the loading point, and the actual horizontal position of the vertical actuator during the centrifugal model test;

[0008] The actual horizontal displacement of the pile top is estimated based on the pile rotation angle and dynamically updated deformation mode coefficients.

[0009] Based on the deviation between the actual horizontal displacement of the pile top and the actual horizontal position, a horizontal movement command is generated to drive the vertical actuator to follow horizontally.

[0010] Based on the deviation between the target vertical load and the actual vertical load, a vertical fine-tuning command is generated to compensate for the vertical load disturbance caused by horizontal following.

[0011] In conjunction with the first aspect, a two-way load collaborative control device for pile foundations in geotechnical centrifuge model tests includes:

[0012] A two-degree-of-freedom orthogonal motion platform has mutually perpendicular vertical and horizontal degrees of freedom.

[0013] The vertical actuator, installed on the execution end of the two-degree-of-freedom orthogonal motion platform, is used to apply the actual vertical load to the loaded pile and is driven to follow horizontally along the horizontal degree of freedom.

[0014] A horizontal actuator, independently installed on the side of the loaded pile, is used to apply the actual horizontal load to the loaded pile;

[0015] Sensor components are used to collect data in real time on the pile body rotation angle of the loaded pile, the actual vertical load at the loading point, and the actual horizontal position of the vertical actuator.

[0016] The controller is communicatively connected to the two-degree-of-freedom orthogonal motion platform, the vertical actuator, the horizontal actuator, and the sensor assembly, and is used to execute the method described in any of the first aspects.

[0017] Beneficial effects: The present invention introduces a dual closed-loop decoupled collaborative control and a multi-level dynamic coefficient correction mechanism, which helps to suppress the distortion of loading force caused by mechanical motion coupling and avoid pile damage caused by eccentric load. Attached Figure Description

[0018] Figure 1 A flowchart of a method for coordinated control of bidirectional loads on pile foundations in a geotechnical centrifugal model test, provided for an embodiment of this application.

[0019] Figure 2 This is a flowchart for obtaining dynamically updated deformation mode coefficients provided in an embodiment of this application.

[0020] Figure 3 The flowchart provided in this application embodiment describes how, based on the initial deformation mode coefficients, the current loading stage is identified and stage switching is performed through online stage coarse adjustment to obtain the coarse deformation mode coefficients.

[0021] Figure 4 The flowchart provided in this application illustrates how online adaptive fine-tuning eliminates errors in the coarse-tuned deformation mode coefficients at each loading stage to obtain dynamically updated deformation mode coefficients.

[0022] Figure 5 This is a flowchart of the feedforward compensation process for mechanical coupling provided in an embodiment of this application. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] It should be understood that the terms "first," "second," etc., in the specification and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a predetermined order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in sequences other than those illustrated or described herein. Furthermore, the terms "including" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0025] To address the aforementioned issues, the applicant conducted in-depth searches and analyses, and discovered:

[0026] Existing displacement estimation methods employ a simple linear product of pile rotation angle and pile length. This rigid body rotation assumption neglects the downward shift of the rotation center due to soil deformation and the flexural deformation component generated by the flexible pile itself. Under centrifugal large gradient deformation conditions, this rigid model leads to systematic following errors.

[0027] Furthermore, existing following mechanisms exhibit undecoupled kinematic interference during execution. When the actuator chases horizontally, due to non-ideal characteristics such as stiffness, friction, and clearance of the mechanical system, the following motion is transmitted to the loading path through structural coupling. This additional mechanical disturbance caused by displacement following can lead to the actual applied vertical load deviating from the set target and failing to be applied to the loading point designed for the test model. This can easily cause the model pile to become unstable or fail due to eccentric loads.

[0028] To solve these problems, combined with Figures 1 to 5 The present invention will be specifically described through the following embodiments.

[0029] Hereinafter, the loaded pile is also called a model pile, the displacement level criterion is also called the displacement level ratio criterion, and the horizontal servo motor is also called a drive motor. A PI controller is also called a proportional-integral controller, and a PID controller is also called a proportional-integral-derivative controller. γ represents the preset learning rate, also known as the correction coefficient.

[0030] Firstly, an exemplary scheme is provided for a method of coordinated control of bidirectional loads on pile foundations in a geotechnical centrifugal model test.

[0031] The control method described in this embodiment requires a predetermined hardware system. This system includes a two-degree-of-freedom orthogonal motion platform, which has mutually perpendicular vertical and horizontal degrees of freedom. A vertical actuator is mounted on the execution end of the two-degree-of-freedom orthogonal motion platform to apply the actual vertical load to the loaded pile, and can be driven to follow horizontally along the horizontal degree of freedom.

[0032] As an optional hardware actuator, the horizontal following mechanism can employ a ball screw-driven linear module or a linear motor to meet the requirements of long-stroke displacement following. The horizontal actuator can be independently installed on the side of the loaded pile to apply the actual horizontal load to the pile. In centrifugal testing, the model pile will deflect horizontally due to the application of the actual horizontal load. If the vertical loading point does not dynamically follow up, the model pile will be subjected to eccentric load and become unstable. Therefore, this embodiment achieves bidirectional decoupling control of force and position through the following steps.

[0033] Step 101: Real-time acquisition of the pile rotation angle of the loaded pile, the actual vertical load at the loading point, and the actual horizontal position of the vertical actuator during the centrifugal model test.

[0034] In this step, the system's underlying sensor network continuously monitors the operational status of each physical component. Accordingly, the pile rotation angle can be obtained using angle sensors installed at the mud surface or at a known depth of the pile's shallow penetration into the soil; the actual vertical load can be obtained using force sensors located at the loading head of the vertical actuator's top wheel. Simultaneously, the actual horizontal position of the vertical actuator on the horizontal slide rail can be read using linear displacement sensors.

[0035] Optionally, the actual horizontal load can be collected in real time by a force sensor installed at the loading end of the horizontal actuator; the actual horizontal load data is used to calculate the tangential stiffness of the system, providing input for online stage identification, and the configuration can be selected according to the application scenario.

[0036] The real-time sensor data collected above constitutes the input source for the subsequent dual-closed-loop collaborative control system.

[0037] Step 102: Obtain the dynamically updated deformation mode coefficients; estimate the actual horizontal displacement of the pile top based on the pile rotation angle and the dynamically updated deformation mode coefficients.

[0038] In the high-gravity field environment of a centrifuge, direct measurement of the horizontal displacement at the pile top is easily affected by structural spatial interference and high-frequency vibration. Therefore, an indirect estimation method combining geometric mapping and theoretical coefficients can be used. The dynamically updated deformation mode coefficient is a dimensionless characteristic parameter used to characterize the nonlinear stiffness variation of the pile-soil system. Introducing this coefficient can correct the theoretical prediction errors caused by treating the pile as an ideal rigid rod in rotation, and transform the local angle data at shallow measuring points into overall translational displacement data of the pile top.

[0039] Step 103: Based on the deviation between the actual horizontal displacement and the actual horizontal position of the pile top, a horizontal movement command is generated to drive the vertical actuator to follow horizontally; this constitutes the outer loop control logic of the control system, which belongs to the slow dynamic loop that processes slowly changing system variables.

[0040] The estimated actual horizontal displacement of the pile top is used as the target tracking anchor point, and its difference is compared with the feedback current actual horizontal position. Based on the obtained spatial position deviation signal, the controller calculates and generates a horizontal movement command. The horizontal movement command is output to the horizontal servo motor, which drives the slide rail mechanism to move the vertical actuator horizontally, always maintaining the vertical loading force acting on the geometric center of the offset pile top.

[0041] Step 104 generates a vertical fine-tuning command based on the deviation between the preset target vertical load and the actual vertical load to compensate for vertical load disturbances caused by horizontal following. This constitutes the inner-loop control logic of the control system, which is a fast dynamic loop for handling sudden changes in system parameters.

[0042] During the horizontal following movement of the vertical actuator, due to the frictional resistance of the guide rail mechanical structure and the assembly gap, the dynamic characteristics in the horizontal direction will transmit additional stress downward along the loading component, causing the originally constant vertical force state to fluctuate significantly.

[0043] Therefore, this step involves subtracting the expected target vertical load from the actual vertical load fed back by the force measuring unit. The controller then generates a vertical fine-tuning command, further driving the extension and retraction ends of the vertical actuator to make minor vertical displacement adjustments. Since the compensation mechanism can optionally employ a high-frequency response voice coil motor or piezoelectric ceramic actuator, it can actively generate compensating displacement to offset additional load disturbances, achieving coordinated decoupling of displacement following and constant loading force.

[0044] On the other hand, it describes the specific geometric mapping formula for the horizontal displacement at the pile top, and a three-level determination framework for the dynamic deformation mode coefficients to overcome the assumptions of the constant theory. Specifically, it includes:

[0045] Step 201, in estimating the actual horizontal displacement of the pile top based on the pile rotation angle and dynamically updated deformation mode coefficients, can be specifically calculated using the following formula:

[0046] δh(t) = κ(t) × L × sinθ(t);

[0047] Where δh(t) corresponds to the actual horizontal displacement of the pile top, κ(t) corresponds to the dynamically updated deformation mode coefficient, L corresponds to the effective cantilever length from the preset angle sensor measuring point to the pile top, and θ(t) corresponds to the pile body rotation angle.

[0048] Furthermore, the effective cantilever length is specifically the distance from the installation position of the angle sensor to the point of application of the load at the top of the pile along the pile axis; when the sensor is installed at the mud surface elevation, this length is the length of the free section above ground from the top of the pile to the mud surface.

[0049] The above clarifies the geometric mapping relationship from the measured angle to the pile top displacement. It should be understood that the angle sensor is not installed at the pile top, but can be optionally fixed at the mud surface or at a known depth of penetration. Correspondingly, the preset pile penetration depth is specifically defined as the effective cantilever length from the angle sensor's measuring point to the pile top. For flexible piles with flexural deformation, since the local cross-sectional rotation angle measured by the sensor underestimates the overall bending effect of the pile, the calculated actual displacement must be amplified and compensated using a correction factor greater than 1.

[0050] In some alternative implementations, when the deformation of the loaded pile is strictly controlled within a very small deformation range, considering the Taylor expansion approximation characteristics of the sine function at small angles, the sine term can be directly replaced by the radian term. That is, a simplified formula can be used to quickly estimate the actual horizontal displacement at the pile top, and its calculation form is: δh(t)=κ(t)×L×θ(t).

[0051] Step 202, the process of obtaining dynamically updated deformation mode coefficients includes: obtaining the initial deformation mode coefficients corresponding to each loading stage through offline benchmark preset;

[0052] Before conducting the centrifugal loading test, the system pre-establishes foundation coefficient values ​​under different mechanical response states based on known geophysical parameters and model pile mechanical parameters using theoretical formulas or numerical simulations, which can provide data dictionary support for subsequent online calls.

[0053] Step 203: Based on the initial deformation mode coefficients, the current loading stage is identified and the stage is switched through online stage coarse adjustment to obtain the coarse-adjusted deformation mode coefficients.

[0054] Alternatively, based on the initial deformation mode coefficients, the current loading stage is identified and switched in real time during operation to complete the stage coarse adjustment and output the coarse-adjusted deformation mode coefficients.

[0055] Since constant coefficients cannot reflect the gradual yielding behavior of soil as the load increases, the system monitors physical quantities reflecting soil stiffness degradation in real time during operation. When a change in the soil's mechanical state is detected, the system extracts coefficient values ​​matching the current state from the data dictionary constructed at the first level, achieving large-scale parameter coarse adjustment and stage isolation.

[0056] Step 204: Through online adaptive fine-tuning, the coarse-tuned deformation mode coefficients in each loading stage are error-eliminating to obtain dynamically updated deformation mode coefficients.

[0057] Within each mechanical stage, although the average deformation pattern of the soil remains relatively stable, there are still small calculation residuals caused by measurement noise or local soil heterogeneity. The system further integrates redundant auxiliary measurement methods and executes an online recursive algorithm to continuously approximate the true coefficient solution. Specifically, the dynamically updated deformation pattern coefficients of the filtered output are fed into the outer-loop following control logic in real time to ensure the accuracy of the horizontal movement commands.

[0058] On another front, it explains how to perform online coarse-tuning of dynamically updated deformation mode coefficients based on the laws of physical state evolution, and the anti-impact smooth transition mechanism used during parameter switching. The following methods can be used to implement this:

[0059] Step 301: Obtain the real-time collected actual horizontal load, and calculate the system characteristic state quantities in combination with the actual horizontal displacement at the pile top;

[0060] In this step, the control unit receives actual horizontal load data fed back by the force sensor on the side of the horizontal loading device. Since the foundation resistance of the soil is not linearly constant during the loading process, it is necessary to extract variables that can comprehensively reflect the current mechanical attenuation of the system.

[0061] Optionally, algebraic operations are performed on the actual horizontal load and the actual horizontal displacement at the top of the pile to extract the system's characteristic state variables. These state variables can be used to construct a quantitative evaluation criterion for subsequent division of nonlinear mechanical stages.

[0062] Step 302: Input the system characteristic state variables into the preset stage transition criteria for comparison and judgment, and identify the current loading stage;

[0063] Specifically, the system memory stores pre-configured judgment logic boundary conditions. The controller uses the system characteristic state quantities calculated at the current sampling time as input parameters and compares them logically with the given threshold boundaries. Based on the mathematical interval in which the comparison result falls, the system outputs the physical stage label corresponding to the current centrifugal model pile-soil system.

[0064] Step 303: The loading stage is divided into the following stages according to the nonlinear evolution process of the interaction between the loaded pile and the soil: elastic stage, yielding stage and near-failure stage, in order of increasing load.

[0065] In this embodiment, the specific characteristics of the physical stage are defined, namely:

[0066] During the elastic stage, the shallow soil around the pile is in an elastic working state as a whole, and the foundation resistance and displacement show an approximately linear relationship.

[0067] As the load continues to increase and the soil enters the yielding stage, local plastic deformation occurs in the shallow soil, and the soil resistance begins to redistribute to the deeper soil layers.

[0068] When the load approaches the ultimate bearing capacity of the system, it enters the near-failure stage, at which point the soil undergoes large-scale plastic yielding.

[0069] Furthermore, since this control system is positioned for bidirectional loading within a small to medium deformation range, when the status identification result indicates that the system has entered the near-failure stage, the system can trigger a preset protective safety shutdown procedure to stop issuing new follow-up motion commands, record the current ultimate load data, and avoid damage to the centrifuge's actuating equipment caused by large deformation conditions.

[0070] Step 304, correspondingly, the initial deformation mode coefficients for each preset loading stage satisfy a monotonically increasing law, that is:

[0071] The initial deformation mode coefficient corresponding to the elastic stage is less than that corresponding to the yield stage, and the initial deformation mode coefficient corresponding to the yield stage is less than that corresponding to the near-failure stage.

[0072] The position of the rotation center of the loaded pile within the soil determines the value of the deformation mode coefficients. In the elastic stage, the system's rotation center is relatively high, and the pile exhibits shallow stress. Upon entering the yielding stage, the shallow soil gradually withdraws from the load, and the rotation center begins to move downwards, resulting in a larger actual translational displacement at the pile top for the same mud surface rotation angle. Therefore, the initial deformation mode coefficients for each loading stage must numerically adhere to a strict monotonically increasing constraint.

[0073] Step 305: The system characteristic state quantity is the tangent stiffness ratio or the displacement level ratio; the preset stage transition criteria include the tangent stiffness ratio criterion or the displacement level criterion.

[0074] Based on this, the following two stages of identification are provided;

[0075] First, it depends on the dynamic derivative relationship between force and displacement;

[0076] Secondly, it depends only on the normalized geometric deformation.

[0077] Furthermore, the system can select one of the criteria for closed-loop calculation based on the accuracy and type of the currently mounted sensors.

[0078] Step 306: When the stage transition criterion is the tangent stiffness ratio criterion, the system tangent stiffness is calculated based on the increment of the actual horizontal load and the increment of the actual horizontal displacement at the pile top, and the ratio of the system tangent stiffness to the preset initial stiffness is taken as the tangent stiffness ratio.

[0079] The tangent stiffness ratio is compared with the preset first stiffness ratio threshold and the second stiffness ratio threshold to identify the current loading stage.

[0080] As an optional implementation, the tangent stiffness ratio criterion can more sensitively capture the nonlinear yielding behavior of soil. The controller extracts the difference between the actual horizontal loads in adjacent sampling periods as the increment, and similarly extracts the difference between the actual horizontal displacements at the pile top. The quotient of the two differences is defined as the system tangent stiffness.

[0081] Next, the system divides the stiffness value by the preset initial stiffness calibrated early in the loading process to complete the dimensionless processing. For example, a preset first stiffness ratio threshold can be set to 0.8, and a preset second stiffness ratio threshold can be set to 0.4. The stage determination can be performed using the following method:

[0082] When the calculated tangent stiffness ratio is ≥0.8, the system is determined to be in the elastic stage;

[0083] When the ratio is less than 0.8 and greater than or equal to 0.4, the plant is considered to have entered the yielding stage.

[0084] When the ratio is less than 0.4, the system is considered to be in the near-destruction stage.

[0085] Step 307: When the stage transition criterion is the displacement level criterion, the ratio of the actual horizontal displacement of the pile top to the preset pile diameter is taken as the displacement level ratio.

[0086] The horizontal displacement ratio is compared with the preset first displacement ratio threshold and second displacement ratio threshold to identify the current loading stage.

[0087] In some test conditions where high-precision continuous force value recording is lacking, a criterion based on geometric normalization can be selected. The system directly removes the actual horizontal position of the pile top from the obtained data to obtain the model pile diameter of the loaded pile, thus obtaining a dimensionless displacement-to-horizontal ratio.

[0088] For example, a preset first displacement ratio threshold is set to 0.03, and a second displacement ratio threshold is set to 0.10. Based on the size of the interval in which the calculated ratio falls, the corresponding physical loading stage identification result can also be mapped and output.

[0089] Step 308: Select the initial deformation mode coefficient corresponding to the current loading stage as the coarse-tuning deformation mode coefficient.

[0090] Accordingly, the system internally establishes a lookup table, using the identified physical stage name as the retrieval key, and directly retrieves the statically bound coefficient values ​​from memory. The extracted parameters then constitute the reference quantities for calculating the horizontal following displacement during that loading stage.

[0091] Step 309: When the switching moment of the current loading stage is detected, a preset progressive transition function is used to smoothly transition the initial deformation mode coefficients before and after the transition.

[0092] Because the static parameters corresponding to adjacent mechanical stages have discrete steps, if a hard switch is performed in the program, it will cause the displacement command estimated by the controller according to the formula to produce discontinuous abrupt changes, which will cause mechanical shock and violent mechanical coupling oscillations in the servo motion mechanism.

[0093] Therefore, at the time point when the state switch is triggered, a mitigation control strategy can be introduced so that the coefficient continuously and monotonically slides from the old parameter value to the new parameter value within a specified time window.

[0094] Step 310: Output the coarse-tuned deformation mode coefficients after smooth transition using the following formula:

[0095] κ _c (t)=κ _i +(κ _j -κ _i )×[3(τ / T _s ) 2 -2(τ / T _s ) 3 ];

[0096] Among them, κ _c (t) represents the coarse-tuned deformation mode coefficients after smooth transition, κ _i κ represents the initial deformation mode coefficients before transformation. _j T represents the initial deformation mode coefficients after the transformation, τ represents the elapsed time since the switching moment, and T represents the time after the transformation. _s This is the preset transition time.

[0097] The above constructs a cubic polynomial S-shaped mathematical curve. Assuming the current working condition is a transition from the elastic stage to the yielding stage, the parameter κ is retrieved. _i =1.0, κ _j =1.2, the preset transition time of the configuration system is T _s =2.0 seconds.

[0098] When the self-switching action occurs and 1.0 second has elapsed (τ=1.0), the time normalization coefficient τ / T _s =0.5.

[0099] Substituting into the formula, we can obtain the polynomial weight term as 3×0.25-2×0.125=0.5.

[0100] Based on this, the coefficient κ at the current time point is calculated. _c (t) = 1.0 + 0.2 × 0.5 = 1.1.

[0101] This mechanism helps maintain the continuity of the first derivative of the parameter matrix and the displacement commands it controls in the time domain.

[0102] Alternatively, a first-order linear interpolation function can be used to smoothly replace parameters, reducing the computational load on the embedded controller. The alternative calculation form can be expressed as follows:

[0103] κ _c (t)=κ _i +(κ _j -κ _i )×(τ / T _s ).

[0104] On the other hand, the possible implementation methods for adaptive refinement and state reset of multi-sensor fusion are described, specifically as follows:

[0105] Step 401: Obtain the actual displacement measurement value of the pile top collected in real time by the auxiliary displacement sensor;

[0106] In this step, the system adds displacement monitoring hardware independent of the angle acquisition loop. Specifically, the auxiliary displacement sensor can be implemented using a laser displacement sensor or a wire-type displacement sensor.

[0107] In the spatial layout of centrifugal model tests, auxiliary displacement sensors can be deployed remotely and non-contactly. For example, the laser head of a laser displacement sensor can be fixed to the rotating arm structure frame to measure the displacement of a reflective target pasted on the side of the pile, thereby indirectly obtaining the displacement reference value at the top of the pile; or the wire of a pull-wire sensor can be connected to a known height marker on the pile, and the displacement at the top of the pile can be converted based on the known geometric relationship.

[0108] It should be understood that a suitable installation scheme can be selected based on the specific space conditions of the test equipment.

[0109] In centrifugal model tests, the high-gravity acceleration environment causes conventional laser displacement sensors to be subject to high-frequency vibration interference, resulting in transient jumps in their output signals. However, such sensors maintain accuracy in measuring absolute spatial position in the low-frequency domain. In contrast, angle sensors used to measure pile rotation angles exhibit higher vibration resistance and high-frequency response capabilities, but their mapping of absolute displacement relies on theoretical deformation mode coefficients.

[0110] Therefore, introducing the true value of displacement measurement in actual spatial dimension can be used for cross-verification and fusion with the rotation angle extrapolation value, thus making up for the limitations of a single sensing method.

[0111] Step 402: Calculate the predicted horizontal displacement based on the coarse-adjusted deformation mode coefficient, pile rotation angle, and preset pile penetration depth.

[0112] The controller uses the baseline coefficients output after stage identification and smooth switching as the starting point for calculation. Based on the small-angle approximation principle, the controller multiplies the coarse-adjusted deformation mode coefficients, the pile rotation angle, and the preset pile penetration depth to output the current predicted horizontal displacement. This predicted value characterizes the spatial motion trend of the pile top obtained by mapping the rotation angle data under the current assumed nonlinear stiffness level.

[0113] It should also be understood that during the online adaptive fine-tuning process, the predicted horizontal displacement and the denominator of the formula can be calculated using a small angle approximation (sinθ(t)≈θ(t)). For working conditions with large deformation that cannot meet the small angle approximation, θ(t) in the denominator can be replaced with sinθ(t). The appropriate approximation form can be selected according to the actual deformation magnitude.

[0114] Step 403: Calculate the displacement deviation between the actual measured displacement at the pile top and the predicted horizontal displacement;

[0115] Accordingly, the system performs algebraic subtraction on the two displacement data points under the same sampling timestamp. The displacement deviation is obtained by subtracting the previously calculated predicted horizontal displacement from the actual displacement measurement value at the pile top provided by the auxiliary displacement sensor. This deviation term includes the theoretical model residuals caused by local heterogeneity of the soil, high-frequency random observation noise, and systematic estimation errors caused by parameter discrepancies.

[0116] Step 404 yields dynamically updated deformation mode coefficients, which can be corrected online using the following formula:

[0117] κ(t)=κ _c (t)+γ×e(t) / (θ(t)×L);

[0118] Where κ(t) represents the dynamically updated deformation mode coefficients, κ _c(t) represents the coarse adjustment deformation mode coefficient, γ represents the preset learning rate, e(t) represents the displacement deviation, θ(t) represents the pile rotation angle, and L represents the preset effective cantilever length from the angle sensor measuring point to the pile top.

[0119] In this step, an exponentially weighted moving average algorithm is introduced to perform online allocation and convergence calculation of the error term. The preset learning rate controls the step size and iteration speed of each parameter correction and can be determined experimentally based on the displacement tracking accuracy requirements and sensor noise level in practical applications. In this embodiment, γ can be set to 0.15.

[0120] Based on this, using a lower learning rate can filter out high-frequency noise from the auxiliary displacement sensor and improve the stability of the correction process; a higher learning rate can accelerate the system's response speed to sudden changes in local soil stiffness.

[0121] Here is a normalization example:

[0122] Suppose that the normalized fundamental coefficient κ extracted at the current time... _c Given that θ(t) = 1.10, and due to localized soil hardening, the calculated normalized displacement deviation term e(t) / (θ(t)×L) = 0.20. Simultaneously, the system sets the preset normalization learning rate γ = 0.10. Substituting these values ​​into the formula, the dynamic correction increment for this period is calculated to be 0.10 × 0.20 = 0.02.

[0123] The system adds this increment to the base coefficients and outputs the corrected dynamically updated deformation mode coefficients κ(t) = 1.12.

[0124] Through this mechanism, the system can continuously smooth out the local residuals between the theoretical model and the actual working conditions by utilizing information from multiple sensor sources.

[0125] Step 405: When a transition in the current loading stage is detected, the cumulative correction amount generated by the online adaptive fine-tuning is forcibly reset to zero. After entering the new loading stage, the online correction based on the actual displacement measurement value is restarted with the new coarse-tuning deformation mode coefficient as the benchmark.

[0126] The adaptive fine-tuning operation involves micro-disturbance optimization within a predetermined soil physical stage. The cumulative correction includes and records the historical deviation characteristics under this predetermined stage.

[0127] When the system identifies that the loading state has transitioned from the elastic stage to the yielding stage based on criteria such as tangent stiffness ratio, the soil's bearing mechanism and deformation boundary conditions have already shifted. If a zeroing operation is not performed at this point, the system will forcibly introduce the cumulative correction amount unique to the elastic stage into the calculation loop of the yielding stage. This will not only lead to deviations in the displacement estimation at the beginning of the new stage, but may also trigger mathematical divergence in the closed-loop control system.

[0128] Therefore, the controller forcibly erases historical integral and accumulated error data from memory the instant the stage transition flag is triggered. After entering a new loading stage, the system extracts the coarse-tuning deformation mode coefficients matching the new stage as the convergence benchmark with zero starting point, and restarts the closed-loop deviation correction calculation.

[0129] The independent reset mechanism at each stage helps to ensure the logical purity and operational stability of the multi-level parameter determination system throughout the entire loading cycle.

[0130] In this invention, to address the displacement estimation distortion caused by the traditional rigid body rotation assumption, a dynamically updated deformation mode coefficient is introduced. By constructing a three-level parameter determination system that includes offline benchmark pre-setting, online stage coarse adjustment based on stiffness characteristics, and online adaptive fine adjustment through multi-sensor fusion, the systematic errors caused by the downward shift of the rotation center due to soil yielding and the flexural deformation of the flexible pile itself are overcome, enabling real-time estimation of the actual horizontal displacement of the pile top within a small to medium deformation range.

[0131] In some embodiments, the underlying logic of the dual-closed-loop control, the bandwidth decoupling mechanism, and the feedforward compensation transformation process based on system stiffness are described. Accordingly, the following steps can be employed:

[0132] Step 501: Input the deviation between the actual horizontal displacement of the pile top and the actual horizontal position into the outer loop PI controller for proportional-integral calculation, and output the horizontal movement command;

[0133] Accordingly, the controller architecture adopts a dual closed-loop structure with an outer loop and an inner loop. The function of the outer loop is to make the loading point follow the displacement of the pile top in the horizontal direction. Since the settlement and displacement process of the pile top is relatively gradual, its rate of change is constrained by the response characteristics of the pile-soil system and belongs to the category of slow variables.

[0134] For example, the outer-loop PI controller is specifically a proportional-integral controller, used to perform outer-loop following control. After receiving the deviation signal, the controller's proportional operation stage linearly amplifies the current position error, while the integral operation stage performs time-accumulated calculations on the historical error to eliminate the system's steady-state following error. The calculated horizontal motion command is then sent to the horizontal motion mechanism, driving it to perform the corresponding horizontal position adjustment.

[0135] Step 502: Input the deviation between the preset target vertical load and the actual vertical load into the inner loop PID controller for proportional-integral-derivative calculation, and output the vertical fine-tuning command.

[0136] For example, the inner loop is used to keep the vertical loading force constant at a preset target value. The inner loop handles the force disturbance compensation problem, which falls under the category of fast variables.

[0137] Optionally, the inner-loop PID controller is specifically a proportional-integral-derivative (PID) controller. Since force control requires high response speed, the derivative operation stage utilizes the rate of change of the force error signal for proactive adjustment, improving the system's response speed to sudden force changes.

[0138] Furthermore, considering the measurement noise present in the sensor under high gravity acceleration environment, a low-pass filter can be connected in series before entering the differentiation stage to prevent the noise from being amplified by the differentiation stage.

[0139] Furthermore, the controller generates a vertical fine-tuning command based on the received force error signal, driving the vertical actuator to fine-tune the vertical position of the loading point, so that the actual vertical load is restored and maintained at the target level.

[0140] Step 503: In order to achieve time-scale separation and decoupling between horizontal displacement following and vertical load stability, the preset inner loop response bandwidth of the inner loop PID controller is set to be strictly greater than five times the preset outer loop response bandwidth of the outer loop PI controller, so that the compensation response speed of vertical load disturbance is faster than the response speed of horizontal displacement following.

[0141] In a dual-loop control system, the kinematic coupling of the controlled mechanism can cause mutual interference between the two control loops. When the outer loop performs a horizontal following motion, the stiffness and frictional characteristics of the mechanical system can cause fluctuations in the vertical loading force.

[0142] In this step, a time-scale separation mechanism can be optionally established to handle physical coupling effects. Based on the Nyquist stability criterion and closed-loop interaction frequency characteristics in automatic control theory, the frequency response bandwidth of the inner loop control loop is set to be higher than that of the outer loop control loop.

[0143] Specifically, the preset inner loop response bandwidth is set to be five times greater than the preset outer loop response bandwidth. Under this frequency domain configuration, since the inner loop's compensation action for force disturbances is faster than the outer loop's mechanical displacement adjustment, the mechanical disturbances generated by the outer loop can be eliminated by the inner loop controller through reverse displacement action before they accumulate. This achieves orthogonal decoupling of displacement parameters and force parameters at the software algorithm level.

[0144] Step 504, in generating the vertical fine-tuning command based on the deviation between the preset target vertical load and the actual vertical load, also includes feedforward compensation processing for mechanical coupling, namely:

[0145] Based on the pre-calibrated kinematic coupling coefficient and the horizontal motion command, calculate the vertical force feedforward compensation caused by the horizontal following motion of the vertical actuator;

[0146] The vertical force feedforward compensation is superimposed on the vertical fine-tuning feedback signal generated by feedback control based on the actual vertical load deviation to obtain the vertical fine-tuning command.

[0147] Because feedback control systems have a time lag, they only execute corrective actions after an error occurs. To reduce the force fluctuation amplitude caused by horizontal motion, a feedforward compensation loop can be constructed using deterministic mechanical coupling laws.

[0148] Accordingly, before conducting the centrifugal model test, the actuator is driven to run a known displacement trajectory through a calibration test, and the dimensionless parameter representing the coupling law of the physical attitude of the mechanism, namely the kinematic coupling coefficient, is recorded and calculated simultaneously.

[0149] In the real-time control loop, the controller uses the known horizontal motion command and kinematic coupling coefficients to predict the additional vertical displacement and corresponding disturbance force caused by the horizontal movement. The predicted value is the vertical force feedforward compensation. This feedforward is used as a reference bias term and summed with the feedback term output by the PID controller. Thus, the vertical fine-tuning command has the function of anticipating force disturbances.

[0150] Step 505: Obtain the equivalent vertical stiffness of the centrifugal model test loading system; calculate the product of the pre-calibrated kinematic coupling coefficient, the equivalent vertical stiffness, and the horizontal displacement adjustment increment represented by the horizontal motion command to obtain the vertical force feedforward compensation amount. This is used to convert the kinematic coupling displacement into a mechanical compensation command.

[0151] Accordingly, the feedforward calculation formula set internally by the controller is:

[0152] ΔF=k _s ×λ×Δx _a ;

[0153] Where ΔF is the vertical force feedforward compensation amount, k _s The equivalent vertical stiffness of the loading system in the centrifugal model test is given by λ, where λ is the pre-calibrated kinematic coupling coefficient, and Δx is the value of Δx. _a The horizontal displacement adjustment increment is represented by the horizontal motion command.

[0154] In this calculation process, the kinematic coupling coefficient is multiplied by the horizontal displacement adjustment increment, which characterizes the vertical parasitic displacement generated by the horizontal servo motion transmitted through the mechanism.

[0155] Furthermore, by multiplying the parasitic displacement by the equivalent vertical stiffness of the system, the magnitude of the expected disturbance force corresponding to the physical deformation is obtained according to Hooke's Law.

[0156] For example, assume that the system obtains the normalized horizontal displacement adjustment increment Δx _a The value is 1.0, and the normalized kinematic coupling coefficient λ, calibrated through prior testing, is 0.05. Simultaneously, the normalized equivalent vertical stiffness k of this system is input. _s The value is 2.0.

[0157] Substituting the three parameters into the feedforward formula, the normalized feedforward compensation amount ΔF is calculated to be 1.0 × 0.05 × 2.0 = 0.10.

[0158] Based on this, the value of 0.10 will be directly added to the output of the controller to drive the vertical actuator to perform compensation operations before the actual mechanical disturbance occurs.

[0159] The above describes a dual-closed-loop cooperative control architecture with time-scale separation characteristics. A slow-dynamic outer loop is used to dominate horizontal position following, addressing the mechanical coupling interference caused by the spatial motion of the following mechanism. The fast-dynamic inner loop dominates vertical force feedback compensation, supplemented by a feedforward compensation algorithm based on the system's equivalent stiffness and kinematic coupling coefficient, decoupling hardware interference at the software algorithm level. This approach eliminates vertical load fluctuations caused by horizontal drag in real time, ensuring that bidirectional loads are always applied to the design point, thus preventing instability or damage to the experimental model caused by eccentric loading.

[0160] In another embodiment, an exemplary scheme for offline parameter asymptotic calibration and initial threshold self-tuning method is provided, specifically including:

[0161] Step 601: Calculate the relative stiffness characteristic value of the loaded pile based on the soil parameters of the test pile obtained offline;

[0162] In this step, the control system needs to establish the foundation stiffness mapping relationship of the pile-soil system in advance before entering the real-time centrifugal loading program.

[0163] For example, the soil parameters of the test pile specifically include pile diameter, elastic modulus of pile material, moment of inertia of pile section, and horizontal resistance coefficient of foundation. The system extracts the parameters, performs algebraic calculations, and outputs dimensionless relative stiffness characteristic values.

[0164] Accordingly, the relative stiffness characteristic value α can be determined using conventional pile foundation flexibility assessment methods in this field, such as the reciprocal of the characteristic length under the Winkler foundation beam model, or other equivalent pile-soil relative stiffness characterization methods, which can be implemented with reference to relevant pile foundation design codes or technical documents.

[0165] When α is small, the pile exhibits rigid characteristics;

[0166] When α is large, the pile exhibits flexible characteristics.

[0167] It should be understood that this characteristic value objectively reflects the relative bending characteristics of the model pile under the predetermined foundation conditions, and is the benchmark input variable for subsequently establishing the deformation mode coefficients.

[0168] Step 602: Calculate the corresponding initial deformation mode coefficients based on this (relative stiffness eigenvalue).

[0169] In other words, the initial deformation mode coefficients corresponding to the relative stiffness eigenvalues ​​are calculated using the following formula:

[0170] κ _0 =1+(κ _∞ -1)×α^2 / (α^2+α _0 ^2);

[0171] Among them, κ _0 κ represents the initial deformation mode coefficients, α is the relative stiffness eigenvalue, and κ is the eigenvalue. _∞ α is the preset limit correction coefficient for flexible piles. _0 The half-value feature is a preset value.

[0172] This step utilizes a given mathematical asymptotic formula to complete the nonlinear mapping from the stiffness domain to the coefficient domain, introducing upper and lower bound constraints to compensate for extremum defects. Specifically, its boundary response characteristics are analyzed: when the input relative stiffness eigenvalue approaches 0, the calculation result approaches 1.0; when the input relative stiffness eigenvalue approaches infinity, the calculation result monotonically converges to the preset flexible pile limit correction coefficient. The preset half-value eigenvalue is used to control the transition rate of the curve in the stiffness-flexibility transition range.

[0173] For example, a normalized flexibility limit upper limit κ can be set. _∞ =1.5, normalized half-value eigenvalue α _0 =1.0.

[0174] When the system calculates the current normalized relative stiffness characteristic value α=1.0 based on the previous soil parameters, the result is 1.0+0.5×1.0 / 2.0=1.25 when substituted into the formula.

[0175] Based on this, the initial deformation mode coefficient is 1.25.

[0176] This value is stored in the static storage area by the system for use in subsequent coarse adjustment processes.

[0177] According to one aspect of this application, in a three-stage loading system, initial deformation mode coefficients need to be determined sequentially for the elastic stage, yielding stage, and near-failure stage. As the horizontal resistance stiffness of the soil around the pile gradually degrades with increasing load, the relative stiffness characteristic value of the pile-soil system increases sequentially at different stages. Substituting the α values ​​corresponding to the three stages into the formula yields three sequentially increasing initial deformation mode coefficients, satisfying the monotonically increasing constraint. The α value for each stage can be calculated based on the expected secant stiffness of the soil at that stage. The secant stiffness of the soil can be determined based on offline finite element analysis or similar experimental experience, or it can be determined using pile-soil nonlinear analysis methods.

[0178] Alternatively, the offline benchmark preset of the initial deformation mode coefficients can also be achieved through other equivalent calibration methods. Alternative methods include using finite element simulation software to extract the foundation reaction curve for numerical iterative solution, or conducting a normal gravity preloading calibration experiment before the formal hypergravity centrifuge test and directly extracting empirical coefficients by comparing physical displacements.

[0179] Step 603: During the initial loading elasticity phase, continuously calculate and statistically analyze the fluctuation range of the system's tangential stiffness;

[0180] In the initial loading phase of the model test, the system is theoretically in a fully elastic state because the soil has not yet undergone large-scale plastic yielding. Due to the influence of high-frequency noise from the sensors and local soil compaction effects, the tangential stiffness calculated in real time is not a constant. Within the sampling time window after the test starts, the controller extracts extreme values ​​from the continuously sampled system tangential stiffness. The extracted data sequence constitutes the fluctuation range, used to characterize the background noise level of the soil's elastic stiffness under the current test environment.

[0181] Step 604: Based on the lower limit of the fluctuation range, automatically adjust the preset first stiffness ratio threshold and second stiffness ratio threshold so that the updated stage transition threshold matches the initial stiffness of the system in the current test.

[0182] Based on this, the system uses the acquired background statistical characteristics to calibrate the boundary parameters for stage determination. If a fixed threshold is used directly, the system faces the risk of erroneously triggering stage transitions due to single-point stiffness drops caused by environmental noise.

[0183] In this step, the controller extracts the lower limit boundary value of the fluctuation range as a new benchmark reference point, sets the preset first stiffness ratio threshold to a predetermined value lower than the lower limit boundary, and proportionally lowers the preset second stiffness ratio threshold.

[0184] This mechanism enables the system's judgment logic to adapt to the initial compaction differences under different foundation soil conditions, eliminate misjudgment data caused by high-frequency disturbances, and ensure the robustness of stage identification.

[0185] According to one aspect of this application, a loading follower device for bidirectional load collaborative control of pile foundation in geotechnical centrifugal model test is provided. The loading device includes a vertical actuator, a top wheel loading head, a slider, a slide rail, a model pile, a horizontal actuator, a horizontal loading head, an angle sensor, and a motor.

[0186] Optionally, the vertical actuator is installed on the upper side of the slide rail, and the top wheel loading head is fixed below the vertical actuator, with the top wheel loading head in contact with the center point of the model pile; the vertical actuator contains a sensor, and when the model pile is not in contact with the top wheel loading head, the vertical actuator moves the top wheel loading head down until it contacts the model pile, so that the vertical actuator can automatically follow vertically during the centrifugal test.

[0187] Optionally, the horizontal actuator is installed on the side of the model pile, and the horizontal loading head is fixed to the front end of the horizontal actuator. The horizontal actuator contains a sensor. When the model pile is not in contact with the horizontal loading head, the horizontal actuator moves the horizontal loading head horizontally closer to the pile foundation until it contacts the model pile, so that the horizontal actuator can automatically follow horizontally during the centrifugal test.

[0188] Optionally, the angle sensor can measure the horizontal rotation angle of the pile body, and the horizontal displacement can be calculated based on the pile length.

[0189] Optionally, the motor can control the horizontal movement of the vertical actuator in real time, and the displacement is determined according to the horizontal displacement of the pile top, so as to realize the automatic horizontal following of the vertical actuator during the centrifugal test loading process.

[0190] For example, the motor calculates the horizontal displacement by measuring the rotation angle through the angle sensor, and controls the vertical actuator and the top wheel loading head to move horizontally through the slide rail; when vertical and horizontal loads are applied simultaneously during the centrifugal test, when the model pile moves or deflects horizontally, the top wheel loading head moves with the model pile, so that the top wheel loading head is always located at the designed load application point.

[0191] According to another aspect of this application, a two-way load collaborative control device for a geotechnical centrifugal model test pile foundation includes a two-degree-of-freedom orthogonal motion platform, a vertical actuator, a horizontal actuator, a sensor assembly, and a controller.

[0192] Among them, the two-degree-of-freedom orthogonal motion platform has mutually perpendicular vertical and horizontal degrees of freedom;

[0193] The vertical actuator is installed on the execution end of the two-degree-of-freedom orthogonal motion platform to apply the actual vertical load to the loaded pile. It can be driven to follow horizontally along the horizontal degree of freedom.

[0194] The horizontal actuator is independently installed on the side of the loaded pile and is used to apply the actual horizontal load to the loaded pile.

[0195] The sensor assembly is used to collect in real time the pile body rotation angle of the loaded pile, the actual vertical load at the loading point, the actual horizontal load on the loaded pile, and the actual horizontal position of the vertical actuator.

[0196] The controller is communicatively connected to the two-degree-of-freedom orthogonal motion platform, the vertical actuator, the horizontal actuator, and the sensor assembly to execute a two-way load cooperative control method.

[0197] In some embodiments, the sensor assembly further includes an auxiliary displacement sensor, which is used to acquire the actual displacement measurement value of the pile top of the loaded pile in real time, so that the controller can perform online adaptive fine-tuning of the dynamically updated deformation mode coefficients.

[0198] In terms of overall spatial layout and assembly relationship, the two-degree-of-freedom orthogonal motion platform is arranged across the top of the model pile to achieve decoupled horizontal and vertical motion;

[0199] The vertical actuator applies a vertical load to the model pile from above.

[0200] The horizontal actuator is located on the side of the model pile and applies a horizontal overburden load to the model pile.

[0201] The controller centrally receives data collected by the sensor components and synchronously sends control commands to the motion platform and actuators, forming a complete hardware control closed loop.

[0202] According to another aspect of this application, the horizontal motion degree of freedom of the two-degree-of-freedom orthogonal motion platform is realized through a horizontal following mechanism;

[0203] The horizontal following mechanism includes a slide rail spanning above the load-bearing pile, a slider slidingly engaged with the slide rail, and a drive motor;

[0204] The vertical actuator is fixed below the slider;

[0205] The controller controls the drive motor to drive the slider and vertical actuator to move horizontally along the slide rail, so that the loading point set at the bottom of the vertical actuator is always aligned with the center point of the top of the loaded pile.

[0206] In the specific physical connection and motion transmission, the slide rail is horizontally fixed above the model box, and the slider is installed on the slide rail and can slide along the axis of the slide rail;

[0207] The motor serves as the power source and is connected to the slider. The vertical actuator is suspended and fixed below the slider, moving synchronously with it.

[0208] When the model pile shifts or deflects horizontally under lateral load, the motor receives the horizontal movement command from the controller and drives the slider to move left and right on the slide rail with the vertical actuator.

[0209] With this structure, the vertical actuator can follow the horizontal displacement of the model pile in real time during its loading process, ensuring that the vertical load is always applied to the designed load point and avoiding the model pile from being unstable or damaged due to eccentric load.

[0210] According to one aspect of this application, a top wheel loading head is provided at the bottom of the vertical actuator, and the top wheel loading head contacts the center point of the upper surface of the loaded pile. A contact sensing sensor is configured inside the vertical actuator. When the loaded pile is not in contact with the top wheel loading head, the vertical actuator drives the top wheel loading head to move vertically downwards according to the signal from the contact sensing sensor until it makes close contact with the loaded pile, thus achieving automatic vertical positioning and following during the centrifugal test. The rolling contact configuration between the top wheel loading head and the pile top can reduce the relative sliding friction resistance generated during horizontal following movement.

[0211] In the horizontal direction, a horizontal actuator is mounted on a slide rail on the side of the loaded pile, and a horizontal loading head is fixed to the front end of the horizontal actuator to apply a horizontal load to the loaded pile. The horizontal actuator also contains a contact sensing sensor. When the loaded pile is not in contact with the horizontal loading head, the horizontal actuator drives the horizontal loading head to move horizontally towards the pile foundation based on the signal from the contact sensing sensor until it makes close contact with the side of the loaded pile.

[0212] It should be understood that this structure enables the bidirectional loading head to automatically and accurately conform to the model pile during the initial stage of the test loading, ensuring the reliability and consistency of the loading boundary conditions.

[0213] According to one aspect of this application, the sensor assembly includes an angle sensor for measuring the horizontal rotation angle of the pile. The angle sensor is fixedly installed at the mud surface elevation of the loaded pile or at a predetermined depth in the shallow soil layer to avoid spatial structural interference with the vertical actuator located directly above the loaded pile, and provides the controller with reference rotation angle data for calculating the actual horizontal displacement of the pile top.

[0214] In the actual layout of the centrifugal model test, the area directly above the model pile is mainly occupied by the top wheel loading head and the vertical actuator that moves horizontally in real time. Installing angle sensors at the shallow depth of the pile or at the mud surface physically avoids the motion envelope of the top loading components, preventing mechanical collisions and mutual compression under high gravity. Simultaneously, after the angle sensor measures the cross-sectional rotation angle at this depth, the controller can directly calculate the horizontal displacement of the model pile based on this rotation angle and the known pile length parameters, providing data input for the horizontal following mechanism.

[0215] The optional embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solution of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for coordinated control of bidirectional loads on pile foundations in a geotechnical centrifuge model test, characterized in that, include: Real-time acquisition of the pile rotation angle of the loaded pile, the actual vertical load at the loading point, and the actual horizontal position of the vertical actuator during the centrifugal model test; The actual horizontal displacement of the pile top is estimated based on the pile rotation angle and dynamically updated deformation mode coefficients. Based on the deviation between the actual horizontal displacement of the pile top and the actual horizontal position, a horizontal movement command is generated to drive the vertical actuator to follow horizontally. Based on the deviation between the target vertical load and the actual vertical load, a vertical fine-tuning command is generated to compensate for the vertical load disturbance caused by horizontal following. The process of obtaining dynamically updated deformation mode coefficients includes: obtaining initial deformation mode coefficients for each loading stage through offline benchmark presets; based on the initial deformation mode coefficients, identifying the current loading stage through online stage coarse adjustment and switching stages to obtain coarse-adjusted deformation mode coefficients; and using online adaptive fine adjustment to eliminate errors in the coarse-adjusted deformation mode coefficients within each loading stage to obtain dynamically updated deformation mode coefficients. Specifically, based on the initial deformation mode coefficient, the current loading stage is identified and stage switching is performed through online stage coarse adjustment to obtain the coarse deformation mode coefficient, including: acquiring the real-time collected actual horizontal load, calculating the system characteristic state quantity in combination with the actual horizontal displacement of the pile top; inputting the system characteristic state quantity into the stage transition criterion for comparison and judgment to identify the current loading stage; and selecting the initial deformation mode coefficient corresponding to the current loading stage as the coarse deformation mode coefficient. Among them, the initial deformation mode coefficient corresponding to the current loading stage is selected as the coarse-tuned deformation mode coefficient. Specifically, at the moment when the switching of the current loading stage is detected, the progressive transition function is called to smoothly transition the initial deformation mode coefficients before and after the transition to obtain the coarse-tuned deformation mode coefficient. Specifically, online adaptive fine-tuning is used to eliminate errors in the coarse-tuned deformation mode coefficients at each loading stage, resulting in dynamically updated deformation mode coefficients. This process includes: acquiring the actual displacement measurement value of the pile top collected in real time by auxiliary displacement sensors; calculating the predicted horizontal displacement based on the coarse-tuned deformation mode coefficients, pile rotation angle, and preset pile penetration depth; calculating the displacement deviation between the actual displacement measurement value of the pile top and the predicted horizontal displacement; and performing online correction to obtain dynamically updated deformation mode coefficients. Specifically, based on the deviation between the actual horizontal displacement and the actual horizontal position of the pile top, a horizontal movement command is generated. This includes: inputting the deviation between the actual horizontal displacement and the actual horizontal position of the pile top into the outer loop proportional-integral (PI) controller for proportional-integral calculation and outputting a horizontal movement command; and generating a vertical fine-tuning command based on the deviation between the target vertical load and the actual vertical load.

2. The method according to claim 1, characterized in that, The inner loop response bandwidth of the inner loop proportional-integral-derivative PID controller is set to be 5 times greater than the outer loop response bandwidth of the outer loop proportional-integral PI controller, so that the compensation response speed for vertical load disturbance is faster than the response speed for horizontal displacement following.

3. The method according to claim 1, characterized in that, Based on the deviation between the preset target vertical load and the actual vertical load, the vertical fine-tuning command generates feedforward compensation processing for mechanical coupling, including: Based on the kinematic coupling coefficient and the horizontal motion command, calculate the vertical force feedforward compensation caused by the horizontal following motion of the vertical actuator; The vertical force feedforward compensation is superimposed on the fine-tuning feedback signal generated based on the actual vertical load deviation to obtain the vertical fine-tuning command.

4. The method according to claim 1, characterized in that, The initial deformation mode coefficients for each loading stage are obtained through offline benchmark presets, specifically including: Based on the soil parameters of the test piles obtained offline, the relative stiffness characteristic value of the loaded piles was calculated. Based on this, the corresponding initial deformation mode coefficients are calculated.

5. A bidirectional load collaborative control device for small deformation pile foundations based on a geotextile centrifuge, characterized in that, For performing the method as described in claim 1, comprising: A two-degree-of-freedom orthogonal motion platform has mutually perpendicular vertical and horizontal degrees of freedom. The vertical actuator, installed on the execution end of the two-degree-of-freedom orthogonal motion platform, is used to apply the actual vertical load to the loaded pile and is driven to follow horizontally along the horizontal degree of freedom. A horizontal actuator, independently installed on the side of the loaded pile, is used to apply the actual horizontal load to the loaded pile; Sensor components are used to collect data in real time on the pile body rotation angle of the loaded pile, the actual vertical load at the loading point, and the actual horizontal position of the vertical actuator. The controller is communicatively connected to the two-degree-of-freedom orthogonal motion platform, the vertical actuator, the horizontal actuator, and the sensor assembly.

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