Centrifuge dual-degree-of-freedom coupled loading control method and system

Abstract

The application discloses a centrifuge double-freedom coupling loading control method and system. The method comprises the following steps: in the centrifugal loading process, real-time acquisition of measured load and displacement signals; calculation of dynamic parasitic force of the centrifugal environment and deduction from the load signal to obtain a real load feedback value; calculation of geometric coupling net additional bending moment caused by model deformation based on the displacement signal, and conversion into a single equivalent force correction; combination of the equivalent force correction and a pre-constructed parameterized target equation to obtain an updated target load; calculation of the normal deviation of the current loading point from the target path in the normalized load coordinate system based on the real load and the updated target load; and execution of inter-channel decoupling control and adaptive adjustment of the advance rate of the dimensionless loading parameter according to the deviation. The application eliminates the supergravity dynamic noise and large deformation eccentric interference, and realizes high-fidelity tracking closed-loop control in a multi-dimensional load space.

Description

Technical Field

[0001] This invention relates to the field of geotechnical centrifuge model testing technology, and in particular to a two-degree-of-freedom coupled loading control method and system for centrifuges. Background Technology

[0002] Current bidirectional loading systems for centrifuges primarily employ an independent dual-channel servo control architecture. The horizontal and vertical actuators in the system track their respective independent time-series target curves and rely on sensor feedback from their respective channels for independent single-axis closed-loop control. In the underlying mechanical measurement and control benchmark acquisition phase, such systems typically only perform static zeroing operations under constant gravity (equivalent to one times Earth's gravity). Once the formal loading phase begins, the unprocessed raw electrical signals from the sensors are directly used as the feedback source for the force control loop.

[0003] Existing independent loading control systems face the dilemma of intertwined dynamic distortion of mechanical signals and spatial force distortion in extreme centrifugal fields. Specifically, they lack effective mechanisms for stripping away multi-source dynamic parasitic forces and fail to properly handle geometric eccentric coupling and singularity issues caused by large deformations. For example, under ultra-high centrifugal acceleration, the Coriolis force excited by horizontally moving components dynamically changes with the loading speed. Existing static zeroing cannot eliminate such dynamic parasitic forces, and the real-time calculation of this dynamic parameter is prone to algebraic loop timing deadlock with high-frequency servo computation, leading to distortion of measured feedback. Furthermore, settlement and lateral displacement of the geotechnical model can induce significant additional geometric bending moments. Existing conventional compensation logic is prone to division-to-zero divergence singularity collapse in the initial small deformation stage of loading due to the need to divide by a very small eccentricity. In addition, fragmented single-channel control lacks a unified two-dimensional spatial normal deviation feedback mechanism, making it difficult to accurately and adaptively track the preset composite failure trajectory in the stage of strong nonlinear yielding of soil. Summary of the Invention

[0004] Purpose of the invention: To provide a two-degree-of-freedom coupled loading control method and system for centrifuges, in order to solve the above-mentioned problems existing in the prior art.

[0005] Technical solution: A two-degree-of-freedom coupled loading control method for a centrifuge, comprising:

[0006] During the centrifugal loading process, the measured load signal and measured displacement signal of the loading system are acquired in real time.

[0007] Calculate the dynamic parasitic forces exerted on the loading system by the centrifugal environment;

[0008] The actual load feedback value is obtained by subtracting the dynamic parasitic force from the measured load signal;

[0009] Calculate the net additional bending moment caused by the deformation of the experimental model based on the measured displacement signal;

[0010] Convert the net additional bending moment due to geometric coupling into an equivalent correction amount;

[0011] By combining the equivalent correction amount with the pre-constructed parameterized objective equation, the updated target load is obtained;

[0012] Based on the actual load feedback value and the updated target load, calculate the path normal deviation of the current loading point from the target loading path in the normalized load coordinate system.

[0013] Inter-channel decoupling control is performed based on the path normal deviation, and the advance rate of the dimensionless loading process parameters is adaptively adjusted.

[0014] According to another aspect of this application, a centrifuge dual-degree-of-freedom coupled loading system is also provided, including a reaction beam, a horizontal loading mechanism, a vertical loading mechanism, and a controller;

[0015] The horizontal loading mechanism and the vertical loading mechanism are set on the upper side of the reaction beam and configured to simultaneously apply horizontal and vertical forces to the test model;

[0016] The controller is communicatively connected to both the horizontal and vertical loading mechanisms, and is configured to execute the centrifuge two-degree-of-freedom coupled loading control method of any embodiment.

[0017] Beneficial effects:

[0018] I. A multi-source parasitic force analytical compensation model was constructed, encompassing the dynamic increment of centrifugal self-weight, rotational friction, and Coriolis force. Specifically, to address the control loop data suspension caused by Coriolis force calculations, a one-cycle delay strategy was introduced. This strategy reconstructs the dynamic compensation equation for the current cycle by calling the historical displacement differential velocity from the previous cycle. This breaks the algebraic loop deadlock between velocity feedback and servo output within the same cycle and filters out high-frequency physical noise.

[0019] Second, calculate the net additional bending moment caused by the intersection of lateral and longitudinal displacements, and convert it into an equivalent horizontal force correction. Using the numerically stable effective vertical lever arm as the sole denominator factor, the easily zeroed horizontal eccentricity parameter in existing technologies is replaced, eliminating the risk of algorithm singularity collapse and ensuring absolute convergence of the full-range load space distortion compensation.

[0020] Third, a path parameterization framework based on a normalized two-dimensional coordinate system is introduced. By calculating the dimensionless global normal projection deviation from the actual stress point to the target curve, and using a matrix network that recursively identifies the natural force-displacement increment data to generate a feedforward decoupling compensation quantity, the dual-axis control is unified into an optimization and tracking process oriented towards a single spatial geometric error. This not only eliminates the computational weight distortion caused by range differences, but also achieves a closed-loop anti-deviation effect by adaptively adjusting the loading progress according to the soil yield state. Attached Figure Description

[0021] Figure 1 This is a flowchart of the bidirectional coupling loading method for centrifuges according to the present invention.

[0022] Figure 2 This is a flowchart of the present invention for calculating the dynamic parasitic force of the centrifugal environment acting on the loading system.

[0023] Figure 3 This is a flowchart of the calculation of Coriolis parasitism according to the present invention.

[0024] Figure 4 This is a schematic diagram of the loading device of the present invention.

[0025] Figure 5 This is a schematic diagram of the horizontal loading mechanism in this invention.

[0026] Figure 6 This is a schematic diagram of the vertical loading mechanism in this invention.

[0027] Figure 7 This is a schematic diagram of the hydraulic components in this invention.

[0028] In the above figures: 1—Reaction beam; 2—Reaction beam connecting plate; 3—Model box locking block; 4—Horizontal loading mechanism; 5—Vertical loading mechanism; 6—Hydraulic component; 7—Frame horizontal position adjustment top block; 8—Test model; 9—Horizontal cylinder; 10—Displacement sensor; 11—Horizontal loading device mounting bracket; 12—Horizontal cylinder anti-rotation guide mechanism; 13—Loading head support bracket; 14—Lifting rolling bearing; 15—Loading head; 16—Horizontal force sensor; 17—Vertical cylinder; 18—Vertical cylinder anti-rotation guide mechanism; 19—Vertical loading device mounting bracket; 20—Vertical displacement sensor; 21—Vertical force sensor; 22—Vertical loading device rolling loading head; 23—Hydraulic component mounting seat; 24—Horizontal cylinder servo valve seat; 25—Horizontal cylinder servo valve; 26—Vertical cylinder servo valve seat; 27—Vertical cylinder servo valve; 28—Main inlet valve seat; 29—Main inlet valve. Detailed Implementation

[0029] like Figure 1 As shown in Example 1, a bidirectional coupling loading method for a centrifuge is provided, which generally includes the following steps:

[0030] Step 101: Obtain the predicted value of the structural elastic deformation of the loading system under the target centrifugal acceleration.

[0031] In the preparation phase of centrifuge model testing, the structural alignment problem under ultra-high gravity field conditions needs to be addressed first. The target centrifugal acceleration is typically set to tens to hundreds of standard gravitational accelerations, such as 100g. Under this extreme acceleration, even high-strength steel structures will exhibit significant elastic deformation.

[0032] In this step, the obtained predicted values ​​of structural elastic deformation are used to quantify the positional offset of key load-bearing components of the loading system under centrifugal force. By calculating and obtaining these predicted values ​​in advance, a basis can be provided for subsequent physical space pre-compensation, avoiding loading eccentricity caused by structural deformation during high-speed centrifuge operation.

[0033] Step 102: Based on the predicted value of structural elastic deformation, reserve the initial position deviation in the opposite direction to complete the initial alignment of the test model and the loading system.

[0034] When installing equipment under constant gravity, or 1g, the operator or automated centering mechanism will not align the loading head with the stress center of the test model completely, but will intentionally offset it by an initial position deviation that is equal in magnitude and opposite in direction to the predicted value of the elastic deformation of the structure.

[0035] For example, if it is predicted that the vertical loading head will shift downwards by 3.4 mm and horizontally outwards by 0.25 mm under a centrifugal field, then during 1g static alignment, the vertical gap is intentionally increased by 3.4 mm, and the horizontal position is shifted in the opposite direction by 0.25 mm. When the centrifuge reaches the set target centrifugal acceleration, the structural elastic deformation of the entire loading system precisely offsets the reserved initial position deviation, allowing the loading system to automatically achieve precise alignment in a high-speed rotating dynamic environment. This reverse pre-compensation mechanism solves the problem of positional distortion caused by the rapid increase in self-weight of the centrifuge's heavy-load loading mechanism from a purely physical perspective.

[0036] In summary, the initial alignment of the loading system is achieved through execution steps 101 and 102. The data acquisition and processing process is described in detail below.

[0037] Step 103: During the centrifugal loading process, the measured load signal and measured displacement signal of the loading system are acquired in real time.

[0038] During the formal execution of the bidirectional coupled loading test, the control system needs to acquire the underlying physical state feedback at an extremely high sampling frequency. Considering the centrifuge scaling effect, which significantly compresses the time history of the model test, the control cycle of the hydraulic servo system is typically set between 1 and 5 ms, corresponding to a sampling rate in the range of 200 Hz to 1000 Hz. Under this high-frequency sampling cycle, the raw electromechanical conversion data of the horizontal and vertical channels, i.e., the measured load signal and the measured displacement signal, are synchronously read through force sensors and displacement gauges arranged in each axis. These unfiltered raw signals constitute the sole data source for the entire control algorithm, reflecting the true mechanical and kinematic state of the test model under the action of soil resistance at the current moment.

[0039] Step 104: Calculate the dynamic parasitic force exerted on the loading system by the centrifugal environment based on the physical parameters of the loading system and the measured displacement signal.

[0040] Unlike conventional 1g constant gravity tests, sensor readings in ultra-high centrifugal fields contain a large amount of spurious mechanical components unrelated to the actual soil mechanical response. In this step, the calculated dynamic parasitic forces encompass various disturbances caused by centrifuge rotation and the movement of the loading mechanism itself. These parasitic forces are not static constants but are highly coupled to the current angular velocity of the centrifuge, the real-time spatial position of the loading mechanism, and its velocity. If these dynamic parasitic forces are not separated from the original signals, the control system will issue servo actions based on erroneous reaction force signals, leading to severe distortion of the soil constitutive relationship or failure envelope obtained from the test.

[0041] Step 105: Subtract the dynamic parasitic force from the measured load signal to obtain the true load feedback value.

[0042] The acquired measured load signal, which includes physical noise, is synchronously differentially calculated with the dynamic parasitic force. The net value after removing centrifugal weight amplification, frictional resistance, and rotational dynamic effects is the true load feedback value. This feedback value represents the actual interaction force between the test model and the foundation soil, and is the only reliable benchmark for subsequent geometric eccentricity correction and closed-loop control error comparison.

[0043] Step 106: Based on the actual load feedback value and the measured displacement signal, calculate the net additional bending moment caused by the deformation of the test model.

[0044] At the microscale of centrifugal model testing, minute displacements in the test model can lead to significant changes in the load arm, i.e., the geometric coupling effect. By analyzing the measured displacement signals in real time, the transient deformation of the model in the horizontal and vertical dimensions is extracted. Due to the change in the height of the horizontal force and the eccentricity of the vertical force application point, an additional overturning moment is generated on the model. This step quantifies the spatial stress state distortion caused by the nonlinear deformation of the soil during the test loading process by calculating the combined additional moment caused by the combined action of displacements in these two orthogonal dimensions in real time, i.e., the net additional bending moment of geometric coupling.

[0045] Step 107: Convert the net additional bending moment of geometric coupling into an equivalent correction amount.

[0046] To counteract the aforementioned geometric distortions, dynamic correction of the control target is necessary. The three-dimensional torsional trend, i.e., the net additional bending moment due to geometric coupling, is mapped back to the one-dimensional linear loading channel using the principle of mechanical equivalence, and converted into an equivalent force correction. The aim is to avoid introducing complex direct torque control loops into the dual-axis independent servo control architecture. Instead, by superimposing a virtual translational correction force, the loading system can still output an equivalent bending moment effect to the experimental model that conforms to the initial design expectations within the deformed physical space.

[0047] Step 108: Combine the equivalent correction amount with the pre-constructed parameterized objective equation to obtain the updated target load.

[0048] The control system pre-stores mathematical curves describing the entire experimental loading process, i.e., pre-constructed parameterized target equations. Within each extremely short control calculation cycle, the nominal target force that should be applied at the current theoretical time point is calculated from this equation. An equivalent correction is subtracted from the nominal target force to offset excessive overturning moment. The updated target load, obtained after superposition processing, is a dynamic tracking command incorporating real-time geometric nonlinear feedback, guiding the hydraulic cylinder to the precise mechanical position it should pursue every millisecond.

[0049] Step 109: Based on the actual load feedback value and the updated target load, calculate the path normal deviation of the current loading point from the target loading path in the normalized load coordinate system.

[0050] After obtaining the pure true reaction force and the compensated target command, the control system did not adopt the traditional dual-channel independent PID error calculation method. In order to eliminate the huge difference in magnitude between the vertical tens of kilonewtons large load and the horizontal hundreds of newtons small load, the calculation process was placed in a dimensionless normalized load coordinate system.

[0051] Within this uniform coordinate system, the shortest geometric distance from the coordinate point representing the current actual stress state to the perpendicular line drawn to the preset ideal curve, i.e., the target loading path, is calculated; this distance is the path normal deviation. This deviation is a purely spatial deviation index, abandoning the mandatory constraint of the time axis, and reflects the overall degree of deviation between the current bidirectional combined force application state and the ideal force ratio.

[0052] Step 110: Perform inter-channel decoupling control based on the path normal deviation, and adaptively adjust the advance rate of the dimensionless loading process parameters to generate decoupling control quantities and output them to the loading system to execute servo actions.

[0053] As the execution endpoint of the entire control method, the system simultaneously commands two orthogonal servo channels based on the single geometric deviation index output in step 109. The process of decoupling control between the channels essentially involves generating compensation signals to resist channel interference through an internal identification algorithm, enabling the horizontal and vertical cylinders to coordinate and "pull" the actual load point deviating from the curve back to the target trajectory. Simultaneously, the magnitude of the path normal deviation directly influences the time flow: when the normal deviation is too large, indicating that the system is struggling or the soil is undergoing severe yielding, the system automatically reduces or even freezes the advance rate of the dimensionless loading process parameter representing virtual time; after the deviation is eliminated and reduced by the decoupling controller, the advance resumes. This adaptive mechanism of using spatial error to predict time progress greatly avoids uncontrolled deviation of the loading path under complex nonlinear conditions.

[0054] Example 2 provides a method for multi-level position calibration and pre-compensation of structural elastic deformation of a centrifuge, which is the core calculation and pre-compensation process of calibrating the position of physical hardware equipment and estimating spatial deformation before the centrifuge is running at high speed.

[0055] In one possible embodiment, the step of obtaining the predicted value of the structural elastic deformation of the loading system under the target centrifugal acceleration specifically includes:

[0056] Step 201: Obtain the uniformly distributed load and span parameters of the reaction beam where the loading system is located, and calculate the deflection at the center of the reaction beam in combination with the target centrifugal acceleration.

[0057] The uniformly distributed load on the reaction beam refers to the line load uniformly distributed along the beam's length, generated by the beam's own structural weight and the weight of its attached loading mechanisms under a static gravity field. The span parameter is the effective geometric length between the fixed support points at both ends of the reaction beam. Since centrifugal model tests need to be conducted in a hypergravity field, the target centrifugal acceleration is typically set to tens to hundreds of times the conventional gravitational acceleration. Under this mechanical environment, the reaction beam, as the fundamental load-bearing structure of the entire loading system, experiences downward bending deformation that is synchronously amplified by the centrifugal field. Specifically, the system uses a static deformation calculation model of a simply supported beam under a uniformly distributed load, multiplying the load parameters under constant gravity by the centrifugal amplification factor to deduce the maximum structural deformation under the target centrifugal acceleration state.

[0058] In some embodiments, the deflection δ at the center of the reaction beam _beam =(5*q0*n*L 4 ) / (384*E*I);

[0059] Where q0 is the uniformly distributed load under constant gravity conditions, n is the amplification factor of the target centrifugal acceleration relative to constant gravity acceleration, L is the span of the reaction beam, E is the elastic modulus of the reaction beam material, and I is the geometric moment of inertia of the reaction beam section.

[0060] The deflection at the center of the reaction beam objectively reflects the degree of vertical settlement of the horizontally loaded reference plane when the system rotates at high speed. By analytically calculating this deflection value, errors caused by empirical estimation are eliminated, providing a quantitative physical benchmark for subsequent vertical position deviation control.

[0061] In some alternative implementations, for non-standard working conditions where the reaction beam cross-section is non-uniform or contains local concentrated mass blocks, the finite element discretization method can be used instead of the above-mentioned integral analytical formula. Specifically, the processing system acquires the three-dimensional geometric mesh model of the reaction beam and the distribution data of the concentrated mass points, calculates the displacement field of each discrete node under the action of the target centrifugal acceleration centrifugal force vector using a preset global stiffness matrix, and extracts the vertical displacement component of the node corresponding to the geometric center of the loading device, outputting it as the deflection at the center of the reaction beam.

[0062] Step 202: Obtain the self-weight torque and cantilever length of the horizontal loading device mounting frame of the loading system, and calculate the cantilever offset of the mounting frame in combination with the target centrifugal acceleration.

[0063] A horizontal loading device mounting bracket is a load-bearing support rigidly connected to the reaction beam and extending horizontally outward to mount the hydraulic cylinder. The self-weight moment is generated by the material mass distribution of the mounting bracket itself and its suspended moving parts. The cantilever length is defined as the horizontal geometric distance from the outer force-bearing end of the mounting bracket to the fixed root of the reaction beam. In a centrifugal force field, the cantilever structure of the mounting bracket will experience local deflection due to the centrifugal force perpendicular to the loading axis, causing the absolute geometric position of the horizontal loading head to deviate from the original design's centerline of symmetry. The system evaluates this local deflection displacement based on the elastic deformation theory model of the cantilever beam end subjected to a concentrated moment.

[0064] Among them, the cantilever offset δ of the mounting bracket _bracket =(M _self *n*l 2 ) / (2*E _bracket *I _bracket );

[0065] Among them, M _self Let E be the torque due to gravity under constant gravity, n be the amplification factor of the target's centrifugal acceleration, l be the cantilever length, and E be the torque due to gravity. _bracket I represents the elastic modulus of the mounting bracket material. _bracket Let be the geometric moment of inertia of the mounting frame cross section.

[0066] By extracting and calculating this offset, the spatial interference problem caused by the asymmetric support structure of the high-thrust horizontal loading mechanism due to the deflection of the loading axis was solved, ensuring the accuracy of the horizontal force vector in subsequent bidirectional loading commands.

[0067] Furthermore, in the process of calculating the cantilever offset of the mounting frame, if the horizontal loading mechanism contains multiple independent equipment units discretely distributed along the cantilever axis, the control module can decompose the self-weight torque into a discrete superposition of multiple independent sub-torques and perform item-by-item accumulation calculation to improve the accuracy of local offset prediction for complex heterogeneous structures.

[0068] Step 203: The center deflection of the reaction beam and the cantilever offset of the mounting frame are vector-superimposed to obtain the total predicted offset as the predicted value of the structural elastic deformation.

[0069] Vector superposition refers to combining scalar displacements distributed along different coordinate axes in a three-dimensional Cartesian coordinate system to generate a vector data structure representing the composite spatial displacement. The predicted value of structural elastic deformation is the final output parameter of this coordinate transformation and vector synthesis. Specifically, the processor assigns the deflection at the center of the reaction beam calculated in step 201 to the vertical coordinate axis attribute, generating a vertical displacement component; and assigns the cantilever offset of the mounting frame calculated in step 202 to the horizontal coordinate axis attribute, generating a horizontal displacement component. These two components are then combined into a displacement matrix, outputting the total predicted offset, thus completing the parameter update.

[0070] Through vector superposition processing logic, the discrete structural mechanics analysis results are uniformly transformed into a coordinate system deviation control set that the control system can directly identify and call. This parameter integration mechanism, which jointly extracts the overall system sinking component and the local cantilever deflection component, completely reconstructs the physical distortion field of the centrifuge when it reaches steady-state speed in digital space, providing a complete three-dimensional dataset for final alignment compensation.

[0071] As an extension of the above steps, the mathematical representation of the predicted elastic deformation of the structure can also be configured as a six-degree-of-freedom generalized displacement vector that includes angular deflection parameters. In addition to the translational components, the system calculates the pitch and yaw angle prediction deviations of the horizontal loading axis based on the curvature equation at the connection node between the reaction beam and the mounting frame, thereby adapting to extreme high-precision miniature model tests that are sensitive to rotational errors.

[0072] Step 204: Based on the predicted value of structural elastic deformation, a reverse initial position deviation is reserved for the loading system under static gravity field to complete the initial alignment of the test model and the loading system.

[0073] The static gravity field refers to the standard 1x Earth's gravity test environment when the centrifuge spindle is stationary or braked. The initial position deviation is a reverse geometric gap actively applied by a manual or automated positioning platform between the loading execution terminal and the loaded model during the mechanical structure assembly and physical zeroing stages. After obtaining the comprehensive offset output in step 203, the control unit drives positioning components such as the three-axis fine-tuning bracket to displace equal distances in opposite coordinate systems. Based on the aforementioned calculation results, in the static assembly procedure, the system controls the vertical gap adjuster to add an additional 3.4 mm of free travel and controls the horizontal adjustment module to move 0.25 mm in the opposite direction of the expected offset, locking this coordinate state as the initial set origin.

[0074] The reserved initial position deviation alters the standard calibration protocol of conventional laboratory equipment, which requires all mechanical origins to be absolutely centered and aligned when stationary. This control strategy, which introduces a reverse geometric deviation in advance to dynamically compensate for centrifugal physical errors, ensures that when the centrifuge speed increases to the target centrifugal acceleration, the elastic tensile and bending deformations of the structure under ultra-high centrifugal force can precisely and equivalently compensate for the reserved static gap. The loading mechanism will automatically return to the theoretically designed orthogonal force-bearing surface at the instant the mechanical output is applied to the contact test model, utilizing the system's own flexible deformation. This mechanism eliminates the need for additional, fragile dynamic displacement servo compensation motors within the high-overload, high-speed rotating, sealed chamber of the centrifuge; it achieves precise spatial alignment under ultra-high gravity conditions solely through static reverse preset operation.

[0075] Based on this, a supplementary implementation method is provided. After completing the physical alignment and starting the centrifuge to the target centrifugal acceleration, but before controlling the hydraulic cylinder to contact the test model to output load, the control system adds an online verification and zero-point calibration process for the no-load residual deformation. In specific operation, the data acquisition board acquires the readings of each axial displacement sensor in real time, performs differential comparison with the theoretical expected value of the initial position deviation, outputs the residual spatial deviation after static pre-compensation, and records it to the error register. At the same time, the real-time voltage signal of the bidirectional force sensor is acquired in a free-suspension state without bearing any model reaction force, maps it, and solidifies it as the reference environment zero-drift constant. After entering the formal loading process, the underlying algorithm continuously subtracts this reference environment zero-drift constant from all transient mechanical acquisition samples to filter out extremely low-frequency interference signals introduced by equipment assembly prestress and sensor thermal drift.

[0076] Example 3: Before the formal closed-loop control begins, the data processing procedure for dimensionality reduction mathematical mapping and multi-mode parameterized equation construction for physical testing requirements is as follows:

[0077] Before acquiring the measured load and displacement signals of the loading system in real time, a parameterized objective equation is pre-constructed, namely:

[0078] Step 301: Obtain the preset target loading path in the two-dimensional load space formed by the vertical load and the horizontal load.

[0079] The two-dimensional load space is specifically a Cartesian coordinate system constructed by coordinate axes representing vertical physical forces and coordinate axes representing horizontal physical forces. The target loading path refers to the pre-defined trajectory of the stress state evolution of the test model under external excitation until it reaches a specific foundation bearing capacity state or failure envelope. Obtaining this path involves reading a series of discrete or continuous mechanical coordinate points stored in the calculation module. By acquiring the pre-defined target loading path, the system transforms the purpose of the geotechnical centrifuge model test into basic geometric trajectory data executable by the underlying controller.

[0080] In some alternative implementations, the method of obtaining the target loading path may include reading a pre-configured structured text file, or receiving the coordinates of multiple key control nodes input from the operation interface and using a spline interpolation algorithm to generate a smooth and continuous physical trajectory curve in the two-dimensional load space.

[0081] Step 302: Extract the initial vertical load, the target endpoint vertical load, the initial horizontal load, and the target endpoint horizontal load from the boundary conditions.

[0082] Boundary conditions define the physical start and end states of the entire experimental loading process. The initial vertical and horizontal loads correspond to the foundation force setting benchmarks at the loading start point; the target endpoint vertical and horizontal loads correspond to the expected full-scale state of the ultimate loading test. Extracting these four characteristic values ​​aims to define the absolute range of physical mechanical quantities within the two-dimensional load space. For example, in a certain extraction operation, the initial vertical load might be 0 Newtons, the target endpoint vertical load 500 Newtons, the initial horizontal load 0 Newtons, and the target endpoint horizontal load 200 Newtons. Obtaining this absolute range provides the necessary numerical benchmarks for subsequent scalar transformation processing.

[0083] Furthermore, when the test model has residual prestress or the equipment has counterweight offset, the extracted initial vertical load is not fixed at 0 Newtons, but is directly read as the average value of the system static reaction force after zero-point calibration compensation, to ensure that the boundary condition parameter extraction process is consistent with the initial tension state of the underlying physical hardware.

[0084] The following is a detailed description of the process:

[0085] Extract the boundary conditions of the target loading path and establish a mathematical mapping relationship between the two-dimensional load space and the dimensionless loading process parameters;

[0086] Based on mathematical mapping relationships, the target loading path is transformed into a pre-constructed parameterized target equation.

[0087] Step 303: Define vertical and horizontal path shape functions with dimensionless loading process parameters as independent variables, and set that the start and end points of the vertical and horizontal path shape functions satisfy normalized boundary conditions in the parameter interval. That is, set the function value of the vertical and horizontal path shape functions to be zero when the dimensionless loading process parameter is equal to zero, and the function value to be one when the dimensionless loading process parameter is equal to one.

[0088] The dimensionless loading process parameter, denoted by the variable λ, is defined as a pure scalar value within the real number interval [0,1], used to abstractly represent the actual physical time variable. The vertical path shape function f... _V (λ) and the horizontal path shape function f _h (λ) represents a single-input mathematical mapping relationship with λ as the sole independent variable. The normalized boundary conditions are defined as follows: when λ equals 0, the values ​​of the two shape functions are strictly 0; when λ equals 1, the values ​​of the two shape functions are strictly 1. This abstraction removes the constraint of the absolute time axis, making the dual-channel joint control algorithm independent of the specific hydraulic loading physical rate, and focusing the control objective on the relative mathematical proportion between the horizontal and vertical force application channels that evolves synchronously with λ.

[0089] As one implementation method, higher-order polynomials can be used to construct the curve when logically compiling the shape function. For example, setting f... _V (λ)=3*λ 2 -2*λ 3 The continuously differentiable smooth polynomial satisfies the normalized boundary condition that the function value is 0 when λ equals 0 and the function value is 1 when λ equals 1, and its first derivative is equal to 0 at both the start and end points, which can eliminate the acceleration impact of the cylinder speed command during the start-stop transition phase of the experiment.

[0090] Step 304: Construct vertical parameterized equations using the initial vertical load, the target endpoint vertical load, and the vertical path shape function; and construct horizontal parameterized equations using the initial horizontal load, the target endpoint horizontal load, and the horizontal path shape function.

[0091] Based on the aforementioned extracted absolute physical range and dimensionless shape function, the processor performs algebraic multiplication and addition operations to construct the dynamic objective equation. The logic for constructing the vertical parameterized equation is as follows: calculate the absolute range difference between the target endpoint vertical load and the initial vertical load, multiply it by the vertical path shape function, and then add the initial vertical load.

[0092] V _target (λ)=V _0 +(V _1 -V _0 )*f _V (λ);

[0093] Among them, V _target (λ) represents the current vertical target load corresponding to the process parameter λ, V _0 V is the initial vertical load. _1 For the vertical load at the target endpoint, f _V (λ) is the vertical path shape function.

[0094] Similarly, construct the horizontal parameterized equations:

[0095] H _target (λ)=H _0 +(H _1 -H _0 )*f _h (λ); where H _target (λ) represents the current horizontal target load corresponding to the process parameter λ, H _0 For the initial horizontal load, H _1 For the target endpoint horizontal load, f _h (λ) is the shape function of the horizontal path.

[0096] Through the above parameterized equations, the three-dimensional force space parameters carrying physical units are reduced in dimension and projected into a parameter space uniquely determined by the scalar λ.

[0097] In some alternative implementations, for test conditions with intermediate pause settings or discontinuous step loading characteristics, the controller constructs parameterized equations by combining multiple consecutive sub-interval equations using piecewise functions. At the critical nodes connecting each segment, algorithmic constraints on the continuity of function values ​​and the first derivative are applied to prevent discontinuous step loads from occurring in the target voltage command sent to the servo valve during segment switching.

[0098] Step 305: Combine the vertical parameterized equations with the horizontal parameterized equations to obtain the pre-constructed parameterized objective equations.

[0099] Combining the vertical and horizontal parameterized equations refers to packaging two independent mathematical polynomials into a system of simultaneous equations sharing a single-sided variable λ within the main storage area of ​​the storage medium. This system of equations constitutes the parameterized objective equation. Therefore, upon receiving any given λ value within the [0,1] interval, this system of equations will perform synchronous calculations and output uniquely determined vertical and horizontal theoretical force benchmarks. This replaces the traditional independent function generator based solely on the time dimension, providing a calling interface for an adaptive progress prediction mechanism controlled by closed-loop feedback of displacement deviation.

[0100] Specifically, the data processing unit can also be configured to discretize the pre-constructed parameterized objective equation. The processor divides the independent variable λ into 1000 equally spaced discrete intervals, iteratively calls the parameterized objective equation to calculate the corresponding 1000 sets of target point matrix coordinates, and encapsulates them into a structured one-dimensional lookup table. In the real-time feedback loop, the servo controller directly executes the lookup instructions and supplements them with bilinear interpolation to obtain the transient theoretical load value, thereby reducing the floating-point multiplication computation load of the microprocessor.

[0101] Constant vertical load horizontal loading mode: The vertical path shape function is set to increase to the normalized target value (normalized full scale value) with the dimensionless loading process in the first stage and remain constant in the second stage thereafter. The horizontal path shape function is set to maintain the initial value in the first stage and continuously increase with the dimensionless loading process in the second stage.

[0102] This mode is the first execution mode, which logically divides the parameter evolution space into two non-overlapping dimensionless interval subsets. For example, the interval 0 to 0.3 of λ is preset as the first stage, and the interval 0.3 to 1.0 is the second stage. Under this distribution, the vertical path shape function f _V The function value (λ) in the first stage is defined as λ / 0.3, and the function value in the second stage is defined as a constant 1. Correspondingly, the horizontal path shape function f _hThe function value (λ) is defined as a constant 0 in the first stage and as (λ-0.3) / 0.7 in the second stage. This mode logic matches the test specification that a steady-state vertical self-weight stress field must be established before applying lateral load in centrifuge tests, thus avoiding premature unconsolidated shear failure of shallow soil caused by biaxial synchronous output of initial values.

[0103] Furthermore, to conform to the consolidation seepage characteristics of saturated soil, an independent static transition zone can be configured between the first and second stages of this model. For example, λ can be specified as an open interval of 0.3 to 0.4, f _V (λ) is always equal to 1 and f _h (λ) is always equal to 0. This value is in a silent interval corresponding to the pressure-holding consolidation stage where the pore water pressure at the bottom of the test model is completely dissipated.

[0104] Equal-proportional loading mode: The shape functions of both the vertical and horizontal paths are set to increase linearly with the dimensionless loading process to keep the ratio of the horizontal target load to the vertical target load constant.

[0105] This is the second execution mode. In this mode, the shape function calls for both the vertical and horizontal channels use the same linear slope mapping model. In the simplest configuration, f is uniformly set. _V (λ)=λ and f _h (λ) = λ. Substituting this into the parameterized objective equation, it can be concluded that at any transient node of the loading cycle, the calculated ratio of the current horizontal target load to the current vertical target load is always equal to the ratio of the set target endpoint horizontal load to the target endpoint vertical load. This mode is used to synthesize a resultant force vector with an absolutely fixed spatial pointing angle, ensuring the uniqueness of the loading path during the process of obtaining the stress envelope of the test foundation, and eliminating the interference of complex cross-loading history on soil stiffness degradation.

[0106] Optionally, an exponentially weighted mapping strategy can be used to improve the linear relationship, for example, by uniformly setting f. _V (λ)=λ^k and f _h (λ)=λ k When the exponential constant k is set to be greater than 1, the derivative of the output function exhibits an increasing characteristic, resulting in a smaller absolute force increment in the early stage of the experiment and a larger force increment near the failure stage. This is to adapt to the sensing characteristics of nonlinear materials in soil and rock that require denser sample acquisition before reaching the yield envelope.

[0107] Displacement control sweep mode: Based on the parameterized objective equation, the vertical channel is triggered to enter the displacement control mode to maintain a constant vertical displacement, and the horizontal channel is triggered to execute a uniform displacement increase command, so that the actual loading path slides along the failure envelope of the test model in the two-dimensional load space.

[0108] This is the third execution mode. This mode is used for continuous detection of the physical failure boundary within the load space. When this mode is selected, the output signal of the parameterized objective equation is reoriented and redistributed. The main control program switches the vertical servo loop from closed-loop force control mode to closed-loop displacement control mode via a logic threshold, locking the actual vertical settlement by reading position feedback to stop downward movement; simultaneously, it outputs a target displacement control scalar that increases linearly with time to the horizontal servo loop. Under this condition, since the absolute vertical displacement is fixed, as the horizontal forced shear displacement accumulates, the model soil enters the softening or plastic yielding stage. The vertical measured reaction force recorded by the system will automatically exhibit drop-attenuation along with the change in the horizontal measured reaction force, forming a trajectory set that continuously slides along the actual physical failure envelope. This mechanism replaces the inefficient process of using multiple independent samples to perform repeated monotonous loading to fit the boundary curve, allowing the extraction of a complete failure envelope distribution set in a single continuous operation of the centrifuge.

[0109] In an alternative detection embodiment, if the test requires obtaining dynamic tangential stiffness parameters, the control unit, while executing the uniform displacement command in the horizontal channel, additionally superimposes a high-frequency, low-amplitude sinusoidal displacement disturbance signal onto the target input of the vertical closed-loop displacement controller, thereby realizing the extraction of complex frequency domain features of coupled dynamic stiffness during the slip evolution along the envelope.

[0110] Example 4: Low-level signal processing and timing control logic for stripping away physical noise and performing high-frequency dynamic mechanical feedback correction in a hypergravity rotation environment.

[0111] The dynamic parasitic forces acting on the loading system under centrifugal conditions are calculated as follows:

[0112] Step 401: Calculate the centrifugal self-weight parasitic force based on the mass and rotation radius of the vertical channel components of the loading system.

[0113] After the centrifugal acceleration reaches a steady state, the components installed downstream of the vertical force sensor generate an equivalent centrifugal gravity due to their own mass in the high-speed rotating field. This force is picked up by the force sensor and constitutes the first type of physical noise in the measured load signal. The calculation of this centrifugal self-weight parasitic force is divided into two stages: static reference and dynamic increment. The system first performs zero-point online calibration in a suspended state without contacting the test model to obtain the vertical static zero drift constant including the initial centrifugal self-weight. After entering the loading stage, as the vertical loading mechanism extends downward, the rotation radius of the relevant components increases, resulting in an increase in the centrifugal self-weight.

[0114] The dynamic increment of the parasitic force due to centrifugal weight ΔF_parasitic,V=m _V *ω 2 *δ _V,act ;

[0115] Where, m _V Let ω be the total mass of the vertical channel components, ω be the angular velocity of the centrifuge, and δ be the total mass of the components in the vertical channel. _V,act This represents the actual vertical settlement.

[0116] In some embodiments, if the vertical channel is composed of multiple irregularly shaped bodies with uneven density, the accurate equivalent mass center and initial rotation radius can be obtained by performing volume integral operations on the discrete three-dimensional mass element matrix.

[0117] Step 402: Calculate the parasitic friction force based on the centrifugal force generated by the mass supported by the rolling bearing in the horizontal channel of the loading system and the preset rolling friction coefficient.

[0118] Since the moving parts of the horizontal loading mechanism also bear extremely high gravitational loads perpendicularly downwards along the centrifugal acceleration direction in the centrifugal field, the lifting rolling bearing provides the necessary mechanical support to prevent the moving parts from flexing. This positive supporting force is inevitably converted into frictional force resisting the motion on the rolling contact surface when the horizontal loading head moves horizontally. This resistance is mixed into the output of the horizontal force sensor, constituting the second type of physical noise.

[0119] Frictional parasitic force F_parasitic,friction=μ_r*m _h *ω 2 *r _h ;

[0120] Where μ_r is the preset rolling friction coefficient, m _h To support the mass of the rolling bearing, ω is the angular velocity of the centrifuge, r _h The radius of rotation of the horizontal channel supporting the rolling bearing.

[0121] Furthermore, in the subsequent compensation calculation stage, by introducing a sign function that reflects the direction of horizontal motion, it is ensured that the direction of eliminating the frictional parasitic force is always opposite to the current physical motion direction.

[0122] Step 403: Based on the horizontal loading velocity extracted differentially from the measured displacement signal and the total mass of the horizontally moving component, calculate the Coriolis parasitic force. The centrifugal self-weight parasitic force, frictional parasitic force, and Coriolis parasitic force are superimposed to obtain the dynamic parasitic force.

[0123] Within the rotating reference frame established by the centrifuge, any mass body undergoing radial or tangential relative motion with respect to the center of rotation will be subject to Coriolis inertial forces. When the horizontal cylinder drives the horizontal moving component to advance at a specific speed, its tangential motion generates a Coriolis force along the vertical radial direction. This force acts directly between the test model and the vertical force sensor, forming a third type of cross-channel physical noise. The controller extracts the horizontal loading velocity based on differential calculations of high-frequency displacement sampling points and calculates it using the following formula:

[0124] Coriolis parasitism F _Coriolis =2*m _moving *ω*v _h ;

[0125] Where, m _moving Let v be the total mass of the horizontally moving parts, ω be the angular velocity of the centrifuge, and v be the total mass of the horizontally moving parts. _h This refers to the horizontal loading speed.

[0126] After acquiring complete dynamic data including the aforementioned centrifugal self-weight parasitic force, frictional parasitic force, and Coriolis parasitic force, the data is removed from the original sensor sampling, and the actual load feedback value is output for closed-loop error comparison.

[0127] To break the data dependency algebraic loop of the control system, a one-time delay strategy is adopted to calculate the Coriolis parasitic force, as follows:

[0128] Step 404: In the calculation of the current k-th control cycle, extract the horizontal loading speed recorded in the (k-1)-th control cycle.

[0129] In real-time digital control systems, the process of calculating the Coriolis parasitic force described above suffers from timing conflicts due to data dependencies. Specifically, correcting the Coriolis force requires obtaining the horizontal loading speed, but changes in the horizontal loading speed depend on the decoupled controller output command of the current control cycle. The controller input, in turn, must wait for updates to the actual load feedback values, including Coriolis force compensation. To address this algebraic loop data suspension problem within the same calculation step, the master control algorithm introduces a timing-misaligned sampling mechanism. A speed status register consisting of a first-in, first-out queue is constructed. When executing the parasitic force stripping command of the current computation cycle, the predicted speed, which has not yet been calculated, is not read; instead, the historical speed value recorded in the previous control interrupt is retrieved.

[0130] Step 405: Input the horizontal loading speed of the (k-1)th control cycle into the Coriolis force calculation model to obtain the Coriolis parasitic force of the current kth control cycle.

[0131] The process of reconstructing the dynamic compensation equation using historical velocity data is achieved through the following formula:

[0132] F _Coriolis (k)=2*m _moving *ω(k)*v _h (k-1);

[0133] Among them, F _Coriolis (k) represents the Coriolis parasitic force in the current k-th control cycle, m _moving Let v be the total mass of the horizontally moving parts, ω(k) be the centrifuge rotational angular velocity in the current k-th control cycle, and v be the total mass of the horizontally moving parts. _h (k-1) represents the horizontal loading speed in the (k-1)th control cycle.

[0134] The compensation lag error introduced by this one-step delay strategy depends on the horizontal displacement acceleration of adjacent control cycles. The hardware servo control cycle of the system is 0.002 seconds. When a horizontal acceleration load of 0.01 m / s² occurs, the velocity difference component of a single cycle is only 0.00002 m / s. Calculations show that the resulting Coriolis force calculation error is far lower than the minimum resolution of commercial high-precision load sensors. Therefore, this timing reassembly algorithm maintains the convergence of the servo loop calculation without introducing perceptible amplitude distortion into the closed-loop system. As an alternative, if the servo controller is equipped with a Kalman state observer with timing extrapolation capabilities, the prior predicted velocity of the current control cycle output by the Kalman filter unit can be used instead of the historical velocity value of the backward differential input to the above formula.

[0135] Example 5: In a bidirectional loading scenario of a centrifugal model test, the process of extracting and calculating the coupling relationship between spatial displacement and physical load, and constructing an equivalent reduction path for net additional bending moment that avoids divergence singularities, is as follows:

[0136] Step 501: The actual load feedback value includes the actual vertical load and the actual horizontal load, and the measured displacement signal includes the actual horizontal displacement and the actual vertical settlement.

[0137] Before performing multi-dimensional mechanical calculations, the main control program needs to establish a unified reference coordinate system and symbolic attributes for all physical quantities. Specifically, the axis pointing downwards along the direction of centrifugal acceleration is set as the positive vertical direction, and the direction of the thrust applied by the horizontal servo mechanism is set as the positive horizontal direction. Based on this geometric convention, the obtained real load feedback value is analyzed and decomposed into the real vertical load acting in the positive vertical direction and the real horizontal load acting in the positive horizontal direction. Simultaneously, the measured displacement signal is analyzed to extract the actual horizontal displacement representing the absolute horizontal movement distance of the test model, and the actual vertical settlement representing the vertical settlement distance of the test model under vertical compression. All displacement parameters are recorded as positive values ​​in the defined positive directions, providing a standardized basic input for subsequent overturning trend determination.

[0138] The following describes the steps for calculating the net additional geometrically coupled bending moment caused by the deformation of the test model based on the actual load feedback value and the measured displacement signal. Specifically, these steps include:

[0139] Step 502: Subtract the product of the actual vertical load and the actual horizontal displacement from the product of the actual horizontal load and the actual vertical settlement to obtain the net additional bending moment of geometric coupling.

[0140] During the loading process, the physical spatial position of the test model dynamically shifts with the stress state, causing the originally set static equilibrium equations to fail. The line of action of the vertical true load deviates from the original central axis due to the actual horizontal displacement of the model, inducing a positive additional bending moment that causes the test model to overturn in the loading direction. Simultaneously, the height of the horizontal true load changes due to the actual vertical settlement of the model, generating a positive additional bending moment in the same direction that promotes overturning. To quantify this oppositely oriented geometric torsional effect, the processor calls the arithmetic logic unit to perform differential aggregation calculations. This process is achieved through the following formula:

[0141] ΔM=V _act *δ _h ,act+H _act *δ _V,act ;

[0142] Where ΔM is the net additional bending moment due to geometric coupling, and V _act For the actual vertical load, δ _h,act H represents the actual horizontal displacement. _act For the true horizontal load, δ _V,act This represents the actual vertical settlement.

[0143] By extracting the algebraic sum of the coupling products using the above formula, the actual additional torque offset borne by the experimental model under the current three-dimensional deformation state was obtained.

[0144] The following details the steps for converting the net additional bending moment due to geometric coupling into an equivalent correction, including:

[0145] Step 503: Divide the net additional bending moment of geometric coupling by the preset or dynamically updated effective lever arm of the horizontal load to obtain the equivalent horizontal force correction.

[0146] After obtaining the parameters representing the degree of overall spatial torsional distortion, the control system needs to map them back into a one-dimensional servo execution channel. The net additional bending moment scalar value of the geometric coupling in three-dimensional space is divided by the dynamically updated effective lever arm of the horizontal load to output a virtual translational compensation force. This calculation process is achieved through the following formula:

[0147] ΔH _geo =ΔM / h _eff ; where ΔH_geo The equivalent horizontal force correction is given by ΔM, where ΔM is the net additional bending moment due to geometric coupling, and h is the value of h. _eff This is the effective lever arm for horizontal loads.

[0148] The equivalent horizontal force correction represents the amount of force that needs to be subtracted to offset the excessive overturning moment in order to compensate for the change in lever arm caused by spatial displacement, while maintaining the original anti-overturning characteristics of the foundation.

[0149] Step 504: The equivalent horizontal force correction is used as the equivalent force correction, and no geometric coupling compensation correction is performed on the vertical load channel.

[0150] In traditional dual-axis control logic, vertical eccentricity caused by horizontal displacement usually requires reverse compensation by calculating the vertical additional force, i.e., introducing a dynamic eccentricity denominator that includes the horizontal displacement variable. However, in the initial stage of loading command issuance, the actual horizontal displacement often approaches 0, causing the dynamic eccentricity denominator to diverge by division by zero, which in turn leads to numerical singularities in the vertical target compensation and control collapse. In this step, the control program forcibly cuts off the geometric compensation data stream leading to the vertical load channel, retaining the original vertical target load command unchanged. By concentrating all geometric coupling effects into a single equivalent horizontal force correction channel, a physically stable lever arm denominator is used to replace the easily zero-oriented eccentricity denominator. This processing logic eliminates the risk of algorithmic division-by-zero singularities within small deformation ranges, ensuring the convergence of floating-point operations of the controller across the entire range.

[0151] The effective lever arm configuration for the horizontal load is dynamically updated according to the vertical deformation of the test model. The specific calculation steps include steps 505 and 506:

[0152] Step 505: Obtain the initial vertical distance from the center of the horizontal loading head to the initial bottom surface of the foundation.

[0153] To accurately calculate the lever arm denominator parameter required in step 503, the memory controller reads the geometric constant recorded during static assembly calibration under constant gravity conditions from the non-volatile storage area. This physical constant is the initial vertical distance from the center of the horizontal loading head to the initial bottom surface of the foundation. Obtaining this absolute distance reference provides an indispensable spatial coordinate origin for dynamically extrapolating the transient lever arm height in the centrifugal field.

[0154] Step 506: Add the initial vertical distance to the actual vertical settlement to obtain the updated effective lever arm of the horizontal load.

[0155] In the centrifuge bidirectional loading system, the horizontal loading device is fixed to a rigid reaction beam, and its absolute vertical elevation in the global space system is locked. When the bottom surface of the model experiences actual vertical settlement under pressure, the distance between the loading point and the base surface undergoes forward tension. The processor performs a forward accumulation operation based on this hardware characteristic. This process is achieved through the following formula:

[0156] h _eff =h _0 +δ _V,act ;

[0157] Among them, h _eff h is the updated effective lever arm for horizontal loads. _0 Let δ be the initial vertical distance. _V,act This represents the actual vertical settlement.

[0158] In some optional implementations, if the system detects that the absolute value of the actual vertical settlement is less than 5% of the initial vertical distance, the controller can use a comparator to execute bypass jump logic, forcing the actual vertical settlement to be assigned a value of 0 to the adder, so that the effective lever arm of the horizontal load is approximately equal to the initial vertical distance. This threshold truncation mechanism can further reduce the high-frequency computational load of the control kernel during the small elastic deformation stage while ensuring the accuracy of mechanical compensation during the large deformation stage.

[0159] Example 6: During the biaxial coupling loading process, the control algorithm for calculating the spatial tracking error, identifying the soil stiffness matrix, and executing the inter-channel feedforward decoupling includes the following steps.

[0160] First, calculate the path normal deviation of the current loading point from the target loading path in the normalized load coordinate system, specifically including:

[0161] Step 601: Obtain the preset vertical load range and horizontal load range.

[0162] In two-degree-of-freedom loading tests, the vertical load typically represents the enormous self-weight of the superstructure, reaching tens of thousands of Newtons; while the horizontal load typically represents wind or wave loads, often only a few hundred Newtons. If the spatial geometric distance between the two is directly calculated in an absolute two-dimensional coordinate system with physical units, the calculated Euclidean distance will be dominated by the massive vertical value due to the severe imbalance in coordinate axis scales, causing the horizontal following error to be overwhelmed by the numerical value. To eliminate the calculation distortion caused by this magnitude difference, the memory pre-records the difference between the target endpoint vertical load and the initial vertical load as the vertical load range, and also records the difference between the target endpoint horizontal load and the initial horizontal load as the horizontal load range. Obtaining these two calibration references provides a definite scaling parameter for subsequent coordinate transformation.

[0163] Step 602: Scale the actual load feedback value into a dimensionless scale using the vertical load range and the horizontal load range to obtain the normalized actual load point located in the normalized load coordinate system.

[0164] The system's computational unit extracts the real-time calculated load feedback values, which include both vertical and horizontal physical units. It then subtracts the corresponding initial load from each value and divides the result by the corresponding range obtained in step 601. Through this linear division operation, the actual collected force state is mapped to a dimensionless space where the value range is compressed to between 0 and 1.

[0165] Normalized vertical coordinate V of the actual load point _norm =(V _true -V _0 ) / (V _1 -V _0 );

[0166] Among them, V _true V represents the actual vertical load with physical units. _0 V is the initial vertical load. _1 The vertical load at the target endpoint.

[0167] Similarly, the same scaling operation is performed on the horizontal channel to obtain the normalized horizontal coordinates of the actual load points. Through this mapping logic, a normalized load coordinate system is constructed, ensuring that the control errors in the horizontal and vertical directions enjoy the same geometric weight in subsequent algorithms.

[0168] Step 603: Perform a local search on the target loading path generated by the parameterized objective equation to determine the local path parameter point that is closest to the normalized actual load point.

[0169] In the normalized load coordinate system, the parameterized objective equation depicts an ideal continuous curve driven by independent variables. Due to the mechanical hysteresis of the hydraulic servo system and the plastic yielding of the soil, the current normalized actual load point often does not fall precisely on this ideal curve. The microprocessor uses the currently set global loading process parameters as the central origin, extracts a small interval of independent variable fluctuation before and after it, and uses the golden section method or gradient descent search algorithm to traverse the discrete curve coordinates within this interval. By continuously comparing the sum of squares of the Euclidean distances, the independent variable parameter value corresponding to the minimum spatial Euclidean distance is selected. The curve geometric coordinates corresponding to this selected parameter value are the local path parameter points.

[0170] Step 604: Calculate the normal projection distance between the normalized actual load point and the local path parameter point, and use the normal projection distance as the path normal deviation.

[0171] After locking onto the nearest curve node, the system calculates the absolute geometric distance between the current actual force coordinates and the perpendicular line drawn to the ideal curve. This distance represents the overall degree to which the current force state of the test model deviates from the expected loading ratio.

[0172] Calculate the path normal deviation e_n:

[0173] e_n=((V _norm -f _V (λ _star ))*f _h _ derivative (λ _star )-(H _norm -f _h (λ _star ))*f _V _ derivative (λ _star )) / sqrt(f _h _ derivative (λ _star )^2+f _V _ derivative (λ _star ) 2 );

[0174] Among them, V _norm f is the normalized vertical coordinate of the actual load point. _V (λ _star ) represents the vertical target coordinates corresponding to the local path parameter points, f _h _ derivative (λ _star H is the first derivative of the horizontal path shape function at the local path parameter point. _norm f is the normalized horizontal coordinate of the actual load point. _h (λ _star f represents the horizontal target coordinates corresponding to the local path parameter point. _V _ derivative (λ _star ) is the first derivative of the vertical path shape function at the local path parameter point.

[0175] The calculated path normal deviation is a purely scalar dimensionless value. For example, when the system calculates and outputs a path normal deviation of 0.02, it indicates the degree to which the current actual combined load state deviates from the ideal path, occupying 2% of the preset global load range. The control system compares this deviation value with a preset tolerance threshold in real time. When the absolute deviation exceeds the limit, the process step size of the current time period is reduced proportionally, realizing adaptive control of spatial error on virtual time.

[0176] Step 605: Obtain the time difference sequence of the actual load feedback value within the preset identification window as force increment data, and obtain the time difference sequence of the measured displacement signal as displacement increment data.

[0177] Soil, as a typical nonlinear elastoplastic medium, exhibits strong cross-coupling characteristics in its horizontal and vertical deformations under biaxial loading.

[0178] To achieve decoupled control, dynamic characteristic values ​​representing the current transient stiffness of the soil must be acquired. The storage controller allocates a configurable sliding data queue in memory, for example, setting the queue depth to accommodate datasets of 50 to 200 consecutive control cycles, corresponding to a physical timescale of 50 to 200 milliseconds. Within this sliding identification window, the system subtracts the actual load feedback values ​​from every two adjacent cycles to generate force increment data, and subtracts the measured displacement signals from adjacent cycles to generate displacement increment data. By employing a strategy of extracting differential increments instead of using absolute sensor readings, the system's steady-state static operating point constants can be filtered out, extracting only the pure microvariable matrix reflecting the transient dynamic response.

[0179] Step 606: Calculate the variance of the displacement increment data within the current identification window. When the variance is lower than the preset continuous excitation threshold, discard the identification calculation of the current window and maintain the cross-coupling matrix of the previous identification window.

[0180] Online identification algorithms that rely on naturally loaded closed-loop data are prone to numerical divergence when the system excitation is insufficient. For example, during the pause phase of the experiment or when only a unidirectional constant pressure holding phase is maintained, the collected displacement increment data is almost equivalent to the sensor noise floor. In order to establish a divergence prevention interception mechanism, the computing unit calculates the statistical variance of all horizontal displacement increment samples and vertical displacement increment samples within the current sliding identification window.

[0181] The system reads the preset continuous excitation threshold from the configuration register, for example, a value of 0.001 square millimeters. When the statistical variance is lower than this continuous excitation threshold, the current data sequence is determined to lack sufficient system excitation characteristics. The main control logic triggers a bypass interrupt, skipping subsequent matrix inversion operations and forcing the output register to use the matrix parameters from the previous successful identification cycle, thus maintaining the stability of the controller.

[0182] Step 607: Based on the force increment data and displacement increment data, online identification is performed using the recursive least squares method to obtain the cross-coupling matrix.

[0183] After passing variance verification, the microprocessor extracts the incremental force and displacement data and substitutes them into a binary linear regression equation network. The system uses a recursive least squares algorithm with a preset forgetting factor for iterative optimization. The preset forgetting factor is typically configured between 0.95 and 0.99 to assign higher weights to the most recently acquired incremental samples, accelerating the algorithm's tracking response to soil stiffness degradation.

[0184] Regression model for the horizontal channel: ΔF _h =K _h H*Δδ _h +K _h V*Δδ _V +ε;

[0185] Where, ΔF _h For horizontal force increment data, K _h H represents the horizontal main diagonal stiffness in the cross-coupling matrix, Δδ _h For horizontal displacement increment data, K _h V represents the cross stiffness in the cross-coupling matrix, Δδ _V ε represents the vertical displacement increment data, and ε is the observation system error constant.

[0186] The regression model for the vertical channel is: ΔFV = KVH × Δδh + KVV × Δδv + εV;

[0187] Where ΔFV represents the vertical force increment data, KVH represents the cross stiffness in the cross-coupling matrix that represents the vertical force response to the horizontal displacement excitation, KVV represents the vertical main diagonal stiffness in the cross-coupling matrix, and εV represents the observation system error constant.

[0188] By simultaneously solving the horizontal and vertical recursive equations, the system outputs a converged 2×2 dimension matrix data structure, namely the cross-coupling matrix. During the silent period before the centrifuge starts and enters the first identification window, the system extracts constant values ​​derived empirically from sand or clay and forcibly overwrites the cross-coupling matrix, setting the initial cross stiffness to 0.

[0189] Step 608: Extract the main diagonal stiffness and cross stiffness of the calculated cross-coupling matrix. If the main diagonal stiffness is negative, or the absolute value of the ratio of cross stiffness to main diagonal stiffness is greater than the preset coupling strength boundary, discard the identification calculation of the current window. Maintain the cross-coupling matrix of the previous identification window. The main diagonal stiffness includes KHH and KVV; the constraint conditions of the coupling strength boundary should be applied to the two ratios |KHV / KHH| and |KVH / KVV| respectively.

[0190] As a second security interception mechanism to prevent matrix singularities and control positive feedback, the processor performs a physical rationality review on the output cross-coupling matrix. The main diagonal stiffness parameter representing the self-response of this channel is extracted. According to the constitutive principles of geotechnical mechanics, its value must always be greater than 0 to ensure positive definiteness constraints. It should be noted that in some embodiments, this invention independently performs positive definiteness checks on the main diagonal stiffness KHH of the horizontal channel and the main diagonal stiffness KVV of the vertical channel. A negative main diagonal stiffness value for either channel triggers the interception operation in this step.

[0191] Extract the cross stiffness parameter representing the cross-channel interference response and divide it by the main diagonal stiffness to calculate the cross coupling ratio. Read the preset coupling strength boundary parameter, for example, set this value to 1.0. If the absolute value of the cross coupling ratio is greater than 1.0, it means that the system has identified that the crosstalk response strength exceeds its own main channel response strength, which is a pseudo-state of failure in practical engineering physics. If any of the above physical violation conditions are triggered, the system immediately destroys the matrix cache of this iteration and restores the historical parameters of the previous compliance cycle.

[0192] The cross-coupling ratio is a derived parameter derived from the corresponding element of the cross-coupling matrix. The present invention uses the cross-coupling matrix for calculation, which includes direct calls to matrix elements and calls to their normalized derivatives. Those skilled in the art will understand that the two methods are equivalent.

[0193] Step 609: Subtract the updated target load from the actual load feedback value to obtain the independent control error of each loading channel.

[0194] After extracting the stiffness parameters, the system regresses to the underlying error comparison loop. The updated target load, corrected for spatial geometric eccentricity compensation, is extracted and then subtracted from the actual load feedback value, corrected for parasitic force dynamic stripping.

[0195] Step 610: Calculate using the cross-coupling matrix and the independent control error of the cross channel to construct a feedforward decoupling compensation amount to offset the dynamic coupling interference between channels.

[0196] To prevent dynamic interference on the physical platform, the algorithm artificially constructs a software coupling path with opposite polarity within the digital controller. The cross-coupling ratio parameter verified in step 608 is extracted and multiplied by the independent control error of the opposite side (not belonging to this channel). This product term is the feedforward decoupling compensation. For example, for the horizontal servo channel, its feedforward decoupling compensation is an inferred value generated by multiplying the vertical independent control error by the vertical-to-horizontal cross-coupling ratio.

[0197] The feedforward decoupling compensation amount is calculated as follows:

[0198] FFH=(KHV / KHH)×eV; FFV=(KVH / KVV)×eH;

[0199] Wherein, FFH is the feedforward decoupling compensation amount for the horizontal channel, FFV is the feedforward decoupling compensation amount for the vertical channel, KHV is the cross stiffness representing the horizontal force response of the vertical displacement excitation in the cross coupling matrix, KHH is the main diagonal stiffness of the horizontal channel, KVH is the cross stiffness of the vertical force response of the horizontal displacement excitation, KVV is the main diagonal stiffness of the vertical channel, eV is the independent control error of the vertical channel, and eH is the independent control error of the horizontal channel. This formula converts the force error signal of the opposite channel into the equivalent disturbance prediction amount of this channel through the stiffness coupling ratio, and cancels it in advance in the basic control amount in step 611.

[0200] Step 611: Combine the independent control error with the feedforward decoupling compensation amount to generate a decoupling control quantity, and output the decoupling control quantity to the loading system to execute servo actions.

[0201] After the basic proportional-integral-derivative (PID) controller calculates the basic control scalar, the feedforward decoupling compensation is subtracted from this basic control scalar. The output of this superposition operation is the final decoupling control quantity. This decoupling control quantity is then converted into an analog voltage signal or a pulse-width modulation (PWM) signal by a digital-to-analog converter (DAC) module, which drives the servo valve in the hydraulic assembly to perform spool valve displacement.

[0202] In practical centrifuge model tests, after adopting the above-mentioned decoupling control method, the path normal deviation of the system in the normalized load coordinate system can be continuously controlled within a small range, the coupling interference of the dual-channel loading response is effectively suppressed, and the steady-state tracking accuracy of the force control channel is significantly improved compared with the traditional independent dual-channel control scheme. Those skilled in the art will understand that the specific control accuracy indicators are affected by factors such as the constitutive type of the controlled soil, the loading rate, and the inherent bandwidth of the hydraulic servo system, and can be further optimized by adjusting the control parameters in actual tests.

[0203] By subtracting the feedforward decoupling compensation, the controller pre-adjusts for the impending combined mechanical and soil disturbance across the channel. In the preferred implementation, the proportional-integral-derivative (PID) parameters of the foundation controller within each loading channel are not arbitrarily set. System maintenance personnel first force the cross stiffness coefficient to 0 at the software level, and then calibrate the foundation gain coefficient for the independent single-channel cylinder and sensor loops using the Ziegler-Nichols empirical step response method. After completing the foundation closed-loop pole configuration, the online identification network access cross term in step 607 is activated for dynamic fine-tuning, thereby ensuring stable output of the decoupled control quantity across the entire frequency band.

[0204] Example 7: When executing a specific centrifugal model loading test path, the process of the underlying control loop achieving safe and smooth mode transition mainly includes:

[0205] Step 701: When the parameterized objective equation is set to the path type that requires vertical displacement control sweep, the disturbance-free switching strategy of the vertical control loop is triggered.

[0206] In centrifuge foundation bearing capacity tests, to obtain the failure envelope characteristics of the soil under specific compressive deformation, a displacement-controlled sweep test is typically configured, i.e., a displacement-controlled sweep path type. Under this condition, the control system cannot maintain a constant mechanical control target; instead, it needs to forcibly lock the current vertical physical displacement after reaching a preset vertical load benchmark. The system logic unit identifies this specific test requirement by parsing the instruction markers of the parameterized target equation. Once the sweep trigger interval is entered, the main control program issues a control mode change command, triggering a disturbance-free switching strategy to prevent the closed-loop control loop from experiencing severe transient shocks to the hydraulic actuators due to sudden changes in the target.

[0207] Step 702: In the last control cycle before the vertical control loop switches from force control mode to displacement control mode, record the current vertical servo control output and extract the current actual vertical displacement (actual vertical settlement) from the measured displacement signal.

[0208] To ensure smoother mode transitions, the underlying physical and digital control states must be captured in the frame preceding the switch. A stabilization wait time parameter is acquired, typically configured to be 0.5 to 2 seconds. When the logic unit determines that the tracking absolute error of the vertical force control loop is <2% and the error convergence duration is > stabilization wait time, the control core freezes a state snapshot in the current control interrupt routine. The final drive voltage command value sent from the digital-to-analog converter to the hydraulic servo valve is extracted as the current vertical servo control output; the absolute physical coordinates fed back from the displacement sensor are simultaneously read as the current actual vertical displacement.

[0209] Step 703: Set the current actual vertical displacement to the initial target value of the displacement control mode after switching.

[0210] After acquiring the historical physical displacement state from the previous time step, the data processor transmits it across modes to the newly activated closed-loop displacement controller. Assigning the current vertical actual displacement as the displacement tracking reference means that, within the first calculation cycle after activation, the internally set command target of the displacement control mode is completely equal to the actual position fed back by the external feedback. This state assignment operation ensures that the initial proportional error output of the proportional-integral-derivative closed-loop comparator is strictly equal to 0, cutting off the disturbance source that could induce a step response at the system input.

[0211] Step 704: Set the current vertical servo control output to the initial integral value of the integrator in the displacement control mode after switching, so as to maintain the continuity of the underlying control output at the moment of mode switching.

[0212] In the basic closed-loop control algorithm, the integrator is responsible for accumulating historical steady-state errors and maintaining the main control energy output. In force control mode, the servo valve opening command to maintain the current hydraulic cylinder pressure state is almost entirely provided by the integrator. If the integrator of the new displacement controller is reset to zero at the moment of mode switching, the control output will drop to 0 instantaneously, causing the hydraulic cylinder to experience a pullback and pressure loss jump. In this step, the extracted current vertical servo control output is directly overwritten into the integral accumulation storage unit. Therefore, at the point where the computing clock cycle crosses during mode switching, the analog control level sent to the physical servo actuator remains absolutely continuous. After completing this bumpless switching procedure, the horizontal loading channel synchronously receives the uniform displacement increase command, driving the test model to smoothly undergo shear slip along the stress envelope.

[0213] Example 8 provides a centrifuge horizontal and vertical dual-degree-of-freedom coupled loading simulation system. The loading device includes a reaction beam 1, a reaction beam connecting plate 2, a model box locking block 3, a horizontal loading mechanism 4, a vertical loading mechanism 5, a hydraulic assembly 6, a frame horizontal position adjustment top block 7, and a test model 8. The test model 8 is fixed below the vertical loading mechanism 5. The horizontal loading mechanism 4 and the vertical loading mechanism 5 are located above the reaction beam 1.

[0214] The horizontal loading mechanism 4 includes a horizontal hydraulic cylinder 9, a displacement sensor 10, a horizontal loading device mounting bracket 11, a horizontal hydraulic cylinder anti-rotation guide mechanism 12, a loading head support bracket 13, a lifting rolling bearing 14, a loading head 15, and a horizontal force sensor 16. The lifting rolling bearing 14 is fixed below the loading head 15 via the loading head support bracket 13.

[0215] The vertical loading mechanism 5 includes a vertical hydraulic cylinder 17, a vertical hydraulic cylinder anti-rotation guide mechanism 18, a vertical loading device mounting bracket 19, a vertical displacement sensor 20, a vertical force sensor 21, and a vertical loading device rolling loading head 22.

[0216] The hydraulic assembly 6 includes a hydraulic assembly mounting base 23, a horizontal cylinder servo valve seat 24, a horizontal cylinder servo valve 25, a vertical cylinder servo valve seat 26, a vertical cylinder servo valve 27, a main inlet valve seat 28, and a main inlet valve 29. The horizontal cylinder servo valve seat 24 is fixed to the hydraulic assembly mounting base 23, and the horizontal cylinder servo valve 25 is connected to the horizontal cylinder 9 for hydraulic actuation. The vertical cylinder servo valve seat 26 is fixed to the hydraulic assembly mounting base 23, and the vertical cylinder servo valve 27 is connected to the vertical cylinder 17 for hydraulic actuation.

[0217] The horizontal and vertical loading mechanisms are located on the upper side of the reaction beam and configured to simultaneously apply horizontal and vertical forces to the test model. The controller is communicatively connected to both the horizontal and vertical loading mechanisms and is configured to execute the centrifuge two-degree-of-freedom coupled loading control method as described in any of the above embodiments. The controller is also communicatively connected to the centrifuge main control system and configured to acquire the rotational angular velocity of the centrifuge spindle in real time.

[0218] The reaction beam 1, serving as the rigid skeleton and reaction base of the entire centrifugal loading system, spans and is fixed to the upper edge of the centrifuge basket or test chamber. The horizontal loading mechanism 4 and the vertical loading mechanism 5 are both spatially arranged and fixedly installed side-by-side on the upper surface of the reaction beam 1. The test model 8 is positioned directly below the vertical loading mechanism 5. When the system performs bidirectional loading, the horizontal loading mechanism 4 outputs thrust or tension in the horizontal direction, while the vertical loading mechanism 5 outputs downward pressure in the vertical direction. These two orthogonal forces ultimately converge on the force-bearing surface of the test model 8, and their reaction forces are transmitted upward along their respective mounting brackets, ultimately being borne by the reaction beam 1 and forming a mechanical closed loop. The controller, as the electronic control hub, establishes bidirectional communication connections via signal cables with the bidirectional servo valves distributed in the hydraulic components 6 and the force and displacement sensors located at the ends of the actuators. Based on this hardware topology, the controller retrieves the internally stored control program and executes the control algorithm, which includes dynamic correction of parasitic forces, equivalent compensation of geometric coupling, and normalized path tracking, to direct the purely mechanical hydraulic actuation frame to complete spatial closed-loop control.

[0219] The controller also establishes a communication connection with the centrifuge's main control system via a data bus to receive the rotational angular velocity signal of the centrifuge spindle in real time. This rotational angular velocity is used to calculate the dynamic parasitic forces in the method, including the centrifuge self-weight parasitic force, frictional parasitic force, and Coriolis parasitic force. During the steady-state operation of the centrifuge, the spindle rotational angular velocity is maintained constant by the centrifuge's main control system's speed closed-loop and continuously broadcast. During the acceleration or deceleration transition phase, the controller reads the real-time update value of this angular velocity according to the same sampling period as the force and displacement sensors to ensure the synchronization of parasitic force compensation calculations with the centrifuge field state.

[0220] The horizontal loading mechanism includes a horizontal hydraulic cylinder, a horizontal force sensor, a loading head, a loading head support bracket, and a lifting rolling bearing. The lifting rolling bearing is fixed below the loading head via the loading head support bracket. The lifting rolling bearing is configured to support the centrifugal weight of the loading head and the horizontal force sensor under the hypergravity environment of the centrifugal test, thereby limiting the vertical bending deformation freedom of the moving parts of the horizontal loading mechanism.

[0221] Regarding the specific components and assembly relationship of the horizontal loading assembly, the horizontal loading device mounting bracket 11 is rigidly bolted to the reaction beam 1, and the horizontal cylinder 9 is fixed to the mounting bracket in a horizontal posture. Along the power transmission path of the horizontal force output, the piston rod end of the horizontal cylinder 9 is connected in series with the horizontal force sensor 16 and the loading head 15. In terms of specific structural form, the loading head support bracket 13 is a downwardly suspended connecting component, and its top end is rigidly locked to the bottom surface of the loading head 15; the lifting rolling bearing 14 is nested in the bottom opening of the loading head support bracket 13 and forms rolling contact with the rigid support guide surface extending below. The core intention of designing this lifting component assembly is to solve the technical problem of shear failure of cantilever components caused by ultra-high centrifugal acceleration. In a hypergravity field with acceleration up to 100 times that of normal gravity, the self-weight of the horizontally extending moving parts such as the horizontal force sensor 16 and the loading head 15 will be magnified proportionally by a hundred times. Without lower support, the enormous centrifugal weight would force the piston rod to undergo severe vertical bending deformation, which would not only increase the risk of jamming and stunting of the horizontal cylinder 9, but also introduce significant frictional interference into the horizontal mechanical measurements. By adding a lifting rolling bearing 14 directly below, the system establishes a rigid normal support force transmission path in the vertical direction, intercepting the downward bending degree of freedom caused by centrifugal weight; at the same time, by utilizing the low-resistance rolling characteristics of the bearing structure itself, the smoothness of the loading head 15's movement in the horizontal forward and backward directions is ensured.

[0222] The vertical loading mechanism includes a vertical cylinder, a vertical force sensor, and a rolling loading head for the vertical loading device. The rolling loading head of the vertical loading device is located below the vertical force sensor and is configured to maintain rolling contact with the top surface of the test model. The rolling loading head of the vertical loading device is configured to transmit vertical force to the test model and release the horizontal mechanical constraints between the vertical loading mechanism and the test model.

[0223] Along the power transmission path of vertical loading, the vertical loading device mounting bracket 19 is fixed to the reaction beam 1, and the vertical cylinder 17 is fixed vertically downward within the mounting bracket, with its output piston rod end connected to the vertical force sensor 21. At the lowest end of the vertical force sensor 21, i.e., at the interface directly in contact with the test model 8, a vertical loading device rolling loading head 22 is assembled. The bottom of this rolling loading head is machined into a smooth rolling curved surface. In actual assembly and loading conditions, it only relies on the vertical servo downward pressure to adhere and press against the horizontal top surface of the test model 8, without any bolts or pins for limiting or fixing between them. The design intent of this contact structure is to achieve physical isolation and decoupling between the transmission of vertical normal force and horizontal tangential displacement. When the horizontal loading mechanism 4 applies a lateral thrust to the test model 8, causing the model to undergo actual horizontal displacement, if the vertical loading head and the top surface of the model are rigidly bound together, the piston rod of the vertical cylinder 17 will become a huge rigid obstacle preventing the model from laterally displacing, thus applying an unknown false resistance in the horizontal direction to the test model 8. With the adoption of a bottom-rolling contact assembly design, the rolling loading head 22 of the vertical loading device can roll or slide relatively freely on the top surface of the model, cutting off the physical path for the vertical loading mechanism 5 to transmit horizontal mechanical constraint force to the test model 8. It should be noted, in conjunction with the underlying control algorithm, that although the rolling component releases the horizontal constraint force at the physical hardware level, the absolute spatial position of the point of force application shifts with the lateral displacement of the model, objectively generating a geometric eccentric moment. This force distortion effect caused by the spatial line of action shift is ultimately compensated by equivalent software through the geometric coupling net additional bending moment calculation conversion logic in the control algorithm.

[0224] The system also includes a frame horizontal position adjustment top block; the frame horizontal position adjustment top block is configured to finely adjust the relative position of the test model and the loading mechanism in the horizontal direction under static gravity field environment, based on the structural elastic deformation prediction value obtained in advance by the controller, so as to lock the alignment state with the reserved reverse initial position deviation.

[0225] The frame horizontal position adjustment top block 7 is a screw rod adjustment mechanism or fine-tuning pad mechanism arranged on the side wall of the overall frame. In terms of spatial assembly, one end abuts against the rigid support surface, and the other end pushes against the positioning flange surface of the reaction beam connecting plate 2 or the model box clamping block 3 that accommodates the test model 8. During the static preparation stage of 1x constant gravity before the main motor of the equipment is started, the operator rotates the frame horizontal position adjustment top block 7, which forces the test model 8 or the loaded frame to undergo a slight relative translation and positioning in the horizontal direction through its mechanical extension and retraction. The design intent of this adjustment structure is to provide a hardware injection interface for inputting physical deviations. Based on the predicted value of structural elastic deformation calculated in advance by the controller using static formulas, the frame horizontal position adjustment top block 7 is specifically used to perform reverse spatial pre-compensation operations. For example, by screwing the top block, a reverse assembly misalignment of 0.25 mm is precisely created on the horizontal positioning surface. When the equipment operates at high speed and undergoes structural deformation under huge centrifugal load, the static physical gap that was artificially reserved in advance by the top block structure will be perfectly filled by the elastic deflection of the reaction beam and the mounting bracket. Ultimately, without relying on complex high-frequency follow-up dynamic compensation machinery, the absolute centering alignment of the loading axis under the super gravity operation condition is achieved through pure static thread adjustment.

Claims

1. A two-degree-of-freedom coupled loading control method for a centrifuge, characterized in that, include: During the centrifugal loading process, the measured load signal and measured displacement signal of the loading system are acquired in real time. Calculate the dynamic parasitic forces exerted on the loading system by the centrifugal environment; The actual load feedback value is obtained by subtracting the dynamic parasitic force from the measured load signal; Calculate the net additional bending moment caused by the deformation of the experimental model based on the measured displacement signal; Convert the net additional bending moment due to geometric coupling into an equivalent correction amount; By combining the equivalent correction amount with the pre-constructed parameterized objective equation, the updated target load is obtained; Based on the actual load feedback value and the updated target load, calculate the path normal deviation of the current loading point from the target loading path in the normalized load coordinate system. Inter-channel decoupling control is performed based on the path normal deviation, and the advance rate of the dimensionless loading process parameters is adaptively adjusted. Calculate the dynamic parasitic forces exerted on the loading system by the centrifugal environment, including: Based on the mass and rotation radius of the vertical channel components of the loading system, calculate the parasitic force of centrifugal self-weight; The frictional parasitic force is calculated based on the centrifugal force generated by the mass supported by the rolling bearing in the horizontal channel of the loading system and the preset rolling friction coefficient. The Coriolis force is calculated based on the horizontal loading velocity extracted from the measured displacement signal differential and the total mass of the horizontally moving component. Calculating Coriolis parasitism includes: In the calculation of the current k-th control cycle, extract the horizontal loading speed recorded in the (k-1)-th control cycle; Input the horizontal loading speed of the (k-1)th control cycle into the Coriolis force calculation model to obtain the Coriolis parasitic force of the current kth control cycle.

2. The method according to claim 1, characterized in that, The actual load feedback values ​​include the actual vertical load and the actual horizontal load, and the measured displacement signals include the actual horizontal displacement and the actual vertical settlement. The steps for calculating the geometrically coupled net additional bending moment caused by the deformation of the test model based on measured displacement signals specifically include: The product of the actual vertical load and the actual horizontal displacement is subtracted from the product of the actual horizontal load and the actual vertical settlement to obtain the net additional bending moment of geometric coupling. The steps for converting the net additional bending moment due to geometric coupling into an equivalent force correction include: Divide the net additional bending moment of geometric coupling by the effective lever arm of the horizontal load to obtain the equivalent horizontal force correction. The equivalent horizontal force correction is used as the equivalent force correction, and no geometric coupling compensation correction is performed on the vertical load channel.

3. The method according to claim 1, characterized in that, Calculate the path normal deviation of the current loading point from the target loading path in the normalized load coordinate system, including: Obtain the preset vertical load range and horizontal load range; The actual load feedback value is scaled in dimensionless manner using the vertical load range and the horizontal load range to obtain the normalized actual load point in the normalized load coordinate system. A local search is performed on the target loading path generated by the parameterized objective equation to determine the local path parameter point that is closest to the normalized actual load point. Calculate the normal projection distance between the normalized actual load point and the local path parameter point, and use the normal projection distance as the path normal deviation.

4. The method according to claim 1, characterized in that, The steps for performing inter-channel decoupling control specifically include: The time difference sequence of the actual load feedback value within the preset identification window is obtained as force increment data, and the time difference sequence of the measured displacement signal is obtained as displacement increment data. Based on force increment data and displacement increment data, online identification is performed using the recursive least squares method to obtain the cross-coupling matrix; The independent control error of each loading channel is obtained by subtracting the updated target load from the actual load feedback value. The feedforward decoupling compensation amount for offsetting the dynamic coupling interference between channels is constructed by using the cross-coupling matrix and the independent control error of the cross channels. The independent control error and the feedforward decoupling compensation amount are combined to generate a decoupling control quantity, and the decoupling control quantity is output to the loading system to execute servo actions.

5. The method according to claim 4, characterized in that, The steps for online identification using the recursive least squares method to obtain the cross-coupling matrix include the following physical and data constraints: Calculate the variance of the displacement increment data within the current identification window. When the variance is lower than the preset continuous excitation threshold, discard the identification calculation of the current window and maintain the cross-coupling matrix of the previous identification window. Extract the main diagonal stiffness and cross stiffness of the calculated cross coupling matrix. If the main diagonal stiffness is negative, or the absolute value of the ratio of cross stiffness to main diagonal stiffness is greater than the preset coupling strength boundary, discard the identification calculation of the current window.

6. The method according to claim 1, characterized in that, Before acquiring the measured load and displacement signals of the loading system in real time, the process also includes the initial alignment step of the loading system, specifically: Obtain the predicted value of the structural elastic deformation of the loading system under the target centrifugal acceleration; Based on the predicted values ​​of structural elastic deformation, an initial positional deviation in the opposite direction is reserved for the loading system under a static gravity field to complete the initial alignment between the test model and the loading system.

7. The method according to claim 6, characterized in that, The steps for obtaining the predicted elastic deformation values ​​of the loading system under the target centrifugal acceleration specifically include: Obtain the uniformly distributed load and span parameters of the reaction beam where the loading system is located, and calculate the deflection at the center of the reaction beam in combination with the target centrifugal acceleration; Obtain the self-weight torque and cantilever length of the horizontal loading device mounting frame of the loading system, and calculate the cantilever offset of the mounting frame in combination with the target centrifugal acceleration; The deflection at the center of the reaction beam and the offset of the cantilever of the mounting frame are vector-superimposed to obtain the total predicted offset as the predicted value of the structural elastic deformation.

8. A two-degree-of-freedom coupled loading system for a centrifuge, characterized in that, It includes a reaction beam, a horizontal loading mechanism, a vertical loading mechanism, and a controller; The horizontal loading mechanism and the vertical loading mechanism are set on the upper side of the reaction beam and configured to simultaneously apply horizontal and vertical forces to the test model; The controller is communicatively connected to the horizontal loading mechanism and the vertical loading mechanism, and the controller is configured to execute the centrifuge two-degree-of-freedom coupled loading control method as described in any one of claims 1 to 7.

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