A method for online monitoring of dynamic stability of a gantry system

Abstract

This invention discloses an online dynamic stability monitoring method for gantry systems, relating to the field of gantry systems. The invention uses gantry deformation datasets and deformation curves obtained from static loading tests to correct and calibrate an initial finite element model, resulting in a high-fidelity finite element model. Based on samples generated by simulation using this high-fidelity finite element model, a target prediction model is trained, thereby eliminating the deviation between the idealized model and the actual structure and ensuring the accuracy of the data foundation. Furthermore, the trained target prediction model replaces traditional finite element iterative calculations, requiring only the current gantry deformation dataset to quickly output real-time deformation curves. While achieving millisecond-level online monitoring, it can deduce continuous deformation curves over the entire travel from a limited gantry deformation dataset, overcoming the limitations of discrete data in traditional single-point monitoring and providing a complete and efficient basis for gantry system evaluation.

Description

Technical Field

[0001] This invention relates to the field of gantry systems, and more particularly to an online method for monitoring the dynamic stability of gantry systems. Background Technology

[0002] As the logistics industry moves towards high-bay, high-density automated warehouses, the rated lifting height of reach trucks continues to break records. Currently, mast systems with lifting heights exceeding 6 meters and employing three or more nested structures have become mainstream. However, with the increase in mast height and significantly improved structural slenderness, the system is prone to severe elastic deformation and swaying under complex operating conditions such as high-level acceleration and deceleration, full-load and off-center loading, and multi-axle coordinated operations. This swaying not only leads to decreased cargo positioning accuracy and reduced operational efficiency but may also cause cargo to fall and structural fatigue damage. Therefore, real-time and accurate monitoring of the overall mast deformation is crucial. However, existing mast sway monitoring methods all have insurmountable shortcomings in practical applications: Traditional methods of manual visual inspection or experience-based judgment are highly subjective, lack quantitative data support, and cannot meet the needs of precision operations. While direct detection methods based on displacement sensors, inclinometers, or optical measurement systems can acquire local data, accurately reconstructing the continuous deformation curve of the entire gantry during multi-stage gantry expansion and contraction often requires densely distributing sensors at multiple locations across each section. This leads to extremely difficult sensor wiring, signal susceptibility to structural interference, and complex and costly high-level calibration. More importantly, relying solely on a sparsely distributed set of sensors makes it difficult to directly interpolate or reconstruct a high-precision overall continuous deformation pattern, resulting in a significant measurement blind zone.

[0003] The strain gauge-based local stress testing method can only reflect the single-point mechanical response. Due to the complex contact nonlinearity and relative sliding between multi-stage gantry, it is difficult to accurately invert the overall attitude and deformation morphology from the local strain. While pure theoretical simulation analysis can simulate overall deformation, its model parameters are often based on ideal conditions, making it difficult to adapt to load changes, wear gaps, and assembly errors in actual operations in real time. This results in a large deviation between the simulation results and the actual conditions, and the computation time cannot meet the requirements of online real-time monitoring.

[0004] In summary, existing technologies are either limited by the engineering implementation difficulties of physical sensors or by the real-time performance and accuracy of pure simulation models. There is a lack of an effective monitoring method that can overcome the limitations of sensor placement and accurately reproduce the overall deformation curve of multi-level gantry in real time. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, such as the difficulty in implementing dense sensor deployments, the inability to infer the overall shape from local measurements, and the insufficient real-time performance and accuracy of pure simulation models, this invention proposes an online dynamic stability monitoring method for gantry systems, comprising: Construct an initial finite element model corresponding to the gantry system under test, and for each gantry system entity under test, preset multiple working conditions, and conduct static loading tests under each working condition to obtain the corresponding gantry deformation dataset and the deformation curve of the gantry system under test. Using the gantry deformation dataset obtained through static loading tests and the deformation curve of the tested gantry system, the parameters of the initial finite element model are corrected and calibrated to obtain a high-fidelity finite element model. Based on a high-fidelity finite element model, various working conditions are simulated to obtain the gantry deformation dataset and deformation curve corresponding to each working condition. The gantry deformation dataset obtained under each working condition is used as the training sample, and the corresponding gantry deformation curve is used as the training label to construct a training set; the training set is used to train a preset machine learning model to obtain a target prediction model. Obtain the current gantry deformation dataset corresponding to the gantry system under test, and use it as the model input. Predict the real-time deformation curve of the gantry system under test through the target prediction model.

[0006] Furthermore, inertial measurement units are respectively provided at the center positions of the upper and lower ends of the upper end face of the gantry system entity under test and each level of the gantry system under test; The inertial measurement unit is configured to acquire attitude angle data of the corresponding gantry end face in real time.

[0007] Furthermore, the preset multiple operating conditions specifically include: By changing the load weight applied to the fork carriage, changing the position of the equivalent connection point, changing the proportion of the overall extension height of the tested mast system to the total lift height, and / or changing the extension height of one or more masts, various working conditions can be combined. The equivalent connection point refers to the mechanical equivalent center of the actual contact area between the fork carriage and the final stage mast where the load is transferred.

[0008] Furthermore, the static loading test includes: Apply the load weight set under the current operating conditions to the tested gantry system entity; Using inertial measurement units installed at the center of the upper and lower end faces of each level of the gantry, the tilt angles of the upper and lower end faces are collected simultaneously; Deformation curves of the gantry system under test are obtained using high-precision external measuring equipment under current working conditions. The self-deflection angle of each stage of the gantry is determined as its own deformation based on the difference between the upper end face inclination angle and the lower end face inclination angle; the upper end face inclination angle is the inclination angle of the upper end face normal line relative to the gravity reference line; the lower end face inclination angle is the inclination angle of the lower end face normal line relative to the gravity reference line. The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

[0009] Furthermore, the static loading test includes performing single-stage loading tests on each level of the gantry system entity under test, including: Fix the lower end face of the current gantry; Based on the extension height of the current gantry under the current working conditions, determine the target stress point location of the current gantry and the relative distance between the current gantry and the previous gantry. Vertical loading interfaces are symmetrically set on both sides of the target stress point in the horizontal direction; A vertical force is applied to the target force point through the vertical loading interface. The magnitude of the vertical force is set to the equivalent resultant force of the load weight under the current working conditions, the self-weight of the current gantry, and the weight transmitted by the upper gantry when there is an upper gantry. At the same time, a horizontal force is directly applied to the target force point, and the magnitude of the horizontal force is set to the equivalent inertial force under the current working condition; Using inertial measurement units installed at the center of the upper and lower end faces of the current gantry, the tilt angles of the upper and lower end faces are collected simultaneously to calculate the deformation of the current gantry itself. The deformation curve of this level of gantry is obtained by using high-precision external measuring equipment; Combine the deformation curves of each level of the gantry to form the deformation curve corresponding to the gantry system under test; The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

[0010] Furthermore, determining the target stress point position of the current-level gantry and its relative distance to the previous-level gantry based on the extension height of the current-level gantry under the current operating conditions specifically includes: When the current gantry is the first-level gantry, the overall geometric center of the first-level gantry is determined as the target stress point; When the current gantry is a gantry other than the first gantry, and the current working conditions are set to the fully extended state, the overall geometric center position of the current gantry along the vertical direction is determined as the target force point. When the current gantry is a gantry other than the first gantry, and the current working conditions are set to be in a non-fully extended state, the overlapping contact area between the current gantry and the previous gantry is determined according to the extension height of the current gantry set in the current working conditions, and the geometric center of the overlapping contact area is determined as the target stress point. Wherein, when the current level gantry is a gantry other than the first level gantry, the relative distance between the current level gantry and the previous level gantry is: In the non-fully extended state, it is equal to the extension height of the current stage gantry set under the current working conditions; In the fully extended state, it is equal to the maximum permissible extension height of that gantry class.

[0011] Furthermore, the parameters of the initial finite element model are corrected and calibrated using the gantry deformation dataset obtained from the static loading test and the deformation curve of the tested gantry system to obtain a high-fidelity finite element model, specifically including: The initial finite element model was run under the working conditions corresponding to each static loading test to obtain multiple sets of simulation deformation curves; The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated. The differences under all working conditions are weighted and summed or synthesized by root mean square error to construct a global objective error function. The global objective error function is used to quantify the overall fit between the simulation results and the measured results under all working conditions. The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated by residual sum of squares or root mean square error. Sensitivity analysis is performed on the initial finite element model. By perturbing the values ​​of each candidate structural parameter in the initial finite element model while keeping the other parameters unchanged, the sensitivity of each candidate structural parameter to the simulation deformation curve is quantified. Candidate structural parameters whose sensitivity exceeds a preset sensitivity threshold are selected as parameters to be corrected. With the goal of minimizing the global objective error function, the values ​​of the parameters to be corrected are iteratively updated using an optimization algorithm or genetic algorithm based on the least squares principle. When the value of the global objective error function is less than a preset threshold, the iteration stops, and the current finite element model is determined as the high-fidelity finite element model.

[0012] Furthermore, the candidate structural parameters specifically include: the normal contact stiffness of the interface between the gantry roller and the channel steel, and the initial assembly gap width at the nested fit of the multi-level gantry.

[0013] Furthermore, the quantification of the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Multiple key measurement points are set on the simulated deformation curve, including the point of maximum deformation of the curve and multiple discrete sampling points; For each candidate structural parameter, perform two consecutive perturbations and calculate the displacement increment of each key measuring point under the two perturbations respectively; Based on the difference between the second displacement increment and the first displacement increment, its rate of change relative to the first displacement increment is calculated to characterize the nonlinear evolution of the displacement response. The maximum absolute value of the rate of change among all key measurement points is selected as the sensitivity of the candidate structural parameter.

[0014] Furthermore, the quantification of the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Construct a fitting error index to characterize the difference between the simulated deformation curve after perturbation and the simulated deformation curve before perturbation; Calculate the rate of change of the fitting error index when the candidate structure parameters change by a unit, and use it as the sensitivity. The fitting error index is: residual sum of squares or root mean square error.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects: (1) This invention uses the gantry deformation dataset and deformation curve obtained from static loading tests to correct and calibrate the initial finite element model to obtain a high-fidelity finite element model, and uses the samples generated by the simulation based on the high-fidelity finite element model to train the target prediction model, thereby eliminating the deviation between the idealized model and the actual structure and ensuring the accuracy of the data basis; then, the trained target prediction model is used to replace the traditional finite element iterative calculation, and only the current gantry deformation dataset needs to be input to quickly output the real-time deformation curve. While realizing millisecond-level online monitoring, it can deduce the continuous deformation curve under the whole stroke from the limited gantry deformation dataset, overcome the limitation of the discrete data of traditional single-point monitoring, and provide a complete and efficient basis for the evaluation of gantry system.

[0016] (2) In the modeling stage, this invention abandons the limitation of relying solely on theoretical design parameters to construct idealized models in traditional simulation analysis. Instead, it introduces the deformation dataset and deformation curves of the gantry system obtained from static loading tests under various working conditions for each tested gantry system entity, and corrects and calibrates the initial finite element model. This process can effectively compensate for model deviations caused by real physical factors such as manufacturing tolerances, differences in material properties, and changes in structural state due to long-term use, and eliminates the systematic error between the theoretical model assumptions and the actual physical state of the tested gantry system entity. Through this correction mechanism based on measured data, the ability of the high-fidelity finite element model to restore the actual mechanical response characteristics of the tested gantry system entity is significantly improved, ensuring that the basic model of the simulation calculation can truly reflect the real state of the tested gantry system entity. This fundamentally solves the problem of large deviations between the pure theoretical simulation results and the real state of the tested gantry system entity, laying a solid foundation for the subsequent generation of high-confidence training samples.

[0017] (3) This invention utilizes a trained target prediction model to replace the online real-time solution process involving large-scale matrix operations in the traditional finite element method. This transforms the nonlinear mechanical iterative calculations, which originally required minutes or even hours to converge, into a millisecond-level feature data inference process. This paradigm shift significantly reduces computational resource consumption and time latency. This allows the method to adapt to rapidly changing working conditions of forklifts, such as high-frequency start-stop, rapid lifting, and multi-axis joint operations, outputting the deformation curve at the current moment in real time. This meets the stringent requirements of high real-time performance and low latency for gantry attitude monitoring in industrial settings, filling the gap in the online application of high-precision simulation models.

[0018] (4) The monitoring results output by this method are no longer the single-point, discrete displacement data provided by traditional sensors, but rather a continuous deformation curve covering the entire stroke of the gantry system under test, derived from the target prediction model. This reconstruction from the gantry deformation dataset to the overall continuous deformation curve overcomes the limitations of traditional single-point monitoring data being discrete and unable to fully characterize the overall elastic deformation of the gantry system under test. By outputting the continuous deformation curve over the entire stroke, this method can intuitively and completely present the spatial deformation state of the gantry system under test during the stress process, providing comprehensive, continuous, and high-dimensional data support for the state assessment of the gantry system under test, and significantly improving the completeness and effectiveness of the monitoring data. Attached Figure Description

[0019] Figure 1 This is a flowchart of an online dynamic stability monitoring method for a gantry system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the deformation of the gantry itself in an embodiment of the present invention; Figure 3This is a schematic diagram showing the relative distance between adjacent gantry levels in an embodiment of the present invention.

[0020] In the picture: 101. Normal line of the lower end face of the gantry; 102. Gantry; 103. Normal line of the upper end face of the gantry; 104. Baseline consistent with the direction of gravity, i.e., gravity baseline; 201. Inertial Measurement Unit; 202. Primary Gantry; 203. Secondary Gantry; 204. Tertiary Gantry; 205. Fork Carrier; 206. Equivalent Connection Point. Detailed Implementation

[0021] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0022] To overcome the shortcomings of existing technologies, such as the difficulty in implementing densely arranged sensors, the inability to invert the overall shape from local measurements, and the insufficient real-time performance and accuracy of pure simulation models, Figure 1 As shown, this invention proposes an online monitoring method for the dynamic stability of a gantry system, comprising: Construct an initial finite element model corresponding to the gantry system under test, and for each gantry system entity under test, preset multiple working conditions, and conduct static loading tests under each working condition to obtain the corresponding gantry deformation dataset and the deformation curve of the gantry system under test. The preset multiple operating conditions specifically include: By changing the load weight applied to the fork carriage, changing the position of the equivalent connection point, changing the proportion of the overall extension height of the tested mast system to the total lift height, and / or changing the extension height of one or more masts, various working conditions can be combined. The equivalent connection point refers to the mechanical equivalent center of the actual contact area between the fork carriage and the final stage mast where the load is transferred.

[0023] It should be noted that in actual physical structures, the connection between the fork carriage and the mast may be achieved through various connecting components such as pins, roller assemblies, and sliders, with contact forms including point, line, or surface contact. To facilitate finite element modeling and mechanical analysis, this invention, based on the principle of static equivalence, abstracts and equates the forces that primarily affect the overall deformation of the mast system in the aforementioned actual contact area to a single equivalent connection point. The selection of this point ensures that the load applied to it is consistent with the bending moment and shear force effects generated on the mast under actual operating conditions, thereby guaranteeing the accuracy of the simulation analysis.

[0024] In one implementation, the static loading test includes: Apply the load weight set under the current operating conditions to the tested gantry system entity; Using inertial measurement units installed at the center of the upper and lower end faces of each level of the gantry, the tilt angles of the upper and lower end faces are collected simultaneously; Deformation curves of the gantry system under test are obtained using high-precision external measuring equipment under current working conditions. The self-deflection angle of each stage of the gantry is determined as its own deformation based on the difference between the upper end face inclination angle and the lower end face inclination angle; the upper end face inclination angle is the inclination angle of the upper end face normal line relative to the gravity reference line; the lower end face inclination angle is the inclination angle of the lower end face normal line relative to the gravity reference line. The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

[0025] Given the enormous size of multi-section telescopic gantry systems in their fully extended state, often exceeding the spatial bearing capacity of conventional laboratories or testing sites, it is difficult to conduct complete static loading tests on the entire gantry system under controlled conditions. To overcome this engineering challenge of limited space, this embodiment proposes a test strategy of breaking down the system into smaller, tiered units for replication. This strategy disassembles the gantry system under test into independent single-stage test units. By fixing the current stage of the gantry within a limited space, independent loading tests are then performed on it. This approach not only effectively avoids dependence on extremely large test sites, reducing the difficulty and cost of test implementation, but also ensures that data equivalent to the overall test can be obtained within a limited space by accurately replicating the local stress state of each stage of the gantry under actual working conditions.

[0026] In another embodiment, the static loading test includes performing single-stage loading tests on each stage of the gantry system entity under test, including: Fix the lower end face of the current gantry; Based on the extension height of the current gantry in the current working conditions (this value is the set value in the working conditions), determine the target stress point position of the current gantry and the relative distance between the current gantry and the previous gantry; The step of determining the target stress point position of the current-level gantry and its relative distance to the previous-level gantry, based on the extension height of the current-level gantry under the current operating conditions (this value is a set value in the operating conditions), specifically includes: When the current gantry is the first-level gantry, the overall geometric center of the first-level gantry is determined as the target stress point; When the current gantry is a gantry other than the first gantry, and the current working conditions are set to the fully extended state, the overall geometric center position of the current gantry along the vertical direction is determined as the target force point. When the current gantry is a gantry other than the first gantry, and the current working conditions are set to be in a non-fully extended state, the overlapping contact area between the current gantry and the previous gantry is determined according to the extension height of the current gantry set in the current working conditions, and the geometric center of the overlapping contact area is determined as the target stress point. Wherein, when the current level gantry is a gantry other than the first level gantry, the relative distance between the current level gantry and the previous level gantry is: In the non-fully extended state, it is equal to the extension height of the current stage gantry set under the current working conditions; In the fully extended state, it is equal to the maximum permissible extension height of that gantry class.

[0027] like Figure 3 As shown, in this embodiment, the gantry system consists of a multi-stage telescopic structure: 201 is an inertial measurement unit installed at the center of the end face of each gantry; 202 is the first-stage gantry (innermost layer), 203 is the second-stage gantry, and 204 is the third-stage gantry (outermost layer), which are sequentially nested vertically and can slide relative to each other; 205 is the fork carriage, which moves up and down along the guide rail of the outermost gantry (the third-stage gantry 204 in this example). 206 in the figure is defined as the equivalent connection point of the fork carriage relative to the gantry system. In the figure, L1 represents the relative distance between the first-stage and second-stage gantry, L2 represents the relative distance between the second-stage and third-stage gantry, and L3 represents the vertical distance from the top of the third-stage gantry to the equivalent connection point 206.

[0028] Vertical loading interfaces are symmetrically set on both sides of the target stress point in the horizontal direction; The vertical loading interface is constructed by welding reinforcing lugs or mounting bolt assemblies to ensure that the load line converges at the target stress point.

[0029] A vertical force is applied to the target force point through the vertical loading interface. The magnitude of the vertical force is set to the equivalent resultant force of the load weight under the current working conditions, the self-weight of the current gantry, and the weight transmitted by the upper gantry when there is an upper gantry. At the same time, a horizontal force is directly applied to the target force point, and the magnitude of the horizontal force is set to the equivalent inertial force under the current working condition; In this embodiment, the equivalent inertial force is not directly measured, but is a theoretical equivalent force value calculated based on kinematic parameters and mechanical principles under preset working conditions. Specifically, firstly, a standard maximum acceleration / deceleration value is set as the working condition input based on typical acceleration and deceleration scenarios of the forklift in actual operation; secondly, the total mass of all participating motion under the current working condition is calculated, including the self-weight of the fork carriage, the load weight on the fork carriage, the self-weight of the current stage mast under test, and the self-weight of all upper-level masts located above the current stage in the current motion chain; finally, according to Newton's second law, the above-set standard acceleration / deceleration value is multiplied by the total mass to calculate the total inertial effect generated by the system at the moment of acceleration and deceleration, and this total inertial effect is equivalent to a horizontal force concentrated on the target force point. In this way, the static loading test can simulate the real horizontal impact load borne by the mast during the dynamic start-stop process of the forklift without the need for complex dynamic acceleration tests on the test site, thus achieving the purpose of reproducing dynamic mechanical characteristics using static means.

[0030] Using inertial measurement units installed at the center of the upper and lower end faces of the current gantry, the tilt angles of the upper and lower end faces are collected simultaneously to calculate the deformation of the current gantry itself. The deformation curve of this level of gantry is obtained by using high-precision external measuring equipment; In this embodiment, the high-precision external measuring device can be a laser tracker, an optical measuring system, or other non-contact displacement monitoring devices with equivalent precision to ensure the accuracy and reliability of deformation data acquisition.

[0031] Combine the deformation curves of each level of the gantry to form the deformation curve corresponding to the gantry system under test; The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

[0032] Specifically, such as Figure 2 As shown, the calculation of the self-deformation is based on the change in tilt angle of the upper and lower end faces of the gantry. Here, 104 is a baseline aligned with the direction of gravity (i.e., the gravity baseline), and 102 represents the current stage of the gantry body. The system uses an inertial measurement unit to measure the angle between the normal line 101 of the lower end face of the gantry and the gravity baseline 104. And the angle between the normal line 103 of the upper end face of the gantry and the gravity reference line 104. (Where, n represents the gantry stage). The deformation of the current gantry stage under load (i.e., relative rotation angle). The difference between the two tilt angles mentioned above is calculated using the following formula: This angular difference directly reflects the degree of elastic deformation of the gantry due to force, eliminating the interference of overall rigid displacement or tilt of the gantry.

[0033] Using the gantry deformation dataset obtained through static loading tests and the deformation curve of the tested gantry system, the parameters of the initial finite element model are corrected and calibrated to obtain a high-fidelity finite element model. In the modeling stage, this invention abandons the limitations of traditional simulation analysis that relies solely on theoretical design parameters to construct idealized models. Instead, it introduces deformation datasets and curves obtained from static loading tests conducted on each tested gantry system entity under various working conditions to correct and calibrate the initial finite element model. This process effectively compensates for model deviations caused by real-world physical factors such as manufacturing tolerances, material property differences, and structural state changes due to long-term use, eliminating systematic errors between theoretical model assumptions and the actual physical state of the tested gantry system entity. Through this calibration mechanism based on measured data, the high-fidelity finite element model significantly improves its ability to reproduce the actual mechanical response characteristics of the tested gantry system entity, ensuring that the basic model for simulation calculations can truly reflect the real state of the tested gantry system entity. This fundamentally solves the problem of significant deviations between pure theoretical simulation results and the real state of the tested gantry system entity, laying a solid foundation for generating high-confidence training samples.

[0034] The process of using the gantry deformation dataset obtained from the static loading test and the deformation curve of the tested gantry system to correct and calibrate the parameters of the initial finite element model to obtain a high-fidelity finite element model specifically includes: The initial finite element model was run under the working conditions corresponding to each static loading test to obtain multiple sets of simulation deformation curves; The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated. The differences under all working conditions are weighted and summed or synthesized by root mean square error to construct a global objective error function. The global objective error function is used to quantify the overall fit between the simulation results and the measured results under all working conditions. The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated by residual sum of squares or root mean square error. Specifically, for each working condition, the fitting error between the simulated deformation curve and the measured deformation curve under that condition is calculated. The calculation method is as follows: Displacement values ​​at discrete sampling points on the measured deformation curve are extracted, and the displacement values ​​output by the finite element simulation under the corresponding working condition are obtained. The difference between the measured displacement value and the simulated displacement value at each sampling point is squared, and then the squared differences of all sampling points are summed to obtain the local error value under this working condition. This local error value essentially reflects the magnitude of the residual sum of squares; the smaller the value, the higher the fit between the simulated deformation curve and the measured deformation curve under this working condition.

[0035] Next, the local error values ​​under all operating conditions are weighted and summed to construct the global objective error function. This function is used to comprehensively characterize the overall fit of the finite element model under all test conditions.

[0036] Sensitivity analysis is performed on the initial finite element model. By perturbing the values ​​of each candidate structural parameter in the initial finite element model while keeping the other parameters unchanged, the sensitivity of each candidate structural parameter to the simulation deformation curve is quantified. Candidate structural parameters whose sensitivity exceeds a preset sensitivity threshold are selected as parameters to be corrected. In one embodiment, quantifying the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Multiple key measurement points are set on the simulated deformation curve, including the point of maximum deformation of the curve and multiple discrete sampling points; For each candidate structural parameter, perform two consecutive small perturbations and calculate the displacement increment of each key measuring point under the two perturbations respectively; Based on the difference between the second displacement increment and the first displacement increment, its rate of change relative to the first displacement increment is calculated to characterize the nonlinear evolution of the displacement response. The maximum absolute value of the rate of change among all key measurement points is selected as the sensitivity of the candidate structural parameter.

[0037] Specifically, the aforementioned index refers to the relative evolution rate of displacement increments at key measuring points under continuous small perturbations of candidate structural parameters. The calculation process consists of three steps: First, the initial deformation state is obtained by simulation immediately after the load is applied and before any parameter correction is made, and the initial displacement values ​​of each key measuring point relative to the undeformed initial state of the structure are recorded. Secondly, a small perturbation is applied to the candidate structural parameters (the perturbation step size is usually set to ±0.1% to ±5% of the initial design value of the parameter, for example, ±1%). The deformation curve after the first perturbation is obtained by simulation. The first perturbation displacement value of each key measuring point relative to the initial undeformed state of the structure is recorded, and the difference between this value and the initial displacement value is calculated and defined as the first displacement increment. Next, based on the first perturbation, a second small perturbation of the same magnitude is applied to the parameter, and the deformation curve after the second perturbation is obtained by simulation. The displacement values ​​of each key measuring point relative to the initial undeformed state of the structure are recorded, and the difference between this value and the displacement value of the first perturbation is calculated and defined as the second displacement increment. Subsequently, for each key measuring point, if its first displacement increment is zero or less than a set threshold, the measuring point is considered invalid and its contribution rate is set to zero. For each valid measuring point, the difference between the second and first displacement increments is calculated and then divided by the first displacement increment. This represents the nonlinear acceleration of the displacement response at that measuring point with parameter perturbation. Finally, the maximum absolute value among the calculation results for all valid measuring points is selected as the final sensitivity of the candidate structural parameter. This scheme accurately captures the instantaneous impact rate and nonlinear characteristics of parameter changes on structural deformation by comparing the displacement increment changes under adjacent perturbation steps. It avoids division-to-zero anomalies and ensures that the sensitivity index truly reflects the structural response trend in key areas.

[0038] In another implementation, quantifying the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Construct a fitting error index to characterize the difference between the simulated deformation curve after perturbation and the simulated deformation curve before perturbation; Calculate the rate of change of the fitting error index when the candidate structure parameters change by a unit, and use it as the sensitivity. The fitting error index is: residual sum of squares or root mean square error.

[0039] Specifically, the initial deformation curve is first simulated immediately after the load is applied, before any parameter corrections are made. Then, a small perturbation is applied to the candidate structural parameters, and the deformation curve of the first perturbation is calculated. The difference between this curve and the initial deformation curve is defined as the first fitting error index. Next, based on the first perturbation, a small perturbation of the same magnitude is applied to the candidate structural parameters again (i.e., a second perturbation), and the deformation curve of the second perturbation is calculated. The difference between this second perturbation deformation curve and the first perturbation deformation curve is defined as the second fitting error index. Subsequently, the difference between the second and first fitting error indices is calculated and divided by the first fitting error index. The resulting relative rate of change is used as the sensitivity of the parameter. By progressively comparing the differences in deformation curves under adjacent perturbation states and their relative evolution rates, the nonlinear influence of each candidate structural parameter on the simulated deformation characteristics is accurately quantified, thereby identifying the key parameters most sensitive to structural accuracy. If the first fitting error index is zero or less than a set threshold, the sensitivity of the candidate structural parameter is set to zero.

[0040] The specific candidate structural parameters include: the normal contact stiffness of the interface between the gantry roller and the channel steel, and the initial assembly gap width at the nested joint of the multi-level gantry.

[0041] With the goal of minimizing the global objective error function, the values ​​of the parameters to be corrected are iteratively updated using an optimization algorithm or genetic algorithm based on the least squares principle. When the value of the global objective error function is less than a preset threshold, the iteration stops, and the current finite element model is determined as the high-fidelity finite element model.

[0042] Based on a high-fidelity finite element model, various working conditions are simulated to obtain the gantry deformation dataset and deformation curve corresponding to each working condition. The gantry deformation dataset obtained under each working condition is used as the training sample, and the corresponding gantry deformation curve is used as the training label to construct a training set; the training set is used to train a preset machine learning model to obtain a target prediction model. The machine learning model can be of various types, such as Convolutional Neural Network (CNN), Long Short-Term Memory Network (LSTM), Random Forest, or Support Vector Machine (SVM). In this embodiment, a Convolutional Neural Network (CNN) is preferably used as the machine learning model.

[0043] Obtain the current gantry deformation dataset corresponding to the gantry system under test, and use it as the model input. Predict the real-time deformation curve of the gantry system under test through the target prediction model.

[0044] This invention utilizes a trained target prediction model to replace the large-scale matrix operations required in traditional finite element methods for online real-time solution. It transforms the nonlinear mechanical iterative calculations, which originally required minutes or even hours to converge, into a millisecond-level feature data inference process. This paradigm shift significantly reduces computational resource consumption and time latency. This allows the method to adapt to rapidly changing operating conditions of forklifts, such as high-frequency start-stop, rapid lifting, and multi-axis coordinated operations, outputting the deformation curve at the current moment in real time. This meets the stringent requirements of high real-time performance and low latency for gantry attitude monitoring in industrial settings, filling the gap in the online application of high-precision simulation models.

[0045] An inertial measurement unit (IMU) is installed at the center of the upper end face and the center of the lower end face of each level of the gantry system under test. The inertial measurement unit is configured to acquire attitude angle data of the corresponding gantry end face in real time.

[0046] In this embodiment, the inertial measurement unit (IMU) is mainly deployed on the upper and lower surfaces of the gantry. These locations were chosen because they have high structural rigidity, clear deformation characteristics, and minimal external environmental interference. This layout not only significantly reduces the number of sensors required and lowers hardware costs, but also makes sensor installation and subsequent maintenance more convenient, thereby effectively improving the overall operational reliability of the system.

[0047] This invention constructs an initial finite element model corresponding to the gantry system under test. Using gantry deformation datasets and curves obtained from static loading tests on each gantry system under various working conditions, the parameters of the initial finite element model are corrected and calibrated, resulting in a high-fidelity finite element model that accurately reflects the actual physical state. Based on this, the high-fidelity finite element model is used to simulate various working conditions to generate a massive dataset of gantry deformation data and curves as training samples and labels. A pre-set machine learning model is then trained to obtain a target prediction model. During the real-time monitoring phase, only the current gantry deformation dataset of the gantry system under test needs to be acquired and input into the target prediction model to quickly predict the corresponding real-time deformation curve of the gantry system. Thus, this invention: This invention addresses the problem of low prediction accuracy in traditional finite element simulations due to idealized model parameters that fail to accurately reproduce the actual structural mechanical properties. By introducing gantry deformation datasets and curves obtained from static loading tests on each tested gantry system entity, the initial finite element model is corrected and calibrated. This eliminates the discrepancy between theoretical model assumptions and the actual physical entity, ensuring that subsequent training data generated using high-fidelity finite element model simulations accurately reflects the true stress and deformation behavior of the tested gantry system. This invention overcomes the shortcomings of traditional high-precision simulation calculations, which are time-consuming and cannot meet the needs of online real-time monitoring. It utilizes a corrected and calibrated high-fidelity finite element model to generate a training set offline to train a target prediction model. This transforms complex finite element iterative calculations into rapid deduction based on the target prediction model, enabling real-time monitoring where only the current gantry deformation dataset needs to be input to output a complete real-time deformation curve in milliseconds. This achieves both high efficiency and real-time performance in monitoring. This invention achieves a complete reconstruction from discrete monitoring data to the overall continuous deformation pattern. Traditional monitoring methods can only acquire discrete data from sensor placement points, while this invention, through a target prediction model, can deduce and output the continuous deformation curve of the mast system under test throughout its entire stroke based on a limited current mast deformation dataset. This fully restores the elastic deformation pattern of the mast system and provides comprehensive and continuous data support for the safety assessment of forklift mast systems.

[0048] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of the components in a specific posture (as shown in the attached figures). If the specific posture changes, the directional indication will also change accordingly. Furthermore, descriptions involving "first," "second," or "a" in the present invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined with "first" or "second" may explicitly or implicitly include at least one of those features. In the description of the present invention, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly defined. In the present invention, unless otherwise explicitly specified and defined, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can be a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal communication of two components or the interaction between two components, unless otherwise explicitly defined. For those skilled in the art, the specific meanings of the above terms in this invention can be understood according to the specific circumstances. Furthermore, the technical solutions of the various embodiments of this invention can be combined with each other, but only on the basis that those skilled in the art can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

Claims

1. A method for online monitoring of the dynamic stability of a gantry system, characterized in that, include: Construct an initial finite element model corresponding to the gantry system under test, and for each gantry system entity under test, preset multiple working conditions, and conduct static loading tests under each working condition to obtain the corresponding gantry deformation dataset and the deformation curve of the gantry system under test. Using the gantry deformation dataset obtained through static loading tests and the deformation curve of the tested gantry system, the parameters of the initial finite element model are corrected and calibrated to obtain a high-fidelity finite element model. Based on a high-fidelity finite element model, various working conditions are simulated to obtain the gantry deformation dataset and deformation curve corresponding to each working condition. The gantry deformation dataset obtained under each working condition is used as the training sample, and the corresponding gantry deformation curve is used as the training label to construct the training set. A pre-defined machine learning model is trained using the training set to obtain a target prediction model; Obtain the current gantry deformation dataset corresponding to the gantry system under test, and use it as the model input. Predict the real-time deformation curve of the gantry system under test through the target prediction model.

2. The method for online monitoring of the dynamic stability of a gantry system according to claim 1, characterized in that, An inertial measurement unit is provided at the center of the upper end face and the center of the lower end face of each level of the gantry system under test. The inertial measurement unit is configured to acquire attitude angle data of the corresponding gantry end face in real time.

3. The method for online monitoring of the dynamic stability of a gantry system according to claim 2, characterized in that, The preset multiple operating conditions specifically include: By changing the load weight applied to the fork carriage, changing the position of the equivalent connection point, changing the proportion of the overall extension height of the tested mast system to the total lift height, and / or changing the extension height of one or more masts, various working conditions can be combined. The equivalent connection point refers to the mechanical equivalent center of the actual contact area between the fork carriage and the final stage mast where the load is transferred.

4. The method for online monitoring of the dynamic stability of a gantry system according to claim 3, characterized in that, The static loading test includes: Apply the load weight set under the current operating conditions to the tested gantry system entity; Using inertial measurement units installed at the center of the upper and lower end faces of each level of the gantry, the tilt angles of the upper and lower end faces are collected simultaneously; Deformation curves of the gantry system under test are obtained using high-precision external measuring equipment under current working conditions. The self-deflection angle of each stage of the gantry is determined as its own deformation based on the difference between the upper end face inclination angle and the lower end face inclination angle; the upper end face inclination angle is the inclination angle of the upper end face normal line relative to the gravity reference line; the lower end face inclination angle is the inclination angle of the lower end face normal line relative to the gravity reference line. The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

5. The method for online monitoring of the dynamic stability of a gantry system according to claim 3, characterized in that, The static loading test includes single-stage loading tests on each level of the gantry system under test, including: Fix the lower end face of the current gantry; Based on the extension height of the current gantry under the current working conditions, determine the target stress point location of the current gantry and the relative distance between the current gantry and the previous gantry. Vertical loading interfaces are symmetrically set on both sides of the target stress point in the horizontal direction; A vertical force is applied to the target force point through the vertical loading interface. The magnitude of the vertical force is set to the equivalent resultant force of the load weight under the current working conditions, the self-weight of the current gantry, and the weight transmitted by the upper gantry when there is an upper gantry. At the same time, a horizontal force is directly applied to the target force point, and the magnitude of the horizontal force is set to the equivalent inertial force under the current working condition; Using inertial measurement units installed at the center of the upper and lower end faces of the current gantry, the tilt angles of the upper and lower end faces are collected simultaneously to calculate the deformation of the current gantry itself. The deformation curve of this level of gantry is obtained by using high-precision external measuring equipment; Combine the deformation curves of each level of the gantry to form the deformation curve corresponding to the gantry system under test; The deformation data set is composed of the deformation of each gantry, the relative distance between adjacent gantry levels, the relative distance between the top of the last gantry and the equivalent connection point, the number of gantry levels in the gantry system under test, and the overall extension height of the gantry system under test.

6. The method for online monitoring of the dynamic stability of a gantry system according to claim 5, characterized in that, The determination of the target stress point position of the current-level gantry and its relative distance to the previous-level gantry, based on the extension height of the current-level gantry under the current operating conditions, specifically includes: When the current gantry is the first-level gantry, the overall geometric center of the first-level gantry is determined as the target stress point; When the current gantry is a gantry other than the first gantry, and the current working conditions are set to the fully extended state, the overall geometric center position of the current gantry along the vertical direction is determined as the target force point. When the current gantry is a gantry other than the first gantry, and the current working conditions are set to be in a non-fully extended state, the overlapping contact area between the current gantry and the previous gantry is determined according to the extension height of the current gantry set in the current working conditions, and the geometric center of the overlapping contact area is determined as the target stress point. Wherein, when the current level gantry is a gantry other than the first level gantry, the relative distance between the current level gantry and the previous level gantry is: In the non-fully extended state, it is equal to the extension height of the current stage gantry set under the current working conditions; In the fully extended state, it is equal to the maximum permissible extension height of that gantry class.

7. The method for online monitoring of the dynamic stability of a gantry system according to claim 4 or 6, characterized in that, The process of using the gantry deformation dataset obtained from the static loading test and the deformation curve of the tested gantry system to correct and calibrate the parameters of the initial finite element model to obtain a high-fidelity finite element model specifically includes: The initial finite element model was run under the working conditions corresponding to each static loading test to obtain multiple sets of simulation deformation curves; The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated. The differences under all working conditions are weighted and summed or synthesized by root mean square error to construct a global objective error function. The global objective error function is used to quantify the overall fit between the simulation results and the measured results under all working conditions. The difference between each set of simulated deformation curves and the corresponding measured deformation curves is calculated by residual sum of squares or root mean square error. Sensitivity analysis is performed on the initial finite element model. By perturbing the values ​​of each candidate structural parameter in the initial finite element model while keeping the other parameters unchanged, the sensitivity of each candidate structural parameter to the simulation deformation curve is quantified. Candidate structural parameters whose sensitivity exceeds a preset sensitivity threshold are selected as parameters to be corrected. With the goal of minimizing the global objective error function, the values ​​of the parameters to be corrected are iteratively updated using an optimization algorithm or genetic algorithm based on the least squares principle. When the value of the global objective error function is less than a preset threshold, the iteration stops, and the current finite element model is determined as the high-fidelity finite element model.

8. The method for online monitoring of the dynamic stability of a gantry system according to claim 7, characterized in that, The specific candidate structural parameters include: the normal contact stiffness of the interface between the gantry roller and the channel steel, and the initial assembly gap width at the nested joint of the multi-level gantry.

9. The method for online monitoring of the dynamic stability of a gantry system according to claim 7, characterized in that, The quantification of the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Multiple key measurement points are set on the simulated deformation curve, including the point of maximum deformation of the curve and multiple discrete sampling points; For each candidate structural parameter, perform two consecutive perturbations and calculate the displacement increment of each key measuring point under the two perturbations respectively; Based on the difference between the second displacement increment and the first displacement increment, its rate of change relative to the first displacement increment is calculated to characterize the nonlinear evolution of the displacement response. The maximum absolute value of the rate of change among all key measurement points is selected as the sensitivity of the candidate structural parameter.

10. The method for online monitoring of the dynamic stability of a gantry system according to claim 7, characterized in that, The quantification of the sensitivity of each candidate structural parameter to the simulated deformation curve specifically includes: Construct a fitting error index to characterize the difference between the simulated deformation curve after perturbation and the simulated deformation curve before perturbation; Calculate the rate of change of the fitting error index when the candidate structure parameters change by a unit, and use it as the sensitivity. The fitting error index is: residual sum of squares or root mean square error.

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