Real-time estimation method for tower crane load swing based on rigid-flexible coupling model

Abstract

The present application relates to the technical field of intelligent control of cranes, and provides a tower crane load swing real-time estimation method based on a rigid-flexible coupling model, comprising: real-time acquisition of load position measurement data and crane control instructions; dynamic determination of measurement data validity through multi-stage verification logic; if the data is invalid, a prediction mode is activated, and numerical integral forward prediction is performed completely depending on a pre-constructed high-fidelity rigid-flexive coupling dynamic model combined with the control instructions; if the data is valid, a correction mode is activated, and the model prediction result is optimally corrected by fusing sensor measurement data. Through the cooperation of the physical model and real-time data, and through a flexible dual-mode switching mode, the present application realizes continuous state estimation during sensor signal interruption, significantly improves the swing prediction accuracy, system robustness and safety of automated operation, and solves the problem that traditional simplified models cannot accurately predict the coupling effect of flexible vibration of the load arm and swing of the load rope.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology for cranes, and more specifically, to a real-time estimation method for the sway of a load lifted by a tower crane based on a rigid-flexible coupling model. Background Technology

[0002] With the rapid development of intelligent construction and building industrialization, tower cranes, as core equipment in the construction industry, have seen their automation and intelligence levels become crucial for driving industrial upgrading. To achieve advanced functions such as automatic obstacle avoidance, precise lifting, and autonomous operation, real-time and accurate acquisition of the movement status of the hook and the load is a critical prerequisite. This relies on deploying external sensing sensors such as LiDAR and depth cameras on the tower crane to build a sensing system capable of providing real-time feedback on the spatial position of the load, thus forming a control closed loop and ensuring operational safety and efficiency.

[0003] However, in real, complex construction site conditions, the aforementioned sensing solutions relying on external sensors face severe challenges. Due to the prevalent dust, temporary obstacles, adverse weather conditions (such as rain, snow, and fog), and potential sensor malfunctions, the measurement data provided by the sensing sensors frequently experiences interruptions, delays, or distortions—that is, signal failure. Under such conditions, the automated system loses its ability to perceive the real-time motion of the suspended load, leading to interruptions in control commands, a sharp drop in operational efficiency, and potentially even safety accidents. To address the problem of state prediction during sensor failure, existing technologies typically employ simplified physical models, such as rigid pendulum or double pendulum models, for short-term prediction. However, these models have inherent flaws: they treat the tower crane structure (especially the boom, which can be tens of meters long) as an absolutely rigid body, while neglecting the elastic expansion and contraction effect of the slings. In actual operations, especially under dynamic conditions such as heavy loads, rapid starts and stops, or large-range rotations, the flexible vibration of the boom and the elastic deformation of the slings create a strong coupling effect with the swaying of the suspended load. Simplified models cannot characterize these complex physical phenomena, resulting in huge deviations between their predictions and the actual trajectory of the suspended object. The measured error can reach tens of centimeters, which is completely unacceptable for the continuous and reliable state estimation requirements of high-precision automated operations.

[0004] In summary, existing technical solutions have significant shortcomings: First, they heavily rely on external sensor data, resulting in low reliability in complex construction site environments and a lack of effective signal failure response mechanisms. Second, the prediction models relied upon when sensors fail are overly simplified, failing to characterize key physical characteristics such as boom flexible vibration and sling elasticity, leading to insufficient model fidelity. As the requirements for state estimation accuracy in automated tower cranes increase, the predictive capabilities of existing methods under unreliable sensor conditions are inherently limited.

[0005] Therefore, there is an urgent need in this field for a novel solution that breaks through the framework of traditional simplified models, fundamentally overcomes the absolute dependence on sensor data, and effectively characterizes the rigid-flexible coupling dynamics of the swinging load, so as to achieve continuous and high-precision state estimation under various working conditions and ensure the safety and continuity of automated operations. Summary of the Invention

[0006] This invention addresses the technical problems existing in the prior art by providing a real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model. This method solves the problems of existing tower cranes losing the perception of the load's motion state during automated operations due to the susceptibility of external sensor signals to interference or interruption, and the inability of traditional simplified dynamic models to accurately predict the complex dynamics caused by the coupling of boom flexibility and sling sway, which leads to decreased control accuracy and increased operational safety risks.

[0007] According to a first aspect of the present invention, a method for real-time estimation of the sway of a load suspended by a tower crane based on a rigid-flexible coupling model is provided, comprising: S1, real-time acquisition of measurement data on the position of the suspended object and control commands for the tower crane; S2, determine the validity of the measurement data based on multi-level verification logic; S3, when the measurement data is invalid, the prediction mode is activated. Based on the pre-constructed rigid-flexible coupling dynamic model of the tower crane and the control command, the state prediction result of the suspended object is obtained through numerical integration forward prediction. When the measurement data is valid, the correction mode is activated, and the state prediction result of the rigid-flexible coupling dynamic model is corrected based on the measurement data to obtain the state estimation result of the suspended object.

[0008] Based on the above technical solution, the present invention can also be improved as follows.

[0009] Optionally, before step S1, a step is also included to construct a rigid-flexible coupled dynamic model of the tower crane in an offline state, specifically including: In offline mode, define the generalized coordinate vector of the tower crane system. To uniformly describe the motion state of a tower crane system, it is represented as:

[0010] in, The slewing angle of the boom. For the position of the car, This is the length of the sling. The first-order bending mode coordinates of the boom are given. Characterizes the amplitude of vertical vibration of the boom caused by forces during its movement. For first-order frequencies, The radial swing angle of the sling. The tangential swing angle of the sling; Based on the generalized coordinate vector The hypothetical modal method is used to perform a reduced-order modeling of the boom's flexible characteristics, thus representing the boom's continuous deflection. Represented as real-time vibration amplitude With first-order mode function The product of the two components, and the first-order mode shape function of the boom determined based on finite element analysis. First-order modal mass With first-order modal stiffness A reduced-order model of the boom's flexibility is obtained; where the boom's continuum deflection... Represented as:

[0011] in, For any position on the boom, , This is the total length of the boom. For a moment, Characterizing real-time vibration amplitude, It is a first-order mode shape function; Based on the generalized coordinate vector The flexible reduced-order model of the boom is used to establish the dynamic equations of the tower crane system using the Lagrange equations, and its matrix form is as follows:

[0012] in, , , The generalized coordinate vectors and their first and second derivatives are, in order. Characterizing speed, Characterizing acceleration, For the mass matrix of the tower crane system, For the Coriolis / centrifugal force matrix of the tower crane system, Here is the stiffness matrix of the tower crane system. Related to the aforementioned flexible reduced-order model of the boom, For control input vector The generalized force vector obtained by mapping.

[0013] Optional, the first-order mode shape function of the boom Obtained through finite element modal analysis, expressed as:

[0014] in, Indicates that it is located on the boom The bending posture at the point, In order to make The normalized coefficient, These are readily available, fixed physical constants; First-order modal mass of the boom The calculation formula is:

[0015] in, For the mass of the boom; First-order modal stiffness of the boom The calculation formula is: .

[0016] Optionally, step S1 includes: Control command vectors are read in real time from the logic controller of the tower crane. , is represented as:

[0017] in, For the current moment, The torque that drives the boom to rotate, The traction force that drives the trolley to move along the boom track. The tension applied to the slings by the winch; Read the current time in real time from the logic controller. boom slewing angle Car position and the natural length of the sling ; The position measurement values ​​of the hook or suspended object in three-dimensional space are obtained in real time from external sensing sensors. :

[0018] in These are the coordinate values ​​of the three axes in the Cartesian coordinate system.

[0019] Optionally, step S2 includes: The validity of the measurement data is verified through three levels in sequence, wherein: The first level of verification includes: checking whether the delay between the timestamp embedded in the data packet and the current system time exceeds a preset first time threshold, and checking whether the sensor status code indicates a normal working state. The second level of verification includes: checking whether the confidence level of the hook or suspended object detection in the sensor's measurement data is higher than the preset confidence level threshold, and whether the number of point clouds, the size of point cloud clusters, the density and the dispersion in the measurement data are all within the corresponding preset ranges; The third level of verification includes: comparing the sensor measurement data at the current moment with the simplified prediction value calculated based on the state estimate at the previous moment; if the Euclidean distance between the two is less than a preset distance threshold, then this level of verification is passed. The sensor's measurement data is considered valid only if it passes all three levels of verification.

[0020] Optionally, before step S3, the following steps are also included: A pre-defined particle filter framework is provided, which maintains a particle set containing N particles. N is a positive integer, i∈[1,N]; Each particle Include: A nonlinear state vector = Used to characterize the boom slewing angle and boom angular velocity ; A conditional linear substate vector Used to characterize, except for the boom slewing angle and boom angular velocity In addition, the other generalized coordinates and their derivatives; A vector corresponding to the conditional linear substate subcovariance matrix ; A particle weight .

[0021] Optionally, step S3 also includes calculating the elements of the system's dynamic equations, specifically including: Based on the previous moment generalized coordinate vector and its first derivative Calculate the instantaneous mass matrix of the tower crane system. Coriolis / Centrifugal Force Matrix and stiffness matrix ;in, The mass matrix The elements are obtained by taking the second-order partial derivatives of the total kinetic energy function of the system; The Coriolis / centrifugal force matrix Using Christofer notation based on the mass matrix It is obtained by calculating its partial derivatives with respect to generalized coordinates; The stiffness matrix Each element is obtained by taking the first-order partial derivative of the total potential energy function of the system; At the same time, based on the current moment Control command vector and the predefined input transformation matrix Calculate the generalized force vector ( ; Within each estimation period, based on the calculated mass matrix Coriolis / Centrifugal Force Matrix Stiffness matrix and generalized force vector The state is propagated independently for each particle in the particle set.

[0022] Optionally, in step S3, the state prediction result of the suspended object is obtained by numerical integration forward prediction based on the pre-constructed rigid-flexible coupling dynamic model of the tower crane and the control command, including: Based on the aforementioned dynamic equations, the rotational angular acceleration corresponding to the current particle is calculated using the Schur complement decomposition. Introducing process noise, affecting the angular acceleration of each particle's rotation. Perform numerical integration to update the nonlinear state of each particle. ; Based on the obtained rotational angular acceleration Calculate the acceleration of the linear substate. A fourth-order Runge-Kutta numerical integrator is used to perform a one-step forward propagation of the linear substates to obtain the prior substates. and prior subcovariance ; Using prior substates For conditional linear substates Assign values ​​and use prior subcovariance. Update the sub-covariance matrix ; The weights of all particles are set to be equal, and the arithmetic average of the states of all particles after propagation is performed to obtain the final prediction result of the motion state of the suspended object.

[0023] Optionally, in step S3, correcting the state prediction results of the rigid-flexible coupling dynamic model based on the measurement data to obtain the state estimation results of the suspended object includes: Based on the aforementioned dynamic equations, the rotational angular acceleration corresponding to the current particle is calculated using the Schur complement decomposition. Introducing process noise, affecting the angular acceleration of each particle's rotation. Perform numerical integration to update the nonlinear state of each particle. ; Based on the obtained rotational angular acceleration Calculate the acceleration of the linear substate. A fourth-order Runge-Kutta numerical integrator is used to perform a one-step forward propagation of the linear substates to obtain the prior substates. and prior subcovariance ; For each particle, the extended Kalman filter is invoked to calculate the Kalman gain, which is then combined with the sensor's position measurement. For prior substates and prior subcovariance Perform an update to obtain the updated linear substate. Sub-covariance matrix The particle weights for each particle are obtained by normalizing the probability density of a Gaussian distribution. ; Based on the updated particle weights, a weighted average is taken of the updated states of all particles in the particle set to obtain the final state estimation result.

[0024] Optionally, step S3 further includes: calculating the effective number of particles after obtaining the final state estimate in each estimation period. ; If the number of effective particles If the particle set is below a preset threshold, the particle set is resampled to generate a new particle set with uniform weights for estimation in the next period.

[0025] According to a second aspect of the present invention, a real-time estimation system for the sway of a tower crane load based on a rigid-flexible coupling model is provided, comprising: The data interface module is configured to acquire real-time measurement data of the suspended object's position and control commands from the tower crane; The data processing module is configured to determine the validity of the measurement data based on multi-level verification logic; The state estimation module is configured to activate the prediction mode when the measurement data is invalid, and obtain the state prediction result of the suspended object through numerical integration forward prediction based on the pre-built rigid-flexible coupling dynamic model of the tower crane and the control command; and to activate the correction mode when the measurement data is valid, and correct the state prediction result of the rigid-flexible coupling dynamic model based on the measurement data to obtain the state estimation result of the suspended object.

[0026] According to a third aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the processor is configured to implement the steps of the above-described method for real-time estimation of the sway of a tower crane load based on a rigid-flexible coupling model when executing a computer management program stored in the memory.

[0027] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, on which a computer management program is stored, wherein when executed by a processor, the computer management program implements the steps of the above-described method for real-time estimation of the sway of a tower crane load based on a rigid-flexible coupling model.

[0028] This invention provides a method, system, electronic device, and storage medium for real-time estimation of the sway of a tower crane load based on a rigid-flexible coupling model. It acquires real-time load position measurement data and control commands, and uses multi-level verification logic to determine the validity of the measurement data. When the data is invalid, a pre-constructed rigid-flexible coupling dynamic model is used in conjunction with the control commands for numerical integration forward prediction (predictive mode). When the data is valid, the model prediction results are corrected using the measurement data (corrected mode), ultimately achieving continuous estimation of the load's motion state. This invention ensures the reliability of mode switching decisions through multi-level verification, accurately describes the coupling effect of the boom's flexible vibration and the sling sway using a rigid-flexible coupling model, and guarantees high-precision state prediction based on the rigid-flexible coupling dynamic model even when sensor signals are interrupted. This effectively improves the continuity and safety of automated tower crane operations under complex conditions. Attached Figure Description

[0029] Figure 1 A flowchart of a real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model provided by the present invention; Figure 2 A flowchart of a real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model, provided for one embodiment; Figure 3 A block diagram of a real-time estimation system for the sway of a tower crane load based on a rigid-flexible coupling model is provided for this invention. Figure 4 A schematic diagram of a possible hardware structure of an electronic device provided by the present invention; Figure 5 This is a schematic diagram of the hardware structure of a possible computer-readable storage medium provided by the present invention. Detailed Implementation

[0030] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0031] Figure 1 A flowchart of a real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model, provided by this invention, is shown below. Figure 1 As shown, the method includes steps S1 to S3: S1 acquires real-time measurement data of the suspended object's position and control commands for the tower crane.

[0032] For example, two types of real-time data are acquired in parallel through a hardware interface: first, control command vectors composed of parameters such as slewing torque, trolley traction force, and lifting tension are directly read from the tower crane's logic controller, along with internal states such as boom slewing angle, trolley position, and sling length measured by the encoder; second, the position measurement values ​​of the hook or suspended load in three-dimensional space are obtained from external sensing sensors such as LiDAR and depth cameras. This step provides all the necessary real-time input information for subsequent state estimation.

[0033] S2, determine the validity of the measurement data based on multi-level verification logic.

[0034] This step performs a three-level cascaded verification on the sensor measurement data acquired in step S1. For example, first, the data freshness and sensor status are verified; second, the target detection confidence and point cloud data quality are verified; and finally, the measured values ​​are compared with the simplified prediction values ​​based on the state at the previous moment to verify motion continuity. Only data that passes all three levels of verification is considered valid, and this judgment result directly determines whether the system subsequently uses the predictive mode or the corrective mode.

[0035] S3, when the measurement data is invalid, the prediction mode is activated. Based on the rigid-flexible coupling dynamic model of the tower crane pre-built in the offline state and the control command, the state prediction result of the suspended object is obtained by numerical integration forward prediction. When the measurement data is valid, the correction mode is activated, and the state prediction results of the rigid-flexible coupling dynamic model are fused and corrected based on the measurement data to obtain the state estimation results of the suspended object.

[0036] This step switches to the corresponding operating mode based on whether the measurement data is valid. When the measurement data is invalid, the system enters the prediction mode. This prediction mode relies entirely on a pre-built rigid-flexible coupled dynamic model. It takes the control command obtained in step S1 as input and performs a one-step forward solution on the differential equation describing the system state using a numerical integration method to predict the motion state of the suspended object at the next moment, thus providing continuous state prediction during sensor signal interruptions.

[0037] When the measurement data is valid, the system enters the correction mode. In this correction mode, the system first obtains the model prediction result according to the control command based on the working mode of the prediction mode. Then, the sensor measurement data obtained in step S1 is compared with the model prediction result, the deviation between the two is calculated, and the model prediction value is weighted and corrected based on this deviation. This fuses the sensor observation value and the physical model prediction value to output a more accurate estimation result of the suspended object's state.

[0038] Understandably, given the deficiencies in the background technology, this invention proposes a real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model. This method achieves continuous and accurate tracking of the load's motion state through the dynamic combination of a physical model and real-time measurement data, effectively solving the problem of continuous state estimation when sensor signals are interrupted. Furthermore, because the model incorporates the coupling effect of the boom's flexible vibration and the sling's sway, it effectively improves the accuracy and reliability of load sway prediction.

[0039] To provide a more intuitive explanation of the technical solution of this invention, the following is combined with... Figure 2 The implementation process is described below. The technical solution of this invention is divided into an offline stage (corresponding to...). Figure 2 The steps S201~S203 shown) and the online estimation stage (corresponding to) Figure 2 (Steps S204~S210 shown).

[0040] 1. Step S201: Construction and Acquisition of Parameters for the Rigid-Flexible Coupled Dynamic Model of Tower Crane In step S201, this embodiment defines a mathematical model that can fully describe the dynamic behavior of the system. This step S201 is the physical basis for the technical solution of this invention to make accurate predictions when sensors fail. By performing refined modeling of the tower crane system, the model fidelity is greatly improved.

[0041] Specifically, the generalized coordinate vector of the tower crane system is first defined. It contains independent variables that describe all degrees of freedom of the system, i.e., the required parameters. Generalized coordinates are a method for describing the state of a system, that is, selecting a minimum set of mutually independent variables that can uniquely determine the position and orientation of each component in the system.

[0042] In this embodiment, the generalized coordinate vector Defined as:

[0043] in, The slewing angle of the boom. For the position of the car, This is the length of the sling. The first-order bending mode coordinates of the boom are given. Characterizes the amplitude of vertical vibration of the boom caused by forces during its movement. For first-order frequencies, The radial swing angle of the sling. The tangential swing angle of the sling; Generalized coordinate vector The generalized coordinate vector contains the above six physical quantities, each of which changes with time and is a function of time. In this embodiment, the first Each moment is specifically represented as follows: , The slewing angle of the boom at any given time represents the angle of rotation of the boom around the vertical axis of the tower center (e.g., 120 degrees), and is output by a rotary encoder installed on the slewing mechanism motor or slewing bearing.

[0044] , The position of the trolley at any given time, i.e., the straight-line distance of the trolley along the center line of the boom (e.g., 50 meters), is output by the rotary encoder on the trolley traction motor.

[0045] , The natural length of the sling at all times, from the time it is released from the winch drum to the hook (in an unloaded state, such as 25 meters), is output by a rotary encoder installed on the winch motor of the hoisting mechanism.

[0046] , The first-order bending mode coordinates at any time quantify the vertical bending vibration of the boom caused by the force during its motion. The value is proportional to the actual deflection at the end of the boom, and it is automatically and coupled to be predicted as other measurable variables evolve without direct measurement.

[0047] , The sling radial swing angle describes the swing angle of the sling in the vertical plane including the boom (e.g., -10 degrees). It is calculated and predicted in real-time using the dynamic model in this embodiment when the load hook is invisible to the lidar (predicted mode). Conversely, when it is visible (corrected mode), it can be calculated using the lidar point cloud coordinates in three-dimensional space combined with the trolley position. Obtained through reverse geometric solution, and used to correct predicted values.

[0048] , The tangential swing angle of the sling at any given moment describes the angle of swing of the sling in a direction perpendicular to the radial swing plane (e.g., 5 degrees), and... It is obtained in a similar manner.

[0049] 2. Step S202: Reduce the order of the modal model based on the assumption of the boom's flexible characteristics. To account for the bending vibration of the long boom during its motion in the dynamic model, this step is based on the generalized coordinate vector defined in step S201. The hypothetical modal method is used to model the flexible characteristics of the boom in a reduced order, with the aim of simplifying the complex continuous vibration into the motion of a finite number of variables.

[0050] During operation, the actual vertical deflection of the boom continuum at any position is measured. Represented as real-time vibration amplitude With first-order mode function The product of these terms, which represents a reduced-order processing of the actual physical sag or lift of the boom, is expressed as:

[0051] in, For any position on the boom, , This is the total length of the boom. For a moment, Characterizing real-time vibration amplitude, It is a first-order mode shape function.

[0052] Specifically, for the first-order mode shape function First, the 3D model of the tower crane generated by the LiDAR scan is meshed, i.e., discretized into tens of thousands of tetrahedrons or hexahedrons. Then, material parameters such as the elastic modulus and Poisson's ratio of the boom steel, along with constraints such as complete fixation (the boom is connected to one end of the tower body), are input into Operational Modal Analysis (OMA). The first five natural vibration frequencies and corresponding mode shapes are obtained from the solver in the finite element analysis tool. The first-order frequency is then selected... The corresponding first-order mode shape is expressed as a polynomial function as follows:

[0053] in, Indicates that it is located on the boom The bending posture at the point (dimensionless). In order to make The normalized coefficient, These are fixed physical constants that can be queried.

[0054] Assumption At the current moment, k takes values ​​in the range of positive integers. For the amplitude of the vibration at the current moment... In this step When initialized to 0; when At that time, the result is estimated online in real time by the dynamic model, that is, predicted from the subsequent step S207.

[0055] Obtain the first-order mode shape function Next, this step further calculates the equivalent modal parameters corresponding to this vibration mode, i.e., the modal mass. and modal stiffness The distributed mass and stiffness characteristics of the entire boom are aggregated onto a single modal coordinate system, which forms the basis for subsequent dynamic modeling.

[0056] Specifically, in this example, the mass of the boom is measured. Calculate modal mass :

[0057] Similarly, utilizing modal mass With first-order frequency Calculate modal stiffness :

[0058] Next, modal mass and modal stiffness Both are stored as constant parameters for use in subsequent steps.

[0059] 3. Step S203: Construction of system dynamic equations The purpose of this step is to establish a core mathematical equation that accurately describes how the motion of various parts of a tower crane interacts and evolves over time under the influence of internal and external forces. This embodiment employs Lagrange mechanics, a systematic and efficient approach widely used in modern engineering. This embodiment derives the motion laws by analyzing the system's energy, which is clearer and less prone to errors, especially for complex multibody systems like tower cranes. By simultaneously solving the kinetic and potential energies of the boom, load, and trolley, an equation describing the system's motion laws is obtained. This equation is further organized into a dynamic equation that is easy for computers to solve, and its matrix form is as follows:

[0060] in, , , The three vectors are, in turn, the generalized coordinate vectors defined in step S201, and their first and second derivatives. Characterizing speed, Characterizing acceleration, its dimension is 1. In this embodiment, and The initial value is set to 0 when the system starts up. During the online real-time estimation phase after the tower crane is in operation, it will be solved according to the equation. Simultaneously update and See subsequent steps S206 and S207 for details.

[0061] The mass matrix of the tower crane system is given by... The square matrix describes the inertial properties of the system. Each element inside is a generalized coordinate vector. The function's value changes with the tower crane's posture; the calculation process is detailed in subsequent step S206.

[0062] For the Coriolis / centrifugal force matrix of the tower crane system, The matrix describes the various complex inertial force effects generated by the rotation of the tower crane system. For example, when the boom rotates, the trolley moving outward is subjected to a lateral Coriolis force. Further calculations are detailed in step S206.

[0063] Here is the stiffness matrix of the tower crane system, which is also... A square formation. Related to the reduced-order model of the boom flexibility, the restoring force property of the system is described, i.e., its ability to resist deformation and deviation from the equilibrium position. Further calculations are detailed in step S206.

[0064] For control input vector The generalized force vector obtained by mapping is The column vector represents all external driving forces and disturbances acting on the system. In each iteration, the control input vector is formed by real-time reading of the force and torque values ​​of the slewing, luffing, and hoisting motors from the crane logic controller (PLC). After combination and transformation, we obtain For details, see steps S204 and S207.

[0065] 4. Step S204: Real-time acquisition of tower crane measurement data This step marks the beginning of the online real-time estimation phase, where the program iterates at a fixed time step (e.g., 0.1 seconds in this embodiment). Within each calculation cycle, for example, at the current time... This step involves communicating with the tower crane control system and external sensors via hardware interfaces to collect three key types of real-time data in parallel. This data constitutes all the information input for subsequent steps to predict or correct the state.

[0066] Specifically, the following procedures are included: (1) After the tower crane operator inputs the command, the current time Control command vectors can be read in real time from the logic controller (such as a PLC) of the tower crane. , is represented as:

[0067] Among them, the control command vector for column vectors, The torque used to drive the boom to rotate is used to drive the entire boom to rotate around the center of the tower. The traction force that drives the trolley to move along the boom track. The tension applied to the sling by the motor of the winch.

[0068] (2) Read the internal motion state in real time from the logic controller (such as PLC) of the tower crane to obtain the generalized coordinate vector at the current moment. Some elements, including That is, the boom rotation angle measured at the current moment. Car position and the natural length of the sling .

[0069] (3) The raw data from external sensing sensors (LiDAR, depth camera, etc.) is used to identify the hook of the tower crane through segmentation and target detection algorithms. Then, its spatial position information is analyzed and transformed by coordinate system to obtain the position measurement value of the hook or the suspended object in three-dimensional space. :

[0070] in These are the coordinate values ​​of the three axes in the Cartesian coordinate system.

[0071] 5. Step S205: Determine the validity of the measurement data from the sensing sensor. In this embodiment, each calculation iteration compares the sensor position measurement values ​​obtained from step S204. A series of rigorous checks are performed to determine whether the current state is reliable and valid, and based on this, decide whether the system should enter the correction mode or the prediction mode in the current cycle. In this embodiment, a multi-level verification logic is used to make the final decision. Only when... Only data that passes all three levels of verification is considered valid.

[0072] (1) First-level verification, which checks the freshness and integrity of the data, including: comparing the timestamp of the sensor measurement data embedded in the data packet with the current system clock. If the time delay does not exceed the preset first time threshold (e.g., 20 milliseconds) and the sensor status code indicates normal working status, then the first-level verification is passed. (2) Second-level verification includes: checking whether the confidence level of the hook or object detection in the sensor measurement data is higher than the preset confidence level threshold, and whether the number of point clouds, point cloud cluster size, density and dispersion in the measurement data are all within the corresponding preset range.

[0073] For example, in step S204, if the confidence level of the point cloud cluster given by the hook or object target detection is greater than 0.8, the number of point clouds is within the preset range, the size of the point cloud cluster of the object bounding box is within the preset range, and the density distribution and dispersion of the point cloud cluster are within the preset range, then the second-level verification is passed.

[0074] (3) The third level of verification includes: comparing the sensor measurement data at the current moment with the simplified prediction value calculated based on the state estimate at the previous moment. If the Euclidean distance between the two is less than the preset distance threshold, then this level of verification is passed.

[0075] For example, the current position measurement value Compared with simplified forecast values To compare, that is:

[0076] in, and These are the position and velocity estimates from the final output of the previous iteration. It's the time step. Calculation. and The Euclidean distance between them is less than the preset value, and if it is less than the preset value, it passes the third-level verification.

[0077] The sensor's measurement data is considered valid only if all three levels of verification are passed. Based on the verification results, the value of the state variable is output, and this determines whether the system should enter the predictive mode or the corrective mode at the current moment.

[0078] 6. Step S206: Tower crane system online operation initialization In this embodiment, the program performs a one-time online phase initialization before entering the real-time estimation iteration.

[0079] Specifically, create a collection A collection of particles with 1 member , This represents the initial time, where i is the particle number. In this embodiment, The value is 1000, that is .

[0080] A pre-defined particle filter framework is provided, wherein the particle filter framework maintains a structure containing the particle filter. A collection of particles with 1 member .

[0081] Among them, the particle set Each particle in Include: A nonlinear state vector = Used to characterize the boom slewing angle and boom angular velocity ; A conditional linear substate vector Used to characterize, except for the boom slewing angle and boom angular velocity In addition, the other generalized coordinates and their derivatives; A vector corresponding to the conditional linear substate subcovariance matrix ; A particle weight .

[0082] In this embodiment, to generate this For each particle, the following operation is performed: First, define a initial mean vector All its elements are initially set to 0, representing There are 12 elements in total, namely: .

[0083] Secondly, define a The initial covariance matrix It is a diagonal matrix, and the diagonal elements take values ​​of 10 ... Off-diagonal elements are 0.

[0084] Next, a multivariate Gaussian random number generator is invoked, using the initial mean vector. The mean and initial covariance matrix are given. For covariance, randomly generated indivual initial state vector .

[0085] Then, for each generated initial state vector It is divided into 4 components: (1) That is, the initial state vector The nonlinear state vector formed by the first and seventh elements.

[0086] (2) That is, the initial state vector The remaining 10 elements, excluding the 1st and 7th elements, constitute the... The conditional linear sub-state vector.

[0087] (3) That is, the initial covariance matrix Remove from middle The corresponding columns and rows Submatrix, that is, the sub-state vector corresponding to the conditional linear substate vector The sub-covariance matrix.

[0088] (4) That is, the weight of the particle, initialized to .

[0089] Finally, , , , It formed the first Each particle member is: .

[0090] 7. Step S207: Calculation of elements of system dynamic equations In this embodiment, at the current moment Utilizing the previous moment The obtained generalized coordinate vector Its first derivative Calculate the dynamic equation The various elements of it.

[0091] Specifically, the quality matrix The elements are derived from the first derivative of the total kinetic energy with respect to the generalized coordinate vector. The second-order partial derivatives of each term in the equation are obtained as follows: The first row and first column are:

[0092] in The parameters are, in order, boom moment of inertia, trolley mass, and load mass, which are read from the physical parameters of the tower crane. , The first-order mode shape function in step S202 is respectively The derivative at the given point and the corresponding real-time vibration amplitude; all other elements in this formula are derived from... Members. The calculation of the remaining elements of the matrix is ​​similar and will not be repeated here.

[0093] Then, based on the mass matrix First derivative with generalized coordinate vector The partial derivatives of each term, using Christofel notation calculate Summing over each element ,in ,in All integers are between 1 and 6. Traversing them in order yields the complete Coriolis / centrifugal force matrix. .

[0094] The stiffness matrix is ​​calculated based on the first-order partial derivative of the total potential energy. First, the potential energy of the suspended object. , As mentioned above, this refers to the mass of the suspended object. It is the acceleration due to gravity. For the previous moment of hoisting z Axis position coordinates. Boom potential energy. ,in and The modal stiffness calculated in step 202 and The amplitude of the oscillation at any given moment. Then, the potential energies are added together, i.e. ,right Taking the first-order partial derivatives of each of the six members in the vector yields six vectors. Combined to form the stiffness matrix .

[0095] Construct using the principle of virtual work Transformation matrix Substitute Calculate the internal elements. In this embodiment, That is, column 1 is ,correspond That is, the torque that drives the boom to rotate acts only on the slewing angle. Secondly, , For the first-order mode shape function in step S202 The mode shape at that point, This corresponds to the change in the length of the sling driven by the lifting force. Finally, using... ( With the control input vector in step S204 Multiplying them yields the generalized force vector, i.e.: ( .

[0096] Within each estimation period, based on the calculated mass matrix Coriolis / Centrifugal Force Matrix Stiffness matrix and generalized force vector The state is propagated independently for each particle in the particle set.

[0097] 8. Step 208: Nonlinear Substate Iteration In this embodiment, at time Update the particles in step 206 nonlinear state vector That is, the nonlinear part For each of its particles ,from arrive calculate.

[0098] Specifically, firstly, the quality matrix... It is broken down into four components, including , , and . for The scalar represents the equivalent rotational moment of inertia of the tower crane system in its current posture; for The row vector represents the inertial coupling term between the subsystem (the rest of the generalized coordinates) and the rotational motion. yes The column vector is . The transpose of represents the inertial coupling term between the rotational motion and the subsystem; for The matrix represents the generalized mass matrix of the subsystem itself.

[0099] Then, calculate The nonlinear part, namely rotational acceleration ,for: .in, The function is calculated using the Schur complement method, that is: .in, ,and , and They are respectively Disassembled scalar and Column vector. Also, All of these are terms that have already been obtained above.

[0100] Finally, for each particle Perform numerical integration; in this embodiment, update Angular velocity at time: and updates From the perspective of time: .in, for and The time span between; and For process noise, it comes from the generalized coordinate vector of historical data of tower cranes. The probability distribution formed by the error measurement of each element is obtained by sampling.

[0101] 9. Step 209: Linear Substate Iteration In this embodiment, at time Update the particles from the previous moment. Conditional linear sub-state vector That is, the linear part: .

[0102] Next, the intermediate results from step S208 are used to calculate... The linear part, namely: .

[0103] Secondly, the fourth-order Runge-Kutta integrator is invoked, based on the conditional linear substate vector from the previous time step. As the initial value, The derivative is used to integrate and obtain the prior substate. In this embodiment, the calculation is as follows: ， ， ， 。

[0104] Update the calculation of the final prior substate: .when hour, Initialize to 0. Then, by analyzing the final prior substate... The Jacobian matrix is ​​obtained by taking the partial derivative. To update the prior subcovariance: .

[0105] Then, based on the validity results obtained from the three-level verification of the measurement data of the sensing sensor in the aforementioned step S205, state estimation is performed using different modes.

[0106] (1) If the measurement data of the sensing sensor is deemed invalid, the conditional linear sub-state vector at the current moment is directly assigned a value using the prior sub-state: And, the prior subcovariance is used to assign values ​​to the subcovariance matrix: Simultaneously, the particle weights revert to uniformity, i.e. .

[0107] (2) If the measurement data from the sensing sensor is deemed valid, then the Kalman filter is invoked for each particle, and the conditional linear sub-state vector of the previous time step is updated according to the conventional extended Kalman filter method. The prior substate The first three items (i.e.) (and the measured value of the suspended object's position inferred by the sensor in step 204) Combined into a new 3D vector, as a measurement function Then use the measurement function. Calculate the prior substate The partial derivatives at the point are used to make up the difference. The Jacobian matrix is ​​obtained; the residual covariance is calculated, and conventional calculations such as Kalman gain are performed. Finally, the particle weights are obtained by normalizing the Gaussian distribution probability density. and the updated conditional linear sub-state vector With covariance matrix .

[0108] 10. Step S210: Final State Estimation In this embodiment, according to step S206, the first... Each particle undergoes the calculation in step S209 to obtain the updated particle set. .

[0109] Specifically, each nonlinear substate and conditional linear substates Reassembled into The complete vector Then, a weighted average is calculated:

[0110] Received This is the current moment. The latest status.

[0111] Then, calculate the effective number of particles. .

[0112] like Then, a regular resampling process with replacement is initiated, resulting in a system with weights all equal to 1. New set of particles This is used for estimation in the next cycle; if Conversely.

[0113] Finally, the latest status As input, calculate the estimated value of the suspended load at this time. And output it to the upper-layer application. Finally, and or Proceed to the next iteration.

[0114] Figure 3 A structural diagram of a real-time estimation system for the sway of a tower crane load based on a rigid-flexible coupling model, provided in an embodiment of the present invention, is shown below. Figure 3As shown, a real-time estimation system for the sway of a tower crane load based on a rigid-flexible coupling model includes a data interface module, a data processing module, and a state estimation module, wherein: The data interface module is configured to acquire real-time measurement data of the suspended object's position and control commands from the tower crane; The data processing module is configured to determine the validity of the measurement data based on multi-level verification logic; The state estimation module is configured to activate the prediction mode when the measurement data is invalid, and obtain the state prediction result of the suspended object through numerical integration forward prediction based on the pre-built rigid-flexible coupling dynamic model of the tower crane and the control command; and to activate the correction mode when the measurement data is valid, and correct the state prediction result of the rigid-flexible coupling dynamic model based on the measurement data to obtain the state estimation result of the suspended object.

[0115] It is understood that the real-time estimation system for the swing of a tower crane load based on a rigid-flexible coupling model provided by the present invention corresponds to the real-time estimation method for the swing of a tower crane load based on a rigid-flexible coupling model provided in the foregoing embodiments. The relevant technical features of the real-time estimation system for the swing of a tower crane load based on a rigid-flexible coupling model can be referred to the relevant technical features of the real-time estimation method for the swing of a tower crane load based on a rigid-flexible coupling model, and will not be repeated here.

[0116] Please see Figure 4 , Figure 4 This is a schematic diagram illustrating an embodiment of the electronic device provided in this invention. For example... Figure 4 As shown, this embodiment of the invention provides an electronic device 400, including a memory 410, a processor 420, and a computer program 411 stored in the memory 410 and executable on the processor 420. When the processor 420 executes the computer program 411, it performs the following steps: S1, real-time acquisition of measurement data on the position of the suspended object and control commands for the tower crane; S2, determine the validity of the measurement data based on multi-level verification logic; S3, when the measurement data is invalid, the prediction mode is activated. Based on the pre-constructed rigid-flexible coupling dynamic model of the tower crane and the control command, the state prediction result of the suspended object is obtained through numerical integration forward prediction. When the measurement data is valid, the correction mode is activated, and the state prediction result of the rigid-flexible coupling dynamic model is corrected based on the measurement data to obtain the state estimation result of the suspended object.

[0117] Please see Figure 5 , Figure 5 This is a schematic diagram illustrating an embodiment of a computer-readable storage medium provided by the present invention. (See diagram below.) Figure 5As shown, this embodiment provides a computer-readable storage medium 500 on which a computer program 411 is stored. When the computer program 411 is executed by a processor, it performs the following steps: S1, real-time acquisition of measurement data on the position of the suspended object and control commands for the tower crane; S2, determine the validity of the measurement data based on multi-level verification logic; S3, when the measurement data is invalid, the prediction mode is activated. Based on the pre-constructed rigid-flexible coupling dynamic model of the tower crane and the control command, the state prediction result of the suspended object is obtained through numerical integration forward prediction. When the measurement data is valid, the correction mode is activated, and the state prediction result of the rigid-flexible coupling dynamic model is corrected based on the measurement data to obtain the state estimation result of the suspended object.

[0118] This invention provides a method, system, and storage medium for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model. By constructing a high-fidelity rigid-flexible coupling dynamic model, the accuracy of load sway state estimation is significantly improved. A generalized coordinate vector is used to uniquely and comprehensively describe the system's motion state, and the hypothetical modal method is employed to reduce the order of the boom's flexibility, thereby accurately capturing the coupling effect between boom vibration and cable sway. Under dynamic conditions such as rapid start-stop, the predicted position error is significantly reduced compared to traditional rigid body models. This invention's first-principles-based modeling avoids deviations caused by simplified models ignoring key physical characteristics, providing high-precision state input for automated control.

[0119] This invention ensures high reliability and adaptability of the system under complex working conditions through a switchable dual-modal estimation method and multi-level verification logic. A three-level cascaded verification (including data freshness, target detection confidence, and motion continuity checks) intelligently determines the validity of sensor data, driving the system to seamlessly switch between predictive mode (pure model-driven) and corrective mode (data-model fusion). When sensors fail due to dust, obstruction, or malfunction, the system can rely entirely on the rigid-flexible coupled dynamic model for numerical integration forward prediction, ensuring the continuity of state estimation. When the data is valid, a particle filter framework optimizes data fusion, effectively avoiding operational interruptions caused by sensor loss and improving the system's anti-interference capability in real-world construction environments.

[0120] This invention also boasts advantages in both ease of engineering deployment and safety assurance. Model parameters (such as modal mass and modal stiffness) are determined offline through finite element analysis or operational modal analysis, eliminating the need for massive data training and enabling rapid adaptation to different tower crane models. Simultaneously, the dual-modal design provides a safety redundancy sensing layer for the control system: when sensors are functioning normally, optimal estimation is achieved by correcting the modes; when signals fail, the predicted modes act as backup state sources, preventing collisions or loss of control risks caused by sudden changes in control commands. This invention effectively reduces safety hazards in automated operations and meets the stringent requirements of intelligent construction for high continuity and high safety.

[0121] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0122] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0123] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0124] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0125] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0126] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0127] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A real-time estimation method for the sway of a load suspended by a tower crane based on a rigid-flexible coupling model, characterized in that, include: S1, real-time acquisition of measurement data on the position of the suspended object and control commands for the tower crane; S2, determine the validity of the measurement data based on multi-level verification logic; S3, when the measurement data is invalid, the prediction mode is activated. Based on the pre-constructed rigid-flexible coupling dynamic model of the tower crane and the control command, the state prediction result of the suspended object is obtained through numerical integration forward prediction. When the measurement data is valid, the correction mode is activated, and the state prediction result of the rigid-flexible coupling dynamic model is corrected based on the measurement data to obtain the state estimation result of the suspended object.

2. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 1, characterized in that, Before step S1, there is also a step of constructing a rigid-flexible coupled dynamic model of the tower crane in an offline state, specifically including: In offline mode, define the generalized coordinate vector of the tower crane system. To uniformly describe the motion state of a tower crane system, it is represented as: in, The slewing angle of the boom. For the position of the car, This is the length of the sling. The first-order bending mode coordinates of the boom are given. Characterizes the amplitude of vertical vibration of the boom caused by forces during its movement. For first-order frequencies, The radial swing angle of the sling. The tangential swing angle of the sling; Based on the generalized coordinate vector The hypothetical modal method is used to perform a reduced-order modeling of the boom's flexible characteristics, thus representing the boom's continuous deflection. Represented as real-time vibration amplitude With first-order mode function The product of the two components, and the first-order mode shape function of the boom determined based on finite element analysis. First-order modal mass With first-order modal stiffness A reduced-order model of the boom's flexibility is obtained; where the boom's continuum deflection... Represented as: in, For any position on the boom, , This is the total length of the boom. For a moment, Characterizing real-time vibration amplitude, It is a first-order mode shape function; Based on the generalized coordinate vector The flexible reduced-order model of the boom is used to establish the dynamic equations of the tower crane system using the Lagrange equations, and its matrix form is as follows: in, , , The generalized coordinate vectors and their first and second derivatives are, in order. Characterizing speed, Characterizing acceleration, For the mass matrix of the tower crane system, For the Coriolis / centrifugal force matrix of the tower crane system, Here is the stiffness matrix of the tower crane system. Related to the aforementioned flexible reduced-order model of the boom, For control input vector The generalized force vector obtained by mapping.

3. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 2, characterized in that, First-order mode function of the boom Obtained through finite element modal analysis, expressed as: in, Indicates that it is located on the boom The bending posture at the point, In order to make The normalized coefficient, These are readily available, fixed physical constants; First-order modal mass of the boom The calculation formula is: in, For the mass of the boom; First-order modal stiffness of the boom The calculation formula is: 。 4. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 3, characterized in that, Step S1 includes: Control command vectors are read in real time from the logic controller of the tower crane. , is represented as: in, For the current moment, The torque that drives the boom to rotate, The traction force that drives the trolley to move along the boom track. The tension applied to the slings by the winch; Read the current time in real time from the logic controller. boom slewing angle Car position and the natural length of the sling ; The position measurement values ​​of the hook or suspended object in three-dimensional space are obtained in real time from external sensing sensors. : in These are the coordinate values ​​of the three axes in the Cartesian coordinate system.

5. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 4, characterized in that, Step S2 includes: The validity of the measurement data is verified through three levels in sequence, wherein: The first level of verification includes: checking whether the delay between the timestamp embedded in the data packet and the current system time exceeds a preset first time threshold, and checking whether the sensor status code indicates a normal working state. The second level of verification includes: checking whether the confidence level of the hook or suspended object detection in the sensor's measurement data is higher than the preset confidence level threshold, and whether the number of point clouds, the size of point cloud clusters, the density and the dispersion in the measurement data are all within the corresponding preset ranges; The third level of verification includes: comparing the sensor measurement data at the current moment with the simplified prediction value calculated based on the state estimate at the previous moment; if the Euclidean distance between the two is less than a preset distance threshold, then this level of verification is passed. The sensor's measurement data is considered valid only if it passes all three levels of verification.

6. A real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model according to any one of claims 2 to 5, characterized in that, Before step S3, the following are also included: A pre-defined particle filter framework is provided, which maintains a particle set containing N particles. N is a positive integer, i∈[1,N]; Each particle Include: A nonlinear state vector = Used to characterize the boom slewing angle and boom angular velocity ; A conditional linear substate vector Used to characterize, except for the boom slewing angle and boom angular velocity In addition, the other generalized coordinates and their derivatives; A vector corresponding to the conditional linear substate subcovariance matrix ; A particle weight .

7. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 6, characterized in that, Step S3 also includes calculating the elements of the system's dynamic equations, specifically including: Based on the previous moment generalized coordinate vector and its first derivative Calculate the instantaneous mass matrix of the tower crane system. Coriolis / Centrifugal Force Matrix and stiffness matrix ;in, The mass matrix The elements are obtained by taking the second-order partial derivatives of the total kinetic energy function of the system; The Coriolis / centrifugal force matrix Using Christofer notation based on the mass matrix It is obtained by calculating its partial derivatives with respect to generalized coordinates; The stiffness matrix Each element is obtained by taking the first-order partial derivative of the total potential energy function of the system; At the same time, based on the current moment Control command vector and the predefined input transformation matrix Calculate the generalized force vector ( ; Within each estimation period, based on the calculated mass matrix Coriolis / Centrifugal Force Matrix Stiffness matrix and generalized force vector The state is propagated independently for each particle in the particle set.

8. The method for real-time estimation of load sway in a tower crane based on a rigid-flexible coupling model according to claim 7, characterized in that, In step S3, the state prediction result of the suspended object is obtained by numerical integration forward prediction based on the pre-constructed rigid-flexible coupled dynamic model of the tower crane and the control command, including: Based on the aforementioned dynamic equations, the rotational angular acceleration corresponding to the current particle is calculated using the Schur complement decomposition. Introducing process noise, affecting the angular acceleration of each particle's rotation. Perform numerical integration to update the nonlinear state of each particle. ; Based on the obtained rotational angular acceleration Calculate the acceleration of the linear substate. A fourth-order Runge-Kutta numerical integrator is used to perform a one-step forward propagation of the linear substates to obtain the prior substates. and prior subcovariance ; Using prior substates For conditional linear substates Assign values ​​and use prior subcovariance. Update the sub-covariance matrix ; The weights of all particles are set to be equal, and the arithmetic average of the states of all particles after propagation is performed to obtain the final prediction result of the motion state of the suspended object.

9. A real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model according to claim 8, characterized in that, In step S3, the correction of the state prediction results of the rigid-flexible coupling dynamic model based on the measurement data to obtain the state estimation results of the suspended object includes: Based on the aforementioned dynamic equations, the rotational angular acceleration corresponding to the current particle is calculated using the Schur complement decomposition. Introducing process noise, affecting the angular acceleration of each particle's rotation. Perform numerical integration to update the nonlinear state of each particle. ; Based on the obtained rotational angular acceleration Calculate the acceleration of the linear substate. A fourth-order Runge-Kutta numerical integrator is used to perform a one-step forward propagation of the linear substates to obtain the prior substates. and prior subcovariance ; For each particle, the extended Kalman filter is invoked to calculate the Kalman gain, which is then combined with the sensor's position measurement. For prior substates and prior subcovariance Perform an update to obtain the updated linear substate. Sub-covariance matrix The particle weights for each particle are obtained by normalizing the probability density of a Gaussian distribution. ; Based on the updated particle weights, a weighted average is taken of the updated states of all particles in the particle set to obtain the final state estimation result.

10. A real-time estimation method for the sway of a tower crane load based on a rigid-flexible coupling model according to claim 9, characterized in that, Step S3 further includes: calculating the effective number of particles after obtaining the final state estimate in each estimation period. ； If the number of effective particles If the particle set is below a preset threshold, the particle set is resampled to generate a new particle set with uniform weights for estimation in the next period.

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