Arch dam concrete cable crane hoisting track prediction method

Abstract

The present application belongs to the field of concrete dam construction organization, and relates to an arch dam concrete cable crane hoisting trajectory prediction method, comprising: 1) constructing a space coordinate system to determine the spatial positioning node of the cable crane; 2) using a sensor to obtain real-time position information of the spatial positioning node of the cable crane; 3) using Kalman filtering to filter and denoise the real-time position information of the spatial positioning node of the cable crane; 4) calculating the real-time position information of the spatial positioning node of the cable crane after preprocessing to obtain the time sequence motion state parameters of the cable crane; 5) constructing a cable crane trolley-lifting rope-hoisting tank system dynamics model; 6) predicting the swing angle of the cable crane hoisting tank based on the cable crane trolley-lifting rope-hoisting tank system dynamics model and obtaining the hoisting tank motion trajectory. The present application provides an arch dam concrete cable crane hoisting trajectory prediction method which can improve the prediction accuracy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of concrete dam construction organization, and relates to an arch dam concrete cable crane hoisting track prediction method, in particular to an arch dam concrete cable crane hoisting track prediction method based on data driving. BACKGROUND

[0002] In the arch dam concrete pouring process, the operation mode and operation efficiency of the construction machinery are crucial to the safety, progress and quality of the engineering construction. The arch dam construction cycle is long, the scale is large, and the process is complex. In order to achieve the goal of dam continuous high-quality and high-intensity construction, more and more engineering machinery is applied to the arch dam construction, involving various types of construction machinery with different functions and operation modes. In the concrete pouring link, various construction equipment such as cable crane, flat warehouse machine and vibrating machine are needed to cooperate to complete the work. While the cable crane hoists the concrete, it also faces the cross operation with other machinery such as tower crane and portal crane. Therefore, in the concrete hoisting process, the movement track of the cable crane hoist tank is related to the movement safety and operation efficiency of the cable crane.

[0003] The movement track analysis of the cable crane hoist tank is an effective method to ensure the operation safety and efficiency. However, in the arch dam construction, there are many warehouse surface mechanical equipment and personnel, the layout is three-dimensional and staggered, and has strong dynamics. Moreover, the cable crane runs at a high speed, accompanied by hoist tank swing, so the accuracy of the movement track prediction analysis is required. The existing track prediction method does not consider the swing of the cable crane hoist tank, and cannot provide accurate track prediction results, resulting in loss of hoisting efficiency and even safety risk in the construction process. SUMMARY

[0004] In order to solve the above technical problems existing in the background art, the present application provides an arch dam concrete cable crane hoisting track prediction method which can improve the prediction accuracy.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0006] An arch dam concrete cable crane hoisting track prediction method, characterized in that the arch dam concrete cable crane hoisting track prediction method comprises the following steps:

[0007] 1) Construct a space coordinate system and determine the spatial positioning nodes of the cable crane; the spatial positioning nodes of the cable crane include the spatial positioning nodes of the trolley and the spatial positioning nodes of the hoist tank;

[0008] 2) Use a sensor to obtain real-time position information based on the spatial positioning nodes of the cable crane in step 1), the real-time position information including the coordinates of the trolley and the hoist tank in the space coordinate system;

[0009] 3) using Kalman filter to filter and denoise the real-time position information of the spatial positioning nodes of the cable crane obtained in step 2);

[0010] 4) calculating the real-time position information of the spatial positioning nodes of the cable crane obtained after the pretreatment in step 3) to obtain the time sequence motion state parameters of the cable crane, wherein the time sequence motion parameters of the cable crane include the horizontal and vertical motion speed and acceleration of the trolley, the instantaneous swing angle of the ladle, the angular velocity and angular acceleration of the ladle;

[0011] 5) using Lagrange mechanics method to construct a dynamic model of the trolley-lifting rope-ladle system of the cable crane;

[0012] 6) based on the dynamic model of the trolley-lifting rope-ladle system of the cable crane obtained in step 5), taking the time sequence motion state parameters of the cable crane obtained in step 4) as input parameters to predict the swing angle of the ladle of the cable crane and obtain the motion trajectory of the ladle.

[0013] Preferably, the specific implementation of step 1) is to obtain the coordinates of the trolley and the ladle and the projection coordinates on the yox plane: a spatial coordinate system is constructed with the river direction as the x axis, the transverse river direction as the y axis and the vertical direction as the z axis, the coordinates of the trolley are A(x A , y A , z A ), the coordinates of the ladle are B(x B , y B , z B ), the projection coordinates of the trolley on the yox plane are A ′ (x A , y A , z B ), and the projection coordinates of the ladle on the y axis and the x axis are B x (x B , 0, z B ) and B y (0, y B , z B ) respectively.

[0014] Wherein:

[0015] A point represents the trolley;

[0016] B point represents the ladle;

[0017] A ′ point represents the projection point of the A point to the yox plane;

[0018] B x point represents the projection point of the B point to the x axis;

[0019] B yB point to the y-axis projection point;

[0020] x A A point on the x-axis position;

[0021] y A A point on the y-axis position;

[0022] z A A point on the z-axis position;

[0023] x B B point on the x-axis position;

[0024] y B B point on the y-axis position;

[0025] z B B point on the z-axis position.

[0026] Preferably, the specific way of obtaining the real-time position information of the spatial positioning node of the cable machine in step 2) is:

[0027] The coordinates of the trolley and the hanging pot are respectively:

[0028]

[0029]

[0030] The speed of the trolley and the hanging pot is respectively:

[0031]

[0032]

[0033] Wherein:

[0034] m is the mass of the hanging pot;

[0035] M is the mass of the trolley;

[0036] l is the length of the hoisting rope;

[0037] i is the length change rate of the hoisting rope;

[0038] θ x is the angle between the hoisting rope and the x-axis when the cable machine hanging pot swings;

[0039] θ y is the angle between the hoisting rope and the y-axis when the cable machine hanging pot swings;

[0040] x M indicates the traction force F M experienced by the trolley, the coordinate of the force direction, the projection length on the x-axis;

[0041] y M F denotes the traction force received by the trolley M the coordinate of the force direction, the length of the projection on the y-axis;

[0042] z M F denotes the traction force received by the trolley M the coordinate of the force direction, the length of the projection on the z-axis;

[0043] x m F denotes the traction force received by the trolley l the coordinate of the force direction, the length of the projection on the x-axis;

[0044] y m F denotes the traction force received by the trolley l the coordinate of the force direction, the length of the projection on the y-axis;

[0045] z m F denotes the traction force received by the trolley l the coordinate of the force direction, the length of the projection on the z-axis;

[0046] v Mx is the speed of the trolley along the x-axis;

[0047] v My is the speed of the trolley along the y-axis;

[0048] v Mz is the speed of the trolley along the z-axis;

[0049] v mx is the speed of the trolley along the x-axis;

[0050] v my is the speed of the trolley along the y-axis;

[0051] v mz is the speed of the trolley along the z-axis;

[0052] is the speed of the trolley along the x-axis;

[0053] is the speed of the trolley along the z-axis.

[0054] Preferably, the instantaneous swing angle of the trolley in step 4) comprises the angle θ between the hoisting rope and the x-axis when the trolley is swinging x and the angle θ between the hoisting rope and the y-axis when the trolley is swinging y ;

[0055] the angle θ between the hoisting rope and the x-axis when the trolley is swinging x is calculated as follows:

[0056]

[0057] the angle θ between the hoisting rope and the y-axis when the cable crane is swinging y is given by:

[0058]

[0059] where:

[0060] denotes the vector from point A to point B; x

[0061] denotes the vector from point A to point A; ′

[0062] denotes the vector from point A to point B;

[0063] denotes the modulus of the vector

[0064] denotes the modulus of the vector

[0065] denotes the modulus of the vector

[0066] Preferably, the calculation of the horizontal and vertical movement speed and acceleration of the cable crane trolley in step 4) is as follows: the expression of the speed of the cable crane trolley along the x-axis direction is:

[0067]

[0068] where:

[0069] is the movement speed of the cable crane trolley along the x-axis direction at the (i+1)th sampling time;

[0070] is the movement speed of the cable crane trolley along the x-axis direction at the ith sampling time;

[0071] Δt is the sampling time interval;

[0072] is the acceleration of the cable crane trolley along the x-axis direction at the ith sampling time, the expression of the acceleration xi is given by:

[0073]

[0074] where:

[0075] ​​​​​ It is the displacement of the cable car trolley along the x-axis between the i-th sampling time and the (i+1)-th sampling time.

[0076] The expression for the velocity of the cable car trolley along the z-axis is:

[0077]

[0078] in:

[0079] It is the speed of the cable car along the z-axis at the (i+1)th sampling time;

[0080] Let be the velocity of the cable car trolley along the z-axis at the i-th sampling time;

[0081] Δt is the sampling time interval;

[0082] It is the acceleration of the cable car trolley along the z-axis at the i-th sampling time. The expression is:

[0083]

[0084] in:

[0085] It is the displacement of the cableway trolley along the z-axis between the i-th sampling time and the (i+1)-th sampling time. Preferably, the angular velocity and angular acceleration of the cableway hoisting tank in step 4) are calculated as follows:

[0086] The expression for the angular velocity of the cable crane's suspended tank about the x-axis is:

[0087]

[0088] in:

[0089] It is the angular velocity of the cable crane's suspended tank around the x-axis at the (i+1)th sampling time;

[0090] It is the angular velocity of the cable crane's suspended tank around the x-axis at the i-th sampling moment;

[0091] Δt is the sampling time interval;

[0092] The rotational angular acceleration of the cableway's hoisting tank about the x-axis at the i-th sampling time; The expression is:

[0093]

[0094] wherein:

[0095] θ xi is the rotation angle of the cable crane hoist around the x-axis between the i-th sampling moment and the i+1-th sampling moment; the expression of the angular velocity of the cable crane hoist around the y-axis direction is:

[0096]

[0097] wherein:

[0098] is the angular velocity of the cable crane hoist around the y-axis direction at the i+1-th sampling moment;

[0099] is the angular velocity of the cable crane hoist around the y-axis direction at the i-th sampling moment;

[0100] Δt is the sampling time interval;

[0101] is the rotation angular acceleration of the cable crane hoist around the y-axis direction at the i-th sampling moment; the expression of the

[0102]

[0103] wherein:

[0104] θ yi is the rotation angle of the cable crane hoist around the y-axis between the i-th sampling moment and the i+1-th sampling moment; the expression of the angular velocity of the cable crane hoist around the z-axis direction is:

[0105]

[0106] wherein:

[0107] is the angular velocity of the cable crane hoist around the z-axis direction at the i+1-th sampling moment;

[0108] is the angular velocity of the cable crane hoist around the z-axis direction at the i-th sampling moment;

[0109] Δt is the sampling time interval.

[0110] Preferably, the method for constructing the cable crane trolley-lifting rope-hoist system dynamics model in step 5) is:

[0111] the Lagrange equation is obtained, and the general form of the Lagrange equation is as follows:

[0112]

[0113] ​

[0114] wherein: L is a Lagrange operator, T is kinetic energy of the system, V is potential energy of the system, q is a variable, i is a variable number, f i is a generalized external force;

[0115] A cable crane trolley-lifting rope-hanging tank system dynamics model is established based on the Lagrange equation:

[0116]

[0117] The cable crane trolley-lifting rope-hanging tank system dynamics model is:

[0118]

[0119] wherein:

[0120] m is the mass of the hanging tank;

[0121] M is the mass of the trolley;

[0122] l is the length of the lifting rope;

[0123] i is the length change rate of the lifting rope;

[0124] θ x is the angle between the lifting rope and the x-axis when the cable crane hanging tank swings;

[0125] θ y is the angle between the lifting rope and the y-axis when the cable crane hanging tank swings;

[0126] is the speed of the hanging tank along the x-axis;

[0127] is the speed of the hanging tank along the z-axis;

[0128] g is the acceleration of gravity;

[0129] are the accelerations of the trolley along the x-axis and z-axis directions respectively;

[0130] is the angular velocity of rotation around the x-axis;

[0131] is the angular acceleration of rotation around the x-axis.

[0132] The present application has the following beneficial effects:

[0133] The application provides a cable crane hoisting trajectory prediction method for arch dam concrete, comprising the following steps: 1) constructing a space coordinate system and determining the space positioning nodes of the cable crane; the space positioning nodes of the cable crane include the space positioning nodes of the trolley and the space positioning nodes of the hoisting tank; 2) acquiring real-time position information based on the space positioning nodes of the cable crane in step 1) by using a sensor, wherein the real-time position information includes the coordinates of the trolley and the hoisting tank in the space coordinate system; 3) performing filtering and noise reduction preprocessing on the real-time position information of the space positioning nodes of the cable crane acquired in step 2) by using Kalman filtering; 4) calculating the real-time position information of the space positioning nodes of the cable crane after preprocessing obtained in step 3) to acquire time sequence motion state parameters of the cable crane, wherein the time sequence motion parameters of the cable crane include the horizontal and vertical motion speed and acceleration of the trolley of the cable crane, the instantaneous swing angle of the hoisting tank, the angular velocity and angular acceleration of the hoisting tank; 5) constructing a dynamics model of the cable crane trolley-lifting rope-hoisting tank system by using the Lagrange mechanics method; 6) taking the time sequence motion state parameters of the cable crane acquired in step 4) as input parameters to predict the swing angle of the hoisting tank of the cable crane and obtain the motion trajectory of the hoisting tank based on the dynamics model of the cable crane trolley-lifting rope-hoisting tank system obtained in step 5). The application considers the time-varying characteristics of the motion of the cable crane trolley and the length of the lifting rope, constructs a dynamics model of the cable crane trolley-lifting rope-hoisting tank system, and predicts the trajectory position information of the hoisting tank of the cable crane according to real-time state data information, thereby further improving the trajectory prediction accuracy and solving the problem of large error of the trajectory prediction result of the traditional model, and the application can be applied to the extension of the cable crane hoisting efficiency and safety analysis. BRIEF DESCRIPTION OF DRAWINGS

[0134] Figure 1 is a cable crane positioning node schematic diagram;

[0135] Figure 2 is a construction entity motion schematic diagram along the x-axis direction;

[0136] Figure 3 is an object rotation schematic diagram;

[0137] Figure 4 is a cable crane trolley-lifting rope-hoisting tank system simplified model;

[0138] Figure 5 is a comparison between the hoisting tank swing angle monitoring value and the calculated value;

[0139] Figure 6 is a comparison between the hoisting tank monitoring trajectory and the calculated value. DETAILED DESCRIPTION

[0140] As Figures 1-6 , the application provides a cable crane hoisting trajectory prediction method, comprising the following steps:

[0141] 0) Construct a spatial coordinate system and determine the spatial positioning nodes of the cable crane; the spatial positioning nodes of the cable crane include the spatial positioning nodes of the trolley and the spatial positioning nodes of the hoisting tank.

[0142] 1) Use sensors to acquire the positions of the cable crane trolley and cable crane canister in real time, and clean, reduce noise and standardize the collected data to improve the accuracy of subsequent analysis results.

[0143] 2) Establish a spatial coordinate system with the direction along the river as the x-axis, the direction across the river as the y-axis, and the vertical direction as the z-axis. Obtain the coordinates of the trolley and the cable car hoist, as well as the coordinates of the projection of the trolley and the hoist onto the YOX plane.

[0144] The coordinates A(x) of the cable car are obtained in real time by a position sensor. A y A , z A The coordinates B(x) of the cable car hoisting tank and the cable car hoisting tank. B y B , z B );

[0145] Construct a nodal model showing the spatial relationship between the cable crane trolley, hoisting rope, and hoisting tank, as shown in the attached figure. Figure 1 As shown; obtain the coordinates of the projections of the trolley and the hanging tank onto the YOX plane: A ′ (x A y A , z B B x (x B ,0,z B ) and B y (0, y B , z B );

[0146] 3) Based on the real-time position coordinates of the trolley and the hoisting tank, calculate the hoisting depth L (lifting rope length) of the cable crane and the swing angle θ of the hoisting tank in the x and y directions. x θ y .

[0147] The lifting depth L (length of the hoisting rope) of the cable crane and the swing angle θ of the suspended tank in the x and y directions. x θ y The calculation formula is shown below;

[0148] hoisting rope length:

[0149] The swing angles of the hanging tank in the x and y directions:

[0150] in:

[0151] This indicates the distance from point A to point B.x Vector of a point;

[0152] This indicates the distance from point A to point A. ′ Vector of a point;

[0153] This represents the vector from point A to point B;

[0154] Representing vectors The model;

[0155] Representing vectors The model;

[0156] Representing vectors The model.

[0157] 4) Calculate the timing state parameters of the trolley and the hoisting tank.

[0158] Calculate the time-series motion state parameters of the vehicle: velocity and acceleration.

[0159] Because of the high frequency of data collection and the short time interval between adjacent sets of data, the movement of the construction entity along a certain dimension in each time interval can be approximated as uniformly accelerated motion.

[0160] Taking motion along the x-axis as an example, as shown in the attached figure. Figure 2 As shown, the sampling time interval for the three sets of positioning data is Δt. According to the formula for uniformly accelerated motion, we can obtain the following equation: In the formula, x i It represents the displacement of the entity along the x-axis between the i-th and i+1-th sampling times; Let be the velocity of the entity along the x-axis at the i-th sampling moment.

[0161] Furthermore, the acceleration of the entity along the x-axis at the i-th sampling moment can be obtained as follows:

[0162] The end motion state of the entity in the i-th sampling interval is the initial motion state in the (i+1)-th sampling interval, based on the initial velocity along the x-axis at the (i+1)-th time point. and acceleration The velocity corresponding to the next sampling moment can be calculated as follows:

[0163] Similarly, the motion parameters of the trolley along the z-axis can be calculated, as shown in the following formula:

[0164]

[0165]

[0166] The initial velocity of the car in each segment of the trajectory is 0, i.e., v0 = 0. Based on the above formula, the velocity and acceleration at each sampling moment of the entire trajectory can be derived recursively.

[0167] Calculate the timing state parameters of the hanging tank: angular velocity and angular acceleration.

[0168] Similarly, due to the high frequency of data acquisition and the short time interval between adjacent sets of data, the rotation of the construction entity around a certain dimension in each time interval can be approximated as uniformly accelerated rotation in rotational motion.

[0169] Taking rotation about the x-axis as an example, as shown in the attached figure. Figure 3 As shown, the sampling time interval for the three sets of positioning data is Δt. According to the formula for uniformly accelerated rotation, we can obtain: In the formula, θ xi Let be the angle of rotation of the entity around the x-axis between the i-th sampling time and the (i+1)-th sampling time. Let ω be the angular velocity of the entity's rotation around the x-axis at the i-th sampling moment.

[0170] Furthermore, the rotational angular acceleration of the entity about the x-axis at the i-th sampling moment can be obtained as follows:

[0171] The end motion state of the entity in the i-th sampling interval is the initial motion state in the (i+1)-th sampling interval, based on the initial angular velocity around the x-axis at the (i+1)-th time point. and angular acceleration The angular velocity corresponding to the next sampling moment can be calculated as follows:

[0172] Similarly, the rotation parameters of the entity about the y-axis can be calculated, as shown below.

[0173]

[0174]

[0175] The initial angular velocity of the hanging tank in each segment of the trajectory is 0, i.e., ω0=0. Based on the above formula, the angular velocity and angular acceleration at each sampling moment of the entire trajectory are derived one by one.

[0176] 5) Cable crane and canister trajectory prediction model

[0177] The cable crane trolley-lifting rope-cab system is a typical underactuated system. Besides the system itself, it is also affected by external environmental factors such as wind, causing the crib to swing in different directions. For ease of theoretical analysis, the motion of the cable crane trolley-lifting rope-cab system needs to be abstracted, resulting in the following: Figure 4 The abstract physical model shown is required for further simplification to analyze its essence. Here, the mass of the hanging tank, the mass and elasticity of the rope, and the damping coefficient of the load swing are ignored.

[0178] In the construction of the arch dam concrete strip, a fixed-line material feeding method is adopted, with the main trolley stationary and only the auxiliary trolley in motion. Based on this, a model is constructed, defining the direction from the main tower to the auxiliary tower of the cable crane as the positive x-axis, establishing a right-handed coordinate system, with the mass of the hoisting bucket as m, the mass of the auxiliary trolley as M, the length of the hoisting rope as 1, and the angle between the hoisting rope and the x-axis when the hoisting bucket swings as θ. x The angle between the y-axis and the y-axis is θ. y The traction force of the car is F M The tension in the hoisting rope is F. l .

[0179] The coordinates of the trolley and the hanging tank are as follows:

[0180]

[0181]

[0182] The speeds of the trolley and the suspended tank are respectively:

[0183]

[0184]

[0185] In the cable car trolley-lifting rope-hoisting tank system F M F l F w The input quantities are x, y, z, 1, and θ. x and θ y As output quantities, systems are characterized by multiple variables and high coupling; the inputs and outputs of a system do not have a one-to-one correspondence. Constructing a system dynamics model using Newtonian mechanics would be quite difficult. Lagrange mechanics, on the other hand, only requires calculating the kinetic and potential energies of the cable car trolley and the hoisting tank, making it simpler than the Newton-Euler equations method, while still fully reflecting the dynamic characteristics of the system. Therefore, this paper adopts the Lagrange mechanics method for modeling.

[0186] The general form of the Lagrange equation is as follows:

[0187]

[0188]

[0189] In the formula, L is a Lagrange operator, T is kinetic energy of the system, V is potential energy of the system, q is a variable, i is a variable number, f i is a generalized external force.

[0190] The kinetic energy T and the potential energy V of the system can be expressed as:

[0191]

[0192] The Lagrange operator L can be obtained from the above formula:

[0193]

[0194] The Lagrange equation set of the cable crane trolley-lifting rope-suspended tank system can be established:

[0195]

[0196] The cable crane trolley-lifting rope-suspended tank dynamics model is:

[0197]

[0198] In the model, the acceleration in the x and z directions, the length of the lifting rope and the rate of change thereof are all inputs of the model, and the swing angle of the suspended tank is an output; when the above parameters at a future time are input into the model, the swing angle of the suspended tank at the future time can be calculated, so that the position of the suspended tank at the future time can be predicted. Figure 5 and Figure 6 are specific examples.

[0199] The specific process of the prediction is as follows: the initial position of the trolley, the initial length of the rope, the initial swing angle, the speed and the angular acceleration of the suspended tank, and the speed, the acceleration, the rate of change of the length of the rope and the change acceleration of the trolley in a future period of time are known. Then, the swing angle of the suspended tank in the future period of time can be solved through the cable crane trolley-lifting rope-suspended tank dynamics model. Finally, the position of the trolley in the future period of time, the length of the rope and the swing angle solved are added to solve the coordinates of the suspended tank. Although the speed of the trolley and the rate of change of the length of the rope are not included in the dynamics model, they will be used in the solving of the position of the trolley and the length of the rope in the future period of time. After the position of the trolley and the length of the rope are obtained, the coordinates of the suspended tank are solved by adding the swing angle. In fact, the suspended tank trajectory prediction involved in the present application is a trajectory prediction considering the swing of the suspended tank.

[0200] This invention considers the time-varying characteristics of the cable crane trolley motion and the hoisting rope length, and constructs a trajectory prediction model that takes into account the swing of the cable crane's hoisting can. This model can predict the hoisting trajectory of the concrete cable crane in arch dams based on real-time data, improving the accuracy of the trajectory prediction model. It can be extended to applications such as cable crane hoisting efficiency and safety analysis. A comparison between the monitored and calculated values ​​of the can's swing angle is attached. Figure 5 As shown, a comparison between the monitoring trajectory and calculated values ​​of the hanging tank is attached. Figure 6 As shown.

Claims

1. A method for predicting the trajectory of a concrete cable crane used in an arch dam, characterized in that: The method for predicting the trajectory of concrete cable crane hoisting in arch dams includes the following steps: 1) Construct a spatial coordinate system and determine the spatial positioning nodes of the cable crane; the spatial positioning nodes of the cable crane include the spatial positioning nodes of the trolley and the spatial positioning nodes of the hoisting tank. 2) Use sensors to obtain real-time position information of the spatial positioning node of the cable car in step 1), the real-time position information including the coordinates of the trolley and the hoisting tank in the spatial coordinate system; 3) Use Kalman filtering to perform filtering and noise reduction preprocessing on the real-time position information of the spatial positioning nodes of the cable car obtained in step 2); 4) Calculate the real-time position information of the preprocessed spatial positioning node of the cableway obtained in step 3) to obtain the temporal motion state parameters of the cableway. The temporal motion parameters of the cableway include the horizontal and vertical motion speed and acceleration of the cableway trolley, the instantaneous swing angle of the hoisting tank, the angular velocity and angular acceleration of the hoisting tank. 5) A dynamic model of the cable crane trolley-lifting rope-hoisting tank system was constructed using Lagrange mechanics methods; 6) Based on the dynamic model of the cable car trolley-lifting rope-hoisting tank system obtained in step 5), the temporal motion state parameters of the cable car obtained in step 4) are used as input parameters to predict the swing angle of the cable car hoisting tank and obtain the hoisting tank's motion trajectory.

2. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 1, characterized in that: The specific implementation of step 1) is as follows: Obtain the coordinates of the cable car trolley and the gondola, and their projected coordinates on the YOX plane: Construct a spatial coordinate system with the direction along the river as the x-axis, the direction across the river as the y-axis, and the vertical direction as the z-axis. The coordinates of the cable car trolley are A(x... A y A , z A The coordinates of the cableway canister are B(x). B y B , z B The projected coordinates of the cable car trolley on the yox plane are A. ′ (x A y A , z B The projected coordinates of the cableway canister on the y-axis and x-axis are B, respectively. x (x B ,0,z B ) and B y (0, y B , z B ); in: Point A represents the car; Point B represents the hanging tank; A ′ The point represents the projection of point A onto the yox plane; B x The point represents the projection of point B onto the x-axis; B y The point represents the projection of point B onto the y-axis; x A This indicates the position of point A on the x-axis; y A This indicates the position of point A on the y-axis; z A This indicates the position of point A on the z-axis; x B This indicates the position of point B on the x-axis; y B This indicates the position of point B on the y-axis; z B This indicates the position of point B on the z-axis.

3. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 2, characterized in that: The specific method for obtaining the real-time location information of the cable car's spatial positioning node in step 2) is as follows: The coordinates of the trolley and the hanging tank are as follows: The speeds of the trolley and the suspended tank are respectively: in: m is the mass of the hanging tank; M is the mass of the car; l is the length of the hoisting rope; This refers to the rate of change of the hoisting rope length; θ x It is the angle between the hoisting rope and the x-axis when the cable crane hoisting tank swings; θ y It is the angle between the hoisting rope and the y-axis when the cable crane hoisting tank swings; x M The value in the middle represents the traction force F acting on the car. M The coordinates of the direction of force, and the length of its projection on the x-axis; y M The value in the middle represents the traction force F acting on the car. M The coordinates of the direction of force, and the length of its projection on the y-axis; z M The value in the middle represents the traction force F acting on the car. M The coordinates of the direction of force, and the length of its projection on the z-axis; x m The value in the middle represents the tension F in the hoisting rope. l The coordinates of the direction of force, and the length of its projection on the x-axis; y m The value in the middle represents the tension F in the hoisting rope. l The coordinates of the direction of force, and the length of its projection on the y-axis; z m The value in the middle represents the tension F in the hoisting rope. l The coordinates of the direction of force, and the length of its projection on the z-axis; v Mx It is the speed of the trolley along the x-axis; v My It is the speed of the trolley along the y-axis; v Mz It is the speed of the trolley along the z-axis; v mx It is the velocity of the hanging tank along the x-axis; v my The velocity of the hanging tank along the y-axis; v mz It is the velocity of the hanging tank along the z-axis; It is the velocity of the hanging tank along the x-axis; It is the velocity of the hanging tank along the z-axis.

4. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 3, characterized in that: In step 4), the instantaneous swing angle of the hoisting tank includes the angle θ between the hoisting rope and the x-axis when the hoisting tank swings. x And the angle θ between the hoisting rope and the y-axis when the cable crane's canister swings. y ; The angle θ between the hoisting rope and the x-axis when the cableway hoisting tank swings is... x The calculation method is as follows: When the cableway hoisting tank swings, the angle θ between the hoisting rope and the y-axis... y The expression is: in: This indicates the distance from point A to point B. x Vector of a point; This indicates the distance from point A to point A. ′ Vector of a point; This represents the vector from point A to point B; Representing vectors The model; Representing vectors The model; Representing vectors The model.

5. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 3, characterized in that: The calculation method for the horizontal and vertical speeds and accelerations of the cable car trolley in step 4) is as follows: The expression for the velocity of the cable car trolley along the x-axis is: in: It is the speed of the cable car along the x-axis at the (i+1)th sampling time; Let be the velocity of the cable car trolley along the x-axis at the i-th sampling time; Δt is the sampling time interval; It is the acceleration of the cable car trolley along the x-axis at the i-th sampling time. The expression is: in: It is the displacement of the cable car trolley along the x-axis between the i-th sampling time and the (i+1)-th sampling time. The expression for the velocity of the cable car trolley along the z-axis is: in: It is the speed of the cable car along the z-axis at the (i+1)th sampling time; Let be the velocity of the cable car trolley along the z-axis at the i-th sampling time; Δt is the sampling time interval; It is the acceleration of the cable car trolley along the z-axis at the i-th sampling time. The expression is: in: It is the displacement of the cable car trolley along the z-axis between the i-th sampling time and the i+1-th sampling time.

6. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 3, characterized in that: The calculation method for the angular velocity and angular acceleration of the cable crane's hoisting tank in step 4) is as follows: The expression for the angular velocity of the cable crane's suspended tank about the x-axis is: in: It is the angular velocity of the cable crane's suspended tank around the x-axis at the (i+1)th sampling time; It is the angular velocity of the cable crane's suspended tank around the x-axis at the i-th sampling moment; Δt is the sampling time interval; The rotational angular acceleration of the cableway's hoisting tank about the x-axis at the i-th sampling time; The expression is: in: θ xi Let be the angle of rotation of the cableway's canister around the x-axis between the i-th sampling time and the (i+1)-th sampling time. The expression for the angular velocity of the cable crane's suspended tank about the y-axis is: in: It is the angular velocity of the cable crane's suspended tank around the y-axis at the (i+1)th sampling moment; It is the angular velocity of the cable crane's suspended tank around the y-axis at the i-th sampling moment; Δt is the sampling time interval; The rotational angular acceleration of the cableway's suspended tank about the y-axis at the i-th sampling time; The expression is: in: θ yi Let be the angle of rotation of the cableway hoisting tank around the y-axis between the i-th sampling time and the (i+1)-th sampling time.

7. The method for predicting the trajectory of a concrete cable crane for arch dams according to claim 3, characterized in that: The method for constructing the dynamic model of the cable trolley-lifting rope-suspended tank system in step 5) is as follows: The Lagrange equation is obtained, and its general form is as follows: In the formula: L is the Lagrange operator, T is the system kinetic energy, V is the system potential energy, q is a variable, i is the variable number, and f is the variable number. i External forces in a broad sense; A dynamic model of the cableway trolley-lifting rope-suspended tank system is established based on the Lagrange equation: The dynamic model of the cable crane trolley-lifting rope-suspended tank system is as follows: in: m is the mass of the hanging tank; M is the mass of the car; l is the length of the hoisting rope; This refers to the rate of change of the hoisting rope length; θ x θ is the angle between the hoisting rope and the x-axis when the cable crane's canister swings. y It is the angle between the hoisting rope and the y-axis when the cable crane hoisting tank swings; It is the velocity of the hanging tank along the x-axis; It is the velocity of the hanging tank along the z-axis; g is the acceleration due to gravity; These are the accelerations of the trolley along the x-axis and z-axis, respectively. The angular velocity is the rotational velocity about the x-axis; Let be the angular acceleration about the x-axis.

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