Roller linear motion guide rail vibration analysis method based on multi-task interaction PINN and global vibration model

Abstract

The invention discloses a roller linear motion guide rail vibration analysis method based on a multi-task interaction PINN and a global vibration model, and the method comprises the following steps: (1) setting a global Cartesian coordinate system, and defining five motion freedom degrees of a sliding block; (2) describing an RLMG system by using a Lagrange equation, and generating a matrix form vibration equation of the system; (3) simplifying the contact among the roller body, the track and the sliding block into a spring-damping system, and establishing a local contact coordinate system; (4) calculating the speed and position change of the roller body relative to the sliding block based on rigid body kinematics; (5) by scaling the multi-degree-of-freedom coupling equation and performing dimensionless operation, introducing the dimensionless RLMG vibration equation into a PINN loss function, and applying soft constraint to encode dynamic constraint; (6) transforming an original time variable based on a time scale factor selected in a dimensionless manner, inputting the transformed original time variable into the designed interactive network for prediction, and embedding an initial value condition through hard constraint to enable the prediction of the network to strictly meet an initial condition; and (7) using a gradient algorithm to calculate a derivative output by prediction, inputting the derivative into a dimensionless equation, and generating a corresponding sub-loss function. Calculating the optimal weight of each sub-loss by using a BE-BKA (Behavior Enhanced Black Wing Proteulation Algorithm); (8) adaptively adjusting the network weight by using a multi-gradient collaborative optimization method; according to the invention, the requirements of real-time control and vibration response prediction in industrial application are met.

Description

Technical Field

[0001] The present invention relates to the field of roller linear motion guide vibration technology, and in particular to a roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model. Background Art

[0002] The development of high-end precision machine tools requires that the linear feed system has large load-bearing capacity and high transmission accuracy. Roller linear motion guides (RLMG) have been widely used in feed systems due to their high stiffness and low friction. In actual industrial manufacturing, the complex dynamic vibration of RLMG will greatly affect the performance, precision, life and reliability of heavy-duty mechanical systems. Therefore, it is necessary to analyze the dynamic behavior of RLMG in real time to ensure the efficient operation of machine tool motion. However, existing vibration models often ignore the complex nonlinear and strong coupling characteristics of multi-degree-of-freedom (DOF) displacements. Since the rolling elements and sliders in the guide system have nonlinear contact behaviors in multiple degrees of freedom, these nonlinear effects not only affect the contact stiffness, but also induce complex dynamic responses, especially under heavy load and high speed conditions. In addition, the strong coupling between multiple degrees of freedom further increases the complexity of the system, making the vibration characteristics difficult to predict and control. More importantly, the existing models have obvious limitations in solution speed, especially when faced with complex nonlinear equations and strongly coupled multi-degree-of-freedom systems, traditional numerical solution methods often require a lot of computing resources and time. This computational bottleneck greatly reduces the practicality of the model in real-time prediction and control applications, and it cannot meet the needs of efficient and rapid response in industrial production. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model, so as to solve the problems that the existing RLMG vibration model ignores the complex nonlinearity and strong coupling of multi-degree-of-freedom (DOF) displacement and the model solution speed cannot meet the requirements of real-time vibration reduction.

[0004] Technical solution: The present invention discloses a roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model, comprising the following steps:

[0005] (1) Set up a global Cartesian coordinate system at the center of the RLMG track and define the five degrees of freedom of the slider, including horizontal (Fx, δx), vertical (Fy, δy), pitch (Mx, γx), yaw (My, γy) and roll (Mz, γz);

[0006] (2) Use the Lagrange equation to describe the RLMG system and generate the matrix vibration equation of the system by defining the kinetic energy dissipation energy and potential energy;

[0007] (3) Simplify the contact between the roller, track and slider into a spring-damper system, establish a local contact coordinate system, and calculate the mass matrix, stiffness matrix, and damping matrix;

[0008] (4) Calculate the velocity and position changes of the roller relative to the slider based on rigid body kinematics; analyze the dynamic changes of the contact angle and structural excitation force to obtain the rolling contact behavior;

[0009] (5) By scaling the multi-degree-of-freedom coupling equations and making them dimensionless, the dimensionless RLMG vibration equations are introduced into the PINN loss function, and soft constraints are applied to encode the dynamic constraints.

[0010] (6) Based on the dimensionless selected time scale factor, the original time variable is transformed and input into the designed interaction network for prediction. At the same time, the initial value conditions are embedded through hard constraints so that the network prediction strictly meets the initial conditions;

[0011] (7) Use the gradient algorithm to calculate the derivative of the predicted output and input it into the dimensionless equation to generate the corresponding sub-loss function. Use the behavior-enhanced black kite algorithm BE-BKA to calculate the optimal weight of each sub-loss;

[0012] (8) Use multi-gradient collaborative optimization method to adaptively adjust network weights.

[0013] Furthermore, the formula of step (2) is as follows:

[0014] The Lagrangian equation of RLMG motion is expressed as:

[0015]

[0016] Kinetic energy T and dissipated energy D are expressed as:

[0017]

[0018] The potential energy of RLMG includes: the potential energy generated by the deformation of the roller body due to the vibration of the carriage, the formula is as follows:

[0019]

[0020] The specially designed structural parameters make the potential energy generated by the deformation of the roller body, which is generated by the structural excitation force F acting on the slider. c The generalized excitation force [F] acting on the RLMG system is expressed as:

[0021] [F]=[F r ]+[F c ]

[0022] Substituting kinetic energy T, dissipated energy D, potential energy U, and generalized excitation force [F] into the Lagrangian equation of RLMG motion, the overall vibration equation of RLMG is written in matrix form:

[0023]

[0024] Where T is the kinetic energy of the system vibration, D is the dissipated energy of the system, U is the potential energy of the system, [F] is the vector of the generalized excitation force on the system, [δ r ] is the generalized displacement vector, where [F r ] is the external force acting on the slider, [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

[0025] Furthermore, in step (3), the stiffness matrix [K] is expressed as:

[0026]

[0027] The damping matrix [C] of the slider is expressed as:

[0028]

[0029] in, and [k ijN ] are the positions of each spring in the global coordinate O xyz The position matrix, angle matrix and stiffness matrix in, and [c ijN ] are the values ​​of each damper at the global coordinate O xyz The position matrix, angle matrix and damping matrix in .

[0030] Furthermore, in step (4), it is assumed that the roller body maintains pure rolling during the working process, and the movement of each roller to the next roller position is regarded as a cycle. The position of the rolling body in the global coordinate system when it passes through different working stages is:

[0031]

[0032] in, Represents the distance of the roller relative to the left side of the slider after time t, v b is the speed of the slider, v rb Represents the speed of the roller relative to the slider, l r represents the length of the slider, i represents the number of a track, l is the vertical distance between the center axes of the two rollers on the same track, represents the pitch displacement of the ith track roller body;

[0033] The change of the equivalent spring contact angle is expressed as:

[0034]

[0035] Among them, d b It represents the diameter of the roller after being compressed by the preload, α 0,ijN is the initial contact angle of roller j on track i, Δx ijN and Δy ijN Indicates the amount of spring deformation caused by the vibration of the slider.

[0036] The structural excitation force is expressed as:

[0037]

[0038] Among them, N e is the number of effective rollers in each track, is the composite preload, p e are the coefficients corresponding to different orbits, and are the coordinates of the roller body in the global coordinate system.

[0039] Furthermore, in step (5), the dimensionless form of the RLMG overall vibration equation is:

[0040]

[0041] The mean square error of the differential equation network under soft constraints is:

[0042]

[0043] The hard constraints added are:

[0044]

[0045] The pipeline loss function under soft constraints is:

[0046]

[0047] in, is the input of the network, are the parameters of the network, including hyperparameters and weight parameters, is the output of the network, δ0 and v0 are the initial values ​​of displacement and velocity respectively, w i is the weight of each task, Defined Training data for the internal configuration points in .

[0048] Furthermore, in step (6), the interactive network is specifically as follows: it includes 1 shared layer module and 5 parallel modules; wherein the shared layer module extracts global features, and the five parallel network modules are responsible for extracting independent features of each degree of freedom and modeling dynamic changes.

[0049] Furthermore, in step (7), the behavior-enhanced black kite algorithm BE-BKA is specifically as follows: the BE-BKA algorithm introduces the optimal search strategy into the individual search strategy, dynamically adjusts the individual search range and balances local and global searches; the mathematical formula of the optimal search strategy is expressed as:

[0050]

[0051] in, represents the position of the ith black-winged kite in the jth dimension at the tth iteration, represents the current optimal individual of iteration t, and n is the coefficient that changes with the number of iterations.

[0052] The roller linear motion guide vibration analysis system based on multi-task interactive PINN and global vibration model of the present invention comprises:

[0053] Coordinate module: used to set the global Cartesian coordinate system at the center of the RLMG track and define the five degrees of freedom of motion of the slider, including horizontal (Fx, δx), vertical (Fy, δy), pitch (Mx, γx), yaw (My, γy) and roll (Mx, γz);

[0054] Vibration equation module: Use Lagrange equations to describe the RLMG system, and generate the matrix vibration equations of the system by defining kinetic energy dissipation energy and potential energy;

[0055] Local contact coordinate module: used to simplify the contact between the roller, track and slider into a spring-damper system, establish a local contact coordinate system, and calculate the mass matrix, stiffness matrix, and damping matrix;

[0056] Analysis module: used to calculate the speed and position changes of the roller relative to the slider based on rigid body kinematics; analyze the dynamic changes of the contact angle and structural excitation force to obtain the rolling contact behavior;

[0057] Dynamic constraint module: It is used to introduce the dimensionless RLMG vibration equation into the PINN loss function by scaling the multi-degree-of-freedom coupling equations and making them dimensionless, and apply soft constraints to encode dynamic constraints.

[0058] Interaction network module: used to transform the original time variable based on the dimensionless selected time scale factor, and input it into the designed interaction network for prediction. At the same time, the initial value conditions are embedded through hard constraints so that the network prediction strictly meets the initial conditions.

[0059] Weight module: used to calculate the derivative of the predicted output using the gradient algorithm and input the dimensionless equation to generate the corresponding sub-loss function. The behavior-enhanced black kite algorithm BE-BKA is used to calculate the optimal weight of each sub-loss;

[0060] Adjustment module: used to adaptively adjust network weights using multi-gradient collaborative optimization method.

[0061] An electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and is characterized in that when the computer program is loaded into the processor, it implements any one of the roller linear motion guide vibration analysis methods based on multi-task interactive PINN and global vibration models.

[0062] A storage medium described in the present invention stores a computer program, characterized in that when the computer program is executed by a processor, it implements any one of the roller linear motion guide vibration analysis methods based on multi-task interactive PINN and global vibration models.

[0063] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the RLMG global vibration model can accurately analyze the complex nonlinear strong coupling vibration of multiple degrees of freedom; the multi-task interactive PINN method can adapt to the complex working conditions of the rolling linear guide system in actual operation, and provide strong technical support for the real-time monitoring and performance optimization of the equipment; by combining the shared layer and the parallel network architecture, the accurate prediction of the multi-degree-of-freedom coupling behavior in the complex system can be achieved, and the motion state of different degrees of freedom can be processed separately while extracting the global features, ensuring that the interaction between the various parts of the system is accurately modeled; the behavior-enhanced black kite algorithm (BE-BKA), by performing kent mapping on the initial population and introducing the behavior pattern of the optimal individual, the algorithm can better explore the global optimal solution and accelerate the solution process in complex problems; using the multi-gradient collaborative optimization strategy, the strategy can coordinate the direction of each loss gradient value. Then, combined with the proposed multi-task loss balance optimization (whose advantage is the adaptive scaling of the gradient value of each loss), the generalization performance of the multi-task interactive solution model can be effectively enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram of the process of implementing the method of the present invention;

[0065] Figure 2 3D structural diagram of RLMG of the present invention;

[0066] Figure 3 It is a schematic cross-sectional view of a slider of the RLMG of the present invention;

[0067] Figure 4Schematic diagram of different working stages of the RLMG of the present invention;

[0068] Figure 5 It is a simplified model of the RLMG system of the present invention;

[0069] Figure 6 The present invention performs time-varying analysis on the contact angle in a global coordinate system;

[0070] Figure 7 The overall framework of multi-task interaction proposed by the present invention;

[0071] Figure 8 The test device of the present invention;

[0072] Fig. 9 This is a diagram of the vibration results of RLMG calculated using different calculation methods in the present invention. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0074] like Figure 1 As shown, an embodiment of the present invention provides a roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model, comprising the following steps:

[0075] S1 Set up a global Cartesian coordinate system O at the orbital center of the RLMG xyz , define the five degrees of freedom of motion of the slider. When the carriage moves, the rolling elements perform periodic reciprocating motion in the carriage.

[0076] Figure 1 The typical structure of a linear rolling guide system (RLMG) is shown, which mainly includes a slider, a guide rail, several rollers, a cage, and four tracks. When the slider moves, the rollers will make periodic reciprocating motion inside the slider. In order to establish the vibration model of the slider, a global Cartesian coordinate system O is set at the center of the four tracks. xyz , the five degrees of freedom are: horizontal (F x ,δ x ), vertical (F y ,δ y ), pitch(M x ,γ x ), Yaw(M y ,γ y ) and roll (M z ,γ z ).

[0077] Figure 2 The plane shown in is perpendicular to the global coordinate system (Q xyz )’s z-axis, α ijkThe contact angle of the kth spring in the simplified spring system of the jth roller on the i-th track.

[0078] Figure 3 The rollers on the track are shown to be in periodic reciprocating motion. During the movement of the slider, each roller will go through the transition phase I (0 to l c ), load-bearing stage (l c To r -l c )、Transition Phase II(l r -l c To r ), and finally returns to the recycling stage. b Indicates the moving speed of the slider, l r and l c Represent the slider length and transient stage length respectively. Represents the roller pitch displacement of track i.

[0079] S2 uses the Lagrange equation to describe the RLMG system. By defining kinetic energy T, dissipated energy D, and potential energy U, the matrix form vibration equation of the system is generated.

[0080] For the global vibration analysis modeling of RLMG, the elasticity and friction between the roller, track and slider can be simplified as springs and dampers, respectively. In addition, RLMG can be considered as a suspension system consisting of a slider, multiple springs and dampers. Based on the above assumptions, the Lagrangian equation of RLMG motion can be expressed as:

[0081]

[0082] In the formula, T is the kinetic energy of the system vibration, D is the dissipated energy of the system, U is the potential energy of the system, [F] is the vector of the generalized excitation force on the system, [δ r ] is the generalized displacement vector.

[0083] For the RLMG vibration system, the kinetic energy T and dissipated energy D can be expressed as:

[0084]

[0085] The potential energy of RLMG includes two aspects. On the one hand, the potential energy generated by the deformation of the roller body caused by the vibration of the slider.

[0086] Yes, it can be written as:

[0087]

[0088] On the other hand, there is the potential energy generated by the deformation of the roller body due to the specially designed structural parameters (such as the designed preload and top cover). In order to take the influence of the slider preload and top load into the vibration equation of RLMG, the potential energy generated by the specially designed structural parameters can be considered as the structural excitation force F acting on the slider. c generated because they are caused by the structural design parameters rather than the vibration of the system. The generalized excitation force [F] acting on the RLMG system can be expressed as:

[0089] [F]=[F r ]+[F c ]

[0090] Substituting the above into the Lagrange equation, the RLMG overall vibration equation is written in matrix form:

[0091]

[0092] Where [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

[0093] S3 simplifies the contact between the roller, track and slider into a spring-damper system and establishes a local contact coordinate system. ijN u ijN w ijN , on this basis, the mass matrix [M], stiffness matrix [K] and damping matrix [C] are calculated.

[0094] The detailed simplified model of the RLMG system is shown in Figure 4 As shown in the figure. Each roller body is equivalent to multiple springs and dampers along its axis. The local contact coordinates (o ijN u ijN w ijN ). According to the given spring o ijN and ij1 The x and y coordinates of the damper o ijN and ij1 The position in the global coordinate system can be used to calculate the coordinates of other springs and dampers in the global coordinate system by linear interpolation.

[0095] In establishing the global coordinate O xyz In , each coordinate axis is the principal axis of inertia of the RLMG. Therefore, the mass matrix of the car can be written as:

[0096]

[0097] Where m is the mass of the slider, j is x ,j y ,j z They represent the moment of inertia of the slider around the x-axis, y-axis, and z-axis respectively.

[0098] The simplified spring is elastic only in the w direction, k ijN Represents the stiffness matrix of the nth spring of the jth roller on the i track:

[0099]

[0100] in:

[0101]

[0102] In the formula, is the time-varying compression deformation of the roller body, L eff is the effective contact length between the roller and the track. E is the equivalent Young's modulus, N is the equivalent spring number of a roller, t s To indicate the thickness of the steel section.

[0103] Each spring is located at the global coordinate O xyz The position matrix in can be expressed as:

[0104]

[0105] where x ijN ,y ijN ,z ij is the position coordinate of the spring in the global coordinate system, and k refers to the spring.

[0106] Each spring is located at the global coordinate O xyz The angle matrix on can be expressed as:

[0107]

[0108] The detailed angle relationship between the local contact coordinate system and the global coordinate system in the spring angle matrix is ​​shown in Table 1:

[0109] Table 1. Angle relationship between local contact coordinates and global coordinates in the spring angle matrix

[0110]

[0111] According to the above analysis results, the slider stiffness matrix [K] can be expressed as:

[0112]

[0113] Using the same modeling method, in the global coordinate O xyz The coefficient matrix of the damper at the ijN position [c ijk ], Position Matrix and the angle matrix It can be expressed as:

[0114]

[0115] Where c is the damping coefficient, and N represents the number of equivalent springs of a roller.

[0116] The angle relationship between the local contact coordinate system and the global coordinate system in the damper angle matrix is ​​shown in Table 2:

[0117] Table 2. Angular relationship between local contact coordinates and global coordinates in the damper angle matrix

[0118]

[0119] S4 assumes that the roller body keeps pure rolling during operation, and takes the movement of each roller to the next roller position as a cycle. The speed and position changes of the roller body relative to the slider are calculated based on rigid body kinematics. The dynamic changes of the contact angle and structural excitation force are further analyzed to obtain the rolling contact behavior.

[0120] Both the stiffness matrix [K] and the damping matrix [C] contain position and angle variables, which change continuously as the rolling element passes through different working stages. In order to calculate the changes in position and angle in the global coordinate system, the time-varying contact behavior of each roller element and the structural excitation force [F c ]. Assume that during the operation of RLMG, the roller is in a pure rolling state without sliding motion. Therefore, the speed of the roller can be determined by the rigid body kinematics theory, and the formula is as follows:

[0121]

[0122] In the formula, v b is the speed of the slider.

[0123] The speed of the roller relative to the slider is:

[0124]

[0125] The roller moves from j to j+1, and one cycle is obtained. After time t, the distance of the roller relative to the left side of the slider is:

[0126]

[0127] Where l is the vertical distance between the axes of the two rollers. Represents the pitch displacement of the roller on the i-th track.

[0128] The position of the jth roller on the ith track at time t is in the global coordinate system O xyz The changes in can be expressed as:

[0129]

[0130] The contact angle variation of the equivalent spring and damper of each track is analyzed, e.g. Figure 6 As shown in the figure, the equivalent spring caused by the vibration of the carriage is in the global coordinate O xyz The horizontal displacement Δx ijk and vertical displacement Δy ijk It can be obtained by the following formula:

[0131]

[0132] The equivalent spring deformation caused by the vibration of the slider can be expressed as:

[0133]

[0134] according to Figure 6 According to the geometric relationship shown in , the change of the equivalent spring contact angle can be expressed as:

[0135]

[0136] Where d0 is the original diameter of the spring (roller diameter), α 0,ijN is the initial contact angle of the roller, is the deformation of the equivalent spring, It is a composite preload.

[0137] Next, we will analyze the time-varying structural excitation force [F c ].

[0138] The elastic release amount of each roller in transition stage I, load stage and transition stage II can be expressed as:

[0139]

[0140] Where a and λ are the coefficient and exponent respectively.

[0141] Under the combined effect of the preload force (generated by the preload displacement Δδ0) and the top cover (transition stage), the composite preload deformation of each roller can be calculated as:

[0142]

[0143] The composite preload is:

[0144]

[0145] Structural excitation force [F c ] can be achieved by preloading the composite force Decomposed into horizontal force, vertical force, pitch force, yaw force and roll force, it can be expressed as:

[0146]

[0147] Where, is the number of effective contact rollers in each track, p1, p2, p3, p4, and p5 are coefficients corresponding to different tracks, as defined in Table 3:

[0148] Table 3. p1, p2, p3, p4, and p5 values ​​for different orbits

[0149]

[0150] Finally, according to Figure 6 The geometric relationship between the rollers and the time-varying deformation of each roller can be expressed as:

[0151]

[0152] where Δw ijN is the spring deformation caused by the slider vibration, which can be obtained in the above. Especially when When , it means that the roller is separated from the track, the equivalent spring coefficient and damping coefficient are set to zero.

[0153] S5 scales the multi-degree-of-freedom coupling equations to make them dimensionless and introduces the dimensionless RLMG vibration equations into the PINN loss function.

[0154] For the multi-degree-of-freedom coupled equations of RLMG, there is one independent variable t and multiple dependent variables, which can be expressed in dimensionless form as follows:

[0155]

[0156] Substituting the above dimensionless variables into the vibration equation in step S2, the dimensionless form of the overall vibration equation of RLMG can be obtained as:

[0157]

[0158] The characteristic time scale can be expressed as:

[0159]

[0160] Based on the time scale, the characteristic scales of other dependent variables of RLMG can be derived:

[0161]

[0162] In the formula, δ xc ,δ yc ,γ xc ,γ yc ,γ zc is the maximum vibration value of the corresponding degree of freedom, K c,11 for The maximum value of

[0163] On this basis, the total loss function of the RLMG overall vibration equation can be expressed as:

[0164]

[0165]

[0166] Among them, w i is the weight of each task, is the loss of each degree of freedom equation, Defined The training data of the internal configuration points.

[0167] S6 transforms the original time variable based on the dimensionless selected time scale factor and inputs it into the designed interaction network for prediction. At the same time, it embeds the initial value conditions through “hard constraints” to ensure that the prediction of the network after “hard” constraints strictly meets the initial conditions.

[0168] Before feeding the training data into the network, the time scaling factor t selected in step S5 is used. c The time data is scaled and then input into the interaction network for prediction. Figure 7 As shown, it consists of a shared network and 5 parallel networks.

[0169] After the interactive network output passes the hard constraint, the network output strictly satisfies the initial conditions. The output can be expressed as:

[0170]

[0171] In the formula, is the input of the network, are the parameters of the network, including hyperparameters and weight parameters, is the output of the network, δ0 and v0 are the initial values ​​of displacement and velocity respectively.

[0172] S7 uses a gradient algorithm to calculate the derivative of the predicted output, inputs it into a dimensionless equation, and generates the corresponding sub-loss function. The behavior-enhanced black kite algorithm (BE-BKA) is used to calculate the optimal weight of each sub-loss to improve the optimization effect of different tasks.

[0173] By using the gradient algorithm, the predicted output of the model is firstly derived and the calculated derivative is substituted into the dimensionless vibration equation to form the sub-loss function in step S6.

[0174] Then the behavior-enhanced black kite algorithm (BE-BKA) is used to calculate the optimal weight of each sub-loss. The specific steps are as follows:

[0175] (A) After calculating the loss of each degree of freedom, the random initial solution matrix is ​​subjected to Kent chaos mapping to obtain the initial population. It is ensured that all values ​​are greater than 0 and the sum of each group of solutions is equal to 1.

[0176] The mathematical model of Kent chaos mapping can be expressed as:

[0177]

[0178] In the formula, a is the control parameter. In the process of generating the initial population, the matrix size (pop, dim) is randomly generated, where pop represents the population size and dim represents the problem dimension. The initial values ​​are uniformly distributed in (0, 1), and then each value in the matrix is ​​mapped by the above formula to obtain the initial population.

[0179] (B) The total loss is obtained from the weighted sum of the sub-losses, and then the fitness of each existing individual is evaluated based on the total loss.

[0180] The fitness function aims to optimize the weights of the sub-losses while satisfying the constraints that the sum of the weights is equal to 1 and the weight of each sub-loss is greater than 0. The fitness function can be formulated to minimize the total loss while maintaining a balance between the sub-losses. The fitness function can be expressed as:

[0181]

[0182] (C) The population is updated by performing attack behaviors. After the population is updated, the fitness values ​​and the best performing individuals can be recalculated and tracked respectively, thus ensuring continuous improvement of the entire optimization process.

[0183] The mathematical formula of the improved attack behavior enhancement strategy can be expressed as:

[0184]

[0185] In the formula, represents the position of the ith black-winged kite in the jth dimension at the tth iteration, represents the current optimal individual of iteration t, n is the coefficient that changes with the number of iterations, r is a random number between 0 and 1, p is a fixed value, and T is the maximum number of iterations.

[0186] (D) Then a migration mechanism is applied to dynamically adjust the leadership roles of the leaders in the population, ensuring that the optimal individuals guide the update process. This adaptive leadership strategy can effectively discover the optimal solution.

[0187] The mathematical formula of migration behavior can be expressed as:

[0188]

[0189] In the formula, C(0,1) represents the Cauchy mutation, F i represents the fitness value of the current position of the jth dimension obtained by any black-winged kite in the tth iteration, F ri It represents the fitness value of the random position of the jth dimension obtained by any black-winged kite in the tth iteration.

[0190] (E) If the maximum number of iterations is reached, the optimization process ends and provides the final weight for each sub-loss. Otherwise, the algorithm returns to step (S3) and continues to search for the optimal population until the convergence condition is met.

[0191] S8 uses a multi-gradient collaborative optimization method to solve the gradient conflict problem in the shared layer and adaptively adjusts the network weights to improve the model convergence speed.

[0192] For the optimization of the shared network, the specific process of the multi-task gradient conflict technology used by the multi-gradient collaborative optimization strategy can be expressed as:

[0193] (E) For each degree of freedom, the loss is calculated and back-propagated through the network to obtain the gradient of each sub-loss. The gradient contribution of each sub-loss to the shared layer is then combined into a column vector, denoted as g i , to determine if there are two gradient conflicts.

[0194] (F) According to the gradient conflict correction criterion, each task randomly selects the original gradient g of other tasks i Perform gradient detection. If there is a gradient conflict, correct it. Otherwise, keep it unchanged until the gradients of all tasks are corrected and the corrected gradients are obtained.

[0195] Modification criteria:

[0196] Calculate two gradient column vectors g i and g j The cosine value of is used to determine whether the gradients conflict. If both cosine values ​​are negative, this indicates a gradient conflict. If the two gradients conflict, use g i In with g j The projection in the vertical direction replaces g i ,Right now If the two gradients do not conflict, the original gradient g i Remain unchanged.

[0197] (G) Based on the corrected gradient Rearrange the contributions of each sub-loss on the shared network layer into the original gradient format This ensures that the corrected gradient matches the structure of the network layer.

[0198] (H) Corrected gradients for all tasks The final sum gradient is then distributed back to the network for updating parameters, ensuring that the shared layers benefit from the multi-task correction process.

[0199] In order to verify the present invention, the vibration test device designed is as follows Figure 8 As shown, Figure 8 The main components of the device are shown. A ball screw mechanism (4) driven by a servo motor (1) is used. The acceleration and deceleration and speed of the servo motor are precisely controlled by a programmable logic controller, allowing the RLMG to run at any preset speed. The heavy workpiece (2) is fixed to the entire top surface of the slider by bolts. In order to capture the vibration data generated by the vertical force, several acceleration sensors (5) are fixed on the side of the slider. These sensors can continuously collect real-time data, which is transmitted to the PC through the data acquisition system. Finally, the collected signal data is processed by the customized software on the PC, which can automatically display the vibration displacement curve in real time. The experimental results are shown in Fig. 9 As shown in the figure, the experimental results show that compared with the traditional model, the method of the present invention is more competitive and can effectively capture multi-degree-of-freedom complex nonlinear strong coupling vibrations. This proves that the method of the present invention has a strong advantage in solving high-dimensional, high-frequency, and strong coupling problems, and can be easily applied to other multi-degree-of-freedom motion systems.

[0200] An embodiment of the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded into the processor, implements any one of the roller linear motion guide vibration analysis methods based on multi-task interactive PINN and global vibration models.

Claims

1. A vibration analysis method for roller linear motion guide based on multi-task interactive PINN and global vibration model, characterized in that: The following steps are involved: (1) Set up a global Cartesian coordinate system at the center of the RLMG track and define the five degrees of freedom of the slider, including horizontal (Fx, δx), vertical (Fy, δy), pitch (Mx, γx), yaw (My, γy) and roll (Mz, γz); (2) Use the Lagrange equation to describe the RLMG system and generate the matrix vibration equation of the system by defining the kinetic energy dissipation energy and potential energy; (3) Simplify the contact between the roller, track and slider into a spring-damper system, establish a local contact coordinate system, and calculate the mass matrix, stiffness matrix, and damping matrix; (4) Calculate the velocity and position changes of the roller relative to the slider based on rigid body kinematics; analyze the dynamic changes of the contact angle and structural excitation force to obtain the rolling contact behavior; (5) By scaling the multi-degree-of-freedom coupling equations and making them dimensionless, the dimensionless RLMG vibration equations are introduced into the PINN loss function, and soft constraints are applied to encode the dynamic constraints. (6) Based on the dimensionless selected time scale factor, the original time variable is transformed and input into the designed interaction network for prediction. At the same time, the initial value conditions are embedded through hard constraints so that the network prediction strictly meets the initial conditions; (7) Use the gradient algorithm to calculate the derivative of the predicted output and input it into the dimensionless equation to generate the corresponding sub-loss function. Use the behavior-enhanced black kite algorithm BE-BKA to calculate the optimal weight of each sub-loss; (8) Use multi-gradient collaborative optimization method to adaptively adjust network weights.

2. A roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1, characterized in that: The formula for step (2) is as follows: The Lagrangian equation of RLMG motion is expressed as: Kinetic energy T and dissipated energy D are expressed as: The potential energy of RLMG includes: the potential energy generated by the deformation of the roller body due to the vibration of the carriage, the formula is as follows: The specially designed structural parameters make the potential energy generated by the deformation of the roller body, which is generated by the structural excitation force F acting on the slider. c The generalized excitation force [F] acting on the RLMG system is expressed as: [F]=[F r ]+[F c ] Substituting kinetic energy T, dissipated energy D, potential energy U, and generalized excitation force [F] into the Lagrangian equation of RLMG motion, the overall vibration equation of RLMG is written in matrix form: Where T is the kinetic energy of the system vibration, D is the dissipated energy of the system, U is the potential energy of the system, [F] is the vector of the generalized excitation force on the system, [δ r ] is the generalized displacement vector, where [F r ] is the external force acting on the slider, [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

3. The roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1 is characterized in that: In step (3), the stiffness matrix [K] is expressed as: The damping matrix [C] of the slider is expressed as: in, and [k ijN ] are the positions of each spring in the global coordinate O xyz The position matrix, angle matrix and stiffness matrix in, and [c ijN ] are the values ​​of each damper at the global coordinate O xyz The position matrix, angle matrix and damping matrix in .

4. The roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1 is characterized in that: Step (4) Assume that the roller body keeps pure rolling during the working process, and each roller moves to the next roller position as a cycle. The position of the rolling body in the global coordinate system when it passes through different working stages is: in, Represents the distance of the roller relative to the left side of the slider after time t, v b is the speed of the slider, v rb Represents the speed of the roller relative to the slider, l r represents the length of the slider, i represents the number of a track, l is the vertical distance between the center axes of the two rollers on the same track, represents the pitch displacement of the ith track roller body; The change of the equivalent spring contact angle is expressed as: Among them, d b It represents the diameter of the roller after being compressed by the preload, α 0,ijN is the initial contact angle of roller j on track i, Δx ijN and Δy ijN Indicates the amount of spring deformation caused by the vibration of the slider. The structural excitation force is expressed as: Among them, N e is the number of effective rollers in each track, is the composite preload, p e are the coefficients corresponding to different orbits, and are the coordinates of the roller body in the global coordinate system.

5. The roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1, characterized in that: In step (5), the dimensionless form of the RLMG overall vibration equation is: The mean square error of the differential equation network under soft constraints is: The hard constraints added are: The pipeline loss function under soft constraints is: in, is the input of the network, are the parameters of the network, including hyperparameters and weight parameters, is the output of the network, δ0 and v0 are the initial values ​​of displacement and velocity respectively, w i is the weight of each task, Defined Training data for the internal configuration points in .

6. The roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1, characterized in that: In step (6), the interactive network is specifically as follows: it includes 1 shared layer module and 5 parallel modules; wherein the shared layer module extracts global features, and the five parallel network modules are responsible for extracting independent features of each degree of freedom and modeling dynamic changes.

7. The roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to claim 1, characterized in that: In step (7), the behavior-enhanced black kite algorithm BE-BKA is specifically as follows: the BE-BKA algorithm introduces the optimal search strategy into the individual search strategy, dynamically adjusts the individual search range and balances local and global searches; the mathematical formula of the optimal search strategy is expressed as: in, represents the position of the ith black-winged kite in the jth dimension at the tth iteration, represents the current optimal individual of iteration t, and n is the coefficient that changes with the number of iterations.

8. A roller linear motion guide vibration analysis system based on multi-task interactive PINN and global vibration model, characterized in that: include: Coordinate module: used to set the global Cartesian coordinate system at the center of the RLMG track and define the five degrees of freedom of motion of the slider, including horizontal (Fx, δx), vertical (Fy, δy), pitch (Mx, γx), yaw (My, γy) and roll (Mz, γz); Vibration equation module: Use Lagrange equations to describe the RLMG system, and generate the matrix vibration equations of the system by defining kinetic energy dissipation energy and potential energy; Local contact coordinate module: used to simplify the contact between the roller, track and slider into a spring-damper system, establish a local contact coordinate system, and calculate the mass matrix, stiffness matrix, and damping matrix; Analysis module: used to calculate the speed and position changes of the roller relative to the slider based on rigid body kinematics; analyze the dynamic changes of the contact angle and structural excitation force to obtain the rolling contact behavior; Dynamic constraint module: It is used to introduce the dimensionless RLMG vibration equation into the PINN loss function by scaling the multi-degree-of-freedom coupling equations and making them dimensionless, and apply soft constraints to encode dynamic constraints. Interaction network module: used to transform the original time variable based on the dimensionless selected time scale factor, and input it into the designed interaction network for prediction. At the same time, the initial value conditions are embedded through hard constraints so that the network prediction strictly meets the initial conditions. Weight module: used to calculate the derivative of the predicted output using the gradient algorithm and input the dimensionless equation to generate the corresponding sub-loss function. The behavior-enhanced black kite algorithm BE-BKA is used to calculate the optimal weight of each sub-loss; Adjustment module: used to adaptively adjust network weights using multi-gradient collaborative optimization method.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into the processor, it implements the roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to any one of claims 1 to 7.

10. A storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, a roller linear motion guide vibration analysis method based on multi-task interactive PINN and global vibration model according to any one of claims 1 to 7 is implemented.

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