A loading calibration mechanism, system and parameter optimization method

Abstract

The present application discloses a loading calibration mechanism, system and parameter optimization method, which relates to the technical field of loading calibration. The loading calibration mechanism includes a static platform, a moving platform, a loading rod and a plurality of legs connected between the static platform and the moving platform; one end of the loading rod is connected to the moving platform, and the other end of the loading rod is used for loading; the legs include servo electric cylinders and first tension and compression sensors, the first tension and compression sensors are arranged at the ends of the piston rods of the servo electric cylinders, the servo electric cylinders are connected to the static platform, and the first tension and compression sensors are connected to the moving platform; the servo electric cylinders are used to adjust the lengths of the legs and output forces. The loading calibration structure of the present application adjusts the lengths of the respective legs through servo electric cylinders to adjust the pose of the moving platform, so as to achieve accurate and stable loading of vector forces.

Description

Technical Field

[0001] The present application relates to the field of loading calibration, and particularly to a loading calibration mechanism, a system and a parameter optimization method. Background Art

[0002] Currently, the calibration method of the aero-engine force measurement system is usually a calibration method based on in-situ loading. This method realizes the in-situ force loading of the sensor by different configurations of weights, so as to complete the calibration of the sensor. This calibration method has cumbersome configuration, low accuracy and poor stability, which is not conducive to the development of test work. Therefore, it is crucial to develop a loading calibration mechanism that can load and calibrate stably and accurately for the aero-engine force measurement system. Summary of the Invention

[0003] The purpose of the present application is to provide a loading calibration mechanism, a system and a parameter optimization method, which can achieve stable and accurate loading.

[0004] To achieve the above purpose, the present application provides the following solutions:

[0005] In a first aspect, the present application provides a vector loading calibration mechanism, which includes: a static platform, a moving platform, a loading rod, and a plurality of legs connected between the static platform and the moving platform;

[0006] One end of the loading rod is connected to the moving platform, and the other end of the loading rod is used for loading;

[0007] The leg includes a servo electric cylinder and a first tension and compression sensor. The first tension and compression sensor is arranged at the end of the piston rod of the servo electric cylinder. The servo electric cylinder is connected to the static platform, and the first tension and compression sensor is connected to the moving platform;

[0008] The servo electric cylinder is used to adjust the length of the leg and output force.

[0009] In a second aspect, the present application provides a vector loading calibration system, which includes: a frame, a loading connection device, and the above-mentioned vector loading calibration mechanism;

[0010] The vector loading calibration mechanism is arranged on the frame;

[0011] The other end of the loading rod of the vector loading calibration mechanism is connected to the loading connection device;

[0012] During loading, the object under load is arranged on the frame, and the loading connection device is in contact with the object under load.

[0013] Thirdly, the present application provides a parameter optimization method, which is applied to the above vector loading calibration mechanism. The parameter optimization method includes the following steps:

[0014] Based on the kinematic model of the vector loading calibration mechanism, determine the relationship between the parameter variables of the vector loading calibration mechanism and different performance evaluation indexes; the parameter variables include: moving platform radius, static platform radius, arrangement of hinge points on the moving platform, arrangement of hinge points on the static platform, leg length, and loading rod length; different performance evaluation indexes include: workspace evaluation index, stiffness evaluation index, and load-bearing performance evaluation index;

[0015] Construct a training sample set according to the relationship between the parameter variables and different performance evaluation indexes;

[0016] Construct mapping models of the relationship between the parameter variables and each performance evaluation index respectively according to the training sample set, and obtain the mapping models for calculating each performance evaluation index;

[0017] According to the mapping models for calculating each performance evaluation index, use an intelligent optimization algorithm to determine the parameter variables that optimize each performance evaluation index.

[0018] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application:

[0019] The present application provides a loading calibration mechanism, a system, and a parameter optimization method. The loading calibration mechanism includes a static platform, a moving platform, a loading rod, and a plurality of legs connected between the static platform and the moving platform; the legs include servo electric cylinders and first tension and compression sensors, the first tension and compression sensors are arranged at the ends of the piston rods of the servo electric cylinders, the servo electric cylinders are connected to the static platform, and the first tension and compression sensors are connected to the moving platform; the servo electric cylinders are used to adjust the lengths of the legs and output forces. The loading calibration structure of the present application adjusts the lengths of the respective legs through the servo electric cylinders to adjust the pose of the moving platform and achieve accurate and stable loading of vector forces. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a schematic structural diagram of a loading calibration mechanism provided by an embodiment of the present application;

[0022] Figure 2Schematic structural diagram of a vector loading calibration system provided by an embodiment of the present application;

[0023] Figure 3 Schematic structural diagram of a loading connection device provided by an embodiment of the present application;

[0024] Figure 4 Flow chart of a parameter optimization method provided by an embodiment of the present application;

[0025] Figure 5 Schematic structural principle diagram of a loading calibration mechanism provided by an embodiment of the present application;

[0026] Figure 6 Schematic diagram of the working space of a loading calibration mechanism provided by an embodiment of the present application;

[0027] Figure 7 Flow chart of the NSGA-II algorithm provided by an embodiment of the present application;

[0028] Figure 8 Schematic diagram of a Pareto solution set provided by an embodiment of the present application.

[0029] Reference numerals:

[0030] 1. Static platform; 2. Composite spherical hinge; 3. Servo motor; 4. Servo electric cylinder; 5. First tension and compression sensor; 6. Hook hinge; 7. Moving platform; 8. Second tension and compression sensor; 9. First slide rail group; 10. Second slide rail group; 11. First loading plate; 12. Second loading plate. Detailed implementation manners

[0031] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0032] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0033] In an exemplary embodiment, as Figure 1 shown, a vector loading calibration mechanism is provided, including: a static platform 1, a moving platform 7, a loading rod ( Figure 1which is not shown in the figure) and a plurality of legs connected between the static platform 1 and the moving platform 7. Each leg forms a UPS structure and is connected to the static platform 1 and the moving platform 7 through a composite spherical hinge 2 and a Hooke's joint 6 respectively. The moving pair is composed of a servo motor 3 and a servo electric cylinder 4 to realize the change of the leg length, and the pose adjustment of the moving platform 7 is realized through different length configurations of the six legs, the vector force is loaded, and the vector force is measured by the first tension-compression sensor 5. Among them, the composite spherical hinge 2 is composed of a horizontal Hooke's joint and a revolute pair.

[0034] In an exemplary embodiment, as Figure 2 shown, a vector loading calibration system is provided, including: a frame, a loading connection device, and the above-mentioned vector loading calibration mechanism.

[0035] The static platform is connected to the frame and arranged horizontally. The servo electric cylinder 4 (moving pair) is connected to the static platform 1 through the composite spherical hinge 2, then the first tension-compression sensor 5 is connected, and it is connected to the moving platform through the Hooke's joint 6. The connection methods of the six legs are exactly the same. The moving platform 7 and the loading rod are rigidly connected. The loading rod is connected to the loading connection device through a spherical hinge, and the loading connection device is connected to the loaded object, as Figure 3 shown. The loading connection device includes a first loading plate 11 and a second loading plate 12. The loading rod is connected to the first loading plate 11 through a spherical hinge. The first loading plate 11 is connected to the second loading plate 12 through four second tension-compression sensors 8 (the decoupled measurement of the vector force is realized by four tension-compression sensors), and then is connected to the loaded object through the first slide rail group 9 and the second slide rail group 10. In this embodiment, the movement on the plane is realized by two groups of slide rails, and the force perpendicular to the plane is transmitted, avoiding the lateral force received by the sensor. Such a structure completes the decoupled measurement of the vector force and the loading of the vector force.

[0036] Exemplarily, the frame is a horizontal frame. The horizontal frame connects the vector loading calibration mechanism and the loaded object through flanges and bolts. The loading rod is rigidly connected to the moving platform 1 through welding or other means and is connected to the connection device in the form of a spherical hinge, and then is connected to the loaded object.

[0037] The moving platform 7 applies a vector force to the loaded object through the loading rod, and the frame unifies the loaded object and the loading calibration mechanism on a horizontal plane, simulating the thrust of an actual turbojet engine.

[0038] Since different size parameters have a great impact on the performance of the loading calibration mechanism, in order to ensure the optimal performance of the loading calibration mechanism, multi-objective optimization is required. The intelligent optimization algorithms mainly used for the optimization problem include the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm. Since NSGA-II can more effectively maintain the diversity of the population and avoid local optimal solutions when dealing with multi-objective optimization problems, and compared with PSO, NSGA-II shows better performance in different test scales, which makes it an ideal choice for the optimization problem of parallel mechanisms. During the optimization process, in order to obtain accurate calculation results of the global performance index (GPI), it is necessary to increase the density of discrete nodes, and a large number of discrete nodes significantly increases the computational cost of calculation and iteration. As the main method to reduce the computational cost of the global performance index, the mapping model method reduces the computational cost by establishing the mapping relationship between GPI and design parameters. The commonly used methods include multiple regression (MR), neural network (NN), and Gaussian process regression (GPR). Multiple regression provides a practical and cost-effective modeling option with its simplicity, high interpretability, low data requirements, and computational efficiency in the case of limited resources and a clear need to explain the relationship between variables, and is very suitable for the accurate parameter analysis and system performance optimization of the parallel mechanism optimization design.

[0039] Therefore, in an exemplary embodiment, a parameter optimization method is provided, as Figure 4 shown, the parameter optimization method is applied to the above vector loading calibration mechanism, and the parameter optimization method includes the following steps:

[0040] Step 101, based on the kinematic model of the vector loading calibration mechanism, determine the relationship between the parameter variables of the vector loading calibration mechanism and different performance evaluation indicators; the parameter variables include: moving platform radius, static platform radius, arrangement of hinge points on the moving platform, arrangement of hinge points on the static platform, leg length, and loading rod length; different performance evaluation indicators include: workspace evaluation indicator, stiffness evaluation indicator, and load-bearing performance evaluation indicator.

[0041] Step 102, construct a training sample set according to the relationship between the parameter variables and different performance evaluation indicators.

[0042] Step 103, respectively construct mapping models of the relationship between the parameter variables and each performance evaluation indicator according to the training sample set, and obtain mapping models for calculating each performance evaluation indicator.

[0043] Step 104, according to the mapping models for calculating each performance evaluation indicator, use an intelligent optimization algorithm to determine the parameter variables that optimize each performance evaluation indicator.

[0044] In another exemplary embodiment of the present application, in order to determine the relationship between the parameter variables of the vector loading calibration mechanism and different performance evaluation indicators, step 101 above is replaced by steps 201 to 203:

[0045] Step 201, establish a kinematic model:

[0046] To optimize the design of the loading calibration mechanism, it is first necessary to establish a kinematic model of the loading calibration mechanism. As Figure 5 shown, in the following analysis, let the independent variable be L i , and the output variables be and P.

[0047] The definition of inverse kinematics is to solve the vector after the given end position and attitude (the position of the moving platform relative to the base and the attitude of the coordinate system P-x'y'z' relative to the coordinate system O-xyz). i Define the vectors a i and b i as the position vectors of A i and B in the moving coordinate system and the base coordinate system respectively, as well as the position vector of the moving platform relative to the base and the rotation matrix of the moving coordinate system relative to the base coordinate system Define where

[0048]

[0049] Then, according to the geometric relationship, we can obtain:

[0050]

[0051] Taking the modulus on both sides of the equation, we can obtain the length of the branch chain:

[0052]

[0053] The angles between the Hooke joints, ball joints, and the Z-axis connecting the moving platform and the static platform can be expressed as:

[0054] arccos(l i / |l i |·(0,0,1))

[0055] Then, the unit direction vector of the branch chain is:

[0056] s i = l i / L i

[0057] In the equation s i = l i / L i Taking the time derivative of both ends gives the velocity of the moving platform A i as:

[0058]

[0059] where is the velocity of the moving platform A i , v p represents the velocity of the position vector , and ω represents the rotational angular velocity of the position vector .

[0060] Decompose the velocity of the branch chain in the static platform coordinate system onto the branch chain direction to obtain the moving velocity v L of the branch chain joint, where the vector set s = [s 1 , …, s 6

[0061]

[0062] Therefore, the velocity Jacobian matrix can be defined as:

[0063] J = [s T (r a × s) T -1

[0064]

[0065] Furthermore, the velocity Jacobian matrix can be defined as:

[0066] J = [s T (r a × s) T -1

[0067] Step 202, establish the workspace:

[0068] Establish constraint equations based on the working ranges of engineering components such as ball joints, Hooke joints, and servo cylinders selected

[0069] Obtain a series of coordinates in the workspace through the form of scanning in the Cartesian coordinate system, and obtain the leg lengths and joint angles of the Hooke joints and ball joints through the inverse kinematics model

[0070] Successively perform constraint judgments on the leg lengths and joint angles obtained kinematically, retain the points that meet the conditions, and finally form the workspace of the mechanism, as shown in Figure 6 .

[0071] Step 203, establish performance evaluation indicators:

[0072] ​​​1. Workspace evaluation index:

[0073] After analysis, it is found that the shape of the mechanism workspace in this solution is a spherical surface with the loading rod as the radius. As Figure 6 shown, since the shape of the workspace is irregular, the operable workspace is defined as all circular trajectories on the plane. Therefore, the area of the operable workspace is linearly positively correlated with the angle between the Z-axis of the moving platform and the Z-axis of the base. Therefore, the global workspace index (WSI) is defined as:

[0074] WSI = β min

[0075] where β is the angle between the connecting rod QP and the Z-axis of the base coordinate system.

[0076] 2. Stiffness evaluation index

[0077] Stiffness is used to evaluate the ability of the mechanism to resist deformation under the action of external forces. Higher stiffness can ensure the stability of the overall structure of the mechanism during the force application process, which is crucial for the accuracy in the process of load spectrum reproduction. To simplify the problem, it is assumed that the moving platform and joints of the parallel mechanism are rigid bodies, and the stiffness of the parallel mechanism is defined as the leg stiffness k i Combined into the stiffness matrix K l = diag[k 1 , …, k 6 .

[0078]

[0079] where L i is the length of the i-th leg, E = 2.11×10 11 Pa is the elastic modulus, and A = 1.3×10 -3 m 2 is the cross-sectional area of the leg.

[0080] Combined with the Jacobian matrix, the overall stiffness matrix K of the parallel mechanism is calculated.

[0081] K = J T K l J

[0082] The current stiffness index includes various evaluation methods such as eigenvalues, determinants, and traces. In this application, the sum of the diagonal elements of the most commonly used stiffness matrix is used to measure the overall stiffness. Therefore, the local stiffness performance index (LSI) is:

[0083]

[0084] where GSI is the global stiffness index, and LSI nis the stiffness of the nth point in the working space of the vector loading calibration mechanism, and N is the number of points in the working space of the vector loading calibration mechanism.

[0085] In order to evaluate the overall stiffness of the mechanism, a global stiffness index (GSI) needs to be established. The common method is to average the LSI in the workspace area:

[0086]

[0087] Among them, η m is the weighted value of the mth degree of freedom of the stiffness in the working space of the vector loading calibration mechanism, K n,mm is the mth diagonal element of the stiffness matrix of the nth point in the workspace of the vector loading calibration mechanism. For example, mm = 11 means the stiffness in the x direction, and mm = 22 means the stiffness in the y direction. The stiffness matrix of the nth point in the workspace of the vector loading calibration mechanism is constructed by the components of the stiffness of the nth point in the workspace of the vector loading calibration mechanism in each degree of freedom. K n,mm It is related to the Jacobian matrix.

[0088] 3. Load-bearing performance evaluation indicators

[0089] During the force loading process, different sizes affect the driving force of different branches. In certain positions, a branch may produce a bearing capacity far exceeding that of other branches, which can easily cause branch overload and seriously affect the bearing capacity of the overall configuration, which is very unfavorable for the load spectrum reproduction ability. Therefore, in order to increase the bearing capacity of the parallel mechanism during the force loading process, it is necessary to optimize the driving force of the parallel mechanism branch, and define the ratio of the branch driving force to the external load as the local bearing capacity index (LLI):

[0090]

[0091] Among them, max =(τ 1 …τ 6 ) max is the maximum branch driving force for a specific posture in the workspace, F load is the output load of the dynamic platform, Τ max =(τ 1 …τ 6 ) max and F load are related to the Jacobian matrix, the force Jacobian matrix J F =J T , the relationship between load and driving force is Τ=J F -1 F load. To better evaluate the load-bearing capacity of the parallel mechanism, the maximum value of LLI in the workspace is taken as the global load-bearing capacity index (GLI):

[0092] GLI = max(LLI)

[0093] In another exemplary embodiment of the present application, in order to establish the training sample set, step 102 above is replaced by steps 301 - 303:

[0094] Step 301: Design independent variables according to dimensional parameters. In the present application, the radii of the moving platform and the static platform, the arrangement of hinge points on the moving platform and the static platform, as well as the lengths of the legs and the loading rods have very important effects on the performance of the loading calibration mechanism. Therefore, these five parameters are selected as the five dimensions in the independent variable space, and the independent variable space is designed accordingly. Since the evaluation index can be directly used as the fitness function, the three dimensions of the fitness space are simply defined as three performance evaluation indexes.

[0095] Step 302: Construct the required fitting samples in the independent variable space by the Latin Hypercube Sampling (LHS) method. First, uniform partitioning is performed on the five dimensions, and uniform sampling is carried out in each area to ensure that the samples are evenly distributed in the design parameter space, reducing the number of iterations. Using this method, 1000 groups of samples are generated, and the performance evaluation indexes of these 1000 groups of samples are calculated to form the fitness space. So far, 1000 groups of samples in one-to-one correspondence between the independent variable space and the fitness space are obtained.

[0096] In another exemplary embodiment of the present application, in order to establish the mapping model, step 103 above can be implemented by the following steps:

[0097] The training samples generated in step 102 are input into the MARS model, and a mapping model is constructed based on the basis functions and their products in a forward stepwise linear regression manner. Its form is as follows:

[0098]

[0099] h 0 (x 1 …x n ) = 1

[0100]

[0101] where s km = ±1, is the predicted value of the target variable, representing the output of the MARS model, is composed of basis functions related to the M sub-regions, and each segment of the basis function is the product of univariate spline basis functions s km selected from the basis function set. is the intercept term of the model, estimated by the least squares method. is the coefficient of the m-th segment of the basis function h m (x), estimated by the least squares method, h 0 (X) is a constant term, usually 1, M is the number of basis functions, h m (X) is the m-th segment of the basis function, constituting the non-linear part of the model, K m is the number of variables in the m-th segment of the basis function, s km takes values of ±1, controlling the increasing or decreasing direction of the basis function, x k,m is the k,m-th component in the input vector X, representing the k-th variable corresponding to the m-th basis function, t km is the threshold value, representing the cut-off point, i.e., the dividing line, which determines the piecewise characteristic of the basis function at this point. The + represents the positive part function, defined as: [x] + = max(0, x).

[0102] Furthermore, in order to optimize the parameter variables, step 104 above can be implemented by the following steps:

[0103] In the traditional method, the distribution factor is exactly the same for different independent variables, without considering that different independent variables have different sensitivities. Therefore, in order to combine the mapping model and jointly reduce the cost of parameter optimization, sensitivity analysis needs to be carried out.

[0104] Since the mapping model is a model with an explicit formula, analyzing the importance (i.e., sensitivity) of the independent variables in the parameter variables is divided into the following steps 401 and step 402:

[0105] Step 401, calculate the cumulative contribution degree of each variable in all basis functions.

[0106] Calculate the basis function contribution degree: For each basis function B m (x), calculate the absolute value |c m | of its corresponding coefficient c m . For each variable x i , calculate the sum of the contribution degrees of all basis functions containing this variable.

[0107] Let s i be the importance of the variable x i , then:

[0108]

[0109] where, M i represents the set of basis functions containing the variable x i .

[0110] Step 402: To make the importance measures comparable among different variables, the above importance can be standardized.

[0111] The standardization method can be to divide the importance of each variable by the sum of the importance of all variables.

[0112]

[0113] where p is the total number of variables.

[0114] For more sensitive independent variables, strengthening the local search ability can enable the algorithm to explore the local range of independent variables more concentratedly, enhancing the convergence of the algorithm. Therefore, a larger distribution factor should be set. For less sensitive independent variables, the poor global search ability is more likely to lead to the problem of falling into local optimal solutions. Therefore, a smaller distribution factor needs to be set. Combining the above analysis, a weighted vector v is defined, and a weighted distribution factor η is defined q :

[0115]

[0116] η q = v·η

[0117] So far, the sensitivity analysis and the design of the distribution factor according to sensitivity are completed.

[0118] Based on the above mapping model and formaldehyde distribution factor, as Figure 7 shown, the specific implementation process of step 104 includes the following steps 501 - step 508:

[0119] Step 501: Generate an initial population: According to the defined independent variable space, randomly generate an initial population P 0 , with a population size of M.

[0120] Step 502: Evaluate the population: Through the mapping model, calculate the fitness function value of each individual in the population, greatly reducing the computational cost due to scanning.

[0121] Step 503: Non-dominated sorting: Classify the population according to non-dominated ranks to generate multiple Pareto Fronts. Among them, the first front (Front 1) contains all non-dominated solutions, the second front (Front 2) contains the solutions dominated by the solutions in the first front, and so on. Maintain the population diversity. The crowding distance is calculated based on the objective function values and represents the distance between each individual and its neighboring individuals.

[0122] Step 504: Generate an offspring population through selection, crossover, and mutation methods:

[0123] Selection: Use the tournament selection mechanism to select parent individuals for reproduction. Tournament selection considers the non-dominated rank and crowding distance of individuals, and preferentially selects individuals with a low non-dominated rank and a large crowding distance.

[0124] Crossover: Perform a crossover operation on the selected parent individuals to generate offspring individuals. Commonly used crossover methods include single-point crossover, multi-point crossover, and simulated binary crossover (SBX). The specific formula is as follows:

[0125]

[0126] where, x' i,k and x' j,k are the k-th parameters in the i-th and j-th individuals in the offspring population respectively, x i,k and x j,k are the k-th parameters in the i-th and j-th individuals in the parent population respectively, β k is the adjustment factor for the k-th parameter; η k is the distribution factor for the k-th parameter, and u is a random number within the interval [0, 1].

[0127] In the crossover operation, a high distribution factor makes the gene values of the generated offspring individuals closer to those of the parent individuals, and the difference in gene values between the offspring and the parent after crossover is smaller. This setting tends to search locally in the solution space. A high distribution factor makes the gene values of the generated offspring individuals closer to those of the parent individuals, and the difference in gene values between the offspring and the parent after crossover is smaller. This setting tends to search locally in the solution space.

[0128] Mutation: Perform a mutation operation on the offspring individuals to increase the diversity of solutions. Commonly used mutation methods include polynomial mutation and Gaussian mutation. The specific formula is as follows:

[0129] x' ik = x ik ` + δ × (u k - l k );

[0130]

[0131] where, x″ i,k is the k-th parameter in the i-th individual in the mutant population, δ k is the mutation factor for the k-th parameter, x upper,k and x lower,k are the upper and lower boundaries of the value range of the k-th parameter respectively, δ 1k and δ 2k are the first and second intermediate variables for the k-th parameter respectively, δ 1k = (x'i,k -x lower,k ) / (x upper,k -x lower,k ), δ 2k =(x upper,k - x' i,k ) / (x upper,k - x lower,k ).

[0132] In the mutation operation, the distribution factor determines the range of gene mutation, that is, how the new genes are distributed within the possible mutation range. A low η value will produce a large δ, resulting in a larger mutation step size and increasing gene diversity. A high β value will make δ smaller, so that the mutated gene value is close to the original value, tending to local search.

[0133] Therefore, according to different sensitivities, in order to maximize the search efficiency, the independent variables with high sensitivity should have a large distribution factor to enhance the local search ability and avoid the destruction of excellent genes due to mutation and crossover. For the less sensitive independent variables, a smaller distribution factor should be given to increase their global search ability and make them have higher search efficiency.

[0134] Step 505, generate the combined population:

[0135] Combined population: Combine the current population P t with the offspring population Q t to generate the combined population R t , whose size is 2M.

[0136] Non-dominated sorting: Perform non-dominated sorting on the combined population R t to generate multiple fronts.

[0137] Step 506, select the next generation population: Select the first M individuals from the combined population R t as the next generation population P t+1 . In the selection process, the non-dominated rank is given priority. If the number of individuals in a certain front exceeds the remaining quota, the individuals are selected according to the crowding distance.

[0138] Step 507, terminate the iteration

[0139] In the final Pareto solution set, a set of solutions that do not dominate each other is included. In order to select the optimal solution, this application considers setting a weight vector for three performance indicators.

[0140] v = (w 1 , w 2 , w 3 )

[0141] Select the solution pointed to by the weight vector in the Pareto solution set, as Figure 8 shown.Figure 8 The x, y, and z coordinates represent the performance indicators under this dimensional parameter. Taking the independent variable parameters represented by this solution as the optimal parameters of this application can effectively guide the structural design and performance optimization of the vector loading calibration mechanism.

[0142] According to the specific embodiments provided by this application, the following technical effects are disclosed in this application:

[0143] 1. In the traditional loading mechanism, the moving platform and the loaded object are fixedly connected and the position and attitude cannot be adjusted. This causes vector forces in any direction to be applied in the same position and attitude. Different position and attitudes have different Jacobian matrices. For the same vector force, there must be an optimal position and attitude that can minimize the leg force. In view of this, this application designs a structure that can adjust the position and attitude for loading, so that different vector forces can be loaded in the optimal position and attitude.

[0144] 2. The traditional multi-objective optimization algorithm is carried out for the scattered points in the working space of the loading calibration mechanism. Due to the complex kinematic model of the loading calibration mechanism itself, directly calculating the global performance indicators from the scattered points in the working space is very costly in terms of computing. At the same time, the traditional optimization scheme cannot effectively consider the characteristics between different optimization objectives, resulting in a waste of computing costs. For this reason, this application first establishes a spline regression model (i.e., mapping model) for the scattered points in the working space and the global performance indicators, and designs different weighting indicators for different global performance indicators through sensitivity analysis, effectively reducing the computing cost.

[0145] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0146] Specific examples are used in this article to elaborate on the principle and implementation manner of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, based on the idea of this application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A parameter optimization method for a vector loading calibration mechanism, characterized in that: The vector loading calibration mechanism comprises: a static platform, a dynamic platform, a loading rod, and a plurality of legs connected between the static platform and the dynamic platform; One end of the loading rod is connected to the moving platform, and the other end of the loading rod is used for loading; The outrigger comprises a servo electric cylinder and a first tension and pressure sensor, wherein the first tension and pressure sensor is arranged at the end of the piston rod of the servo electric cylinder, the servo electric cylinder is connected to the static platform, and the first tension and pressure sensor is connected to the dynamic platform; The servo electric cylinder is used to adjust the length of the outrigger and output force; The parameter optimization method applied to the vector loading calibration mechanism comprises the following steps: Based on the kinematic model of the vector loading calibration mechanism, the relationship between the parameter variables of the vector loading calibration mechanism and different performance evaluation indicators is determined; the parameter variables include: the radius of the moving platform, the radius of the static platform, the hinge point arrangement on the moving platform, the hinge point arrangement on the static platform, the leg length and the loading rod length; the different performance evaluation indicators include: the workspace evaluation index, the stiffness evaluation index and the load-bearing performance evaluation index; According to the relationship between parameter variables and different performance evaluation indicators, a training sample set is constructed; According to the training sample set, a mapping model of a relational expression between a parameter variable and each performance evaluation index is constructed to obtain a mapping model for calculating each performance evaluation index; According to the mapping model used to calculate each performance evaluation index, an intelligent optimization algorithm is used to determine the parameter variables that optimize each performance evaluation index; The relationship between parameter variables and workspace evaluation indicators is: WSI=β min ; Among them, WSI is the workspace index, β min is the angle between the line connecting the center of the static platform and the center of the dynamic platform and the Z axis of the base coordinate system, where the Z axis of the base coordinate system is perpendicular to the static platform; The relationship between parameter variables and stiffness evaluation index is: Among them, GSI is the global stiffness index, LSI n is the stiffness of the nth point in the working space of the vector loading calibration mechanism, N is the number of points in the working space of the vector loading calibration mechanism, η n,m is the weighted value of the mth degree of freedom of the stiffness of the nth point in the working space of the vector loading calibration mechanism, K n,mm is the mth diagonal element of the stiffness matrix of the nth point in the working space of the vector loading calibration mechanism, and the stiffness matrix of the nth point in the working space of the vector loading calibration mechanism is constructed by the components of the stiffness of the nth point in the working space of the vector loading calibration mechanism in each degree of freedom; The relationship between parameter variables and load-bearing performance evaluation indicators is: GLI = max(LLI); Among them, LLI is the local load capacity index, GLI is the load performance evaluation index, F load is the output load of the dynamic platform, Τ max It is the maximum branch driving force.

2. The parameter optimization method for a vector loading calibration mechanism according to claim 1, characterized in that: One end of the support leg is connected to the static platform through a composite ball joint, and the other end of the support leg is connected to the dynamic platform through a Hooke's joint; the composite ball joint is composed of a horizontal Hooke's joint and a revolute pair.

3. The parameter optimization method for a vector loading calibration mechanism according to claim 1, characterized in that: According to the relationship between parameter variables and different performance evaluation indicators, a training sample set is constructed, including: The Latin hypercube sampling method is used to establish the parameter variable sample; According to the relationship between the parameter variables of the vector loading calibration mechanism and different performance evaluation indicators, different performance evaluation indicators of each parameter variable sample are calculated to construct a training sample set.

4. The parameter optimization method for a vector loading calibration mechanism according to claim 1, characterized in that: The intelligent optimization algorithm is the NSGA-II algorithm.

5. The parameter optimization method for a vector loading calibration mechanism according to claim 1 or 4, characterized in that: According to the mapping model used to calculate each performance evaluation index, an intelligent optimization algorithm is used to determine the parameter variables that optimize each performance evaluation index, including: Use parameter variables as individuals to initialize the population; Using the mapping model used to calculate each performance evaluation index, calculate each performance evaluation index of each individual in the population of the current iteration; According to the performance evaluation indicators of each individual in the population of the current iteration, the individuals in the population of the current iteration are selected, crossed and mutated to generate the initial population of the next iteration; Merge the population of the current iteration with the initial population of the next iteration to obtain a combined population; According to the performance evaluation index of each individual in the combined population, M individuals are selected from the combined population as the population for the next iteration; M is the number of individuals in the population for each iteration; Return to the step of "using the mapping model for calculating each performance evaluation index to calculate each performance evaluation index of each individual in the population of the current iteration" until the iteration end condition is met, and output the optimal individual of the current iteration as the parameter variable for optimizing each performance evaluation index.

6. The parameter optimization method for a vector loading calibration mechanism according to claim 5, characterized in that: The initial population of the next iteration includes the parent population, child population and mutant population of the next iteration; according to the performance evaluation indicators of each individual in the population of the current iteration, the individuals in the population of the current iteration are selected, crossed and mutated to generate the initial population of the next iteration, which specifically includes: According to the performance evaluation indicators of each individual in the population of the current iteration, the tournament selection mechanism is used to select individuals in the population of the current iteration to generate the parent population of the next iteration; According to the distribution factors of each parameter in the parameter variable, the individuals in the parent population are crossed using the following formula to generate the next iteration of the child population; the parameter distribution factors are calculated based on the coefficients of the parameters in each basis function in the mapping model used to calculate each performance evaluation index; Among them, x' i,k and x' j,k are the kth parameters of the i-th and j-th individuals in the offspring population, respectively, and x i,k and x j,k are the kth parameters of the i-th and j-th individuals in the parent population, β k is the adjustment factor of the kth parameter; η k is the distribution factor of the kth parameter, and u is a random number in the interval [0,1]; According to the distribution factors of each parameter in the parameter variable, the following formula is used to mutate the individuals in the offspring population to generate the mutant population for the next iteration; x″ i,k =x′ i,k +δ k (x upper,k -x lower,k ); Among them, x″ i,k is the kth parameter of the i-th individual in the mutant population, δ k is the variation factor of the kth parameter, x upper,k and x lower,k are the upper and lower boundaries of the value range of the kth parameter, respectively, 1k and δ 2k are the first and second intermediate variables of the kth parameter, δ 1k =(x′ i,k -x lower,k ) / (x upper,k -x lower,k ), δ 2k =(x upper,k -x′ i,k ) / (x upper,k -x lower,k ).

7. The parameter optimization method for a vector loading calibration mechanism according to claim 5, characterized in that: The vector loading calibration mechanism is applied to a vector loading calibration system, and the vector loading calibration system further comprises: a frame and a loading connection device; The vector loading calibration mechanism is arranged on the frame; The other end of the loading rod of the vector loading calibration mechanism is connected to the loading connection device; During loading, the loaded object is placed on the frame, and the loading connection device is in contact with the loaded object.

8. The parameter optimization method for a vector loading calibration mechanism according to claim 7, characterized in that: The loading connection device comprises: a first loading plate and a second loading plate; The first loading plate is connected to the other end of the loading rod via a ball joint; The first loading plate and the second loading plate are connected via four evenly distributed second tension and pressure sensors; A first slide rail group and a second slide rail group perpendicular to each other are arranged on a side of the second loading plate facing the loaded object.

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