Loading calibration mechanism and system and parameter optimization method

Abstract

The invention discloses a loading calibration mechanism and system and a parameter optimization method. Relates to the technical field of loading calibration. The loading calibration mechanism comprises a static platform, a movable platform, a loading rod and a plurality of supporting legs connected between the static platform and the movable platform, one end of the loading rod is connected with the movable platform, and the other end of the loading rod is used for loading; the support leg comprises a servo electric cylinder and a first pull pressure sensor, the first pull pressure sensor is arranged at the end part of a piston rod of the servo electric cylinder, the servo electric cylinder is connected with the static platform, and the first pull pressure sensor is connected with the movable platform; the servo electric cylinder is used for adjusting the length of the supporting leg and outputting force. According to the loading calibration structure, the lengths of the supporting legs are adjusted through the servo electric cylinders, so that the pose of the movable platform is adjusted, and precise and stable loading of the vector force is achieved.

Description

Technical Field

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

[0002] At present, the calibration method of aircraft engine force measurement system is usually based on in-situ loading. This method realizes in-situ force loading of the sensor through different configurations of weights to complete the calibration of the sensor. This calibration method is cumbersome to configure, has low accuracy and poor stability, which is not conducive to the development of testing work. Therefore, it is crucial to develop a stable and accurate loading calibration mechanism for aircraft engine force measurement system. Summary of the invention

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

[0004] To achieve the above objectives, this application provides the following solutions:

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

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

[0009] In a second aspect, the present application provides a vector loading calibration system, the vector loading calibration system comprising: 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 loaded object is placed on the frame, and the loading connection device is in contact with the loaded object.

[0013] In a third aspect, the present application provides a parameter optimization method, which is applied to the above-mentioned vector loading calibration mechanism, and the parameter optimization method comprises the following steps:

[0014] 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;

[0015] According to the relationship between parameter variables and different performance evaluation indicators, a training sample set is constructed;

[0016] 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;

[0017] According to the mapping model used to calculate each performance evaluation index, an intelligent optimization algorithm is adopted to determine the parameter variables that optimize each performance evaluation index.

[0018] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0019] The present application provides a loading calibration mechanism, system and parameter optimization method. The loading calibration mechanism includes a static platform, a dynamic platform, a loading rod and a plurality of legs connected between the static platform and the dynamic platform; the legs include a servo electric cylinder and a first tension and pressure sensor, 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 legs and output force. The loading calibration structure of the present application adjusts the length of each leg through the servo electric cylinder to adjust the posture of the dynamic platform and realize accurate and stable loading of vector force. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 A schematic diagram of the structure of a loading calibration mechanism provided in one embodiment of the present application;

[0022] Figure 2A schematic diagram of the structure of a vector loading calibration system provided in one embodiment of the present application;

[0023] Figure 3 A schematic diagram of the structure of a loading connection device provided in one embodiment of the present application;

[0024] Figure 4 A flow chart of a parameter optimization method provided in one embodiment of the present application;

[0025] Figure 5 A structural schematic diagram of a loading calibration mechanism provided in one embodiment of the present application;

[0026] Figure 6 A schematic diagram of a working space of a loading and calibration mechanism provided in an embodiment of the present application;

[0027] Figure 7 A flowchart of the NSGA-II algorithm provided in one embodiment of the present application;

[0028] Figure 8 A schematic diagram of a Pareto solution set provided in an embodiment of the present application.

[0029] Reference numerals:

[0030] 1. Static platform; 2. Compound ball joint; 3. Servo motor; 4. Servo electric cylinder; 5. First pulling pressure sensor; 6. Hook hinge; 7. Moving platform; 8. Second pulling pressure sensor; 9. First slide rail group; 10. Second slide rail group; 11. First loading plate; 12. Second loading plate. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0032] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0033] In an exemplary embodiment, Figure 1 As shown, a vector loading calibration mechanism is provided, including: a static platform 1, a dynamic platform 7, a loading rod ( Figure 1The invention relates to a plurality of legs connected between the static platform 1 and the dynamic platform 7. Each leg forms a UPS structure and is connected to the static platform 1 and the dynamic platform 7 respectively through a composite ball joint 2 and a Hooke's joint 6. The moving pair is composed of a servo motor 3 and a servo electric cylinder 4 to achieve the change of the leg length, and the posture adjustment of the dynamic platform 7 is achieved through the different length configurations of the six legs, the loading of the vector force is achieved, and the vector force is measured through the first tension pressure sensor 5. Among them, the composite ball joint 2 is composed of a horizontal Hooke's joint and a rotating pair.

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

[0035] The static platform is connected to the frame in a horizontal arrangement. The static platform 1 is connected to the servo electric cylinder 4 (moving pair) through a composite ball joint 2, and then connected to the first tension pressure sensor 5 and connected to the dynamic platform through a Hooke's joint 6. The connection method of the six legs is exactly the same. The dynamic platform 7 is rigidly connected to the loading rod. The loading rod is connected to the loading connection device through a ball joint, and the loading connection device is connected to the loaded object, such as Figure 3 As 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 ball joint. The first loading plate 11 is connected to the second loading plate 12 through four second tension and pressure sensors 8 (the four tension and pressure sensors realize the decoupling measurement of vector force), and then connected to the loaded object through the first slide rail group 9 and the second slide rail group 10. In this embodiment, the two groups of slide rails realize the movement on the plane, transmit the force perpendicular to the plane, and prevent the sensor from receiving lateral force. Such a structure completes the decoupling measurement of vector force and the loading of vector force.

[0036] Exemplarily, the frame is a horizontal frame, which connects the vector loading calibration mechanism and the loaded object through flanges and bolts. The loading rod and the moving platform 1 are connected in a rigid manner such as welding, and are connected to the connecting device through a ball joint, and then 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 dimensional parameters have a great influence on the performance of the loading and calibration mechanism, multi-objective optimization is required to ensure the loading and calibration mechanism has the best performance. The main intelligent optimization algorithms used in the optimization problem include genetic algorithm (GA) and particle swarm optimization (PSO). 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 parallel mechanism optimization problems. In the optimization process, in order to obtain accurate global performance index (GPI) calculation results, it is necessary to increase the density of discrete nodes, and a large number of discrete nodes significantly increase the computational cost of calculation and iteration. As the main method to reduce the computational cost of global performance index, the mapping model method reduces the computational cost by establishing a mapping relationship between GPI and design parameters. Commonly used methods include multivariate regression (MR), neural network (NN), and Gaussian process regression (GPR). With its model simplicity, high interpretability, low data requirements and computational efficiency, multivariate regression provides a practical and cost-effective modeling option when resources are limited and clear explanations of variable relationships are required. It is very suitable for precise parameter analysis and system performance optimization of parallel mechanism optimization design.

[0039] Therefore, in an exemplary embodiment, a parameter optimization method is provided, such as Figure 4 As shown, the parameter optimization method is applied to the above-mentioned vector loading calibration mechanism, and the parameter optimization method comprises 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: the radius of the dynamic platform, the radius of the static platform, the hinge point arrangement on the dynamic platform, the hinge point arrangement on the static platform, the leg length and the loading rod length; the different performance evaluation indicators include: workspace evaluation index, stiffness evaluation index and load-bearing performance evaluation index.

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

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

[0043] Step 104 , based on 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.

[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, the above step 101 is replaced by steps 201 to 203:

[0045] Step 201, establishing a kinematic model:

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

[0047] The definition of inverse kinematics is to solve the vector after given the end position posture (the position of the moving platform relative to the base and the posture of the coordinate system Px′y′z′ relative to the coordinate system O-xyz) Define vector a i and b i A i and B i The position vectors in the moving coordinate system and the base coordinate system, 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 definition in for:

[0048]

[0049] According to the geometric relationship, we can get:

[0050]

[0051] Modulo both sides of the formula, we can get the length of the branch chain:

[0052]

[0053] The angle between the Hooke joint and the spherical joint connecting the dynamic platform and the static platform and the Z axis 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 formula i = l i / L i Taking the derivative of both ends with respect to time, we can get the moving platform A i The speed is:

[0058]

[0059] in, For dynamic platform A i The speed, v p Represents the position vector The velocity of the The angular velocity of rotation.

[0060] Decompose the velocity of the branch chain in the static platform coordinate system into the branch chain direction and obtain the moving velocity v of the branch chain joint L , where the vector set s = [s1,…,s6]

[0061]

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

[0063] J=[s T (r a ×s) T ] -1

[0064]

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

[0066] J=[s T (r a ×s) T ] -1

[0067] Step 202, create a workspace:

[0068] Constraint equations are established based on the working range of the selected engineering components such as ball joints, Hooke's joints, servo cylinders, etc.

[0069] A series of coordinates in the workspace are obtained by scanning in the Cartesian coordinate system, and the leg length and the joint angles of the Hooke's joint and the spherical joint are obtained through the inverse kinematics model.

[0070] The leg lengths and joint angles obtained from kinematics are constrained in turn, and the points that meet the conditions are retained, and finally the working space of the mechanism is formed, such as Figure 6 shown.

[0071] Step 203, establish performance evaluation indicators:

[0072] 1. Workspace evaluation indicators:

[0073] After analysis, it is found that the shape of the working space of the mechanism in this scheme is a sphere with the loading rod as the radius, such as Figure 6 As shown in the figure, 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 a mechanism to resist deformation under external forces. Higher stiffness can ensure the stability of the overall structure of the mechanism during force application, which is crucial for the accuracy of load spectrum reproduction. To simplify the problem, assume that the dynamic platform and joints of the parallel mechanism are rigid bodies, and define the stiffness of the parallel mechanism as the branch stiffness k i The combined stiffness matrix K l =diag[k1,…,k6].

[0078]

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

[0080] The overall stiffness matrix K of the parallel mechanism is calculated in combination with the Jacobian matrix.

[0081] K=J T K l J

[0082] The current stiffness index includes evaluation by various methods such as eigenvalue, determinant, trace, etc. This application uses the most commonly used sum of the diagonal elements of the stiffness matrix to measure the overall stiffness, so the local stiffness performance index (LSI) is:

[0083]

[0084] 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, 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 =(τ1…τ6) 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 =(τ1…τ6) 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 In order 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 a training sample set, the above step 102 is replaced by steps 301 to 303:

[0094] Step 301: Design independent variables according to the size parameters. In this application, the radius of the moving platform and the static platform, the arrangement of the hinge points on the moving platform and the static platform, and the length of the legs and the length of the loading rod have a very important influence 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 indicators.

[0095] Step 302: In the independent variable space, the required fitting samples are constructed by the Latin Hypercube Sampling (LHS) method. First, uniform partitioning is performed in five dimensions, and uniform sampling is performed in each zone to ensure that the samples are evenly distributed in the design parameter space, thereby 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. Thus, 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 a mapping model, the above step 103 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 forward stepwise linear regression method through the basis functions and their products, and its form is as follows:

[0098]

[0099] h0(x1…x n )=1

[0100]

[0101] where s km = ±1, is the predicted value of the target variable, indicating the output of the MARS model. It consists of basis functions associated with M segments of sub-regions, where each segment of basis function is a univariate spline basis function s selected from the basis function set km The product of . is the intercept term of the model, estimated by the least squares method, is the mth segment basis function h m The coefficients of (x) are estimated by the least squares method, h0(X) is a constant term, usually 1, M is the number of basis functions, and h m(X) is the mth segment basis function, which constitutes the nonlinear part of the model, K m is the number of variables in the mth segment basis function, s km The value is ±1, which controls whether the basis function is increasing or decreasing. k,m is the k,mth component in the input vector X, representing the kth variable corresponding to the mth basis function, t km is the value of , indicating the cutting point, i.e. the dividing line, which determines the piecewise characteristics of the basis function at the point of , + indicates the positive partial function, defined as: [x] + =max(0,x).

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

[0103] In traditional methods, the distribution factors are 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 is required.

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

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

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

[0107] Assume i For variable x i The importance of

[0108]

[0109] Among them, M i Indicates that the variable x is included i The set of basis functions.

[0110] Step 402: In order to make the importance metrics comparable between different variables, the importance may be standardized.

[0111] This can be done by dividing the importance of each variable by the sum of the importance of all variables.

[0112]

[0113] Here, p is the total number of variables.

[0114] For independent variables with higher sensitivity, strengthening the local search capability can make the algorithm more concentrated in exploring the local range of the independent variables, which enhances the convergence of the algorithm. Therefore, a larger distribution factor should be set. For independent variables with lower sensitivity, poor global search capability will more easily lead to the problem of local optimal solution. Therefore, a smaller distribution factor needs to be set. Combined with the above analysis, the weighted vector v is defined, and the weighted distribution factor η is defined. q :

[0115]

[0116] η q =v·η

[0117] At this point, the sensitivity analysis and the design of distribution factors based on sensitivity are completed.

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

[0119] Step 501, generate an initial population: according to the defined independent variable space, randomly generate an initial population P0, the population size is M.

[0120] Step 502, evaluating the population: by using the mapping model, the fitness function value of each individual in the population is calculated, which greatly reduces the computational cost caused by scanning.

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

[0122] Step 504, generate a progeny 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, giving priority to individuals with low non-dominated rank and 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:

[0125]

[0126] 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]

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

[0128] Mutation: Perform mutation operations on offspring individuals to increase the diversity of solutions. Common mutation methods include polynomial mutation and Gaussian mutation. The specific formula is:

[0129] x' ik =x ik `+δ×(u k -l k );

[0130]

[0131] 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 ) / (xupper,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. Low η values ​​will produce larger δ, resulting in a longer mutation step and increased gene diversity. High β values ​​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 larger distribution factor to enhance the local search ability and avoid the destruction of excellent genes due to mutation and crossover. The independent variables that are not sensitive enough should be given a smaller distribution factor to increase their global search ability and make them have higher search efficiency.

[0134] Step 505, generate a combined population:

[0135] Combined population: The current population P t With the offspring population Q t Merge to generate the joint population R t , its size is 2M.

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

[0137] Step 506, select the next generation population: from the combined population R t Select the first M individuals as the next generation population P t+1 The selection process gives priority to the non-dominated ranks. If the number of individuals in a certain frontier exceeds the remaining quota, individuals are selected based on the embracement distance.

[0138] Step 507, terminate the iteration

[0139] The final Pareto solution set includes a group of mutually non-dominated solutions. In order to select the optimal solution, this application considers setting a weight vector for the three performance indicators.

[0140] v=(w1,w2,w3)

[0141] Choose a solution that the weight vector points to in the Pareto solution set, such as Figure 8 As shown, Figure 8 The xyz coordinates represent the performance indicators under the size parameters respectively. The independent variable parameters represented by the solution are used as the optimal parameters of this application, which can effectively guide the structural design and performance optimization of the vector loading calibration mechanism.

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

[0143] 1. The traditional loading mechanism dynamic platform and the loaded object are fixedly connected and the position and posture cannot be adjusted. This means that no matter what direction the vector force is applied, it is applied in the same position and posture. Different position and posture have different Jacobian matrices. This means that for the same vector force, there must be an optimal position and posture that can minimize the outrigger force. In view of this, the present application designs a structure that can adjust the position and posture for loading, so that loading can be achieved in the optimal position and posture for different vector forces.

[0144] 2. The traditional multi-objective optimization algorithm is performed on the workspace scatter points of the loading and calibration mechanism. Due to the complex kinematic model of the loading and calibration mechanism itself, it is very wasteful to directly calculate the global performance indicators from the workspace scatter points. At the same time, the traditional optimization scheme cannot effectively consider the characteristics between different optimization objectives, resulting in a waste of computational costs. For this reason, this application first establishes a spline regression model (i.e., a mapping model) for the workspace scatter points and the global performance indicators, and designs different weighted indicators for different global performance indicators through sensitivity analysis, which effectively reduces the computational cost.

[0145] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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, they should be considered to be within the scope of this specification.

[0146] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A vector loading calibration mechanism, It is 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 a 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.

2. The vector loading calibration mechanism according to claim 1, It is 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. A vector loading calibration system, It is characterized in that The vector loading calibration system comprises: a frame, a loading connection device and the vector loading calibration mechanism according to any one of claims 1 to 2; 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.

4. The vector loading calibration system according to claim 3, It is 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.

5. A parameter optimization method, It is characterized in that The parameter optimization method is applied to the vector loading calibration mechanism according to any one of claims 1 to 2, and the parameter optimization method 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 adopted to determine the parameter variables that optimize each performance evaluation index.

6. The parameter optimization method according to claim 5, It is characterized in that 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 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.

7. The parameter optimization method according to claim 5, It is 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.

8. The parameter optimization method according to claim 5, It is characterized in that The intelligent optimization algorithm is the NSGA-II algorithm.

9. The parameter optimization method according to claim 5 or 8, It is 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.

10. The parameter optimization method according to claim 9, It is 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 ).

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