Machine tool model correction analysis optimization method based on dynamic evolution point set

Abstract

The invention provides a machine tool model correction analysis optimization method based on a dynamics evolution point set, and belongs to the field of machine tool finite element analysis. Firstly, a finite element model of a machine tool is established; secondly, constructing an improved Kriging agent model based on a dynamic evolution point set; and then, optimizing machine tool identification parameters by adopting a heterogeneous comprehensive learning particle swarm optimization algorithm improved based on a dynamic evolution point set. Finally, the optimized machine tool recognition parameters are substituted into the machine tool Kriging agent model, and a corrected machine tool finite element model is obtained. According to the method, the problem that the original Kriging model information coverage degree is not enough can be solved; when the model correction problem of the machine tool is solved, the agent model with higher precision can be generated; a heterogeneous comprehensive learning particle swarm optimization algorithm is improved through a dynamic evolution point set, so that the problem of non-uniform point set distribution of a traditional algorithm is solved, model parameters can be quickly and accurately identified, and the purpose of efficiently correcting a machine tool model is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of finite element analysis of machine tools, and relates to a method for optimizing the correction analysis of a machine tool model based on a dynamic evolution point set. Background Art

[0002] Modeling a machine tool by finite element and performing numerical simulation analysis has become an important means for analyzing machine tool problems. When performing finite element modeling analysis on a machine tool, since bolts are usually used to connect the structures of the machine tool, the discontinuity between these structures determines that the machine tool cannot be simply regarded as integrally formed, and it is necessary to correct the stiffness parameters of the finite element model of the machine tool. Otherwise, it is impossible to accurately simulate and analyze the deformation of the structural joint surface. Therefore, parameter correction of the finite element model of the machine tool is an essential step. This is particularly crucial for high-precision numerical control machine tools because the stiffness deformation of the whole machine structure directly affects the machining accuracy and the stability of the machine tool.

[0003] Due to the sensitivity of machine tool design to calculation accuracy, the constructed surrogate model of the machine tool must meet the requirements of high precision. Currently, commonly used surrogate models include Gaussian process regression, neural network, Kriging model, etc. Among them, Gaussian process regression can handle non-linear relationships, provide uncertainty estimation, and the prediction results are smooth, which is suitable for situations where data points are sparse or there is noise. However, its computational complexity is relatively high, it is sensitive to the selection of kernel functions and the adjustment of hyperparameters, and its efficiency on large-scale data sets is low. The neural network has a strong non-linear fitting ability and feature learning ability, can handle complex input-output relationships, and has a certain robustness to noise and outliers. However, the neural network requires a large amount of data and computing resources for training, is sensitive to the initial weights, is prone to overfitting problems, and the interpretability of the model is poor. The Kriging model has the characteristics of high interpolation accuracy and good spatial smoothness, and is widely used, which is a good choice for constructing a high-precision surrogate model of a machine tool. However, the existing Kriging models mostly generate sample points by using random point sets or Latin hypercube point sets. Due to the randomness of point selection, the uniformity of the point sets is difficult to guarantee, and the information coverage degree is insufficient. And the accuracy of the surrogate model is related to the uniformity of the sample point set it uses. The better the uniformity of the sample point set used, the higher the accuracy of the generated surrogate model.

[0004] In addition, parameter identification is also an important part in the finite element model updating of machine tools. That is, by minimizing the error between the predicted response of the machine tool surrogate model and the true response of the measuring points on the machine tool, the key parameters in the machine tool can be identified, thereby improving the fitting accuracy of the finite element model of the machine tool. The parameter identification of the finite element model of the machine tool can essentially be regarded as a non-linear parameter optimization problem, and currently optimization algorithms are often used to solve it. In recent years, a batch of optimization algorithms with stronger search capabilities have emerged, such as the spider wasp optimization algorithm, the grey goose optimization algorithm, the heterogeneous comprehensive learning particle swarm optimization algorithm, etc. Among them, the heterogeneous comprehensive learning particle swarm optimization algorithm balances the global search and local search capabilities of the particle swarm algorithm and is one of the most excellent variants of the famous particle swarm algorithm. However, the heterogeneous comprehensive learning particle swarm optimization algorithm searches and optimizes by generating a random point set, and there is a drawback that it is difficult to effectively cover the search space due to the uneven distribution of the point set.

[0005] At present, some surrogate models and optimization algorithms are also adopted in the finite element analysis of most machine tools, but these methods basically solve the optimization of the structural parameters of the machine tool and do not consider the problem of machine tool model updating. For example, in the Chinese invention patent "Machine tool spindle structure parameter optimization method based on minimalist particle swarm optimization algorithm" (application number 201810612782.2), this patent uses the minimalist particle swarm optimization algorithm to optimize the parameters of the machine tool spindle structure, does not consider the model updating of the machine tool spindle structure, and although the minimalist particle swarm optimization algorithm improves the efficiency, its search ability also decreases, resulting in the inability to find the global optimal solution. In the Chinese invention patent "A method for optimizing the internal structure design of a machine tool bed" (application number 201410452765.9), this patent establishes a surrogate model of the machine tool bed and realizes the optimization of the internal structure of the machine tool bed, but does not consider the problem of model updating of the machine tool bed. Summary of the Invention

[0006] In view of the main problems existing in the prior art, the present invention proposes a machine tool model updating analysis and optimization method based on a dynamically evolving point set to solve the problem of machine tool model updating. The parameter correction of the finite element model of the machine tool by the present invention can discover potential problems in the early design stage, avoid expensive modifications in the later stage, and save costs and time. The present invention solves the problem that the original Kriging model has insufficient information coverage by constructing a Kriging surrogate model improved based on a dynamically evolving point set. When solving the problem of machine tool model updating, a surrogate model with higher accuracy can be generated. And by improving the heterogeneous comprehensive learning particle swarm optimization algorithm with a dynamically evolving point set, the drawback that the original heterogeneous comprehensive learning particle swarm optimization algorithm has an uneven point set distribution and is difficult to effectively cover the search space is solved, and at the same time, the model parameters can be quickly and accurately identified, achieving the purpose of efficient machine tool model updating.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for optimizing the modification analysis of a machine tool model based on a dynamically evolving point set. The method for optimizing the modification analysis of the machine tool model is as follows: First, establish a finite element model of the machine tool; secondly, construct a Kriging surrogate model improved based on the dynamically evolving point set. Then, use the heterogeneous comprehensive learning particle swarm optimization algorithm improved based on the dynamically evolving point set to optimize the identified parameters of the machine tool. Finally, substitute the optimized identified parameters of the machine tool into the Kriging surrogate model of the machine tool to obtain the modified finite element model of the machine tool. It includes the following steps:

[0009] The first step is to establish a finite element model of the machine tool. Specifically:

[0010] Step 1.1, import the existing machine tool model into the 3D modeling software to obtain the 3D model of the machine tool; or model the 3D model of the machine tool according to the engineering drawings to obtain the 3D model of the machine tool.

[0011] Step 1.2, import the 3D model of the machine tool into the finite element analysis software to establish the finite element model of the machine tool. Set the material properties of the machine tool in the finite element analysis software, and apply constraints and loads to the finite element model of the machine tool at the corresponding positions according to the constraints and loads received by the machine tool.

[0012] Step 1.3, according to the actual engineering requirements, determine the identified parameters of the machine tool in the finite element model and the range of the identified parameters of the machine tool.

[0013] The second step is to construct a Kriging surrogate model of the machine tool improved based on the dynamically evolving point set. Specifically:

[0014] Step 2.1, obtain an initial input sample set suitable for constructing the Kriging surrogate model of the machine tool based on the dynamically evolving point set. The initial input sample set is the set of all identified parameters of the machine tool in Step 1.3. Combine all the identified parameters to form the identified parameter vector ξ of the machine tool, that is, the input sample. Specifically as follows:

[0015] First, let the identified parameter vector ξ of the machine tool be within the hypercube Φ = [0, 1] S where S represents the number of identified parameters of the machine tool.

[0016] Secondly, within the hypercube Φ = [0, 1] S perform multiple random samplings on the identified parameters in the identified parameter vector ξ of the machine tool to form a number of input samples. Combine the above-mentioned number of input samples to form an input sample set, defined as Α S×X = {ξ1, ξ2, …, ξ X}, where X represents the number of samples, ξ1 represents the first sample, ξ2 represents the second sample, ξ XIf the Xth sample is represented, then the coordinates of the ith sample are ξ i =(ξ i,1 , ξ i,2 , …, ξ i,S ), where ξ i,1 represents the value of the first recognition parameter in the ith sample, ξ i,2 represents the value of the second recognition parameter in the ith sample, ξ i,S represents the value of the Sth recognition parameter in the ith sample.

[0017] Again, map and transform the values of the recognition parameters in each sample into the values within the range of the original recognition parameters according to the range of the machine tool recognition parameters in Step 1.3.

[0018] Finally, according to the dynamic evolution method, iterate the input sample set Α S×X to obtain the dynamic evolution point set, and use it as the initial input sample set of the machine tool Kriging surrogate model.

[0019] Step 2.2, according to the actual situation of the machine tool, arrange a number of measuring points on the machine tool. The measuring points can measure the response of the point when the machine tool is under constraints and loads. In the finite element model of the machine tool, arrange measuring points at the same positions, and calculate the responses of all measuring points through finite element software. Use the calculated response values of the measuring points as the output set of the machine tool Kriging surrogate model.

[0020] Step 2.3, the problem of the machine tool model parameters based on the Kriging surrogate model is expressed as:

[0021]

[0022] where f(ξ) represents that the problem of the machine tool model parameters can be expressed as a function of the machine tool recognition parameter vector ξ, is the response vector of the machine tool predicted by the Kriging surrogate model; ξ is the machine tool recognition parameter vector, obtained from the initial input sample set in Step 2.1; β is the response vector of the machine tool measuring points calculated by finite element software, that is, obtained from the output set of the Kriging surrogate model in Step 2.2.

[0023] Complete the construction of the machine tool Kriging surrogate model improved based on the dynamic evolution point set according to the initial input sample set and the output set of the Kriging surrogate model.

[0024] Thirdly, use the heterogeneous comprehensive learning particle swarm optimization algorithm improved based on the dynamic evolution point set to optimize the machine tool recognition parameters. Specifically:

[0025] Step 3.1, improve the heterogeneous comprehensive learning particle swarm optimization algorithm: specifically as follows:

[0026] Step 3.1.1, define the population size in the heterogeneous comprehensive learning particle swarm optimization algorithm as Y, the maximum number of iterations as N, and the feasible solution as where z i represents the lower bound of the range in the feasible solution, represents ξ in the feasible solution i 0 the upper bound of the range; S represents the spatial dimension, which has the same meaning as in Step 2.1.

[0027] Define the population of the heterogeneous comprehensive learning particle swarm optimization algorithm as:

[0028]

[0029] where n is the iteration number of the population; ξ n,1 is the feasible solution after n iterations of the first population; ξ n,2 is the feasible solution after n iterations of the second population; ξ n,Y is the feasible solution after n iterations of the Yth population.

[0030] The initial population in the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is represented as:

[0031]

[0032] where z = (z1, z2, …, z S ) T , z represents the lower bound vector of the feasible solution range, z1 represents the lower bound of the range in the feasible solution, z S represents the lower bound of the range in the feasible solution, z S represents the lower bound of the range in the feasible solution; represents the upper bound vector of the feasible solution range, represents the upper bound of the range in the feasible solution, represents the upper bound of the range in the feasible solution, represents the upper bound of the range in the feasible solution; represents the Kronecker product; represents the Hadamard product; I Y is a vector with all elements being 1, with a size of 1 × Y; λ0 is a random number matrix uniformly distributed between 0 and 1, and the size of the random number matrix is S × Y.

[0033] The present invention replaces the random number matrix λ0 of the initial population based on the dynamically evolving point set to obtain the improved initial population as follows:

[0034]

[0035] Among them, L 0 represents a dynamically evolving point set of size S×Y, obtained by the dynamic evolution method; I N represents a vector with all elements being 1, of size 1×N.

[0036] Step 3.1.2: Divide the population into an exploratory sub-population and an exploitative sub-population, with the sizes of the two sub-populations being Y1 and Y2 respectively, and Y = Y1 + Y2.

[0037] The expression of the velocity update formula for the exploratory sub-population of the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is:

[0038]

[0039] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; d n is the self-learning factor of the exploratory sub-population; λ n,1,i is a random number vector uniformly distributed between 0 and 1, of size S×1; l n,i is a random comprehensive learning vector, enabling the i-th particle to learn the best experience of all other particles; ξ n,i represents the feasible solution of the i-th population after the n-th iteration; i represents the population number; Y1 represents the size of the exploratory sub-population.

[0040] The expression of the velocity update formula for the exploitative sub-population of the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is:

[0041]

[0042] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; e n,1 = 2.5 - 2n / N, e n,1 is the first self-learning factor in the exploitative sub-population, n represents the number of iterations, N represents the maximum number of iterations; λ n,2,i is a random number matrix uniformly distributed between 0 and 1, with the matrix size of S×1; l n,iis a random comprehensive learning vector, ξ n,i is expressed as the feasible solution after the n-th iteration of the i-th population; e n,2 = 0.5 + 2n / N, e n,2 is the second self-learning factor in the exploitative sub-population; λ n,3,i represents a random number matrix uniformly distributed between 0 and 1, with the matrix size of S×1; ξ n,best = argmin(f(ξ n,i ))), 1 ≤ i ≤ Y, ξ n,best represents the optimal feasible solution after the n-th iteration; f(ξ n,i ) is expressed as the function form of the feasible solution ξ after the n-th iteration of the i-th population n,i ; i represents the population number; Y represents the number of populations; Y1 represents the size of the exploratory sub-population.

[0043] The present invention improves the exploratory sub-population based on the kinetic evolution point set:

[0044]

[0045] where, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; d n is the self-learning factor of the exploratory sub-population; represents the kinetic evolution point set of size S×1 of the i-th population, obtained by the kinetic evolution method; l n,i is a random comprehensive learning vector, enabling the i-th particle to learn the best experience of all other particles; ξ n,i is expressed as the feasible solution after the n-th iteration of the i-th population; i represents the population number; Y1 represents the size of the exploratory sub-population.

[0046] The present invention also improves the exploitative sub-population based on the kinetic evolution point set:

[0047]

[0048] where, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; v n,i is the velocity of the i-th population at the n-th iteration; g n is the inertia coefficient; e n,1 = 2.5 - 2n / N, e n,1 is the first self-learning factor in the exploitative sub-population, n represents the number of iterations, and N represents the maximum number of iterations; Denote the dynamic evolution point set of size \(S\times1\) for the \(i\)-th population, obtained by the dynamic evolution method; \(l\) n,i is a random comprehensive learning vector, enabling the \(i\)-th particle to learn the best experience of all other particles; \(\xi\) n,i Denote the feasible solution after \(n\) iterations for the \(i\)-th population; \(e\) n,2 \(= 0.5 + 2n / N\), \(e\) n,2 is the second self-learning factor for the exploitation sub-population; \(\lambda\) n,3i Denote a random number matrix uniformly distributed between 0 and 1, with matrix size \(S\times1\) \(\xi\) n,best \(= \arg\min(f(\xi\) n,i ))), \(1\leq i\leq Y\), \(\xi\) n,best Denote the optimal feasible solution after the \(n\)-th iteration; \(f(\xi\) n,i ) Denote the feasible solution after \(n\) iterations for the \(i\)-th population \(\xi\) n,i The functional form of; \(i\) represents the population number; \(Y\) represents the number of populations; \(Y1\) represents the size of the exploration sub-population;

[0049] Step 3.2, according to the number of machine tool identification parameters obtained in Step 1.3, confirm the dimension \(S\) of the problem; Set the number of populations as \(Y\), the number of exploration sub-population and exploitation sub-population \(Y1\) and \(Y2\), and the maximum number of iterations as \(N\). Determine \(z\) according to the range of machine tool identification parameters obtained in Step 1.3 and

[0050] Step 3.3, obtain the initial population \(\varPsi_0\) through formula (4).

[0051] Step 3.4, take the least square error between the machine tool response vector predicted by the machine tool Kriging surrogate model and the true response vector obtained from the measuring points as the optimization objective function:

[0052]

[0053] where, \(\beta\) real Denote the true machine tool response vector obtained from the measuring points; is the machine tool response vector predicted by the Kriging surrogate model; \(\xi\) is the machine tool identification parameter vector, which can be obtained from the initial input sample set in Step 2.1.

[0054] Step 3.5, obtain the exploration sub-population and exploitation sub-population through formula (7) and formula (8).

[0055] Step 3.6, iteration formula:

[0056] \(\xi\) n+1,i \(= \xi\) n,i + v n+i ), \(1\leq i\leq Y\) (10);

[0057] Iterate the machine tool identification parameters according to formula (10) until the number of iterations \(n = N\), and obtain the optimized machine tool identification parameters.

[0058] Step 4: Substitute the machine tool identification parameters optimized in step 3.6 into the machine tool Kriging surrogate model in step 2 to obtain the corrected machine tool finite element model.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] (1) The present invention improves the traditional Kriging surrogate model based on the dynamic evolution point set. Compared with the original Kriging surrogate model, a machine tool Kriging surrogate model with higher accuracy is constructed to replace the solution of the machine tool finite element equation, reducing the computational amount of machine tool model correction. It provides a suitable surrogate model for the machine tool model correction analysis and optimization method based on the dynamic evolution point set.

[0061] (2) The present invention improves the heterogeneous comprehensive learning particle swarm optimization algorithm based on the dynamic evolution point set, which can improve the optimization speed, quickly and accurately identify the model parameters, and achieve the purpose of efficient machine tool model correction. It provides a suitable optimization algorithm for the machine tool model correction analysis and optimization method based on the dynamic evolution point set.

[0062] (3) The present invention adopts the traditional Kriging surrogate model improved by the dynamic evolution point set and the heterogeneous comprehensive learning particle swarm optimization algorithm improved by the dynamic evolution point set, successfully solves the machine tool model correction analysis problem, and establishes a machine tool model correction analysis and optimization method based on the dynamic evolution point set. Description of the Drawings

[0063] Figure 1 is a flow chart of the machine tool finite element model correction and optimization method based on the dynamic evolution point set. Detailed Embodiments

[0064] The present invention will be described in detail below with reference to the drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives the detailed implementation manner and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0065] Refer to Figure 1 the flow chart of the machine tool finite element model correction and optimization method based on the dynamic evolution point set to correct the machine tool model. The specific steps are as follows:

[0066] Step 1: Establish a finite element model of the machine tool. Specifically:

[0067] Step 1.1: Import the existing machine tool model into the 3D modeling software to obtain the machine tool 3D model.

[0068] Step 1.2, Import the 3D model of the machine tool into the finite element analysis software to establish the finite element model of the machine tool. Set the material properties of the machine tool in the finite element analysis software, and apply constraints and loads to the finite element model of the machine tool at the corresponding positions according to the constraints and loads received by the machine tool.

[0069] Step 1.3, According to the actual engineering requirements, use the stiffness coefficient at the bolt connection in the machine tool as the identification parameter. There are a total of 8 identification parameters, and the distribution range of the stiffness coefficients at all bolt connections in the machine tool is [3E9, 1E10] N / m.

[0070] Second step, Construct a Kriging surrogate model of the machine tool improved based on the dynamic evolution point set. Specifically:

[0071] Step 2.1, Obtain the initial input sample set suitable for constructing the Kriging surrogate model of the machine tool based on the dynamic evolution point set. The initial input sample set is the set of all machine tool identification parameters in Step 1.3. Specifically as follows: Combine all the identification parameters to form the machine tool identification parameter vector ξ, that is, the input sample.

[0072] First, let the machine tool identification parameter vector ξ be within the hypercube Φ = [0, 1] S where S represents the number of machine tool identification parameters.

[0073] Secondly, within the hypercube Φ = [0, 1] S perform multiple random samplings on the identification parameters in the vector ξ to form several input samples. Combine the above several input samples to form the input sample set Α 8×100 = {ξ1, ξ2, …, ξ 100}, 100 represents the number of samples, ξ1 represents the first sample, ξ2 represents the second sample, ξ X represents the 100th sample, then the coordinates of the i-th sample are ξ i = (ξ i,1 , ξ i,2 , …, ξ i,8 ), where ξ i,1 represents the value of the first identification parameter in the i-th sample, ξ i,2 represents the value of the second identification parameter in the i-th sample, ξ i,8 represents the value of the S-th identification parameter in the i-th sample.

[0074] Again, map and transform the values of the identification parameters in each sample into the values within the range of the original identification parameters according to the range of the machine tool identification parameters in Step 1.3, that is, ξ i = (1E10 - 3E9)ξ i + 3E9.

[0075] Finally, according to the dynamic evolution method, for the input sample set Α8×100 Iteration is carried out to obtain the set of dynamic evolution points, which is used as the initial input sample set of the machine tool Kriging surrogate model.

[0076] Step 2.2: According to the actual situation of the machine tool, 14 measuring points are arranged on the machine tool. All the measuring points can measure the response of the point under the constraints and loads of the machine tool. In the finite element model of the machine tool, measuring points are arranged at the same positions, and the responses of all the measuring points are calculated by finite element software. The response values of the calculated measuring points are used as the output set of the machine tool Kriging surrogate model.

[0077] Step 2.3: The problem of the machine tool model parameters based on the Kriging surrogate model is expressed as:

[0078]

[0079] Among them, f(ξ) represents that the problem of the machine tool model parameters can be expressed in the form of a function of the machine tool identification parameter vector ξ. is the predicted machine tool response vector by the Kriging surrogate model; ξ is the machine tool identification parameter vector, obtained from the initial input sample set in Step 2.1; β is the machine tool measuring point response vector calculated by finite element software, that is, obtained from the output set of the Kriging surrogate model in Step 2.2.

[0080] Based on the initial input sample set and the output set of the Kriging surrogate model, the construction of the improved machine tool Kriging surrogate model based on the dynamic evolution point set is completed.

[0081] The third step is to optimize the stiffness coefficient of the bolt connection of the machine tool by using the improved heterogeneous comprehensive learning particle swarm optimization algorithm based on the dynamic evolution point set. Specifically:

[0082] Step 3.1: Improve the heterogeneous comprehensive learning particle swarm optimization algorithm as follows:

[0083] Step 3.1.1: Define the population size in the heterogeneous comprehensive learning particle swarm optimization algorithm as Y = 100, the maximum number of iterations as N = 1000, and the feasible solution as Among them z i represents the lower bound of the range in the feasible solution, represents the upper bound of the range in the feasible solution; 8 represents the spatial dimension, which has the same meaning as in Step 2.1.

[0084] Define the population of the heterogeneous comprehensive learning particle swarm optimization algorithm as:

[0085]

[0086] Among them, n is the iteration number of the population; ξ n,1is the feasible solution after n iterations of the first population; ξ n,2 is the feasible solution after n iterations of the second population; ξ n,100 is the feasible solution after n iterations of the 100th population.

[0087] The initial population in the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is expressed as:

[0088]

[0089] where z = (z1, z2, …, z8) T , z represents the lower bound vector of the feasible solution range, z1 represents the lower bound of the range in the feasible solution, and z8 represents the lower bound of the range in the feasible solution, and z8 represents the lower bound of the range in the feasible solution; represents the upper bound vector of the feasible solution range, represents the upper bound of the range in the feasible solution, represents the upper bound of the range in the feasible solution, represents the upper bound of the range in the feasible solution; represents the Kronecker product; represents the Hadamard product; I Y is a vector with all elements being 1, with a size of 1×100; λ0 is a random number matrix uniformly distributed between 0 and 1, and the size of the random number matrix is 8×100.

[0090] In the present invention, the random number matrix λ0 of the initial population is replaced based on the dynamic evolution point set, and the improved initial population is:

[0091]

[0092] where L 0 represents a dynamic evolution point set with a size of 8×100, obtained by the dynamic evolution method; I N represents a vector with all elements being 1, with a size of 1×1000.

[0093] Step 3.1.2: Divide the population into an exploration sub-population and an exploitation sub-population. The sizes of the two sub-populations are Y1 = 40 and Y2 = 60 respectively, and Y = Y1 + Y2 = 100.

[0094] The expression of the velocity update formula for the exploration sub-population in the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is:

[0095]

[0096] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; d n is the self-learning factor of the exploratory sub-population; λ n,1,i is a random number vector uniformly distributed between 0 and 1, with a size of 8×1; l n,i is a random comprehensive learning vector, enabling the i-th particle to learn the best experience of all other particles; ξ n,i represents the feasible solution after the n-th iteration of the i-th population; i represents the population number.

[0097] The expression of the velocity update formula for the development sub-population of the traditional heterogeneous comprehensive learning particle swarm optimization algorithm is:

[0098]

[0099] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; e n,1 = 2.5 - 2n / 1000, e n,1 is the first self-learning factor in the development sub-population, n represents the number of iterations, 1000 represents the maximum number of iterations; λ n,2,i is a random number matrix uniformly distributed between 0 and 1, with a matrix size of 8×1; l n,i is a random comprehensive learning vector, ξ n,i represents the feasible solution after the n-th iteration of the i-th population; e n,2 = 0.5 + 2n / 1000, e n,2 is the second self-learning factor in the development sub-population; λ n,3,i represents a random number matrix uniformly distributed between 0 and 1, with a matrix size of 8×1; ξ n,best = argmin(f(ξ n,i )), 1 ≤ i ≤ 100, ξ n,best represents the optimal feasible solution after the n-th iteration; f(ξ n,i ) represents the function form of the feasible solution ξ n,i after the n-th iteration of the i-th population; i represents the population number.

[0100] The present invention improves the exploratory sub-population based on the dynamic evolution point set:

[0101]

[0102] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; g n is the inertia coefficient; v n,i is the velocity of the i-th population at the n-th iteration; d n is the self-learning factor of the exploratory sub-population; represents a kinetic evolution point set of size 8×1 for the i-th population, obtained by the kinetic evolution method; l n,i is a random comprehensive learning vector that enables the i-th particle to learn the best experience of all other particles; ξ n,i represents the feasible solution after the n-th iteration of the i-th population; i represents the population number.

[0103] The present invention also improves the exploitative sub-population based on the kinetic evolution point set:

[0104]

[0105] Among them, v n+1,i represents the velocity of the i-th population at the (n + 1)-th iteration; v n,i is the velocity of the i-th population at the n-th iteration; g n is the inertia coefficient; e n,1 = 2.5 - 2n / 1000, e n,1 is the first self-learning factor in the exploitative sub-population, n represents the number of iterations, and 1000 represents the maximum number of iterations; represents a kinetic evolution point set of size 8×1 for the i-th population, obtained by the kinetic evolution method; l n,i is a random comprehensive learning vector that enables the i-th particle to learn the best experience of all other particles; ξ n,i represents the feasible solution after the n-th iteration of the i-th population; e n,2 = 0.5 + 2n / 1000, e n,2 is the second self-learning factor in the exploitative sub-population; λ n,3i, represents a random number matrix uniformly distributed between 0 and 1, with a matrix size of 8×1 ξ n,best = argmin(f(ξ n,i ))), 1 ≤ i ≤ 100, ξ n,best represents the optimal feasible solution after the n-th iteration; f(ξ n,i ) represents the function form of the feasible solution ξ n,i after the n-th iteration of the i-th population; i represents the population number.

[0106] Step 3.2. According to the number of machine tool identification parameters obtained in Step 1.3, confirm that the dimension of the problem S = 8; set the population size to Y = 100, the sizes of the exploratory sub-population and the exploitative sub-population to Y1 = 40 and Y2 = 60 respectively, and the maximum number of iterations to N = 1000. Determine z = [3E9, 3E9, …, 3E9] based on the range of the machine tool identification parameters obtained in Step 1.3 and

[0107] Step 3.3. Obtain the initial population Ψ0 through formula (4).

[0108] Step 3.4. Take the least squares error between the machine tool response vector predicted by the machine tool Kriging surrogate model and the true response vector obtained from the measurement points as the optimization objective function:

[0109]

[0110] where β real represents the true response vector of the machine tool obtained from the measurement points; is the machine tool response vector predicted by the Kriging surrogate model; ξ is the machine tool identification parameter vector, which can be obtained from the initial input sample set in Step 2.1.

[0111] Step 3.5. Obtain the exploratory sub-population and the exploitative sub-population through formula (7) and formula (8).

[0112] Step 3.6. Iterative formula:

[0113] ξ n+1,i = ξ n,i + v n+i , 1 ≤ i ≤ Y (10);

[0114] Iterate the machine tool identification parameters according to formula (10) until the number of iterations n = 1000, and obtain the optimized machine tool identification parameters.

[0115] Fourth step. Substitute the machine tool identification parameters optimized in Step 3.6 into the machine tool Kriging surrogate model in the second step to obtain the corrected machine tool finite element model.

[0116] The above embodiments only represent the implementation modes of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A machine tool model correction analysis and optimization method based on dynamic evolution point set, characterized in that: The machine tool model correction analysis and optimization method comprises the following steps: The first step is to establish a finite element model of the machine tool to obtain the machine tool identification parameters and the range of the machine tool identification parameters; The second step is to construct a machine tool Kriging proxy model based on the improved dynamic evolution point set; In the third step, the machine tool identification parameters are optimized by using the heterogeneous comprehensive learning particle swarm optimization algorithm based on the improved dynamic evolution point set; In the fourth step, the machine tool identification parameters obtained by optimization in the third step are substituted into the machine tool Kriging proxy model in the second step to obtain the modified machine tool finite element model.

2. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 1 is characterized in that: The specific steps of the first step are as follows: Step 1.1, importing an existing machine tool model into a 3D modeling software to obtain a 3D model of the machine tool; or modeling the 3D model of the machine tool according to the engineering drawing to obtain a 3D model of the machine tool; Step 1.2, import the three-dimensional model of the machine tool into the finite element analysis software to establish the finite element model of the machine tool; set the material properties of the machine tool in the finite element analysis software, and apply constraints and loads to the finite element model of the machine tool at corresponding positions according to the constraints and loads of the machine tool; Step 1.3, according to the actual engineering requirements, determine the machine tool identification parameters of the finite element model and the range of the machine tool identification parameters.

3. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 1 is characterized in that: The specific steps of the second step are as follows: Step 2.1, based on the dynamic evolution point set, an initial input sample set suitable for constructing a machine tool Kriging proxy model is obtained; the initial input sample set is a set of all machine tool identification parameters in the first step; Step 2.2, according to the actual situation of the machine tool, a number of measuring points are arranged on the machine tool, and the measuring points can measure the response of the point under the constraint and load of the machine tool; in the finite element model of the machine tool, the measuring points are arranged at the same position, and the response of all the measuring points is calculated by the finite element software; the response values ​​of the calculated measuring points are used as the output set of the machine tool Kriging proxy model; Step 2.3, the machine tool model parameter problem based on the Kriging proxy model is expressed as: Among them, f(ξ) represents the machine tool model parameter problem and can be expressed as the machine tool identification parameter vector ξ The functional form of is the machine tool response vector predicted by the Kriging proxy model; ξ is the machine tool identification parameter vector, obtained from the initial input sample set in step 2.1; β is the machine tool measurement point response vector calculated by the finite element software, obtained from the Kriging proxy model output set in step 2.2; The construction of the machine tool Kriging proxy model based on the improved dynamic evolution point set is completed according to the initial input sample set and the Kriging proxy model output set.

4. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 1 is characterized in that: In step 2.1, the initial input sample set of the machine tool Kriging proxy model is constructed, and the specific process is as follows: All identification parameters are combined to form a machine tool identification parameter vector ξ, i.e., the input sample; First, let the machine tool identification parameter vector ξ be in the hypercube Φ = [0,1] S In, S represents the number of machine tool identification parameters; Secondly, in the hypercube Φ=[0,1] S Within, the identification parameters in the machine tool identification parameter vector ξ are randomly sampled multiple times to form a number of input samples; the above-mentioned several input samples are combined to form an input sample set, which is defined as Α S×X ={ξ1,ξ2,…,ξ X }, where X represents the number of samples, ξ1 represents the first sample, ξ2 represents the second sample, ξ X represents the Xth sample, then the coordinate of the i-th sample is ξ i =(ξ i,1 ,ξ i,2 ,…,ξ i,S ), where ξi,1 represents the value of the first identification parameter in the i-th sample, ξ i,2 represents the value of the second identification parameter in the i-th sample, ξ i,S represents the value of the Sth identification parameter in the i-th sample; Again, the value of the identification parameter in each sample is converted into a value within the original identification parameter range according to the range mapping of the machine tool identification parameter in step 1.3; Finally, according to the dynamic evolution method, the input sample set Α S×X Iterations are performed to obtain a set of dynamic evolution points, which are used as the initial input sample set of the machine tool Kriging proxy model.

5. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 3 is characterized in that: The specific steps of the third step are as follows: Step 3.1, improve the heterogeneous comprehensive learning particle swarm optimization algorithm; Step 3.2, according to the number of machine tool identification parameters, determine the dimension S of the problem; set the population size to Y, the number of exploration sub-populations and development sub-populations to Y1 and Y2, and the maximum number of iterations to N; determine z and Step 3.3, obtain the initial population Ψ0 through step 3.1; Step 3.4, the least squares error between the machine tool response vector predicted by the machine tool Kriging proxy model and the actual response vector obtained from the measuring point is used as the optimization objective function: Among them, β real Represents the real response vector of the machine tool obtained at the measuring point; is the machine tool response vector predicted by the Kriging proxy model; ξ is the machine tool identification parameter vector, obtained from the initial input sample set in step 2.1; Step 3.5, obtaining the exploration sub-population and the development sub-population through the heterogeneous comprehensive learning particle swarm optimization algorithm improved in step 3.1; Step 3.6, iterative formula: x n+1,i =ξ n,i +v n+i ,1≤i≤Y (10) The machine tool identification parameters are iterated according to formula (10) until n=N, and the optimized machine tool identification parameters are obtained.

6. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 5 is characterized in that: In step 3.1, the heterogeneous comprehensive learning particle swarm optimization algorithm is improved as follows: Step 3.1.1, define the population size in the heterogeneous comprehensive learning particle swarm optimization algorithm as Y, the maximum number of iterations as N, and the feasible solution as in z i Indicates a feasible solution The lower bound of the range, Indicates a feasible solution The upper limit of the range; S represents the spatial dimension and has the same meaning as step 2.1; The population of the heterogeneous comprehensive learning particle swarm optimization algorithm is defined as: Where n is the number of iterations of the population; ξ n,1 is the feasible solution of the first population after n iterations; ξ n,2 is the feasible solution of the second population after n iterations; ξ n,Y is the feasible solution of the Yth population after n iterations; Based on the dynamic evolution point set, the random number matrix λ0 of the initial population is replaced, and the improved initial population Ψ0 is obtained as follows: Where z=(z1,z2,…,z S ) T , z represents the lower bound vector of the feasible solution range, z1 represents the feasible solution The lower bound of the range, z S Indicates a feasible solution The lower bound of the range, z S Indicates a feasible solution The lower bound of the range; represents the upper bound vector of the feasible solution range, Indicates a feasible solution The upper bound of the range, Indicates a feasible solution The upper bound of the range, Indicates a feasible solution The upper bound of the range; represents the Kronecker product; represents the Hadamard product; L 0 represents a set of dynamic evolution points of size S×Y, obtained by the dynamic evolution method; I N It means that each element is 1 and the size is 1×N; Step 3.1.2, divide the population into an exploratory subpopulation and an exploitative subpopulation. The sizes of the two subpopulations are Y1 and Y2, respectively, and Y = Y1 + Y2; Improve the exploratory subpopulation based on the dynamic evolution point set: Among them, v n+1,i represents the speed of the ith population at the n+1th iteration; g n is the inertia coefficient; v n,i is the speed of the ith population at the nth iteration; d n is the self-learning factor of the exploratory subpopulation; represents the set of dynamic evolution points of the i-th population with a size of S×1, obtained by the dynamic evolution method; l n,i is a random comprehensive learning vector that enables the i-th particle to learn the best experience of all other particles; ξ n,i It represents the feasible solution of the ith population after n iterations; i represents the population number; Y1 represents the size of the exploratory subpopulation; Improve the development subpopulation based on the dynamic evolution point set: Among them, v n+1,i represents the velocity of the ith population at the n+1th iteration; v n,i is the speed of the ith population at the nth iteration; g n is the inertia coefficient; e n,1 =2.5-2n / N,e n,1 is the first self-learning factor of the development subpopulation, n represents the number of iterations, and N represents the maximum number of iterations; represents the set of dynamic evolution points of the i-th population with a size of S×1, obtained by the dynamic evolution method; l n,i is a random comprehensive learning vector that enables the i-th particle to learn the best experience of all other particles; ξ n,i It is represented as the feasible solution of the ith population after n iterations; e n,2 =0.5+2n / N,e n,2 is the second self-learning factor of the development subpopulation; n,3,i Represents a random number matrix uniformly distributed between 0 and 1, with a matrix size of S×1ξ n,best =argmin(f(ξ n,i )),1≤i≤Y,ξ n,best represents the optimal feasible solution after the nth iteration; f(ξ n,i ) is represented as the feasible solution ξ of the i-th population after n iterations n,i Function form; i represents the population number; Y represents the population size; Y1 represents the size of the exploratory subpopulation.

7. The machine tool model correction analysis and optimization method based on dynamic evolution point set according to claim 6 is characterized in that: In step 3.5, the exploration sub-population and the development sub-population are obtained by formula (7) and formula (8).

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