Numerical control machine tool spindle thermal error modeling method of multi-innovation LM support vector machine

Abstract

The invention provides a numerical control machine tool spindle thermal error modeling method of a multi-innovation LM support vector machine, and belongs to the technical field of numerical control machine tool spindle thermal error modeling. The technical problem that real-time monitoring and feedback of the thermal error of the precise numerical control machine tool spindle are not timely is solved. Comprising the following steps: 1) constructing a numerical control machine tool spindle thermal error model based on a support vector machine so as to finally fit feedback output of feature point temperature-spindle thermal errors; and step 2) constructing a multi-innovation adaptive LM method for estimating parameters of a support vector machine model. The method has the advantages that the method has ideal engineering application value based on the multi-information adaptive LM support vector machine regression strategy, system data are fully utilized, the anti-noise interference capability is enhanced, and the identification precision of the algorithm is improved.

Description

Technical Field

[0001] The invention relates to the technical field of modeling of thermal errors of spindles of numerically controlled machine tools, and in particular to a method for modeling thermal errors of spindles of numerically controlled machine tools using a multi-innovation LM support vector machine. Background Art

[0002] At present, in the field of spindle thermal error control, commonly used modeling techniques include multiple linear regression (MLR), time series analysis (TS), artificial neural network (ANN), support vector machine regression (SVR) and other methods. Among them, the use of multiple linear regression technology to construct a thermal error model and implement a thermal error compensation strategy based on it can significantly reduce the maximum error amplitude caused by temperature changes. Compared with other methods, SVR technology shows excellent prediction accuracy and strong robustness when processing small sample experimental data modeling, so it is particularly suitable for spindle thermal error modeling. The uneven distribution of heat generated by the internal heat source of the machine tool is the root cause of the thermal error. In order to effectively suppress thermal errors, establishing a circulating cooling system to remove the accumulated heat of the heat-generating components has become an important solution and plays a key role in solving the problem of machine tool thermal errors.

[0003] At a time when science and technology are advancing rapidly, support vector machines (SVMs) as a generalized linear classifier for supervised learning have entered people's field of vision and have been widely used in many fields, including but not limited to classification, regression, anomaly detection, cluster analysis, etc. Support vector machines (SVMs) are an important method in the field of machine learning. They aim to construct an optimal hyperplane to achieve data classification or regression prediction. Recently, the paper Handling imbalanced classification problems with support vector machines via evolutionary bilevel optimization studied a solution to the imbalance problem of support vector machines using an evolutionary bilevel optimization algorithm; the paper Parametric non-parallel support vector machines for pattern classification derived a parameterized non-parallel support vector machine for binary pattern classification of large-scale modules. Analysis and comparison of the above literature shows that SVM has many advantages such as obtaining the global optimal solution and good model robustness. However, these applications usually involve a large amount of high-dimensional data, and the distribution of data points is often complex and nonlinear, which brings difficulties to data processing. Therefore, further research is still needed for nonlinear system identification. At the same time, in view of the high computational complexity of support vector machines and their sensitivity to noise and outliers, the present invention adopts the concept of Levenberg-Marquardt (LM) iteration, and improves the algorithm by introducing multiple innovation identification strategies and adaptive damping factors, so as to increase the convergence speed and numerical stability in practical applications.

[0004] The multi-innovation strategy can enrich system data by adding prior information to parameter estimation. Compared with the traditional single-innovation algorithm, the multi-innovation algorithm has significant advantages in improving data utilization efficiency, improving algorithm performance, enhancing robustness and adaptability, and optimizing parameter identification. Therefore, when the paper Establishment and identification of MIMO fractional Hammerstein model with colored noise for PEMFC system introduces multi-innovation into the LM method, the estimation accuracy is improved; the paper Hyperspectral image classification based on non-parallel support vector machine introduces the least squares term of the sample to minimize the additional empirical risk of the parallel support vector machine. Since the support vector machine can solve the fitting problem of uncertain systems, the present invention extends it to nonlinear system identification. Compared with the above literature, it is found that the multi-innovation strategy promotes the concept of single-innovation correction, expands the dimension of identification innovation, and makes full use of the characteristics of innovation as useful information to improve the accuracy of parameter estimation and state estimation, thereby improving the identification effect. By utilizing the observation information at multiple time points, the state estimation process can be optimized and the accuracy and stability of the estimation can be improved. Therefore, the present invention studies a type of SVM nonlinear system identification method combined with a multi-innovation strategy, which better solves the complex problem of multiple inputs and outputs and has important research significance.

[0005] By combining multi-innovation with the LM algorithm, a variety of mathematical models and systems can be obtained. In recent years, this combination has received widespread attention. The paper Hierarchical recursive Levenberg-Marquardt algorithm for radial basis function autoregressive models adds multi-innovation to the hierarchical recursive LM algorithm for radial basis function autoregressive models; the paper Online identification of non-homogeneous fractional order Hammerstein continuous systems based on the principle of multi-innovation introduces the multi-innovation principle into the traditional LM method for identifying fractional order Hammerstein continuous systems. Based on the above literature, it can be found that the concept of multi-innovation is applicable to the LM algorithm. Therefore, the present invention combines these two methods and applies them to optimize the support vector machine (SVM) model. Summary of the invention

[0006] The present invention provides the identification of the autoregressive nonlinear system of thermal error of a CNC machine tool spindle by using a support vector machine (SVM), and establishes the loss function of the SVM by using the weight vector and the deviation term that need to be estimated; in order to minimize the loss function, the Levenberg-Marquardt (LM) iterative optimization is applied; in addition, a multi-innovation identification strategy and an adaptive damping factor are introduced to improve the algorithm, and then a CNC machine tool spindle thermal error modeling method of a multi-innovation LM support vector machine is derived, and the method has fast convergence speed and high identification accuracy.

[0007] The idea of ​​the present invention is: Support vector machine (SVM) is an important method in the field of machine learning, which aims to construct an optimal hyperplane to realize data classification or regression prediction. Since support vector machine can solve the fitting problem of uncertain system, the present invention extends it to nonlinear system identification, and establishes an autoregressive nonlinear SVM model of thermal error of CNC machine tool spindle. The multi-information strategy can enrich system data by adding prior information in parameter estimation. Therefore, when multi-information is introduced into the LM method, the estimation accuracy is greatly improved. In the present invention, multi-information and LM are integrated and applied to the identification of the support vector machine model of thermal error of CNC machine tool spindle.

[0008] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a CNC machine tool spindle thermal error modeling method based on multi-innovation LM support vector machine regression, comprising the following steps:

[0009] Step 1) constructing a CNC machine tool spindle thermal error model based on support vector machine (SVM) to ultimately fit the feedback output of feature point temperature-spindle thermal error;

[0010] Step 1-1) constructing a nonlinear spindle thermal error model based on the thermal characteristics of the machine tool;

[0011] Step 1-2) Apply support vector machine to approximate the autoregressive nonlinear function F(·) in the model;

[0012] Step 1-3) Calculate the minimum risk value;

[0013] Steps 1-4) In the parameter vector Based on this, the loss function of the support vector machine is constructed

[0014] Step 2) constructing a support vector machine model based on multi-innovation adaptive LM optimization;

[0015] Step 2-1) Establish multiple innovation vectors E(l, t), information matrix Ψ(l, t) and stacked output vector G(l, t);

[0016] Step 2-2) Update the loss function

[0017] Step 2-3) Calculate the gradient vector of the loss function

[0018] Step 2-4) Construct the Hessian matrix of the gradient vector

[0019] Step 2-5) Estimate the weight vector γ and bias term β based on LM;

[0020] Step 2-6) Calculate the increment ξ of the kth iteration;

[0021] Step 2-7) Calculate the ratio of the objective function increment to the quadratic function increment Y k ;

[0022] Step 2-8) Obtain the adaptive damping factor according to the improved rule.

[0023] The present invention provides a further optimization scheme for a CNC machine tool spindle thermal error modeling method using a multi-innovation LM support vector machine, comprising the following steps:

[0024] (1-1) Construct an autoregressive model of a nonlinear dynamic system to approximate the thermal error model of the CNC machine tool spindle:

[0025] g(t)=F(r(t),…,r(tn r ),g(t),…,g(tn g )) (1)

[0026] Where t is the time variable, r(t) and g(t) represent the real-time input and real-time output of the CNC machine tool spindle thermal error nonlinear system at time t, respectively. r and n g is the corresponding order, and F(·) represents a nonlinear function that is well defined but unknown in advance.

[0027] (1-2) In order to generate an estimate close to the true output g(t) A suitable model must be developed. Therefore, the support vector machine method is used to approximate the autoregressive nonlinear function F(·), and the model is

[0028] g(t)=F(u(t))=γ Τ φ[u(t)]+β (2)

[0029] definition is the input vector, the superscript T indicates transpose, and g(t) is the scalar output. Represents the original input vector The nonlinear function mapped to a higher-dimensional feature space is called a projection function, where p is the dimension before projection and q is the dimension after projection. represents the weight vector, Represents the deviation term.

[0030] (1-3) In order to obtain the minimum value of structural risk, the loss function of the support vector machine is defined as:

[0031]

[0032] and is subject to the following equality constraints:

[0033] g(t)=γ Τ φ[u(t)]+β+ε(t) (4)

[0034] in, Indicates that the loss function of the support vector machine achieves the minimum value. α is the regularization parameter, which is used to control the smoothness of the solution and the importance of data fitting. Represents the error between the actual output and the predicted output.

[0035] (1-4) Define the parameter vector as Define the loss function of the support vector machine as follows:

[0036]

[0037] It can be seen that the parameter vector containing the weight vector γ and the bias term β in the support vector machine Therefore, it is necessary to estimate it through an efficient and accurate algorithm.

[0038] (2-1) Apply the LM iteration method to solve the optimization problem of SVM. Let k be the iteration variable and K be the maximum iteration value. When iterating k times, the estimated values ​​of the weight vector γ and the bias term β are and Parameter vector The estimated value at iteration k is The innovation length is l, and the scalar innovation term ε(t) is expanded into an l-dimensional innovation vector Ε(l,t), that is,

[0039]

[0040] Where t, t-1, …, t-l+1 represent time. When l = 1, the LM support vector machine algorithm with multiple innovations degenerates into a single innovation LM support vector machine algorithm. The information matrix Ψ(l, t) and the stacked output vector G(l, t) are defined as

[0041]

[0042] Therefore, there is

[0043]

[0044] The loss function (5) becomes

[0045]

[0046] Among them, 1 l It is represented as an l-dimensional column vector, all elements of which are 1, and ||·|| represents the modulus of the vector; Represents the estimated value of the parameter vector The loss function at iteration k.

[0047] (2-2) right and The partial derivative of is given by

[0048]

[0049] in, for For the weight vector The partial derivative of for For deviation The partial derivative of .

[0050] Then, the gradient vector Can be written as

[0051]

[0052] (2-3) The information matrix Φ(l,t) and the parameter estimation vector Defined as

[0053]

[0054] Based on (13), we define two recursive relations:

[0055]

[0056] Among them, ζ(l,t) is the recursive vector of the information matrix and the output vector, and Γ(l,t) is the recursive matrix of the information matrix. Then, the gradient vector becomes

[0057]

[0058] (2-4) Constructing loss function The Hessian matrix of is calculated as follows:

[0059]

[0060] in, for For parameter vector The second-order partial derivative of contains four matrix elements, namely:

[0061] Loss Function right Take the second-order partial derivative Calculated as

[0062]

[0063] Among them, I q is a q-dimensional unit matrix. The loss function right First take the partial derivative and then Taking partial derivative, we can calculate

[0064]

[0065] Loss Function right First take the partial derivative and then Taking partial derivative, we can calculate

[0066]

[0067] Loss Function right Take the second-order partial derivative and calculate it as

[0068]

[0069] (2-5) Based on LM optimization, the multi-innovation LM iterative SVM algorithm is derived to estimate the weight vector γ and the bias term β:

[0070]

[0071] in, is the k-1 iteration parameter vector The estimated value of is the Hessian matrix of k-1 iterations, is the k-1 iteration parameter vector The estimated value of ω k is the damping factor, Ι represents an identity matrix with q+1 dimensions, and the superscript -1 represents the inversion of the matrix.

[0072] (2-6) Let the increment of the parameter estimation vector be ω k is a damping factor used to control the effect of ξ on the iteration step size. Increment ξ in the kth iteration kExpressed as

[0073]

[0074] in, is the loss function for k-1 iterations, is the gradient function for k-1 iterations.

[0075] (2-7) At the iteration point The following quadratic function is defined at:

[0076]

[0077] Then the ratio of the objective function increment to the quadratic function increment is:

[0078]

[0079] (2-8) When k When it is large, the quadratic function ρ(ξ k ) at point The objective function Good fit, ω should be reduced k To increase ξ k On the contrary, when Υ k When ρ(ξ k ) at point The fit with the objective function is not good, so ω should be increased. k To limit ξ k When Υ k When moderate, k The above improvement rules for the adaptive damping factor can be summarized as follows:

[0080]

[0081] Among them, ω k is the damping factor of the current iteration, ω k-1 is the damping factor of the previous iteration. The computational complexity of the multi-innovation adaptive LM support vector machine method is 2l(q 2 t+2qt+q 2 +3q+2)+9q 2 +24q+21. Therefore, its computational complexity increases with the increase of the innovation length l, and a suitable l can be selected to reduce the computational burden.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] (1) The present invention models the thermal error of the spindle of a CNC machine tool by using a support vector machine (SVM) and optimizes it by using the LM method. The SVM nonlinear model has robustness, high-dimensional data processing capability and noise resistance. And the optimization process of LM has fast convergence. Therefore, the technology of the present invention simplifies the complex model, reduces the computational burden in the prior art, and greatly improves the computational speed and recognition accuracy of the identification method.

[0084] (2) The present invention applies a multi-innovation identification strategy and an adaptive damping factor to improve the performance of the LM algorithm. The multi-innovation method can make full use of system information and improve identification accuracy, and the adaptive damping factor can control the convergence speed and stability. In short, the identification method of the present invention is accurate in calculation and has high identification accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0086] Figure 1 It is a schematic diagram of the CNC machine tool spindle thermal error experimental platform and sensor measuring points of the present invention;

[0087] Figure 2 It is a flowchart of the operation steps of the multi-innovation adaptive LM support vector machine algorithm in the present invention;

[0088] Figure 3 : is a relationship diagram of the estimation error δ and iteration k of the multi-innovation adaptive LM support vector machine method under different noise variances in Example 1 of the present invention;

[0089] Figure 4 A comparison diagram of parameter estimation values ​​and true values ​​based on the multi-innovation adaptive LM support vector machine method in Example 1 of the present invention;

[0090] Figure 5 : is a relationship diagram of the estimation error δ and iteration k of the multi-innovation adaptive LM support vector machine method in embodiment 2 of the present invention under different innovation lengths l;

[0091] Figure 6 It is an output fitting curve of different innovation lengths l based on the multi-innovation adaptive LM support vector machine method in Example 2 of the present invention. DETAILED DESCRIPTION

[0092] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0093] See also Figures 1 to 6 The technical solution of the embodiment is a CNC spindle thermal error modeling based on a multi-information LM support vector machine. Figure 1 The method of the present invention is applied to the following CNC spindle thermal error modeling. The system parameters are determined as follows: the initial temperature of the spindle system is about 22°C, the initial oil temperature is set to 17.5°C, the oil temperature command input cycle is 120s, the control target is set to 20.5μm, the historical cooling experimental data is used as training data, and the LM algorithm is used to optimize the selected parameters, and finally a trained support vector machine thermal error model is obtained. The entire model training process is carried out in Matlab software, and finally a thermal error model of the spindle is established.

[0094] Example 1

[0095] In Example 1, it is assumed that there is a nonlinear projection relationship from one-dimensional space to five-dimensional space. If the input vector of the support vector machine consists only of the input {r(t),…,r(tn r )}, the following nonlinear random model is considered in the simulation:

[0096] g(t)=γ Τ φ[u(t)]+β+ε(t), γ=[0.41,0.56,0.90,2.34,-0.91] Τ , β=0.99,

[0097] φ[u(t)]=[sin(r(t)),cos(r(t-1)),r 2 (t-2),e r(t-3) ,r 3 (t-4)] Τ

[0098] The input r(t) is a sequence of mutually uncorrelated measurable random signals with zero mean and unit variance, and the noise ε(t) is a sequence of zero mean and unit variance. 2 =0.1 2 ,0.5 2 ,1.0 2 Gaussian sequence. The parameter estimation error δ is defined as in For the kth time The estimated value of , and the true parameter vector is The innovation length l is set to 3, and the final error δ and parameter estimation of the algorithm under different noise variances are as follows: Figure 3 and Figure 4 shown.

[0099] Example 2

[0100] In order to further verify the effectiveness of the multi-innovation LM support vector machine method, the input {r(t),…,r(tn r )} and output {g(t),…,g(tn g The input vector of the support vector machine composed of )} was studied, and the nonlinear function modeling of a vector projected from one-dimensional space to six-dimensional space is as follows:

[0101] g(t)=γ Τ φ[u(t)]+β+ε(t)

[0102] The true value of the parameter vector is

[0103]

[0104] The true value of the information vector is

[0105] φ[u(t)]=[r 2 (t),sin(r(t-1)),cos(r(t-2))+g(t),exp(g(t)),sin(g(t-1)*r(t)),cos(g(t-2))] Τ

[0106] In the simulation, the mean is zero and the variance is σ 2 =0.6 2 The Gaussian sequence is used as the noise sequence ε(t). The innovation length l is set to 3, 4 and 5 respectively. The estimation error under different innovation lengths is as follows: Figure 5 As shown, the fitting of the actual output and the estimated output is as follows Figure 6 shown.

[0107] A method for modeling thermal error of a CNC machine tool spindle by multi-innovation LM support vector machine regression in embodiments 1 and 2 comprises the following steps:

[0108] (1) A CNC machine tool spindle thermal error model based on support vector machine (SVM) is constructed. The specific steps are as follows:

[0109] Step 1: Build a nonlinear spindle thermal error model based on the thermal characteristics of the machine tool;

[0110] Step 2: Based on this model, a nonlinear spindle thermal error model based on the thermal characteristics of the machine tool is constructed as follows:

[0111] g(t)=F(r(t),…,r(tn r ),g(t),…,g(tn g )) (1)

[0112] Where t is the time variable, r(t) and g(t) represent the real-time input and real-time output of the CNC machine tool spindle thermal error nonlinear system at time t, respectively. r and n g is the corresponding order, and F(·) represents a nonlinear function that is well defined but unknown in advance.

[0113] To obtain an estimate close to the true output g(t) Update the model to:

[0114] g(t)=F(u(t))=γ Τ φ[u(t)]+β (2)

[0115] in is the input vector, the superscript T indicates transpose, and g(t) is the scalar output. Represents the original input vector The nonlinear function mapped to a higher-dimensional feature space is called a projection function, where p is the dimension before projection and q is the dimension after projection. represents the weight vector, Represents the deviation term.

[0116] Step 3: In order to obtain the minimum value of structural risk in the spindle thermal error model, the loss function of the support vector machine is defined as follows:

[0117]

[0118] The loss function is constrained as follows:

[0119] g(t)=γ Τ φ[u(t)]+β+ε(t) (4)

[0120] in, Indicates that the loss function of the support vector machine achieves the minimum value. α is the regularization parameter, which is used to control the smoothness of the solution and the importance of data fitting. Represents the error between the actual output and the predicted output.

[0121] Step 4: Define the parameter vector as Define the loss function of the support vector machine as follows:

[0122]

[0123] Since the parameter vector in the support vector machine contains the weight vector γ and the bias term β Therefore, it is necessary to use an efficient and accurate algorithm for estimation.

[0124] (2) Construct a CNC machine tool spindle thermal error modeling method process based on multi-information LM support vector machine regression.

[0125] Step 1: Create multiple innovation vectors Ε(l, t), information matrix Ψ(l, t) and stacked output vector G(l, t);

[0126] Step 2: Update the loss function

[0127] Step 3: Calculate the gradient vector of the loss function

[0128] Step 4: Construct the Hessian matrix of the loss function

[0129] Step 5: Estimate the weight vector γ and bias term β based on LM;

[0130] Step 6: Calculate the increment ξ of the kth iteration k ;

[0131] Step 7: Calculate the ratio of the objective function increment to the quadratic function increment Y k ;

[0132] Step 8: Obtain the adaptive damping factor ω according to the improved rule k .

[0133] (3) According to the process of the CNC machine tool spindle thermal error modeling method based on multi-innovation LM support vector machine regression, the CNC machine tool spindle thermal error modeling optimization method based on multi-innovation LM support vector machine regression is constructed as follows:

[0134]

[0135] Ψ(l,t)=[φ[u(t)],φ[u(t-1)],…,φ[u(t-l+1)]] (8)

[0136] G(l,t)=[g(t),g(t-1),…,g(t-l+1)] Τ (9)

[0137]

[0138]

[0139]

[0140] See also Figure 2 , the specific steps of the above method are:

[0141] (1) When iterating k times, the estimated values ​​of the weight vector γ and the bias term β are defined as and Construct the parameter vector through formula (6) The estimated value at iteration k

[0142] (2) Calculate the information matrix Ψ(l, t) and the stacked output vector G(l, t) by equations (8) and (9);

[0143] (3) According to equations (7) and (10), the new information vector E(l,t) is obtained;

[0144] (4) The loss function is obtained through formula (11):

[0145] (5) Calculate through equations (12) and (13) right and The partial derivative of , and based on formula (14) we get the gradient vector

[0146] (6) According to equation (15), define the information matrix Φ(l,t) and the parameter estimation vector The information matrix and the recursive vector ζ(l, t) of the output vector and the recursive matrix Γ(l, t) of the information matrix are calculated by equations (16) and (17), and then the gradient vector is updated according to equation (18):

[0147] (7) The loss function is obtained through equations (19)-(23): The Hessian matrix

[0148] (8) Update the estimated weight vector γ and bias term β through the multi-innovation LM iterative SVM algorithm formula (24);

[0149] (9) Calculate the increment ξ according to formula (25) k , calculate the iteration point according to formula (26) The quadratic function ρ(ξ) at the position is calculated by using formula (27): k ;

[0150] (10) Update the adaptive damping factor ω according to the rule of formula (28): k .

[0151] The definitions of the variables are as follows:

[0152] Define t as a time variable, the input is u(t), the output is y(t), r(t) and g(t) represent the real-time input and real-time output of the CNC machine tool spindle thermal error nonlinear system at time t, respectively. r and n gis the corresponding order, F(·) represents a well-defined but unknown nonlinear function, Represents the original input vector The nonlinear function mapped to the q-dimensional feature space is called the projection function, where p is the dimension before projection and q is the dimension after projection. represents the weight vector, represents the bias term; the superscript T represents the transpose.

[0153] definition Indicates that the loss function of the support vector machine achieves the minimum value. α is the regularization parameter, which is used to control the smoothness of the solution and the importance of data fitting. Definition Represents the error between the actual output and the predicted output; the parameter vector is defined as i is the number of loops of the sum function, and also serves as the independent variable of the function; definition is the estimated value of g(t).

[0154] Define k as the iteration variable, K as the maximum iteration value; define the estimated values ​​of the weight vector γ and the bias term β at the time of iteration k as and Define the parameter vector The estimated value at iteration k is Define the length of the new information as l, define Ε(l,t) as an l-dimensional new information vector; define Ψ(l,t) and Φ(l,t) as information matrices, and G(l,t) as the stacked output vector. Definition 1 l Represented as an l-dimensional column vector, where all elements are 1, and ||·|| represents the modulus of the vector; definition is the loss function of the support vector machine; definition Represents the estimated value of the parameter vector The loss function at iteration k.

[0155] definition for For the weight vector The partial derivative of for For deviation The partial derivative of for The gradient vector of ; define ζ(l,t) as the recursive vector of the information matrix and the output vector, Γ(l,t) as the recursive matrix of the information matrix; define is the loss function The Hessian matrix of is the loss function right Take the second-order partial derivative and define I q is a q-dimensional unit matrix, and we define is the loss function right First take the partial derivative and then Take the partial derivative and define Loss Function right First take the partial derivative and then Take the partial derivative and define is the loss function right Take the second-order partial derivative.

[0156] definition is the parameter vector for k-1 iterations The estimated value of is the Hessian matrix for k-1 iterations, Ι represents a unit matrix with q+1 dimensions, and the superscript -1 represents the inversion of the matrix. The increment of the parameter estimation vector is defined as Definition k is the damping factor used to control the effect of ξ on the iteration step size, and the increment calculated in the kth iteration is defined as ξ k ;definition for The loss function at k-1 iterations is, for Gradient function at k-1 iterations.

[0157] Define ρ(ξ) as the value at the iteration point The quadratic function, Υ k is the ratio of the increment of the objective function to the increment of the quadratic function, ω k-1 is the damping factor at k-1 iterations.

[0158] The identification effect of the designed identification method can be found in Figure 3 , Figure 4 , Figure 5 , Figure 6 According to the identification results, the method of the present invention has the following advantages in terms of identification error, estimation accuracy and convergence speed: 2 As the length of the new information l increases, the identification error increases and the estimation accuracy decreases. However, this effect is very small and the worst accuracy is within the error tolerance range. As the new information length l increases, the identification error decreases. Therefore, the multi-innovation method can improve the estimation accuracy. However, when l increases to a certain value, the identification accuracy tends to stabilize.

[0159] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling thermal errors of CNC machine tool spindles based on multi-innovation LM support vector machines, characterized in that: The steps include: Step 1) constructing a CNC machine tool spindle thermal error model based on support vector machine (SVM), and fitting the feedback output of feature point temperature-spindle thermal error; Step 2) Construct a multi-information adaptive LM method to optimize the support vector machine model.

2. The method for modeling thermal error of a CNC machine tool spindle using a multi-innovation LM support vector machine according to claim 1, characterized in that: The step 1) comprises the following steps: (1-1) A nonlinear spindle thermal error model is constructed based on the thermal characteristics of the machine tool; (1-2) Based on this model, a nonlinear spindle thermal error model is constructed using support vector machine as follows: g(t)=F(u(t))=γ Τ φ[u(t)]+β(1) Where t is the time variable, r(t) and g(t) represent the real-time input and real-time output of the CNC machine tool spindle thermal error nonlinear system at time t, respectively. r and n g is the corresponding order, F(·) represents a well-defined but unknown nonlinear function, and is defined is the input vector, the superscript T indicates transposition, g(t) is the scalar output, Represents the original input vector Map to The nonlinear function of the dimensional feature space is called the projection function, p is the dimension before projection, q is the dimension after projection, represents the weight vector, represents the deviation term; (1-3) The loss function of the support vector machine is defined as follows: in, It indicates that the loss function of the support vector machine achieves the minimum value, α is the regularization parameter, which is used to control the smoothness of the solution and the importance of data fitting, and ε(t) represents the error between the actual output and the predicted output; (1-4) In the parameter vector Based on this, the loss function of the support vector machine is constructed as follows:

3. According to the multi-innovation LM support vector machine CNC machine tool spindle thermal error modeling method according to claim 1, the step 2) is specifically: (2-1) Apply the LM iteration method to establish the multi-information vector E(l,t), information matrix Ψ(l,t) and stacked output vector G(l,t); (2-2) Update the loss function (2-3) Calculate the gradient vector of the loss function include for For the weight vector The partial derivative of for For deviation The partial derivative of (2-4) Construct the Hessian matrix of the loss function Right now For parameter vector The second-order partial derivative of , which contains four matrix elements, namely: loss function right Take the second-order partial derivative Loss Function right First take the partial derivative and then Taking partial derivatives Loss Function right First take the partial derivative and then Taking partial derivatives Loss Function right Take the second-order partial derivative (2-5) Estimate the weight vector γ and bias term β based on LM; (2-6) Calculate the increment ξ of the kth iteration k ; (2-7) Calculate the ratio of the objective function increment to the quadratic function increment Y k ; (2-8) According to the improved rule, the adaptive damping factor ω is obtained k .

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