Large machine tool static structure uncertainty response estimation method based on key condition quotient

Abstract

The invention provides a large machine tool static structure uncertainty response estimation method based on a key condition quotient, and belongs to the field of uncertainty quantification. Firstly, a finite element model of a machine tool static structure is established; secondly, Nm measuring points are arranged on a machine tool structure, and measuring data of the measuring points are obtained; then, a correlation coefficient between each piece of measurement data and the response is evaluated, and a key condition matrix is obtained; and finally, based on the key condition quotient, obtaining an analytic expression of a response mean value and a covariance matrix, and carrying out numerical solution by adopting a generalized quasi-Monte Carlo method. According to the invention, based on a key condition quotient, a key measurement condition is selected according to a covariance matrix of measurement data of a measurement point, and efficient and accurate estimation of real response is realized; a parameter identification step is skipped, so that extraction of key measurement conditions can be effectively realized, and accurate estimation of real response is realized; the estimation problem of the uncertainty system response of the machine tool in the presence of the measurement condition can be solved.

Description

Technical Field

[0001] The present invention belongs to the field of uncertainty quantification, and relates to a method for estimating the uncertainty response of a large machine tool static structure based on a key condition quotient, and in particular to a method for estimating the uncertainty response of a large machine tool static structure based on a key condition quotient under measurement conditions. Background Art

[0002] Considering the influence of uncertainty, measuring the uncertainty of the structural output response is one of the core concerns of the reliability design of large machine tool structures. In recent years, researchers have proposed many excellent uncertainty analysis methods to quantify the uncertainty of random structural output responses, such as random perturbation method, generalized chaos polynomial method, quasi-Monte Carlo method, etc., which have played an important role in the field of reliability analysis. These uncertainty quantification analysis methods can effectively calculate the mean, variance, probability density function and other statistical information of random responses. However, in real large machine tool structures, the parameters are not truly random, but have deterministic values, so their true responses are not truly random. Take a batch of machine tool beams with the same size made by the same process as an example. Although the physical parameters (such as elastic modulus) of different machine tool beams are different due to the deviation of construction process and materials, the elastic modulus must be determined for any specific machine tool beam. Therefore, under the action of a certain load, the true displacement of the machine tool beam is also determined. However, the evaluation of the mean and variance of random response based on uncertainty quantification methods can only statistically describe the possible probabilistic distribution of the true displacement, but cannot give the true response. Obviously, the true response can provide a better reference for structural design.

[0003] In order to estimate the true response, it is necessary to determine the true values ​​of the uncertain parameters in the structure. In actual engineering, in order to determine the values ​​of the uncertain parameters of the structure, researchers often measure the measurement points arranged on the structure, identify the structural parameters based on the measured values, and then substitute the identified parameters into the analysis model to obtain the true response of the structure. However, the computational complexity of the parameter identification method is limited by the number of identified parameters. When considering uncertain factors such as random fields, there will be a large number of parameters to be identified, and the computational complexity of the parameter identification method is too large. At present, considering the randomness in the measurement data, the true response is estimated. In addition to parameter identification, there is also a filtering algorithm, among which the most commonly used is the Kalman filter method proposed by Kalman, but it is difficult to handle strong nonlinear systems.

[0004] Most of the current uncertainty response estimation methods for large machine tool structures cannot handle the estimation problem of uncertain system responses when measurement conditions exist. For example, the Chinese invention patent "Machine tool response modeling method, system and response prediction method based on transfer learning" (application number 202111570003.5), when dealing with the problem of machine tool response prediction, does not take into account the estimation of uncertain system responses when measurement conditions exist. The Chinese invention patent "A method for estimating the parameters and uncertainties of aircraft engine system parameters considering measurement noise" (application number 202311095121.4), this patent takes into account measurement noise and handles the problem of uncertainty estimation of aircraft engine system parameters, but does not take into account response estimation and cannot be directly applied to the problem of uncertainty response estimation of machine tool structures. Summary of the invention

[0005] In view of the main problems existing in the prior art, the present invention proposes a method for estimating the uncertainty response of a large machine tool static structure based on a key condition quotient, which can handle the estimation problem of the uncertainty system response of a machine tool under measurement conditions. Based on the key condition quotient, the probability density function, mean and variance of the true response of the structure can be directly estimated by using the measurement information with the greatest reference value for the response, skipping the parameter identification step, effectively realizing the extraction of key measurement conditions, and achieving accurate estimation of the true response.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for estimating the uncertainty response of a large machine tool static structure based on a key condition quotient is provided. The method firstly establishes a finite element model of the static structure of the machine tool; secondly, sets N m measurement points, and obtain the measurement data of the measurement points. Then, evaluate the correlation coefficient between each measurement data and the response, and obtain the key condition matrix. Finally, based on the key condition quotient, the analytical expression of the mean and covariance matrix of the response is obtained, and the generalized quasi-Monte Carlo method is used for numerical solution. It includes the following steps:

[0008] The first step is to establish a finite element model of the static structure of the machine tool, specifically:

[0009] Step 1.1, import an existing machine tool model into the 3D modeling software, or model the 3D model of the machine tool according to the engineering drawing to obtain the 3D model of the machine tool.

[0010] Step 1.2, import the machine tool 3D model into the finite element analysis software to establish the machine tool finite element model. Set the material properties of the machine tool in the finite element analysis software, and apply constraints and loads to the machine tool finite element model at corresponding positions according to the constraints and loads on the machine tool.

[0011] Step 1.3, according to the actual situation of the machine tool, determine the random parameter ε of the machine tool structure and the random parameter θ of the load, as well as the distribution type and distribution range of the random parameters.

[0012] The second step is to set N on the machine tool structure. m Measurement points, specifically:

[0013] Step 2.1: Use measuring instruments to measure at corresponding measuring points to obtain measurement data of all points. where y i Represents the measurement data of the i-th measurement point, i=1,2,…,N m .

[0014] Step 2.2, measurement error of each measurement point are considered as independent random variables with mean μ v and the covariance matrix is ​​R v According to the accuracy of the measuring instrument, the distribution of the measurement error v at each measuring point is determined.

[0015] Step 2.3, get the random measurement equation:

[0016] y=h(u(x))+v (1)

[0017] Where y is the measurement data of all points, which has the same meaning as step 2.1; h(u(x)) represents the value calculated based on the response u(x); x represents the spatial coordinates of a node of the machine tool; v represents the measurement error of each measurement point, which has the same meaning as step 2.2.

[0018] The third step is to evaluate the correlation coefficient between each measurement data and the response to obtain the key condition matrix, specifically:

[0019] Step 3.1, use finite element software to calculate the response u(x) of the tool machine.

[0020] Step 3.2, evaluate each measurement data y by formula (2) i The correlation coefficient r between the response u(x) i (x):

[0021]

[0022] Among them, cov(.) represents the covariance formula.

[0023] Step 3.3, based on |r i (x)|Measurement data y i The reference value of |r i The larger the value of (x)|, the greater the measured data y iThe greater the estimated reference value for the response u(x), the greater the value is, and vice versa. According to the actual situation, only |r i (x)|>0.5 is used as the key measurement data z. The expression of the key measurement data z is:

[0024]

[0025] Among them, p(x) is the key condition matrix, which consists of 0 and 1.

[0026] Step 3.4, based on the key condition matrix p(x), obtain the random measurement equation that only considers the key conditions:

[0027] z=p(x)y=p(x)h(u(x))+β,β=p(x)v (4)

[0028] Among them, β represents the random error of z; v represents the measurement error of each measurement point.

[0029] The fourth step is to obtain the analytical expressions of the mean and covariance matrix of the response based on the key condition quotient, specifically:

[0030] Step 4.1, express the response u(x) as a function of displacement, that is in is the conversion function between any response and displacement response, and the independent variable is is the displacement response.

[0031] Step 4.2, the finite element model of the static structure of the machine tool is uniformly expressed as:

[0032]

[0033] in, are the displacement vector and the load vector respectively. represents the nonlinear restoring force vector of the static structure of the machine tool. The solution of formula (5) is expressed as Represents the displacement function, the independent variables are ε and θ, ε represents the random parameters of the machine tool structure, and θ represents the random parameters of the load.

[0034] Then the finite element model of the measurement condition randomness is expressed as:

[0035]

[0036] Among them, N T (x) represents the shape function of the finite element model of the static structure of the machine tool, which can be obtained by the finite element method; represents the displacement function, the independent variables are ε and θ, ε represents the random parameter of the machine tool structure, and θ represents the random parameter of the load; It is expressed as the conversion function between any response and displacement response, and the independent variable is It is represented as the conversion function between any response and displacement response, with independent variables x, ε, and θ; p(x) represents the critical condition matrix; h(u(x)) represents the value calculated based on the response u(x); β(x) represents the random error of z; Represents the value calculated based on key measurement data, with the independent variables x, ε, and θ.

[0037] Step 4.3, according to formula (7), we get the conditional probability density ρ u(x)|z (u(x)|z), as follows:

[0038]

[0039] Among them, ρ ε,θ (ε,θ) represents the joint probability density function of random parameters ε and θ; express The probability density function of ; δ represents the Dirac function.

[0040] Step 4.4, get the response mean and the covariance matrix P u The analytical expression of (x) is:

[0041]

[0042] Step 5: Evaluate the probability density function ρ β (β), specifically:

[0043] Step 5.1, according to the distribution of the measurement error v obtained in step 2.2, it is obtained that β=pv also follows a Gaussian distribution, and its mean and covariance matrix are expressed as:

[0044] μ β =pμ v (10)

[0045]

[0046] Among them, μ β represents the mean value of the measurement error β of the key measurement data; p represents the key condition matrix; μ v represents the mean value of the measurement error v; R β Represents the covariance matrix of the measurement error β of the key measurement data; R v Represents the covariance matrix of the measurement error v.

[0047] Step 5.2, the evaluation probability density function ρ can be obtained from formula (10) and formula (11): β(β) is expressed as:

[0048]

[0049] Among them, N k is the dimension of the measurement error β of the key measurement data.

[0050] The sixth step is to use the generalized quasi-Monte Carlo method for numerical solution, specifically:

[0051] Step 6.1, determine the joint probability density function ρ of the random parameters ε and θ based on the distribution type and distribution range of the random parameters obtained in step 1.3 ε,θ (ε,θ).

[0052] Step 6.2, according to the joint probability density function ρ ε,θ (ε,θ) and the range distribution of random parameters ε and θ, random sampling of the random parameter ε of the machine tool structure and the random parameter θ of the load can be obtained, so that n groups of sample points ε can be obtained. i and θ i According to the sample points obtained by sampling, the weight w of each sample point is obtained based on the unequal weight calculation method of generalized chaotic polynomials. i .

[0053] Step 6.3, each group of sample points ε i and θ i Substitute the finite element model F(ε i ,u)=f(θ i ), and the solution is calculated

[0054] Step 6.4, based on the generalized quasi-Monte Carlo method, numerical integration is performed to estimate the mean and covariance of the response, which are expressed as:

[0055]

[0056] in, represents the estimated response mean; w i Represents the weight of each sample point; N T (x) represents the shape function of the finite element model of the static structure of the machine tool, which can be obtained by the finite element method; represents the displacement function, with ε as the independent variable i and θ i , ε i represents the random parameters of the machine tool structure in the i-th sample, θ i represents the random load parameter of the machine tool structure in the i-th sample; P u (x) represents the estimated response covariance; is the mean response value obtained in step 4.4; η i To simplify the parameters, the specific expression is:

[0057]

[0058] Finally, based on formula (13) and formula (14), the value of the machine tool uncertainty system response under measurement conditions is calculated.

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

[0060] (1) The present invention is based on the key condition quotient and selects key measurement conditions according to the covariance matrix of the measurement data of the measurement points, thereby achieving efficient and accurate estimation of the true response, and providing a possibility for estimating the uncertainty response of the static structure of large machine tools.

[0061] (2) The present invention is based on the key condition quotient and skips the parameter identification step, thereby solving the problem of excessive calculation complexity of the parameter identification method and the problem of complex calculation of the uncertainty response estimation of the static structure of large machine tools.

[0062] (3) Based on the key condition quotient, the present invention solves the uncertainty response estimation method of the static structure of large machine tools and fills the gap in the uncertainty response estimation of the static structure of machine tools. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a flow chart for estimating the uncertainty response of static structure of large machine tools based on key condition quotient under measurement conditions. DETAILED DESCRIPTION

[0064] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method 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 flowchart of estimating the uncertainty displacement response of a large machine tool beam based on the key condition quotient under measurement conditions includes the following steps:

[0066] The first step is to establish a finite element model of the static structure of the machine tool, specifically:

[0067] Step 1.1, import the existing machine tool beam model into the 3D modeling software to obtain the 3D model of the machine tool beam.

[0068] Step 1.2, import the three-dimensional model of the machine tool beam into the finite element analysis software to establish the finite element model of the machine tool beam. Set the material properties of the machine tool beam in the finite element analysis software, and apply constraints and loads to the finite element model of the machine tool beam at corresponding positions according to the constraints and loads on the machine tool beam.

[0069] Step 1.3, according to the actual situation of the machine tool beam, determine the random parameters ε of the machine tool beam structure: the stiffness of the bolt connection, which satisfies the uniform distribution and the distribution range is [3E9,1E10]N / m; the load random parameters θ: the position where the force is applied, which satisfies the uniform distribution and the distribution range is [-1,1]m.

[0070] The second step is to set N on the machine tool structure. m =6 measurement points, specifically:

[0071] Step 2.1, use three high-precision laser sensors "KG06-50A", "KG06-30A" and KG05-30A" to collect measurement data, distributed corresponding to measurement points 1, 2, measurement points 3, 4 and measurement points 5, 6, and obtain the measurement data of all points y = (y 1 ,y 2 ,…,y 6 ) T , where y i Represents the measurement data of the i-th measurement point, i=1,2,…,6.

[0072] Step 2.2, the measurement error v of each measurement point = (v 1 ,v 2 ,…,v 6 ) T can be regarded as mutually independent random variables, and follow the mean μ v and the covariance matrix is ​​R v According to the accuracy of the measuring instrument, it can be confirmed that each measuring point obeys μ v =0 mean Gaussian distribution, the standard deviations of the measurement errors of the three models are σ v =1×10 -6 , 5×10 -7 and 1×10 -7 The covariance matrix of the measurement error can be obtained as R v .

[0073] Step 2.3, get the random measurement equation:

[0074] y=h(u(x))+v (1)

[0075] Where y is the measurement data of all points, which has the same meaning as step 2.1; h(u(x)) represents the value calculated based on the response u(x); x represents the spatial coordinates of a node of the machine tool; v represents the measurement error of each measurement point, which has the same meaning as step 2.2.

[0076] The third step is to evaluate the correlation coefficient between each measurement data and the response to obtain the key condition matrix, specifically:

[0077] Step 3.1, use finite element software to calculate the response u(x) of the tool machine.

[0078] Step 3.2, evaluate each measurement data y by formula (17) i The correlation coefficient r between the response u(x) i (x):

[0079]

[0080] Among them, cov(.) represents the covariance formula.

[0081] Step 3.3, based on |r i (x)| to measure the measurement data y i The reference value of |r i The larger the value of (x)|, the greater the measured data y i The greater the estimated reference value for the response u(x), the greater the value is, and vice versa. According to the actual situation, only |r i The measurement data with (x)|>0.5 is taken as the key measurement data z. The expression of the key measurement data z is:

[0082]

[0083] Among them, p(x) is the key condition matrix, which consists of 0 and 1.

[0084] In this implementation case, according to the correlation coefficient |r i (x)|, and the displacement response The most strongly correlated measurement points are the first and second measurement points, so we can use equation (16) to find:

[0085]

[0086] Step 3.4, based on the key condition matrix p(x), obtain the random measurement equation that only considers the key conditions:

[0087] z=p(x)y=p(x)h(u(x))+β,β=p(x)v (4)

[0088] Among them, β represents the random error of z; v represents the measurement error of each measurement point.

[0089] The fourth step is to obtain the analytical expressions of the mean and covariance matrix of the response based on the key condition quotient, specifically:

[0090] Step 4.1, express the response u(x) as a function of displacement, that is in is the conversion function between any response and displacement response, and the independent variable is is the displacement response.

[0091] Step 4.2, the finite element model of the static structure of the machine tool is uniformly expressed as:

[0092]

[0093] in, are the displacement vector and the load vector respectively. represents the nonlinear restoring force vector of the static structure of the machine tool. The solution of formula (21) is expressed as Represents the displacement function, the independent variables are ε and θ, ε represents the random parameters of the machine tool structure, and θ represents the random parameters of the load.

[0094] Then the finite element model of the measurement condition randomness is expressed as:

[0095]

[0096] Among them, N T (x) represents the shape function of the finite element model of the static structure of the machine tool, obtained by the finite element method; represents the displacement function, the independent variables are ε and θ, ε represents the random parameter of the machine tool structure, and θ represents the random parameter of the load; It is expressed as the conversion function between any response and displacement response, and the independent variable is It is represented as the conversion function between any response and displacement response, with independent variables x, ε, and θ; p(x) represents the critical condition matrix; h(u(x)) represents the value calculated based on the response u(x); β(x) represents the random error of z; Represents the value calculated based on key measurement data, with the independent variables x, ε, and θ.

[0097] Step 4.3, according to formula (7), we get the conditional probability density ρ u(x)|z (u(x)|z), as follows:

[0098]

[0099] Among them, ρ ε,θ(ε,θ) represents the joint probability density function of random parameters ε and θ; express The probability density function of ; δ represents the Dirac function.

[0100] Step 4.4, get the response mean and the covariance matrix P u The analytical expression of (x) is:

[0101]

[0102] Step 5: Evaluate the probability density function ρ β (β), specifically:

[0103] Step 5.1, according to the distribution of the measurement error v obtained in step 2.2, it is obtained that β=pv also follows a Gaussian distribution, and its mean and covariance matrix are expressed as:

[0104] μ β =pμ v (10)

[0105]

[0106] Among them, μ β represents the mean value of the measurement error β of the key measurement data; p represents the key condition matrix; μ v represents the mean value of the measurement error v; R β Represents the covariance matrix of the measurement error β of the key measurement data; R v Represents the covariance matrix of the measurement error v.

[0107] Step 5.2, the evaluation probability density function ρ can be obtained from formula (10) and formula (11): β (β) is expressed as:

[0108]

[0109] Among them, N k is the dimension of the measurement error β of the key measurement data.

[0110] The sixth step is to use the generalized quasi-Monte Carlo method for numerical solution, specifically:

[0111] Step 6.1, based on the distribution type and distribution range of the stiffness ε of the bolt connection and the position θ where the force is applied obtained in step 1.3, the respective probability density functions ρ can be obtained ε (ε) and ρ θ (θ), and then we get the joint probability density function ρ ε,θ (ε,θ).

[0112] Step 6.2, according to the joint probability density function ρ ε,θ (ε,θ) and the range distribution of random parameters ε and θ, random sampling of the random parameter ε of the machine tool structure and the random parameter θ of the load can be obtained, so that n groups of sample points ε can be obtained. i and θ i According to the sample points obtained by sampling, the weight w of each sample point is obtained based on the unequal weight calculation method of generalized chaotic polynomials. i .

[0113] Step 6.3, each group of sample points ε i and θ i Substitute the finite element model F(ε i ,u)=f(θ i ), and the solution is calculated

[0114] Step 6.4, based on the generalized quasi-Monte Carlo method, numerical integration is performed to estimate the mean and covariance of the response, which are expressed as:

[0115]

[0116] in, represents the estimated response mean; w i Represents the weight of each sample point; N T (x) represents the shape function of the finite element model of the static structure of the machine tool, which can be obtained by the finite element method; represents the displacement function, with ε as the independent variable i and θ i , ε i represents the random parameters of the machine tool structure in the i-th sample, θ i represents the random load parameter of the machine tool structure in the i-th sample; P u (x) represents the estimated response covariance; is the mean response value obtained in step 4.4; η i To simplify the parameters, the specific expression is:

[0117]

[0118] Finally, based on formula (13) and formula (14), the value of the machine tool uncertainty system response under measurement conditions is calculated.

[0119] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for estimating the uncertainty response of static structure of large machine tools based on key condition quotient, characterized in that: The large machine tool static structure uncertainty response estimation method comprises the following steps: The first step is to establish a finite element model of the static structure of the machine tool; The second step is to set N on the machine tool structure. m measuring points, and obtaining the measuring data of the measuring points; The third step is to evaluate the correlation coefficient between each measurement data and the response to obtain the key condition matrix; The fourth step is to obtain the analytical expressions of the mean and covariance matrix of the response based on the key condition quotient; Step 5: Evaluate the probability density function ρ β (β); In the sixth step, the generalized quasi-Monte Carlo method is used to perform numerical solution and calculate the value of the machine tool uncertainty system response when there are measurement conditions.

2. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 1 is characterized in that: The first step comprises the following steps: Step 1.1, importing an existing machine tool model into a 3D modeling software, or modeling a 3D model of a machine tool according to an 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 situation of the machine tool, determine the random parameter ε of the machine tool structure and the random parameter θ of the load, as well as the distribution type and distribution range of the random parameters.

3. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 1 is characterized in that: The second step comprises the following steps: Step 2.1: Use measuring instruments to measure at corresponding measuring points to obtain measurement data of all points. where y i Represents the measurement data of the i-th measurement point, i=1,2,…,N m ; Step 2.2, measurement error of each measurement point are considered as independent random variables with mean μ v and the covariance matrix is ​​R v Gaussian distribution; according to the accuracy of the measuring instrument, determine the distribution of the measurement error v at each measuring point; Step 2.3, get the random measurement equation: y=h(u(x))+v (1) Where y is the measurement data of all points; h(u(x)) represents the value calculated based on the response u(x); x represents the spatial coordinates of a node of the machine tool; and v represents the measurement error of each measurement point.

4. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 3 is characterized in that: The third step comprises the following steps: Step 3.1, using finite element software to calculate the response u(x) of the tool machine; Step 3.2, evaluate each measurement data y by formula (2) i The correlation coefficient r between the response u(x) i (x): Among them, cov(.) represents the covariance formula; Step 3.3, based on |r i (x)|Measurement data y i The reference value of the key measurement data z is obtained, where |r i The larger the value of (x), the greater the measured data y i The greater the estimated reference value for the response u(x), and vice versa; Step 3.4, based on the key condition matrix p(x), obtain the random measurement equation that only considers the key conditions: z=p(x)y=p(x)h(u(x))+β,β=p(x)v (4) Among them, β represents the random error of z; v represents the measurement error of each measurement point.

5. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 4 is characterized in that: In step 3.3, according to the actual situation, only select |r i (x)|>0.5 is used as the key measurement data z; the expression of the key measurement data z is: Among them, p(x) is the key condition matrix, which consists of 0 and 1.

6. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 4 is characterized in that: The fourth step comprises the following steps: Step 4.1, express the response u(x) as a function of displacement, that is in is the conversion function between any response and displacement response, and its independent variable is is the displacement response; Step 4.2, the finite element model of the static structure of the machine tool is uniformly expressed as: in, f are the displacement vector and load vector respectively; represents the nonlinear restoring force vector of the static structure of the machine tool. The solution of formula (5) is expressed as represents the displacement function, the independent variables are ε and θ, ε represents the random parameter of the machine tool structure, and θ represents the random parameter of the load; Then the finite element model of the measurement condition randomness is expressed as: Among them, N T (x) represents the shape function of the finite element model of the static structure of the machine tool, obtained by the finite element method; represents the displacement function, the independent variables are ε and θ, ε represents the random parameter of the machine tool structure, and θ represents the random parameter of the load; It is expressed as the conversion function between any response and displacement response, and the independent variable is It is represented as the conversion function between any response and displacement response, with independent variables x, ε, and θ; p(x) represents the critical condition matrix; h(u(x)) represents the value calculated based on the response u(x); β(x) represents the random error of z; represents the value calculated based on key measurement data, with independent variables x, ε, and θ; Step 4.3, according to formula (7), we get the conditional probability density ρ u(x)|z (u(x)|z), as follows: Among them, ρ ε,θ (ε,θ) represents the joint probability density function of random parameters ε and θ; express The probability density function of ; δ represents the Dirac function; Step 4.4, get the response mean and the covariance matrix P u (x).

7. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 6 is characterized in that: In step 4.4, the response mean and the covariance matrix P u The expression of (x) is:

8. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 6 is characterized in that: The fifth step comprises the following steps: Step 5.1, according to the distribution of the measurement error v obtained in step 2.2, it is obtained that β=pv also follows a Gaussian distribution, and its mean and covariance matrix are expressed as: m β =pm v (10) Among them, μ β represents the mean value of the measurement error β of the key measurement data; p represents the key condition matrix; μ v represents the mean value of the measurement error v; R β Represents the covariance matrix of the measurement error β of the key measurement data; R v represents the covariance matrix of the measurement error v; Step 5.2, the evaluation probability density function ρ can be obtained from formula (10) and formula (11): β The expression of (β) is: Among them, N k is the dimension of the measurement error β of the key measurement data.

9. A method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 8, characterized in that: The sixth step comprises the following steps: Step 6.1, determine the joint probability density function ρ of the random parameters ε and θ based on the distribution type and distribution range of the random parameters obtained in step 1.3 ε,θ (ε,θ); Step 6.2, according to the joint probability density function ρ ε,θ (ε,θ) and the range distribution of random parameters ε and θ, random sampling of the random parameter ε of the machine tool structure and the random parameter θ of the load is performed to obtain n groups of sample points ε i and θ i According to the sample points obtained by sampling, the weight w of each sample point is obtained based on the unequal weight calculation method of generalized chaotic polynomials i ; Step 6.3, each group of sample points ε i and θ i Substitute the finite element model F(ε i ,u)=f(θ i ), and the solution is calculated Step 6.4, based on the generalized quasi-Monte Carlo method, numerical integration is performed to estimate the mean and covariance of the response, which are expressed as: in, represents the estimated response mean; w i Represents the weight of each sample point; N T (x) represents the shape function of the finite element model of the static structure of the machine tool, which can be obtained by the finite element method; represents the displacement function, with ε as the independent variable i and θ i , ε i represents the random parameters of the machine tool structure in the i-th sample, θ i represents the random load parameter of the machine tool structure in the i-th sample; P u (x) represents the estimated response covariance; is the mean response value obtained in step 4.4; η i To simplify the parameters; Based on formula (13) and formula (14), the value of the machine tool uncertainty system response under measurement conditions is calculated.

10. The method for estimating the static structural uncertainty response of a large machine tool based on a key condition quotient according to claim 9, characterized in that: In step 6.4, n i The specific expression is:

Images