RELIABILITY CALCULATION METHOD OF THE THERMAL ERROR MODEL OF A MACHINE TOOL BASED ON DEEP NEURAL NETWORK AND THE MONTE CARLO METHOD

Abstract

A method for calculating the reliability of the thermal error model of a machine tool based on deep neural network (DNN) and the Monte Carlo method, which belongs to the field of the thermal error compensation of computer numerical control (CNC) machine tools. Firstly, according to the probability distribution of the thermal parameters and thermal error model, a set of data for training the DNN is generated. Next, the DNN is constructed based on the deep belief networks (DBNs) and trained with the training data. Then, a group of random sampling data is obtained according to the probability distribution of the thermal characteristic parameters of the machine tool, and the group of random sampling is taken as the input and the output is obtained by the trained depth neural network. Finally, the reliability of the thermal error model is calculated based on the Monte Carlo method.

Claims

1. A method for calculating the reliability of the thermal error model of a machine tool based on deep neural network DNN and Monte Carlo method, wherein, firstly, according to the probability distribution of the thermal parameters and thermal error model, a set of data for training the DNN is generated; next, the DNN is constructed based on the deep belief networks DBNs and trained with the training data; then, a group of random sampling data is obtained according to the probability distribution of the thermal characteristic parameters of the machine tool, and the group of random sampling is taken as the input and the output is obtained by the trained depth neural network; finally, the reliability of the thermal error model is calculated based on the Monte Carlo method; the specific steps are given below: the first step is to generate data for training depth neural network; (1) generating input data for training based on the mean value M and the coefficient C of variation of the thermal characteristic parameters of the machine tool, the standard deviation S is calculated according to Equation (1);
S=MC(1) according to the probability distribution of the thermal characteristic parameters of machine tools, the mean value M, and the standard deviation S, a group of random sampling of the thermal characteristic parameters x(i), i=1, 2, . . . , n; are selected; the random sampling is the input data for training; (2) generating output data for training according to Equation (2), the thermal characteristic parameters of the machine tool are calculated, and the mean value is taken, the average prediction residual of the thermal error model of the machine tool is as follows:
=[.sub.n=2.sup.P.sub.m=1.sup.J|E.sub.c(n,m)|]/[(P1)J](2) in Equation (2), P is the total number of the machine tool thermal error tests, J is the number of points for each test of the feed shaft of the machine tool, and Ec (n,m) is the predicted residual value of the m-th test point in the n-th thermal error test when the thermal characteristic parameter is taken as the mean value; when the value of thermal characteristic parameter x(i) is calculated according to Equation (3), the average predicted residual error .sub.Res(i) of the thermal error model of machine tool feed shaft is as follows:
.sub.Res(i)=[.sub.n=2.sup.P.sub.m=1.sup.J|E.sub.Res(n,m,i)|]/[(P1)J], i=1,2, . . . ,n(3) in Equation (3), E.sub.Res(n, m, i) is the predicted residual value of the m-th test point in the n-th thermal error test when the thermal characteristic parameter is x(i); supposing that function Z(i) is
Z(i)=N(.sub.Res(i)), i=1,2, . . . ,n(4) then, N is the tolerance coefficient, and if [N(.sub.Res(i))]0, then it can be judged that the thermal error model of the machine tool feed shaft is reliable; if [N(.sub.Res(i))]>0, then it can be judged that the thermal error model of machine tool feed shaft is failure; The indicator function of this function is
Z.sup.I(i)=I[Z(i)], i=1,2, . . . ,n(5) where Z.sup.I(i), i=1, 2, . . . , and n is the output data for training; the second step is the construction and training of the DNN the DNN is constructed based on the DBN, and the DNN consists of an m-layer restricted Boltzmann machine RBM and a BP network; the constructed DNN is trained based on the data {x(i),Z.sup.I(i)}, i=1, 2, . . . , n; firstly, the greedy algorithm is used to train the RBM of each layer without supervision; then, the feature vector of the RBM in the last layer is used as the input vector for supervised training of the BP network; in the third step, the thermal characteristic parameters of the machine tool are randomly sampled, and the corresponding network output is calculated; according to the probability distribution form, the mean value M and the standard deviation S of thermal characteristic parameters of machine tool, xs(i), i=1, 2, . . . , m is generated by random sampling of these parameters, and the value of m is not less than 10.sup.7; taking x.sub.s(i) as the input, the output Z.sub.S.sup.I(i), i=1, 2, . . . , and m is calculated by the trained DNN; the fourth step is to calculate the reliability of the thermal error model based on the Monte Carlo method; based on data Z.sub.S.sup.I(i), i=1, 2, . . . , m, and according to Equation (6), the failure probability pf of the thermal error model of machine tool is $\begin{array}{cc}{\hat{p}}_f=\frac{1}{m}.Math.{.Math.}_{i=1}^m.Math.Z_s^I\left(i\right).& \left(6\right)\end{array}$

Description

DESCRIPTION OF THE DRAWINGS

[0029] The sole FIGURE is a calculation flow chart.

DETAILED DESCRIPTION

[0030] To make the object, technical solutions, and advantages of the invention clearer, the invention will be described in detail in combination with the attached drawings. Taking the thermal error model of machine tool feed shaft shown in Equation (7) as an example, the influence of some thermal characteristic parameters changes in the model on the prediction effect can be calculated. The thermal error model of the feed axis discretizes the lead screw into M segments, and each segment length is L. For any element L.sub.i of the lead screw, the heat balance equation is as follows:

[00002]$\begin{array}{cc}.Math..Math.Q\left(t\right)=Q\left(t\right)-Q_c\left(t\right)-Q_t\left(t\right).Math..Math..Math..Math.Q\left(t\right)=c.Math..Math..Math..Math.L_i.Math.S.Math..Math..Math..Math.T_{L_i}\left(t\right).Math..Math.Q=0.12.Math..Math..Math.f_w.Math.{}_0.Math.{\mathrm{nM}}_w.Math..Math.Q_c\left(t\right)=h{S}^{}\left(T_{L_i}\left(t\right)-T_f\left(t\right)\right).Math..Math.t.Math..Math.Q_t\left(t\right)=S\frac{\left(T_{L_i}\left(t\right)-T_{L_{i+1}}\left(t\right)\right)+\left(T_{L_i}\left(t\right)-T_{L_{i-1}}\left(t\right)\right)}{L}.Math..Math.t& \left(7\right)\end{array}$

[0031] In these equations, Q is the heat generated by friction of L.sub.i at time t, Q.sub.c is the heat exchange between L.sub.i and surrounding air at time t, Q.sub.t is the heat transfer between L.sub.i and microelements at both sides at time t, Q is the difference between the heat generated and heat dissipation of L.sub.i, c is the specific heat capacity of lead screw, is the density of lead screw, S is the equivalent cross-sectional area of lead screw, .sub.L,(t) is the temperature rise of L.sub.i at time t, f.sub.w is the coefficient related to the type of nut and the lubrication method, .sub.0 is the kinematic viscosity of the lubricant, n is the rotating speed of the lead screw, M.sub.w is the total friction moment of the lead screw, h is the heat exchange coefficient, S is the cooling area of L.sub.i, T.sub.f(t) is the air temperature in contact with the lead screw surface, and is the heat conduction coefficient of the lead screw.

[0032] When the machine tool is worn, the airflow around the lead screw and the lubrication changes, and the thermal characteristic parameters Q, h, and , may change. Therefore, the influence of these parameters' changes on the prediction effect of the thermal error model of the machine tool feed shaft is calculated.

[0033] The calculation flow is shown in the FIGURE, and the specific implementation is given below.

[0034] The first step is to generate data for training the DNN.

[0035] (1) Generating Input Data for Training

[0036] The input of the depth neural network is the thermal characteristic parameters Q, h, and . Let the changes of Q, h, and conform to the normal distribution, and their mean values are 1.04J, 15.14 W/(m.sup.2* C.), and 4.9010.sup.5 W/(m* C.), respectively. The coefficients of the variation are 0.08, 0.12, and 0.005. According to Equation (1), the standard deviations of Q, h, and , are S.sub.Q=0.08J, S.sub.h=1.8.sup.2 W/(m.sup.2* C.), and S.sub.=2.4510.sup.5 W/(m* C.), respectively.

[0037] Based on the premise of a normal distribution, according to the mean and standard deviation of Q, h, and , 2,000 groups of random sampling are obtained {q(i),h(i),(i)}(i=1, 2, . . . , 2000), that is, the input data for network training.

[0038] (2) Generating Output Data for Training

[0039] Based on the thermal error model of the machine tool feed axis, according to Equation (2), the average prediction residual of the thermal error model of the feed shaft is calculated when Q, h, and are taken as the mean values.

[0040] According to Equation (3), the average residual .sub.Res (i), i=1, 2, . . . , 2000, corresponding to each group {q(i),h(i),A(i)}, is calculated.

[0041] According to Equation (3), the average residuals .sub.Res (i), i=1, 2, . . . , 2000, corresponding to each group {q(i),h(i),(i)} are calculated.

[0042] According to Equation (4) and Equation (5), the indicator function of the thermal error model function of the feed shaft of the machine tool Z.sup.I(i), i=1, 2, . . . , 2000 is calculated, that is, the output data for network training.

[0043] The second step is constructing and training deep neural network.

[0044] The DNN is constructed based on the DBN. The network consists of a five-layer RBM) and a BP network. In the first RBM, there are 3 neurons in the explicit layer and 9 neurons in the implicit layer. There are 9 neurons in the explicit and implicit layers remaining in the RBM. The output vector of the RBM in the last layer is the input vector of the BP network. The BP network consists of one input layer, one hidden layer, and one output layer. The input layer contains 9 neurons, the hidden layer contains 5 neurons, and the output layer contains 2 neurons.

[0045] Based on the data {q(i),h(i),A(i),Z.sup.I(i)}, i=1, 2, . . . , 2000, and the constructed deep confidence network is trained. Firstly, the gradient descent method is used for unsupervised training in the RBM of each layer, and then the eigenvector of the upper layer is used as the input vector for supervised training of the BP network.

[0046] In the third step, the thermal characteristic parameters are randomly sampled, and the corresponding network output is calculated.

[0047] Based on the premise of a normal distribution, 10.sup.7 groups of random sampling {q.sub.s(i),h.sub.s(i),.sub.s(i)}(i=1, 2, . . . , 10.sup.7) can be obtained according to the mean and standard deviation of Q, h, and . Taking the random sampling as the input, the trained depth confidence network is applied to calculate the output Z.sub.s.sup.I(i), i=1, 2, . . . , 10.sup.7.

[0048] The fourth step is to calculate the reliability of the thermal error model based on the Monte Carlo method.

[0049] Based on data Z.sub.s.sup.I(i), i=1, 2, . . . , 10.sup.7, and, according to Equation (6), the failure probability of the thermal error model of the machine tool. The final calculation result is {circumflex over (p)}.sub.f=0.0609.