Circular Profile Monitoring Based On Gaussian Process Model

Geometric specifications measure the accuracy of parts.It is of great significance to study quality control.For rotating parts,roundness is an important index.It limits the fluctuation of circular form errors.The Gaussian process model,combined with profile monitoring method,is proposed to monitor the deviations of the actual radius from the nominal value of circular profiles,which can ensure the quality of mechanical products.This thesis carries out the research as follows.Based on the theoretical study of Gaussian process,the following two types of Gaussian process models are established for the deviation: 1)the Gaussian process model based on single covariance function;2)the Gaussian process model based on composing covariance functions.For the first type,mean function and covariance function are selected as constant term and squared exponential respectively.It characterizes the relationship between the deviations of the observation points and the corresponding position coordinates,which can describe the circular shape changes.Considering the complex characteristics,further improvement research is made on the basis of the first type of model.Covariance functions with different characteristics including linear covariance function and periodic covariance function are added.Then three types of Gaussian process models are established.Next is profile monitoring.Design a control chart based on the above model parameters to monitor the circular profiles.Taking the cylinder bores of B12 engines as an example,case study is conducted to verify the practicability and feasibility of the models.Finally,the simulation experiment analysis is carried out.Taking spatial autoregressive model as the baseline model,six out-of-control models are established by introducing different changes.Simulation experiments are designed to compare the monitoring performance of different models in phase II.It shows that the detection rate of the Gaussian process model based on single covariance function SE is about 43.1%,which can effectively monitor the production process.The Gaussian process models based on combined covariance functions including SE+LIN,SE+PER and SE+LIN+PER have certain improvement effect.The detection rate increases by about 4%,34.7% and 39.3% respectively.Besides,the results of simulation experiments show that the average run length ARL of the Gaussian process models based on covariance functions including SE,SE+LIN,SE+PER and SE+LIN+PER decreases in turn.It suggests that the Gaussian process method based on composing covariance functions has good monitoring performance for circular profiles.