Research And Application Of Gaussian Process Regression Method For Functional Data

The data obtained by intensive sampling in continuous space often have functional characteristics.These data can be studied by the classic multivariate statistical method,but the information contained in the functions hidden behind the data is indeed ignored.Functional data analysis(FDA)uses basis functions to convert discrete data into a functional form,and treats the discrete data observed along a continuous space as a whole for analysis.Therefore,it is less dependent on assumptions,and the derivative of the curve can be calculated to mine more information.The most important step in the FDA modeling process is to convert discrete data into functional data,which can be used for regression analysis of functional data.Gaussian process regression(GPR)is a regression method based on the Bayesian framework.Its core method is to use the kernel function to model the covariance structure.Because it is assumed that the regression model follows the prior of the Gaussian process,the GPR model not only has good calculation properties of the kernel function,but also has good statistical properties that can give 95%confidence intervals of the predicted values,However,since the GPR model only models the covariance function,it is difficult to predict new samples.Therefore,based on functional data analysis and gaussian process regression,we also model the mean and covariance structure.First assume that the mean structure is a functional linear number model,and then convert it to the parameter estimation of the GPR model,and use the maximized marginal likelihood function to estimate the parameter?of the kernel function,thereby constructing a functional data regression based on Gaussian process regression(GPFR)Model,and improve the kernel function of GPFR,and found that the improved GPFR model has very good prediction performance.This article uses three different types of data(barometric pressure and temperature data in meteorological data in Beijing area;tunneling speed data for a certain shield machine operation,as well as multi-dimensional simulation data and multi-dimensional shield machine data)to conduct experimental explorations on the three models of GPR,FDA and GPFR,and compares the mean square error(MSE),absolute mean error(MAE)and R squared error(R~2)as evaluation indicators.It is found that the improved GPFR model is superior to the GPR and FDA models in terms of accuracy,especially in multidimensional data.Shield machine is indispensable in subway construction.How to use the main parameters of the shield machine to accurately predict the tunneling speed of the shield machine has always been the difficulty of the construction process.This article uses the above three regression models to analyze the multi-dimensional shield machine data.The study found that the improved GPFR model uses the main parameters of the shield machine operation(running time,cutter head speed,and propulsion pressure)to predict the propulsion speed(MSE,MAE)with small error(MSE,MAE)and high accuracy,and the prediction effect is far better than FDA and GPR models.The prediction effect is far superior to the FDA and GPR models.At the same time,it is found that the true propulsion speed value of the shield machine falls within the 95%confidence interval of the predicted value.indicating that the improved GPFR model uses the main parameters of the shield machine to give a more accurate prediction of the driving speed.