Efficient Gaussian process modelling of section weights in polymer stretch blow moulding

The injection stretch blow moulding (ISBM) has been widely applied in polyethylene terephthalate bottles production process. The modelling of the blowing conditions is important for the control of the process. In this paper, a nonparametric modelling method namely Gaussian Process is employed and applied to estimate the section weights during the process. A key issue in Gaussian Process modelling is to iteratively compute the covariance matrix inversion which is often extremely time-consuming as the optimization of the Gaussian process requires to call the marginal likelihood function and its gradient function. The matrix decomposition methods like Cholesky and QR decomposition have shown to be able to significantly reduce the computation complexity in solving linear problems, and they are also used in Gaussian process modelling in computing the product of a matrix inversion with a column vector in this paper. The algorithm complexities are analysed and compared, and it is shown that the proposed method is particularly useful as the matrix size increases. The proposed method is then used to model the section weights in polymer stretch blow moulding, and the results confirm the efficiency of the proposed method in significantly reducing the computational effort.