Industrial time series forecasting based on improved Gaussian process regression

Industrial processes often include shifting operating phases and dynamics, and system uncertainty. Industrial time series data may obey different distributions because of the time-varying characteristic. Therefore, a single global model cannot describe the local characteristics of multiple distributions. In this work, a hybrid GMM-IGPR model is proposed to solve this kind of time series prediction problem by using an improved Gaussian process regression (GPR) based on Gaussian mixture model (GMM) and a variant of the basic particles swarm optimization (PSO). In a first treatment to the time series, different distributions of the original dataset are characterized by adopting the GMM as a cluster method. Then, multiple localized GPR models are built to characterize the different properties between inputs and output within various clusters. In order to optimize the proposed algorithms, this paper utilizes the DEPSO which introduces differential evolution (DE) operator into the basic PSO algorithm to estimate hyperparameters of the GPR model, instead of using the traditional conjugate gradient (CG) method. Lastly, the Bayesian inference strategy is used to estimate the posterior probabilities of the test data with respect to different clusters. The various localized GPR models are integrated through these posterior probabilities as the weightings so that a global predictive model is developed for the final prediction. The effectiveness of the proposed algorithm is verified by means of a numerical example and a real industrial winding process. Statistical tests of experimental results compared with other popular prediction models demonstrate the good performance of the proposed model.