Dealing with small sample size problems in process industry using virtual sample generation: a Kriging-based approach

The operational data of advanced process systems have met with explosive growth, but its fluctuations are so slight that the number of the extracted representative samples is quite limited, making it difficult to reflect the nature of the process and to establish prediction models. In this study, inspired by the process of fisherman repairing nets, a Kriging-based virtual sample generation (VSG) named Kriging-VSG is proposed to generate feasible virtual samples in data sparse regions. Then, the accuracy of prediction models is further enhanced by applying the generated virtual samples. In order to reasonably find data sparse regions, a distance-based criterion is imposed on each dimension to identify important samples with large information gaps. Similar to the process of fisherman repairing nets, a certain dimension is initially fixed at different quantiles. A dimension-wise interpolation process using Kriging is then performed on the center between important samples with large information gaps. To validate the performance of the proposed Kriging-VSG, two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene are carried out. The results indicate that the proposed Kriging-VSG outperforms other methods.