Novel virtual sample generation using conditional GAN for developing soft sensor with small data

In terms of data-driven soft sensing modeling of industrial processes, it is practically necessary to collect sufficient process data. Unfortunately, sometimes only few samples are available as a result of physical restrictions and time costs, resulting in insufficient data and incomplete data representative. It is increasingly important and urgent to deal with the small data problem in developing soft sensors. To handle those practical issues, a new virtual sample generation approach based on conditional generative adversarial network (CGAN-VSG) is proposed. In the proposed CGAN-VSG approach, the local outlier factor (LOF) is first integrated with the K-means++ algorithm to find the scarcity regions of small data along output space. Secondly, a couple of output samples of interest that match the overall output trend are generated to fill up the scarcity regions. Third, CGAN is utilized to produce corresponding input samples with those generated output samples of interest. Finally, lots of virtual inputs and outputs are obtained to enhance the accuracy of data-driven soft sensor with small data. To validate the superior of the proposed CGAN-VSG approach, standard functions are firstly selected to investigate into the quality of generated input and output virtual samples. In addition, a real-world application of a cascade reaction process named high-density polyethylene (HDPE) is carried out. Simulation results suggest that the presented CGAN-VSG approach is superior to several other state-of-the-art methods, such as TTD, MTD and bootstrap, in the term of accuracy.