A virtual sample generation approach based on a modified conditional GAN and centroidal Voronoi tessellation sampling to cope with small sample size problems: Application to soft sensing for chemical process

In the chemical industries, it is occasionally hard to acquire plenty of samples for developing a soft sensor due to physical limitations and high cost of measurements. To overcome this issue, we come up with a virtual sample generation approach to synthesis new samples to rationally enlarge training sets for soft sensing. Firstly, by applying the centroidal Voronoi tessellation sampling, uniformly distributed new samples x are obtained, for the sake of as possible filling up data scarcity regions. Secondly, the corresponding output of those new samples is determined by the conditional distribution P(y vertical bar x) captured by a modified conditional GAN implicitly. The negative logarithmic prediction density is then taken to be a measure of closeness between generated samples and real samples. To examine the effectiveness of our approach, numerical simulations over a benchmarking function and a chemical process application were carried out. Experimental results suggested that in contrast to other existing state-of-the-art approaches, our approach can yield more authentic samples but also give rise to significant improvement in soft sensor's performance. (C) 2020 Elsevier B.V. All rights reserved.