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|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.