Soft sensor design with small datasets using a difference-based neural network

Soft sensors are mathematical models of industrial processes that are often used for monitoring and control. Data-driven techniques based on artificial intelligence are generally used for identifying these models. Data scarcity is a challenging problem that occurs when the variable to be estimated must be measured by laboratory analysis. Here, a difference-based neural network called Δ-Net is proposed to develop dynamic nonlinear soft sensors when only a few hundred labeled data are available. The Δ-Net, which exploits the case difference heuristic approach, is based on two parallel neural networks responsible for processing pairs of input samples. The Δ-Net is trained on an augmented dataset obtained by pairwise ordering the small original dataset. The outputs of the subnets are then combined to estimate the difference between the corresponding outputs of the pairs. The reconstruction of the output sample is computed as the mean of the distances from the sample to a set of anchor points, to increase the robustness of the prediction. The proposed approach has been applied to well-known industrial benchmarking datasets. The obtained results show superior performance compared to other data augmentation approaches, including bootstrap resampling, variational autoencoders and Wasserstein generative adversarial networks.