Enhanced virtual sample generation based on manifold features: Applications to developing soft sensor using small data.

In the process industry, it is essential to establish a data-driven soft sensor to predict the key variable that is difficult to online measure directly. The accuracy performance of data-driven soft sensors relies heavily on data. Unfortunately, it is hard to acquire sufficient and informative data from the samples with limited number, which is called as the small sample problem. For handling the small sample problem, it is a good solution to generating virtual samples according to the distribution of original data. This paper proposes an enhanced method of virtual sample generation utilizing manifold features to develop soft sensors using small data. First, T-Distribution Stochastic Neighbor Embedding (t-SNE) is utilized to extract the features of input data. The main idea of generating virtual samples is to use the interpolation algorithm to obtain virtual t-SNE input features and then the random forest algorithm is utilized to get the virtual outputs using virtual t-SNE input features. Finally, virtual samples using the proposed t-SNE based virtual sample generation (t-SNE-VSG) can be achieved. For the sake of confirming the effectiveness and feasibility of the presented t-SNE-VSG, a standard data set is first used. What is more, a small data set from an actual industrial process of Purified Terephthalic Acid is used to establish a soft sensor model. The results from simulations show that the accuracy performance of the soft sensor established with small data can be effectively improved by adding the virtual samples generated by t-SNE-VSG. In addition, t-SNE-VSG achieves superior accuracy to state-of-the-art virtual sample generation methods.