Novel Virtual Sample Generation Based on Locally Linear Embedding for Optimizing the Small Sample Problem: Case of Soft Sensor Applications

In the steady state of complex chemical processes, process data with slight fluctuation are highly repeated. The information on the process data with slight fluctuation is limited and unreliable, which causes the small sample problem. As a result, a soft sensor built using small samples is unacceptable in terms of accurate performance. In order to enhance soft sensor accuracy under the small sample problem, a novel locally linear embedding based virtual sample generation (LLEVSG) approach is put forward. In the proposed LLEVSG method, locally linear embedding is first used to extract features from the original data space. Next, back-propagation neural network (BPNN) and a method of random interpolation are utilized to generate effective virtual samples in the sparse region of the original data. To verify the performance of the proposed LLEVSG method, two case studies of developing soft sensors for a production system of purified terephthalic acid (PTA) and a process of high density polyethylene (HDPE) are carried out. The simulation results confirm that the accuracy of a soft sensor with virtual samples can be improved. In addition, the proposed LLEVSG achieves higher accuracy than other virtual sample generation approaches, indicating the small sample problem is effectively solved by the proposed LLEVSG method.