Novel Virtual Sample Generation Approach Using Cubic Spline Interpolation Based Autoencoder for Industrial Soft Sensing Under the Condition of Limited Samples

Industrial soft sensing plays a pivotal role in estimating key process variables to facilitate advanced control and process optimization in contemporary industrial settings. Presently, data-driven soft sensor techniques have gained widespread adoption in modern process industries. However, a significant challenge arises when constructing soft sensing models with a limited number of samples, termed the limited sample problem, which necessitates urgent attention. The technique of virtual sample generation (VSG) emerges as a promising solution to address this limitation. To tackle this issue, this paper proposes a novel VSG approach employing cubic spline interpolation-based autoencoder (CSI-AE) for establishing industrial soft sensing under conditions of limited samples. In the presented CSI-AE model, cubic spline interpolation is employed in the feature output layer of the autoencoder (AE) to derive virtual features. Subsequently, leveraging the potent reconfiguration capabilities of the autoencoder, new virtual input variables are generated through the decoder of the autoencoder using these virtual features. Finally, virtual output variables are derived using a gate recurrent unit (GRU) model based on the virtual input variables. To assess the effectiveness of the presented CSI-AE model, industrial process data collected from an actual Pure Terephthalic Acid (PTA) system is utilized. Simulation results validate the validity and accuracy of the presented CSI-AE model.