Process optimization and control can become challenging when the measurements are affected by irregular noise. Classical approaches utilize Gaussian method like Kalman filtering to alleviate the sensory noise. However, many industries involve skewed noise in their processes. While the closed skew normal (CSN) distribution generalizes a Gaussian distribution with additional parameters, its dimension increases during recursive estimation, making it impractical. Even though there exist some techniques for the solution, they are typically either too complicated or inaccurate for the higher dimensional problems. This study proposes a novel online optimization scheme to reduce the dimensionality of a CSN distribution while considering the properties of the complete empirical distribution. Since the objective function used during the optimization step considers the geometry of the metric space, the proposed scheme achieves the higher accuracy without sacrificing computational efficiency. After finding the reliable combination of objective function and optimizer, the proposed filter is applied to two real-time pilot-scale experiments. The results indicate that it is beneficial for recursive state estimation in the presence of skewed noise.

This paper proposes a performance evaluation method for few-shot learning-based system identification. The basic idea behind the proposed approach is to use “probably approximately correct (PAC)” to assess the obtained boundary of identification errors. The study demonstrates effectiveness of the proposed solution when the noise is not white and there are only limited data samples for the identification in practical applications. The contributions of this study include: 1) modeling errors are quantified via the $L_\infty$ norm; 2) the bounded noises are considered; 3) it is shown that both the modeling and prediction errors can be reduced by increasing the size of training data. Rigorous mathematical analysis and a case study demonstrate the effectiveness of the proposed performance evaluation strategy.

This paper presents a segmental autoencoder-based fault detection (FD) framework for nonlinear dynamic systems. The basic idea behind the proposed FD scheme is to identify a generalized kernel representation based on the representation knowledge learned from an autoencoder. By using the system data, several cascades, linking nonlinear operators, are employed to obtain a data-based model which describes the nonlinear dynamic behaviors. With the help of the segmental structure of an autoencoder, a residual generator is then constructed. Rigorous mathematical analysis and an application on a continuous stirred tank reactor demonstrate the effectiveness of the proposed FD method.