Arun K Tangirala

Most of the controllers used in process industries are proportional, integral and derivative (PID) controllers. Missing data is common in these industries due to many reasons such as sensor malfunctioning, data transmission loss etc. The performance of PID control scheme will degrade if operated in presence of missing data. Hence in this paper a method based on compressed sensing techniques is proposed for online reconstruction of missing data and performance is shown with an application to process control. The proposed algorithm is demonstrated on three simulated studies and results show that the proposed algorithm gives comparable results with classical PID control scheme with no missing data.

The subject of compressed sensing, especially, the related concept of sparse representation has been growing into an exciting area with a diverse set of applications in the fields of image sensing and analysis, signal compression, network reconstruction, etc. The efficacy of the associated techniques depends on the ability to discover a suitable basis for a sparse representation of the underlying signal. This paper presents a method for discovering this basis adaptively from the data. Specifically, the method estimates the dictionary of basis functions that maps the sub-sampled signal to the sparse representation of the signal. We present an application of this technique to the reconstruction of missing data, which is an important problem in all data-driven methods. Two case studies, namely, the reconstruction of missing data in a liquid level system and missing pixels of a 2-D signal (image) are presented. Results show that the proposed algorithm outperforms the existing KSVD algorithm in terms of both accuracy and speed of the reconstruction. © IFAC.

Most of the controllers used in process industries are proportional, integral and derivative (PID) controllers. Missing data is common in these industries due to many reasons such as sensor malfunctioning, data transmission loss etc. The performance of PID control scheme will degrade if operated in presence of missing data. Hence in this paper a method based on compressed sensing techniques is proposed for online reconstruction of missing data and performance is shown with an application to process control. The proposed algorithm is demonstrated on three simulated studies and results show that the proposed algorithm gives comparable results with classical PID control scheme with no missing data.

Missing data is a commonly encountered and challenging issue in data-driven process analysis. Several methods that attempt to estimate missing observations for the purpose of control, identification, etc. have been developed over the decades. However, existing methods tend to produce erroneous estimates when the percentage of missing data is high and mostly do not exploit the benefit of parsimonious or sparse signal representations. Recently developed compressed sensing (CS) techniques are naturally suited to handle the problem of missing data recovery since they provide powerful signal recovery methods that take advantage of sparse representations of signals in a set of functions, known as the overcomplete dictionary. A majority of these signal recovery algorithms assume that the dictionary is known beforehand. This paper presents a method to estimate missing observations using CS ideas, but with an adaptive learning of the overcomplete dictionary from data. The method is particularly devised for signals that have a block-diagonal sparse representation, an assumption that is not too restrictive. An iterative optimization method, consisting of an iterative CS problem on block-segmented data, for discovering this sparsifying dictionary is presented. Further, we present theoretical and practical guidelines for the segmentation size. It is shown that the error at each iteration is bounded for the exact, i.e., zero model mismatch and noise-free, case. Demonstrations on five different systems illustrate the efficacy of the proposed method with respect to recovery of missing data and convergence properties. Finally, the method is observed to require fewer observations than a fixed dictionary for a given reconstruction accuracy.

Most of the controllers used in process industries are proportional, integral and derivative (PID) controllers. Missing data is common in these industries due to many reasons such as sensor malfunctioning, data transmission loss etc. The performance of PID control scheme will degrade if operated in presence of missing data. Hence in this paper a method based on compressed sensing techniques is proposed for online reconstruction of missing data and performance is shown with an application to process control. The proposed algorithm is demonstrated on three simulated studies and results show that the proposed algorithm gives comparable results with classical PID control scheme with no missing data.

Most of the controllers used in process industries are proportional, integral and derivative (PID) controllers. Missing data is common in these industries due to many reasons such as sensor malfunctioning, data transmission loss etc. The performance of PID control scheme will degrade if operated in presence of missing data. Hence in this paper a method based on compressed sensing techniques is proposed for online reconstruction of missing data and performance is shown with an application to process control. The proposed algorithm is demonstrated on three simulated studies and results show that the proposed algorithm gives comparable results with classical PID control scheme with no missing data.

Most of the controllers used in process industries are proportional, integral and derivative (PID) controllers. Missing data is common in these industries due to many reasons such as sensor malfunctioning, data transmission loss etc. The performance of PID control scheme will degrade if operated in presence of missing data. Hence in this paper a method based on compressed sensing techniques is proposed for online reconstruction of missing data and performance is shown with an application to process control. The proposed algorithm is demonstrated on three simulated studies and results show that the proposed algorithm gives comparable results with classical PID control scheme with no missing data.