Data-Driven Soft Sensor Design with Multiple-Rate Sampled Data: A Comparative Study

Abstract

Multirate systems are common in industrial processes where quality measurements have slower sampling rates than other process variables. Since intersample information is desirable for effective quality control, different approaches have been reported to estimate the quality between samples, including the numerical interpolation, polynomial transformation, data lifting, and weighted partial least squares (WPLS). Two modifications to the original data lifting approach are proposed in this paper: reformulating the extraction of a fast model as an optimization problem and ensuring the desired model properties through Tikhonov Regularization. A comparative investigation of the four approaches is performed. Their applicability, accuracy, and robustness to process noise are evaluated with a single-input single-output (SISO) system. The modified data lifting and WPLS approaches are implemented to design quality soft sensors for cement kiln processes using data collected from a simulator and a plant log system. Preliminary results reveal that the WPLS approach is able to provide accurate one-step-ahead prediction. The regularized data lifting technique predicts the product quality of cement kiln systems reasonably well, demonstrating the potential to be used for effective quality control and as an advanced component of process analytical technology (PAT).

Review on the Traction System Sensor Technology of a Rail Transit Train

“…In the digital control system, a single sampling method is somewhat limited under certain conditions, and researchers have paid much attention to multiple sampling theory. The digital control system that boasts multiple sampling rates can realize different control functions that the single-sampling-rate digital control system hardly attains, such as simultaneous stabilization, strong stabilization, and system robustness improvement [ 30 , 31 ]. A multi-rate model reference adaptive system (MRAS) is proposed in [ 32 ] to estimate the rotor time constant, and to obtain a highly stable and less noisy estimation result for the rotor time constant for the asynchronous motor.…”

Knowledge based recursive non-linear partial least squares (RNPLS)

“…Another aspect to take into account in the development of reliable industrial data-driven soft sensors is the structure of the available data (missing data, acquisition frequency, presence of outliers, variables resolution, etc.). In the scientific literature there are works that address the existence of outliers [37,38,39], missing data [40] and different sampling rates (multirate data) [41,42,43]. Facing this last aspect in different ways.…”

Building Optimal Multiresolution Soft Sensors for Continuous Processes

“…In this case, all variables have the same resolution (highly localized in time), but different sampling rates. For these situations, several multirate solutions were already proposed in the literature. − However, the case of multiresolution is often overlooked, despite its prevalence and relevancy in industry. It involves situations where the recorded observations have different granularities.…”