(601f) Using Data Variety for Modeling and Control of Batch Processes

In this age of big data and Internet of Things (IOT), massive amount of data is generated by various sensing devices. Big data are generally characterized by 3 Vs namely, volume, data variety (temperatures and pressures along with infrared spectroscopy, acoustic, or video images) and velocity [1]. In addition to these, sometimes additional parameters - veracity and value, are included to characterize the challenges associated with big data. Several of these challenges (such as those related to databases) are best addressed within the fields of computer science and business analytics applications. An aspect of big data that falls within the realm of process control problems is that of handling data variety and veracity.

While not necessarily identified in the contributions as 'big data solutions', several researchers have developed feedback control schemes that utilize traditional (temperatures etc.) as well as distributed (in the form of particle size distribution measurements) [2] either as part of a first-principles based approach or in purely data driven models [3-6]. The present work aims to address the outstanding big data modeling and control problem (particularly in the context of batch operations), as detailed below.

The process model (used for feedback control) is generally understood to be one of two kinds- so called first principles models, where the structure of the model is given by governing equations (appropriate balances, laws of thermodynamics), or data driven model, where the structure of the model is chosen based on simplicity of model development (albeit cognizant of the ability to predict process dynamics). Both models, however have parameters that need to be identified/determined, and this can only be done via measurements. In this sense, the availability of more data (or variety of data) generally increases the ability to capture the process dynamics better and thus presents an opportunity for advanced control implementation.

A popular advanced model-based control approach, model predictive control (MPC), has increasingly been studied for the control of batch processes (see, e.g., MPC formulations that utilize first principles models [7-10] and for data-driven approaches [11-15]). The presence of variety of data (henceforth referred to as data variety), however, poses a challenge with first-principles model-based control. In this approach, the model complexity increases to explain data variety. For instance, in case of a particulate process, while the temperature and concentration measurements can be described using ordinary differential equations, prediction of particle size distribution requires population balance equations. Although results exist in the literature where first-principles based approach have been successfully used for control, use of alternative, data driven approaches remains attractive due to the abundance of data and the associated simplicity of model development.

This motivates the development of data driven modeling and control approaches to handle the emerging big data opportunity. Over past several decades, data-analytics in process systems engineering have gained prominence. Largely, methods have been developed and applications demonstrated for traditional data [16-19] with limited results illustrating robust archiving (volume) aspect of the big data in batch processes [20]. One well known approach to data driven batch quality modeling and control is to use latent variable methods. Some of the contributions in this area have dealt with data variety issue directly [3-5] or in conjunction with first-principles model [6]. The simplest implementation of these methods uses so called batch-wise unfolding where each row represents a complete batch duration. However, this unfolding method introduces problems dealing with batches of unequal duration. To address these problems, two methods have been introduced. One method uses a monotonically increasing variable to align batches. The second, more advanced method, uses a technique developed for alignment of sound in voice recognition called dynamic time warping (DTW [20]. While these approaches are useful tools for batch monitoring, they are not as helpful for control because it is unclear how to map future variable trajectories back to the real time domain.

In summary, while possible for monitoring, these models cannot be directly utilized to vary batch durations to achieve improved product quality in a feedback control framework that uses big data. To account for these limitations, for traditional data, a multi-model approach was proposed in [12]. These models were based on the 'current measurements' of the process instead of the 'time'. In more recent work, a subspace-based modeling and control approach for batch quality control was proposed, comprising a state space dynamic model and a quality model, that also did not require batches to be of the same duration for building the model [14]. While these recent results are based on building models using traditional data, they present an opportunity to be adapted to handle the big data problem.

Motivated by these considerations, this work presents the use of data variety for modeling and control of batch particulate process using a two-tier subspace identification based approach. Two formulations are presented: a) minimizing the volume of fines in the final product by leveraging the variety of measurements and b) control of shape of the particle size distribution in the product.

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