Abnormal Operation Tracking through Big-Data-Based Gram–Schmidt Orthogonalization: Production of n-Propyl Propionate in a Simulated Moving-Bed Reactor: A Case Study

Abstract

Big Data Analytics plays a crucial role in Industry 4.0 by offering tools to improve the decision-making process. These tools comprise data management infrastructures and analytical methods. Among the economic sectors, the chemical process industry already holds mature data management structures but poorly explored analytical tools. In this sense, this work proposes an online analytical tool that can deal with Big Data to be used for identifying abnormal operations in chemical processes. It deals with a modified dynamic sensitivity matrix (DSM) and Gram−Schmidt orthogonalization (GSO) to prioritize process variables under abnormal behavior and scaling the impact they have on plant performance. In order to evaluate the effectiveness of the proposed method, the synthesis of n-propyl-propionate in a challenging simulated moving-bed reactor (SMBR) process is the object of this study. Simulations are carried out within a software-in-the-loop mode through the integration between Matlab and gPROMs. The results show that the proposed algorithm correctly prioritized the variables concerning their impact on the process performance during abnormal behavior. The capabilities of the proposed method were tested in two campaigns: considering abnormalities in two and three operating variables, respectively. In both, the method correctly prioritized their correction order based on their impact on the process performance. Finally, a "what-if" scenario shows that choosing the correction order at random leads to abnormal behavior for longer periods of time.

Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

“…It determines the parameters that should be kept fixed in each series of experiments and is carried out until the highest magnitude reaches a predefined Cutoff Value (CV). The principle ranks the sensitivity of parameters based on their magnitude, M ( p i ), given by M false( p i false) = S p i T S p i ⁣ p i = 1 , ... , n p where S pi is the p-th column of matrix S .…”

“…The orthogonalization is carried out in relation to the column of matrix S with the highest magnitude, S max , yielding S ort , given by S ort = S max false( bold-italicS boldmax bold-italicT bold-italicS boldmax false) · S max T S A residual matrix, S′ , is then calculated: bold-italicS ′ = S − S ort …”

“…The orthogonalization is carried out in relation to the column of matrix S with the highest magnitude, S max , yielding S ort , given by A residual matrix, S′ , is then calculated: …”

“…The orthogonal projection of a vector onto itself does not alter its value. Then, the column with the highest magnitude does not change after orthogonalization, yielding a residual matrix with a null column corresponding to the parameter with the highest effect . The principle of Gram-Schmidt orthogonalization continues with a new orthogonalization of S ′ , yielding a new residual matrix, S ″ .…”

“…Santana et al (2021) suggest plotting the magnitudes and numbering them as indices of their descending order, as Figure 4 exemplifies. 49 CV is the average of the first magnitude, whose derivate approaches zero (nearly horizontal derivative line), and its precedent. CV determination enables dismissal of the parameters that do not significantly influence the process outputs and, hence, should be kept aside from parameter estimation.…”