(180r) Observability and Redundancy Labelling Methodology in Pressurized Water Treatment Systems

Modern water treatment plants can employ hundreds to thousands of sensors for process monitoring and control. Despite this, there are often limited useful data for a given plant, due to improper or suboptimal sensor placement. Optimizing existing layouts, or better yet, properly planning sensor placement as part of the design process, deserves a rigorous approach, as it can help mitigate costs, detect faults, and increase measurement accuracy. Prior studies have employed graph theory to label observable process variables and redundant sensors. These studies then proceed to addressed the problem of sensor placement as a multi-objective optimization problem, considering process variable observability, sensor redundancy, and the cost associated with sensor installation and maintenance. Graph-based labelling approaches are robust, but they are only usable for a handful of nonlinear systems. Pressure changes across membranes, pipes, fittings, and fluid machines such as centrifugal pumps, often exhibit nonlinear relationships with fluid flowrate. The inclusion of these relationships is nevertheless vital to properly label observability and redundancy for reverse osmosis, packed columns, and other unit operation where pressure cannot be neglected in the constraint equations.

Numerical approaches can be used for structural labelling in such nonlinear systems. These methods typically involve linearization of the constraint equations, dividing the resulting Jacobian matrix into measured and unmeasured components, and subsequent generation of a projection matrix. A drawback of these approaches are they often require the identification of zeros in matrix rows and columns, which can be hampered by floating point precision and numerical accuracy. One approach to mitigate this is symbolically calculating the Jacobian and the successive projection matrices. In this work, a novel approach to structural observability and redundancy labelling is presented, utilizing a symbolic evaluation of the unmeasured variable Jacobian matrix in reduced row echelon form (RREF). This method is benchmarked against graph theory labelling techniques, as well as existing alternative numerical labelling approaches. The RREF approach is shown to be robust and universally applicable regardless of the system, as illustrated with example use cases for linear, bilinear, and nonlinear constraints. Finally, a case study of a reverse osmosis desalination system is is investigated to illustrate how the RREF labelling method can be used for determining Pareto-optimal sensor layouts for a nonlinear pressurized system.

This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government and the publisher, by accepting the article for publication, acknowledge that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, and to allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doepublic-access-plan).