Optimal Selection of Reference Components and Measurements in Reaction Systems

Abstract

The number of moles of components in reaction systems can be decomposed into reaction variants (states that change with the progress of reactions) and reaction invariants (states that do not change with progress of reactions). The concept of reaction variants/invariants is used in modeling, control, and design applications. For computation of reaction variants, it has been shown that a subset of components needs to be measured and labeled as reference components. This idea ensures that measurement of a subset of components is sufficient in order to estimate the unmeasured components using reference components and known information on flow rates, inlet compositions, volume, and initial conditions. There are several feasible subsets of components which can be measured for computation of reaction variants and estimation of unmeasured components. In practice, measurements are corrupted with noise. Further, there is a cost associated with measurement of each component due to the nature of the instrument or protocol. In this work, we address the problem of selection of reference components or measurements. First, structural conditions for selecting the minimum number of reference components are revisited for homogeneous and heterogeneous reaction systems. It is shown that the component mole numbers lie in a lower dimensional affine subspace under the assumption of known inlet flow rates and compositions, initial conditions, and volumes. Then, we formulate optimization problems for optimal selection of reference components that maximize the quality of the estimates with constraints on cardinality (number of components to be measured) and cost associated with measurement. These formulations are demonstrated using examples of homogeneous reactions and heterogeneous reactions for different reactor configurations and cost associated with sensors.

Convex Optimization Approach to Design Sensor Networks using Information Theoretic Measures

“…The goal is to determine the best combination of sensors to achieve the desired level of accuracy in the measurement of the process variables. This problem can be formulated as an optimal design problem where the goal is to optimize a utility function based on one or more of the following criteria: (a) minimizing the average estimation error that signifies the ability to obtain accurate estimates of process variables using data reconciliation, [1][2][3][4][5] (b) minimizing the operational cost or hardware cost of a plant, [6][7][8][9][10] (c) maximizing network reliability, or the sensor networks' ability to estimate process variables even in the situation where one or more sensors fail. [11][12][13][14][15][16] In addition, observability is often enforced such that the sensor networks can be used to estimate unmeasured variables using measurements and the process model.…”

“…Nabil and Narasimhan 2 developed a sensor network design formulation that incorporated the notion of process economics by defining a loss in operational profit, and it was shown to minimize the trace of the weighted error covariance matrix. Furthermore, Balaji et al 3 applied the A-optimal sensor selection criterion in a reaction system with a linear measurement model.…”

Convex optimization approach to design sensor networks using information theoretic measures

“…The goal is to determine the best combination of sensors to achieve the desired level of accuracy in the measurement of the process variables. This problem can be formulated as an optimal design problem where the goal is to optimize a utility function based on one or more of the following criteria: (a) minimizing the average estimation error that signifies the ability to obtain accurate estimates of process variables using data reconciliation, [1][2][3][4][5] (b) minimizing the operational cost or hardware cost of a plant, [6][7][8][9][10] (c) maximizing network reliability, or the sensor networks' ability to estimate process variables even in the situation where one or more sensors fail. [11][12][13][14][15][16] In addition, observability is often enforced such that the sensor networks can be used to estimate unmeasured variables using measurements and the process model.…”

“…Narasimhan and Rengaswamy 23 proposed a commensurable metric for quantifying the value of a sensor network from a fault diagnostic perspective. Furthermore, Balaji et al 3 applied the A-optimal sensor selection criterion in a reaction system with a linear measurement model. From a computational viewpoint, Menon et al 24 proposed a computationally efficient branch and bound method for optimal sensor selection.…”