A new and improved MILP formulation to optimize observability, redundancy and precision for sensor network problems

Abstract

in Wiley InterScience (www.interscience.wiley.com).New mathematical formulations of observability, redundancy, and an improved formulation for precision are provided which can be explicitly and analytically solved using mixed integer linear programming (MILP). By using the Schur complement found at the heart of both Gaussian elimination and Cholesky factorization for direct block matrix reduction and the variable classification and covariance calculations found in the reconciliation, regression, and regularization approach of Kelly, it is possible to efficiently optimize the overall instrumentation cost considering both estimability and variability as constraints during the branch-and-bound search of the MILP. Two illustrative examples are highlighted which minimize the cost of sensor placement subject to software and hardware redundancy of the measured variables, observability of the unmeasured variables, and their precision (i.e., inverse of their variance). This formulation is well suited to the problems of designing as well as retrofitting sensor locations in arbitrary networks.

Refinery production scheduling toward Industry 4.0

“…The virtual refinery is a new underlying philosophical paradigm in the petroleum refining industry that requires a knowledge breakthrough, or even a cultural 'break-with' inside the entire organization. For instance, the versatility provided by virtual instrumentation (software-redundant measurement systems (Kelly and Zyngier, 2008a)) allows firms to readily estimate the customized data required to properly running RPS applications. Moreover, by replacing complex and expensive hardware systems (e.g., online analyzers) with conventional hardware (computers) and software (e.g., process simulators), synthetic instruments also allow refiners to reduce the operating and maintenance costs of physical instruments.…”

“…Instead, many consider state estimation (Kalman Filtering) as the way forward, but it does not handle nonlinearities properly. In fact, state estimation is just a subset of data reconciliation that has been proven effective (Kelly and Zyngier, 2008a).…”

New efficient breadth‐first/level traversal tree search method for the design and upgrade of sensor networks

“…We now illustrate the detail of steps in the level by level search for the design Case 3 (MFP3). The list of sensors in ascending order of cost is [5,3,6,1,7,2,8,4,13,17,15,20,24,18,10,22,9,11,21,14,23,16,12,19] Let the set R be defined as follows: R ¼ [1,2,3,4,5,6,7,8,9,10,11,12,13]. The depth-first tree search after exploring 500 nodes identifies [R, 14,16,17,18,19,20,22] as current best (containing 20 sensors and the current best cost is 3878, node XQ) at node 406.…”

“…We now illustrate the detail of steps in the level by level search for the design Case 3 (MFP3). The list of sensors in ascending order of cost is [5,3,6,1,7,2,8,4,13,17,15,20,24,18,10,22,9,11,21,14,23,16,12,19] (vector SC). For simplicity, we use the indexes (or locations) of sensors in the vector SC to indicate the measurement locations.…”

“…In addition, this method as well as the one proposed by Chmilewski et al 7 can only be used to solve minimum-cost sensor network problems subject to precision constraints when data reconciliation is used to exploit software redundancy. Most recently, Kelly and Zyngier 8 presented an MILP model based on the Schur complements theorem to design sensor network for processmonitoring purpose. The authors showed that the model can Correspondence concerning this article should be addressed to M. J. Bagajewicz at bagajewicz@ou.edu.…”