A linear sensor system is a system in which the sensor measurements have a linear relationship to the source variables that cannot be measured directly. Linear sensor systems are widely deployed in advanced manufacturing processes, wireless transportation systems, electrical grid systems, and oil and gas pipeline systems to monitor and control various physical phenomena critical to the smooth function of such systems. The source variables capture these complex physical phenomena which are then estimated based on the sensor measurements. Two of the critical parameters to be considered while modeling any linear sensor system are the degree of redundancy and reliability. The degree of redundancy is the minimum number of sensor failures that a system can withstand without compromising the identifiability of any source variables. The reliability of a sensor system is a probabilistic evaluation of the ability of a system to tolerate sensor failures. Unfortunately, the existing approaches to compute the degree of redundancy and estimate the reliability are limited in scope due to their inability to solve problems in large-scale.
In this research, we establish a new knowledge base for computing the degree of redundancy and estimating the reliability of large-scale linear sensor systems. We first introduce a heuristic convex optimization algorithm that uses techniques from compressed sensing to find highly reliable approximate values for the degree of redundancy.
Due to the distributed nature of linear sensor systems often deployed in practical applications, many of these systems embed certain structures. In our second approach, we study these structural properties in detail utilizing matroid theory concepts of connectivity and duality and propose decomposition theorems to disintegrate the redundancy degree problem into subproblems over smaller subsystems. We solve these subproblems using mixed integer programming to obtain the degree of redundancy of the overall system. We further extend these decomposition theorems to help with dividing the reliability evaluation problem into smaller subproblems. Finally, we estimate the reliability of the linear sensor system by solving these subproblems employing mixed integer programming embedded within a recursive variance reduction framework, a technique commonly used in network reliability literature.
We implement and test developed algorithms using a wide range of standard test instances that simulate real-life applications of linear sensor systems. Our computational studies prove that the proposed algorithms are significantly faster than the existing ones. Moreover, the variance of our reliability estimate is significantly lower than the previous estimates
