Networked Computing for Structural Health Monitoring

This paper studies the problem of distributed computation over a wireless network of resource constrained sensor nodes. In particular, we focus our attention on sensor networks used for structural health monitoring. Within this context, the heaviest computation is to determine the singular value decomposition (SVD) to extract mode shapes (eigenvectors) of a structure. Compared to collecting raw vibration data and performing SVD at a central location, computing SVD within the network can result in a significantly smaller energy consumption and delay. Recent results have proposed methods to decompose SVD, which is a well-defined centralized operation, into components that can be carried out in a distributed way. What is missing, and is the focus of this paper, is how to determine a nearoptimal communication structure that enables the distribution of this computation and the reassembly of the final results, with the objective of minimizing energy consumption subject to a computational delay constraint. We show that this reduces to a generalized clustering problem; a cluster forms a unit on which a component of the overall computation is performed. We establish that this problem is NP-hard. By relaxing the delay constraint, we derive a lower bound to this problem. We also show that the optimal solution to the unconstrained problem has a simple structure that reveals insights into the solution of the original constrained problem. We then propose an integer linear program (ILP) to solve the constrained problem exactly as well as an approximate algorithm with a proven approximation ratio. We also present a distributed version of the approximate algorithm. Numerical results are presented to demonstrate the effectiveness of the approximate and distributed algorithms.