Compressive and Coded Change Detection: Theory and Application to Structural Health Monitoring

In traditional sparse recovery problems, the goal is to identify the support of compressible signals using a small number of measurements. In contrast, in this thesis the problem of identification of a sparse number of statistical changes in stochastic phenomena is considered when decision makers only have access to compressed measurements, i.e., each measurement is derived by a subset of features. Herein, we propose a new framework that is termed Compressed Change Detection. The main approach relies on integrating ideas from the theory of identifying codes with change point detection in sequential analysis. If the stochastic properties of certain features change, then the changes can be detected by examining the covering set of an identifying code of measurements. In particular, given a large number N of features, the goal is to detect a small set of features that undergoes a statistical change using a small number of measurements. Sufficient conditions are derived for the probability of false alarm and isolation to approach zero in the asymptotic regime where N is large. As an application of compressed change detection, the problem of detection of a sparse number of damages in a structure for Structural Health Monitoring (SHM) is considered. Since only a small number of damage scenarios can occur simultaneously, change detection is applied to responses of pairs of sensors that form an identifying code over a learned damage-sensing graph. Generalizations of the proposed framework with multiple concurrent changes and for arbitrary graph topologies are presented

Compressed Change Detection

In traditional sparse recovery problems, the goal is to identify the support of compressible signals using a small number of measurements. In contrast, in this paper the problem of identification of a sparse number of statistical changes in stochastic phenomena is considered. This framework, which is newly introduced herein, is termed Compressed Change Detection. In particular, given a large number N of features, the goal is to detect a small set of features that undergoes a statistical change using a small number of measurements. The main approach relies on integrating ideas from the theory of identifying codes with change point detection in sequential analysis. If the stochastic properties of certain features change, then the changes can be detected by examining the covering set of an identifying code. Sufficient conditions are derived for the probability of detection to approach 1 in the asymptotic regime where N is large. Several applications and generalizations of the proposed framework are presented. © 2014 IEEE

Compressed Change Detection

In traditional sparse recovery problems, the goal is to identify the support of compressible signals using a small number of measurements. In contrast, in this paper the problem of identification of a sparse number of statistical changes in stochastic phenomena is considered. This framework, which is newly introduced herein, is termed Compressed Change Detection. In particular, given a large number N of features, the goal is to detect a small set of features that undergoes a statistical change using a small number of measurements. The main approach relies on integrating ideas from the theory of identifying codes with change point detection in sequential analysis. If the stochastic properties of certain features change, then the changes can be detected by examining the covering set of an identifying code. Sufficient conditions are derived for the probability of detection to approach 1 in the asymptotic regime where N is large. Several applications and generalizations of the proposed framework are presented. © 2014 IEEE

Compressed Change Detection For Structural Health Monitoring

The problem of detection of a sparse number of damages in a structure is considered. The idea relies on the newly developed framework for compressed change detection [1], which leverages the unique covering property of identifying codes to detect statistical changes in stochastic phenomena. Since only a small number of damage scenarios can occur simultaneously, change detection is applied to responses of pairs of sensors that form an identifying code over a learned damage-sensing graph. An asymptotic analysis of the detection delay and the probability of detection of the proposed approach is provided when the number of damage scenarios is large