Quickest Change Detection

Abstract

The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to biomedical signal processing. In all of these applications the observations being monitored undergo a change in distribution in response to a change or anomaly in the environment, and the goal is to detect the change as quickly as possibly, subject to false alarm constraints.In this chapter, two formulations of the quickest change detection problem, Bayesian and minimax, are introduced, and optimal or asymptotically optimal solutions to these formulations are discussed. Then some generalizations and extensions of the quickest change detection problem are described. The chapter is concluded with a discussion of applications and open issues. I. INTRODUCTIONThe problem of quickest change detection comprises three entities: a stochastic process under observation, a change point at which the statistical properties of the process undergo a change, and a decision maker that observes the stochastic process and aims to detect this change in the statistical properties of the process. A false alarm event happens when the change is declared by the decision maker before the change actually occurs. The general objective of the theory of quickest change detection is to design algorithms that can be used to detect the change as soon as possible, subject to false alarm constraints.The quickest change detection problem has a wide range of important applications, including biomedical signal and image processing, quality control engineering, financial markets, link failure detection in communication networks, intrusion detection in computer networks and security systems, chemical or biological warfare agent detection systems (as a protection tool against terrorist attacks), detection of the onset of an epidemic, failure detection in manufacturing systems and large machines, target detection

Power system line outage detection and identification — A quickest change detection approach

“…that is the supremum in (13) is achieved at γ = 1 [6]. This is useful from the view point of simulating the test.…”

“…Next, we provide a precise mathematical description of this problem and the QCD algorithm that we will use to detect a line outage. We refer the readers to [6] for a detailed survey on QCD theory and algorithms. …”

“…In QCD, a decision maker observes a sequence of random variables, the distribution of which changes abruptly due to some event. The objective is to detect this change in distribution as quickly as possible subject to a constraint on the false alarm rate; see [6] for a survey. We model the incremental change in voltage angle and power injection measurements obtained from PMUs as random variables.…”

Sequential Detection of Multiple Change Points in Networks: A Graphical Model Approach

“…2) Initialize messages (one for each directed edge ) to the all ones vector. Compute for according to (11) 3) Pass messages from a node to each of its descendants (that is, for which is a directed edge) according to (10). Do this, recursively, starting from each of the leaves until you reach the root .…”

“…The message that node sends to its neighbor , at time , is denoted as and computed as (10) for , where for for (11) and is the neighborhood set of . Here, superscript denotes the complement of a set (in the set of natural numbers), that is .…”