  In this paper, we study the design and analysis of optimal detection scheme
for sensors that are deployed to monitor the change in the environment and are
powered by the energy harvested from the environment. In this type of
applications, detection delay is of paramount importance. We model this problem
as quickest change detection problem with a stochastic energy constraint. In
particular, a wireless sensor powered by renewable energy takes observations
from a random sequence, whose distribution will change at a certain unknown
time. Such a change implies events of interest. The energy in the sensor is
consumed by taking observations and is replenished randomly. The sensor cannot
take observations if there is no energy left in the battery. Our goal is to
design a power allocation scheme and a detection strategy to minimize the worst
case detection delay, which is the difference between the time when an alarm is
raised and the time when the change occurs. Two types of average run length
(ARL) constraint, namely an algorithm level ARL constraint and an system level
ARL constraint, are considered. We propose a low complexity scheme in which the
energy allocation rule is to spend energy to take observations as long as the
battery is not empty and the detection scheme is the Cumulative Sum test. We
show that this scheme is optimal for the formulation with the algorithm level
ARL constraint and is asymptotically optimal for the formulations with the
system level ARL constraint.
