Recent trends in Structural Health Monitoring (SHM) systems have demonstrated the growing interest in autonomous, embeddable devices able to perform in-situ inspection and to work conjointly and wirelessly in a global sensor network. Hence, the energy aspect is of prior importance when dealing with such systems. However, most signal processing methods for assessing the integrity of a structure still rely on linear transforms or operators, such as Fourier or amplitude analysis, which for example require analog-to-digital converters that consume a lot of energy. As well, in addition of optimizing the signal processing, another important part is the use of a proper energy management for the whole system. Hence, the purpose of this paper is twofold. First, it aims at reviewing a particular set of low energy cost methods for Structural Health Monitoring consisting of deriving a Damage Index (DI) obtained from the comparison of the LW signature with a reference signal using logical operators that greatly reduce the required computational energy. A particular emphasis will be placed not only on the performance of the exposed techniques, but also on their energy consumption as well as their sensitivity and robustness facing environmental drifts. It will therefore be shown that the use of non-linear operators for the comparison permits ultra-low energy requirements while allowing detection abilities similar to classical approaches. The second objective of this paper is to discuss the implementation of the whole system in an efficient way using proper management strategies. This issue will be discussed through an example of a self-powered SHM scheme powered using ambient vibrations.