טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentSaraf Yaakov
SubjectInfo-Gap Detection of Anomalies
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yakov Ben-Haim


Abstract

We present a new optimal approach for vector updating under severe conditions of uncertainty, where the uncertainty is described by info-gap models. This approach is applied both to vector estimation in static systems and to anomaly detection in dynamic systems. Probability-based algorithms, either for learning, estimation or hypotheses testing, assume a structure of a probability density function. The validity of such an assumption becomes questionable when we encounter a severe lack of information on the system model and the accompanying uncertainties, with very few measurements available. Info-gap models, which organize events into a family of nested sets of events without employing distribution functions, seem appealing as a tool for formulating learning and hypothesis test algorithms under such circumstances. The three main topics of the thesis are:

  1.  We present a new optimal approach for estimating a vector based on a given batch of very few vector measurements and discuss how the resultant vector can be utilized in a simple task of assessing a cantilever robustness to failure .
  2. We discuss anomaly detection in linear dynamic systems based on very few sequential measurements, where info-gap models describe the additive process and measurement uncertainties. The performance of the anomaly detector is tested in a simple vibrating system consisting of a mass and two springs, and compared against a generalized likelihood ratio detector.
  3. A new theorem, which is related to the Neyman-Pearson lemma, is derived for cases where the info-gap detector is used. In these cases the uncertainties are described not by probability density functions but rather by info-gap models .