Abnormality localization for industrial processes described by distributed parameter systems is vital but seldom studied to the best of our knowledge. In this chapter, a systematic framework is proposed to address this problem for a class of linear parabolic distributed parameter systems using a limited number of in-domain measurements plus one boundary measurement rather than the full-state measurement. The proposed methodology consists of an abnormality detection filter and an abnormality localization filter design based on the backstepping techniques and eigenspectrum. For the detection purpose, the residual is evaluated in a lumped manner; For the localization purpose, a distributed residual is first constructed and then evaluated in a distributed manner. Numerical simulations on a heat transfer rod are conducted to demonstrate the effectiveness of the proposed method.