This paper describes a statistical approach to fault detection and isolation for linear time-varying (LW) systems subject to additive faults with time-varying profiles. The proposed approach combines a generalized likelihood ratio (GLR) test with a recursive filter that cancels out the dynamics of the monitored fault effects. To our knowledge, the proposed recursive filter is new for the considered faults. The resulting algorithm handles fault isolation with weaker assumptions than usual, in particular regarding the requirements on the number of sensors and on the stability of the monitored system. Numerical results for leakage detection in a gas transportation network illustrate the effectiveness of the proposed method. (C) 2014 Elsevier Ltd. All rights reserved.