In this paper, we propose a new approach to Fault Isolation (FI) based on isolation indicators extracted from multi-dimensional system identification models. Given a set of models pointing to a fault (called violated models), the indicators comprise the following information: (1) the degree of violation of the actual samples in all violated models, (2) the quality (trustworthiness) of the violated models and (3) the influence of each variable across all violated models, measured by amalgamated gradient information. We propose two variants of our FI approach: a crisp variant which uniquely determines the variable/channel where the fault is most likely to have occurred, and a fuzzy variant which provides a descending list of fault likelihoods over all variables/channels in the violated models. We evaluated our approach using various types of data-driven modeling techniques (ridge regression, PLS, fuzzy systems approximation) for setting up the system identification models and a Fault Detection (FD) scheme based on a dynamic on-line analysis of residual signals extracted from the models. The evaluation is based on real-word data sets recorded at two different multi-sensor networks that include fifty measurement channels (system variables) in average: one installed for condition monitoring at rolling mills and one for supervising driving simulation cycles at engine test benches. An important aspect of our FI approach is that it can be applied to any FD system that uses reference models ?these can be analytical, expert-based or data-driven? provided that some quality information criteria (model-based and sample-based) are available.