We propose a residual-based approach for fault detection at rolling mills based on data-driven soft computing techniques. It transforms the original measurement signals into a model space by identifying the multi-dimensional relationships contained in the system. Residuals, calculated as deviations from the identified relations and normalized with the model uncertainties, are analyzed on-line with incremental/decremental statistical techniques. The identification of the models and the fault detection concept are conducted solely based on the on-line recorded data streams. Thus, neither annotated samples nor fault patterns/models, which are often very time-intensive and costly to obtain, need to be available a priori. As model architectures, we used pure linear models, a new genetic variant of Box?Cox models (termed as Genetic Box?Cox) reflecting weak non-linearities and Takagi?Sugeno fuzzy models being able to express more complex non-linearities, which are trained with sparse learning techniques. This choice gives us a clue about the degree of non-linearity contained in the system. Our approach is compared with several state-of-the-art approaches including a PCA-based approach, a univariate time-series analysis, a one-class SVM (fault-free) pattern recognizer in the signal space and a combined approach based on time-series model parameter changes.