The paper proposes a low-rank structured parameter identification method for multilinear models. Multilinear models extend the class of linear time-invariant models and can depict more complex dynamics. Tensor representations of these models keep the dimensionality but provide very efficient storage and computation methods of the models by applying decomposition and normalization procedures. The proposed parameter identification method is an automated grey box approach, where no manual modeling is required. A pre-structuring process reduces the parameter identification problem and converts it to a sparse representation to make it applicable to large scale applications while preserving the interpretability of the parameters as property of the normalized multilinear models. An application example for anomaly detection of building systems is given with simulation data for the HVAC system of a seminar room.