The identification of the components used in formulated petroleum products such as lubricants is a work intensive process involving different chemical separation technique and manual data analysis. Ion Mobility Spectrometry coupled with Mass Spectrometry (IM-MS) is a powerful analytical tool to detect a large variety of component in a single measurement. The challenge is to deal with the complex, high volume, multidimensional data set yielded at each experiment. The aim of this work is to develop signal processing and machine learning methods allowing automated identification of the components in a product by comparing its IM-MS signal to a database of signatures from potential candidates. The Synapt G2 HDMS Spectrometer used for the study offers two dimensions of separation and can be used to monitor positive or negative ions, leading to a 4-dimensional fingerprint for each component. In a first step, the problem can be reformulated as the 4-modal supervised estimation of linear mixing coefficients under the constraint of positivity and shared sparse support. Solving this problem involves two main challenges: - The first challenge is to ensure the robustness of the identification process with respect toknown experimental variability. A preliminary work has shown that spectra exhibit differences in peak positions between different measurements of the same components, which is incompatible with classical supervised mixing model. We will present a novel method based on the representation of each mass spectrum as a realization of a mixture of Gaussian processes with invariant parameters, estimated by an EM algorithm, and the application of decomposition strategies in that new parameter space. The proposed method has four advantages: robustness with respect to experimental variability, interpretability, the ability to adjust the level of details used for the detection, and the straightforward extension to multidimensional data. The performances of the proposed algorithm will be evaluated on a set of 85 mixtures of 20 constituents. - The second challenge is to solve the unmixing problem by taking advantage of the 4 dimensions of separation. Existing algorithms handle only one-dimensional dictionaries of potential candidates. A new variant of the Orthogonal Matching Pursuit (OMP) algorithm has been used to enable joint estimation of the mixing model using a multimodal dictionary. Preliminary results and perspectives on that promising approach will be presented.