Identifying the mechanical response of a material without presupposing any constitutive equation is possible thanks to the Data-Driven Identification algorithm developed by Leygue et. al. (Data-based derivation of material response. Computer Methods in Applied Mechanics and Engineering 331, 184-196 (2018)). This algorithm allows to measure stresses from displacement fields and forces applied to a given structure; the peculiarity of the technique is the absence of underlying constitutive equation. In the case of real experiments, the algorithm has been successfully applied in Dalémat et. al. (Measuring stress field without constitutive equation. Mechanics of Materials 136, 103087 (2019)), where a perforated elastomer sheet is deformed under large strain. Displacements are gathered with Digital Image Correlation and net forces with a load cell. However, those real data are incomplete for two reasons: some displacement values (close to the edges or in a noise-affected area) are missing and the force information is incomplete with respect to the original DDI algorithm requirements. The present study proves that with appropriate data handling, stress fields can be identified in a robust manner. The solution relies on recovering those missing data smartly enough, so that no assumption, except that the application of the balance of linear momentum has to be made. The influence of input parameters of the method is also discussed. The overall study is conducted on synthetic data: perfect and altered data are used to prove robustness of the proposed solutions. Therefore, the paper can be considered as a practical guide for implementing the DDI method.