The monitoring of industrial robots is often ensured by generic simulators which model the equational aspect of the target machines. We propose an original approach to complete the equational simulator of a milling machine using the accumulated data from the used sensors. This approach creates a specific simulator for each machining situation by taking the triplet (material, cutting tool, workpiece) into account. This improvement brings great added value to the industrial experts and improves the efficiency of industrial robots. It allows them to better follow and interpret the behavior of machines during the milling process. In addition to correct the simulator using real data, our method detects also the anomalies during the real manufacturing performance and fixes the minor bugs along the observed real data during its continuous simulation mimicry. The additional interest of our model remains the precise definition of the complementary model between the real system and the equational simulator. This makes it possible, by using an inductive approach to search for regularities in the model in order to better interpret the structural differences between the model and the system and to better understand the situations linked to their functionalities or undesirable situations. The intensive experiments on real data validate our model and open up many perspectives for future works.