Most industrial processes are run by induction machines (IMs). Condition monitoring of IM assures their continuity of service, and it may avoid highly costly breakdowns. Among the methods for condition monitoring, online motor current signature analysis is being attracting a rising interest, because it is non-invasive, and it can identify a wide variety of faults at early stage. To favour the development of on-line fault diagnosis techniques, it is necessary to have real-time currents with which test the new techniques and devices. Models running in real time in hardware-in-the-loop (HIL) simulators are a suitable alternative to balance the drawbacks of test benches (costly, limited machines, faults and working conditions). These models must be accurate enough to reflect the effects of a fault and they must be running in real time. A promising technique based on the equivalent circuit parameters calculation of IM by finite element analysis (FEA) is attracting a rising interest due to its reliability, performance and the possibility of being run in a HIL. Nevertheless, prior to running in a HIL, it is necessary to compute the IM parameters using FEA, which requires long simulation times and high computing resources. Consequently, covering a whole range of degrees of a giving fault could be unaffordable. What is proposed in this paper is to apply the sparse subspace learning (SSL) in combination with the hierarchical Lagrangian interpolation (HLI) to obtain the parametric solutions of the faulty IM model that cover the whole range of severity of a given fault, with a reduced number of FEA simulations. By means of this approach it is possible not only to boost the computation speed but also to achieve a significant reduction of memory requirements while retaining reasonable accuracy compared to traditional FEA, so enabling the real-time simulation of predictive models.