First principles models are commonly obtained using finite element or finite difference methods. One of the advantages of these models is that the states in the model have a clear physical interpretation. This makes of them perfect candidates for the monitoring of the states of the system. Unfortunately, the CPU time associated with each evaluation of these complex models is often far too large for these models to be used for online monitoring purposes. This paper introduces a general method to approximate a computationally expensive first principles model with a quasi-linear parameter varying (q-LPV) model. Besides approximating the original model accurately and conserving the physical interpretation of the states, the resulting q-LPV model has generally a much simpler structure than the original model. This in turn implies that the CPU time associated with each model evaluation is generally considerably reduced, allowing the use of these models for online monitoring. Unlike other q-LPV identification techniques, the proposed method extensively uses the availability of the original first principles model. (C) 2009 Elsevier Ltd. All rights reserved.