In structural health monitoring (SHM), risk assessment and decision strategies rely primarily on sensor responses. Simulated data can be generated to emulate the monitoring phenomena under different natural operational and environmental conditions in order to discriminate relevant features and thus identify potential anomalies. Reduced order modelling techniques and one-class machine learning algorithms allow to efficiently achieve this goal for a fixed number and location of sensors. However, since the number of sensors available on a structure is often a limitation for SHM, identifying the optimal locations that maximize the observability of the discriminant features becomes a fundamental task. In this work we propose to use the variational approximation of sparse Gaussian processes to systematically place a fixed number of sensors over a structure of interest. The healthy parametric variations of the structure are included by clustering the inducing inputs, i.e., the outcome of variational inference. This technique is tested on several numerical examples and is demonstrated to be efficient in detecting damages. In particular, it allows for considering the realistic case where damage types and locations are a priori unknown, thus, overcoming the main limitation of existing sensor placement strategies for SHM.