This paper describes a novel means for creating a nonlinear extension of principal component analysis (PCA) using radial basis function (RBF) networks. This algorithm comprises two distinct stages: projection and self-consistency. The projection stage contains a single network, trained to project data from a high- to a low-dimensional space. Training requires solution of a generalized eigenvector equation. The second stage, trained using a novel hybrid nonlinear optimization algorithm, then performs the inverse transformation. Issues relating to the practical implementation of the procedure are discussed, and the algorithm is demonstrated on a nonlinear test problem. An example of the application of the algorithm to data from a benchmark simulation of an industrial overheads condenser and reflux drum rig is also included. This shows the usefulness of the procedure in detecting and isolating both sensor and process faults. Pointers for future research in this area are also given.