Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Identification of nonlinear vibrating structures: Part I -- Formulation

A self-starting multistage, time-domain procedure is presented for the identification of nonlinear, multi-degree-of-freedom systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or nonuniform support motions. Recursive least-squares parameter estimation methods combined with nonparametric identification techniques are used to represent, with sufficient accuracy, the identified system in a form that allows the convenient prediction of its transient response under excitations that differ from the test signals. The utility of this procedure is demonstrated in a companion paper