Method to solve redundant inverse problems based on a Latent Semantic Analysis approach. Application to an aerojet engine

A method for the solution of a certain class of inverse problems is presented. In particular, the method is of interest in cases in which the operation of the engineering system under consideration is extensively monitored, in the sense that the number of output parameters is larger than the number of input parameters. This redundancy of output data often occurs in aerospace engineering applications. The method is based on the Latent Semantic Analysis formulation with a modification specifically adapted to the problem under consideration. The method belongs to the family of the so-called Reduced Order Models since the search for the input parameters is made on spaces whose dimensionality is lower than that of the original space. The main advantage of the method is that most of the computational effort can be shifted off-line, thereby allowing for its use in real time (on-line) applications. The method is described by addressing the inverse problem of input parameter characterization in an aerojet engine.