Preliminary Results on Generalized Transmissibility Operators

Transmissibility operators are mathematical objects that characterize the relationship between outputs of a dynamic system. Transmissibility operators have been used in applications including health monitoring, fault detection, fault localization, fault mitigation, output prediction, state estimation, and system identification. The transmissibility relationship can be either constructed if a model of the system is available, or estimated otherwise. The constructed or estimated transmissibility is used along with one subset of outputs to predict the response of the other subset of outputs. Transmissibility operators are usually constructed or estimated such that the dimension of the transmissibility input is equal to the dimension of the excitation signal acting on the underlying system. Numerical evidence introduced in previous papers showed that the accuracy of the predicted output improves as the number of transmissibility inputs increases. In this paper, we relax the assumption that requires the dimension of the transmissibility input to be equal to the dimension of the excitation signal acting on the underlying system, which results in a more general mathematical representation of transmissibility operators, which we call generalized transmissibility operators.