Identification of Nonlinear Differential Equation Models from Generalized Frequency Response Functions

A new algorithm called the total least squares with structure selection (TLSSS) has been proposed to identify continuous time differential equation models from complex frequency response data. The algorithm combines the advantages of both the total least squares and orthogonal least squares with structure selection (OLSSS). The error reduction ratio (ERR) feature of OLSSS are exploited to provide an effective way of detecting the correct model structure or which terms to include into the model and the total least squares algorithm provides accurate estimates of the parameters when the data is corrupted with noise. The performance of the algorithm has been compared with the weighted complex orthogonal estimator and has been shown to be superior.