A sparse approach to transfer function estimation via Least Absolute Shrinkage and Selection Operator

Estimating transfer functions from sampled input–output data is a critical task in system identification. Traditional approaches, such as least square optimization, often result in dense parameter estimates, which can be less interpretable and computationally intensive. This paper introduces a novel method for transfer function estimation by applying the Least Absolute Shrinkage and Selection Operator (LASSO), which promotes sparsity in the identified coefficients. The proposed approach enables sparse identification of both the numerator and denominator coefficients of the transfer function. The efficacy of the method is demonstrated through numerical experiments and application to the estimation of the natural frequencies of a turbine blade from its impulse response. By leveraging LASSO, we achieve a more parsimonious and interpretable model that captures the essential dynamics of the system. The results highlight the advantages of sparse modelling in system identification and its potential for improving the understanding and prediction of complex mechanical systems.