Combined Deterministic-Stochastic Frequency-Domain Subspace Identification for Experimental and Operational Modal Analysis

Abstract

Until recently frequency-domain subspace algorithms were limited to identify deterministic models from input/output measurements. In this paper, a combined deterministic-stochastic frequency-domain subspace algorithm is presented to estimate models from input/output spectra, frequency response functions or power spectra for application as experimental and operational modal analysis. The relation with time-domain subspace identification is elaborated. It is shown by both simulations and real-life test examples that the presented method outperforms traditional frequency-domain subspace methods.

Explaining operational modal analysis with data from an arch bridge

“…The fitting of experimental data to a model is an optimization problem based on a cost function, which can be solved either through the linear least squares method or with the maximum likelihood (ML) estimator [17]. All the possible combinations of the previously referred models and fitting procedures are explored in [13], together with a different class of methods (realization algorithms) that use frequency domain state-space models, designated stochastic frequency-domain subspace identification methods. In [18], it is introduced an alternative frequency domain identification algorithm based on the concept of transmissibility functions.…”

“…This disadvantage can be avoided by the use of the so-called positive or half-spectrum. It is demonstrated, for instance in [13], that the modal decomposition of the half-spectrum is given by…”

“…However, it is not adequate to be directly fitted to experimental data, as it is highly nonlinear. Matrix fraction models (fully described in [13]) are more abstract models that can be more easily fitted to measured data and then used to obtain estimates of modal parameters.…”

Análise Modal Operacional No Domínio Do Tempo: Um Estudo Crítico Dos Métodos De Identificação

“…Ao substituir a PSD do ruído branco na Eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) onde δ(t) é a função delta de Dirac. Pelo do teorema de Parseval [32], não é possível obter uma realização de um ruído branco propriamente dito.…”

“…Coso o contrário, são relacionados ao filtro de forçamento. Ao ser comparada com a análise modal experimental (EMA) [20], onde a identificação é feita através do sinais de força e resposta, a análise modal operacional contém vantagens e desvantagens. As principais vantagens estão relacionadas à identificação de estruturas que não podem ser trazidas para laboratórios, como por exemplo, prédios, pontes, turbinas eólicas, satélites em orbita, etc.…”