Section: New Results

identification of linear systems

Evaluation of confidence intervals and computation of sensitivities for subspace methods

Participants : Michael Doehler, Laurent Mevel.

Stochastic Subspace Identification methods have been extensively used for the modal analysis of mechanical, civil or aeronautical structures for the last ten years. So-called stabilization diagrams are used, where modal parameters are estimated at successive model orders, leading to a graphical procedure where the physical modes of the system are extracted and separated from spurious modes. Recently an uncertainty computation scheme has been derived allowing the computation of uncertainty bounds for modal parameters at some given model order. In this paper, two problems are addressed. Firstly, a fast computation scheme is proposed reducing the computational burden of the uncertainty computation scheme by an order of magnitude in the model order compared to a direct implementation. Secondly, a new algorithm is proposed to derive the uncertainty bounds for the estimated modes at all model orders in the stabilization diagram. It is shown that this new algorithm is both computationally and memory efficient, reducing the computational burden by two orders of magnitude in the model order[14] .

Subspace methods in frequency domain

Participants : Philippe Mellinger, Michael Doehler, Laurent Mevel.

In this paper a combined subspace algorithm and a way to quantify uncertainties of its resulting identified modal parameter has been presented. Even if the algorithm is data-driven, it was proven that uncertainties can still be quantified by using the square subspace matrix without any modification neither on the identified modal parameters or on the stabilization diagrams. A comparison between uncertainty quantification based on this data-driven combined subspace algorithm and the well-known covariance-driven stochastic subspace algorithm shows good results on this new method. Both values and confidence intervals are similar. However combined algorithm gives better results considering spurious modes. [27] .

Subspace Identification for Linear Periodically Time-varying Systems

Participants : Laurent Mevel, Ahmed Jhinaoui.

Many systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as Linear Time-Invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a Linear Periodically Time-Varying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground. [22] , [23] , [18] .