Recently, a new non-iterative frequency-domain parameter estimation method was proposed. It is based on a (weighted) least-squares approach and uses multiple-input-multiple-output frequency response functions as primary data. This so-called “PolyMAX” or polyreference least-squares complex frequency-domain method can be implemented in a very similar way as the industry standard polyreference (time-domain) least-squares complex exponential method: in a first step a stabilisation diagram is constructed containing frequency, damping and participation information. Next, the mode shapes are found in a second least-squares step, based on the user selection of stable poles. One of the specific advantages of the technique lies in the very stable identification of the system poles and participation factors as a function of the specified system order, leading to easy-to-interpret stabilisation diagrams. This implies a potential for automating the method and to apply it to “difficult” estimation cases such as high-order and/or highly damped systems with large modal overlap. Some real-life automotive and aerospace case studies are discussed. PolyMAX is compared with classical methods concerning stability, accuracy of the estimated modal parameters and quality of the frequency response function synthesis.

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This article will present and discuss the approach and the first results of a long-term dynamic monitoring campaign on an offshore wind turbine in the Belgian North Sea. It focuses on the vibration levels and modal parameters of the fundamental modes of the support structure. These parameters are crucial to minimize the operation and maintenance costs and to extend the lifetime of offshore wind turbine structure and mechanical systems. In order to perform a proper continuous monitoring during operation, a fast and reliable solution, applicable on an industrial scale, has been developed. It will be shown that the use of appropriate vibration measurement equipment together with state-of-the art operational modal analysis techniques can provide accurate estimates of natural frequencies, damping ratios, and mode shapes of offshore wind turbines. The identification methods have been automated and their reliability has been improved, so that the system can track small changes in the dynamic behavior of offshore wind turbines. The advanced modal analysis tools used in this application include the poly-reference least squares complex frequency-domain estimator, commercially known as PolyMAX, and the covariance-driven stochastic subspace identification method. The implemented processing strategy will be demonstrated on data continuously collected during 2 weeks, while the wind turbine was idling or parked.

This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different approaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples.

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