Chapter 4 A Principle for Obtaining Pragmatic Uncertainty Bounds on Modal Parameters Jonas G. Kjeld and Anders Brandt Abstract In the field of structural dynamics, determination of damping contributions of civil structures is a subject influenced with considerable uncertainties. Many different modal parameter estimation techniques are available to describe the dynamic behavior using only the modal response, both in frequency and time domain, but common for all is the struggle to obtain stable damping values. This paper deals with the extraction of modal parameters on simulated data through Operational Modal Analysis with focus on establishing uncertainty bounds for the damping estimates. We investigate a pragmatic principle to bound the errors, including both random and bias errors. Modal parameters are extracted by applying a low order and a high order parameter estimation method which makes it possible to establish uncertainty bounds of the total damping. These uncertainty bounds represent a lower and a higher boundary for the damping estimates corresponding to each of the identified natural modes of the test structure. Attaching a statistical confidence interval to the estimates allows for a better understanding of the uncertainties related to the damping values obtained through Operational Modal Analysis. Keywords Operational modal analysis · Damping quantification · Uncertainty bounds · Signal processing · Offshore structures 4.1 Introduction In Operational Modal Analysis (OMA) of large civil structures, it is usually possible to identify consistent modal parameters in terms of natural frequencies and mode shapes but when it comes to damping of the structure, it appears to be much more difficult to quantify consistent estimates. If we consider an offshore wind turbine (OWT), the structure is exposed to a number of different operational conditions in terms of climatic changes, scour depth, the active system of the OWT itself and many other parameters. The variations in operational conditions influence the dynamic behavior of the structure and this is potentially the reason why it is so difficult to obtain stable damping estimates. Some of these challenges are described in [1, 2]. Today, a variety of modal parameter estimation (MPE) methods are available and while they all are capable of identifying and extract modal parameters of a given system, the results turn out to be slightly different. It is possible to establish a general formulation for many of the MPE methods based on either the Frequency Response Function (FRF) or Impulse Response Function (IRF) which makes it more intuitive to grasp the difference in modal parameters each method computes. A unified formulation for modal identification is presented in [3] which makes it possible to compare the most commonly used MPE methods. The motivation for this paper comes from the experience that it is very difficult to obtain reliable damping estimates. If we include multiple MPE methods and investigate their characteristic equations, we expect that a confidence interval can be defined which bounds the errors, including both random and bias errors. In this paper, the pragmatic uncertainty bounds are defined by studying the modal parameters obtained by using the Mulitple-reference Ibrahim Time Domain (MITD) method J. G. Kjeld ( ) Department of Technology and Innovation, University of Southern Denmark, Odense, Denmark Civil and Structure, Vattenfall Vindkraft A/S, Kolding, Denmark e-mail: jonas.kjeld@vattenfall.com; jokje@iti.sdu.dk A. Brandt Department of Technology and Innovation, University of Southern Denmark, Odense, Denmark e-mail: abra@iti.sdu.dk © The Society for Experimental Mechanics, Inc. 2021 B. Dilworth (ed.), Topics in Modal Analysis & Testing, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47717-2_4 31
RkJQdWJsaXNoZXIy MTMzNzEzMQ==