Chapter 5 The New Poly-reference Complex Frequency Formulated in Modal Model (pCF-MM): A New Trend in Experimental Modal Analysis Sandro D. R. Amador and Rune Brincker Abstrac t In Experimental and Operational Modal Analysis (EMA and OMA), the main challenge is to extract the experimental modal properties of the tested structures from the vibration measurements in a very accurate and robust manner. The EMA and OMA can be carried out in time or frequency domain by fitting a parametric model to time or frequency domain measurements, so that the modal properties can be subsequently extracted for the obtained normal matrices. In this chapter, a novel poly-reference modal identification technique formulated in the frequency domain is proposed. The advantage of the proposed approach with regard to the existing techniques is that it yields numerical (non-physical) modes with negative damping, making it easier to distinguish the physical modes. The accuracy and robustness of such an approach is demonstrated by means of an application example at last part of the chapter. Keyword s OMA · Modal analysis · System identification · Vibrations 5.1 Introduction Over the last five decades, there have been ground breaking advancements in modern experimental structural dynamics, namely in EM Aan d OMA . In the late 70s, the Ibrahi mTim e Domai n (ITD) [1, 2] was introduced to the modal analysis community as the first single-reference Leas t Square s (LS ) modal identification technique capable of handling multiple output measurements at once. Later on, the poly-reference L S Comple x Exponential (pLSCE) [3, 4] was proposed to estimate the modal properties by fitting anAuto-Regressive (AR ) model to the measured free decay functions. Th epLSC Ealgorithm consists of a poly-referenceL Smodal identification technique, meaning that it is capable of taking into account multiple input and multiple output measurements at once in the identification process. Shortly after the invention o f th e pLSCE, the ITD was reformulated into a poly-reference L Stechnique [5]. Though the ITD an d th e pLSC Ewer e th e first poly-reference modal analysis algorithms ever invented, to this day, they are still regarded by many as some of the most robust modal analysis algorithms available. In the 90s, other model identification techniques like the Stochastic Subspac e Identification (SSI ) technique [6, 7] and the Frequenc y Domai n Decomposition (FDD) [8] were proposed, entailing a revolution in OMA. Recently, around the mid-2000s, the frequency domain poly-reference technique known as poly-reference Leas t Square s Comple x Frequency domain (pLSCF) [9, 10, 11] was proposed to perform broadband frequency domain modal identification. In this chapter, a novel poly-reference modal identification technique is proposed. Such an approach is formulated in the frequency domain using the z-domain modal model, hence the name poly-reference Comple x Frequenc y formulated in Moda l Mode l (pCF-MM). Similar to the ITD technique, the idea behind the pCF-MM is to formulate an eigenvalue problem by comparing the two different samples of the measured vibration data. The advantages of the pCF-MM with regard to the existing techniques include, for instance, increased robustness in sorting the physical modal properties from the numerical ones. In order to illustrate these benefits from a practical perspective, the performance of the novel pCF-M Mtechnique is assessed by means of a real OMA of two steel platform specimens. S. D. R. Amador ( ) Department of Civil and Mechanical Engineering (CONSTRUCT), Technical University of Denmark (DTU), Kgs. Lyngby, Denmark e-mail: sdio@dtu.dk; rune@brincker-monitoring.com R. Brincker Brincker Monitoring ApS, Copenhagen K, Denmark © The Society for Experimental Mechanics, Inc. 2024 B. J. Dilworth et al. (eds.), Topics in Modal Analysis & Parameter Identification, Volume 9 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-34942-3_5 49
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