Autonomous Modal Parameter Estimation: Application Examples D.L. Brown, R.J. Allemang, A.W.Phillips Structural Dynamics Research Laboratory School of Dynamic Systems College of Engineering and Applied Science University of Cincinnati Cincinnati, OH 45221-0072 USA Email: David.L.Brown@UC.EDU ABSTRACT Autonomous modal parameter estimation is an attractive approach when estimating modal parameters (frequency, damping, mode shape, and modal scaling) as long as the results are physically reasonable. Frequently, significant post processing is required to tune the autonomous estimates. A general autonomous method is demonstrated with no post processing of the modal parameters. Example case histories are given for simple measurement cases taken from the laboratory (circular plate) as well as realistic field measurement cases involving significant noise and difficulty (bridge). These application case histories explore the successes and failures of the autonomous modal parameter estimation method and demonstrate the limitations of practical application of automated methods. Nomenclature Ni = Number of inputs. No = Number of outputs. NS = Short dimension size. NL = Long dimension size. ωi = Discrete frequency (rad/sec). si = Generalized frequency variable. [H( ωi)] = FRF matrix (No ×Ni)) [ α] = Denominator polynomial matrix coefficient. [ β] = Numerator polynomial matrix coefficient. m= Model order for denominator polynomial. n = Model order for numerator polynomial. v = Model order for base vector. r = Mode number. UMPA = Unified Matrix Polynomial Algorithm MAC = Modal Assurance Criterion 1. Introduction The desire to estimate modal parameters automatically, once a set or multiple sets of test data are acquired, has been a subject of great interest for more than 40 years [1-24]. In the 1960s, when modal testing was limited to analog test methods, several researchers were exploring the idea of an automated test procedure for determining modal parameters [1-3]. Today, with the increased memory and compute power of current computers used to process test data, an automated or autonomous, modal parameter estimation procedure is entirely possible and is being attempted by numerous researchers. Before proceeding with a discussion of autonomous modal parameter estimation, some philosophy and definitions regarding what is considered autonomous is required. In general, autonomous modal parameter estimation refers to an automated procedure that is applied to a modal parameter estimation algorithm so that no user interaction is required once the process is initiated. This typically involves setting a number of parameters or thresholds that are used to guide the process in order to exclude solutions that are not acceptable to the user. When the procedure finishes, a set of modal parameters is identified that can then be reduced or expanded if necessary. The goal is that no further reduction, expansion or interaction with the process will be required. In order to discuss autonomous modal parameter estimation, some background is needed to clarify terminology and T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 403 DOI 10.1007/978-1-4419-9299-4_34, © The Society for Experimental Mechanics, Inc. 2011
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