Chapter38 Optimal Phasing Combinations for Multiple Input Source Excitation Kevin L. Napolitano and Nathanael C. Yoder Abstract Multiple input random source excitation has proven to be an excellent method for measuring high-quality frequency response functions. Multiple-reference deterministic source excitation methods, such as multiple-reference sine sweeps, have been developed as well. The key to these deterministic methods is ensuring that the reference auto spectral matrix is invertible. This is achieved by (1) sweeping through each frequency at least as many times as there are numbers of active references and (2) changing the relative phasing or magnitude between the sources with each pass. This paper presents a method of defining an optimal set of source phasing combinations for a given the number of sources and a given number of desired phasing combinations. Assuming each source is fully activated during testing, this set of phasing combinations will produce a perfectly conditioned source auto spectral matrix. Keywords Modal testing • Source excitation • Sine sweep • Multiple input • Sine dwell 38.1 Introduction Multiple input random source excitation has proven to be an excellent method for measuring high-quality frequency response functions. Deterministic sinusoidal excitation techniques such as (single or multiple) discrete sine wave inputs, or sine sweeps, are often used when the random signals are not strong enough to overcome the noise floor of the test article [1]. As with random source excitation, allowing all the sources to be active simultaneously helps spread energy throughout a structure while also reducing overall testing time. The key to ensuring that any excitation method can produce multiple-input frequency response functions is to ensure that the reference auto spectrum matrix, [SXX], is well conditioned so that it can be inverted [2, 3]. This is achieved by (1) stepping or sweeping through each frequency at least as many times as the number of source signals and (2) changing the relative phasing between the sources with each pass. This paper defines a method for generating optimal relative phase combinations for a given “M” number of sources, for a given “N” number of phase cases. Each phase case will be associated with one frame of test data. The optimal solution is defined as all sources being fully engaged during each phase case and the resulting source auto spectrum matrix [SXX] being perfectly conditioned, i.e., proportional to the identity matrix. First the special case where the number of sources matches the number of phasing cases is discussed. The method is then expanded to an arbitrary number of sources and phase cases, and methods for varying the phasing are discussed. After discussing how to apply these techniques to two different deterministic signal types, fixed sine and sinusoidal sweep, an example of the method using multiple-reference burst chirp excitation is presented. K.L. Napolitano ( ) • N.C. Yoder ATA Engineering, Inc., 11995 El Camino Real, Suite 200, San Diego, CA 92130, USA e-mail: kevin.napolitano@ata-e.com R. Allemang (ed.), Topics in Modal Analysis II, Volume 8: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04774-4__38, © The Society for Experimental Mechanics, Inc. 2014 411
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