xiv PREFACE
and unexpected (e.g., nonlinear) behavior can be noted and dealt with prior to engagement in
detailed data analysis. Multiple Input/Multiple Output (MI/MO) spectral analysis procedures
are the primary cornerstone for detailed measured data analysis. A cumulative coherence tech-
nique, based on Cholesky (triangular) decomposition of partially correlated excitation sources,
provides a systematic tool for (1) assessment of the role (prominence) of individual excitations
and (2) localization and characterization of nonlinear aspects of dynamic response (when promi-
nent). e product of measured data analysis is estimated frequency response functions (FRFs)
and accompanying coherence functions.
Experimental modal analysis is a discipline that benefits from techniques developed dur-
ing the analog era (prior to 1971) and the digital era (after 1971). Intuitive graphical procedures
for preliminary experimental modal analysis owe much of their content to analog era technol-
ogy as well as newer procedures that highlight overall modal content (generally termed modal
indicator functions); this represents the last opportunity for correction of problematic FRF data
prior to detailed experimental modal analysis. A wide range of experimental modal analysis tech-
niques have been developed during the post 1971 digital era. e techniques fall into two dis-
tinct categories, namely: (1) curve fitting procedures and (2) effective dynamic system estimation
procedures. Simultaneous Frequency Domain (SFD) techniques belong to the latter category.
Recent challenges encountered in NASA MSFC’s Integrated Spacecraft and Payload Element
(ISPE) modal test in 2016, associated with the “many modes” problem led to development of
the SFD-2018 technique. is latest SFD innovation possesses a variety of features that alleviate
the “many modes” challenge. Specifically, SFD-2018 validates estimated complex modes by a
decoupling operation that defines single mode (SDOF equivalent) FRFs. is SFD-2018 oper-
ation is reminiscent of multi-shaker tuning, single mode isolation techniques developed during
the analog era, without requiring multi-shaker tuning. In addition, since SFD-2018 automati-
cally computes left-hand eigenvectors of an estimated state-space plant, the product of left- and
right-hand eigenvector matrices automatically produces a mathematically perfect orthogonality
matrix without reliance on a possibly flawed Test Analysis Mass (TAM) matrix. is feature of
SFD-2018 alleviates common difficulties associated with satisfaction of both NASA STD-5002
and USAF Space Command SMC-S-004 test mode orthogonality criteria.
TAM mass matrix dependent test mode orthogonality and test-analysis cross-
orthogonality criteria specified in NASA STD-5002 and USAF Space Command SMC-S-004
are widely used in the U.S. aerospace community. e most commonly employed strategy for
systematic test analysis correlation involves employment of “real” experimental modes that are
defined based on real mode curve fitting and/or approximate test modes constructed from the
real component of estimated complex test modes. In most situations, this strategy is deemed
appropriate. e NASA/MSFC ISPE modal test appears to present severe challenges to the
commonly employed strategy. In response to this difficulty, a new complex test mode-based
test-analysis cross-orthogonality procedure, which is independent of the TAM mass matrix,
was developed. is provides further alleviation of difficulties presented by commonly employed