xiii
Preface
e Integrated Test Analysis Process (ITAP) for structural dynamic systems, presented in this
book, offers in-depth expositions of six key process steps (recognizing the fact that measured
data acquisition is the domain of highly specialized professionals, possibly requiring a completely
separate book to properly cover that discipline).
Definition of an appropriate test article finite element model (FEM) involves (a) deter-
mination of the anticipated operational system’s dynamic environments (specifically their fre-
quency bandwidth and intensity envelopes). In the case of launch vehicles and spacecraft, NASA
and USAF Space Command organizations specify typical bandwidths associated with dynamic
environments (generally at or below 70 Hz for environments that do not include acoustic and
shock load phenomena). Once the bandwidth of the dynamic environment is established, spatial
resolution requirements for the test article FEM’s structural components are defined based on
upper frequency bound to wavelength relationships. As the FEM must be suited for adjustment
of uncertain features, it must include definition of joints and component interfaces in a man-
ner consistent with engineering drawings. e wealth of theoretical and experimental resources,
especially for shell-type structures, offers opportunities to intelligently restrict attention to key
sensitivity parameters.
Development of an effective modal test plan requires careful study of the test article’s FEM
predicted vibration modes. Specifically, close attention should be paid to analytical modal kinetic
energy distributions in addition to modal frequencies and geometric mode shapes. Appreciation
of the fact that modal kinetic energy is mathematically an “unpacking” of the mass-weighted or-
thogonality matrix points to the importance of modal kinetic energy to assist initial selection of
response measurement (accelerometer) allocation. A common challenge associated with shell-
type launch vehicle and spacecraft structures is the “many modes” problem that arises from the
fact that many overall shell breathing modes occur in the same frequency band as overall body
bending, torsion, and axial modes. Difficulties associated with this “many modes” problem may
be alleviated by a well-informed target mode selection process based on modal decomposition of
predicted flight dynamic events. Simplistic modal effective mass criteria, which employ target
mode selection for restricted situations involving base excitation environments, are not relevant
for more general situations. A definitive approach for allocation of response measurement (ac-
celerometer) allocation is offered by the residual kinetic energy (RKE) method, which is widely
employed in the U.S. aerospace community.
Preliminary measured data analysis employing a variety of metrics including probability
density functions, autospectra, time history and associated spectrograms, and shock spectra is an
invaluable prerequisite for detailed data analysis. Issues associated with anomalous data channels
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
PREFACE xv
cross-orthogonality criteria. Further analysis of ISPE test data suggests that ambiguities may
occur as a result of employment of real test mode approximations. Specifically, complex mode
orthogonality “unpacking” operations that produce test mode orthogonality distributions that
are not necessarily in agreement with the commonly employed “real” test mode strategy. is
difficulty led to introduction of an alternative “roadmap for a highly improved integrated test
analysis process.”
Real test mode-based reconciliation of FEMs and modal test data depends upon accurate,
efficient parametric sensitivity analysis of the test article FEM and employment of robust modal
cost functions. Augmentation of baseline model modes with a set of residual modes (called
the residual mode augmentation (RMA) method) has been shown to eliminate unsatisfactory
compromises inherent in a popular technique called structural dynamic modification (SDM).
Employment of a balanced modal cost function was first successfully applied for test analysis
reconciliation as part of the ISS P5 modal test conducted at NASA MSFC in 2001. It was
determined at that time that Nelder–Meade Simplex optimization did not perform satisfactorily,
while a Monte Carlo search strategy offered a robust search option. An exercise demonstrating
hysteretic nonlinear system identification employing minimization of a time history based error
norm is included as a final application. Nonlinearity and complex test modes are possibly the
next challenges to be addressed in the continuing adventure called the integrated test analysis
process for structural dynamic systems.
Robert N. Coppolino
October 2019
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