A linear least-squares version of the algorithm of mode isolation for identifying modal properties. Part I: Conceptual development

Ginsberg, Jerry H.; Allen, M.

doi:10.1121/1.1765195

Cited by 9 publications

(6 citation statements)

References 3 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm, dubbed the Algorithm of Mode Isolation (AMI), was first presented by Drexel and Ginsberg [13] and later extended and validated by Allen and Ginsberg [14][15][16][17][18][19][20]. The algorithm works on frequency domain response data by identifying and subtracting modes from the data until it is reduced to noise (care is taken to avoid identifying and subtracting spurious modes), and the modes identified are then refined through an iterative procedure.…”

Section: Suitable Linear Response Identification Methodsmentioning

confidence: 99%

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Allen

Mayes

2010

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

Abstract:This work presents a class of time-frequency methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier Transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed Zeroed Early-time Fast Fourier Transforms (ZEFFTs), acquire the usual shape of linear Frequency Response Functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip or impact nonlinearities.

show abstract

Section: Suitable Linear Response Identification Methodsmentioning

confidence: 99%

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Allen

Mayes

2010

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

show abstract

“…Recently, Yin and Duhamel [23] reported using a similar technique, though they used finite difference formulas to identify the modal parameters, whereas AMI uses a least-squares fit. Improvements to the AMI algorithm presented originally by Drexel and Ginsberg and results of test problems are documented in [11,12,[24][25][26][27][28]. AMI is based upon the recognition that the FRF data to be fit is a superposition of individual modal contributions.…”

Section: The Algorithm Of Mode Isolationmentioning

confidence: 99%

“…After mode isolation, composites of the synthesised FRFs for individual modes were compared to composites of the isolation residual FRFs. (The isolation residual is the data fit in the mode isolation phase, defined in [28] as the original FRF data minus the contributions of all identified modes except for the mode in focus.) The agreement between the Nyquist composite of the isolation residual for each individual mode and the Nyquist composite of the synthesised FRF was excellent for all of the modes except for modes 4 and 5.…”

Section: Analysis With Ami-simomentioning

confidence: 99%

“…The notation f Pr signifies the Pth element of the rth mode vector, or the Prth element of the displacement portion of the modal matrix, and fA P;r g is the Pth column of the residue matrix for mode r: The eigenvalue is related to the natural frequency o r and damping ratio z r by l r ¼ Àz r o r þ o r ð1 À z 2 r Þ 1=2 . See [28] or [29] for a more detailed discussion of the state space eigenvalue problem and mode vector normalisation.…”

Section: The Algorithm Of Mode Isolationmentioning

confidence: 99%

See 1 more Smart Citation

A global, single-input–multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data

Allen

Ginsberg

2006

Mechanical Systems and Signal Processing

Self Cite

View full text Add to dashboard Cite

“…The response was sampled fifty times per half revolution of the shaft, so the lifting procedure creates in 50 sets of time responses for each output. The DFTs of these lifted responses was found, two of which are shown in the bottom pane of Figures 3 and 4 The set of 200 lifted responses were processed using the Algorithm of Mode Isolation [51,[59][60][61], which considered all 200 responses simultaneously, automatically identifying both of the modes of the system. The respective residues for each response point-shaft angle combination were also identified by AMI, and the algorithm verified that only two modes were present in the response by observing that the response was reduced to noise after removing these modal contributions from the data.…”

Section: Response Model Identificationmentioning

confidence: 99%

Frequency-Domain Identification of Linear Time-Periodic Systems Using LTI Techniques

Allen

2009

Journal of Computational and Nonlinear Dynamics

View full text Add to dashboard Cite

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines and nonlinear systems linearized about a periodic trajectory; all of these have been treated analytically in the literature. However, few methods exist for experimentally characterizing LTP systems. This paper presents a set of tools that can be used to experimentally characterize an LTP system, using a frequency domain approach and utilizing existing algorithms to perform parameter identification. One of the approaches is based on lifting the response to obtain an equivalent Linear Time-Invariant (LTI) form and the other based on Fourier series expansion. The development focuses on the pre-processing steps needed to apply LTI identification to the measurements, the post-processing needed to reconstruct the LTP model from the identification results and the interpretation of the measurements. This approach elucidates the similarities between LTP and LTI identification, allowing the experimentalist to transfer insight from time-invariant systems to the LTP identification problem. The approach determines the model order of the system, and post processing reveals the shapes of the time-periodic functions comprising the LTP model. Further post-processing is also presented that allows one to generate the full state transition matrix and the time-varying state matrix of the system from the parametric model if the measurement set is adequate. The experimental techniques are demonstrated on simulated measurements from a Jeffcott rotor mounted on an anisotropic, flexible shaft, supported by anisotropic bearings. INTRODUCTIONMany important dynamic systems can be modeled as Linear Time-Periodic (LTP). When a system has periodically varying parameters, it is exceedingly important to discover and accurately model this character since it can lead to parametric resonances which are not present for a Linear TimeInvariant (LTI) approximation to the system. Floquet initiated the study of LTP systems in the 1800's [1], and modern Floquet theory has been applied to a variety of mechanical systems such as helicopters [ [10][11][12]. Linear time-periodic system models are also frequently encountered in analysis of nonlinear systems, as it often proves beneficial to linearize the nonlinear system about a periodic trajectory to study its stability.Much progress has been made in the past twenty years towards analysis and control of linear and nonlinear time-periodic systems, as many concepts for LTI systems are readily extended to LTP systems [5,13]. On the other hand, experimental techniques are well developed for LTI systems, but LTP system identification has received relatively little attention. Experimental methods are needed in a number of applications, for example when it is impossible to determine the parameters or periodic functions comprising the LTP model for a system from first principles. They may also be useful to ...

show abstract

A linear least-squares version of the algorithm of mode isolation for identifying modal properties. Part I: Conceptual development

Cited by 9 publications

References 3 publications

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

A global, single-input–multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data

Frequency-Domain Identification of Linear Time-Periodic Systems Using LTI Techniques

Contact Info

Product

Resources

About