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

Mechanical Systems and Signal Processing

Mayes

2010

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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.

Section: Suitable Linear Response Identification Methodsmentioning

confidence: 99%

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

Mechanical Systems and Signal Processing

Mayes

2010

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“…The peak picking method can be used to identify the Fourier coefficients , r l C from the power spectra in Figure 3, and this approach was found to provide good accuracy in most cases. However, better results were obtained by fitting the measurements to single DOF modes using the Algorithm of Mode Isolation (AMI) [31]. This algorithm was modified from the version in [31] to fit squared modes to the power spectrum near each mode.…”

Section: Validationmentioning

confidence: 99%

“…However, better results were obtained by fitting the measurements to single DOF modes using the Algorithm of Mode Isolation (AMI) [31]. This algorithm was modified from the version in [31] to fit squared modes to the power spectrum near each mode. The AMI algorithm identified the natural frequencies, damping ratios and mode shapes , r l C of the mode manifest at each of the peaks in the spectrum.…”

Section: Validationmentioning

confidence: 99%

Output-only Modal Analysis using Continuous-Scan Laser Doppler Vibrometry and application to a 20 kW wind turbine

Yang

Mechanical Systems and Signal Processing

2012

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Abstract:Continuous-scan laser Doppler vibrometry (CSLDV) is a method whereby one continuously sweeps the laser measurement point over a structure while measuring, in contrast to the conventional scanning LDV approach where the laser spot remains stationary while the response is collected at each point. The continuousscan approach can greatly accelerate measurements, allowing one to capture spatially detailed mode shapes along a scan path in the same amount of time that is typically required to measure the response at a single point. The method is especially beneficial when testing large structures, such as wind turbines, whose natural frequencies are very low and hence require very long time records. Several CSLDV methods have been presented that employ harmonic excitation or impulse excitation, but no prior work has performed CSLDV with an unmeasured, broadband random input. This work extends CSLDV to that class of input, developing an outputonly CSLDV method (OMA-CSLDV). This is accomplished by adapting a recently developed algorithm for linear time-periodic systems to the CSLDV measurements, which makes use of harmonic power spectra and the harmonic transfer function concept developed by Wereley. The proposed method is validated on a randomly excited free-free beam, where one-dimensional mode shapes are captured by scanning the laser along the length of the beam. The natural frequencies and mode shapes are extracted from the harmonic power spectrum of the vibrometer signal and show good agreement with the first seven analytically-derived modes of the beam. The method is then applied to identify the shapes of several modes of a 20kW wind turbine using a ground based laser and with only a light breeze providing excitation.

“…Hence, concepts such as the Mode Indicator Function [47,48] and MIMO identification [49], which are important tools for detecting close natural frequencies, are directly applicable. If P is large, then there will be a large number of outputs and one should seek an algorithm that can efficiently handle that case, such as the Least Squares Complex Frequency Domain Algorithm (LSCF) [50] or the Algorithm of Mode Isolation (AMI) [51][52][53][54]. One important feature of all of these approaches is that they consider all of the responses simultaneously to obtain the best global estimate of the Floquet exponents.…”

Section: Lifting Approachmentioning

confidence: 99%

“…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

Journal of Computational and Nonlinear Dynamics

2009

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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 ...