Recent Improvements of the Algorithm of Mode Isolation

2003 ◽  
Author(s):  
Jerry H. Ginsberg ◽  
Matthew S. Allen
Keyword(s):  
Frequency Response ◽  
Least Squares ◽  
Natural Frequencies ◽  
Least Squares Method ◽  
A Priori ◽  
Single Mode ◽  
Computational Effort ◽  
Complex Frequency ◽  
Linear Least Squares ◽  
Mode Isolation

The Algorithm of Mode Isolation (AMI) identifies the natural frequencies, modal damping ratios, and mode vectors of a system by proceesing complex frequency response data. It uses an iterative procedure based on the fact that a general frequency response function is a superposition of modal contributions. The iterations focus successively on a singel mode. The mode that is in focus is isolated by subtracting the other modal contributions using prior estimates of their modal properties. This process leads to a self-contained identification of the number of modes that participate in any frequency band, whereas other techniques require a priori guesses. This paper describes modifications intended to improve AMI’s accuracy and reduce its computational effort. These involve the use of a new linear least squares method for identifying the natural frequency and dmaping ratio of a single mode, a linear least squares global fit of the data in order to identify mode vectors. Results are presented for a model of a cantilever beam with suspended spring-mass-dashpot system. This system was used by Drexel, Ginsberg, and Zaki [Journal of Vibration and Acoustics, 2003 (forthcoming)] to assess the prior version’s ability to identify weakly excited modes and modes having close natural frequencies in the presence of high noise levels. Application of the modeified version of AMI to the same system is shown to lead to significantly more accurate damping ratios are mode vectors, with equally good natural frequencies.

State Space Implementation of the Algorithm of Mode Isolation

2003 ◽  
Vol 125 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Michael V. Drexel ◽  
Jerry H. Ginsberg ◽  
Bassem R. Zaki
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Analytical Framework ◽  
Complex Frequency ◽  
Response Data ◽  
Modal Damping Ratio ◽  
Mode Isolation ◽  
The Time Domain

The Algorithm of Mode Isolation (AMI) extracts modal properties from complex frequency response data. Previous work used classic undamped modes as the analytical framework for the algorithm. The present work extends the algorithm to implement damped modal analysis, in which the eigenvalues and eigenvectors are complex. In order to assess how well this reformulation performs when natural frequencies are close and drive point mobilities are low, a prototypical system consisting of a cantilever beam with attached subsystems is introduced. One of these subsystems is selected to be a tuned vibration absorber for the isolated beam, so the system features a combination of modes whose natural frequencies are close and modes whose drive point mobility is low. The time domain response of this system is evaluated, contaminated with substantial white noise, and then FFT processed in order to obtain synthetic complex frequency response data. The performance of AMI is evaluated by comparing extracted values for natural frequency, modal damping ratio, and complex normal mode vectors to the analytical values. The results reveal that the pair of modes having proximite natural frequencies are accurately identified. Natural frequencies and damping ratios for those modes whose drive mobility is low are identified by processing the ensemble of frequency response functions, but identification of normal mode coefficients for such modes remains problematic.

scholarly journals Detection and localization of multiple small damages in beam

2021 ◽  
Vol 13 (1) ◽  
pp. 168781402098732
Author(s):  
Ayisha Nayyar ◽  
Ummul Baneen ◽  
Syed Abbas Zilqurnain Naqvi ◽  
Muhammad Ahsan
Keyword(s):  
Frequency Response ◽  
Natural Frequencies ◽  
Signal To Noise Ratio ◽  
Moving Average ◽  
A Priori ◽  
Damage Index ◽  
High Signal ◽  
Frequency Range ◽  
Spatial Locality ◽  
System Frequency

Localizing small damages often requires sensors be mounted in the proximity of damage to obtain high Signal-to-Noise Ratio in system frequency response to input excitation. The proximity requirement limits the applicability of existing schemes for low-severity damage detection as an estimate of damage location may not be known  a priori. In this work it is shown that spatial locality is not a fundamental impediment; multiple small damages can still be detected with high accuracy provided that the frequency range beyond the first five natural frequencies is utilized in the Frequency response functions (FRF) curvature method. The proposed method presented in this paper applies sensitivity analysis to systematically unearth frequency ranges capable of elevating damage index peak at correct damage locations. It is a baseline-free method that employs a smoothing polynomial to emulate reference curvatures for the undamaged structure. Numerical simulation of steel-beam shows that small multiple damages of severity as low as 5% can be reliably detected by including frequency range covering 5–10th natural frequencies. The efficacy of the scheme is also experimentally validated for the same beam. It is also found that a simple noise filtration scheme such as a Gaussian moving average filter can adequately remove false peaks from the damage index profile.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

Beam closed orbit correction and feedback by constrained linear least squares method in Hefei light source

2010 ◽  
Vol 22 (1) ◽  
pp. 155-158
Author(s):  
宣科 Xuan Ke ◽  
王琳 Wang Lin ◽  
李川 Li Chuan ◽  
李为民 Li Weimin ◽  
王季刚 Wang Jigang ◽  
...  
Keyword(s):  
Least Squares ◽  
Light Source ◽  
Least Squares Method ◽  
Closed Orbit ◽  
Linear Least Squares ◽  
Orbit Correction

scholarly journals Ellipse Coefficient Map-Based Geomagnetic Fingerprint Considering Azimuth Angles

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 708
Author(s):  
Ju-Hyeon Seong ◽  
Seung-Hyun Lee ◽  
Kyoung-Kuk Yoon ◽  
Dong-Hoan Seo
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Azimuth Angle ◽  
High Signal ◽  
Linear Least Squares ◽  
Positioning Accuracy ◽  
Signal Stability ◽  
Novel Approach ◽  
Magnetic Vectors ◽  
Equalization Method

Geomagnetic fingerprint has been actively studied because of the high signal stability and positioning resolution even when the time has elapsed. However, since the measured three-axis geomagnetism signals at one position are irregular according to the change of the azimuth angle, a large-sized database which is stored magnitudes per angles is required for robust and accurate positioning against the change of the azimuth angle. To solve this problem, this paper proposes a novel approach, an elliptic coefficient map based geomagnetic fingerprint. Unlike the general fingerprint, which stores strength or magnitude of the geomagnetism signals depending on the position, the proposed algorithm minimized the size of databased by storing the Ellipse coefficient map through the ellipse equation derived from the characteristics of 2-D magnetic vectors depending on the position. In addition, the curvature bias of ellipse was reduced by applying the normalized linear least-squares method to 2-D geomagnetic characteristics and the positioning accuracy was improved by applying the weighted geomagnetic signal equalization method.

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