Q2. What are some of the popular output-only methods?
Frequency based output-only methods include the orthogonal polynomial methods [6, 7], complex mode indicator function [8], and frequency domain decomposition [9].
Q3. What are some time domain output-only methods?
Some time domain output-only methods are the Ibrahim time domain method [1], polyreference method [2], eigensystem realization algorithm [3], least square complex exponential method [4], independent component analysis [10, 11]and stochastic subspace identification methods [5].
Q4. What is the effect of forcing on the eigenvalue problem?
Analysis suggests that, for undamped systems, if the expected value of the product between response and excitation variables is zero, then the smooth orthogonal decomposition converges to an equivalent representation of the undamped structural eigenvalue problem, and therefore should produce estimated modal frequencies and mode shapes for randomly excited structures.
Q5. What is the forcing function for a linear vibratory system?
If the forcing functions are modeled as white noise, then Cfjl(τ) = γjδ(τ)δjl, where δ(τ) is the Dirac delta function, and δjl is the Kronecker delta.
Q6. What are the advantages of output-only analysis over traditional modal analysis?
Recent additions to the time domain output-only family are the smooth orthogonal decomposition [12] and state-variable modal decomposition methods [13, 14], that have shown good results for modal analysis of free response cases.
Q7. What is the maximum damping ratio in the example problem?
The example problem studied had a maximum damping ratio of ζ = 0.027 in the system corresponding to fundamental frequency of ω1 = 0.1838.
Q8. What are the advantages of output-only analysis?
3) Contrary to traditional modal analysis, in many cases output-only analysis can eliminate the need of testing the structure at various locations (or components).
Q9. What is the mean of the product of displacement matrix and forcing vector?
It was shown that the mean of the product of displacement matrix and forcing vector approaches zero as sufficiently large number of samples are captured.
Q10. What is the eigenvalue problem in the matrix?
(8)The elements in the matrix 1 N XXT represent cross correlations (with zero delay) between responses, and are expected to be nonzero.
Q11. what is the effect of a random excitation on a random system?
While this work focused on white-noise excitation, if it can be shown that the mean of product between the response and the forcing approaches zero (in reference to Eqs. (8) and (10)) for other classes of random excitation, this would broaden the applicability of smooth orthogonal decomposition for randomly excited systems.
Q12. What is the modal participation of the system?
Insight to modal participation is not directly obtained, but can come from analysis of the modal coordinates, dependent on how modal vectors are normalized.
Q13. What is the condition for which the eigenvalue problem is not solved?
Under this condition, the smooth orthogonal decomposition, even with random excitation, would produce the modal frequencies and mode shapes of the system.
Q14. What is the maximum singular value of the matrices?
The maximum singular values of these matrices are plotted in Fig. 4, indicating that 1 N XFT approaches zero (while the other matrices’ singular values settle to finite values), thereby becoming negligible for large N .
Q15. What is the modal frequency of the ftm?
In this form hil(t) is a linear combination of modal coordinate impulse response functions, each sinusoidal with a modal frequency.
Q16. What is the modal parameter for the NExT?
NExT would accommodate using output-only methods for modal parameter identification in case of independent (uncorrelated) white noise forcing.