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Frequency Response and Coherence function estimation methods

Patwardhan, Rohit S
http://orcid.org/0000-0002-5528-6232
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592169805143687

Abstract Details

2020, MS, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
The frequency response function (FRF) is arguably the most important measurement to be made in the analysis of a dynamic system. Numerous methods have been devised to obtain the most effective and efficient way of estimating an FRF. Through this thesis, the different FRF estimation techniques developed over the years have been detailed. Algorithms that compute an ordinary least squares (OLS) estimate of the FRF, assuming uncorrelated measurement noise to be present either on the output (H1) or the input (H2) signals, have been compared with those that employ total least squares (TLS) equations, such as Hv, by making use of an augmented input-output auto and cross power (GFFX or GXFF ) matrix at every frequency. A different approach for OLS methods, using Cholesky decomposition has been discussed. Comparison has also been made between a TLS algorithm that employs eigenvalue decomposition (HED, more commonly denoted as Hv) and one that uses singular value decomposition (HSVD). Further discussion has been included of the said TLS algorithms computing the FRFs for one output at a time, as historically presented in the development of the Hv algorithm, with a case that evaluates the FRF matrix for all the outputs simultaneously. The development of the corresponding coherence functions has been presented, highlighting the method dependent paradigms that led to concepts such as virtual coherence and partial coherence while underscoring their equivalence with multiple coherence calculations. Some of the existing conditioned coherence metrics have been shown to be inconsistent from an input-output standpoint. The corrected interpretations have been subsequently described for these. Thus, an effort has been made to provide comprehensive documentation regarding the traditional and the relatively new FRF and coherence estimation techniques. A comparative analysis has been presented to highlight the similarities and differences between algorithms.
Randall Allemang, Ph.D. (Committee Chair)
Allyn Phillips, Ph.D. (Committee Member)
Yongfeng Xu, Ph.D. (Committee Member)
73 p.
Mechanical Engineering
frequency response function; coherence; least squares estimation; vibration measurements

Recommended Citations

Citations

  • Patwardhan, R. S. (2020). Frequency Response and Coherence function estimation methods [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592169805143687

    APA Style (7th edition)

  • Patwardhan, Rohit. Frequency Response and Coherence function estimation methods. 2020. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592169805143687.

    MLA Style (8th edition)

  • Patwardhan, Rohit. "Frequency Response and Coherence function estimation methods." Master's thesis, University of Cincinnati, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1592169805143687

    Chicago Manual of Style (17th edition)

ucin1592169805143687
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This open access ETD is published by University of Cincinnati and OhioLINK.