Abstract
Frequency domain modal parameter estimation from input–output data requires direct measurement or estimation of the input and output signals. In different applications those measurements, especially the excitation signals, are difficult to obtain and/or the assumptions could be poor or inappropriate (high uncertainty or high levels of noise). In this situations, the output–output relations can be used as auxiliary or complementary equations. The current work presents a framework for the identification of modal parameters estimation using maximum likelihood estimation incorporating the output–output relations in addition to the input–output ones. Since the output–output relations are independent of the input signals and its related uncertainty they will improve the system estimation. The ML estimator presents properties of consistency and efficiency and converge to the noiseless solution, but it involve calculating the inverse of the covariance matrix. An extended practice is to consider or assume that the noise of the frequency responses is uncorrelated, in this sense the covariance matrix becomes diagonal and the computational time is reduced. However, the price to pay is that the efficiency of the estimator is altered (the estimator does not reach the Cramer-Rao lower bound). The current work shows that incorporating the output–output relations to the input–output set of equations generates results closer to the ML estimator with a reduced computational load.
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Weijtjens, W., De Sitter, G., Devriendt, C., Guillaume, P.: Operational modal parameter estimation of MIMO systems using transmissibility functions. Automatica 50 (2), 559–564 (2014)
Devriendt, C., Steenackers, G., Sitter, G.D., Guillaume, P.: From operating deflection shapes towards mode shapes using transmissibility measurements. Mech. Syst. Signal Process. 24 (3), 665–677 (2010)
Devriendt, C., Guillaume, P.: Identification of modal parameters from transmissibility measurements. J. Sound Vib. 314 (1–2), 343–356 (2008)
Mao, Z., Todd, M.: A model for quantifying uncertainty in the estimation of noise-contaminated measurements of transmissibility. Interdiscip. Integr. Aspects Struct. Health Monit. Mech. Syst. Signal Process. 28, 470–481 (2012)
Worden, K.: Structural fault detection using a novelty measure. J. Sound Vib. 201 (1), 85–101 (1997)
Worden, K., Manson, G., Fieller, N.: Damage detection using outlier analysis. J. Sound Vib. 229 (3), 647 – 667 (2000)
Johnson, T.J., Adams, D.E.: Transmissibility as a differential indicator of structural damage. J. Vib. Acoust. 124 (4), 634 – 641 (2002)
Afolabi, D.: An anti-resonance technique for detecting structural damage. In: Proceedings of Fifth International Model Analysis Conference, pp. 491–495 (1987)
Worden, K., Manson, G., Allman, D.: Experimental validation of a structural health monitoring methodology: part i. novelty detection on a laboratory structure. J. Sound Vib. 259 (2), 323–343 (2003)
Manson, G., Worden, K., Allman, D.: Experimental validation of a structural health monitoring methodology: part ii. novelty detection on a GNAT aircraft. J. Sound Vib. 259 (2), 345–363 (2003)
Manson, G., Worden, K., Allman, D., Experimental validation of a structural health monitoring methodology: part III. Damage location on an aircraft wing. J. Sound Vib. 259 (2), 365–385 (2003)
Johnson, T.: Analysis of dynamic transmissibility as a feature for structural damage detection. Master’s thesis, Purdue University (2001)
Guillaume, P., Pintelon, R., Schoukens, J.: Description of a parametric maximum likelihood estimator in the frequency domain for multi-input, multi-output systems and its application to flight flutter analysis. Mech. Syst. Signal Process. 4 (5), 405 – 416 (1990)
Schoukens, J., Pintelon, R., Renneboog, J.: A maximum likelihood estimator for linear and nonlinear systems-a practical application of estimation techniques in measurement problems. IEEE Trans. Instrum. Meas. 37 (1), 10–17 (1988)
Schoukens, J., Pintelon, R., van der Ouderaa, E., Renneboog, J.: Survey of excitation signals for FFT based signal analyzers. IEEE Trans. Instrum. Meas. 37 (3), 342–352 (1988)
Pintelon, R., Schoukens, J.: System Identification: A Frequency Domain Approach. Wiley, Hoboken (2012)
Guillaume, P., Verboven, P., Vanlanduit, S.: Frequency-domain maximum likelihood identification of modal parameters with confidence intervals. In: ISMA23th (ed.) Proceedings of the 23rd International Seminar on Modal Analysis, Leuven, pp. 359–366 (1998)
Wilks, S.S.: Multidimensional statistical scatter. In: Anderson, T.W. (ed.) Collected Papers: Contributions to Mathematical Statistics, pp. 597–614. Wiley, New York (1967)
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This work was partially supported by SRP-OPTIMech Vrije Universiteit Brussels (VUB).
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Olarte, O., Guillaume, P. (2017). Improving Modal Parameter Estimation by Complementary Output–Output Relations. In: Mains, M., Blough, J. (eds) Topics in Modal Analysis & Testing, Volume 10. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54810-4_6
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DOI: https://doi.org/10.1007/978-3-319-54810-4_6
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