23 MPUQ-b: Bootstrapping Based Modal Parameter Uncertainty Quantification—Methodology and Application 253 Fig. 23.12 Comparison of MPUQ-b and Monte Carlo histograms of 3rd mode (Case 1) 23.4 Conclusions This paper showcased Bootstrapping based modal parameter uncertainty quantification (MPUQ-b) methodology. The methodology is described in step by step manner and its characteristics, advantages and limitations are discussed. Comparisons are also presented with respect to error propagation approach. It is shown how MPUQ-b combines the strength of bootstrapping technique with standard modal parameter estimation tools like stabilization and cluster diagrams to devise a simple, yet very effective and powerful technique for uncertainty quantification purposes. Biggest strength of this approach is that it does not require any rigorous mathematical treatment, making it readily applicable, irrespective of the modal parameter estimation algorithm or signal processing procedure. Yet another favorable property of MPUQ-b is that it does not involve any demanding assumptions. It does depend on the quality of the data collected but this is true for any method of uncertainty quantification. Validation exercise, described in the paper, shows that MPUQ-b results are comparable to those from Monte Carlo simulations, which mimic the multiple experiment scenario, aimed at getting the sampling distribution. It is also highlighted that MPUQ-b, or for that matter any other uncertainty quantification technique, does not account for errors due to modelling and signal processing. Established good practices in this regard should be adhered to avoid or minimize them. As illustrated, resampling characteristic of bootstrapping enables MPUQ-b to generate bootstrap samples to work with and also paves the way for the use of several data visualization tools, providing useful insight about the estimated modal parameters. With wide range of both qualitative and quantitative tools of statistical inference, MPUQ-b is a promising approach and encouraging results provide assurances towards its application to real-life scenarios. References 1. Bendat, J.S., Piersol, A.G.: Engineering Applications of Correlation and Spectral Analysis, Second edn. John Wiley, New York (1993) 2. Heylen, W., Lammens, S., Sas, P.: Modal analysis theory and testing. PMA Katholieke Universteit, Leuven (1995) 3. Taylor, J.R.: An Introduction to Error Analysis, 2nd edn. University Science Books, Sausalito, CA (1997) 4. Vold, H., Rocklin, T.. The numerical implementation of a multi-input modal estimation algorithm for mini-computers. In: Proceedings of the 1st IMAC, Orlando, FL, November (1982). 5. Vold, H., Kundrat, J., Rocklin, T., Russell, R.: A multi-input modal estimation algorithm for mini-computers. SAE Trans. 91(1), 815–821 (1982) 6. Reynders, E., Pintelon, R., De Roeck, G.: Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mech. Syst. Signal Process. 22, 948–969 (2008) 7. Longman, R.W., and Juang, J., A variance based confidence criterion for ERA identified modal parameters. In: AAS PAPER 87-454, AAS/AIAA Astrodynamics Conference, MT, United States (1988). 8. Juang, J.N., Pappa, R.S.: An Eigensystem realization algorithm for modal parameter identification and model reduction. AIAA J. Guid. Control Dyn. 8(4), 620–627 (1985)
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