0
Research Papers

Frequency Response-Based Uncertainty Analysis of Vibration System Utilizing Multiple Response Gaussian Process

[+] Author and Article Information
Wangbai Pan

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China;
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: 14110290001@fudan.edu.cn

Guoan Tang

Professor
Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China
e-mail: tangguoan@fudan.edu.cn

Jiong Tang

Professor
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jiong.tang@uconn.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 16, 2018; final manuscript received April 18, 2019; published online June 5, 2019. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 141(5), 051010 (Jun 05, 2019) (11 pages) Paper No: VIB-18-1166; doi: 10.1115/1.4043609 History: Received April 16, 2018; Accepted April 18, 2019

This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Brincker, R., Zhang, L., and Andersen, P., 2000, “Modal Identification From Ambient Responses Using Frequency Domain Decomposition,” IMAC 18: Proceedings of the International Modal Analysis Conference (IMAC), San Antonio, TX, Feb. 7–10, pp. 625–630.
Shu, L., Wang, M. Y., Fang, Z., Ma, Z., and Wei, P., 2011, “Level set Based Structural Topology Optimization for Minimizing Frequency Response,” J. Sound Vib., 330(24), pp. 5820–5834. [CrossRef]
Bandara, R. P., Chan, T. H. T., and Thambiratnam, D. P., 2014, “Frequency Response Function Based Damage Identification Using Principal Component Analysis and Pattern Recognition Technique,” Eng. Struct., 66(4), pp. 116–128. [CrossRef]
Limongelli, M. P., 2010, “Frequency Response Function Interpolation for Damage Detection Under Changing Environment,” Mech. Syst. Signal Process., 24(8), pp. 2898–2913. [CrossRef]
Kim, C. J., Oh, J. S., and Park, C. H., 2014, “Modelling Vibration Transmission in the Mechanical and Control System of a Precision Machine,” CIRP Ann. Manuf. Technol., 63(1), pp. 349–352. [CrossRef]
Hu, J., Sun, L., Yuan, X., Wang, S., and Chi, Y., 2017, “Modeling of Type 3 Wind Turbine With df/dt Inertia Control for System Frequency Response Study,” IEEE Trans. Power Syst. 32(4), pp. 2799–2809. [CrossRef]
Xia, Z., and Tang, J., 2013, “Characterization of Dynamic Response of Structures With Uncertainty by Using Gaussian Processes,” ASME J. Vib. Acoust., 135(5), p. 051006. [CrossRef]
Muscolino, G., Santoro, R., and Sofi, A., 2014, “Explicit Frequency Response Functions of Discretized Structures With Uncertain Parameters,” Comput. Struct., 133, pp. 64–78. [CrossRef]
Hinke, L., Dohnal, F., Mace, B. R., Waters, T. P., and Ferguson, N. S., 2009, “Component Mode Synthesis as a Framework for Uncertainty Analysis,” J. Sound Vib., 324(1–2), pp. 161–178. [CrossRef]
Yang, J., Faverjon, B., Peters, H., Margurg, S., and Kessissoglou, N., 2017, “Deterministic and Stochastic Model Order Reduction for Vibration Analyses of Structures With Uncertainties,” ASME J. Vib. Acoust., 139(2), p. 021007. [CrossRef]
Rasmussen, C. E., and Williams, C. K. I., 2006, Gaussian Processes for Machine Learning, The MIT Press, Cambridge, MA.
DiazDela, F. A., and Adhikari, O. S., 2010, “Structural Dynamic Analysis Using Gaussian Process Emulators,” Eng. Comput., 27(5), pp. 580–605. [CrossRef]
Arendt, P. D., Apley, D. W., and Chen, W., 2012, “Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability,” ASME J. Mech. Des., 134(10), p. 100908. [CrossRef]
Fricker, T. E., Oakley, J. E., Sims, N. D., and Worden, K., 2011, “Probabilistic Uncertainty Analysis of an FRF of a Structure Using a Gaussian Process Emulator,” Mech. Syst. Signal Process., 25(8), pp. 2962–2975. [CrossRef]
Diazdelao, F. A., Adhikari, S., Flores, E. I. S., and Friswell, M. I., 2013, “Stochastic Structural Dynamic Analysis Using Bayesian Emulators,” Comput. Struct., 120, pp. 24–32. [CrossRef]
Arendt, P. D., Chen, W., and Apley, D. W., 2012, “Improving Identifiability in Model Calibration Using Multiple Responses,” ASME J. Mech. Des., 134(10), p. 100909. [CrossRef]
Kontar, R., Zhou, S., and Horst, J., 2017, “Estimation and Monitoring of Key Performance Indicators of Manufacturing Systems Using the Multi-Output Gaussian Process,” Int. J. Prod. Res., 55(8), pp. 2304–2319. [CrossRef]
Liu, Y., Zhou, K., and Lei, Y., 2015, “Using Bayesian Inference Framework Towards Identifying Gas Species and Concentration From High Temperature Resistive Sensor Array Data,” J. Sens. 2015, pp. 1–10.
Kennedy, M. C., and O'Hagan, A., 2001, “Bayesian Calibration of Computer Models,” J. R. Stat. Soc., 63(3), pp. 425–464. [CrossRef]
Eidsvik, J., Finley, A. O., Banerjee, S., and Havard, R., 2012, “Approximate Bayesian Inference for Large Spatial Datasets Using Predictive Process Models,” Comput. Stat. Data Anal., 56(6), pp. 1362–1380. [CrossRef]
Williams, C. K. I., and Barber, D., 1998, “Bayesian Classification With Gaussian Processes,” IEEE Trans. Pattern Anal. Mach. Intell., 20(12), pp. 1342–1351. [CrossRef]
Filippone, M., and Girolami, M., 2014, “Pseudo-Marginal Bayesian Inference for Gaussian Processes,” IEEE Trans. Pattern Anal. Mach. Intell., 36(11), pp. 2214–2226. [CrossRef] [PubMed]
Gustavsen, B., and Semlyen, A., 1999, “Rational Approximation of Frequency Domain Responses by Vector Fitting,” IEEE Trans. Power Delivery, 14(3), pp. 1052–1061. [CrossRef]
Zeng, R. X., and Sinsky, J. H., “Modified Rational Function Modeling Technique for High Speed Circuits,” IEEE MTT-S: Proceedings of the International Microwave Symposium, San Francisco, CA, Feb., pp. 1951–1954.
Veletsos, A. S., and Ventura, C. E., 1986, “Modal Analysis of Non-Classically Damped Systems,” Earthquake Eng. Struct. Dyn., 14(2), pp. 217–243. [CrossRef]
Einar, N. S., 2014, Structural Dynamics, Springer, New York.
Meirovitch, L., 1990, Dynamics and Control of Structures, John Wiley & Sons, Hoboken, NJ.
Li, E.-P., Liu, E.-X., Li, L.-W., and Leong, M.-S., 2004, “A Coupled Efficient and Systematic Full-Wave Time-Domain Macromodeling and Circuit Simulation Method for Signal Integrity Analysis of High-Speed Interconnects,” IEEE Trans. Adv. Packag., 27(1), pp. 213–223. [CrossRef]
Grivet-Talocia, S., and Bandinu, M., 2006, “Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses,” IEEE Trans. Electromagn. Compat., 48(1), pp. 104–120. [CrossRef]
Karimifard, P., Gharehpetian, G. B., and Tenbohlen, S., 2007, “Determination of Axial Displacement Extent Based on Transformer Winding Transfer Function Estimation Using Vector-Fitting Method,” Int. Trans. Electr. Energy Syst., 18(4), pp. 423–436.
Grivet-Talocia, S., and Gustavsen, B., 2015, Passive Macromodeling: Theory and Applications, John Wiley & Sons, Hoboken, NJ.
Conti, S., and O'Hagan, A., 2009, “Gaussian Process Emulation of Dynamic Computer Codes,” Biometrika, 96(3), pp. 663–676. [CrossRef]
Conti, S., and O'Hagan, A., 2010, “Bayesian Emulation of Complex Multi-Output and Dynamic Computer Models,” J. Stat. Plan. Infer., 140(3), pp. 640–651. [CrossRef]
Bilionis, I., and Zabaras, N., 2012, “Multi-Output Local Gaussian Process Regression: Applications to Uncertainty Quantification,” J. Comput. Phys., 231(17), pp. 5718–5746. [CrossRef]
Johnson, R. A., and Wichern, D. W., 2002, Applied Multivariate Statistical Analysis, Prentice Hall, Upper Saddle River, NJ.
Larrañaga, P., Karshenas, H., Bielza, C., and Santana, R., 2013, “A Review on Evolutionary Algorithms in Bayesian Network Learning and Inference Tasks,” Inf. Sci., 233(2), pp. 109–125. [CrossRef]
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., 2002, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Eberhart, R., and Kennedy, J., 1995, “A New Optimizer Using Particle Swarm Theory,” IEEE MHS'95: The 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43.
Sahin, F., Yavuz, MÇ, Arnavut, Z., and Uluyol, O., 2007, “Fault Diagnosis for Airplane Engines Using Bayesian Networks and Distributed Particle Swarm Optimization,” Parallel Comput., 33(2), pp. 124–143. [CrossRef]
Iman, R. L., 2008, Latin Hypercube Sampling, John Wiley & Sons, Hoboken, NJ.
Wang, X., and Tang, J., 2009, “Damage Identification Using Piezoelectric Impedance Approach and Spectral Element Method,” J. Intell. Mater. Syst. Struct., 20(8), pp. 907–921. [CrossRef]
Shuai, Q., Zhou, K., Zhou, S., and Tang, J., 2017, “Fault Identification Using Piezoelectric Impedance Measurement and Model-Based Intelligent Inference With Pre-Screening,” Smart Mater. Struct., 26(4), p. 045007. [CrossRef]
MSC Software Corporation, 2012, MSC Nastran Quick Reference Guide, MSC Software Corporation, Newport Beach, CA.

Figures

Grahic Jump Location
Fig. 1

Pre-scanning example

Grahic Jump Location
Fig. 2

Flowchart of MRGP establishment and application

Grahic Jump Location
Fig. 3

Discrete structure configuration

Grahic Jump Location
Fig. 4

(a) Example of FRF amplitude, (b) relative error in amplitude, (c) example of FRF in phase, and (d) absolute error in phase

Grahic Jump Location
Fig. 5

Local maxima illustration

Grahic Jump Location
Fig. 6

(a) FRF amplitude results of case 3 and (b) relative error in amplitude of case 3

Grahic Jump Location
Fig. 7

Beam structure. The finite element model is divided into 10 segments. For each segment, change of mass (due to either uncertainty or damage occurrence) is concentrated at the center node.

Grahic Jump Location
Fig. 8

(a) Identification results for nodes with damage in line 1 and (b) identification results for nodes with damage in line 2

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In