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Cited by 79

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Gaussian Process Time-Series Models for Structures under Operational Variability

Avendaño-Valencia, Luis David, Chatzi, Eleni N., Koo, Ki Young, Brownjohn, James M. W.·2017·Frontiers in Built Environment
DOI 10.3389/fbuil.2017.00069
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Abstract

A wide range of vibrating structures are characterized by variable structural dynamics resulting from changes in environmental and operational conditions, posing challenges in their identification and associated condition assessment. To tackle this issue, the present contribution introduces a stochastic modeling methodology via Gaussian Process (GP) time-series models. In the presently introduced approach, the vibration response is represented by means of a random coefficient time-series model, whose coefficients comply with a GP regression on the environmental and operational parameters. The approach may be implemented in conjunction to any type of linear-in-the-parameters time-series model, ranging from simple AR models to more complex non-linear or non-stationary time-series models. The obtained GP time-series modeling approach provides an effective and compact global representation of the vibrational response of a structure under a wide span of environmental and operational conditions. The effectiveness of the postulated GP time-series models is demonstrated through two case studies: the first involves the identification of the vertical vibration response of the Humber bridge, evaluated over a period of three years; the second considers the long-term simulated vibration response of a wind turbine featuring non-stationary dynamics stemming from the rotor speed. In both cases, the variation of the average wind speed is the main driver of uncertainty, while, through application of the proposed GP time-series models, it is possible to track the resulting variation in modal quantities.

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Figures

FIGURE 1 Histogram displaying the distribution of the average wind speeds available for the identification of the model.
FIGURE 1 Histogram displaying the distribution of the average wind speeds available for the identification of the model.CC-BY · From the PDF
FIGURE 2 Typical 1-day variation of the PSD of the acceleration response and the average wind speed: (A) PSD (spectrogram)Hamming window, length 8,192 samples, overlap 5,792 samples ; (B) 2min average wind speed.
FIGURE 2 Typical 1-day variation of the PSD of the acceleration response and the average wind speed: (A) PSD (spectrogram)Hamming window, length 8,192 samples, overlap 5,792 samples ; (B) 2min average wind speed.CC-BY · From the PDF
FIGURE 3 Selection of the order of the AR model. (A) Prior RSS/SSS and BIC curves for increasing model orders na = 1, 2, . . . , 100; (B) frequency stabilization plot of the AR model for increasing model orders with the Welch PSD estimateHamming window, length 512 samples, 256 samples overlap .
FIGURE 3 Selection of the order of the AR model. (A) Prior RSS/SSS and BIC curves for increasing model orders na = 1, 2, . . . , 100; (B) frequency stabilization plot of the AR model for increasing model orders with the Welch PSD estimateHamming window, length 512 samples, 256 samples overlap .CC-BY · From the PDF
FIGURE 4 Selection of the basis order of the GP-AR(72) model. Left: prior RSS/SSS obtained for the training and validation subsets; Right: posterior RSS/SSS obtained for the training and validation subsets.
FIGURE 4 Selection of the basis order of the GP-AR(72) model. Left: prior RSS/SSS obtained for the training and validation subsets; Right: posterior RSS/SSS obtained for the training and validation subsets.CC-BY · From the PDF
FIGURE 5 Prior and posterior estimates of the first four parameters of the GP-AR(72) p =4 model for the average wind speed range from 0 to 25 m/s.
FIGURE 5 Prior and posterior estimates of the first four parameters of the GP-AR(72) p =4 model for the average wind speed range from 0 to 25 m/s.CC-BY · From the PDF
FIGURE 6 GP-AR(72) p =4 model-based PSD, natural frequencies, and damping ratios as a function of the average wind speed in the range 0-25 m/s. Frequency range and damping ratio limited to [0, 500] mHz and [0, 10]%, respectively. (A) PSD of the bridge vibration as a function of AWS; (B) natural frequencies and damping ratios as a function of AWS.
FIGURE 6 GP-AR(72) p =4 model-based PSD, natural frequencies, and damping ratios as a function of the average wind speed in the range 0-25 m/s. Frequency range and damping ratio limited to [0, 500] mHz and [0, 10]%, respectively. (A) PSD of the bridge vibration as a function of AWS; (B) natural frequencies and damping ratios as a function of AWS.CC-BY · From the PDF
FIGURE 7 Distribution of selected natural frequencies and damping ratios obtained from the GP-AR(72) p =4 model. Solid line, modal quantities from prior parameter estimates; dots, modal quantities from posterior parameter estimates; shaded areas, 50 and 90% confidence intervals derived from the parameter mean and covariance matrix. Left column: natural frequencies in mHz; right column: damping ratios.
FIGURE 7 Distribution of selected natural frequencies and damping ratios obtained from the GP-AR(72) p =4 model. Solid line, modal quantities from prior parameter estimates; dots, modal quantities from posterior parameter estimates; shaded areas, 50 and 90% confidence intervals derived from the parameter mean and covariance matrix. Left column: natural frequencies in mHz; right column: damping ratios.CC-BY · From the PDF
Image 8
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Image 9
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Image 10
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FIGURE 11 GP-LPV-AR model-based 'frozen' Power Spectral Density evaluated for a full rotation period of the wind turbine blade, and for increasing wind speeds.
FIGURE 11 GP-LPV-AR model-based 'frozen' Power Spectral Density evaluated for a full rotation period of the wind turbine blade, and for increasing wind speeds.CC-BY · From the PDF
FIGURE 12 GP-LPV-AR model-based average 'frozen' natural frequencies and damping ratios of the wind turbine blade response evaluated for increasing wind speeds. Solid line indicates the average value, while shaded areas indicate estimates of the 95% confidence intervals.
FIGURE 12 GP-LPV-AR model-based average 'frozen' natural frequencies and damping ratios of the wind turbine blade response evaluated for increasing wind speeds. Solid line indicates the average value, while shaded areas indicate estimates of the 95% confidence intervals.CC-BY · From the PDF

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Metadata

Authors
Avendaño-Valencia, L. D., Chatzi, E. N., Koo, K. Y., & Brownjohn, J. M. W.
Venue
Frontiers in Built Environment
Publisher
Frontiers Media SA
Published
2017-12-08
Volume
3
ISSN
2297-3362
DOI
10.3389/fbuil.2017.00069
Cited by
79
References
0
Funders
  • Eidgenössische Technische Hochschule Zürich (FEL-45 14-2)
  • European Research Council (ERC-2015-StG 679843)

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