Bayesian Optimal Sensor Placement for Modal Identification of Civil Infrastructures

Costas Argyris, Costas Papadimitriou, Panagiotis Panetsos

Abstract

A Bayesian optimal experimental design (OED) method is proposed in this work for estimating the best locations of sensors in structures so that the measured data are most informative for estimating reliably the structural modes. The information contained in the data is measured by the Kullback-Leibler (K-L) divergence between the prior and posterior distribution of the model parameters taken in modal identification to be the modal coordinates. The optimal sensor placement that maximizes the expected K-L divergence is shown also to minimize the information entropy of the posterior distribution. Unidentifiability issues observed in existing formulations when the number of sensors is less than the number of identified modes, are resolved using a non-uniform prior in the Bayesian OED. An insightful analysis is presented that demonstrates the effect of the variances of Bayesian priors on the optimal design. For dense mesh finite element models, sensor clustering phenomena are avoided by integrating in the methodology spatially correlated prediction error models. A heuristic forward sequential sensor placement algorithm and a stochastic optimization algorithm are used to solve the optimization problem in the continuous physical domain of variation of the sensor locations. The theoretical developments and algorithms are applied for the optimal sensor placement design along the deck of a 537 m concrete bridge.

Keywords

Bayesian inference; Kullback-Leibler divergence; information entropy; structural dynamics.

Full Text:

PDF

References

Simoen E, Moaveni B, Conte JP and Lombaert G, 2013, Uncertainty quantification in the assessment of progressive damage in a 7-story full-scale building slice, Journal of Engineering Mechanics (ASCE), vol.139(12): 1818-1830.

Beck JL and Katafygiotis LS, 1998, Updating models and their uncertainties. I: Bayesian statistical framework, Journal of Engineering Mechanics (ASCE), vol.124(4): 455–461.

Yuen KV, 2012, Updating large models for mechanical systems using incomplete modal measurement, Mechanical Systems and Signal Processing, vol.28: 297–308.

Yuen KV, 2010, Bayesian Methods for Structural Dynamics and Civil Engineering, John Wiley and Sons: NJ.

Lam HF, Katafygiotis LS and Mickleborough NC, 2004, Application of a statistical model updating approach on phase I of the IASC-ASCE structural health monitoring benchmark study, Journal of Engineering Mechanics - ASCE, vol.130(1): 34–48.

Vanik MW, Beck JL and Au SK, 2000, Bayesian probabilistic approach to structural health monitoring, Journal of Engineering Mechanics (ASCE), vol.126(7): 738-745.

Li D, 2011, Sensor placement methods and evaluation criteria in structural health monitoring, Ph. D. thesis, University of Siegen, Siegen.

Kammer DC, 1991, Sensor placements for on orbit modal identification and correlation of large space structures, Journal of Guidance, Control and Dynamics, vol.14: 251-259.

Kammer DC, 1992, Effects of noise on sensor placement for on-orbit modal identification of large space structures, Journal of dynamic systems, measurements and control - Transactions of the ASCE, vol.114(3): 436–443.

Li DS, Li HN and Fritzen CP, 2009, A note on fast computation of effective independence through QR downdating for sensor placement, Mechanical Systems and Signal Processing, vol.23: 1160–1168.

Shah P and Udwadia FE, 1978, A methodology for optimal sensor locations for identification of dynamic systems, Journal of Applied Mechanics, vol.45: 188–196.

Udwadia FE, 1994, Methodology for optimal sensor locations for parameter identification in dynamic systems, Journal of Engineering Mechanics (ASCE), vol.120(2): 368–390.

Papadimitriou C, Beck JL and Au SK, 2000, Entropy-based optimal sensor location for structural model updating, Journal of Vibration and Control, vol.6(5): 781-800.

Yuen KV, Katafygiotis LS, Papadimitriou C and Mickleborough NC, 2001, Optimal sensor placement methodology for identification with unmeasured excitation. Journal of Dynamic Systems, Measurement and Control, vol.123(4): 677–686.

Ye S and Ni YQ, 2012 Information entropy based algorithm of sensor placement optimization for structural damage detection, Smart Structures and Systems, vol.10(4–5): 443–458.

Papadimitriou C. and Lombaert G, 2012, The effect of prediction error correlation on optimal sensor placement in structural dynamics, Mechanical Systems and Signal Processing, vol.28: 105-127.

Kammer DC, 2005, Sensor set expansion for modal vibration testing, Mechanical systems and signal processing, vol.19(4): 700–713.

Papadimitriou C, 2004, Optimal sensor placement methodology for parametric identification of structural systems, Journal of Sound and Vibration, vol.278(4): 923-947.

Stephan C, 2012, Sensor placement for modal identification, Mechanical Systems and Signal Processing, vol.27: 461–470.

Papadimitriou D and Papadimitriou C, 2015, Optimal sensor placement for the estimation of turbulence model parameters in CFD, International Journal for Uncertainty Quantification, vol.5(6): 545-568.

Leyder C, Ntertimanis VK, Chatzi E and Frangi A, 2015, Optimal sensor placement for the modal identification of an innovative timber structure. Volume 1st ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2015, pp. 467–476, National Technical University of Athens.

Leyder C, Chatzi E, Frangi A and Lombaert G, 2016, Comparison of optimal sensor placement algorithms via implementation on an innovative timber structure, IALCCE Conference, Fifth International Symposium on Life-Cycle Civil Engineering (IALCCE 2016), 16-19 October, 2016, Delft, The Netherlands.

Chow HM, Lam HF, Yin T and Au SK, 2011, Optimal sensor configuration of a typical transmission tower for the purpose of structural model updating, Structural Control and Health Monitoring, vol.18(3): 305–320.

Yuen K-V and Kuok S-C, 2015, Efficient Bayesian sensor placement algorithm for structural identification: a general approach for multi-type sensory systems, Earthquake Engineering and Structural Dynamics, vol.44(5): 757-774.

Lindley DV, 1956, On a measure of the information provided by an experiment, The Annals of Mathematical Statistics, vol.27: 986–1005

Huan X and Marzouk YM, 2013, Simulation-based optimal Bayesian experimental design for nonlinear systems, Journal of Computational Physics, vol.232(1): 288-317.

H.ansen N, Muller SD and Koumoutsakos P, 2003, Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES), Evolutionary Computation, vol.11(1): 1-18.

Chaloner K and Verdinelli I, 1995, Bayesian experimental design: A review, Statistical Science,vol.10: 273–304.


DOI: http://dx.doi.org/10.18063/JSC.2016.02.001
(220 Abstract Views, 91 PDF Downloads)

Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Costas Argyris, Costas Papadimitriou, Panagiotis Panetsos

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


 

Journal of Smart Cities is a peer-reviewed, open-access journal. All journal content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.