Technical Papers
Mar 30, 2018

Structural Health Monitoring Sensor Network Optimization through Bayesian Experimental Design

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4, Issue 2

Abstract

Structural health monitoring (SHM) may be exploited to estimate the mechanical properties of existing structures and check for potential damage. Among commonly used methodologies for property characterization, the Bayesian approach holds the lead because it is endowed with the particular advantage of quantifying associated uncertainties. These uncertainties arise owing to diverse factors including (1) sensor accuracy and positioning, (2) environmental influences, and (3) modeling errors. In minimizing the influence of sensor-related uncertainties, an optimal design may be adopted for the SHM campaign to maximize the information content of the measurements. Here, a procedure based on Bayesian experimental design is proposed to quantify the expected utility of the sensor network. The positions of the used sensors are selected in a way that maximizes the Shannon information gain between the prior and posterior probability distributions of the parameters to be estimated. In order to numerically solve the resulting optimization problem, surrogate models based on polynomial chaos expansion (PCE) and stochastic optimization methods are used. The use of surrogates allows one to reduce the computational cost of the associated model runs. The method is applied to a large-scale example, namely the Pirelli Tower in Milan.

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Acknowledgments

The first author acknowledges the financial support by IDEA League through a Ph.D. Student Grant. The authors also acknowledge the Chair of Risk, Safety and Uncertainty Quantification and the Computational Science and Engineering Laboratory at ETH Zürich for having provided the MATLAB-based softwares UQLab and CMA-ES, used in the implementation of the method. Authors are indebted to Gianluca Barbella and Federico Perotti, who provided the numerical model of the Pirelli Tower.

References

Altman, N. S. (1992). “An introduction to kernel and nearest-neighbor nonparametric regression.” Am. Statistician, 46(3), 175–185.
Barbella, G. (2009). “Frequency domain analysis of slender structural systems under turbulent wind excitation.” Ph.D. thesis, Politecnico di Milano, Milan, Italy.
Barbella, G., Perotti, F., and Simoncini, V. (2011). “Block Krylov subspace methods for the computation of structural response to turbulent wind.” Comput. Methods Appl. Mech. Eng., 200(23), 2067–2082.
Bayer, P., Duran, E., Baumann, R., and Finkel, M. (2009). “Optimized groundwater drawdown in a subsiding urban mining area.” J. Hydrol., 365(1), 95–104.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Berkooz, G., Holmes, P., and Lumley, J. L. (1993). “The proper orthogonal decomposition in the analysis of turbulent flows.” Ann. Rev. Fluid Mech., 25(1), 539–575.
Bernardo, J. M. (1979). “Expected information as expected utility.” Ann. Stat., 7(3), 686–690.
Blatman, G. (2009). “Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis.” Ph.D. thesis, Blaise Pascal Univ., Clermont-Ferrand, France.
Blatman, G., and Sudret, B. (2010). “An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis.” Probab. Eng. Mech., 25(2), 183–197.
Blatman, G., and Sudret, B. (2011). “Adaptive sparse polynomial chaos expansion based on least angle regression.” J. Comput. Phys., 230(6), 2345–2367.
Bliss, C. A., Frank, M. R., Danforth, C. M., and Dodds, P. S. (2014). “An evolutionary algorithm approach to link prediction in dynamic social networks.” J. Comput. Sci., 5(5), 750–764.
Bruggi, M., and Mariani, S. (2013). “Optimization of sensor placement to detect damage in flexible plates.” Eng. Optim., 45(6), 659–676.
Capellari, G., Chatzi, E., and Mariani, S. (2016). “An optimal sensor placement method for SHM based on Bayesian experimental design and polynomial chaos expansion.” Proc., 7th European Community on Computational Methods in Applied Sciences and Engineering, Vol. 3, Crete, Greece, 6272–6282.
Capellari, G., Chatzi, E., and Mariani, S. (2017a). “Optimal design of sensor networks for damage detection.” Proc. Eng., 199, 1864–1869.
Capellari, G., Chatzi, E., and Mariani, S. (2017b). “Parameter identifiability through information theory.” Proc., 2nd ECCOMAS Thematic Conf. on Uncertainty Quantification in Computational Sciences and Engineering, Crete, Greece.
Chaloner, K., and Verdinelli, I. (1995). “Bayesian experimental design: A review.” Stat. Sci., 10(3), 273–304.
Chisari, C., Macorini, L., Amadio, C., and Izzuddin, B. (2017). “Optimal sensor placement for structural parameter identification.” Struct. Multidiscip. Optim., 55(2), 647–662.
Cover, T. M., and Thomas, J. A. (2012). Elements of information theory, Wiley, New York.
DeGroot, M. H. (1962). “Uncertainty, information, and sequential experiments.” Ann. Math. Stat., 33(2), 404–419.
Eftekhar Azam, S., and Mariani, S. (2013). “Investigation of computational and accuracy issues in POD-based reduced order modeling of dynamic structural systems.” Eng. Struct., 54, 150–167.
Ghanem, R., and Spanos, P. D. (1990). “Polynomial chaos in stochastic finite elements.” J. Appl. Mech., 57(1), 197–202.
Golub, G., and Kahan, W. (1965). “Calculating the singular values and pseudo-inverse of a matrix.” J. Soc. Ind. Appl. Math. Ser. B Numer. Anal., 2(2), 205–224.
Hadjidoukas, P. E., Angelikopoulos, P., Papadimitriou, C., and Koumoutsakos, P. (2015). “π4u: A high performance computing framework for Bayesian uncertainty quantification of complex models.” J. Comput. Phys., 284, 1–21.
Hansen, N. (2006). “The CMA evolution strategy: A comparing review.” Towards a new evolutionary computation. Advances on estimation of distribution algorithms, J. Lozano, P. Larranaga, I. Inza, and E. Bengoetxea, eds., Springer, New York, 75–102.
Hansen, N., and Ostermeier, A. (2001). “Completely derandomized self-adaptation in evolution strategies.” Evol. Comput., 9(2), 159–195.
Hansen, N., Ostermeier, A., and Gawelczyk, A. (1995). “On the adaptation of arbitrary normal mutation distributions in evolution strategies: The generating set adaptation.” Proc., 6th Int. Conf. on Genetic Algorithms, Morgan Kaufmann Publishers, San Francisco, 57–64.
Heo, G., and Jeon, J. (2016). “An experimental study of structural identification of bridges using the kinetic energy optimization technique and the direct matrix updating method.” Shock Vib., 3287976.
Heo, G., Wang, M., and Satpathi, D. (1997). “Optimal transducer placement for health monitoring of long span bridge.” Soil Dyn. Earthquake Eng., 16(7–8), 495–502.
Heredia-Zavoni, E., and Esteva, L. (1998). “Optimal instrumentation of uncertain structural systems subject to earthquake ground motions.” Earthquake Eng. Struct. Dyn., 27(4), 343–362.
Hotelling, H. (1933). “Analysis of a complex of statistical variables into principal components.” J. Educ. Psychol., 24(6), 417–441.
Huan, X., and Marzouk, Y. M. (2013). “Simulation-based optimal Bayesian experimental design for nonlinear systems.” J. Comput. Phys., 232(1), 288–317.
Kammer, D. C. (1991). “Sensor placement for on-orbit modal identification and correlation of large space structures.” J. Guidance Control Dyn., 14(2), 251–259.
Kammer, D. C. (1996). “Optimal sensor placement for modal identification using system-realization methods.” J. Guidance Control Dyn., 19(3), 729–731.
Katafygiotis, L. S., and Beck, J. L. (1998). “Updating models and their uncertainties. II: Model identifiability.” J. Eng. Mech., 463–467.
Konakli, K., and Sudret, B. (2016). “Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions.” J. Comput. Phys., 321, 1144–1169.
Kraskov, A., Stögbauer, H., and Grassberger, P. (2004). “Estimating mutual information.” Phys. Rev. E, 69(6), 066138.
Lindley, D. V. (1956). “On a measure of the information provided by an experiment.” Ann. Math. Stat., 27(4), 986–1005.
Mai, C. V., Spiridonakos, M. D., Chatzi, E. N., and Sudret, B. (2016). “Surrogate modeling for stochastic dynamical systems by combining nonlinear autoregressive with exogenous input models and polynomial chaos expansions.” Int. J. Uncertainty Quantif., 6(4), 313–339.
Mallardo, V., and Aliabadi, M. (2014). “Optimal sensor placement for structural, damage and impact identification: A review.” SDHM Struct. Durability Health Monit., 9(4), 287–323.
Marelli, S., and Sudret, B. (2014). “Uqlab: A framework for uncertainty quantification in MATLAB.” 2nd Int. Conf. on Vulnerability, Risk Analysis and Management, ASCE, Reston, VA, 2554–2563.
MATLAB [Computer software]. MathWorks, Natick, MA.
Meo, M., and Zumpano, G. (2005). “On the optimal sensor placement techniques for a bridge structure.” Eng. Struct., 27(10), 1488–1497.
Papadimitriou, C. (2004). “Optimal sensor placement methodology for parametric identification of structural systems.” J. Sound Vib., 278(4), 923–947.
Papadimitriou, C., Beck, J. L., and Au, S.-K. (2000). “Entropy-based optimal sensor location for structural model updating.” J. Vib. Control, 6(5), 781–800.
Papadimitriou, C., and Lombaert, G. (2012). “The effect of prediction error correlation on optimal sensor placement in structural dynamics.” Mech. Syst. Sig. Process., 28, 105–127.
Ramesh, S., Kannan, S., and Baskar, S. (2012). “Application of modified NSGA-II algorithm to multi-objective reactive power planning.” Appl. Soft Comput., 12(2), 741–753.
Ryan, K. J. (2003). “Estimating expected information gains for experimental designs with application to the random fatigue-limit model.” J. Comput. Graphical Stat., 12(3), 585–603.
Shannon, C. E. (1948). “A mathematical theory of communication.” Bell Syst. Tech. J., 27(3), 379–423.
Sobczyk, K. (1987). “Theoretic information approach to identification and signal processing.” Reliab. Optim. Struct. Syst., 33, 373–383.
Spiridonakos, M. D., Chatzi, E. N., and Sudret, B. (2016). “Polynomial chaos expansion models for the monitoring of structures under operational variability.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civil Eng., 2(3), B4016003.
Szabó, Z. (2014). “Information theoretical estimators toolbox.” J. Mach. Learn. Res., 15(1), 283–287.
Udwadia, F. E. (1994). “Methodology for optimum sensor locations for parameter identification in dynamic systems.” J. Eng. Mech., 368–390.
Vanik, M. W., Beck, J. L., and Au, S. (2000). “Bayesian probabilistic approach to structural health monitoring.” J. Eng. Mech., 738–745.
Walters-Williams, J., and Li, Y. (2009). “Estimation of mutual information: A survey.” Rough sets and knowledge technology, Springer, New York, 389–396.
Wiener, N. (1938). “The homogeneous chaos.” Am. J. Math., 60(4), 897–936.
Xiu, D., and Karniadakis, G. E. (2003). “Modeling uncertainty in flow simulations via generalized polynomial chaos.” J. Comput. Phys., 187(1), 137–167.
Yang, C., and Lu, Z. (2017). “An interval effective independence method for optimal sensor placement based on non-probabilistic approach.” Sci. China Technol. Sci., 60(2), 186–198.
Yao, L., Sethares, W. A., and Kammer, D. C. (1993). “Sensor placement for on-orbit modal identification via a genetic algorithm.” AIAA J., 31(10), 1922–1928.
Yuen, K.-V. (2010). Bayesian methods for structural dynamics and civil engineering, Wiley, New York.

Information & Authors

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4Issue 2June 2018

History

Received: Jun 9, 2017
Accepted: Nov 22, 2017
Published online: Mar 30, 2018
Published in print: Jun 1, 2018
Discussion open until: Aug 30, 2018

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Authors

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Giovanni Capellari [email protected]
Ph.D. Student, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy (corresponding author). E-mail: [email protected]
Eleni Chatzi, Ph.D., A.M.ASCE [email protected]
Associate Professor, Dept. of Civil, Environmental and Geomatic Engineering, Institute of Structural Engineering, Eidgenössische Technische Hochschule Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland. E-mail: [email protected]
Stefano Mariani, Ph.D. [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy. E-mail: [email protected]

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