Bayesian Optimal Sensor Placement for Damage Detection in Frequency-Domain Dynamics
Publication: Journal of Engineering Mechanics
Volume 148, Issue 12
Abstract
Identification and monitoring of structural damage have a growing importance in the maintenance of aging structures. Specifically, an optimal sensor configuration capable of fully identifying structural damage is desired. One innovative approach is casting the optimal sensor placement problem as a decision-centric, utility-maximization framework. By choosing mutual information (or relative entropy) as the utility criteria, sensor placements are chosen to maximize information about structural damage parameters. To accelerate this optimal experimental design (OED) problem, we propose the parameterization of damage using binary variables and the corresponding integration of the Bernoulli prior into this Bayesian OED framework. By limiting the damage parameter design space, we can direct the computational effort toward optimizing over informative and practical structural damage scenarios. Additionally, we convert the OED problem into a convex optimization problem, ensuring that sensor placement solutions contain the maximum information. We evaluate our proposed modified OED framework using a deterministic damage estimator also informed by the Bernoulli prior. We quantify the performance of sensor placements using a mean-squared error (MSE) metric, and we show that optimally selected sensors outperform randomly selected sensors, in general. We also provide a potential heuristic in selecting a sensor budget through the consideration of utility.
Practical Applications
In this work, we present a theoretical framework that identifies a set of optimal locations for sensor placement for damage detection in large structures. Given a sufficiently defined finite element model of a structure, this framework can identify a set of optimal sensor placements. Then, physically placing any sensor that can measure field data (e.g., displacements or accelerations) at these positions will yield experimental data that is most informative about potential damage scenarios at key components. Sensors can include and are not limited to accelerometers, strain gauges, fiber optic sensors, and laser vibrometers, among others. Ideally, sensors should minimally interfere with the structure’s dynamics. Furthermore, any measurement data should be processed to displacements in the frequency domain to seamlessly fit in the theoretical framework with minimal modifications. We expect practitioners to use the framework to numerically model and design experimental sensor configurations before physically placing any sensors on a structure to minimize any experimental burden.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The three presented numerical models and the OED code are available from the corresponding author.
Acknowledgments
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US Department of Energy or the United States Government.
References
Aquino, W., G. Bunting, S. T. Miller, and T. F. Walsh. 2019. “A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests.” Comput. Methods Appl. Mech. Eng. 345 (Mar): 323–335. https://doi.org/10.1016/j.cma.2018.11.002.
ASME. 2017. Operation and maintenance of nuclear power plants. New York: ASME.
Atkinson, A., A. Donev, and R. Tobias. 2007. Vol. 34 of Optimum experimental designs, with SAS. Oxford: Oxford University Press.
Avci, O., O. Abdeljaber, S. Kiranyaz, M. Hussein, M. Gabbouj, and D. J. Inman. 2021. “A review of vibration-based damage detection in civil structures: From traditional methods to machine learning and deep learning applications.” Mech. Syst. Sig. Process. 147 (Jan): 107077. https://doi.org/10.1016/j.ymssp.2020.107077.
Bansal, S., and S. H. Cheung. 2022. “On the bayesian sensor placement for two-stage structural model updating and its validation.” Mech. Syst. Sig. Process. 169 (Apr): 108578. https://doi.org/10.1016/j.ymssp.2021.108578.
Beck, J. L., and L. S. Katafygiotis. 1998. “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech. 124 (4): 455–461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455).
Bhattacharyya, P., and J. Beck. 2020. “Exploiting convexification for bayesian optimal sensor placement by maximization of mutual information.” Struct. Control Health Monit. 27 (10): e2605. https://doi.org/10.1002/stc.2605.
Bosch, J., D. Kay, M. Stoll, and A. J. Wathen. 2014. “Fast solvers for cahn–hilliard inpainting.” SIAM J. Imag. Sci. 7 (1): 67–97. https://doi.org/10.1137/130921842.
Bunting, G., et al. 2018. Sierra structural dynamics-users notes 4.50. Albuquerque, NM: Sandia National Laboratories.
Burger, M., and R. Stainko. 2006. “Phase-field relaxation of topology optimization with local stress constraints.” SIAM J. Control Optim. 45 (4): 1447–1466. https://doi.org/10.1137/05062723X.
Capellari, G., E. Chatzi, and S. Mariani. 2018a. “Cost–benefit optimization of structural health monitoring sensor networks.” Sensors 18 (7): 2174. https://doi.org/10.3390/s18072174.
Capellari, G., E. Chatzi, and S. Mariani. 2018b. “Structural health monitoring sensor network optimization through bayesian experimental design.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 4 (2): 04018016. https://doi.org/10.1061/AJRUA6.0000966.
Chaloner, K., and I. Verdinelli. 1995. “Bayesian experimental design: A review.” Stat. Sci. 10 (3): 273–304. https://doi.org/10.1214/ss/1177009939.
Chisari, C., L. Macorini, C. Amadio, and B. A. Izzuddin. 2017. “Optimal sensor placement for structural parameter identification.” Struct. Multidiscip. Optim. 55 (2): 647–662. https://doi.org/10.1007/s00158-016-1531-1.
Company, W. E. 2011. Ap1000 design control document. Cranberry Township, PA: Westinghouse Electric Company, Westinghouse Electric Company LLC.
Company, W. E. 2015. Comprehensive vibration assessment program (cvap) vibration analysis program for the ap1000 plant (wcap-17984-np). Cranberry Township, PA: Westinghouse Electric Company, Westinghouse Electric Company LLC.
Das, S., P. Saha, and S. Patro. 2016. “Vibration-based damage detection techniques used for health monitoring of structures: A review.” J. Civ. Struct. Health Monit. 6 (3): 477–507. https://doi.org/10.1007/s13349-016-0168-5.
Doebling, S. W., C. R. Farrar, and M. B. Prime. 1998. “A summary review of vibration-based damage identification methods.” Shock Vibr. Dig. 30 (2): 91–105. https://doi.org/10.1177/058310249803000201.
Fan, W., and P. Qiao. 2011. “Vibration-based damage identification methods: A review and comparative study.” Struct. Health Monit. 10 (1): 83–111. https://doi.org/10.1177/1475921710365419.
Flynn, E. B., and M. D. Todd. 2010. “Bayesian probabilistic structural modeling for optimal sensor placement in ultrasonic guided wave-based structural health monitoring.” In Vol. 7648 of Smart sensor phenomena, technology, networks, and systems 2010. Bellingham: International Society for Optics and Photonics.
Friswell, M. I. 2006. “Damage identification using inverse methods.” Philos. Trans. R. Soc. London, Ser. A 365 (1851): 393–410. https://doi.org/10.1098/rsta.2006.1930.
Haber, E., L. Horesh, and L. Tenorio. 2008. “Numerical methods for experimental design of large-scale linear ill-posed inverse problems.” Inverse Prob. 24 (5): 055012. https://doi.org/10.1088/0266-5611/24/5/055012.
Haber, E., L. Horesh, and L. Tenorio. 2009. “Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems.” Inverse Prob. 26 (2): 025002. https://doi.org/10.1088/0266-5611/26/2/025002.
Hansen, P. C. 2010. Vol. 7 of Discrete inverse problems: Insight and algorithms. Philadelphia, PA: SIAM.
Huan, X., and Y. M. Marzouk. 2013. “Simulation-based optimal bayesian experimental design for nonlinear systems.” J. Comput. Phys. 232 (1): 288–317. https://doi.org/10.1016/j.jcp.2012.08.013.
Hughes, T. J. 2012. The finite element method: Linear static and dynamic finite element analysis. New York: Dover Publications.
Joshi, S., and S. Boyd. 2008. “Sensor selection via convex optimization.” IEEE Trans. Signal Process. 57 (2): 451–462. https://doi.org/10.1109/TSP.2008.2007095.
Kammer, D. C. 1996. “Optimal sensor placement for modal identification using system-realization methods.” J. Guid. Control Dyn. 19 (3): 729–731. https://doi.org/10.2514/3.21688.
Kouri, D., D. Ridzal, B. Van Bloemen Waanders, and G. Von Winckel. 2014. Rapid optimization library. Albuquerque: Sandia National Laboratories.
Lam, H. F., L. S. Katafygiotis, and N. C. Mickleborough. 2004. “Application of a statistical model updating approach on phase I of the iasc-asce structural health monitoring benchmark study.” J. Eng. Mech. 130 (1): 34–48. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:1(34).
Lee, T., K. Dunn, and C. Chang. 1982. “On observability and unbiased estimation of nonlinear systems.” In System modeling and optimization, 258–266. Berlin, Heidelberg: Springer.
Li, J., S. Law, and Y. Ding. 2012. “Substructure damage identification based on response reconstruction in frequency domain and model updating.” Eng. Struct. 41 (Aug): 270–284. https://doi.org/10.1016/j.engstruct.2012.03.035.
Li, X., and S. Law. 2010. “Adaptive tikhonov regularization for damage detection based on nonlinear model updating.” Mech. Syst. Sig. Process. 24 (6): 1646–1664. https://doi.org/10.1016/j.ymssp.2010.02.006.
Lin, J.-F., Y.-L. Xu, and S.-S. Law. 2018. “Structural damage detection-oriented multi-type sensor placement with multi-objective optimization.” J. Sound Vib. 422 (May): 568–589. https://doi.org/10.1016/j.jsv.2018.01.047.
Loutas, T., and A. Bourikas. 2017. “Strain sensors optimal placement for vibration-based structural health monitoring. The effect of damage on the initially optimal configuration.” J. Sound Vib. 410 (Dec): 217–230. https://doi.org/10.1016/j.jsv.2017.08.022.
Mariani, S., M. Bruggi, F. Caimmi, P. Bendiscioli, and M. De Fazio. 2013. “Sensor deployment over damage-containing plates: A topology optimization approach.” J. Intell. Mater. Syst. Struct. 24 (9): 1105–1122. https://doi.org/10.1177/1045389X13480570.
Nath, P., Z. Hu, and S. Mahadevan. 2017. “Sensor placement for calibration of spatially varying model parameters.” J. Comput. Phys. 343 (Aug): 150–169. https://doi.org/10.1016/j.jcp.2017.04.033.
Papadimitriou, C. 2004. “Optimal sensor placement methodology for parametric identification of structural systems.” J. Sound Vib. 278 (4–5): 923–947. https://doi.org/10.1016/j.jsv.2003.10.063.
Ryan, E. G., C. C. Drovandi, J. M. McGree, and A. N. Pettitt. 2016. “A review of modern computational algorithms for Bayesian optimal design.” Int. Stat. Rev. 84 (1): 128–154. https://doi.org/10.1111/insr.12107.
Sohn, H., C. R. Farrar, F. M. Hemez, D. D. Shunk, D. W. Stinemates, B. R. Nadler, and J. J. Czarnecki. 2003. A review of structural health monitoring literature: 1996–2001. Los Alamos, NM: Los Alamos National Laboratory.
Titurus, B., and M. Friswell. 2008. “Regularization in model updating.” Int. J. Numer. Methods Eng. 75 (4): 440–478. https://doi.org/10.1002/nme.2257.
Udwadia, F. E. 1994. “Methodology for optimum sensor locations for parameter identification in dynamic systems.” J. Eng. Mech. 120 (2): 368–390. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:2(368).
Virtanen, P., et al. 2020. “Scipy 1.0: Fundamental algorithms for scientific computing in python.” Nat. Methods 17 (3): 261–272. https://doi.org/10.1038/s41592-019-0686-2.
Yang, C., K. Liang, and X. Zhang. 2020. “Strategy for sensor number determination and placement optimization with incomplete information based on interval possibility model and clustering avoidance distribution index.” Comput. Methods Appl. Mech. Eng. 366 (Jul): 113042. https://doi.org/10.1016/j.cma.2020.113042.
Yang, Y., M. Chadha, Z. Hu, and M. D. Todd. 2022. “An optimal sensor placement design framework for structural health monitoring using bayes risk.” Mech. Syst. Sig. Process. 168 (Apr): 108618. https://doi.org/10.1016/j.ymssp.2021.108618.
Yin, T., and F.-L. Zhang. 2022. “Sensor placement for model identification of multi-story buildings under unknown earthquake ground motion.” Eng. Struct. 251 (Jan): 113548. https://doi.org/10.1016/j.engstruct.2021.113548.
Zhu, D., X. Dong, and Y. Wang. 2016. “Substructure stiffness and mass updating through minimization of modal dynamic residuals.” J. Eng. Mech. 142 (5): 04016013. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001063.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 8, 2021
Accepted: Jul 11, 2022
Published online: Oct 12, 2022
Published in print: Dec 1, 2022
Discussion open until: Mar 12, 2023
ASCE Technical Topics:
- Aging (material)
- Analysis (by type)
- Architectural engineering
- Bayesian analysis
- Building management
- Business management
- Continuum mechanics
- Deterioration
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Infrastructure
- Innovation
- Lifeline systems
- Maintenance and operation
- Materials characterization
- Materials engineering
- Mathematics
- Measurement (by type)
- Parameters (statistics)
- Practice and Profession
- Sensors and sensing
- Solid mechanics
- Statistical analysis (by type)
- Statistics
- Structural dynamics
- Utilities
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.