Mixed Model and Gaussian Process to Investigate the External Influence on the Propagation Time of Ultrasonic Waves on Masonry Walls
Pub. online: 14 November 2024
Type: Data Science In Action
Open Access
Open Access
Received
12 February 2024
12 February 2024
Accepted
2 July 2024
2 July 2024
Published
14 November 2024
14 November 2024
Abstract
The ultrasonic testing has been considered a promising method for diagnosing and characterizing masonry walls. As ultrasonic waves tend to travel faster in denser materials, their use is common in evaluating the conditions of various materials. Presence of internal voids, e.g., would alter the wave path, and this distinct behavior could be employed to identify unknown conditions within the material, allowing for the assessment of its condition. Therefore, we applied mixed models and Gaussian processes to analyze the behavior of ultrasonic waves on masonry walls and identify relevant factors impacting their propagation. We observed that the average propagation time behavior differs depending on the material for both models. Additionally, the condition of the wall influences the propagation time. Gaussian process and mixed model performances are compared, and we conclude that these models can be useful in a classification model to automatically identify anomalies within masonry walls.
References
Araújo E, Sousa I, Paz R, Costa CH, Mesquita E (2020). Physical and mechanical characterization of traditional Brazilian clay bricks from different centuries. Journal of Building Pathology and Rehabilitation, 5(1): 1–12. https://doi.org/10.1007/s41024-019-0067-3
Banerjee S, Gelfand AE, Finley AO, Sang H (2008). Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 70(4): 825–848. https://doi.org/10.1111/j.1467-9868.2008.00663.x
Binda L, Saisi A, Zanzi L (2003). Sonic tomography and flat-jack tests as complementary investigation procedures for the stone pillars of the temple of s. Nicolò l’Arena (Italy). NDT & E International, 36(4): 215–227. Structural Faults and Repair. https://doi.org/10.1016/S0963-8695(02)00066-X
Cheng L, Ramchandran S, Vatanen T, Lietzén N, Lahesmaa R, Vehtari A, et al. (2019). An additive gaussian process regression model for interpretable non-parametric analysis of longitudinal data. Nature Communications, 10(1): 1–11. https://doi.org/10.1038/s41467-018-07882-8
Ebden M (2015). Gaussian processes: A quick introduction. arXiv preprint: https://arxiv.org/abs/1505.02965.
Edwards LJ, Stewart PW, MacDougall JE, Helms RW (2006). A method for fitting regression splines with varying polynomial order in the linear mixed model. Statistics in Medicine, 25(3): 513–527. https://doi.org/10.1002/sim.2232
Grimm K, Zhang Z, Hamagami F, Mazzocco M (2013). Modeling nonlinear change via latent change and latent acceleration frameworks: Examining velocity and acceleration of growth trajectories. Multivariate Behavioral Research, 48(1): 117–143. https://doi.org/10.1080/00273171.2012.755111
Karch JD, Brandmaier AM, Voelkle MC (2020). Gaussian process panel modeling—machine learning inspired analysis of longitudinal panel data. Frontiers in Psychology, 11: 351. https://doi.org/10.3389/fpsyg.2020.00351
Kot P, Muradov M, Gkantou M, Kamaris GS, Hashim K, Yeboah D (2021). Recent advancements in non-destructive testing techniques for structural health monitoring. Applied Sciences, 11(6): 2750. https://doi.org/10.3390/app11062750
Laird NM, Ware JH (1982). Random-effects models for longitudinal data. Biometrics, 38(4): 963–974. https://doi.org/10.2307/2529876
Mesquita E, Martini R, Alves A, Mota L, Rubens T, Antunes P, et al. (2018). Heterogeneity detection of Portuguese–Brazilian masonries through ultrasonic velocities measurements. Journal of Civil Structural Health Monitoring, 8(5): 847–856. https://doi.org/10.1007/s13349-018-0312-5
Miranda L, Cantini L, João Guedes J, Binda L, Costa A (2013). Applications of sonic tests to masonry elements: Influence of joints on the propagation velocity of elastic waves. Journal of Materials in Civil Engineering, 25(6): 667–682. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000547
Neal RM (2011). MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, 2: 113–162. https://doi.org/10.1201/b10905-6
Quintana FA, Johnson WO, Waetjen LE, Gold EB (2016). Bayesian nonparametric longitudinal data analysis. Journal of the American Statistical Association, 111(515): 1168–1181. https://doi.org/10.1080/01621459.2015.1076725
Schulz E, Speekenbrink M, Krause A (2018). A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions. Journal of Mathematical Psychology, 85: 1–16. https://doi.org/10.1016/j.jmp.2018.03.001
Sela RJ, Simonoff JS (2012). RE-EM trees: A data mining approach for longitudinal and clustered data. Machine Learning, 86(2): 169–207. https://doi.org/10.1007/s10994-011-5258-3
Valluzzi MR, Cescatti E, Cardani G, Cantini L, Zanzi L, Colla C, et al. (2018). Calibration of sonic pulse velocity tests for detection of variable conditions in masonry walls. Construction & Building Materials, 192: 272–286. https://doi.org/10.1016/j.conbuildmat.2018.10.073
Verstrynge E, Lacidogna G, Accornero F, Tomor A (2021). A review on acoustic emission monitoring for damage detection in masonry structures. Construction & Building Materials, 268: 121089. https://doi.org/10.1016/j.conbuildmat.2020.121089
Zuanetti DA, da Paz RF, Rodrigues T, Mesquita E (2021). Clustering ultrasonic waves propagation time: A hierarchical polynomial semiparametric approach. Applied Stochastic Models in Business and Industry, 37(5): 894–907. https://doi.org/10.1002/asmb.2609
