JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1145 10.6339/24-JDS1145 Data Science in Action Mixed Model and Gaussian Process to Investigate the External Influence on the Propagation Time of Ultrasonic Waves on Masonry Walls PazRosineide Fernando darfdapaz@ufc.br1∗ ZuanettiDaiane Aparecida2 RodriguesRenan Vinicius2 MesquitaEsequiel Universidade Federal do Ceará, Campus of Russas, Ceará, Brazil Universidade Federal de São Carlos, Statistical Departament, São Carlos, São Paulo, Brazil Corresponding author. Email: rfdapaz@ufc.br. 202414112024001181222024272024 2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2024 Open access article under the CC BY license.

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.

 automated monitoring characterization of masonry non-destructive test statistical application References ABNT (2020). NBR 16805. Associação Brasileira de Normas Técnicas, Rio de Janeiro - Brazil. 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 Gibbs MN (1998). Bayesian gaussian processes for regression and classification. Ph.D. thesis, University of Cambridge. 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 Grimm KJ, McArdle JJ, Hamagami F (2007). Nonlinear growth mixture models in research on cognitive aging. In: Longitudinal Models in the Behavioral and Related Sciences (K AS, van Montfort, J Oud, eds.). Lawrence Erlbaum Associates Publishers. Grimm KJ, Ram N, Estabrook R (2016). Growth Modeling: Structural Equation and Multilevel Modeling Approaches. Guilford Publications. 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 Lizotte DJ, Wang T, Bowling MH, Schuurmans D (2007). Automatic gait optimization with Gaussian process regression. In: IJCAI, volume 7, 944–949. 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 Plummer M, Best N, Cowles K, Vines K (2006). CODA: Convergence diagnosis and output analysis for MCMC. R News, 6(1): 7–11. 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 R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Rasmussen CE (2003). Gaussian processes in machine learning. In: Summer School on Machine Learning, 63–71. Springer. Rodrigues AM (2009). Linear mixed models: A practical guide using statistical software. Silva Lusitana, 17: 123–125. Rodrigues RV (2021a). Análise estatística de dados ultrassônicos para a seleção de características da alvenaria que comprometem sua estabilidade. Bachelor’s thesis, Universidade Federal de São Carlos, Brazil. Rodrigues TC (2021b). Análise exploratória de dados ultrassônicos para reconhecimento de vazios em alvenarias maciças. Bachelor’s thesis, Universidade Federal do Ceará, Brazil. 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 Shi JQ, Choi T (2011). Gaussian Process Regression Analysis for Functional Data. Chapman and Hall/CRC. Singer JM, Andrade Dd (1986). Análise de Dados Longitudinais. Simpósio Nacional de Probabilidade e Estatística, 7. Stan Development Team (2024). RStan: The R interface to Stan. R package version 2.32.6. 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 Williams CK, Rasmussen CE (2006). Gaussian Processes for Machine Learning. MIT Press, Cambridge, MA. 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