Dimensionality Reduction in Modal Analysis for Structural Health Monitoring

Authors: Elia Favarelli, Enrico Testi, Andrea Giorgetti

Abstract:

Autonomous structural health monitoring (SHM) of many structures and bridges became a topic of paramount importance for maintenance purposes and safety reasons. This paper proposes a set of machine learning (ML) tools to perform automatic feature selection and detection of anomalies in a bridge from vibrational data and compare different feature extraction schemes to increase the accuracy and reduce the amount of data collected. As a case study, the Z-24 bridge is considered because of the extensive database of accelerometric data in both standard and damaged conditions. The proposed framework starts from the first four fundamental frequencies extracted through operational modal analysis (OMA) and clustering, followed by time-domain filtering (tracking). The fundamental frequencies extracted are then fed to a dimensionality reduction block implemented through two different approaches: feature selection (intelligent multiplexer) that tries to estimate the most reliable frequencies based on the evaluation of some statistical features (i.e., entropy, variance, kurtosis), and feature extraction (auto-associative neural network (ANN)) that combine the fundamental frequencies to extract new damage sensitive features in a low dimensional feature space. Finally, one-class classification (OCC) algorithms perform anomaly detection, trained with standard condition points, and tested with normal and anomaly ones. In particular, principal component analysis (PCA), kernel principal component analysis (KPCA), and autoassociative neural network (ANN) are presented and their performance are compared. It is also shown that, by evaluating the correct features, the anomaly can be detected with accuracy and an F1 score greater than 95%.

Keywords: Anomaly detection, dimensionality reduction, frequencies selection, modal analysis, neural network, structural health monitoring, vibration measurement.

References:

[1] R. Ferrari, D. Froio, E. Chatzi, F. Pioldi, and E. Rizzi, “Experimental and numerical investigations for the structural characterization of a historic RC arch bridge,” in Proc. Int. Conf. on Comp. Methods in Structural Dynamics and Earthquake Eng., vol. 1, Athens, Greece, May 2015, pp. 2337–2353.
[2] A. Benedetti, M. Tarozzi, G. Pignagnoli, and C. Martinelli, “Dynamic investigation and short-monitoring of an historic multi-span masonry arch bridge,” in Proc. Int. Conf. on Arch Bridges, vol. 11, Porto, Portugal, Oct. 2019, pp. 831–839.
[3] A. Benedetti, G. Pignagnoli, and M. Tarozzi, “Damage identification of cracked reinforced concrete beams through frequency shift,” Materials and Structures, vol. 51, pp. 1–15, Oct. 2018.
[4] A. Benedetti, C. Colla, G. Pignagnoli, and M. Tarozzi, “Static and dynamic investigation of the taro masonry bridge in parma, italy,” in Proc. Int. Conf. on Struct. Analysis of Hist. Const., vol. 18, Cusco, Per`u, Sep. 2019, pp. 2264–2272.
[5] G. D. Roeck, “The state-of-the-art of damage detection by vibration monitoring: the SIMCES experience,” J. of Structural Control, vol. 10, no. 2, pp. 127–134, May 2003.
[6] K. Worden, C. Farrar, J. Haywood, and M. Todd, “A review of nonlinear dynamics applications to structural health monitoring,” Structural Control and Health Monitoring, vol. 15, no. 4, pp. 540–567, Jul. 2008.
[7] G. Fabbrocino and C. Rainieri, Operational modal analysis of civil engineering structures. New York: Springer-verlag, May 2014.
[8] S. Taylor, K. Farinholt, E. Flynn, E. Figueiredo, D. L. Mascarenas, E. A. Moro, G. Park, M. Todd, and C. Farrar, “A mobile-agent-based wireless sensing network for structural monitoring applications,” Measurement Science and Technology, vol. 20, no. 4, pp. 1–14, Jan. 2009.
[9] C. M. Bishop, Pattern Recognition and Machine Learning. Springer Verlag, Aug. 2006.
[10] J. Watt, R. Borhani, and A. K. Katsaggelos, Machine Learning Refined. Cambridge University Press, 2016.
[11] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. MIT Press, 2016.
[12] E. Favarelli and A. Giorgetti, “Machine learning for automatic processing of modal analysis in damage detection of bridges,” IEEE Trans. on Instrumentation and Measurement, 2020.
[13] L. Pucci, E. Testi, E. Favarelli, and A. Giorgetti, “Human activities classification using biaxial seismic sensors,” IEEE Sensors Letters, vol. 4, no. 10, pp. 1 – 4, Oct. 2020.
[14] Z-24 bridge data.
[Online]. Available: https://bwk.kuleuven.be/bwm/z24
[15] E. P. Carden and J. M. W. Brownjohn, “Fuzzy clustering of stability diagrams for vibration-based structural health monitoring,” Computer-Aided Civil and Infrastructure Eng., vol. 23, no. 5, pp. 360–372, May 2008.
[16] C. Wu, H. Liu, X. Qin, and J. Wang, “Stabilization diagrams to distinguish physical modes and spurious modes for structural parameter identification,” Journal of Vibroeng., vol. 19, no. 4, pp. 2777–2794, Jun. 2017.
[17] D. Brigante, C. Rainieri, and G. Fabbrocino, “The role of the modal assurance criterion in the interpretation and validation of models for seismic analysis of architectural complexes,” in Proc. Int. Conf. on Structural Dynamics (Eurodin), vol. 199, Rome, Italy, Sep. 2017, pp. 3404–3409.
[18] A. Cabboi, F. Magalha˜es, C. Gentile, and A´ . Cunha, “Automated modal identification and tracking: Application to an iron arch bridge,” Structural Control and Health Monitoring, vol. 24, no. 1, p. e1854, Feb. 2017.
[19] M. Pastor, M. Binda, and T. Harˇcarik, “Modal assurance criterion,” Procedia Engineering, vol. 48, pp. 543–548, 2012.
[20] E. Reynders and G. D. Roeck, “Continuous vibration monitoring and progressive damage testing on the z 24 bridge,” Encyclopedia of structural health monitoring, vol. 10, pp. 127–134, May 2009.
[21] E. Reynders, J. Houbrechts, and G. D. Roeck”, “Fully automated (operational) modal analysis,” Mechanical Systems and Signal Processing, vol. 29, pp. 228–250, May 2012.
[22] A. Santos, M. Silva, C. Sales, J. Costa, and E. Figueiredo, “Applicability of linear and nonlinear principal component analysis for damage detection,” in Proc. IEEE Int. Instr. and Meas. Tech. Conf. (I2MTC), Pisa, Italy, May 2015, pp. 869–874.
[23] E. Favarelli, E. Testi, L. Pucci, and A. Giorgetti, “Anomaly detection using wifi signal of opportunity,” in Proc. IEEE Int. Conf. on Signal Proc. and Comm. Sys. (ICSPCS), Surfers Paradise, Gold Coast, Australia, Dec. 2019, pp. 1–7.
[24] E. Favarelli, E. Testi, and A. Giorgetti, “One class classifier neural network for anomaly detection in low dimensional feature spaces,” in Proc. IEEE Int. Conf. on Signal Proc. and Comm. Sys. (ICSPCS), Surfers Paradise, Gold Coast, Australia, Dec. 2019, pp. 1–7.
[25] P. Perera and V. M. Patel, “Learning deep features for one-class classification,” IEEE Trans. Image Process, vol. 28, no. 11, pp. 5450–5463, Nov. 2019.
[26] R. Chalapathy, A. K. Menon, and S. Chawla, “Anomaly detection using one-class neural networks,” CoRR, vol. abs/1802.06360, Aug. 2018.
[27] H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interd. Reviews: Comp. Stat., vol. 2, no. 4, pp. 433–459, 2010.
[28] B. Sch¨olkopf, A. Smola, and K.-R. M¨uller, “Kernel principal component analysis,” in Proc. Int. conf. on artificial neural networks, vol. 1327, no. 6. Lausanne, Switzerland: Springer, Oct. 1997, pp. 583–588.
[29] B. Sch¨olkopf, A. Smola, E. Smola, and K.-R. M¨uller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Comp., vol. 10, pp. 1299–1319, Jul. 1998.
[30] M. Silva, A. Santos, E. Figueiredo, R. Santos, C. Sales, and J. Costa, “A novel unsupervised approach based on a genetic algorithm for structural damage detection in bridges,” Eng. Applications of Artificial Intelligence, vol. 52, pp. 168–180, Jun. 2016.
[31] M. Silva, A. Santos, R. Santos, E. Figueiredo, C. Sales, and J. C. Costa, “Agglomerative concentric hypersphere clustering applied to structural damage detection,” Mechanical Systems and Signal Processing, vol. 92, pp. 196–212, Feb. 2017.