Sustainable Earth Trends

Sustainable Earth Trends

Identifying Damage in 3D Skeletal Structures Using a Two-Stage Probabilistic Approach by the MTLBO Optimization Algorithm

Document Type : Original Research Article

Authors
Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran
Abstract
This paper introduces an advanced structural health monitoring (SHM) framework that integrates Bayesian data fusion with a Modified Teaching–Learning-Based Optimization (MTLBO) algorithm to improve damage identification in space frames and truss structures. The proposed method utilizes multiple vibration-based damage indices, including Modal Strain Energy (MSE), Frequency Response Function Strain Energy (FRFSE), Flexibility Strain Energy (FSE), and Residual Force-Based (RFB) indicators, derived from natural frequencies and mode shapes. These indices collectively enhance damage localization accuracy while reducing the number of false or redundant damaged elements, thereby improving computational efficiency. Through the application of Bayesian data fusion, the approach establishes a robust probabilistic framework that effectively integrates different damage indicators to refine detection results. The incorporation of the MTLBO algorithm further enhances the convergence speed and accuracy of the optimization process, expediting the identification of damage across complex structural systems. Moreover, by employing a probabilistic objective function, the framework demonstrates notable resilience to measurement noise, ensuring reliable performance under uncertain conditions. A key innovation of this study lies in the simultaneous probabilistic treatment of both damage localization and damage severity estimation, enabling more precise, noise-resistant, and computationally efficient damage detection. This hybrid methodology represents a significant advancement in SHM, offering a robust and practical solution for real-world structural assessment and maintenance applications.
Keywords
Subjects

Alkayem, N.F. & Cao, M., 2018. Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison. Engineering Optimization, 50(10), pp.1695-1714.
Bagherahmadi, S.A. & Seyedpoor, S.M., 2018. Structural damage detection using a damage probability index based on frequency response function and strain energy concept. Structural Engineering and Mechanics, 67(4), pp.327-336.
Barman, S.K., Jebieshia, T.R., Tiwari, P., Maiti, D.K. & Maity, D., 2019. Two-stage inverse method to detect delamination in composite beam using vibration responses. AIAA Journal, 57(3), 1312-1322.
Barman, S.K., Mishra, M., Maiti, D.K. & Maity, D., 2021. Vibration-based damage detection of structures employing Bayesian data fusion coupled with TLBO optimization algorithm. Structural and Multidisciplinary Optimization, 64(4), 2243-2266.
Cedeño-Rodríguez, M.D., Yanez, S.J., Saavedra-Flores, E.I., Guzmán, C.F. & Pina, J.C., 2025. Vibration-Based Damage Prediction in Composite Concrete–Steel Structures Using Finite Elements. Buildings, 15(2), p.200.
Cruz, P.J. & Salgado, R., 2009. Performance of vibration‐based damage detection methods in bridges. Computer‐Aided Civil and Infrastructure Engineering, 24(1), 62-79.
Das, S., Saha, P. & Patro, S.K., 2016. Vibration-based damage detection techniques used for health monitoring of structures: a review. Journal of Civil Structural Health Monitoring, 6(3), pp.477-507.
Das, T. & Guchhait, S., 2024. A 2D-CNN-based two-stage structural damage localization and quantification technique using time domain vibration data. International Journal of Structural Stability and Dynamics, 24(20), p.2450232.
Dinh-Cong, D., Vo-Duy, T., Ho-Huu, V. & Nguyen-Thoi, T., 2019. Damage assessment in plate-like structures using a two-stage method based on modal strain energy change and Jaya algorithm. Inverse Problems in Science and Engineering, 27(2), pp.166-189.
Dinh-Cong, D., Vo-Duy, T., Ho-Huu, V. & Nguyen-Thoi, T., 2019. Damage assessment in plate-like structures using a two-stage method based on modal strain energy change and Jaya algorithm. Inverse Problems in Science and Engineering, 27(2), pp.166-189.
Fan, W. & Qiao, P., 2011. Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring, 10(1), 83-111.
Gerist, S. & Maheri, M.R., 2016. Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization. Journal of Sound and Vibration, 384, 210-226.
Ghasemi, M.R., Nobahari, M. & Shabakhty, N., 2018. Enhanced optimization-based structural damage detection method using modal strain energy and modal frequencies. Engineering with Computers, 34(3), pp.637-647.
Ghiasi, R., Fathnejat, H. & Torkzadeh, P., 2019. A three-stage damage detection method for large-scale space structures using forward substructuring approach and enhanced bat optimization algorithm. Engineering with Computers, 35(3), pp.857-874.
Hızal, Ç. & Aktas, E., 2021. Structural Health Monitoring-Integrated Reliability Assessment of Engineering Structures. In Reliability-Based Analysis and Design of Structures and Infrastructure (pp. 117-128). CRC Press.
Humar, J., Bagchi, A. & Xu, H., 2006. Performance of vibration-based techniques for the identification of structural damage. Structural Health Monitoring, 5(3), pp.215-241.
Kaveh, A. & Zolghadr, A., 2017. Cyclical parthenogenesis algorithm for guided modal strain energy based structural damage detection. Applied Soft Computing, 57, 250-264.
Kim, J.T. & Stubbs, N., 2002. Improved damage identification method based on modal information. Journal of Sound and Vibration, 252(2), 223-238.
Li, W., Fan, Y. & Xu, Q., 2020. Teaching-learning-based optimization enhanced with multiobjective sorting based and cooperative learning. IEEE Access, 8, 65923-65937.
Machado, M.R., Adhikari, S. & Dos Santos, J.M.C., 2017. A spectral approach for damage quantification in stochastic dynamic systems. Mechanical Systems and Signal Processing, 88, 253-273.
Mishra, M., Barman, S.K., Maity, D. & Maiti, D.K., 2020. Performance studies of 10 metaheuristic techniques in determination of damages for large-scale spatial trusses from changes in vibration responses. Journal of Computing in Civil Engineering, 34(2), 04019052.
Montalvao, D., Maia, N.M.M. & Ribeiro, A.M.R., 2006. A review of vibration-based structural health monitoring with special emphasis on composite materials. Shock and Vibration Digest, 38(4), pp.295-324.
Montazer, M. & Seyedpoor, S.M., 2014. A new flexibility based damage index for damage detection of truss structures. Shock and Vibration, 2014(1), p.460692.
Niu, P., Ma, Y. & Yan, S., 2019. A modified teaching–learning-based optimization algorithm for numerical function optimization. International Journal of Machine Learning and Cybernetics, 10(6), 1357-1371.
Pandey, A.K. & Biswas, M., 1994. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 169(1), pp.3-17.
Radzieński, M., Krawczuk, M. & Palacz, M., 2011. Improvement of damage detection methods based on experimental modal parameters. Mechanical Systems and Signal Processing, 25(6), 2169-2190.
Rao, R.V., Savsani, V.J. & Vakharia, D.P., 2011. Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design, 43(3), pp.303-315.
Ruiz, D.V., de Braganca, C.S.C., Poncetti, B.L., Bittencourt, T.N. & Futai, M.M., 2024, January. Vibration-based structural damage detection strategy using FRFs and machine learning classifiers. In Structures (Vol. 59, p. 105753). Elsevier.
Ruiz, D.V., de Bragança, C.S.C., Poncetti, B.L., Bittencourt, T.N. & Futai, M.M., 2025. Structural damage detection for a small population of nominally equal beams using PSO-optimized Convolutional Neural Networks. Mechanical Systems and Signal Processing, 225, 112276.
Salawu, O.S., 1997. Detection of structural damage through changes in frequency: a review. Engineering Structures, 19(9), 718-723.
Shekhar, S., Freddi, F., Ghosh, J. & Lad, D., 2023. Influence of corrosion on failure modes and lifetime seismic vulnerability assessment of low‐ductility RC frames. Earthquake Engineering & Structural Dynamics, 52(15), 5162-5184.
Shi, Z.Y., Law, S.S. & Zhang, L.M., 2002. Improved damage quantification from elemental modal strain energy change. Journal of Engineering Mechanics, 128(5), 521-529.
Shih, H.W., Thambiratnam, D.P. & Chan, T.H.T., 2009. Vibration based structural damage detection in flexural members using multi-criteria approach. Journal of Sound and Vibration, 323(3-5), 645-661.
Simoen, E., De Roeck, G. & Lombaert, G., 2015. Dealing with uncertainty in model updating for damage assessment: A review. Mechanical Systems and Signal Processing, 56, 123-149.
 Tibaduiza Burgos, D.A., Gomez Vargas, R.C., Pedraza, C., Agis, D. & Pozo, F., 2020. Damage identification in structural health monitoring: A brief review from its implementation to the use of data-driven applications. Sensors, 20(3), 733.
Vamvoudakis-Stefanou, K.J., Sakellariou, J.S. & Fassois, S.D., 2018. Vibration-based damage detection for a population of nominally identical structures: Unsupervised Multiple Model (MM) statistical time series type methods. Mechanical Systems and Signal Processing, 111, 149-171.
Yan, A.M., Kerschen, G., De Boe, P. & Golinval, J.C., 2005. Structural damage diagnosis under varying environmental conditions—Part I: A linear analysis. Mechanical Systems and Signal Processing, 19(4), 847-864.
Zhang, Y. & Yang, W., 2013. Bayesian strain modal analysis under ambient vibration and damage identification using distributed fiber Bragg grating sensors. Sensors and Actuators A: Physical, 201, 434-449.