Damage Detection in Double Layer Grids with Modal Strain Energy Method and Dempster-Shafer Theory

Document Type : Research Papers

Authors

1 Babol Noshirvani University of Technology.

2 Faculty of civil engineering, Babol Noshirvani university of technology

3 Department of Civil Engineering, Payame Noor University (PNU).

Abstract

Change in modal strain energy is one of the indicators used to detect damage in structures. However, in structures with high degrees of freedom, such as double-layer grids, this method requires a relatively large number of mode shapes which in practice is difficult to determine. Therefore, it is necessary to reduce the number of required mode shapes. In this study, a damage detection technique based on modal strain energy and Dempster-Shafer evidence theory is presented for locating damage in double layer grids using only a few number of mode shapes. First, by calculating mode shapes of the grid in undamaged and damaged states, the modal strain energy based index for each mode shape is determined. Then, the results obtained from separate mode shapes are combined using Dempster-Shafer theory to achieve better results. In order to investigate the effect of noise on damage detection, 3% random noise is added to mode shapes. To demonstrate the performance of the proposed method, different single and multiple damage cases with different damage intensities are considered. Numerical results show that using 5 mode shapes, the presented technique can detect up to 3 damaged elements with different damage intensities in different parts of the grid with good accuracy (probability of 92.3%). Considering the fact that the classical modal strain energy method fails to distinguish even 1 damaged element in the double layer grid, the result shows significant improvement.

Keywords


Arekar, V.A., Patil, Y.D. and Patil, H.S. (2016). “Development of a new connector for double layer space grids”, Perspectives in Science, 8, 525-528.

Carrasco, C.J., Osegueda, R.A., Ferregut, C.M. and Grygier, M. (1997). “Damage localization in a space truss model using modal strain energy”, In: Proceedings-SPIE the International Society for Optical Engineering, Orlando, Florida, USA, pp. 1786-1792.

Chen, M. and Xia, X. (2011). “A new combination rule of DS theory”, IEEE International Conference on Computer Science and Automation Engineering, 3, 202-205.

Cheng, Y.Y., Zhao, C.Y. and Zhang, J. (2019). “A novel damage detection method based on flexibility identification theory and data fusion technique”, Scientia Iranica A, 26(4), 2286-2298.

Davoodi, M.R., Mahdavi, M. and Mostafavian, S.A. (2012). “Experimental and analytical determination of dynamic properties of a steel frame with bolted flange joints”, Proceedings of International Conference on Engineering and Information Technology (ICEIT2012), Toronto, Canada.

Dawari, V.B. and Vesmawala, G.R. (2016). “Structural damage identification of beam structures using two stage method based on modal strain energy indicators and artificial neural networks”, Journal of Vibroengineering, 18(1), 119-128.

Dempster, A.P. (1967). “Upper and lower probabilities induced by a multivalued mapping”, The Annals of Mathematical Statistics, 38(2), 325-339.

Ding, Z.H., Yao, R.Z., Huang, J.L., Huang, M. and Lu, Z.R. (2017). “Structural damage detection based on residual force vector and imperialist competitive algorithm”, Structural Engineering and Mechanics, 62(6), 709-717.

Ding, Y., Yao, X., Wang, S. and Zhao, X. (2019). “Structural damage assessment using improved Dempster-Shafer data fusion algorithm”. Earthquake Engineering and Engineering Vibration, 18(2), 395-408.‏

Grande, E. and Imbimbo, M. (2014). “A multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy”, Journal of Civil Structural Health Monitoring, 4(2), 107-118.

Grande, E. and Imbimbo, M. (2016). “A multi-stage approach for damage detection in structural systems based on flexibility”, Mechanical Systems and Signal Processing, 76, 455-475.

Guo, H.Y. (2006). “Structural damage detection using information fusion technique”, Mechanical Systems and Signal Processing, 20(5), 1173-1188.

Guo, H.Y. and Li, Z.L. (2011). “Two-stage multi-damage detection method based on energy balance equation”, Journal of Nondestructive Evaluation, 30(3), 186-200.

Guo, H., Zhou, R. and Zhang, F. (2019). “Structural nonlinear damage detection using improved Dempster-Shafer theory and time domain model”, Journal of Vibroengineering, 21(6), 1679-1693.‏

Ma, S.L., Jiang, S.F. and Weng, L.Q. (2014). “Two-stage damage identification based on modal strain energy and revised particle swarm optimization”, International Journal of Structural Stability and Dynamics, 14(5), 1440005.

Mahdavi, M., Davoodi, M.R. and Mostafavian, A. (2012). “Determination of joint stiffness of a three story steel frame by finite element model updating”, Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.

Messina, A., Williams, E.J. and Contursi, T. (1998). “Structural damage detection by a sensitivity and statistical-based method”, Journal of Sound and Vibration, 216(5), 791-808.

Mostafavian, S.A., Davoodi, M.R. and Vaseghi Amiri, J. (2012). “Ball joint behavior in a double layer grid by dynamic model updating”, Journal of Constructional Steel Research, 76, 28-38.

Ren, W.-X. and De Roeck, G. (2002). “Structural damage identification using modal data, I: Simulation verification”, Journal of Structural Engineering, 128(1), 87-95.

Rezaifar, O. and Doost Mohammadi, M.R. (2016). “Damage detection of axially loaded beam: A frequency-based method”, Civil Engineering Infrastructures Journal, 49(1), 165-172.

Seyedpoor, S.M. (2012). “A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization”, International Journal of Non-Linear Mechanics, 47(1), 1-8.

Shafere, G. (1976). A mathematical theory of evidence, Princeton University Press.

Shi, Z., Law, S.S. and Zhang, L. (2000). “Structural damage detection from modal strain energy change”, Journal of Engineering Mechanics, 126(12), 1216-1223.

Shi, Z.Y., Law, S.S. and Zhang, L.M. (1998). “Structural damage localization from modal strain energy change”, Journal of Sound and Vibration, 218(5), 825-844.

Srinivas, V., Ramanjaneyulu, K. and Jeyasehar, C.A. (2011). “Multi-stage approach for structural damage identification using modal strain energy and evolutionary optimization techniques”, Structural Health Monitoring, 10(2), 219-230.

Torkzadeh, P., Goodarzi, Y. and Salajegheh, E. (2013). “A two-stage damage detection method for large-scale structures by kinetic and modal strain energies using heuristic particle swarm optimization”, International Journal of Optimization in Civil Engineering, 3(3), 465-482.

Wei, Z., Liu, J. and Lu, Z. (2017). “Structural damage detection using improved particle swarm optimization”, Inverse Problems in Science and Engineering, 26(6), 792-810.‏

Wei, Z.T., Liu, J.K. and Lu, Z.R. (2016). “Damage identification in plates based on the ratio of modal strain energy change and sensitivity analysis”, Inverse Problems in Science and Engineering, 24(2), 265-283.

Yasi, B. and Mohammadizadeh, M.R. (2018). “Identification of structural defects using computer algorithms”, Civil Engineering Infrastructures Journal, 51(1), 55-86.

Zhao, X.K., Wang, R.L., Gu, H.C., Song, G.B. and Mo, Y.L. (2014). “Innovative data fusion enabled structural health monitoring approach”, Mathematical Problems in Engineering, Vol. 2014, Article ID. 369540, 10 p.

Arekar, V.A., Patil, Y.D. and Patil, H.S. (2016). “Development of a new connector for double layer space grids”, Perspectives in Science, 8, 525-528.
Carrasco, C.J., Osegueda, R.A., Ferregut, C.M. and Grygier, M. (1997). “Damage localization in a space truss model using modal strain energy”, In: Proceedings-SPIE the International Society for Optical Engineering, Orlando, Florida, USA, pp. 1786-1792.
Chen, M. and Xia, X. (2011). “A new combination rule of DS theory”, IEEE International Conference on Computer Science and Automation Engineering, 3, 202-205.
Cheng, Y.Y., Zhao, C.Y. and Zhang, J. (2019). “A novel damage detection method based on flexibility identification theory and data fusion technique”, Scientia Iranica A, 26(4), 2286-2298.
Davoodi, M.R., Mahdavi, M. and Mostafavian, S.A. (2012). “Experimental and analytical determination of dynamic properties of a steel frame with bolted flange joints”, Proceedings of International Conference on Engineering and Information Technology (ICEIT2012), Toronto, Canada.
Dawari, V.B. and Vesmawala, G.R. (2016). “Structural damage identification of beam structures using two stage method based on modal strain energy indicators and artificial neural networks”, Journal of Vibroengineering, 18(1), 119-128.
Dempster, A.P. (1967). “Upper and lower probabilities induced by a multivalued mapping”, The Annals of Mathematical Statistics, 38(2), 325-339.
Ding, Z.H., Yao, R.Z., Huang, J.L., Huang, M. and Lu, Z.R. (2017). “Structural damage detection based on residual force vector and imperialist competitive algorithm”, Structural Engineering and Mechanics, 62(6), 709-717.
Ding, Y., Yao, X., Wang, S. and Zhao, X. (2019). “Structural damage assessment using improved Dempster-Shafer data fusion algorithm”. Earthquake Engineering and Engineering Vibration, 18(2), 395-408.‏
Grande, E. and Imbimbo, M. (2014). “A multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy”, Journal of Civil Structural Health Monitoring, 4(2), 107-118.
Grande, E. and Imbimbo, M. (2016). “A multi-stage approach for damage detection in structural systems based on flexibility”, Mechanical Systems and Signal Processing, 76, 455-475.
Guo, H.Y. (2006). “Structural damage detection using information fusion technique”, Mechanical Systems and Signal Processing, 20(5), 1173-1188.
Guo, H.Y. and Li, Z.L. (2011). “Two-stage multi-damage detection method based on energy balance equation”, Journal of Nondestructive Evaluation, 30(3), 186-200.
Guo, H., Zhou, R. and Zhang, F. (2019). “Structural nonlinear damage detection using improved Dempster-Shafer theory and time domain model”, Journal of Vibroengineering, 21(6), 1679-1693.‏
Ma, S.L., Jiang, S.F. and Weng, L.Q. (2014). “Two-stage damage identification based on modal strain energy and revised particle swarm optimization”, International Journal of Structural Stability and Dynamics, 14(5), 1440005.
Mahdavi, M., Davoodi, M.R. and Mostafavian, A. (2012). “Determination of joint stiffness of a three story steel frame by finite element model updating”, Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.
Messina, A., Williams, E.J. and Contursi, T. (1998). “Structural damage detection by a sensitivity and statistical-based method”, Journal of Sound and Vibration, 216(5), 791-808.
Mostafavian, S.A., Davoodi, M.R. and Vaseghi Amiri, J. (2012). “Ball joint behavior in a double layer grid by dynamic model updating”, Journal of Constructional Steel Research, 76, 28-38.
Ren, W.-X. and De Roeck, G. (2002). “Structural damage identification using modal data, I: Simulation verification”, Journal of Structural Engineering, 128(1), 87-95.
Rezaifar, O. and Doost Mohammadi, M.R. (2016). “Damage detection of axially loaded beam: A frequency-based method”, Civil Engineering Infrastructures Journal, 49(1), 165-172.
Seyedpoor, S.M. (2012). “A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization”, International Journal of Non-Linear Mechanics, 47(1), 1-8.
Shafere, G. (1976). A mathematical theory of evidence, Princeton University Press.
Shi, Z., Law, S.S. and Zhang, L. (2000). “Structural damage detection from modal strain energy change”, Journal of Engineering Mechanics, 126(12), 1216-1223.
Shi, Z.Y., Law, S.S. and Zhang, L.M. (1998). “Structural damage localization from modal strain energy change”, Journal of Sound and Vibration, 218(5), 825-844.
Srinivas, V., Ramanjaneyulu, K. and Jeyasehar, C.A. (2011). “Multi-stage approach for structural damage identification using modal strain energy and evolutionary optimization techniques”, Structural Health Monitoring, 10(2), 219-230.
Torkzadeh, P., Goodarzi, Y. and Salajegheh, E. (2013). “A two-stage damage detection method for large-scale structures by kinetic and modal strain energies using heuristic particle swarm optimization”, International Journal of Optimization in Civil Engineering, 3(3), 465-482.
Wei, Z., Liu, J. and Lu, Z. (2017). “Structural damage detection using improved particle swarm optimization”, Inverse Problems in Science and Engineering, 26(6), 792-810.‏
Wei, Z.T., Liu, J.K. and Lu, Z.R. (2016). “Damage identification in plates based on the ratio of modal strain energy change and sensitivity analysis”, Inverse Problems in Science and Engineering, 24(2), 265-283.
Yasi, B. and Mohammadizadeh, M.R. (2018). “Identification of structural defects using computer algorithms”, Civil Engineering Infrastructures Journal, 51(1), 55-86.
Zhao, X.K., Wang, R.L., Gu, H.C., Song, G.B. and Mo, Y.L. (2014). “Innovative data fusion enabled structural health monitoring approach”, Mathematical Problems in Engineering, Vol. 2014, Article ID. 369540, 10 p.
Volume 54, Issue 2
December 2021
Pages 253-266
  • Receive Date: 23 December 2019
  • Revise Date: 01 June 2020
  • Accept Date: 09 August 2020
  • First Publish Date: 12 July 2021