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Damage detection in a cantilever beam using noisy mode shapes with an application of artificial neural network-based improved mode shape curvature technique

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Abstract

Experimentally and numerically obtained displacement mode shapes are utilized as input data to artificial neural networks (ANNs) and mode shape curvature technique. Frequency responses (FRs) in the form of displacement mode shapes with varying damage levels are extracted using the Bruel & Kjaer instrument. Two identical specimens of a cantilever beam are considered with different damage locations. It is demonstrated that the measured frequency response needs to be made error-free to locate damages. ANN training algorithms are utilized to reduce the measurement error from the measured frequency response (FR) data set. The analysis is more robust due to the use of ANN application before extracting mode shape curvature. The trained data sets are then utilized to produce the mode shapes curvatures for all the damage cases using central difference approximation. Damage severity and locations are then identified by analyzing the absolute mode shape curvature differences in different damage scenarios.

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Abbreviations

FRF:

Frequency response function

ANN:

Artificial neural network

ODS:

Operational deflection shape

M :

Mass

D :

Dam**

K :

Stiffness

FFT:

Fast flourier transform

X(ω):

Output response

F(ω):

Input force

H(ω):

Frequency response for displacement

α(ω):

Frequency response for acceleration

y ″ :

Curvature

h :

Element length

S mm :

Power spectrum

γ 2(ω):

The coherence

v :

Number of input/output

e k :

Experimental data set

p k :

Predicted data set

N k :

Zk (Normalized value)

Z k :

Input/output data set

Z k , min :

Data set (minimum value)

Z k , max :

Data set (maximum value)

MSE:

Mean square error

MAPE:

Mean absolute percentage error

R :

Regression coefficient

AMSC:

Absolute mode shape curvature

PCA:

Principal component analysis

Trainlm:

Levenberg–Marquardt (lm) back propagation

Trainscg:

Scaled conjugate gradient (scg) back propagation

Trainrp:

Resilient back propagation

Traingda:

Gradient descent with adoptive learning rate back propagation

Traingdx:

Gradient descent with momentum and adoptive learning rate back propagation

References

  • Bandara, R. P., Chan, T. H. T., & Thambiratnam, D. P. (2014). Structural damage detection method using frequency response functions. Structural Health Monitoring, 13(4), 418–429.

    Google Scholar 

  • Basheer, I. A., & Hajmeer, M. (2000). Artificial neural networks: Fundamentals, computing, design, and application. Journal of Microbiological Methods, 43(1), 3–31.

    Google Scholar 

  • Bhowmik, S., Panua, R., Debroy, D., & Paul, A. (2017) Artificial neural network prediction of diesel engine performance and emission fueled with Diesel–Kerosene–Ethanol Blends: A fuzzy-based optimization. Journal of Energy Resources Technology 139(4) (2017).

  • Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford University Press.

    MATH  Google Scholar 

  • Brigham, E. O. (1988). The Fast fourier transform and applications. Prentice Hall.

    Google Scholar 

  • Cao, M., Radzieński, M., Wei, Xu., & Ostachowicz, W. (2014). Identification of multiple damages in beams based on robust curvature mode shapes. Mechanical Systems and Signal Processing, 46(2), 468–480.

    Google Scholar 

  • Cawley, P., & Adams, R. D. (1979). The location of defects in structures from measurements of natural frequencies. The Journal of Strain Analysis for Engineering Design, 14(2), 49–57.

    Google Scholar 

  • Cay, Y., Çiçek, A., Kara, F., & Sağiroğlu, S. (2012). Prediction of engine performance for an alternative fuel using artificial neural network. Applied Thermal Engineering, 37, 217–225.

    Google Scholar 

  • Chakraborty, A., Roy, S., & Banerjee, R. (2016). An experimental based ANN approach in map** performance-emission characteristics of a diesel engine operating in dual-fuel mode with LPG. Journal of Natural Gas Science and Engineering, 28, 15–30.

    Google Scholar 

  • Chaudhry, Z., & Ganino, A. J. (1994). Damage detection using neural networks: An initial experimental study on debonded beams. Journal of Intelligent Material Systems and Structures, 5(4), 585–589.

    Google Scholar 

  • Dackermann, U., Li, J., & Samali, B. (2013). Identification of member connectivity and mass changes on a two-storey framed structure using frequency response functions and artificial neural networks. Journal of Sound and Vibration, 332(16), 3636–3653.

    Google Scholar 

  • Duvnjak, I., Damjanović, D., Bartolac, M., & Skender, A. (2021). Mode shape-based damage detection method (MSDI): Experimental validation. Applied Sciences, 11(10), 4589.

    Google Scholar 

  • Dworakowski, Z., Ambroziński, Ł, Packo, P., Dragan, K., Stepinski, T., & Uhl, T. (2014). Application of artificial neural networks for damage indices classification with the use of Lamb waves for the aerospace structures. Key Engineering Materials, 588, 12–21.

    Google Scholar 

  • Elshafey, A. A., Marzouk, H., & Haddara, M. R. (2011). Experimental damage identification using modified mode shape difference. Journal of Marine Science and Application, 10(2), 150–155.

    Google Scholar 

  • Ewins, D. J. (1984). Modal testing: Theory and practice (Vol. 15). Research Studies Press.

    Google Scholar 

  • Fan, W., & Qiao, P. (2011). Vibration-based damage identification methods: A review and comparative study. Structural Health Monitoring, 10(1), 83–111.

    Google Scholar 

  • Ghiasi, R., Torkzadeh, P., & Noori, M. (2014). Structural damage detection using artificial neural networks and least square support vector machine with particle swarm harmony search algorithm. International Journal of Sustainable Materials and Structural Systems, 1(4), 303–320.

    Google Scholar 

  • Hardenberg, H. O., & Schaefer, A. J. (1981). The use of ethanol as a fuel for compression ignition engines. No. 811211. SAE Technical paper.

  • Hassiotis, S., & Jeong, G. D. (1995). Identification of stiffness reductions using natural frequencies. Journal of Engineering Mechanics, 121(10), 1106–1113.

    Google Scholar 

  • Ismail, H. M., Ng, H. K., Queck, C. W., & Gan, S. (2012). Artificial neural networks modelling of engine-out responses for a light-duty diesel engine fuelled with biodiesel blends. Applied Energy, 92, 769–777.

    Google Scholar 

  • Janeliukstis, R., Ručevskis, S., & Kaewunruen, S. (2019). Mode shape curvature squares method for crack detection in railway pre-stressed concrete sleepers. Engineering Failure Analysis, 105, 386–401.

    Google Scholar 

  • Kaveh, A., Hoseini Vaez, S. R., & Hosseini, P. (2019a). Enhanced vibrating particles system algorithm for damage identification of truss structures. Scientia Iranica, 26(1), 246–256.

    Google Scholar 

  • Kaveh, A., Hosseini Vaez, S. R., Hosseini, P., & Fathali, M. A. (2019b). A new two-phase method for damage detection in skeletal structures. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(1), 49–65.

    Google Scholar 

  • Kaveh, A., Javadi, S. M., & Maniat, M. (2014). Damage assessment via modal data with a mixed particle swarm strategy, ray optimizer, and harmony search. 95–106.

  • Kaveh, A., & Mahdavi, V. R. (2016). Damage identification of truss structures using CBO and ECBO algorithms. Asian J Civil Eng, 17(1), 75–89.

    Google Scholar 

  • Kaveh, A., & Maniat, M. (2014). Damage detection in skeletal structures based on charged system search optimization using incomplete modal data. International Journal of Civil Engineering, 12(2), 193–200.

    Google Scholar 

  • Kaveh, A., & Maniat, M. (2015). Damage detection based on MCSS and PSO using modal data. Smart Structures and Systems, 15(5), 1253–1270.

    Google Scholar 

  • Kaveh, A., Vaez, S. R. H., Hosseini, P., & Fallah, N. (2016). Detection of damage in truss structures using Simplified Dolphin Echolocation algorithm based on modal data. Smart Structures and Systems, 18(5), 983–1004.

    Google Scholar 

  • Kaveh, A., & Zolghadr, A. (2012). An improved charged system search for structural damage identification in beams and frames using changes in natural frequencies. 321–339.

  • Kaveh, A., & Zolghadr, A. (2015). An improved CSS for damage detection of truss structures using changes in natural frequencies and mode shapes. Advances in Engineering Software, 80, 93–100.

    Google Scholar 

  • Kaveh, A., & Zolghadr, A. (2017a). Cyclical parthenogenesis algorithm for guided modal strain energy based structural damage detection. Applied Soft Computing, 57, 250–264.

    Google Scholar 

  • Kaveh, A., & Zolghadr, A. (2017b). Guided modal strain energy-based approach for structural damage identification using tug-of-war optimization algorithm. Journal of Computing in Civil Engineering, 31(4), 04017016.

    Google Scholar 

  • Kim, J.-T., Ryu, Y.-S., Cho, H.-M., & Stubbs, N. (2003). Damage identification in beam-type structures: Frequency-based method vs mode-shape-based method. Engineering Structures, 25(1), 57–67.

    Google Scholar 

  • Lestari, W., Qiao, P., & Hanagud, S. (2007). Curvature mode shape-based damage assessment of carbon/epoxy composite beams. Journal of Intelligent Material Systems and Structures, 18(3), 189–208.

    Google Scholar 

  • Limongelli, M. P. (2010). Frequency response function interpolation for damage detection under changing environment. Mechanical Systems and Signal Processing, 24(8), 2898–2913.

    Google Scholar 

  • Lippmann, R. P. (1987). An introduction to computing with neural nets. IEEE Assp Magazine, 4(2), 4–22.

    Google Scholar 

  • Liu, X., Lieven, N. A. J., & Escamilla-Ambrosio, P. J. (2009). Frequency response function shape-based methods for structural damage localisation. Mechanical Systems and Signal Processing, 23(4), 1243–1259.

    Google Scholar 

  • Maia, N. M. M., Silva, J. M. M., Almas, E. A. M., & Sampaio, R. P. C. (2003). Damage detection in structures: From mode shape to frequency response function methods. Mechanical Systems and Signal Processing, 17(3), 489–498.

    Google Scholar 

  • Marwala, T. (2000). Damage identification using committee of neural networks. Journal of Engineering Mechanics, 126(1), 43–50.

    Google Scholar 

  • Masri, S. F., Nakamura, M., Chassiakos, A. G., & Caughey, T. K. (1996). Neural network approach to detection of changes in structural parameters. Journal of Engineering Mechanics, 122(4), 350–360.

    Google Scholar 

  • Masri, S. F., Smyth, A. W., Chassiakos, A. G., Caughey, T. K., & Hunter, N. F. (2000). Application of neural networks for detection of changes in nonlinear systems. Journal of Engineering Mechanics, 126(7), 666–676.

    Google Scholar 

  • Nayyar, A., Baneen, U., Naqvi, S. A. Z., & Ahsan, M. (2021). Detection and localization of multiple small damages in beam. Advances in Mechanical Engineering, 13(1), 1687814020987329. https://doi.org/10.1177/1687814020987329

    Article  Google Scholar 

  • Neves, A. C., González, I., Leander, J., & Karoumi, R. (2017). Structural health monitoring of bridges: A model-free ANN-based approach to damage detection. Journal of Civil Structural Health Monitoring, 7(5), 689–702.

    Google Scholar 

  • Ni, Y. Q., Zhou, X. T., & Ko, J. M. (2006). Experimental investigation of seismic damage identification using PCA-compressed frequency response functions and neural networks. Journal of Sound and Vibration, 290(1–2), 242–263.

    Google Scholar 

  • Pan, J., Zhang, Z., Wu, J., Ramakrishnan, K. R., & Singh, H. K. (2019). A novel method of vibration modes selection for improving accuracy of frequency-based damage detection. Composites Part B Engineering, 159, 437–446.

    Google Scholar 

  • Pandey, A. K., Biswas, M., & Samman, M. M. (1991). Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 145(2), 321–332.

    Google Scholar 

  • Pérez, M. A., Gil, L., & Oller, S. (2014). Impact damage identification in composite laminates using vibration testing. Composite Structures, 108, 267–276.

    Google Scholar 

  • Qiao, P., Kan, Lu., Lestari, W., & Wang, J. (2007). Curvature mode shape-based damage detection in composite laminated plates. Composite Structures, 80(3), 409–428.

    Google Scholar 

  • Roy, S., Banerjee, R., & Bose, P. K. (2014a). Performance and exhaust emissions prediction of a CRDI assisted single cylinder diesel engine coupled with EGR using artificial neural network. Applied Energy, 119, 330–340.

    Google Scholar 

  • Roy, S., Banerjee, R., Das, A. K., & Bose, P. K. (2014b). Development of an ANN based system identification tool to estimate the performance-emission characteristics of a CRDI assisted CNG dual fuel diesel engine. Journal of Natural Gas Science and Engineering, 21, 147–158.

    Google Scholar 

  • Rucevskis, S., & Wesolowski, M. (2010). Identification of damage in a beam structure by using mode shape curvature squares. Shock and Vibration, 17(4–5), 601–610.

    Google Scholar 

  • Salawu, O. S. (1997). Detection of structural damage through changes in frequency: A review. Engineering Structures, 19(9), 718–723.

    Google Scholar 

  • Samali, B., Dackermann, U., & Li, J. (2012). Location and severity identification of notch-type damage in a two-storey steel framed structure utilising frequency response functions and artificial neural network. Advances in Structural Engineering, 15(5), 743–757.

    Google Scholar 

  • Sampaio, R. P. C., Maia, N. M. M., Almeida, R. A. B., & Urgueira, A. P. V. (2016). A simple damage detection indicator using operational deflection shapes. Mechanical Systems and Signal Processing, 72, 629–641.

    Google Scholar 

  • Wang, Y., Liang, M., & **ang, J. (2014). Damage detection method for wind turbine blades based on dynamics analysis and mode shape difference curvature information. Mechanical Systems and Signal Processing, 48(1–2), 351–367.

    Google Scholar 

  • Weinstein, J. C., Sanayei, M., & Brenner, B. R. (2018). Bridge damage identification using artificial neural networks. Journal of Bridge Engineering, 23(11), 04018084.

    Google Scholar 

  • Worden, K., Farrar, C. R., Haywood, J., & Todd, M. (2008). A review of nonlinear dynamics applications to structural health monitoring. Structural Control and Health Monitoring, 15(4), 540–567.

    Google Scholar 

  • Yusaf, T. F., Buttsworth, D. R., Saleh, K. H., & Yousif, B. F. (2010). CNG-diesel engine performance and exhaust emission analysis with the aid of artificial neural network. Applied Energy, 87(5), 1661–1669.

    Google Scholar 

  • Zang, C., & Imregun, M. (2001). Structural damage detection using artificial neural networks and measured FRF data reduced via principal component projection. Journal of Sound and Vibration, 242(5), 813–827.

    MATH  Google Scholar 

  • Zenzen, R., Khatir, S., Belaidi, I., & Wahab, M. A. (2018). Structural health monitoring of beam-like and truss structures using frequency response and particle swarm optimization. Numerical modelling in engineering (pp. 390–399). Singapore: Springer.

    Google Scholar 

  • Zhong, S., Oyadiji, S. O., & Ding, K. (2008). Response-only method for damage detection of beam-like structures using high accuracy frequencies with auxiliary mass spatial probing. Journal of Sound and Vibration, 311(3–5), 1075–1099.

    Google Scholar 

  • Zhou, Y.-L., Figueiredo, E., Maia, N., & Perera, R. (2015). Damage detection and quantification using transmissibility coherence analysis. Shock and Vibration, 2015, 1–16.

    Google Scholar 

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  1. Department of Civil Engineering, National Institute of Technology Agartala, Agartala, India

    Sonu Kumar Gupta & Surajit Das

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  1. Sonu Kumar Gupta
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Correspondence to Sonu Kumar Gupta.

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Gupta, S.K., Das, S. Damage detection in a cantilever beam using noisy mode shapes with an application of artificial neural network-based improved mode shape curvature technique. Asian J Civ Eng 22, 1671–1693 (2021). https://doi.org/10.1007/s42107-021-00404-w

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