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Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran

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Abstract

The main purpose of the present study is to enhance high-level noisy data by a wavelet-based iterative filtering algorithm for identification of natural frequencies during ambient wind vibrational tests on a petrochemical process tower. Most of denoising methods fail to filter such noise properly. Both the signal-to-noise ratio and the peak signal-to-noise ratio are small. Multiresolution-based one-step and variational-based filtering methods fail to denoise properly with thresholds obtained by theoretical or empirical method. Due to the fact that it is impossible to completely denoise such high-level noisy data, the enhancing approach is used to improve the data quality, which is the main novelty from the application point of view here. For this iterative method, a simple computational approach is proposed to estimate the dynamic threshold values. Hence, different thresholds can be obtained for different recorded signals in one ambient test. This is in contrast to commonly used approaches recommending one global threshold estimated mainly by an empirical method. After the enhancements, modal frequencies are directly detected by the cross wavelet transform (XWT), the spectral power density and autocorrelation of wavelet coefficients. Estimated frequencies are then compared with those of an undamaged-model, simulated by the finite element method.

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References

  1. Doebling S W, Farrar C R, Prime M B. A summary review of vibration-based damage identification methods. Journal of Shock and Vibration, 1998, 30(2): 91–105

    Google Scholar 

  2. Doebling S W, Farrar C R, Prime M B, Shevitz D W. Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. OSTI.GOV Technical Report LA-13070-MS ON: DE96012168; TRN: 96:003834. 1996

  3. Le T H, Tamura Y. Modal identification of ambient vibration structure using frequency domain decomposition and wavelet transform. In: Proceedings of the 7th Asia-Pacific Conference on Wind Engineering. Taipei, China: APCWE, 2009

    Google Scholar 

  4. Wijesundara K K, Negulescu C, Foerster E, Monfort Climent D. Estimation of modal properties of structures through ambient excitation measurements using continuous wavelet transform. In: Proceedings of 15WCEE. Lisbon: SPES, 2012, 1: 15–18

    Google Scholar 

  5. Abdel-Ghaffar A M, Scanlan R H. Ambient vibration studies of golden gate bridge: I. Suspended structure. Journal of Engineering Mechanics, 1985, 111(4): 463–182

    Google Scholar 

  6. Harik I, Allen D, Street R, Guo M, Graves R, Harison J, Gawry M. Free and ambient vibration of Brent-Spence Bridge. Journal of Structural Engineering, 1997, 123(9): 1262–1268

    Google Scholar 

  7. Farrar C, James G. System identification from ambient vibration measurements on a bridge. Journal of Sound and Vibration, 1997, 205(1): 1–18

    Google Scholar 

  8. Siringoringo D M, Fujino Y. System identification of suspension bridge from ambient vibration response. Engineering Structures, 2008, 30(2): 462–477

    Google Scholar 

  9. Sohn H. A Review of Structural Health Monitoring Literature: 1996–2001. Los Alamos National Laboratory Report. 2004

  10. Kijewski T, Kareem A. Wavelet transforms for system identification in civil engineering. Computer-Aided Civil and Infrastructure Engineering, 2003, 18(5): 339–355

    Google Scholar 

  11. Lin J, Qu L. Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis. Journal of Sound and Vibration, 2000, 234(1): 135–148

    Google Scholar 

  12. Al-Raheem K F, Roy A, Ramachandran K P, Harrison D K, Grainger S. Rolling element bearing faults diagnosis based on autocorrelation of optimized: Wavelet de-noising technique. International Journal of Advanced Manufacturing Technology, 2009, 40(3–4): 393–402

    Google Scholar 

  13. Yan B, Miyamoto A, Brühwiler E. Wavelet transform-based modal parameter identification considering uncertainty. Journal of Sound and Vibration, 2006, 291(1–2): 285–301

    Google Scholar 

  14. Jiang X, Adeli H. Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings. International Journal for Numerical Methods in Engineering, 2007, 71(5): 606–629

    MATH  Google Scholar 

  15. Osornio-Rios R A, Amezquita-Sanchez J P, Romero-Troncoso R J, Garcia-Perez A. MUSIC-ANN analysis for locating structural damages in a truss-type structure by means of vibrations. Computer-Aided Civil and Infrastructure Engineering, 2012, 27(9): 687–698

    Google Scholar 

  16. Carassale L, Percivale F. POD-based modal identification of wind-excited structures. In: Proceedings of the 12th International Conference on Wind Engineering. Cairns, 2007, 1239–1246

  17. Tamura Y. Advanced Structural Wind Engineering. Tokyo: Springer, 2013, 347–376

    Google Scholar 

  18. Meo M, Zumpano G, Meng X, Cosser E, Roberts G, Dodson A. Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms. Mechanical Systems and Signal Processing, 2006, 20(5): 1112–1133

    Google Scholar 

  19. Lardies J, Gouttebroze S. Identification of modal parameters using the wavelet transform. International Journal of Mechanical Sciences, 2002, 44(11): 2263–2283

    MATH  Google Scholar 

  20. He X, Moaveni B, Conte J P, Elgamal A, Masri S F. Modal identification study of Vincent Thomas bridge using simulated wind-induced ambient vibration data. Computer-Aided Civil and Infrastructure Engineering, 2008, 23(5): 373–388

    Google Scholar 

  21. Ni Y C, Lu X L, Lu W S. Field dynamic test and Bayesian modal identification of a special structure—The Palms Together Dagoba. Structural Control and Health Monitoring, 2016, 23(5): 838–856

    Google Scholar 

  22. Zhang F L, Ventura C E, Xiong H B, Lu W S, Pan Y X, Cao J X. Evaluation of the dynamic characteristics of a super tall building using data from ambient vibration and shake table tests by a Bayesian approach. Structural Control and Health Monitoring, 2017, 25(2): 1–18

    Google Scholar 

  23. Kang N, Kim H, Sunyoung Choi & Seongwoo Jo, Hwang J S, Yu E. Performance evaluation of TMD under typhoon using system identification and inverse wind load estimation. Computer-Aided Civil and Infrastructure Engineering, 2012, 27(6): 455–473

    Google Scholar 

  24. Wenzel H, Pichler D. Ambient Vibration Monitoring. Vienna: John Wiley & Sons, 2005

    Google Scholar 

  25. Brownjohn J M W. Structural health monitoring of civil infrastructure. Philosophical Transactions of the Royal Society A, 2007, 365(1851): 589–622

    Google Scholar 

  26. He X H, Hua X G, Chen Z Q, Huang F L. EMD-based random decrement technique for modal parameter identification of an existing railway bridge. Engineering Structures, 2011, 33(4): 1348–1356

    Google Scholar 

  27. Huang C S, Hung S L, Lin C I, Su WC. A wavelet-based approach to identifying structural modal parameters from seismic response and free vibration data. Computer-Aided Civil and Infrastructure Engineering, 2005, 20(6): 408–423

    Google Scholar 

  28. Ivanovic S, Trifunac M D, Novikova E I, Gladkov A A, Todorovska M I. Instrumented 7-Storey Reinforced Concrete Building in Van Nuys, California: Ambient Vibration Survey Following the Damage from the 1994 Northridge Earthquake. Report No. CE 9903. 1999

  29. Ivanovic S S, Trifunac M D, Todorovska M I. Ambient vibration tests of structures—A review. ISET Journal of Earthquake Technology, 2000, 1: 165–197

    Google Scholar 

  30. Brownjohn J M W, De Stefano A, Xu Y L, Wenzel H, Aktan A E. Vibration-based monitoring of civil infrastructure: Challenges and successes. Journal of Civil Structural Health Monitoring, 2011, 1(3–4): 79–95

    Google Scholar 

  31. Roeck G D. The state-of-the-art of damage detection by vibration monitoring: The SIMCES experience. Structural Control and Health Monitoring, 2003, 10(2): 127–134

    Google Scholar 

  32. He D, Wang X, Friswell M I, Lin J. Identification of modal parameters from noisy transient response signals. Structural Control and Health Monitoring, 2017, 24(11): 1–10

    Google Scholar 

  33. Juang J N, Pappa R S. Effects of noise on modal parameters identified by the eigensystem realization algorithm. Journal of Guidance, Control, and Dynamics, 1986, 9(3): 294–303

    Google Scholar 

  34. Dorvash S, Pakzad S N. Effects of measurement noise on modal parameter identification. Smart Materials and Structures, 2012, 21(6): 065008

    Google Scholar 

  35. Li P, Hu S L J, Li H J. Noise issues of modal identification using eigensystem realization algorithm. Procedia Engineering, 2011, 1: 1681–1689

    Google Scholar 

  36. Yoshitomi S, Takewaki I. Noise-effect compensation method for physical-parameter system identification under stationary random input. Structural Control and Health Monitoring, 2009, 16(3): 350–373

    Google Scholar 

  37. Huang C S, Su W C. Identification of modal parameters of a time invariant linear system by continuous wavelet transformation. Mechanical Systems and Signal Processing, 2007, 21(4): 1642–1664

    Google Scholar 

  38. Yan B, Miyamoto A. A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms. Computer-Aided Civil and Infrastructure Engineering, 2006, 21(1): 9–23

    Google Scholar 

  39. Su W C, Huang C S, Chen C H, Liu C Y, Huang H C, Le Q T. Identifying the modal parameters of a structure from ambient vibration data via the stationary wavelet packet. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(10): 738–757

    Google Scholar 

  40. Su W C, Liu C Y, Huang C S. Identification of instantaneous modal parameter of time-varying systems via a wavelet-based approach and its application. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(4): 279–298

    Google Scholar 

  41. Chen S L, Liu J J, Lai H C. Wavelet analysis for identification of damping ratios and natural frequencies. Journal of Sound and Vibration, 2009, 323(1–2): 130–147

    Google Scholar 

  42. Yi T H, Li H N, Zhao X Y. Noise smoothing for structural vibration test signals using an improved wavelet thresholding technique. Sensors (Basel), 2012, 12(8): 11205–11220

    Google Scholar 

  43. Huang N E. Hilbert-Huang Transform and its Applications. Singapore: World Scientific, 2011, 1–26

    Google Scholar 

  44. Teolis A. Computational Signal Processing with Wavelets. Basel: Springer Science & Business Media, 2012

    MATH  Google Scholar 

  45. Misiti M, Misiti Y, Oppenheim G, Poggi J M. Wavelets and their Applications. Wiltshire: John Wiley & Sons, 2013

    MATH  Google Scholar 

  46. Mallat S. Wavelet Analysis & Its Applications. London: Academic Press, 1999

    MATH  Google Scholar 

  47. Van Fleet P. Discrete Wavelet Transformations: An Elementary Approach with Applications. New Jersey: John Wiley & Sons, 2011

    MATH  Google Scholar 

  48. Jansen M. Noise Reduction by Wavelet Thresholding. New York: Springer Science & Business Media, 2012

    MATH  Google Scholar 

  49. Soman K P. Insight into Wavelets: From Theory to Practice. New Delhi: PHI Learning Pvt. Ltd., 2010

    Google Scholar 

  50. Jiang X, Mahadevan S, Adeli H. Bayesian wavelet packet denoising for structural system identification. Structural Control and Health Monitoring, 2007, 14(2): 333–356

    Google Scholar 

  51. Coifman R R, Wickerhauser M V. Adapted waveform “de-Noising” for medical signals and images. IEEE Engineering in Medicine and Biology Magazine, 1995, 14(5): 578–586

    Google Scholar 

  52. Coifman R R, Wickerhauser M V. Experiments with adapted wavelet de-noising for medical signals and images. In: Time Frequency and Wavelets in Biomedical Signal Processing, IEEE press series in Biomedical Engineering. New York: Wiley-IEEE Press, 1998

    Google Scholar 

  53. Hadjileontiadis L J, Panas S M. Separation of discontinuous adventitious sounds from vesicular sounds using a wavelet-based filter. IEEE Transactions on Biomedical Engineering, 1997, 44(12): 1269–1281

    Google Scholar 

  54. Hadjileontiadis L J, Liatsos C N, Mavrogiannis C C, Rokkas T A, Panas S M. Enhancement of bowel sounds by wavelet-based filtering. IEEE Transactions on Biomedical Engineering, 2000, 47(7): 876–886

    Google Scholar 

  55. Ranta R, Heinrich C, Louis-Dorr V, Wolf D. Interpretation and improvement of an iterative wavelet-based denoising method. IEEE Signal Processing Letters, 2003, 10(8): 239–241

    Google Scholar 

  56. Ranta R, Louis-Dorr V, Heinrich C, Wolf D. Iterative wavelet-based denoising methods and robust outlier detection. IEEE Signal Processing Letters, 2005, 12(8): 557–560

    Google Scholar 

  57. Starck J L, Bijaoui A. Filtering and deconvolution by the wavelet transform. Signal Processing, 1994, 35(3): 195–211

    MATH  Google Scholar 

  58. Peyré G. Advanced Signal, Image and Surface Processing-Numerical Tours. Université Paris-Dauphine, 2010

  59. Grinsted A, Moore J C, Jevrejeva S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 2004, 11(5/6): 561–566

    Google Scholar 

  60. Rafiee J, Tse P W. Use of autocorrelation of wavelet coefficients for fault diagnosis. Mechanical Systems and Signal Processing, 2009, 23(5): 1554–1572

    Google Scholar 

  61. Jiang X, Adeli H. Wavelet packet-autocorrelation function method for traffic flow pattern analysis. Computer-Aided Civil and Infrastructure Engineering, 2004, 19(5): 324–337

    Google Scholar 

  62. Bruns A. Fourier-, Hilbert-and wavelet-based signal analysis: Are they really different approaches? Journal of Neuroscience Methods, 2004, 137(2): 321–332

    Google Scholar 

  63. Le Van Quyen M, Foucher J, Lachaux J P, Rodriguez E, Lutz A, Martinerie J, Varela F J. Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. Journal of Neuroscience Methods, 2001, 111(2): 83–98

    Google Scholar 

  64. Rainieri C, Fabbrocino G. Operational Modal Analysis of Civil Engineering Structures. New York: Springer, 2014

    Google Scholar 

  65. Brownjohn J M W. Ambient vibration studies for system identification of tall buildings. Earthquake Engineering & Structural Dynamics, 2003, 32(1): 71–95

    Google Scholar 

  66. Mahato S, Teja M V, Chakraborty A. Adaptive HHT (AHHT) based modal parameter estimation from limited measurements of an RC-framed building under multi-component earthquake excitations. Structural Control and Health Monitoring, 2015, 22(7): 984–1001

    Google Scholar 

  67. Peng Z K, Tse P W, Chu F L. An improved Hilbert-Huang transform and its application in vibration signal analysis. Journal of Sound and Vibration, 2005, 286(1–2): 187–205

    Google Scholar 

  68. Yang W X. Interpretation of mechanical signals using an improved Hilbert-Huang transform. Mechanical Systems and Signal Processing, 2008, 22(5): 1061–1071

    Google Scholar 

  69. Bao C, Hao H, Li Z X, Zhu X. Time-varying system identification using a newly improved HHT algorithm. Computers & Structures, 2009, 87(23–24): 1611–1623

    Google Scholar 

  70. Wu Z, Huang N E. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Data Science and Adaptive Analysis, 2009, 1(1): 1–41

    Google Scholar 

  71. Daubechies I, Lu J, Wu H T. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 2011, 30(2): 243–261

    MathSciNet  MATH  Google Scholar 

  72. Brevdo E, Wu H T, Thakur G, Fuckar N S. Synchrosqueezing and its applications in the analysis of signals with time-varying spectrum. Proceedings of the National Academy of Sciences of the United States of America, 2011, 1: 1079–1094

    Google Scholar 

  73. Perez-Ramirez C A, Amezquita-Sanchez J P, Adeli H, Valtierra-Rodriguez M, Camarena-Martinez D, Romero-Troncoso R J. New methodology for modal parameters identification of smart civil structures using ambient vibrations and synchrosqueezed wavelet transform. Engineering Applications of Artificial Intelligence, 2016, 1: 1–12

    Google Scholar 

  74. Li C, Liang M. Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform. Mechanical Systems and Signal Processing, 2012, 1: 205–217

    Google Scholar 

  75. Feng Z, Chen X, Liang M. Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mechanical Systems and Signal Processing, 2015, 52–1: 360–375

    Google Scholar 

  76. Staszewski W J. Identification of damping in MDOF systems using time-scale decomposition. Journal of Sound and Vibration, 1997, 203(2): 283–305

    Google Scholar 

  77. Areias P, Rabczuk T, Camanho P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 1: 50–63

    Google Scholar 

  78. Nanthakumar S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

    MathSciNet  Google Scholar 

  79. Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

    Google Scholar 

  80. Hamdia K M, Ghasemi H, Zhuang X, Alajlan N, Rabczuk T. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 1: 95–109

    MathSciNet  MATH  Google Scholar 

  81. Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 1: 19–31

    Google Scholar 

  82. Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 1: 113–137

    Google Scholar 

  83. Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122

    MathSciNet  MATH  Google Scholar 

  84. Areias P, Msekh M, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 1: 116–143

    Google Scholar 

  85. Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 1: 27–41

    Google Scholar 

  86. Areias P, Reinoso J, Camanho P P, César de Sá J, Rabczuk T. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 1: 339–360

    Google Scholar 

  87. Anitescu C, Hossain M N, Rabczuk T. Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes. Computer Methods in Applied Mechanics and Engineering, 2018, 1: 638–662

    MathSciNet  MATH  Google Scholar 

  88. Chau-Dinh T, Zi G, Lee P S, Rabczuk T, Song J H. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92–1: 242–256

    Google Scholar 

  89. Budarapu P R, Gracie R, Bordas S P, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148

    Google Scholar 

  90. Talebi H, Silani M, Bordas S P, Kerfriden P, Rabczuk T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071

    MathSciNet  Google Scholar 

  91. Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 1: 126–143

    Google Scholar 

  92. Talebi H, Silani M, Rabczuk T. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 1: 82–92

    Google Scholar 

  93. Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 1: 102–109

    Google Scholar 

  94. Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 1: 322–350

    MathSciNet  MATH  Google Scholar 

  95. Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

    MathSciNet  Google Scholar 

  96. Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 1: 762–782

    MathSciNet  MATH  Google Scholar 

  97. Rabczuk T, Areias P, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548

    MathSciNet  MATH  Google Scholar 

  98. Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

    MathSciNet  MATH  Google Scholar 

  99. Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 1: 48–71

    MathSciNet  MATH  Google Scholar 

  100. Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411

    Google Scholar 

  101. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

    MATH  Google Scholar 

  102. Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

    MATH  Google Scholar 

  103. Rabczuk T, Belytschko T, Xiao S. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063

    MathSciNet  MATH  Google Scholar 

  104. Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

    MathSciNet  MATH  Google Scholar 

  105. Hughes T J, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39–41): 4135–4195

    MathSciNet  MATH  Google Scholar 

  106. Nguyen-Thanh N, Nguyen-Xuan H, Bordas S P A, Rabczuk T. Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering, 2011, 200(21–22): 1892–1908

    MathSciNet  MATH  Google Scholar 

  107. Nguyen V P, Anitescu C, Bordas S P, Rabczuk T. Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 1: 89–116

    MathSciNet  Google Scholar 

  108. Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 1: 239–258

    MathSciNet  MATH  Google Scholar 

  109. Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger K U, Bazilevs Y, Rabczuk T. Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424

    MathSciNet  MATH  Google Scholar 

  110. Nguyen-Thanh N, Valizadeh N, Nguyen M, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 1: 265–291

    MathSciNet  MATH  Google Scholar 

  111. Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 1: 1157–1178

    MathSciNet  MATH  Google Scholar 

  112. Vu-Bac N, Duong T, Lahmer T, Zhuang X, Sauer R, Park H, Rabczuk T. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 1: 427–455

    MathSciNet  MATH  Google Scholar 

  113. Ghasemi H, Park H S, Rabczuk T. A multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 1: 47–62

    MathSciNet  MATH  Google Scholar 

  114. Ghorashi S S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 1: 138–146

    Google Scholar 

  115. Kumari S, Vijay R. Effect of symlet filter order on denoising of still images. Advances in Computers, 2012, 3(1): 137–143

    Google Scholar 

  116. Rousseeuw P J, Leroy A M. Robust Regression & Outlier Detection. Hoboken: John Wiley & Sons, 1987

    MATH  Google Scholar 

  117. Samadi J. Seismic Behavior of structure-equipment in a petrochemical complex to evaluate vulnerability assessment: A case study. Thesis for the Master’s Degree. Tehran: Civil Engineering, University of Tehran, 2010

    Google Scholar 

  118. Jensen A, la Cour-Harbo A. Ripples in Mathematics: The Discrete Wavelet Transform. Heidelberg: Springer Science & Business Media, 2001

    MATH  Google Scholar 

  119. Soman K. Insight into Wavelets: From Theory to Practice. New Delhi: PHI Learning Pvt. Ltd., 2010

    Google Scholar 

  120. Wickerhauser M V. Adapted Wavelet Analysis: From Theory to Software. Natick: AK Peters/CRC Press, 1996

    MATH  Google Scholar 

  121. Donoho D L, Johnstone J M. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 1994, 81(3): 425–455

    MathSciNet  MATH  Google Scholar 

  122. Stein C M. Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 1981, 9(6): 1135–1151

    MathSciNet  MATH  Google Scholar 

  123. Yousefi H, Ghorashi S S, Rabczuk T. Directly simulation of second order hyperbolic systems in second order form via the regularization concept. Communications in Computational Physics, 2016, 20(1): 86–135

    MathSciNet  MATH  Google Scholar 

  124. Yousefi H, Noorzad A, Farjoodi J. Multiresolution based adaptive schemes for second order hyperbolic PDEs in elastodynamic problems. Applied Mathematical Modelling, 2013, 37(12–13): 7095–7127

    MathSciNet  MATH  Google Scholar 

  125. Selesnick I W, Bayram I. Total Variation Filtering, White paper, Connexions Web site. 2010

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Acknowledgements

The authors gratefully acknowledge the financial support of Iran National Science Foundation (INSF).

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Authors and Affiliations

  1. High Performance Computing Lab, School of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

    Hassan Yousefi & Soheil Mohammadi

  2. School of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

    Alireza Taghavi Kani & Iradj Mahmoudzadeh Kani

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  1. Hassan Yousefi
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Yousefi, H., Taghavi Kani, A., Mahmoudzadeh Kani, I. et al. Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran. Front. Struct. Civ. Eng. 14, 446–472 (2020). https://doi.org/10.1007/s11709-019-0605-8

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  • DOI: https://doi.org/10.1007/s11709-019-0605-8

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