Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Variable input observer for nonstationary high-rate dynamic systems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Engineering systems experiencing events of amplitudes higher than 100 gn for a duration under 100 ms, here termed high-rate dynamics, can undergo rapid damaging effects. If the structural health of such systems could be accurately estimated in a timely manner, preventative measures could be employed to minimize adverse effects. For complex high-rate problems, adaptive observers have shown promise due to their capability to deal with nonstationary, noisy, and uncertain systems. However, adaptive observers have slow convergence rates, which impede their applicability to the high-rate problems. To improve on the convergence rate, we propose a variable input space concept for optimizing the use of data history of high-rate dynamics, with the objective to produce an optimal representation of the system of interest. Using the embedding theory, the algorithm sequentially selects and adapts a vector of inputs that preserves the essential dynamics of the high-rate system. In this paper, the variable input space is integrated in a wavelet neural network, which constitutes a variable input observer. The observer is simulated using experimental data from a high-rate system. Different input space adaptation methods are studied, and the performance is also compared against an optimized fixed input strategy. It is found that a smooth transition of the input space eliminates error spikes and yields faster convergence. The variable input observer is further studied in a hybrid model-/data-driven formulation, and results demonstrate significant improvement in performance gained from the added physical knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Hong J, Laflamme S, Dodson J, Joyce B (2018) Introduction to state estimation of high-rate system dynamics. Sensors 18(217):1–16

    Google Scholar 

  2. Lowe R, Dodson J, Foley J (2014) Microsecond prognostics and health management. IEEE Reliab Soc Newslett 60:1–5

    Google Scholar 

  3. Connor J, Laflamme S (2014) Structural motion engineering. Springer, Berlin

    Google Scholar 

  4. Oliveira RMF, Ferreira E, Oliveira F, Azevedo S (1994) A study on the convergence of observer-based kinetics estimators in stirred tank bioreactors. Korean Inst Chem Eng 6(6):367–371

    Google Scholar 

  5. Mondal S, Chakraborty G, Bhattacharyya K (2008) Robust unknown input observer for nonlinear systems and its application to fault detection and isolation. J Dyn Syst Meas Contr 130(4):1–5

    Google Scholar 

  6. Stricker K, Kocher L, Van Alstine D, Shaver GM (2013) Input observer convergence and robustness: application to compression ratio estimation. Control Eng Pract 21(4):565–582

    Google Scholar 

  7. Wang Y, Rajamani R, Bevly DM (2014) Observer design for differentiable lipschitz nonlinear systems with time-varying parameters. In: 53rd Annual conference on decision and control (CDC), IEEE, pp 145–152

  8. Kim BK, Chung WK, Ohba K (2009) Design and performance tuning of sliding-mode controller for high-speed and high-accuracy positioning systems in disturbance observer framework. IEEE Trans Ind Electron 56(10):3798–3809

    Google Scholar 

  9. Shahrokhi M, Morari M (1982) A discrete adaptive observer and identifier with arbitrarily fast rate of convergence. IEEE Trans Autom Control 27(2):506–509

    MATH  Google Scholar 

  10. Khayati K, Zhu J (2013) Adaptive observer for a large class of nonlinear systems with exponential convergence of parameter estimation. In: International conference on control, decision and information technologies (CoDIT), IEEE, pp 100–105

  11. Byrski W, Byrski J (2014) On-line fast identification method and exact state observer for adaptive control of continuous system. In: 11th World congress on intelligent control and automation (WCICA), IEEE, pp 4491–4497

  12. Laflamme S, Slotine JE, Connor J (2012) Self-organizing input space for control of structures. Smart Mater Struct 21(11):115015

    Google Scholar 

  13. Bowden G, Dandy G, Maier H (2005) Input determination for neural network models in water resources applications. Part 1–background and methodology. J Hydrol 301(1–4):75–92

    Google Scholar 

  14. da Silva A, Alexandre P, Ferreira V, Velasquez R (2008) Input space to neural network based load forecasters. Int J Forecast 24(4):616–629

    Google Scholar 

  15. Sindelar R, Babuska R (2004) Input selection for nonlinear regression models. IEEE Trans Fuzzy Syst 12(5):688–696

    Google Scholar 

  16. Hong X, Mitchell R, Chen S, Harris C, Li K, Irwin G (2008) Model selection approaches for non-linear system identification: a review. Int J Syst Sci 39(10):925–946

    MathSciNet  MATH  Google Scholar 

  17. Moniz L, Nichols J, Nichols C, Seaver M, Trickey S, Todd M, Pecora L, Virgin L (2005) A multivariate, attractor-based approach to structural health monitoring. J Sound Vib 283(1–2):295–310

    Google Scholar 

  18. Cao L, Laflamme S, Hong J, Dodson J (2018) Input space dependent controller for civil structures exposed to multi-hazard excitations. Eng Struct 166:286–301

    Google Scholar 

  19. Worden K, Farrar C, Haywood J, Todd M (2008) A review of nonlinear dynamics applications to structural health monitoring. Struct Control Health Monit 15(4):540–567

    Google Scholar 

  20. Chinde V, Cao L, Vaidya U, Laflamme S (2016) Damage detection on mesosurfaces using distributed sensor network and spectral diffusion maps. Meas Sci Technol 27(4):045110

    Google Scholar 

  21. Liu G, Mao Z, Todd M, Huang Z (2014) Damage assessment with state-space embedding strategy and singular value decomposition under stochastic excitation. Struct Health Monit 13(2):131–142

    Google Scholar 

  22. da Silva APA, Ferreira VH, Velasquez RM (2008) Input space to neural network based load forecasters. Int J Forecast 24:616–629

    Google Scholar 

  23. Yu D, Gomm J, Williams D (2000) Neural model input selection for a MIMO chemical process. Eng Appl Artif Intell 13:15–23

    Google Scholar 

  24. Li K, Peng J (2007) Neural input selection—a fast model-based approach. Neurocomputing 70:762–769

    Google Scholar 

  25. Tikka J (2009) Simultaneous input variable and basis function selection for RBF networks. Neurocomputing 72:2649–2658

    Google Scholar 

  26. Kourentzes N, Crone S (2010) Frequency independent automatic input variable selection for neural networks for forecasting. In: The 2010 international joint conference on neural networks, pp 1–8

  27. Monroig E, Aihara K, Fujino Y (2009) Modeling dynamics from only output data. Phys Rev E 79(5):56208

    MathSciNet  Google Scholar 

  28. Cao L, Laflamme S (2018) Real-time variable multidelay controller for multihazard mitigation. J Eng Mech 144(2):04017174

    Google Scholar 

  29. Hong J, Laflamme S, Dodson J (2018) Study of input space for state estimation of high-rate dynamics. Struct Control Health Monit 25(6):e2159

    Google Scholar 

  30. Tarassento L (1998) Guide to neural computing applications. Butterworth-Heinemann, Oxford

    Google Scholar 

  31. Zhang Q, Benveniste A (1992) Wavelet networks. IEEE Trans Neural Netw 3(6):889–898

    Google Scholar 

  32. Martin-del Brio B, Serrano-Cinca C (1993) Self-organizing neural networks for the analysis and representation of data: Some financial cases. Neural Comput Appl 1(3):193–206

    Google Scholar 

  33. Cannon M, Slotine JJ (1995) Space-frequency localized basis function networks for nonlinear system estimation and control. Neural Comput Appl 9(3):293–342

    MATH  Google Scholar 

  34. Zhang JS, Xiao XC (2000) Predicting chaotic time series using recurrent neural network. Chin Phys Lett 17(2):88

    Google Scholar 

  35. Frank RJ, Ray N, Hunt SP (2001) Time series prediction and neural networks. J Intell Rob Syst 31(1–3):91–103

    MATH  Google Scholar 

  36. Hong J, Laflamme S, Dodson J (2016) Variable input observer for structural health monitoring of high-rate systems. Quant Nondestruct Eval 43:070003

    Google Scholar 

  37. Hong J, Cao L, Laflamme S, Dodson J (2017) Robust variable input observer for structural health monitoring of systems experiencing harsh extreme environments. In: 11th International workshop on structural health monitoring, vol 11, pp 1–8

  38. Kohonen T (1998) The self-organizing map. Neurocomputing 21(1–3):1–6

    MATH  Google Scholar 

  39. Laflamme S, Slotine J-JE, Connor JJ (2011) Wavelet network for semi-active control. J Eng Mech 137(7):462–474

    Google Scholar 

  40. Takens F (1980) Detecting strange attractors in turbulence. Dyn Syst Turbul Warwick 1980:366–381

    Google Scholar 

  41. Sauer T, Yorke J, Casdagli M (1991) Embeddology. J Stat Phys 65:579–616

    Google Scholar 

  42. Stark J (1993) Recursive prediction of chaotic time series. J Nonlinear Sci 3(1):197–223

    MathSciNet  MATH  Google Scholar 

  43. Cellucci CJ, Albano AM, Rapp PE (2003) Comparative study of embedding methods. Phys Rev E 67(46):066210

    MathSciNet  Google Scholar 

  44. Fraser A, Swinney H (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33(2):1134–1140

    MathSciNet  MATH  Google Scholar 

  45. Kennel M, Brown R, Abarbanel H (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411

    Google Scholar 

  46. Beliveau A, Hong J, Coker J, Glikin N (2012) COTS piezoresistive shock accelerometers performance evaluation. Shock Vib Exchange 83:1–10

    Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the financial support from the Air Force Office of Scientific Research (AFOSR) award number FA9550-17-1-0131, and AFRL/RWK contract number FA8651-17-D-0002. Additionally, the authors would like to acknowledge Dr. Janet Wolfson for providing the experimental data. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the US Air Force.

Author information

Authors and Affiliations

  1. Department of Civil, Construction, and Environmental Engineering, Iowa State University, Ames, IA, 50011, USA

    Jonathan Hong & Simon Laflamme

  2. ATLSS Engineering Research Center, Lehigh University, Bethlehem, PA, 18015, USA

    Liang Cao

  3. Air Force Research Laboratory, Eglin AFB, FL, 32542, USA

    Jacob Dodson

  4. University of Dayton Research Institute, Eglin AFB, FL, 32542, USA

    Bryan Joyce

Authors
  1. Jonathan Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simon Laflamme
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liang Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jacob Dodson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bryan Joyce
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonathan Hong.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hong, J., Laflamme, S., Cao, L. et al. Variable input observer for nonstationary high-rate dynamic systems. Neural Comput & Applic 32, 5015–5026 (2020). https://doi.org/10.1007/s00521-018-3927-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-018-3927-x

Keywords

Search

Navigation