Skip to main content

Computational Inverse Techniques

  • Chapter
  • First Online:
Numerical Simulation-based Design
  • 606 Accesses

Abstract

The computational inverse technique-based high-fidelity numerical modeling is a comprehensive analysis of the experimental data and the numerical simulation model instead of a simple modeling analysis process or an optimal iteration process. Appropriate physical experiments are required to ensure the relatively strong sensitivity between the measured responses and the modeling parameters, while the numerical solution is expected to be available. In addition, the identification of the model parameters should address three problems, i.e., high computational intensity and the ill-posedness of the system, improvement for the identification efficiency and stability and the optimality of the solution to a specific extent.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Liu, G. R., & Han, X. (2003). Computational inverse techniques in nondestructive evaluation. Florida: CRC Press.

    Book  Google Scholar 

  2. Tarantola, A., & Valette, B. (1982). Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics, 20(2), 219–232.

    Article  MathSciNet  Google Scholar 

  3. Aster, R. C., Borchers, B., & Thurber, C. H. (2011). Parameter estimation and inverse problems. Academic Press.

    Google Scholar 

  4. Engl, H. W., Hanke, M., & Neubauer. A. (1996). Regularization of inverse problems. Springer Science & Business Media.

    Google Scholar 

  5. Tikhonov, A. N., Arsenin, V. I. A., & John, F. (1977). Solutions of ill-posed problems. Washington, DC: Winston.

    MATH  Google Scholar 

  6. Hadamard, J. (1923). Lectures on the cauchy problems in linear partial differential equations. New Haven: Yale University Press.

    MATH  Google Scholar 

  7. Castillo, E., Conejo, A. J., Mínguez, R., et al. (2006). A closed formula for local sensitivity analysis in mathematical programming. Engineering Optimization, 38(1), 93–112.

    Article  MathSciNet  Google Scholar 

  8. Saltelli, A., Tarantola, S., Campolongo, F., et al. (2004). Sensitivity analysis in practice: A guide to assessing scientific models. Wiley.

    Google Scholar 

  9. Pastres, R., Franco, D., Pecenik, G., et al. (1997). Local sensitivity analysis of a distributed parameters water quality model. Reliability Engineering & System Safety, 57(1), 21–30.

    Article  Google Scholar 

  10. Zhang, J., & Heitjan, D. F. (2006). A simple local sensitivity analysis tool for nonignorable coarsening: Application to dependent censoring. Biometrics, 62(4), 1260–1268.

    Article  MathSciNet  Google Scholar 

  11. Saltelli, A., & Marivoet, J. (1990). Non-parametric statistics in sensitivity analysis for model output: A comparison of selected techniques. Reliability Engineering & System Safety, 28(2), 229–253.

    Article  Google Scholar 

  12. Campolongo, F., Cariboni, J., & Saltelli, A. (2007). An effective screening design for sensitivity analysis of large moels. Environmental Modelling and Software, 22(10), 1509–1518.

    Article  Google Scholar 

  13. McRae, G. J., Tilden, J. W., & Seinfeld, J. H. (1982). Global sensitivity analysis—A computational implementation of the Fourier amplitude sensitivity test (FAST). Computers & Chemical Engineering, 6(1), 15–25.

    Article  Google Scholar 

  14. Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1–3), 271–280.

    Article  MathSciNet  Google Scholar 

  15. Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93(7), 964–979.

    Article  Google Scholar 

  16. Tian, W. (2013). A review of sensitivity analysis methods in building energy analysis. Renewable and Sustainable Energy Reviews, 20, 411–419.

    Article  Google Scholar 

  17. Saltelli, A., & Sobol, I. M. (1995). About the use of rank transformation in sensitivity analysis of model output. Reliability Engineering & System Safety, 50(3), 225–239.

    Article  Google Scholar 

  18. Korenberg, M., Billings, S. A., Liu, Y. P., et al. (1988). Orthogonal parameter estimation algorithm for non-linear stochastic systems. International Journal of Control, 48(1), 193–210.

    Article  MathSciNet  Google Scholar 

  19. Landweber, L. (1951). An iteration formula for fredholm integral equations of the first kind. American Journal of Mathematics, 73, 615–624.

    Article  MathSciNet  Google Scholar 

  20. Backus, G. E., & Gilbert, F. (1970). Uniqueness in the inversion of inaccurate gross earth data. Philosophical Transactions of the Royal Society, 22, 123–192.

    Article  MathSciNet  Google Scholar 

  21. Awrejcewicz, J., & Krysko, V. A. (2004). Nonclassical thermoelastic problems in nonlinear dynamics of shells: Applications of the Bubnov-Galerkin and finite difference numerical methods. Springer.

    Google Scholar 

  22. Hansen, P. C. (1990). Truncated SVD solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM Journal on Scientific and Statistical Computing, 11, 503–518.

    Article  Google Scholar 

  23. Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for non-orthogonal problems. Technometrics, 12(1), 55–67.

    Article  Google Scholar 

  24. Sun, X. S., Liu, J., Han, X., et al. (2014). A new improved regularization method for dynamic load identification. Inverse Problems in Science and Engineering, 22(7), 1062–1076.

    Article  MathSciNet  Google Scholar 

  25. Paige, C. C., & Saunders, M. A. (1982). LSQR: An algorithm of sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software, 8(1), 43–72.

    Article  MathSciNet  Google Scholar 

  26. Saad, Y., & Schultz, M. H. (1985). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7(3), 856–869.

    Article  MathSciNet  Google Scholar 

  27. Morozov, V. A. (2012). Methods for solving incorrectly posed problems. New York: Springer.

    Google Scholar 

  28. Engl, H. W., Hanke, M., & Neubauer, A. (1996). Regularization of inverse problems. New York: Springer.

    Book  Google Scholar 

  29. Tikhonov, A. N., & Arsenin, V. Y. (1977). Solutions of ill-posed problems. New York: Wiley.

    MATH  Google Scholar 

  30. Golub, G. H., Heath, M., & Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215–223.

    Article  MathSciNet  Google Scholar 

  31. Hansen, P. C., & Leary, D. P. (1993). The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific and Statistical Computing, 14, 1487–1503.

    Article  MathSciNet  Google Scholar 

  32. Hansen, P. C. (1998). Rank-deficient and discrete ill-posed problems. Philadelphia: SIAM.

    Book  Google Scholar 

  33. Liu, J. (2011). Research on computational inverse techniques in dynamic load identification. Changsha: Hunan University.

    Google Scholar 

  34. Wang, Z., & Gao, T. (1990). An introduction to homotopy methods. Chongqin: Chongqin Press.

    Google Scholar 

  35. Krishnakumar, K. (1990). Micro-genetic algorithms for stationary and non-stationary function optimization. In Proceeding of Advances in Intelligent Robotics Systems Conference, International Society for Optics and Photonics (pp. 289–296).

    Google Scholar 

  36. Liu, G. R., Han, X., & Lam, K. Y. (2002). A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves. Computer Methods in Applied Mechanics and Engineering, 191, 1909–1921.

    Article  Google Scholar 

  37. Chen, R. (2014). The research on hybrid inverse method for material characteristic parameters identification and applications. Changsha: Hunan University.

    Google Scholar 

  38. Alavi, A. H., & Gandomi, A. H. (2011). Prediction of principal ground-motion parameters using a hybrid method coupling artificial neural networks and simulated annealing. Computers & Structures, 23–24, 2176–2194.

    Article  Google Scholar 

  39. Himmelblau, D. M. (1972). Applied nonlinear programming. New York: McGraw Hill Inc.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xu Han .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Science Press, Beijing and Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Han, X., Liu, J. (2020). Computational Inverse Techniques. In: Numerical Simulation-based Design. Springer, Singapore. https://doi.org/10.1007/978-981-10-3090-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-3090-1_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3089-5

  • Online ISBN: 978-981-10-3090-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics