Advertisement

Inverse and Feedback Analyses Based on the Finite Element Method

  • Sheng-hong ChenEmail author
Chapter
Part of the Springer Tracts in Civil Engineering book series (SPRTRCIENG)

Abstract

To undertake a successful computation task concerning the construction and operation process of hydraulic structures, one of the mostly concerned obstacles is the limited or incomplete sets of input data. This chapter presents the study on the inverse and feedback analyses for hydraulic structures using the FEM, intended to provide another parametric solution in addition to traditional ones (e.g. field exploration and investigation, laboratory experiment and field test, as well as engineering analogue). The principles and strategies with regard to the specific issues of in situ geo-stresses and material parameters (mechanical, permeable and thermal), are elaborated. The mathematical tools, particularly the algorithms for constrained nonlinear optimization problems arise from the inverse analysis, are presented. The aggression belonging to mathematical programming algorithms and the ANN belonging to heuristic search algorithms are implemented and validated in detail. In addition to a number of validation examples interspersed within the context, this chapter is closed with two engineering application cases (dam foundation, cut slope).

References

  1. Ai-Homoud AS, Tai AB, Taqieddin SA. A comparative study of slope stability methods and mitigative design of a highway embankment landslide with a potential for deep seated sliding. Eng Geol. 1997;47(1–2):157–73.CrossRefGoogle Scholar
  2. Box MJ. A new method of constrained optimization and a comparison with other methods. Comput J. 1965;8(1):42–52.MathSciNetCrossRefGoogle Scholar
  3. Camp C, Pezeshk S, Cao GZ. Optimized design of two-dimensional structures using a genetic algorithm. J Struct Eng. 1998;124(5):551–9.CrossRefGoogle Scholar
  4. Chattefuee S, Hadi AS. Regression analysis by example. 4th ed. New Jersey, USA: Wiley; 2006.CrossRefGoogle Scholar
  5. Chen J, Hopmans JW, Grismer ME. Parameter estimation of two-fluid capillary pressure-saturation and permeability function. Adv Water Resour. 1999;22(5):479–93.CrossRefGoogle Scholar
  6. Chen SH, Chen SF, Shahrour I, Egger P. The feedback analysis of excavated rock slope. Rock Mech Rock Eng. 2001;34(1):39–56.CrossRefGoogle Scholar
  7. Chi SY, Chern JC, Lin CC. Optimized back-analysis for tunnelling-induced ground movement using equivalent ground load model. Tunn Undergr Space Technol. 2001;16(3):159–65.CrossRefGoogle Scholar
  8. de Marsily G, Delhomme JP, Delay F, Buoro A. 40 years of inverse solution in hydrogeology. Earth Planet Sci. 1999;329(2):73–87 (in French).Google Scholar
  9. Draper NR, Smith H. Applied regression analysis. New York, USA: Wiley; 1966.zbMATHGoogle Scholar
  10. Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht, Netherlands: Kluwer Academic Publishers; 1996.CrossRefGoogle Scholar
  11. Erbatur F, Al-Hussainy M. Optimum design of frames. Comput Struct. 1992;45(5–6):887–91.CrossRefGoogle Scholar
  12. Fang KT, Lin DKJ, Winker P, Zhang Y. Uniform design: theory and application. Technometrics. 2000;42(3):237–48.MathSciNetCrossRefGoogle Scholar
  13. Fatullayev A, Can E. Numerical procedure for identification of water capacity of porous media. Math Comput Simul. 2000;52(2):113–20.MathSciNetCrossRefGoogle Scholar
  14. Finsterle S, Faybishenko B. Inverse modelling of a radial multistep outflow experiment for determining unsaturated hydraulic properties. Adv Water Resour. 1999;22(5):431–44.CrossRefGoogle Scholar
  15. Gens A, Ledesma A, Alonso EE. Estimation of parameters in geotechnical back analysis. II: application to a tunnel problem. Comput Geotech. 1996;18(1):29–46.CrossRefGoogle Scholar
  16. Gioda G. Some applications of mathematical programming in geomechanics. In: Desai CS, Gioda G, editors. Numerical methods and constitutive modelling in geomechanics. New York, USA: Springer; 1990. p. 319–50.zbMATHGoogle Scholar
  17. Gioda G, Sakurai S. Back analysis procedures for the interpretation of field measurements in geomechanics. Int J Numer Anal Meth Geomech. 1987;11(6):555–83.CrossRefGoogle Scholar
  18. Goldberg DE. Genetic algorithm in search, optimization and machine learning. 2nd ed. Reading, MA, USA: Addison-Wesley; 1989.zbMATHGoogle Scholar
  19. Groetsch CW. Inverse Problems in the mathematical sciences. New York, USA: Springer; 1993.CrossRefGoogle Scholar
  20. Guo WD. Visco-elastic consolidation subsequent to pile installation. Comput Geotech. 2000;26(2):113–44.CrossRefGoogle Scholar
  21. Haftka RT, Scott EP, Cruz JR. Optimization and experiments: a survey. Appl Mech Rev. 1998;51(7):435–48.CrossRefGoogle Scholar
  22. Hanna S, Jim Yeh TC. Estimation of co-conditional moments of transmissivity, hydraulic head and velocity fields. Adv Water Resour. 1998;22(1):87–95.CrossRefGoogle Scholar
  23. Hoek E. Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion. Int J Rock Mech Min Sci Geomech Abstr. 1990;12(3):227–9.CrossRefGoogle Scholar
  24. Hoek E, Brown ET. Empirical strength criterion for rock masses. J Geotech Eng Div, ASCE. 1980;106(GT9):1013–35.Google Scholar
  25. Hojo A, Nakamura M, Sakurai S, Akutagawa S. Characterization of non-elastic ground behavior of a large underground power house cavern by back analysis. Int J Rock Mech Min Sci. 1997;34(3–4): Paper No. 008.Google Scholar
  26. Hsich PA, Neuman SP. Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media 1, theory. Water Resour Res. 1985;21(11):1655–65.CrossRefGoogle Scholar
  27. Hsich PA, Neuman SP, Stiles GK, Simpson ES. Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media 2, methodology and application to fractured rocks. Water Resour Res. 1985;21(11):1667–76.CrossRefGoogle Scholar
  28. Jhorar RK, Bastiaanssen WGM, Fesses RA, Van Dam JC. Inversely estimating soil hydraulic functions using evapor transpiration fluxes. J Hydrol. 2002;258(1):198–213.CrossRefGoogle Scholar
  29. Johari A, Javadi AA, Habibagahi G. Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network. Comput Geotech. 2011;38(1):2–13.CrossRefGoogle Scholar
  30. Joshi RR. Immune network memory: an inventory approaches. Comput Oper Res. 1995;22(6):575–91.CrossRefGoogle Scholar
  31. Karaboga D, Ozturk C. A novel clustering approach: artificial bee colony (ABC) algorithm. Appl Soft Comput. 2011;11(1):652–7.CrossRefGoogle Scholar
  32. Katsifarakis KL, Karpouzos DK, Theodossiou N. Combined use of BEM and genetic algorithms in groundwater flow and mass transport problems. Eng Anal Bound Elem. 1999;23(7):555–65.CrossRefGoogle Scholar
  33. Kim YT, Lee SR. An equivalent model and back-analysis technique for modelling in situ consolidation behavior of drainage-installed soft deposits. Comput Geotech. 1997;20(2):125–42.MathSciNetCrossRefGoogle Scholar
  34. Kim CY, Bae GJ, Hong SW, Park CH, Moon HK, Shin HS. Neural network based prediction of ground surface settlements due to tunnelling. Comput Geotech. 2001;28(6–7):517–47.CrossRefGoogle Scholar
  35. Krajewski W, Edelmann L, Plamitzer R. Ability and limits of numerical methods for the design of deep construction pits. Comput Geotech. 2001;28(6–7):425–44.CrossRefGoogle Scholar
  36. Kuhn HW. Nonlinear programming: a historical view. In: Giorgi G, Kjeldsen TH, editors. Traces and emergence of nonlinear programming. Basel, Switzerland: Springer; 2014. p. 393–414.CrossRefGoogle Scholar
  37. Kuhn HW, Tucker AW. Nonlinear programming. In: Proceedings of 2nd Berkeley symposium on mathematics, statistics and probability. Berkeley (USA): University of California Press; 1951. p. 481–92.Google Scholar
  38. Lagaros ND, Papadrakakis M, Kokossalakis G. Structural optimization using evolutionary algorithms. Comput Struct. 2002;80(7–8):571–89.CrossRefGoogle Scholar
  39. Ledesma A, Gens A, Alonso EE. Estimation of parameters in geotechnical back analysis. I: maximum likelihood approach. Comput Geoetch. 1996a;18(1):1–27.CrossRefGoogle Scholar
  40. Ledesma A, Gens A, Alonso EE. Parameter and variance estimation in geotechnical back-analysis using prior information. Int J Numer Anal Meth Geomech. 1996b;20(2):119–41.CrossRefGoogle Scholar
  41. Lesnic D, Elliott L, Ingham DB, Clennell B, Knipe RJ. A mathematical model and numerical investigation for determining the hydraulic conductivity of rocks. Int J Rock Mech Min Sci. 1997;34(5):741–59.CrossRefGoogle Scholar
  42. Leu SS, Chen CN, Chang SL. Data mining for tunnel support stability: neural network approach. Autom Constr. 2001;10(4):429–41.CrossRefGoogle Scholar
  43. Li HL, Yang QC. A least-square penalty method algorithm for inverse problems of steady-state aquifer models. Adv Water Res. 2000;23(8):867–80.CrossRefGoogle Scholar
  44. Louis C, Maini YN. Determination of in-situ hydraulic parameters in jointed rock. In: Proceedings of 2nd ISRM congress. Belgrade, Yugoslavia: ISRM; 1970. p. 235–45.Google Scholar
  45. Lynden-Bell D, Gurzadyan V. Victor Amazaspovich Ambartsumian. Biographical Mem Fellows Roy Soc. 1998;44:23.CrossRefGoogle Scholar
  46. Mayer AS, Huang C. Development and application of a coupled-process parameter inversion model based on the maximum likelihood estimation method. Adv Water Res. 1999;22(8):841–53.CrossRefGoogle Scholar
  47. McCall J. Genetic algorithms for modelling and optimisation. J Comput Appl Math. 2005;184(1):205–22.MathSciNetCrossRefGoogle Scholar
  48. Mello Franco JA, Assis AP, Mansur WJ, Telles JCF, Santiago AF. Design aspects of the underground structures of the Serra da Mesa hydroelectric power plant. Int J Rock Mech Min Sci. 1997;34(3–4):Paper No. 016.Google Scholar
  49. Millar DL, Hudson JA. Performance monitoring of rock engineering systems using neural networks. In: Symposium of artificial intelligence in the minerals sector. University of Nottingham, UK: Institute of Mining Metallurgy; 1994. p. A3–A16.Google Scholar
  50. Mitsuo G, Cheng RW. Genetic algorithm and engineering design. New York, USA: Wiley-Interscience; 1997.Google Scholar
  51. Moses F. Optimum structural design using linear programming. J Struct Div, ASCE. 1964;90:89–104.Google Scholar
  52. Murakami A, Hasegawa T, Sakaguchi H. Interpretation of ground performances based on back analysis results. In: Beer G, Booker JR, Carter JP, editors. Computer methods and advances in geomechanics. Rotterdam, Netherlands: AA Balkema; 1991. p. 1011–5.Google Scholar
  53. Nelder JA, Mead R. A simplex method for function minimization. Comput J. 1965;7(4):308–13.MathSciNetCrossRefGoogle Scholar
  54. Nocedal J, Wright SJ. Numerical optimization. New York, USA: Springer; 1999.CrossRefGoogle Scholar
  55. Nutzmann G, Thiele M, Maciejewski S, Joswig K. Inverse modelling techniques for determining hydraulic properties of coarse-textured porous media by transient outflow methods. Adv Water Res. 1998;22(3):273–84.CrossRefGoogle Scholar
  56. Obara Y, Nakamura N, Kang SS, Kaneko K. Measurement of local stress and estimation of regional stress associated with stability assessment of an open-pit rock slope. Int J Rock Mech Min Sci. 2000;37(8):1211–21.CrossRefGoogle Scholar
  57. Ohkami T, Swoboda G. Parameter identification of viscoelastic materials. Comput Geotech. 1999;24(4):279–95.CrossRefGoogle Scholar
  58. Okui Y, Tokunaga A, Shinji M, Mori M. New back analysis method of slope stability by using field measurements. Int J Rock Mech Min Sci. 1997;34 (3–4): Paper No. 234.Google Scholar
  59. Pelizza S, Oreste PP, Pella D, Oggeri C. Stability analysis of a large cavern in Italy for quarrying exploitation of a pink marble. Tunn Undergr Space Technol. 2000;15(4):421–35.CrossRefGoogle Scholar
  60. Romanov VG. Inverse problems of mathematical physics. Utrecht, Netherlands: VNU Science Press; 1987.Google Scholar
  61. Rossmanith HP, Uenishi K. Post-blast bench block stability assessment. Int J Rock Mech Min Sci. 1997; 34(3–4): Paper No. 264.Google Scholar
  62. Roth C, Chiles JP, de Fouquet C. Combining geostatistics and flow simulators to identify transmissivity. Adv Water Res. 1998;21(7):555–65.CrossRefGoogle Scholar
  63. Rumelhart DE, Hinton GE, Williams RJ. Learning internal representations by error propagation. In: Rumelhart DE, McClelland JL, editors. Parallel distributed processing, vol. 1. Massachusetts, USA: MIT Press; 1986. p. 318–62.Google Scholar
  64. Russo D. On the estimation of parameters of log-unsaturated conductivity covariance from solute transport data. Adv Water Res. 1997;20(4):191–205.CrossRefGoogle Scholar
  65. Sakurai S. Lessons learned from field measurements in tunnelling. Tunn Undergr Space Technol. 1997;12(4):453–60.CrossRefGoogle Scholar
  66. Sakurai S, Akutagawa S. Some aspects of back analysis in geotechnical engineering. In: Ribeiro e Sousa L, Grossmann NF, editors. Proceedings on 1993 ISRM international symposium–EUROCK 93. Rotterdam, Netherlands: AA Balkema; 1995. p. 1130–40.Google Scholar
  67. Sakurai S. Direct strain evaluation technique in construction of underground openings. In: Proceedings on 22nd US symposium of rock mechanics. Cambridge, MA, USA: MIT Press; 1981. p. 278–82.Google Scholar
  68. Sakurai S, Takeuchi K. Back analysis of measured displacement of tunnels. Rock Mech Rock Eng. 1983;16(3):173–80.CrossRefGoogle Scholar
  69. Singh B, Viladkar MN, Samadhiya NK, Mehrotra VK. Rock mass strength parameters mobilised in tunnels. Tunn Undergr Space Technol. 1997;12(1):47–54.CrossRefGoogle Scholar
  70. Sklavounos P, Sakellariou M. Intelligent classification of rock masses. In: Adey RA, Rzevski G, Tasso C, editors. Applications of artificial intelligence in engineering—proceedings of the tenth international conference on applications of artificial intelligence in engineering. Udine, Italy: Computational Mechanics Publications; 1995. p. 387–93.Google Scholar
  71. Sonmez H, Ulusay R, Gokceoglu C. A practical procedure for the back analysis of slope failure in closely jointed rock. Int J Rock Mech Min Sci. 1998;35(2):219–33.CrossRefGoogle Scholar
  72. Spendley W, Hext GR, Himsworth FR. Sequential application of simplex designs in optimization and evolutionary operation. Technometrics. 1962;4(4):441–61.MathSciNetCrossRefGoogle Scholar
  73. SriVidya A, Ranganathan R. Reliability based optimal design of reinforced concrete frames. Comput Struct. 1995;57(4):651–61.CrossRefGoogle Scholar
  74. Vasco DW, Karasaki K. Inversion of pressure observations: an integral formulation. J Hydrol. 2001;253(1–4):27–40.CrossRefGoogle Scholar
  75. Wang PP, Zheng C. An efficient approach for successively perturbed groundwater models. Adv Water Res. 1998;21(6):499–508.CrossRefGoogle Scholar
  76. Wen XH, Capilla JE, Deutsch CV, Gomez-Hernandez JJ, Cullick AS. A program to create permeability fields that honour single-phase flow rate and pressure data. Comput Geosci. 1999;25(3):217–30.CrossRefGoogle Scholar
  77. Wen XH, Deutsch CV, Cullick AS. Construction of geostatistical aquifer models integrating dynamic flow and tracer data using inverse technique. J Hydrol. 2002;255(1–4):151–68.CrossRefGoogle Scholar
  78. Werbos PJ. The roots of back propagation: from ordered derivatives to neural networks and political forecasting. New York, USA: Wiley; 1994.Google Scholar
  79. Yang Y, Zhang Q. Application of neural networks to rock engineering systems (RES). Int J Rock Mech Min Sci. 1998;35(6):727–45.CrossRefGoogle Scholar
  80. Yang L, Zhang K, Wang Y. Back analysis of initial rock stress and time-dependent parameters. J Rock Mech Min Sci Geomech Abstr. 1996;33(6):641–5.CrossRefGoogle Scholar
  81. Yang Z, Lee CF, Wang S. Three-dimensional back-analysis of displacements in exploration adits-principles and application. Int J Rock Mech Min Sci. 2000;37(3):525–33.CrossRefGoogle Scholar
  82. Yang ZF, Wang ZY, Zhang LQ, Zhou RG, Xing NX. Back-analysis of viscoelastic displacements in a soft rock road tunnel. Int J Rock Mech Min Sci. 2001;38(3):331–41.CrossRefGoogle Scholar
  83. Yi CJ, Lu M. A mixed-integer linear programming approach for temporary haul road design in rough-grading projects. Autom Constr. 2016;71(2):314–24.CrossRefGoogle Scholar
  84. Yi H, Wanstedt S. The introduction of neural network system and its applications in rock engineering. Eng Geol. 1998;49(3–4):253–60.Google Scholar
  85. Yi D, Xu MY, Chen SH. Application of genetic algorithms to back analysis of initial stress field of rock masses. Chin J Rock Mech Eng. 2001;20(Supp. 2):1918–22 (in Chinese).Google Scholar
  86. Yi D, Chen SH, Ge XR. A methodology combining genetic algorithm and finite element method for back analysis of initial stress field of rock masses. Rock Soil Mech. 2004a;25(7):1077–80 (in Chinese).Google Scholar
  87. Yi D, Xu MY, Chen SH, Ge XR. Application of neural network to back analysis of initial stress field of rock masses. Rock Soil Mech. 2004b;25(6):943–6 (in Chinese).Google Scholar
  88. Zeidenberg M. Neural network models in artificial intelligence. New York, USA: Ellis Horwood; 1990.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Water Resources and Hydropower EngineeringWuhan UniversityWuhanP.R. China

Personalised recommendations