zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Modelling of type I fracture network: Objective function formulation by fuzzy sensitivity analysis. (English) Zbl 1165.74347
Summary: This paper advances the fundamental understanding in mathematical and computational modelling of discrete fracture networks (Type I). It presents a systematic procedure to solve the most important problem in modelling by global optimization - objective function formulation, which negates guesswork in objective function formulation by automatic selection of highly ranked components and their corresponding weighting factors. The procedure starts from real data to identify potential components of the objective function. The components are then ranked by fuzzy sensitivity analysis, based on their effects on the final objective function value and simulation convergence. The final fracture network inversion is subsequently realized and validated. Results of the study provide an explanation why previous methods such as stochastic simulations are not sufficiently reliable, compared to global optimization methods.

74R10Brittle fracture
90C70Fuzzy programming
Full Text: DOI
[1] Mauldon, A. D.: An inverse technique for developing models for fluid-flow in fracture systems using simulated annealing, Water resources research 29, No. 11, 3775-3789 (1993)
[2] Deutsch, C. V.; Cockerham, P. W.: Practical considerations in the application of simulated annealing to stochastic simulation, Mathematical geology 26, No. 1, 67-82 (1994)
[3] Day-Lewis, F. D.; Hsieh, P. A.; Gorelick, S. M.: Identifying fracture-zone geometry using simulated annealing and hydraulic-connection data, Water resources research 36, No. 7, 1707-1721 (2000)
[4] Nakao, S.; Najita, J.; Karasaki, K.: Hydraulic well testing inversion for modeling fluid flow in fractured rocks using simulated annealing: A case study at raymond field site, California, Journal of applied geophysics 45, No. 3, 203-223 (2000)
[5] Gauthier, B. D. M.; Garcia, M.; Daniel, J. M.: Integrated fractured reservoir characterization: A case study in a north africa field, Spe reservoir evaluation engineering 5, No. 4, 284-294 (2002)
[6] Tran, N. H.; Chen, Z.; Rahman, S. S.: Integrated conditional global optimisation for discrete fracture network modelling, Computers geosciences 32, No. 1, 17-27 (2006)
[7] Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P.: Optimization by simulated annealing, Science 220, No. 4598, 671-680 (1983) · Zbl 1225.90162 · doi:10.1126/science.220.4598.671
[8] Sen, M. K.; Stoffa, P. L.: Global optimization methods in geophysical inversion, Advances in exploration geophysics 4, 281 (1995) · Zbl 0871.90107
[9] Kosko, B.: Neural networks and fuzzy systems : A dynamical systems approach to machine intelligence, (1991) · Zbl 0749.93068