Application of the Coupled Local Minimizers Method to the Optimization Problem in the Spectral Analysis of Surface Waves Method
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 134, Issue 10
Abstract
The spectral analysis of surface waves (SASW) method aims to determine the small strain dynamic soil characteristics of shallow soil layers. The method involves an in situ experiment, the determination of an experimental dispersion curve, and the solution of an inverse problem, formulated as a nonlinear least squares problem. The latter is usually solved with a gradient-based local optimization method, which converges fast, but does not guarantee to find the global minimum of the objective function. The method of coupled local minimizers (CLM) combines the advantage of gradient-based local algorithms with the global approach of genetic algorithms. A cooperative search mechanism is set up by simultaneously performing a number of local optimization runs that are coupled by pairs of synchronization constraints. A synthetic example with two design variables (the shear wave velocity of two top layers of a layered half-space consisting of three layers on a half-space), demonstrates that the CLM method succeeds in finding the global minimum of an objective function with multiple minima and can successfully be used to solve the inverse problem in the SASW method. This is further illustrated by a complete inversion of the shear wave velocity profile accounting for seven design variables (the thickness and shear wave velocity of the three layers and the shear wave velocity of the underlying half-space). The inversion algorithm based on the CLM method is subsequently applied to invert the experimental dispersion curve derived from in situ data collected at a test site in Saluggia, Italy, consisting mainly of alluvial sediments. Up to a depth of about , the results show a reasonably good correspondence with crosshole test results.
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Acknowledgments
The results presented in this paper have been obtained within the frame of Project No. UNSPECIFIEDG.0595.06 “In situ determination of material damping in the soil at small deformation ratios” funded by the Research Foundation Flanders and Project No. UNSPECIFIEDOT/05/41” A generic methodology for inverse modelling of dynamic problems in civil and environmental engineering,” funded by the Research Council of K.U.Leuven. The third writer is a Postdoctoral Fellow of the Research Foundation—Flanders (FWO). The support of the FWO is gratefully acknowledged. The fourth writer is a Postdoctoral researcher supported by the Research Council of K.U.Leuven. This financial support is gratefully acknowledged. The writers are very grateful to Professor Sebastiano Foti (Department of Civil Engineering, Politecnico di Torino) who made the surface wave data set collected on the site in Saluggia available for the present investigations. This has been particularly useful to demonstrate the practical applicability of the CLM method to experimental data with sufficient profiling depth.
References
Beaty, K., Schmitt, D., and Sacchi, M. (2002). “Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure.” Geophys. J. Int., 151, 622–631.
Foti, S. (2000). “Multistation methods for geotechnical characterization using surface waves.” Ph.D. thesis, Politecnico di Torino, Torino, Italy.
Gabriels, P., Snieder, R., and Nolet, G. (1987). “In situ measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves.” Geophys. Prospect., 35, 187–196.
Ganji, V., Gucunski, N., and Nazarian, S. (1998). “Automated inversion procedure for spectral analysis of surface waves.” J. Geotech. Geoenviron. Eng., 124(8), 757–770.
Gucunski, N., and Woods, R. (1991). “Inversion of Rayleigh wave dispersion curve for SASW test.” Proc., 5th Int. Conf. on Soil Dynamics and Earthquake Engineering, Karlsruhe, Germany, Elsevier Applied Science, London, 127–138.
Gucunski, N., and Woods, R. (1992). “Numerical simulation of the SASW test.” Soil Dyn. Earthquake Eng., 11, 213–227.
Holland, J. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, Mich.
Kausel, E., and Roësset, J. (1981). “Stiffness matrices for layered soils.” Bull. Seismol. Soc. Am., 71(6), 1743–1761.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). “Optimization by simulated annealing.” Science, 220, 671–680.
Lai, C., Foti, S., and Rix, G. (2005). “Propagation of data uncertainty in surface wave inversion.” J. Environ. Eng. Geophys., 10(2), 219–228.
Lai, C., Rix, G., Foti, S., and Roma, V. (2002). “Simultaneous measurement and inversion of surface wave dispersion and attenuation curves.” Soil Dyn. Earthquake Eng., 22(9–12), 923–930.
Levshin, A., Ritzwoller, M., and Shapiro, N. (2005). “The use of crustal higher modes to constrain crustal structure across Central Asia.” Geophys. J. Int., 160, 961–972.
Matlab. (2006). “Matlab optimization toolbox.” ⟨www.mathworks.com⟩.
Nazarian, S., and Desai, M. (1993). “Automated surface wave method: Field testing.” J. Geotech. Engrg., 119(7), 1094–1111.
Nocedal, J., and Wright, S. (1999). Numerical optimization, Springer, New York.
Park, C., Miller, R., and Xia, J. (1998). “Imaging dispersion curves of surface waves on multi-channel record.” Proc., 68th Annual Int. Meeting, Society of Exploration Geophysicists, Expanded Abstracts, New Orleans, Society of Exploration Geophysicists, 1377–1380.
Park, C., Miller, R., and Xia, J. (1999). “Multichannel analysis of surface waves.” Geophysics, 64(3), 800–808.
Pezeshk, S., and Zarrabi, M. (2005). “A new inversion procedure for spectral analysis of surface waves using a genetic algorithm.” Bull. Seismol. Soc. Am., 95(5), 1801–1808.
Rao, S. (1996). Engineering optimization—Theory and practice, 3rd Ed., Wiley, New York.
Rix, G., Lai, C., and Spang, A., Jr. (2000). “In situ measurement of damping ratio using surface waves.” J. Geotech. Geoenviron. Eng., 126(5), 472–480.
Ryden, N., and Park, C. (2006). “Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra.” Geophysics, 71(4), 49–58.
Sambridge, M. (1999). “Geophysical inversion with a neighbourhood algorithm—I: Searching a parameter space.” Geophys. J. Int., 138, 479–494.
Schevenels, M., Lombaert, G., Degrande, G., and François, S. (2008). “A probabilistic assessment of resolution in the SASW test and its impact on the prediction of ground vibrations.” Geophys. J. Int., 172(1), 262–275.
Suykens, J., and Vandewalle, J. (2002). “Coupled local minimizers: Alternative formulations and extensions.” Proc., 2002 World Congress on Computational Intelligence—International Joint Conf. on Neural Networks IJCNN 2002, Honolulu, 2039–2043.
Suykens, J., Vandewalle, J., and De Moor, B. (2001). “Intelligence and cooperative search by coupled local minimizers.” Int. J. Bifurcation Chaos Appl. Sci. Eng., 11(8), 2133–2144.
Teughels, A. (2003). “Inverse modelling of civil engineering structures based on operational modal data.” Ph.D. thesis, K.U.Leuven, Leuven, Belgium.
Teughels, A., De Roeck, G., and Suykens, J. (2003). “Global optimization by coupled local minimizers and its application to FE model updating.” Comput. Struct., 81(24–25), 2337–2351.
Tokimatsu, K., Tamura, S., and Kosjima, H. (1992). “Effects of multiple modes on Rayleigh wave dispersion characteristics.” J. Geotech. Engrg., 118(10), 1529–1143.
Yuan, D., and Nazarian, S. (1993). “Automated surface wave method: Inversion technique.” J. Geotech. Engrg., 119(7), 1112–1126.
Zomorodian, S., and Hunaidi, O. (2006). “Inversion of SASW dispersion curves based on maximum flexibility coefficients in the wave number domain.” Soil Dyn. Earthquake Eng., 26, 735–752.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 134 • Issue 10 • October 2008
Pages: 1541 - 1553
Copyright
© 2008 ASCE.
History
Received: Jan 31, 2007
Accepted: Feb 6, 2008
Published online: Oct 1, 2008
Published in print: Oct 2008
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