Calculus of variations for estimation in ODE–PDE landslide-like models with discrete-time asynchronous measurements

References

• Ascher, U. M., & Petzold, L. R. (1998). Computer methods for ordinary differential equations and differential-algebraic equations (1st ed., Vol. 61). Society for Industrial and Applied Mathematics.
   Google Scholar
• Atanov Genadii, A., Evseeva Elena, G., & Meselhe Ehab, A. (1999). Estimation of roughness profile in trapezoidal open channels. Journal of Hydraulic Engineering, 125(3), 309–312. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:3(309)
   Web of Science ®Google Scholar
• Bartholomew-Biggs, M. (2008). Nonlinear optimisation with engineering applications (Vol. 19). Springer Science and Business Media.
   Google Scholar
• Bernardie, S., Desramaut, N., Malet, J., Maxime, G., & Grandjean, G. (2014). Prediction of changes in landslide rates induced by rainfall. Landslides, 12(12), 481–494. https://doi.org/10.1007/s10346-014-0495-8
   Google Scholar
• Chae, B. G., Park, H. J., Catani, F., Simoni, A., & Berti, M. (2017). Landslide prediction, monitoring and early warning: A concise review of state-of-the-art. Geosciences Journal, 21(6), 1033–1070. https://doi.org/10.1007/s12303-017-0034-4
   Web of Science ®Google Scholar
• Chavent, G., Dupuy, M., & Lemmonier, P. (1975). History matching by use of optimal theory. Society of Petroleum Engineers Journal, 15(1), 74–86. https://doi.org/10.2118/4627-PA
   Web of Science ®Google Scholar
• Chen, M. L., & Georges, D. (1999). Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model. In Proceedings of the 38th IEEE conference on decision and control (Vol. 5, pp. 4313–4318). IEEE.
   Google Scholar
• Chen, W., Gavalas, G., Seinfeld, J., & Wasserman, M. (1974). A new algorithm for automatic history matching. Society of Petroleum Engineers Journal, 14(06), 593–608. https://doi.org/10.2118/4545-PA
   Google Scholar
• Corominas, J., Moya, J., Ledesma, A., Lloret, A., & Gili, J. (2005). Prediction of ground displacements and velocities from groundwater level changes at the Vallcebre landslide (Eastern Pyrenees, Spain). Landslides, 2(2), 83–96. https://doi.org/10.1007/s10346-005-0049-1
   Web of Science ®Google Scholar
• Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society, 43(1), 50–67. https://doi.org/10.1017/S0305004100023197
   Web of Science ®Google Scholar
• Das, S. K., & Lardner, R. W. (1991). On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. Journal of Geophysical Research: Oceans, 96(C8), 15187–15196. https://doi.org/10.1029/91JC01318
   Web of Science ®Google Scholar
• Ding, Y., & S. S. Y. Wang (2005). Identification of Manning's roughness coefficients in channel network using adjoint analysis. International Journal of Computational Fluid Dynamics, 19(1), 3–13. https://doi.org/10.1080/10618560410001710496
   Web of Science ®Google Scholar
• Ferguson, J. (2004). A brief survey of the history of the calculus of variations and its applications. arXiv:math/0402357.
   Google Scholar
• Frank, F., McArdell, B. W., Huggel, C., & Vieli, A. (2015). The importance of erosion for debris flow runout modelling from applications to the Swiss Alps. Copernicus GmbH.
   Google Scholar
• Graichen, K., & Petit, N. (2008). A continuation approach to state and adjoint calculation in optimal control applied to the reentry problem. IFAC Proceedings Volumes, 41(2), 14307–14312. 17th IFAC World Congress. https://doi.org/10.3182/20080706-5-KR-1001.02424
   Google Scholar
• Herrera, G., Fernandez-Merodo, J. A., Mulas, J., Pastor, M., Luzi, G., & Monserrat, O. (2013). A landslide forecasting model using ground based SAR data: The portalet case study. Engineering Geology, 105(105), 220–230. https://doi.org/10.1016/j.enggeo.2009.02.009
   Google Scholar
• Iverson, R. (2000). Landslide triggering by rain infiltration. Water Resources Research, 36(7), 1897–1910. https://doi.org/10.1029/2000WR900090
   Web of Science ®Google Scholar
• Iverson, R. (2005). Regulation of landslide motion by dilatancy and pore pressure feedback. Journal of Geophysical Research, 110(F2). https://doi.org/10.1029/2004JF000268
   Web of Science ®Google Scholar
• Iverson, R., & George, D. (2016). Modelling landslide liquefaction, mobility bifurcation and the dynamics of the 2014 oso disaster. Geotechnique, 66(3), 175–187. https://doi.org/10.1680/jgeot.15.LM.004
   Web of Science ®Google Scholar
• Jansen, J. (2011). Adjoint-based optimisation of multi-phase flow through porous media – A review. Computers & Fluids, 46(1), 40–51. 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010). https://doi.org/10.1016/j.compfluid.2010.09.039
   Web of Science ®Google Scholar
• Johnson, B. C., Campbell, C. S., & Melosh, H. J. (2016). The reduction of friction in long runout landslides as an emergent phenomenon. Journal of Geophysical Research: Earth Surface, 121(5), 881–889. https://doi.org/10.1002/jgrf.v121.5
   Web of Science ®Google Scholar
• Liu, W., He, S., & Li, X. (2016). A finite volume method for two-phase debris flow simulation that accounts for the pore-fluid pressure evolution. Environmental Earth Sciences, 75(3), 206. https://doi.org/10.1007/s12665-015-4920-7
   Web of Science ®Google Scholar
• McDougall, S. (2017). 2014 Canadian geotechnical colloquium: Landslide runout analysis – Current practice and challenges. Canadian Geotechnical Journal, 54(5), 605–620. https://doi.org/10.1139/cgj-2016-0104
   Web of Science ®Google Scholar
• Michael, P., & Katopodes Nikolaos, D. (1997a). Control of contaminant releases in rivers. I: Adjoint sensitivity analysis. Journal of Hydraulic Engineering, 123(6), 486–492. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:6(486)
   Web of Science ®Google Scholar
• Michael, P., & Katopodes Nikolaos, D. (1997b). Control of contaminant releases in rivers. II: Optimal design. Journal of Hydraulic Engineering, 123(6), 493–503. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:6(493)
   Web of Science ®Google Scholar
• Mishra, M., Besançon, G., Chambon, G., & Baillet, L. (2020). Optimal parameter estimation in a landslide motion model using the adjoint method. In 2020 European control conference (ecc) (pp. 226–231). IEEE.
   Google Scholar
• Mishra, M., Besançon, G., Chambon, G., & Baillet, L. (2021). Combined state and parameter estimation for a landslide model using Kalman filter. IFAC-PapersOnLine, 19th IFAC Symposium on System Identification SYSID 2021, 54(7), 304–309. https://doi.org/10.1016/j.ifacol.2021.08.376
   Google Scholar
• Navon, I. M. (1998). Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dynamics of Atmospheres and Oceans, 27(1), 55–79. https://doi.org/10.1016/S0377-0265(97)00032-8
   Web of Science ®Google Scholar
• Nguyen, V. T., Georges, D., & Besançon, G. (2014). Optimal state estimation in an overland flow model using the adjoint method. In 2014 IEEE conference on control applications (CCA) (pp. 2034–2039). IEEE.
   Google Scholar
• Nguyen, V. T., Georges, D., & Besançon, G. (2016). State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method. Automatica, 67(67), 185–191. https://doi.org/10.1016/j.automatica.2016.01.031
   Google Scholar
• Nguyen, V. T., Georges, D., & Besançon, G. (2018). Calculus of variations approach for state and parameter estimation in switched 1-D hyperbolic PDEs. Optimal Control Applications and Methods, 39(3), 1182–1201. https://doi.org/10.1002/oca.v39.3
   Web of Science ®Google Scholar
• Nguyen, V. T., Georges, D., Besançon, G., & Zin, I. (2015). Application of adjoint method for estimating Manning–Strickler coefficient in Tondi Kiboro catchment. In 2015 IEEE conference on control applications (CCA) (pp. 551–556). IEEE.
   Google Scholar
• Nguyen, V. T., Georges, D., Besançon, G., & Zin, I. (2016). Parameter estimation of a real hydrological system using an adjoint method. IFAC-PapersOnLine, 12th IFAC workshop on adaptation and learning in control and signal processing (ALCOSP), 49(13), 300–305. https://doi.org/10.1016/j.ifacol.2016.07.978
   Google Scholar
• Pradhan, A. M. S., & Kim, Y. T.. (2014). Application and comparison of shallow landslide susceptibility models in weathered granite soil under extreme rainfall events. Environmental Earth Sciences, 73(9), 5761–5771. https://doi.org/10.1007/s12665-014-3829-x
   Web of Science ®Google Scholar
• Ramesh, R., Bithin, D., Murty, B. S., & Narayana, A. (2000). Optimal estimation of roughness in open-channel flows. Journal of Hydraulic Engineering, 126(4), 299–303. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(299)
   Web of Science ®Google Scholar
• Shi, Z. J., & Shen, J. (2004). A gradient-related algorithm with inexact line searches. Journal of Computational and Applied Mathematics, 170(2), 349–370. https://doi.org/10.1016/j.cam.2003.10.025
   Web of Science ®Google Scholar
• Strub, I. S., & Bayen, A. M. (2006). Continuous adjoint method for air traffic flow management. In Proceedings of the 45th IEEE conference on decision and control (pp. 101–106). IEEE.
   Google Scholar
• Zainea, M., Van der Schaft, A., & Buisson, J. (2007). Stabilizing control for power converters connected to transmission lines. In 2007 American control conference (pp. 3476–3481). IEEE.
   Google Scholar