Thesis title: Modeling and information reconstruction from heterogeneous data in the context of gravitational hazards – Application to Harmalière’s landslide

"Experienced Researcher with a demonstrated history of working in the research field. Skilled in Mathematical Modeling, Dynamical Systems, Control Theory, Optimal Control, Network Science, and Electrical Engineering. Strong research professional with experience of working as a Senior Research Fellow at Veermata Jijabai Technological Institute (VJTI), India and a Master of Technology degree focused in Electrical Engineering (Specialization in Control Systems) from VJTI."

THESIS OBJECTIVES

A physics-based dynamical model of landslides, unknown parameters identification, and observer-based hazard evaluation from available measurements.

EARLY WARNING SYSTEMS

Landslide is a gravity-driven downslope movement of soil, debris, or rock near the earth’s surface. It can display heterogeneity in rates and movement types, ranging from catastrophic acceleration to creeping motion. Both scenarios pose a threat to the exposed region’s people, infrastructure, ecosystem, and economy. Traditional landslide risk management strategy suggests avoiding building new infrastructure in such a region based on hazard maps. However, with climate change and rapid urbanization, this strategy seems challenging to implement. Therefore, Early Warning Systems (EWS) are way forward to take timely corrective measures to reduce life and economic losses. These EWS’s rely on landslide monitoring systems, landslide models, and information reconstruction schemes.  

KALMAN FILTER APPLIED FOR RECONSTRUCTING DISPLACEMENT PATTERNS AND UNKNOWN SOIL PROPERTIES OF SLOW-MOVING LANDSLIDES

In the first of our study, we formulated state and parameter estimation issues in an ODE-PDE landslide model as an optimization problem with discrete-time asynchronous synthetic measurements. The calculus of variation based adjoint method (iterative approach) is then utilized to solve the problem. Secondly, we address a similar state and parameter estimation problem in a coupled ODE-PDE landslide model by designing an Observer again for synthetic measurements (continues approach). The observer consists of a copy of the PDE part of the system and a Kalman-like observer for the ODE. It is shown to ensure exponential convergence of the state and parameter estimates employing the Lyapunov tool. Finally, we present an approach for reconstructing displacement patterns and some unknown soil properties of slow-moving landslides, using a special form of the so-called Kalman filter or observer. This approach is validated for the Super-Sauze landslide data from the literature with an extension of the observer to forecast landslide displacement.

PUBLICATIONS

1. Mishra, M., Besançon, G., Chambon, G., and Baillet, L. (2021). Calculus of variations for estimation in ODE-PDE landslide models with discrete-time asynchronous measurements. (submitted to the International Journal of Control)
2. Mishra, M., Besançon, G., Chambon, G., and Baillet, L. (2021). Reconstruction and forecasting of landslide displacement using a Kalman filter approach. (submitted to the Journal Landslides)
3. Mishra, M., Besançon, G., Chambon, G., and Baillet, L. (2021). Combined state and parameter estimation for a landslide model using Kalman filter. 19th IFAC Symposium on System Identification SYSID 2021, 54(7), 304-309, doi:10.1016/j.ifacol.2021.08.376.
4. Mishra, M., Besançon, G., Chambon, G., Baillet, L., Watlet, A., Whiteley, J. S., Boyd, J. P., and Chambers, J. E. (2021). “Application of Kalman filter to reproduce displacement pattern along with the unknown soil properties of slow-moving landslides". EGU General Assembly 2021, Online, 19-30 Apr 2021, EGU21-9396, doi:10.5194/egusphere-egu21-9396.
5. Mishra, M., Besançon, G., Chambon, G., and Baillet, L. (2020). “Observer design for state and parameter estimation in a landslide model". 21th IFAC World Congress, 53(2), 16709-16714, doi:10.1016/j.ifacol.2020.12.1116.
6. Mishra, M., Besançon, G., Chambon, G., and Baillet, L. (2020). “Optimal parameter estimation in a landslide motion model using the adjoint method". In 2020 European Control Conference (ECC), 226-231, doi:10.23919 ECC51009.2020.9143819.