Applying Linear Realization Theory to HJM Markovian Representation

This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms in the mathematical model are replaced by their alternative state-space representations whose parameters are obtained by using the realization theory. The mathematical model is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

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Realization theory

Systems & Control: Foundations & Applications - Mathematical Control Theory ◽

10.1007/978-3-030-44778-6_5 ◽

2020 ◽

pp. 65-76

Author(s):

Jerzy Zabczyk

Keyword(s):

Realization Theory

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Unified landslide hazard assessment using hurdle models: a case study in the Island of Dominica

10.21203/rs.3.rs-1030905/v1 ◽

2021 ◽

Author(s):

Erin Bryce ◽

Luigi Lombardo ◽

Cees van Westen ◽

Hakan Tanyas ◽

Daniela Castro-Camilo

Keyword(s):

Spatial Information ◽

Landslide Hazard ◽

Sufficient Information ◽

Tropical Regions ◽

Landslide Occurrence ◽

Hurdle Models ◽

Modelling Framework ◽

Markovian Representation ◽

Binary Classifiers ◽

A Chain

Abstract Climatically-induced natural hazards are a threat to communities. They can cause life losses and heavy damage to infrastructure, and due to climate change, they have become increasingly frequent. This is especially in tropical regions, where major hurricanes have consistently appeared in recent history. Such events induce damage due to the high wind speed they carry, and the high intensity/duration rainfall they discharge can further induce a chain of hydro-morphological hazards in the form of widespread debris slides/flows. The way the scientific community has developed preparatory steps to mitigate the potential damage of these hydro-morphological threats includes assessing where they are likely to manifest across a given landscape. This concept is referred to as susceptibility, and it is commonly achieved by implementing binary classifiers to estimate probabilities of landslide occurrences. However, predicting where landslides can occur may not be sufficient information, for it fails to convey how large landslides may be. This work proposes using a flexible Bernoulli-log-Gaussian hurdle model to simultaneously model landslide occurrence and size per areal unit. Covariate and spatial information are introduced using a generalised additive modelling framework. To cope with the high spatial resolution of the data, our model uses a Markovian representation of the Matérn covariance function based on the stochastic partial differential equation (SPDE) approach. Assuming Gaussian priors, our model can be integrated into the class of latent Gaussian models, for which inference is conveniently performed based on the integrated nested Laplace approximation method. We use our modelling approach in Dominica, where Hurricane Maria (September 2017) induced thousands of shallow flow-like landslides passing over the island. Our results show that we can not only estimate where landslides may occur and how large they may be, but we can also combine this information in a unified landslide hazard model, which is the first of its kind.

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