| Summary: | © 2015 Dr. Isuri Hansika Wijesundera Predicting the expected time for a random walker to reach a specific target point in composite inhomogeneous media has been researched on for decades due to the important role played by first encounters in numerous fields ranging from disease propagation through disaster propagation to the propagation of gossip. Calculating the mean first passage time (MFPT) in particular has been extensively discussed in physical and biological literature producing impressive results for many special network types. MFPT calculations also have many applications in the engineering context which however has not been as popular perhaps due to the highly theoretical treatment to date. The uncertainty inherent in many real world complex dynamic systems results in the state transitions of such systems behaving as random walks in their respective state spaces. However, these random walks do not always possess the ideal conditions required by many powerful MFPT prediction methods in use. These walks are commonly biased towards attractors formed by non-linear interaction dynamics between the system and the natural environment. This thesis describes the heuristic design of methods to predict MFPT for random walks which show directional dependence and spatial inhomogeneity. The first part of this thesis describes a comprehensive case study of predicting MFPT for the application of cyclone induced flood propagation where a new concept called geographic primitives (GPs) is introduced to address the spatial and directional inhomogeneity. The properties of GPs are encapsulated into transition probability matrices (TPM) where an eigenvalue analysis gives the expected time to failure. The predictions are improved using Bayesian analysis on rainfall data and comparisons with two real datasets validate the model. The second part of the thesis concentrates on developing generic methods to address the directional bias formed by potential fields common in real world random walks. A new transport property called the bias modified walk dimension is introduced as a metric to measure the ease of propagation in the existence of directional bias. Interestingly, this empirical modification gave excellent results when validated with many simulated networks as well as diverse real datasets. Next, this model is extended for the broad class of applications modelled as metastable systems to develop a controller with a feedback of MFPT. The flexibility provided by MFPT to an arbitrary target, as opposed to a global MFPT to reach failure as presented in many research in the area, gives an interesting comparison and further validates the importance of the target state as an optimisation variable. Finally, this thesis discusses methods of MFPT calculation when the network is inhomogeneous in transport properties through dividing the network into convex patches/ clusters introduced as network primitives (NPs) where all nodes within each primitive share common transport properties. This NP division, optimised using particle swarm optimisation, is adapted for a hop-wise prediction to calculate MFPT between any source and target pair as an extension to the methods described earlier. Finally, a case study is presented using a dataset of past cyclone tracks over the North Atlantic Ocean to compare the results with the predictions from methods assuming homogeneous transport properties.
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