A Statistical Perspective on Calibration of Computer Models with Tidal Power Application
LE3 .A278 2015
Master of Science
Mathematics and Statistics
Mathematics & Statistics
The Bay of Fundy has the world’s highest tides, which is why in-stream turbines will be placed in the Digby Neck region for tidal energy. Placing turbines in the water requires accurate observations of water ﬂow, but these observations are expensive and time consuming to collect. FVCOM is a computer model that simulates tides and tidal currents in the Bay of Fundy. The goal of this thesis is to calibrate the bottom friction parameter of FVCOM so that its velocity output best matches physical observations. However, because simulations can take days or weeks to run, it is not feasible to run the computer model many times, which makes calibration diﬃcult. An objective function is formulated that evaluates the discrepancy between the observed and model run harmonic constituents. A sequential design is used to ﬁnd a value of bottom friction that minimizes the objective function, with a minimal number of additional model runs. At each step of the sequential design, Gaussian process model ﬁtting is used to emulate the objective function, and then an expected improvement criterion is used to determine the next bottom friction value which the model will be run with. A cycle of calibration is established through this approach that determines an optimal value of bottom friction. Once the cycle of calibration is established, ways of improving the process are considered. Sources of uncertainty in the objective function formulation are incorporated through a noisy sequential design, which leads to a similar optimal value of bottom friction as with the deterministic approach. A sensitivity analysis is conducted on the weights of the harmonic constituents and different locations in the objective function. An alternate weighting scheme is proposed based on the sensitivity of the weights, which signiﬁcantly aﬀects the optimal value of bottom friction.
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