Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering

This report presents a new methodology, called moment matching, of propagating the uncertainties in estimating repair costs of a building due to future earthquake excitation, which is required, for example, when assessing a design in performance-based earthquake engineering. Besides excitation uncertainties, other uncertain model variables are considered, including uncertainties in the structural model parameters and in the capacity and repair costs of structural and non-structural components. Using the first few moments of these uncertain variables, moment matching requires only a few well-chosen point estimates to propagate the uncertainties to estimate the first few moments of the repair costs with high accuracy. Furthermore, the use of moment matching to estimate the exceedance probability of the repair costs is also addressed. These examples illustrate that the moment-matching approach is quite general; for example, it can be applied to any decision variable in performance-based earthquake engineering. Two buildings are chosen as illustrative examples to demonstrate the use of moment matching, a hypothetical three-story shear building and a real seven-story hotel building. For these two examples, the assembly-based vulnerability approach is employed when calculating repair costs. It is shown that the moment-matching technique is much more accurate than the well-known First-Order-Second-Moment approach when propagating the first two moments, while the resulting computational cost is of the same order. The repair-cost moments and exceedance probability estimated by the moment-matching technique are also compared with those by Monte Carlo simulation. It is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Furthermore, the amount of computation for moment matching scales only linearly with the number of uncertain input variables. Last but not least, a procedure for feature selection is presented and illustrated for the second example. The conclusion is that the most important uncertain input variables among the many influencing the uncertainty in future repair costs are, in order of importance, ground-motion spectral acceleration, component capacity, ground-motion details and unit repair costs

Characterisation of large changes in wind power for the day-ahead market using a fuzzy logic approach

Wind power has become one of the renewable resources with a major growth in the electricity market. However, due to its inherent variability, forecasting techniques are necessary for the optimum scheduling of the electric grid, specially during ramp events. These large changes in wind power may not be captured by wind power point forecasts even with very high resolution Numerical Weather Prediction (NWP) models. In this paper, a fuzzy approach for wind power ramp characterisation is presented. The main benefit of this technique is that it avoids the binary definition of ramp event, allowing to identify changes in power out- put that can potentially turn into ramp events when the total percentage of change to be considered a ramp event is not met. To study the application of this technique, wind power forecasts were obtained and their corresponding error estimated using Genetic Programming (GP) and Quantile Regression Forests. The error distributions were incorporated into the characterisation process, which according to the results, improve significantly the ramp capture. Results are presented using colour maps, which provide a useful way to interpret the characteristics of the ramp events