Linear Combination of Ground Motion Models with Optimized Weights Using Quadratic Programming

Abstract

The epistemic uncertainty of a prediction model can be reduced by linearly combining independent models with appropriate weights. Linear combination indicates that weights are assigned at each model, where their sum is unity, and weighted models are summed for the final combined model. This paper suggests a framework selecting optimized weights minimizing standard deviation of combined models using the quadratic programming technique. Estimating optimized weights for the combination of two models is straightforward and a mathematical equation can be easily derived. However, finding optimized weights for multiple models is not trivial and a numerical approach such as a grid search technique was often used. The quadratic programming, optimizing a quadratic objective function, can be used to find the optimized weights for multiple models effectively. We applied the quadratic programming to the combination of ground motion models to evaluation the effectiveness of the proposed method. The spectral accelerations from seismic records observed at the downhole sensors in South Korea were used as the dataset. We found that the quadratic programming successfully suggested optimized weights minimizing the uncertainty of the combined model.