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Robust Mixed-Effects Segmented Regression Models and Independent Component Analysis

  • Author(s): Zhou, Xiaoyang;
  • Advisor(s): Yao, Weixin;
  • et al.

Renewable energy market has been surging in the United States and around the world in recent years. To mitigate increasing renewable generation uncertainty and intermittency, proactive demand response algorithms and programs are proposed and developed to further improve utilization of load flexibility and increase power system operation efficiency. One of the biggest challenges is how to accurately forecast the electric power demand which is vital to forecast the load impact from demand response resource and control the operations of demand response resources. In Chapter 2, we propose a mixed-effect segmented regression model and its robust estimate for forecasting the electric power demand in Southern California by combining the ideas of random effect regression model, segmented regression model, and trimmed likelihood estimation. Since the log-likelihood of the new model is not differentiable at breakpoints, we propose a new backfitting algorithm to estimate the unknown parameters of the new model. The estimation performance and predictive power of the new model have been demonstrated with both simulation studies and real data application.

In Chapter 3, we propose a new estimation procedure for Independent Component Analysis (ICA) based on the recently introduced Density Information Matrix (DIM). The new ICA algorithm can recover the independent components via a simple eigenanalysis of the defined DIM. Different from existing ICA algorithms, the new method can detect whether there is any ``uninteresting" Gaussian component in the original signal. In addition, the new method can rank the recovered signal in terms of their density information. To estimate the DIM, we propose both a kernel density estimation and Gaussian mixture model estimation methods to approximate the unknown density, and utilize the density square transformation to avoid the numerical integrations and reduce the computation cost. We demonstrate the performance of the proposed ICA algorithms using the simulation studies and three real data applications.

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