Mining Markov chain transition matrix from wind speed time series data

Extracting important statistical patterns from wind speed time series at different time scales is of interest to wind energy industry in terms of wind turbine optimal control, wind energy dispatch/scheduling, wind energy project design and assessment, and so on. In this paper, a systematic way is presented to estimate the first order (one step) Markov chain transition matrix from wind speed time series by two steps. Wind speed time series data is used first to generate basic estimators of transition matrices (i.e. first order, second order, third order, etc.) based on counting techniques. Then an evolutionary algorithm (EA), specifically double-objective evolutionary strategy algorithm (ES), is proposed to search for the first order Markov chain transition matrix which can best match these basic estimators after transforming the first order transition matrix into its higher order counterparts. The evolutionary search for the first order transition matrix is guided by a predefined cost function which measures the difference between the basic estimators and the first order transition matrix, and its high order transformations. To deal with the potential high dimensional optimization problem (i.e. large transition matrices), an enhanced offspring generation procedure is proposed to help the ES algorithm converge efficiently and find better Pareto frontiers through generations. The proposed method is illustrated with wind speed time series data collected from individual 1.5 MW wind turbines at different time scales.