Optimization of Time-Series Data Partitioning for Parameter Identification

This paper presents a data-driven method of parameter identification in nonlinear systems based on the theories of symbolic dynamics. Although construction of finite-state-machine models from symbol sequences has been widely reported, similar efforts have not been expended to investigate partitioning of time series data to optimally generate symbol sequences. A data-set partitioning procedure is proposed to extract features from time series data by optimizing a multi-objective cost functional. Performance of the optimal partitioning procedure is compared with those of other traditional partitioning (e.g., uniform and maximum entropy) schemes. Then, tools of pattern classification are applied to identify the ranges of multiple parameters of a well-known chaotic nonlinear dynamical system, namely the Duffing Equation, from its time series response.