Two-stage transfer learning-based nonparametric system identification with Gaussian process regression

Most system identification methods ignore correlations between different identification tasks and do not make full use of historical models when identifying a new process. In this paper, a two-stage transfer learning-based nonparametric system identification method is proposed to improve model accuracy and to reduce identification costs. First, to overcome the transfer capability limitations of the discrete-time model, the target process is modeled as a continuous-time impulse response (IR) function, which consists of a transfer model part and a residual model part, which is regarded as a zero-mean Gaussian process (GP). Then, by utilizing the process geometrical characteristics, the IR functions are classified into three IR domains, and transformation functions within domain or between domains are designed to learn the relationship between the source process model and the target process model. Finally, a two-stage nonparametric identification algorithm based on GP regression is developed: The first stage is performed to select the appropriate type of transformation function through the weighted-derivative dynamical time warping technique, and the second stage is conducted to estimate the transfer model and residual model by using the empirical Bayes approach. Three case studies are conducted to validate the superiority of the proposed identification method.