Parameter Transfer Identification for Nonidentical Dynamic Systems Using Variational Inference

To identify a reliable model for a dynamic system with nonideal measurements, this article develops a novel parameter transfer identification (PTI) algorithm that leverages the knowledge from a heterogeneous source system. Specifically, a mapping matrix is proposed to transform source parameters into intermediate parameters with dimensions matching the target parameters. By treating the intermediate parameter and mapping matrix as latent variables, variational Bayesian (VB) inference is introduced to efficiently approximate intractable posterior distributions of all unknown parameters, with variances reflecting their uncertainty levels. A probabilistic PTI is then proposed to derive the transfer posterior conditioned on the intermediate parameters, whose analytical form is vital for carrying out VB. Based on this, a heterogeneous PTI is established under the VB framework such that variational posterior distributions for all unknown parameters can be updated iteratively. Finally, an atmospheric fermenter example verifies that the proposed algorithm can bring in model accuracy improvement as high as 60% compared with the nontransfer identification approach, when dealing with nonideal measurements.