Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

Abstract

Nonlinear rational model (NRM) is a generalized nonlinear model, the NAR-MAX model and Volterra model can be regarded as its special cases. In this article, the parameter identification of a class of nonlinear rational models is studied. Due to the coupling of the model output and the information vector, the parameter identification of the NRM is very challenging. To reduce the complexity of the identification, the stochastic gradient algorithm is used. However, the estimate given by traditional stochastic gradient algorithm is biased. To obtain unbiased estimation, the bias is calculated by using the observations and the previous estimate and then compensated to the biased estimate. A variable factor considering the estimation error is introduced to speed up the algorithm. Theoretical analysis shows that the proposed algorithm can obtain an unbiased estimate and has the complexity of O(n). The proposed algorithm is validated by a numerical example and is applied in modeling the dynamics of the cellular toxicity using the tetra-ethyl ammonium chloride. Results show that the proposed algorithm can obtain an accurate estimate for the nonlinear rational model with less computation.

Iterative parameter identification algorithms for transformed dynamic rational fraction input–output systems

“…Among them, rational fraction models widely represent dynamic systems appeared in natural and manmade domains, e.g., chemical engineering, life science and economic operation [10,11,12]. During the past decades, rational fraction models have been gradually applied in the modeling and control of nonlinear systems, particularly in some chemical processes and mechanistic systems [13,14,15]. Recently, parameter identification of rational fraction models have gradually become a hot spot of present research [16,17,18].…”