Online Design of Experiments with Fuzzy Confidence Interval for Identification of Nonlinear Dynamical Processes

This paper presents a new online Design of Experiments methodology for identifying dynamical nonlinear systems. The approach is based on an evolving neuro-fuzzy identification framework that uses the confidence interval of fuzzy rules to measure model convergence. Informative data are crucial for system identification, particularly in the context of nonlinear dynamical processes. When control over the input signals is possible, a tailored experiment can be designed to minimize experiment duration and resource consumption. In contrast to traditional Design of Experiments approaches, which are iterative, our proposed method selects the inputs online at each time step, while identifying the model. We have investigated the use of the Confidence Interval in unsupervised clustering, parameter identification, and Design of Experiments. The performance of the method is compared to related evolving systems on the Mackey-Glass chaotic time series, and its effectiveness is demonstrated on a Piecewise Linear dynamical system with outliers and a real Plate Heat Exchanger pilot plant. The outlying data were successfully rejected online by the proposed methodology, while the real-world experiments detected the initial cold start behaviors and excluded them from the final model. The methodology shows robust Design of Experiments and outlier rejection capabilities, making it a promising approach for identifying dynamical nonlinear systems in a noisy environment.