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- W2979689934 abstract "The goal of this paper is the approximation of a nonlinear, dynamic process. More specifically it is studied whether the nonlinear, dynamic process can be simplified by separating it in its linear dynamic and nonlinear static components. Focus of this work is the approximation of the dynamic proportion with orthonormal basis functions (OBFs). The approximation of the nonlinear static properties is not fixed to a specific technique, but we focus on Takagi-Sugeno fuzzy models. This approach contrasts with other publications like [10], [12], [15], where OBFs are used to model both the dynamic and nonlinear part of the process. By modeling NOBF models, the main task is the optimization of the OBF pole, because it is the hyper-parameter, which affects the model quality most. This contribution focuses on the loss functions used for the optimization of the OBF pole.The loss functions must fulfill several requirements: It has to have a unique minimum, must be computable without prior knowledge of the nonlinear component of the process, be smooth around minima and sufficiently fast to compute. We compare three approaches to approximate the loss function. The first approach is the true loss function, which is the squared error of the nonlinear model and acts as reference. The second approach incorporates the structure of local model networks [3]. Finally, we propose a new approach, which is model free and based on the gamma test. We further analyze for which type of systems the technique is suitable and compare the advantages and disadvantages of the respective approach." @default.
- W2979689934 created "2019-10-18" @default.
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- W2979689934 date "2019-06-01" @default.
- W2979689934 modified "2023-09-28" @default.
- W2979689934 title "Pole Determination for Takagi-Sugeno Fuzzy Laguerre Models" @default.
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- W2979689934 doi "https://doi.org/10.1109/fuzz-ieee.2019.8858869" @default.
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