Abstract
The Hammerstein model identification technique based on swept sine excitation signals proved in numerous applications to be particularly effective for the definition of a model for nonlinear systems. In this paper we address the problem of the robustness of this model parameter estimation procedure in the presence of noise in the measurement step. The relationship between the different functions that enter the identification procedure is analyzed to assess how the presence of additive noise affects model parameters estimation. This analysis allows us to propose an original technique to mitigate the effects of additive noise in order to improve the accuracy of model parameters estimation. The different aspects addressed in the paper and the technique for mitigating the effects of noise on the accuracy of parameter estimation are verified on both synthetic and experimental data acquired with an ultrasonic system. The results of both simulations and experiments on laboratory data confirm the correctness of the assumptions made and the effectiveness of the proposed mitigation methodology.
Highlights
The behavior of physical systems is very often modeled using linear techniques
The different aspects addressed in the paper and the technique for mitigating the effects of noise on the accuracy of parameter estimation are verified on both synthetic and experimental data acquired with an ultrasonic system
The amount of available data is not always adequate to represent the complexity of the system and the computing power is sufficient to handle them. They continue to be widely diffused in the white-box approaches and the gray-box approaches, which place side by side to a number of data-driven only, black box methods: Such techniques integrate in different measures the information derived from the knowledge of the physics of the system and information extracted from the data produced by the nonlinear system
Summary
The behavior of physical systems is very often modeled using linear techniques. The modeling of nonlinear dynamical systems is one of the most challenging research areas in the field of system representation. The amount of available data is not always adequate to represent the complexity of the system and the computing power is sufficient to handle them. For this reason, they continue to be widely diffused in the white-box approaches and the gray-box approaches, which place side by side to a number of data-driven only, black box methods: Such techniques integrate in different measures the information derived from the knowledge of the physics of the system and information extracted from the data produced by the nonlinear system
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