Probability-Based Identification of Hammerstein Systems With Asymmetric Noise Characteristics - Liu, Xin; Wang, Chen; Dai, Wei (IEEE transactions on instrumentation and measurement, 2024)
In the existing identification algorithms, the output noise is usually modeled by using the thick-tailed Laplace and Student's t-distributions instead of the Gaussian distribution to acquire the robustness for the outliers. However, both Laplace and Student's t-distributions exhibit symmetric statistical properties which can lead to certain limitations. In this article, we introduce a robust identification algorithm for Hammerstein output error (OE) systems based on the shifted asymmetric Laplace (SAL) distribution in order to handle the skewed and asymmetric output noise. The skewness parameter and scale parameter of the SAL distribution act as the hyperparameters to govern the statistical property of the SAL distribution and both of them are adaptively extracted from the identification data. That means the statistical property of the SAL distribution is adaptively adjusted by the identification data quality, which could ensure the robustness of the introduced algorithm for the skewed and asymmetric noise as well as the outliers. In addition, the auxiliary model technique is used to solve the problem of unmeasurable process variables of the Hammerstein system; the key-term separation principle is used to reduce the computation complexity of the algorithm. The complete identification problem is mathematically formulated by using the generalized expectation maximization (GEM) algorithm and the estimation formulas of the model and noise parameters are derived simultaneously. Finally, the effectiveness of the algorithm introduced in this article is verified.