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On hierarchical clustering-based identification of PWA model with model structure selection and application to automotive actuators for HiL simulation

  • Mathematical methods in data science
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Abstract

The application of the electronic control unit (ECU) motivates dynamic models with high precision to simulate mechatronic systems for various analysis and design tasks like hardware-in-the-loop (HiL) simulation. Unlike traditional physical models which are established based on the research experience or the mechanics mechanism, in this study, a novel data-driven modeling approach is presented based on the piecewise affine (PWA) identification method. In this work, the highly nonlinear dynamic of automotive actuators is well approximated by the PWA model. To obtain experimental data that can accurately reflect the characteristics of actuators, a test bench was first built. On this basis, the PWA identification of automotive is composed of the data clustering, the model structure selection, and the model parameter estimation. The proposed clustering method improves the widely used balanced iterative reducing and clustering using hierarchies (BIRCH) by introducing a refinement phase for handling clusters with arbitrary shapes. The model structure selection and the parameter estimation are jointly solved by using the optimization method. The presented method is demonstrated with an academic example and an automotive throttle, and the results show that the proposed method can achieve a high model quality, which means that the normalized root mean squared error (NRMSE) is 0.03 and the absolute maximal prediction error can reach 2.43°. Compared to other models like a physical model or a fuzzy model, the improvement using the proposed model can be up to 50%. Thus, the quality of the proposed PWA model is sufficient for HiL simulation.

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Funding

This research is supported by the Natural Science Foundation of Shanxi Province, China (Grant no. 20210302123188).

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  1. College of Computer Science and Technology and College of Data Science, Taiyuan University of Technology, Jinzhong, Shanxi, China

    Zhenxing Ren

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Ren, Z. On hierarchical clustering-based identification of PWA model with model structure selection and application to automotive actuators for HiL simulation. Soft Comput 29, 543–558 (2025). https://doi.org/10.1007/s00500-025-10458-6

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