Optimized Excitation Signal Tailored to Pertinent Dynamic Process Characteristics

TL;DR

The paper addresses the challenge of designing excitation signals for nonlinear dynamic system identification by introducing Incremental Dynamic Space-Filling Design (IDS-FID), an extension of OMNIPUS that combines space-filling input distributions with controllable frequency spectra. IDS-FID builds a proxy-driven regressor-space optimization, iteratively concatenating optimal input parts while shaping the excited spectrum through a decomposed quality function $J = J_1 - \lambda J_2$, balancing space-fillingness and dynamic information. Through a Hammerstein-process–based evaluation and LMN models, the authors demonstrate that IDS-FID can achieve competitive performance across diverse operating conditions, with tunable emphasis on dynamics via $\lambda$ and robustness to algorithmic parameters. The work provides a practical DoE framework for nonlinear system identification that can be tailored to industrial needs and lays groundwork for online DoE extensions that refine the proxy model as data accrues.

Abstract

The effectiveness of data-driven techniques significantly relies on the input signal used to generate the training data. Nevertheless, there is a notable gap in research when it comes to designing excitation signals for identifying nonlinear dynamic systems, likely because of the challenges involved. Based on current knowledge, it is crucial for excitation signals to effectively capture the nonlinearity across the entire operational area and to gather insights into the area-specific dynamic process characteristics. The Incremental Dynamic Space-Filling Design (IDS-FID) strategy designs excitation signals to achieve a space-filling distribution across the input space of a nonlinear approximator used in external dynamics modeling, gathering information throughout its operational area. Simultaneously, the approach enables for a heightened focus on either the systems steady-state or transient responses during information acquisition by altering the excitation signals dynamics, facilitating targeted insights into dynamic process characteristics.

Figures (10)

• Figure 1: External dynamics approach for $p$ inputs, one output and a common dynamic order $m$ for simplicity.
• Figure 2: Flow chart of the iterative optimization.
• Figure 3: Illustrative example of a sequence selection with one input. The proxy model presented here equals the one employed in the evaluation.
• Figure 4: Influence of power $n$ on the shape of $J_{2}(L)$.
• Figure 5: Course of $J(L)$ and its components for an exemplary $u$-value and $n=4$.