Identification of block-oriented nonlinear systems starting from linear approximations: A survey (1607.01217v3)

Abstract: Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the $\epsilon$-approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.

• The paper presents a comprehensive review of methods that use linear approximations, particularly the Best Linear Approximation, to initiate block-oriented nonlinear system identification.
• It details strategies for modeling various structures, including Hammerstein, Wiener, and parallel branch configurations, with techniques such as SVD and pole-zero allocation.
• The survey emphasizes enhanced robustness and efficiency in parameter estimation while outlining future research directions for complex, automated identification algorithms.

Overview of Block-Oriented Nonlinear System Identification Techniques

The paper entitled "Identification of Block-Oriented Nonlinear Systems starting from Linear Approximations: A Survey" by Maarten Schoukens and Koen Tiels provides a comprehensive review of techniques used for identifying block-oriented nonlinear systems, emphasizing approaches that utilize linear approximations as a foundation. Focused on a diverse array of model structures, this survey sets a framework for addressing potential nonlinearities in systems through various structural decompositions.

Key Concepts and Methodologies

Block-oriented nonlinear models, such as Hammerstein, Wiener, Wiener-Hammerstein, and Hammerstein-Wiener, are highlighted in this survey as they offer simplicity in understanding and flexibility in application. These models make use of linear time-invariant (LTI) blocks and static nonlinearities combined in series, parallel, or feedback configurations. The authors introduce the concept of initializing the identification algorithms using linear approximations like the Best Linear Approximation (BLA) and the $\epsilon$-approximation. The BLA framework provides an LTI approximation for the system behavior appropriate for most practical applications, whereas the $\epsilon$-approximation offers a detailed analytic perspective in small signal scenarios.

The paper thoroughly explores different strategies for identifying various block-oriented structures:

• Single Branch Models: For Hammerstein and Wiener structures, the presented methodologies leverage the BLA to simplify the estimation of LTI dynamics and the static nonlinear component. The Wiener-Hammerstein structure requires more sophisticated techniques such as pole and zero allocation strategies due to its complexity.
• Parallel Branch Structures: Techniques involving singular value decomposition (SVD) are applied to segregate multiple dynamic pathways within parallel Hammerstein and Wiener models. This structure's identification is enhanced by examining BLA behavior across differing operating conditions, aiding in isolating independent dynamic elements.
• Feedback Systems: For nonlinear feedback configurations such as simple feedback and Wiener-Hammerstein feedback structures, the BLA or $\epsilon$-approximation methods are adapted to discern the influence of feedback loops, providing a clearer insight into the loop-induced system dynamics.

Implications and Directions for Future Research

The survey underscores the pivotal role of the BLA and other linear approximation frameworks in both guiding model structure selection and serving as generative points for nonlinear system identification. Furthermore, by offering solutions to initialization issues, these methodologies improve the robustness and efficiency of parameter estimation.

This research opens several future exploration opportunities, like:

• Integrating dynamic nonlinearities, such as hysteresis, further into the BLA modeling paradigm.
• Expanding BLA-based identification to more complex or user-defined structures, possibly encompassing intricate multi-input multi-output (MIMO) systems.
• Addressing more diverse noise frameworks and model errors, enhancing the external validity of identified models.
• Increasing automation and user-friendliness in identification algorithms, particularly those with minimal user input, to make these advanced methodologies accessible to non-expert users in the field.

The carefully constructed survey offers valuable resources and methodologies for experienced researchers and practitioners aiming to accurately model nonlinear systems through block-oriented structures. By framing the discussion around BLA-derived initializations, it provides both a solid theoretical foundation and practical guideposts for real-world applications, emphasizing the importance of model structure and input design in achieving accurate system representation.