Flexible Linear-Fractional-Representation-Based Model Augmentation for Efficient Nonlinear System Identification

Core Concepts

A flexible linear-fractional-representation (LFR) based model augmentation structure is proposed that can represent a wide range of existing model augmentation structures. An identification algorithm is developed to estimate ANN implementations of the proposed augmentation structure.

Abstract

The paper introduces a flexible linear-fractional-representation (LFR) based model augmentation structure that can represent a variety of existing model augmentation structures from the literature. The proposed structure combines a baseline model with parameterized augmentation functions in a flexible manner, where an interconnection matrix governs the signals between the baseline model and augmentation functions. The key highlights are: The LFR-based model augmentation structure can represent common model augmentation structures such as parallel, series, and mixed augmentation in both static and dynamic forms. An identification algorithm is developed that can estimate ANN implementations of the proposed LFR-based augmentation structure. The performance and generalization capabilities of the identification algorithm and the augmentation structure are demonstrated on a hardening mass-spring-damper simulation example. The nonlinear dynamic mixed augmentation model achieves the lowest normalized root mean square error (NRMS) on the test data compared to other augmentation structures and a standard ANN-SS model. The augmentation functions are shown to augment the baseline model rather than replacing its dynamics, resulting in an accurate and interpretable model.

Stats

The physical parameters of the 3 DOF hardening mass-spring-damper system are: Mass m1 = 0.5 kg, m2 = 0.4 kg, m3 = 0.1 kg Spring k1 = k2 = k3 = 100 N/m Damper c1 = c2 = c3 = 0.5 Ns/m Hardening a1 = 100 N/m^3, a2 = a3 = 0 N/m^3

Quotes

"The proposed LFR-based model augmentation structure combines a baseline model with augmentation functions in a flexible manner. By shaping this interconnection matrix, we are able to represent a wide range of model augmentation structures proposed in the literature [7], [11]–[13], [15], [20] resulting in an unifying model structure represented in LFR form." "The nonlinear dynamic mixed augmentation results in the lowest NRMS. The nonlinear static mixed augmentation also results in a low NRMS score, but slightly higher than the nonlinear dynamic mixed augmentation. This is expected for augmentation of a system with missing dynamics that can be represented with additional states."

Key Insights Distilled From

Learning-based model augmentation with LFRs

by Jan ... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01901.pdf

Deeper Inquiries

How can the proposed LFR-based model augmentation structure be extended to handle time-varying or parameter-varying baseline models

The proposed LFR-based model augmentation structure can be extended to handle time-varying or parameter-varying baseline models by incorporating dynamic elements into the interconnection matrix and selection matrices. For time-varying models, the interconnection matrix can be updated at each time step to adapt to the changing dynamics of the system. This adaptation can involve updating the selection matrices based on the evolving parameters of the time-varying model. Similarly, for parameter-varying models, the augmentation functions can be designed to adjust their behavior based on the varying parameters of the baseline model. By allowing flexibility in the interconnection structure and the augmentation functions, the LFR-based approach can effectively capture the complexities of time-varying and parameter-varying systems.

What are the potential limitations or drawbacks of the LFR-based augmentation approach compared to other model integration techniques like physics-guided neural networks

While the LFR-based augmentation approach offers flexibility and unification of various model augmentation structures, it may have some limitations compared to other techniques like physics-guided neural networks (PGNNs). One potential drawback is the complexity of designing the interconnection matrix and selection matrices for highly nonlinear or intricate systems. Ensuring that the interconnection structure captures the interactions between the baseline model and the augmentation functions accurately can be challenging, especially for complex systems with nonlinear behaviors. Additionally, the LFR-based approach may require a significant amount of computational resources for optimization and training, especially when dealing with large-scale models or high-dimensional data. PGNNs, on the other hand, leverage explicit physical knowledge to guide the learning process, which can lead to more interpretable and explainable models compared to purely data-driven approaches like LFR-based augmentation.

Can the proposed framework be applied to identify models for complex real-world systems beyond the simulated mass-spring-damper example, and what challenges might arise in such applications

The proposed framework can indeed be applied to identify models for complex real-world systems beyond the simulated mass-spring-damper example. However, several challenges may arise in such applications. One challenge is the availability and quality of data for training the augmented models. Real-world systems often have limited or noisy data, which can impact the accuracy and generalization capabilities of the identified models. Additionally, the complexity of real-world systems may require more sophisticated augmentation functions and interconnection structures to capture the intricate dynamics accurately. Ensuring the scalability and efficiency of the identification algorithm for large-scale or high-dimensional systems is another challenge that needs to be addressed. Furthermore, the interpretability and transparency of the augmented models in real-world applications are crucial for decision-making and control purposes, which may require additional considerations and validation steps.