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In High-Tech Systems (HTS), conflicting demands on positioning accuracy, production speed and cost reduction are ever increasing. To push these demands across existing limits, models with 1) higher dynamic response prediction accuracy and 2) faster response prediction are needed. Within this context, in modular HTS, accurate modeling of mechanical interfaces between subsystems is a major problem. To comply with the industrial demands, we pursue the derivation of low-dimensional, accurate, modular, hybrid HTS models with enhanced mechanical interface modeling by combining the use of First Principles and measured data.

Opportunity 鈥� Creating accurate, low-dimensional, updatable HTS models

Creation of HTS models with increased accuracy and faster response prediction is an ever-ongoing pursuit to speed up model-based design cycles for shorter time to market, improve real-time model-based control performance, and realize real-time model-based Structural Health Monitoring. This also will lead to cost reduction related to design, manufacturing, operation, and maintenance.

Connecting to common practice in HTS industry, we will use a modular modeling approach: each subsystem model of the complex interconnected HTS is typically developed by a specialized design team. Here, subsystems may be in a (controlled) closed loop.

Roadblock - mechanical interface modeling

The currently used FP interface models hamper advancements in HTS modeling because of their level of uncertainty. More specifically, accurate FP modeling of interface stiffness and damping characteristics (e.g., dry friction) is highly challenging and certain physical interface phenomena may even be missed. Moreover, these properties may differ from machine-to-machine and may change during the HTS鈥� lifetime, which is not covered by a nominal FP interface model. Finally, effects of mechanical interface modeling can only be assessed in the assembled HTS configuration, which is unfeasible if the assembly model has high complexity, i.e., is of very high order. Summarizing, the question is how to derive accurate interface models as part of HTS models which can be updated fast under varying conditions.

Research hypothesis - improving FP HTS (interface) models using data

Data measured on the interconnected HTS system contains information about the real interface behavior. Enriching a reduced FP model of the system (including an initial FP interface model) with this data allows for creating an accurate, low-order, modular, hybrid HTS model, which can be updated online.

Solution and research questions

The research hypothesis will be tested by using a unique combination of FP modeling, Modular Model Order Reduction techniques (MMOR) and data-based Machine Learning (ML) techniques. A stepwise approach addressing the following Research Questions (RQ) is formulated below and is visualized in Fig. 2.

1) RQ1 is: how to parameterize the interface models (initially linear)? This may be more straightforward for interfaces with bearings but is less trivial for solid (e.g., bolted) connections over large interfaces. First, initial estimates of linear interface stiffness may be obtained using Finite Element Models. Furthermore, in case of large interfaces, interface model reduction techniques (e.g., Guyan reduction) may be necessary to arrive at acceptable interface model orders.

2) We conjecture that interface modeling errors dominate errors in subsystem models, so RQ2 is: how to obtain accurate, low鈥�dimensional subsystem models? Starting with linear FP modeling of subsystems and the interface models from step 1), we will use a MMOR approach², where assembly accuracy requirements are translated to subsystem accuracy requirements defining the required level of subsystem complexity reduction. If necessary, the reduced subsystem models may be updated with measured data³. Finally, an initial low-order assembly model is obtained by coupling the reduced subsystem models using initial interface models from step 1).

3) RQ3 is: how to use measured data to improve the initial linear interface models as part of the low-order assembly model? Note that it is often impossible to measure at the interface itself. So, only data measured at interconnected subsystems will be available. We envision to use measured data to extend and/or augment⁴ the initial linear interface models with recurrent neural networks capturing effects of missing (nonlinear) interface model terms. Subsequently, using sparse regression (e.g., SINDy⁵) on this neural network, a white, parameterized, augmented interface model may be obtained. Alternatively, a small library of candidate functions could be used, where coefficients of the candidate functions may be identified using the approach in³ as an identification method or other existing parameter estimation methods. After successful identification of the model, it will be investigated if for instance the method developed in³ can be used to update the interface model parameter values in an online fashion during the HTS鈥� lifetime.

4) With this new hybrid modeling approach, we will push existing demands on accuracy and speed of predicted responses past current limits. This will be demonstrated by comparing predicted and measured response data using an experimental setup of an HTS assembly.

REFERENCES

¹ Mathis, A.T. et al. (2020), Applied Mechanics Reviews, Vol. 72, 040802.
² Janssen, L.A.L. et al. (2024), Automatica, Vol. 160, 111423.
³ Kessels, B.M. et al. (2023), Nonlinear Dynamics, Vol. 111: 10255-10285.
⁴ Kessels, B.M. et al. (2025), Nonlinear Dynamics, Vol. 113: 17335鈥�17363.
⁵ Brunton, S.L., Kutz, J.N. (2022), Data Driven Science and Engineering, 2nd edition, Cambridge UP.