Hybrid Modeling for Data-enhanced Multiobjective Optimization of Multibody Systems

In almost all technical systems, we want to optimize several conflicting criteria simultaneously such as, the minimization of the energy consumption, the construction cost, or the system complexity. Instead of a single optimum, we thus need to calculate the Pareto front of optimal compromise solutions (cf. the Figure below).

• Problem: Model-based multiobjective optimization is very expensive
• Solution: Use efficient and accurate surrogate models

• White-box models (e.g. differential equations) with a high degree of physical knowledge are often too complex and/or too inaccurate
• Black-box models (generated e.g. by machine learning methods such as decision trees or neural networks) are often not explainable and cost-intensive (data collection)

Hybrid modeling as a combination of physics-based white-box models and data-driven black-box models, e.g. in the form of a discrepancy model

Implementation and modularization of wheel suspension model in Neweul-M²

• Design of a flexible API for heterogeneous problems 
  and hybrid surrogates
• Support for non-linear, non-convex constraints
• Currently in review, preprint available (Berkemeier et. al., 2023)

• E.g., Julia optimizer Compromise.jl can handle Python callbacks
• Collaboration to test optimizer on hydraulic turbine simulation
  
  • Published in (Rentschler et. al., 2024)
  • Successful improvement of approximate Pareto-optimal solutions
• Benchmarks of now Nonlinear Conjugate Gradient methods
  
  • Preprint available, (Berkemeier et. al., 2024)

• Combining evolutionary algorithms and global surrogates (ANNs or RBFs)
• Application: optimize “safety” and “comfort” in rear suspension simulation
  • Preprint available, (Amakor et al., 2024)

• Experience with coupling FMD software and AI model execution capabilities (e.g., co-simulation, subroutines)
• Other interesting model classes and applications

• Multicriteria optimization of dynamical systems
• Physical and hybrid modeling of dynamical systems

Payrebrune, K. de; Flasskamp, K.; Ströhla, T.; Sattel, T.; Bestle, D.; Röder, B.; Eberhard, P.; Peitz, S.; Stoffel, M.; Gulakala, R.; Borse, A.; Wohlleben, M.; Sextro, W.; Raff, M.; Remy, C. D.; Yadav, M.; Stender, M.; Delden, J. van; Lüddecke, T.; Langer, S. C.; Schultz, J.; Blech, C. (2024). The Impact of AI on Engineering Design Procedures for Dynamical Systems. URL: https://arxiv.org/abs/2412.12230, submitted on  20.11.2024 to Technische Mechanik.

Wohlleben, M.; Röder, B.; Ebel, H.; Muth, L.; Sextro, W.; Eberhard, P.: Hybrid modeling of multibody systems: Comparison of two discrepancy models for trajectory prediction. Proceedings in Applied Mathematics and Mechanics, e202400027, 2024. DOI: 10.1002/pamm.202400027 

Wohlleben, M.; Muth, L.; Peitz, S.; Sextro, W.: Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits. Proceedings in Applied Mathematics and Mechanics, 00, e202300039, 2023. DOI: 10.1002/pamm.202300039

Amakor, A.C.; Berkemeier, M.B.; Wohlleben, M.; Sextro, W.; Peitz, S.; Surrogate-assisted multi-objective design of complex multibody systems, 2024. DOI: 10.48550/arXiv.2412.14854.

Berkemeier, M.B.; Sonntag, K.; Peitz, S.; New Nonlinear Conjugate Gradient Methods with Guaranteed Descent for Multi-Objective Optimization, 2024. Optimization Online: 28824. Available: https://optimization-online.org/?p=28824

Rentschler, T., Berkemeier, M.B., Fraas, S., Tismer, A., Raj, R., Peitz, S., & Riedelbauch, S. (2024). Multi-criteria hydraulic turbine optimization using a genetic algorithm and trust-region postprocessing. Proceedings in Applied Mathematics and Mechanics, e202400126. https://doi.org/10.1002/pamm.202400126