Reduced Order Modeling in the Context of System Level Simulation

I recently had the pleasure of representing ANSYS as an invited plenary speaker at the MoRePaS international workshop on Reduced Order Modeling. Model order reduction techniques and the resulting Reduced Order Models are a critical technological advancement that are extremely important in the context of System Level Simulation. Applications of ROMs are vast, ranging from enabling product designers to more accurately simulate the whole product to enabling real-time system analysis.

In terms of a definition, ROMs can be described as compact, auto-generated representations of full 3-D models that are useful for system simulation. The mathematical and numerical methods that are used to create these compact representations are not new and have been used for things like image compression, etc. ROMs are usually compute and license intensive to create but very fast to simulate once built.

For use in system level simulation, ROMs have well-defined inputs and outputs (electrical ports, parameters mapped to boundary conditions, etc). In terms of accuracy, ROMs typically match within ~5% tolerance, steady-state and/or dynamic responses of the original model. Dynamic response is particularly important in the context of system level simulation.

For system simulation ROMs provide several key benefits:

• Reuse: Easily and automatically generate highly accurate & validated component models without having to re-build and maintain complex models
• Process Compression: Simulate accurate models in 1/10^th to 1/100^th of the time it would take to simulate the full 3-D model
• System Verification: Enable full system verification by simulation combining validated components and subsystems
• Optimization: Perform rapid design optimization and tradeoff analysis at system level, provided that operation is within valid operating region

As one example, ROMs are used extensive to characterize motor behavior for use in modeling and simulating the electric drive train of a hybrid electric vehicle. The technique used to build the motor ROM on geometric symmetry to compress the amount of 3D simulation data required.

The focus of my talk was about laying out the typical ROM creation flow in a commercial setting and the opportunities and trade offs involved in standardization of formats for ROMs.

For practical applications of Reduced Order Models for use in System Level Simulation, take a look at this white paper about Model Reduction Technology and Software/Hardware Collaborative Model-Based Development

Additionally, ANSYS has several patents and publications in this field and continues to invest in the exciting area that holds great promise for our customers. Here is a small subset of the relevant publications:

Rosu, M., Kher, S., Beley, J. D., Ostergaard, D., Bechtold, T., Rauch, R., & Otto, J. (2011, March). Fast and efficient multi-domain system simulation based on coupled heterogeneous model structures. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (Vol. 7977, p. 69).

Asgari, S., Lalgudi, S., Tsuk, M., Kher. S. “Fast and Reliable Macromodeling for Heat Flows under the Linear Time-Invariant Assumption”, Proc. NAFEMS World Congress 2011, pp 9

Hu, Xiao, et al. “A state space thermal model for HEV/EV battery using vector fitting.” Transportation Electrification Conference and Expo (ITEC), 2012 IEEE. IEEE, 2012.

Hu, Xiao, et al. “A linear parameter-varying model for HEV/EV battery thermal modeling.” Energy Conversion Congress and Exposition (ECCE), 2012 IEEE. IEEE, 2012.

Asgari, Saeed, Subramanian N. Lalgudi, and Michael Tsuk. “Analytical integration-based causality checking of tabulated S-parameters.” 19th Topical Meeting on Electrical Performance of Electronic Packaging and Systems. 2010.

Asgari, Saeed, et al. “Application of POD plus LTI ROM to Battery Thermal Modeling: SISO Case.” SAE International Journal of Commercial Vehicles7.2014-01-1843 (2014): 278-285.

Tsuk, Michael J., and Jacob K. White. “State-space model-based simulators and methods.” U.S. Patent No. 8,504,345. 6 Aug. 2013.

Stanton, S., D. Lin, and Z. Tang. “Interior permanent magnet machine analysis using finite element based equivalent circuit model.” 2009 IEEE Vehicle Power and Propulsion Conference. 2009.

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