ROM (Reduced Order Model) refers to a model in which part or all of the original model has been reduced to a lower-dimensional representation.
There are various reduction approaches, but they generally fall into two types: (1) methods that model only the input–output relationship, and (2) methods that reduce the model’s degrees of freedom through modal coordinate transformations and the like.
Here, we focus on the former, introducing ROMs that specifically leverage AI and machine learning methods.
For static problems, modeling is performed using techniques such as response surface methods and neural networks. For dynamic problems, because temporal evolution is important, methods such as RNNs (Recurrent Neural Networks) are used.
- ROM is used for purposes such as the following:
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Speeding up CAE models
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Building real-time models for HILS integration
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Coupled analysis between different CAE solvers
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Coupling test data with CAE
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ROM for Nonlinear Components
- When modeling nonlinear components in CAE such as multibody dynamics, there are challenges such as the following:
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Modeling techniques to represent complex nonlinear characteristics
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Computation time in system analysis
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Nonlinear components may include material nonlinearities such as stiffness and damping elements or friction, as well as geometric nonlinearities such as contact.
In any case, ROM is effective for problems that can be understood as displacement- and velocity (frequency)-dependent behavior under load.
When applying ROM to dynamic problems, methods such as LSTM (Long Short-Term Memory) are used. This is because, to represent phenomena such as free vibration—where displacement and velocity occur even when no external force is applied at a given moment—the model needs a function that remembers history.
Moreover, a model that can consider the length and importance of that memory (lower frequencies tend to have longer-lasting influence) is desirable.
By obtaining the input–output relationship of a component (displacement/velocity and load) through experiments or CAE and modeling it, the model can be linked with system engineering simulation that can be called model-based system engineering.
ROM for Real-Time Simulation
Vehicle models used in HILS and driving simulators are required to run in real time, so their degrees of freedom are limited. By converting a vehicle model that includes elastic bodies and nonlinear characteristics into a ROM without reducing its degrees of freedom at all, real-time performance can be ensured.
The figure shows an example in which a ROM was constructed by applying two methods—LSTM and GRU (Gated Recurrent Unit)—to an Adams/CAR model with more than 1,000 degrees of freedom that includes friction and elastic bodies.
Here, the inputs are the driver’s control operations, and the outputs are the vehicle dynamics. The results show that both methods can achieve speeds about 3–4 times faster than real time while accurately reducing the vehicle dynamics.
