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Reduced Order Modeling

Reduced order modeling is a technique for simplifying full order high-fidelity models by reducing their computational complexity, while preserving their dominant behavior. Working with a reduced order model (ROM) can simplify analysis and control design.

Why Use Reduced Order Modeling?

Using reduced order modeling techniques, you can:

  • Enable use of 3rd party FEA/FEM/CFD models for system-level simulation in Simulink® including hardware-in-the-loop testing — You can combine multiple complex component-level models, including third-party finite element method (FEM) or finite element analysis (FEA) models, into system-level simulation models in Simulink by replacing the complex models with the corresponding ROMs. ROMs are also useful for hardware-in-the-loop testing as they allow real-time simulations. Engineers can create ROMs representing the physical components of the system, which can run on a real-time machine for testing of the control algorithm on embedded hardware.  The reduced computational complexity of ROMs make such testing more feasible.

  • Create virtual sensors — You can use ROMs as virtual sensors for estimating or predicting signals of interest when measuring those signals by using a physical sensor is impractical or impossible.

  • Perform control design — The reduced complexity of ROMs can make control design tasks more tractable. You can design your controller for the reduced order model of a plant and then validate the controller on the original high-fidelity system. You can also use ROMs for control algorithms that require internal prediction models, such as nonlinear model predictive control.

  • Create digital twins — You can create or simplify digital twin models using ROMs. Doing so makes the digital twins more computationally efficient and more suitable for periodic updates to represent the current state of the operational asset.

Reduced Order Modeling Methods

There are two main classes of techniques for building reduced order models: data-driven and linearization-based.

When creating data-driven and linearization-based reduced order models, you must decide what trade-offs you are willing to make to speed up a model. The most suitable type of ROM technique depends on the application. For example, when creating data-driven ROMs, you sacrifice physical insights of the model. When creating a linearization-based ROM, you might need to eliminate system dynamics beyond a certain frequency in the reduced model. An extreme case is when the reduced order model captures only steady-state system behavior.

Data-Driven Methods

Data-driven methods use input-output data from the original high-fidelity first-principles model to construct a ROM that accurately represents the underlying system. Data-driven ROMs can be either static or dynamic models.

The following techniques are useful for creating static ROMs.

If you have System Identification Toolbox™ software, you can develop dynamic ROMs using techniques such as:

If you have Deep Learning Toolbox™ software, you can develop dynamic ROMs using techniques such as:

Nonlinear ARX models can use regression functions based on machine learning algorithms available with Statistics and Machine Learning Toolbox™ software.

Linearization-Based Methods

To create a ROM, you can linearize a nonlinear high-fidelity model at several operating points and combine the resulting linear models into a linear parameter-varying model. For an example, see LPV Approximation of Boost Converter Model (Simulink Control Design).

You can also reduce the number of states in a higher-order linear model using model order reduction techniques. Doing so is particularly helpful when the linearized models of a high-fidelity system or the linear models themselves contain states that do not contribute to the dynamics of interest. For more information, see the following examples:

Once you have a linearized ROM model, you can specify the linearization for model components in Simulink. For an example, see Specify Linearization for Model Components Using System Identification (Simulink Control Design).

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