Reduced Order Modeling: Applications and Techniques for Creating ROMs - MATLAB
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      Reduced Order Modeling: Applications and Techniques for Creating ROMs

      From the series: Reduced Order Modeling

      Reduced order modeling (ROM) is a technique for simplifying a high-fidelity mathematical model by reducing its computational complexity while preserving the dominant behavior of the complex model.

      One common application of reduced order modeling enables simulation of third-party FEA/FEM/CFD models in Simulink® including hardware-in-the-loop testing. Other ROM applications include virtual sensor modeling, control design, and digital twins. This overview also highlights different techniques for creating reduced order models with MATLAB® and Simulink such as data-driven modeling (including static and dynamic models), model-based ROMs, linearization-based methods, and physics-based reduction.

      Published: 4 Dec 2023

      In this video, we'll discuss Reduced Order Modeling, or ROM in short, why engineers use it, different applications of ROM, as well as different techniques for creating reduced order models with Matlab and Simulink. So what is 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.

      Why do engineers use ROM? Let's start with a simple example to understand why. Imagine you are a system engineer developing a control system for a new machine. Your colleagues from a design team or a modeling group created a model of one of the components of the overall system.

      Maybe it is a CFD model of a hydraulic valve, or it is an FEM thermal model of a jet engine turbine blade. Simulation of these high-fidelity models may take hours or even days to complete. Therefore, these high fidelity full-order models, while great for component-level analysis and design, are neither intended nor suitable for near real-time simulation that is often needed for control system design and system level analysis.

      Reduced order modeling enables such simulation by simplifying full-order high-fidelity models. This simplification reduces their computational complexity while preserving their dominant behavior. In addition, ROM also facilitates the design and real-time implementation of control algorithms, where reduced models can replace different components of a control system. We'll see some examples of this as we take a look at different applications of ROM.

      One of the reasons Simulink customers use ROM is to enable simulation of third-party FEA, FEM, or CFD models in Simulink, including hardware in the loop testing. In this scenario, as we just discussed, we can replace detailed high-fidelity models for one or more components with reduced order models. ROMs are also useful for hardware in the loop testing, as they allow real-time simulations.

      Engineers can create ROM representing the physical components of the system, which can run on a real-time machine for testing of the control algorithm on embedded hardware. Another application area of ROM is virtual sensor modeling. You can use your high fidelity model to create a ROM which you can use as a virtual sensor for measuring internal signals of interest. For example, our full-order jet engine blade model can predict the temperature of the blade. We could put fast reduced order model into our controller so that this reduced model can predict blade temperature in real-time in the embedded system.

      Another application of is control design. For example, nonlinear model predictive control requires an internal prediction model of the plant that needs to be evaluated very fast on the embedded system. We can use reduced order model as such an internal prediction model. One more application of ROM is digital twins. You might have a system consisting of detailed models of different components, which you might be interested in updating periodically to function as digital twins of your assets.

      To make these models more suitable for periodic updates that can be computed in a short amount of time, you can create reduced order models. Now that we've seen different applications of ROM, next, we'll discuss different methods for creating reduced order models. We're going to highlight some of these methods along with the relevant tools that you can use to create ROMs.

      One of these methods is data-driven modeling. To develop a data-driven ROM, you collect input/output data from a high-fidelity first principles model. To collect input/output data that covers the design space, you can use design of experiments.

      This data is then used to train a model using deep learning techniques, such as LSTM and neural ODE or system identification and machine learning techniques such as non-linear rx model, with non-linearity represented by a Gaussian process. In addition to creating dynamic reduce models, you can also develop static ROMs. One way to do so is surface mapping, which lets you create a static reduce model from a detailed transient model by approximating the steady state behavior of the system. Techniques such as curve fitting and lookup table tuning are useful for creating static ROMs.

      Another technique for building ROMs is to use model-based methods that rely on meshing FEA models to extract state space representation that can be used for system-level simulation and control design. One example of a tool that uses such model-based methods is flexible body model builder app that is available with Simscape Multibody. Another way to create a ROM is to use linearization based techniques. If you're working with a non-linear Simulink model, you can linearize it at an operating point, reduce the number of states, and use that linear model in the vicinity of the operating point to speed up simulations.

      You can also linearize nonlinear model at several operating points to create a linear parameter varying model that you can use to simulate the system across multiple operating conditions. One of the ROM methods is physics-based reduction. You can model systems at different levels of fidelity by using different components available in Simulink and Simscape Electrical.

      Choosing the right level of fidelity lets you model system behavior at the desired time scale. For example, if you want to improve simulation speed of a high-fidelity power converter model that uses ideal switching, you can replace the converter with an average value model. Similarly, you can model electric motors at different levels of fidelity.

      For example, you can create a detailed PMSM motor drive model you see on the left, or you can use the motor and drive block from Simscape Electrical to create a reduced order model of the PMSM motor drive system. One tool you can use to improve the accuracy of your reduced models is Simulink Design Optimization, which lets you optimize parameters of the reduced model to better match the behavior of the original high-fidelity model. In this video, we've discussed what reduced order modeling is, why engineers use it, different applications of ROM, and different methods for creating ROMs. In the next video, we will focus on one of these methods, the data-driven modeling, and show you how you can create a ROM using machine-learning-based system identification.