In this video we'll discuss reduced order modeling, why
engineers use it, and highlight different techniques
for creating reduced order models
with MATLAB and Simulink.
Oftentimes engineers work with large-scale, high-fidelity
models for analysis and design of complex systems.
Simulations of these high-fidelity models
may take hours or even days to complete.
Reduced order modeling lets you simplify
a high-fidelity mathematical model
by reducing its computational complexity while preserving
the dominant behavior of the complex model.
Engineers use reduced order modeling
in different applications for various reasons.
One of the main reasons for using ROM
is to speed up system-level desktop
simulations of large-scale first-principles models.
In this scenario, we can replace detailed, high-fidelity models
for one or more components with reduced order models.
ROMs are also useful for running real-time simulations
for testing on 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.
Another application of ROM is digital twins.
You might have a system consisting
of detailed models of different components
which you might be interested to update 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.
There are various techniques for creating reduced order models.
We're going to highlight some of these methods,
along with the relevant tools you can use to create ROMs.
One of these methods is data-driven modeling.
To develop a data-driven ROM, design of experiments
is performed to collect input output
data from a high-fidelity first-principles model.
The input output data is then used
to train a model using deep learning
techniques such as LSTM and neural ODEs,
or system identification and machine learning techniques
such as nonlinear ARX model with nonlinear
to be represented by a Gaussian process.
In addition to creating dynamic reduced models
you can also develop static ROMs.
One way to do so is surface mapping
which lets you create a static reduced model
from a detailed transient model by approximating
the steady-state behavior of the system.
Techniques such as curve fitting and lookup tables
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 simulations and control design.
Another way for creating a ROM is
to use linearization based techniques.
If you're working with a nonlinear 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 timescale.
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.
One tool we 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 different applications
where engineers use reduced order
modeling 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 we can create a ROM using machine learning
based system identification.