romAI: generation of a dynamic Reduced-Order Model (ROM) using AI for linear actuators
Altair EmployeeAbstract
In this article, we describe how romAITM can help to generate an efficient and accurate Reduced-Order Model (ROM) of a linear actuator. For the purpose, we start from few transient electromagnetic simulations performed with Altair® Flux®. In the study we also compare 3 different modeling approaches: Look-up tables (LuTs), romAI and FE analyses.
Introduction
ROMs are models which allow to drastically reduce the simulation run time while keeping a good accuracy on the results under interest.
Nowadays, ROMs are widely used in many domains: Digital Twins, Optimizations, Real-Time Simulators just to mention a few.
The romAI application allows the creation of dynamic or static ROMs either linear or non-linear.
In this study, we model the behavior of a linear actuator system during the closing phase.
We will compare different approaches: look-up tables, romAI and FE model in terms of current in the coil and plunger movement (displacement and velocity).
Below, the figure shows the 3 approaches reported in order of increased accuracy going from the top to the bottom.
The look-up tables approach uses magneto-static tables exported by Flux through static analyses. This approach provides accurate results during static or quasi-static scenarios (low velocity of the plunger) but it doesn’t take into account the effect of the eddy currents and so could be not suited in transient situations where the plunger moves with higher velocities.
romAI approach instead, is generated from transient analyses in Flux and considers the non-linearities due to the eddy currents, hence, it is suited for transient scenarios.
Results from Flux simulations provide the most detailed output and represent our reference in the comparison.
Initial data set for the training
We want to explore the behavior of the linear actuator when we apply in input different voltages (different operative conditions) and we have different spring stiffness (different design).
As we deal with a non-linear system, it is convenient to vary these quantities on at least 3 levels.
The below image shows the 9 transient simulations (marked with a x symbol) performed to generate the needed data. In addition, we ran also 3 extra simulations to test the generalization capabilities of romAI within and outside the training domain.
Each simulation generates thousands of valid training instances that can be used during the training process. All the 9 simulations are appended in the same csv file used by the romAI application.
The video shows how in the romAI GUI we can pre-process the data, build the non-linear dynamic ROM and evaluate its accuracy without any coding. It also shows how we can easily reuse the generated ROM into a system simulation environment (Altair® Activate®). Input for the ROM are: Voltage, displacement and velocity of the plunger. The output is the current in the coil and the electromagnetic force acting on the plunger. The state of the system is the current in the coil (defined also as output).
First Results
Results on training data
Below, we report a comparison in terms of coil current, displacement and velocity of the plunger for the different values of voltage and stiffness. In blue, red and green we have the results obtained respectively with romAI, Flux and Look-up tables approaches.
- romAI provides better results than the look-up table approach, very close to Flux results
- Each simulation lasts less than 1s
Results on test data
- romAI generalizes well when the voltage in input is >16V
- romAI loses accuracy when voltage in input is <16V, in this range due to the spring the response of the system shows higher variability and there is the need of more data for a better system estimation
Improved data set for the training
In order to improve the generalization capability of the ROM we decided to add 3 additional simulations to the initial data set to better cover the range where the system response presents the higher variability.
New Results
Results on test data
- Now romAI generalizes well even when voltage in input is <16V
- This is true both within and outside the training set domain
Conclusions
Evaluation on accuracy
- romAI approach allows an accurate reduced-order modeling of the Flux model
- If compared with the LuTs approach, romAI allows to take into account the effect of the eddy currents on the system response providing more accurate results
- In order to get accurate results, it is important to increase the number of simulations used for the training in the range where the system shows a higher response variability (V<16)
- The approach shows a very good generalization capability both within and outside the training domain
Evaluation on simulation run time
- If compared with the LuTs approach, romAI simulations has a similar run time
- If compared with the FE approach (Flux), romAI approach allows much faster simulations while keeping a good accuracy. It enables reducing significantly the time you need to simulate various system configurations, as far as the actuator remains the same.