Finding Optimal Designs in Multivariable Design spaces

With Computer Aided Engineering (CAE) software, multivariable optimizations have become a reality for model designs. Unfortunately, due to the complexity of designs, multivariable optimizations are impractical using traditional trend and hypothesis-based methods. These manual methods can miss peak designs as trends change due to variable interactions in the design space.

This is where automated CAE optimization software, like modeFRONTIER, comes in. modeFRONTIER is able to interact with various CAE software using communication and control nodes. Users set design of experiment (DOE) and optimization algorithms to govern the process until modeFRONTIER determines an optimal design.

Dr. Andrea Shestopalov, Application Manager at Exa Corporation explained, “modeFRONTIER works by having a DOE node and scheduler node. In the scheduler node the user selects an optimization algorithm.”

She added, “Genetic algorithms, like MOGA II or NSGA start with a population of candidates and sorts their performance based on a fitness function. The next set of candidates, or generation, are then decided based on the fitness function through three functions. Cross over, the first function, is like breeding, taking attributes of the best performing designs into a new design. Permutation, the next function, takes the best designs and tweaks them. The final function, mutation, changes a design randomly. Each operation then has a different probability of occurrence set by the user.”

Using modeFRONTIER, and its CFD software node for PowerFLOW, Dr. Shestopalov and her team were able to optimize the side mirror for a client with respect to aeroacoustics.

Optimizing Side Mirrors for Wind Noise Aeroacoustics

PowerFLOW Simulation of turbulent airflow.

The 3-D aeroacoustics and turbulent flow calculations were performed using Exa’s PowerFLOW software. modeFRONTIER was used to optimize the cabin wind noise acoustic levels by controlling PowerFLOW through a prepackaged control-node. Unlike other CFD solvers, PowerFLOW is based on Lattice Boltzmann Method (LBM) whereas solvers traditionally use the Navier-Stokes CFD equations.

“Our explicit solver is transient by nature and LBM achieves a very low dissipation compare to other methods based on Navier-Stokes” stated Dr. Franck Pérot, Sr. Director for Aeroacoustics at Exa. “The results we provide are very accurate and can be obtained on any complex geometries with competitive turnaround times. Since the method is also compressible, we capture in the same simulation the turbulent flow and its acoustics radiation that propagates in the calculation domain. We also offer the capability to predict the cabin noise levels in order to assess passenger comfort”

Design space variables that control the geometry morph.

Once the model is set up and the initial simulations are completed, the user must then define all the variables in the design space. These are the variables modeFRONTIER will control, via user defined algorithms, to optimize the design. In the case of the side mirror, they are as follows:

Mirror Housing: nose radius & channel face opening
Mirror Stalk: Stalk leading edge position & taper
Mirror Sail: Chord height
A-Pillar: Water channel gap height

Then allow modeFRONTIER access the model through the PowerFLOW node. Once access is achieved, set up a design variable table within modeFRONTIER. The design variable table should include the value ranges for each variable to ensure modeFRONTIER will remain within the design space for the DOE and optimization.

For the initial DOE, Dr. Shestopalov’s team used modeFRONTIER’s Incremental Space Filling (ISF) strategy. The algorithm is designed to optimally space the model variations throughout the design space. Dr. Shestopalov explained, “The first set of runs are used to build an initial response surface model (RSM). The ISF algorithm attempts to equally space these first runs to get the maximum amount of information on the response surface.”

The scheduler node for this project was then set to RSM-based adaptive sampling. The algorithm will reduce the need for more runs by creating an RSM and determining areas that have high probabilities for better results. This creates an efficient method for finding an optimal design.

Using the PowerFLOW node in modeFRONTIER, Shestopalov’s team was also able to set up parallel computing. In fact, depending on the high performance computer (HPC) set up, users can run up to 20 PowerFLOW simulations simultaneously, benefitting of a faster convergence to optimal designs and overcoming computational bottlenecks.

Validating the RSM and Results with One-off Cross Validation

Once an optimal design is found and modeFRONTIER calculates the RSM, the user must validate their results. The project team used modeFRONTIER’s one-off cross validation to verify their results. The process involves recreating the RSM with one less data point. The values of that data point are then estimated using the new RSM and the error is calculated between the estimated and actual result. The process is then repeated for each point and the program calculates a mean square error as a validation value.

“We waited until the end and our final data for the validation stage. This way we had more data points in the RSM to work with for the cross validation. This reduced the risk of eliminating an important run when redrawing each RSM. This could create a large sum of square error,” said Dr. Shestopalov.

Validation on this scale would be impractical without CAE software like modeFRONTIER.

Findings Demonstrates the Power of CAE Automated Optimizations

RSM show trends change closer to optima vs closer to baseline.

The final RSM results also express the importance of using CAE optimization software like modeFRONTIER. The RSMs frequently show that trends changed as the design moved closer to an optima in the design space. Therefore, interactions between the multiple variables must exist. Detecting these interactions would be difficult using classic hypothesis based methods.

For instance, it was discovered that although it was detrimental to increase the nose radius near the baseline, it was actually beneficial to increase the radius near the optimal design.

“Some trends around the baseline are opposite to the trends near optimal,” explained Dr. Shestopalov. “Global effects estimates are not consistent with trends across entire design space. If we just used wind tunnels and developed an optimal design based on one variable at a time we would have missed this interaction. We would have had a different answer than when we used simulation and the PowerFLOW node on modeFRONTIER,” expressed Dr. Shestopalov.

In the end, by optimizing the side mirror design, the team was able to reduce the cabin noise by just under one decibel. This is rather impressive for a late design change but could have been a larger improvement if the study were performed at an earlier stage allowing for larger changes to the design. Typically early stage improvements range in 3-5 decibels. By optimizing the rest of the car’s design, there is no telling how much cabin noise can be reduced using modeFRONTIER and its PowerFLOW node.

ESTECO has sponsored promotion of their PowerFLOW nodes on ENGINEERING.com. They have no editorial input to this post - all opinions are mine. Shawn Wasserman