Beyond Optimum: Getting the Best from Simulation & Design Optimisation

Key Stages of Optimisation

Let’s take a simple model and apply optimisation to it in MSC Nastran.

• We can define design variables and assign them to all sorts of parameters in a model – shell thickness, fibre orientation, elastic modulus, beam diameter etc.

• We then set an objective – commonly minimising mass – and constraints on the design such as maximum deflection or modal frequency targets.

• With all this defined, Nastran runs the load case(s) and then computes the sensitivity of the responses to variation in the design variables, modifying the model towards the objective.

This process is iterated until convergence is achieved or it reaches the point where it cannot improve the design any further.

Optimisation Visualised

It's not easy to visualise optimisation, but the best illustration I’ve heard describes the design space as a field.

In this case, your initial design is at location X and elevation represents your objective - so going downhill represents making the design lighter.

Now, let’s give X some sentience.

X looks around it and works out which is the steepest descent - the blue line - and follows it for a bit, checking and redirecting as it goes.

When it reaches the point where either no further downhill progression is possible or progression would violate a constraint, it stops and declares this the optimum point in the field.

In practice, with anything more than trivial examples we have the problem of local minima to contend with.

To update our visual representation, the field is now full of potholes.

Now, as X wanders downhill, it might drop into a pothole.

Every direction from within is uphill (making the design heavier), so it decides it’s reached the optimum, but we can clearly see other points in the field are lower, and they may also meet the constraints set.

Navigating Multiple ‘Optimum’ Solutions

So what can we do about this?

To push the analogy further, we can try starting from different places in the field.

Our path will now be determined by the local ‘geography’ and could result in a better ‘optimum’ than our original start point.

You can take a brute force approach of trying as many start points in the field as possible and optimising from there, and then compare all the end points from all the start points to see which is lowest… but in practice, this could generate thousands and thousands of jobs and take an immense amount of time to solve.

How Global Optimisation Identifies Optimum Designs

In MSC Nastran we have a Multi-Opt toolkit that offers us a smarter solution.

The Global Optimisation module of Multi-opt is designed to address this problem of local minima in the design space. It achieves this in two steps:

1. Initially, it uses Design of Experiments techniques to intelligently sample the whole design space to reduce the number of locations within which local searches are subsequently made.
2. The reduced design space is then sampled. The basic rule used is that, after each pass, it moves on to sample in the region the furthest distance from the previous best outcome location to avoid wasted solution time that results from repeatedly ending up at the same place from multiple nearby start points.

It sounds complicated, but in practice it is very easy to use.

Global Optimisation, or GO, uses a simple xml file to set the parameters of your search.

There are very few parameters required, and the defaults appear to give pretty good results from the testing I’ve done.

The Multi-Opt toolkit is called from the xml file as the input, and off it goes! There are still a fair number of jobs to be run, but if you have multiple Nastran licenses, or sufficient MSC One tokens it can run the jobs in parallel blocks to reduce the elapsed time.

Global Optimisation in Action

So let’s look at another simple example with a flat laminated panel.

Optimisation is required to develop ply definitions in two different materials to achieve some modal frequency goals.

Each element has its own property set of four layers and each layer of each element has a design variable controlling the thickness for a total of 960 design variables.

The baseline model has a nominal 0.1 mm thickness for each layer, which gave us the first mode at 3.6Hz.

We asked Nastran to design this part to minimise the mass while obtaining a minimum of 20Hz for the first mode. From the baseline condition, Nastran came up with a concept that had a total mass of 614g.

We then submitted this to the global optimiser using the default input values.

It ran 53 jobs for the initial sampling, then 503 more for the detailed local searches.

Of these 500, there were 9 that returned a feasible design (i.e. it met the constraints) and had a lower mass than the baseline.

The lowest mass solution had a mass of 394g - 35% lower than our first optimum!

It doesn’t take much imagination to realise that there are possibly even better solutions in this design space, which we could track down by increasing the allowed number of runs from the 500 default.

Running 5000 jobs achieves a mass of 359g for example, a further 5% improvement.

Save Time with TriMech Simulation Solutions

It is true that running hundreds or thousands of optimisation jobs isn’t a quick process, but it is a technique that could get you stronger, and more effective designs.

Even if you don’t use it, it’s helpful to know that an optimiser doesn’t always give you the optimum design, unless you are very skilled at positing the right problem in the first place.

Our team at TriMech Simulation Solutions has a wealth of experience with design optimisation and MSC Nastran, and are very well placed to assist you with any optimisation needs.

Please get in touch if you have a problem you’d like to discuss and, if you want more details on the global optimisation technique, you can read the original paper on which it is based.