Intuition plays a critical role in all stages of a design exploration study, from defining the problem statement to building the simulation model to interpreting the results. But what about the search process itself? Should we make design improvements based on intuition, or should we allow a mathematical search engine to explore the design space for better designs? The answer is both. We call this shared process collaborative design exploration.
The SHERPA search strategy allows you to inject your design ideas before and during an exploration study. Before you start a study, you can seed it with multiple ideas (in the form of actual designs) that might help SHERPA to locate productive regions of the design space more quickly, thus speeding up the overall search. For example, in addition to the baseline design, you might consider seeding the study with other potentially good designs that:
- you have investigated or produced in the past
- your competitors have used
- are feasible, but perhaps not optimal
- are high performing relative to one or more criteria, but not all of them
- have some desirable features, but don’t necessarily perform well
- you have a hunch may work well
- are from a previous HEEDS MDO study
One or more of these injected ideas might contribute to a more efficient search, while the cost of doing this is only the time to enter the variable values that define each of the designs. SHERPA will evaluate the injected designs when the search process is launched, so there is no need to simulate them before injection. Continue reading
Design sensitivities are a measure of how much an objective or constraint response varies due to a small change in a design variable. Based on this definition, they are sometimes referred to as sensitivity derivatives. Let’s discuss how to use them properly, as well as how not to use them.
First, note that the design sensitivities we refer to here are calculated for a particular design, not for a design space. Statistical methods of sensitivity analysis can provide useful information about a design space, but not the type of information we seek here.
Since a design represents a point in the design space, it is clear that sensitivities are defined at a point, as are mathematical derivatives. Two distinct designs within a design space will probably have different sensitivities unless the design space is linear, which is seldom the case for engineering problems. Continue reading
If a valid license is not available for any of your modeling and simulation software during a HEEDS study, the default response is for that design to be classified as an error design. But this behavior can be modified using a pre-analysis command to check for the availability of a license before HEEDS launches each analysis. This simple process can help to avoid many such error designs, making your exploration studies more effective. Let’s review how to do this for FLEXlm based licenses.
We all feel the “need for speed” when trying to find better design solutions through simulation. What can we do to speed up our design exploration studies? Let’s discuss all the options here, including one that may not be obvious.
In a typical study, the total CPU time needed to perform a design exploration study is determined using this simple formula:
Sometimes we have more than one output response that needs to be either minimized or maximized, so we need some way to encourage multiple responses to be as small as possible or as large as possible at the same time. These are called multi-objective design exploration problems.
One of the most common reasons for using multiple objectives is to assess the trade-off between two or more competing responses. In other words, what is the cost to improve one response in terms of making another response worse? Continue reading
During a design exploration study, HEEDS makes many calls to your simulation model to evaluate potential designs. This means that your model needs to accurately predict design performance values (objectives and constraints) over a wide range of inputs (design variables). Most modern simulation models satisfy this requirement without difficulty.
But in some cases, it is too much to ask that a model be perfect for all combinations of variable values. For example:
- In a shape optimization problem, some combinations of shape parameter values might produce invalid geometries, making it impossible to generate a CAD model for those designs. Ideally, shape parameters should be defined in a way that ensures all geometries are valid, but that is not always a realistic expectation.
- Nonlinear or dynamic CAE models occasionally experience problems with convergence or other kinds of numerical errors. Hopefully your models are robust, but it is more difficult to predict the behavior of some designs than others, so numerical errors will occur now and then.
Of course there are many other reasons why a simulation model might terminate prematurely or predict incorrect results. Because many of these cases are unavoidable, HEEDS has been designed to be robust against these model failures. We refer to these as error designs. Continue reading
We often need for a design or a model to perform in a specified way. For example, the parameters in a nonlinear material model should be selected to best match the experimental stress-strain response. The geometrical parameters of a rubber bushing should be designed so that its force-deflection response matches the desired nonlinear stiffness behavior.
Optimization problems like these arise frequently. We refer to them as curve-fitting problems, because the goal is to minimize the difference between the specified target curve and the actual response curve
of our design or model.
Figure 1. The difference between a target curve and a design curve is minimized in a curve fitting optimization problem.
A nice feature in HEEDS is the ability to define the resolution of a continuous variable. Assigning a resolution to a continuous variable seems contradictory, as this essentially transforms the continuous variable into a discrete variable. We often refer to these as “discretized continuous variables,” and there are several advantages to representing variables this way in an optimization search. Let’s explore how you can use variable resolution to enhance your design studies.
What is a variable resolution?
Sometimes we intend for a set of design variables to be independent, but then realize that these variables need to satisfy a given relationship. How can a variable be both independent and dependent at the same time? We call these semi-independent variables.
Let’s illustrate this concept with two separate examples.
In our first example, the goal is to optimize the thickness of each layer in a three-layer laminated composite plate, as shown below. The thickness of the ith layer is ti. But the total thickness of the laminated plate must remain equal to a specified value T, so we have three design variables: t1, t2, t3 and a required relationship:
t1 + t2 + t3 = T (1)
Figure 1. A three-layer laminated composite plate
One of the challenges to finding optimal solutions is the coupling of variables. If we could change one variable at a time, the search process would be so much easier. But in most problems the variables are strongly coupled, so the best value for one variable depends on the values of many other variables.
Often, we have no control over this variable coupling, since it is inherent in the physics model that defines our objectives and constraints. In these cases, we need a powerful optimization search strategy like SHERPA to figure out the complexities of the design landscape and to produce an optimized solution.
But in some cases we make this task harder than it needs to be because of how we represent the problem. That is, sometimes the way we define the problem creates unnecessary coupling or increases the complexity of existing coupling among variables. This makes the optimization search harder, and may decrease the chance of finding the optimal solution within our limited optimization search budget. The good news is that we can often alleviate this situation with a different representation. Continue reading