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
There are many design exploration applications where it is important for performance results to match a certain range of values, whether it be from experimental sources or ideal goals. For example, curves for engine torque vs rpm, bushing deflection vs load, or wing lift vs the angle of attack. Quite often though, the baseline curve data can include fluctuations which makes curve fitting more challenging. There can also be portions of the curve where it is far more important that there be a close fit.
Figure 1. Sample Baseline Curves
To tackle these challenges and to also streamline the curve creation, HEEDS 2016.04 contains additional curve tools to ensure better results alignment. There are now added abilities to:
- Weight curve ranges
- Normalize RMS values
- Simplify imported curve data selection
Let’s review these capabilities in detail to show how they can help. Continue reading
Highlighting a Few New Features that Help You Discover Better Designs, Faster
Often, improvements to the simplest things can have a big impact on your daily tasks. There are many tasks we perform repeatedly when working with HEEDS, and streamlining those saves time and reduces effort. HEEDS 2015.11 contains many enhancements focused on simplifying workflows and I want to highlight a few that help in exploring design performance relationships.
To explore relationships between variables and responses in detail, you typically require multiple plots of the same type, but with different variables to gain a clearer understanding of dependency or influence. However, there are many plot features that are tailored to suit the particular way you want to view the results such as axis scales, data symbols, curves styles, title fonts, and so on.
To avoid having to create a new plot from scratch and redefine all these settings, you can now right click and select the Copy Plot option. This makes an exact copy of the existing plot, with all the customization. You then just need to alter the variables or responses being displayed saving a lot of setup time.
Figure 1. Make a copy of an existing plot with a single right click option
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
There are a lot of great tools in HEEDS to help you gain insight into finding the best design. One area of enhancements in HEEDS 2015.11 focused on parallel plots. In this article, we’ll highlight some ways to use new features of parallel plots in HEEDS to discover better designs, faster.
Parallel plot background
To help show the new capabilities in the context of an engineering problem, let’s look at exploring shape options for a human powered vehicle. There are obviously many dimensions that can be adjusted to improve the design.
Figure 1. Possible parameters to change for a Human Powered Vehicle
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?
Engineering design processes are not always single stream processes. There are times, especially in complex workflows, when the process execution needs to be modified (branched) based on the results of upstream events.
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