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
This new feature provides the ability to treat multiple computer resources as a single resource, without a job queuing system, to parallelize your HEEDS study. It allows for tremendous flexibility in the use and management of disparate computer resources.
As the name suggests, a compute resource set is a set of previously defined compute resources in HEEDS. The set allows you to define a pool of hardware resources that can be used to parallelize one or more analyses in the HEEDS study. The definition is not limited to homogeneous resources but can include any type of compute resource available. For example, a resource set could be a set of Windows workstations (as shown in the example image below), a set of Windows and Linux workstations, some workstations along with a cluster, several different clusters, etc. During the run, HEEDS will manage the job submissions to the resources defined in the set to make sure they are used effectively. Continue reading
The analysis definition process has been upgraded to streamline the definition. The new design facilitates data reuse, simplifies the definition steps and results in a reduced setup time. All the information related to communication with different compute resources has been removed from the analysis setup and moved into its own section.
The process definition now provides support for the use of logic to drive the flow in the analysis process. One or more conditions can be defined at the analysis level to control whether an analysis will be attempted. Several scenarios that would have required specialized external scripts to capture the desired process behavior are now easily handled with this feature. Some of these scenarios are listed below:
- Improve efficiency in the evaluation process by skipping compute intensive analyses when it is clear that the design would not be acceptable
- Continue execution of the process even when some of the analyses result in errors
- Use of an appropriate physics model based on the results of an upstream analysis Continue reading
The calculator functionality in HEEDS MDO has been redeveloped using Python. The new calculator implementation provides significant enhancements over the previous releases. These new enhancements allow you to setup complex formulas with ease without requiring use of an external script or tool. Continue reading
Recent advances in process automation and optimization search technology have made it easier than ever to perform automated design studies and discover innovative solutions. But we still have to define the problem we want to solve and then decide how to represent that problem in our models. These two tasks are sometimes challenging, and they rely heavily on experience and intuition. In this article, as well as some future ones, we will share some of our experience in defining and representing various types of optimization problems. Hopefully you will find some of these techniques useful in your applications.
A common design scenario is to optimize the number and location of certain design features to satisfy performance goals and requirements. For the sake of discussion, let’s consider a specific example of this type of problem. Continue reading