Curve-Fitting

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.

Figure 1. The difference between a target curve and a design curve is minimized in a curve fitting optimization problem.

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Using Variable Resolution to Enhance Design Space Exploration

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?

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Using Semi-Independent Variables to Generate More Feasible Designs and Improve Search Process

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 + t= T                                                                                (1)

Figure 1. A three-layer laminated composite plate

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HEEDS MDO 2015: Compute Resources Set

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

HEEDS MDO 2015: Logic in Process Definition

LogicThe 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

Series Hybrid vs. Parallel Hybrid

Hybrid refers to something that is made up of two or more diverse ingredients. The goal in combining them is to capture and merge the advantages of each ingredient, while overcoming any disadvantages. But ingredients can be combined in many ways, resulting in considerable variation in performance depending on how they are combined.

In optimization search algorithms, as with electric vehicles, there are two main categories of hybrids: series and parallel. To better understand the basic differences between the series and parallel hybrid approaches, let’s consider a simple illustration.
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Collaborative Optimization

collaborative optimizationMany engineers still resist the use of optimization algorithms to help improve their designs. Perhaps they feel that their hard-earned intuition is just too important to the solution process. In many cases, they are right.

At the same time, most optimization algorithms still refuse to accept input from engineers to help guide their mathematical search. The assumption is that the human brain cannot possibly decipher complex relationships among multiple system responses that depend upon large numbers of connected variables. Unfortunately, this is true.  Continue reading