# Design Sensitivity Analysis

Design sensitivity represents a change in response with respect to a change in a design variable, which is typically used for optimization.

Design sensitivity can also be used as a diagnostic tool to understand what components in the system (through associated properties referenced by design variables) have controlling influence on the response in question.

Traditionally, design sensitivity can be cumbersome to request for frequency response analysis. It can only be requested as a part of an optimization run, where multiple design responses have to be created for each frequency response at each analysis frequency; objective function and constraints have to be defined and set in specific ways to force sensitivity output at all analysis frequencies for all design variables. In addition, design sensitivity is typically not output like typical frequency response results - not as complex values, not all analysis frequencies, and not in typical frequency response result output formats, such as H3D or punch.

To improve the usability of Design Sensitivity Analysis for frequency response analysis, a simplified design sensitivity request has been implemented in OptiStruct. The Design Sensitivity Analysis request can be used in a regular frequency response analysis where only design variables need to be specified using the DESVAR cards. The Design Sensitivity Analysis output is in complex values at all analysis frequencies into a .h3d file.

Design sensitivity is defined as a response change per unit design variable change. In this form, the output is highly dependent on the design variable value. For example, a typical panel thickness variable is in the order of 1 mm, which is different by orders of magnitude when compared to a typical bushing stiffness of 1500 N/mm, or a typical mass density of 7.9E-9 mg/mm3. As a result, if design variables are directly related to the property values without any scaling, a unit change in these design variables has a radically different meaning: doubling the panel thickness, a miniscule 0.15% change in the bushing stiffness, and a billion-fold increase in the mass density. This makes it impossible to rank the relative sensitivity of these design variables.

A much more balanced way to compare sensitivities of the underlying properties is to compare them on the common percentage change basis. In the previously cited example, sensitivities can be reasonably ranked on the basis of doubling in all three properties: panel thickness, bushing stiffness, and mass density. For this reason, the NVH Design Sensitivity Analysis utility converts all design sensitivities to a form of response change per doubling of underlying properties, regardless of how the design variables are related to the properties, before they are ranked and plotted.

In HyperGraph, the NVH Design Sensitivity Analysis utility allows you to plot and rank design sensitivity curves from an OptiStruct dsa.0.h3d file. This output can be requested by adding the OUTPUT,H3DSENS,OPT4 card to an optimization solver deck. This option forces design sensitivity output in the complex value format at all analysis frequencies.