Sensitivity analysis – Increment

Sensitivity analysis tries to establish the influence of the input variable on the output of a mathematical model or system (numerical or otherwise). This is a crucial aspect when the sensitivity of a system to uncertain geometry, material properties, manufacturing tolerances, etc. needs to be determined. Based on the results of the sensitivity analysis, inputs important for the design can be focused on.

The sensitivity analysis is performed with Monte Carlo analysis applied directly to the final model and each increment function independently. Each increment function represents an independent contribution to the final statistics, where the first order increment functions (dF1, dF2 etc…) represent the independent contribution of given variable, i.e. how the variable alone influences the final problem. Higher order increment functions (dF1.2, dF1.3, dF2.3.4 etc…) represent the contribution of interaction effects, i.e. how the interaction between variables influences the final problem. However, higher order increment function represents only the pure interaction between variables, i.e. it does not take into account the independent contribution of a given variable. NOTE: Increment sensitivity only includes the influence of given sub-domain (increment function of a variable OR its interaction), while variable sensitivity takes into account all the aspects of a given variable (increment function of the variable AND ALL its interaction effects).
In this program, two sensitivities for an increment function are defined. The first sensitivity is the sensitivity of the mean value, which represents the influence of given increment function on the final expected value. In other words, how selected increment function influences the statistical expected value of the final output. The formula for the mean sensitivity estimation is:

where Sµk represents the sensitivity of mean for increment function k, ST stands for the set of all increment functions and µk represents the k-th increment function. The second sensitivity is the variance sensitivity, which represents the variable’s impact on the final output. Variable’s variance sensitivity is defined as follows:

where Sok represents the sensitivity of variance for increment function k, ST stands for the set of all increment functions and sigma2k represents the variance of k-th increment function. It should be noted that both sensitivities are normalized, thus, their sum equals to 1.

How to use it: #

Table under sets -> options refers to increment function which should be selected as a first in the visualization process. In order to show the sensitivity of a given increment function, one needs to tick the box belonging to the given increment function. Also, one can cycle through all increment functions using the buttons above the plot.

Fig. 1: Sensitivity analysis – Increment

Switches: #

  • Select: <increment>: Choose increment functions to be shown in the plot.
  • Text form: Sensitivities are shown as a table.

Buttons: #

  • Invert: Inversion of checked and unchecked tick boxes selected for the visualization.
  • Select all: Select all available variables.
  • Unselect all: Unselect all available variables.
  • Apply: Changes on the graph will take effect after pressing the apply button.

The graph is fully adjustable with Options, where:

  • Plot title: Title of the graph
  • Title font: Font type and size of the plot title
  • X Axis Label: Label of X axis
  • Y Axis Label: Label of Y axis
  • Axis Font: Font type and size of the plot axis
  • Legend Font: Font type and size of the plot title, toggle on/off
  • Mean sensitivity Color: Color of mean sensitivity bar, toggle on/off
  • Variance sensitivity Color: Color of variance sensitivity bar, toggle on/off

Fig. 2: Sensitivity analysis – Options

Print: #

To store selected results in File (upper left corner) select Save. It will allow you to browse in folders starting in the project folder. The code automatically selects the format to store visualized results.