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# Increment Function Plot

Increment function plot visualizes the influence of a selected increment function. This helps to search the domain of interest and fully understand the statistical aspects of a given problem. Based on the increment plots, the product can be improved or the research problem can be better understood. Moreover, each increment function shows a physical aspect of the problem, which can be used to set direction in future development.
Each increment function adds a separate increment to the final model, which can be visualized. Each increment is visualized considering other variables in their nominal values. In order to closely explain this approach, let us consider the nominal sample (nominal design) to be X = 1, 2, 3 and function of interest is F(x1, x2, x3). We want to visualize the increment function dF1, which represents the change of variable 1. The increment function plot is generated in the following way:

dF1(x1) = F(x1, 2, 3) – F(1, 2, 3)

NOTE: Increment function dF1 is 0 at its nominal value, e.g. dF1 = 0 with x1 = 1.

The higher order increment functions represent the increment for the interaction effects of a given problem, i.e. how the variables cooperate in order to influence the final problem, up to three dimensional functions. Each increment function of a higher order considers other variables at their nominal value. In order to explain it more clearly, let us consider the previously mentioned problem, yet this time, we want to visualize the second order increment function dF1.2(x1, x2). The equation to plot reads:

dF1.2(x1, x2) = F(x1, x2, 3) – F(1, 2, 3) – dF1(x1) – dF2(x2)

From the above equation, it is clearly seen that the plot considers only interaction itself. Therefore, large peaks in one of the corners of the domain represent an interesting point which should be investigated closely. Note that the increment function dF1.2 is 0 if one of the coordinates x1 or x2 is equal to the nominal value, e.g. dF1.2 = 0 with x1 = 1 or x2 = 2.

## How to use it: #

Select an increment function you want to plot and the algorithm automatically plots the selected increment function. In order to see the names of variables used to construct the increment function, one needs to put the mouse pointer over the button and description will pop up. Each marker in the plot represents a sample, which is used to create a given surrogate model. The scale of the graph is automatically adjusted to the size of the given increment.

### Switches: #

• Scale: Adjust the range of increment abscissa (Y for 1-D and Z for 2-D) accordingly to the range of given problem. This feature is useful if one wants to compare the influence of increment function.

Fig. 1: Increment function plot – interaction of three variables

### Buttons: #

• View Details of Points: Display table which shows all samples used in the creation of the increment function. The table contains coordinates of the sample for the graph and with a double click, the sample is highlighted. Also, with double click the full coordinates of the sample are shown next to the label ’Selected Sample:’. One can easily copy coordinates if it is required.
• Apply: Changes on the graph will take effect after pressing the apply button.

The graph is fully adjustable with options, where:

• Amount of Points for Axis: Density of data for plot rendering
• Total Points Rendered: Number of points rendered in plot (info only)
• Plot title: Title of the graph
• Title font: Font type and size of the plot title
• X Range: Restriction of range for X axis, toggle on/off
• Y Range: Restriction of range for Y axis, toggle on/off
• Function Color: Basic color of interpolating curve, toggle on/off
• Points Color: Color of computed sample, toggle on/off
• Legend Font: Font type and size of the legend, toggle on/off
• Axis Font: Font type and size of the plot axis
• X Axis Label: Label of X axis
• Y Axis Label: Label of Y axis
• Z Axis Label: Label of Z axis

NOTE: For the plot of increment function of three interacting variables, X Range and Y Range listed in Options do not apply due to practical reasons. In this case, they have been replaced with a panel showed under the plot. Here one can set a range for each variable (labelled axis).

Fig. 2: Increment function – options

### Print: #

To store selected results in File 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.