Total increment

The Total Increment Function Plot visualizes the influence of a selected interaction. This helps to better understand the influence of the interaction effects and statistics/physics in the problem. Contrary, the total increment shows the behaviour of the function, where all the other variables are held at their nominal value (nominal design). However, in contrast to standard visualization, the increments are additive and therefore, one can easily point the direction of future development. For example, considering total increment $dF_{1.2}$ and $dF_{3.4}$, one can define the best direction for variables $X_1$, $X_2$, $X_3$ and $X_4$.

Theory behind

From the mathematical perspective, the total increment function is defined as a sum of all lower-order increment functions. Variables, which are not part of the total order increment are set to their nominal value (nominal design). To explain it more clearly, let us consider the nominal sample to be $X={1,2,3}$ and the function of interest is $F(x_1,x_2,x_3)$. We want to visualize total increment function $dF_{1.2}(x_1,x_2)$ than the equation reads: $dF_{1.2}(x_1,x_2)=df_{1.2}(x_1,x_2)+df_1(x_1)+df_2(x_2)$ where $df_{1.2}(x_1,x_2)$ is the increment function for the interaction of variables $X_1$ and $X_2$, $df_1(x_1)$ is the increment function for variable $X_1$ and $df_2(x_2)$ is the increment function for variable $x_2$. A deeper explanation of the increment function is provided in the Increment function plot.

How to use the interface

There is a collapsible box on the left side of the tab with the opened result file, where the user can set the data to be displayed. Increment and Total increment buttons on the top switch between these two sub-features. Under these buttons, there is a list of total increment functions of the mathematical model. Items of the list are clickable to select the total increment function to be displayed.

Figure 1: Total Increment Function Plot - Interaction of three variables

The type of the plot may vary depending on the order of the total increment functions. It is possible to show functions with up to three interacting input variables. Second-order functions have the form of a surface, where the total increment function value is also represented by the color of its fill. Coloring is the only way the function value is shown for third-order total increment functions (sum of interactions of three input variables). 3D plots can be rotated while holding the right mouse button and zoomed with the mouse wheel.

Left-clicking into the plot shows coordinates and corresponding total increment value in the plot. Function values of samples used as the source to build the model are highlighted in magenta. Exact values are available through the table shown on the Details of samples button. It shows values of input variables corresponding to the currently selected total increment function and the value of the total increment to the final model. Note that all other input variables are considered to be coordinates of the nominal sample. The table can be saved into a .csv file using the Export points to CSV button.

To export the plot as a .png or .jpg file, the save-file dialogue can be induced by clicking the 💾 icon on the top left of the plot. It is possible to adjust the appearance of the plot using controls from the Plot options section of the panel on the left. The list of controls currently available may vary according to the selected increment function:

• Plot title : Displayed above the plot, contains increment function designation by default.

• X label : Label of the X axis, by default name of the first input variable involved in the selected increment function.

• Y label : Label of the Y axis, output by default or name of the second input variable involved in the selected increment function of higher-order.

• Z label : Label of the Z axis, output by default or name of the third input variable involved in the selected increment function of higher-order.

• W label : Label of the colorbar/increment value scale, output by default.

• Title size : Size of the title font.

• Label size : Size of the label font.

• Show legend : Switching on/off the legend of the plot/the colorbar scale.

• Legend font size : Size of the legend font.

• Color style : Selection menu setting the colormap of input variable values.

• Orthographic proj. : Switch between orthographic (on) and perspective (off) projection of 3D plot.

• Color style : Selection menu setting the colormap of input variable values.

• Points count : Density of data along an axis for plot rendering. Confirmed with Apply button.

• Show samples : Switch on/off source data points of the mathematical model.

• Range X : Double-sided slider allowing to show a slice of the data in detail. Dragging one of the slider's points limits the depicted range of input variable value, one can move with the section along the X-axis by dragging the green bar of the slider (both edge points are highlighted).

• Range Y : Double-sided slider allowing to show a slice of the data in detail. Dragging one of the slider's points limits the depicted range of output value, one can move with the section along the range of the output by dragging the green bar of the slider (both edge points are highlighted). In the case of 2nd order increment function limits values of the input variable along the Y-axis.

• Range Z : Double-sided slider allowing to show a slice of the data in detail. Dragging one of the slider's points limits the depicted range of output value, one can move with the section along the range of the output by dragging the green bar of the slider (both edge points are highlighted). In case the of 3rd order increment function limits values of the input variable along the Z-axis.

• Range W : Double-sided slider allowing to show a slice of the data in detail. Dragging one of the slider's points limits the depicted range of output value, one can move with the section along the range of the output by dragging the green bar of the slider (both edge points are highlighted).

  All ranges in the plot can be also precisely using the ⚙ icon on the right of each slider. This opens a sub-dialogue with entry fields for writing exact values of range limits. These need to be confirmed with the Set button. Setting values outside domain's boundaries will reset range limits to the default state.

• Adjust axes : Toggle if the axis and/or colorbar limits of the plot should be only the range adjusted with the slider above (on) or the full range of the input distribution (off).

• Scale : Adjust the range of increment function value abscissa accordingly to the range of the given problem. The same range of function values is applied for all increment functions.

Figure 2: Total Increment Function Plot - Plot Options