# Data Analysis

### Data Analysis¶

#### Properties¶

By clicking on the Properties rubric, statistical characteristics are pointed out, such as:

- number of cells in the region
- sum, average, variance, standard deviation, minimum and maximum of values

###### Figure 1¶

Figure 1: Statistical property view

The dataset, region of interest and property presentation mode are set by

`Window`

Here the dataset about which statistical information are given is defined.`Region`

Choosing the visible area of interest. So if the whole dataset shell be watched, or only a limited version of the dataset. In case of zooming there is no difference in the image section because the currently visible region will tally with the zooming region.`Timesteps and display mode`

Additionally to the view in Figure 1, the properties like average values, etc., can be listed in a table or displayed as a diagram for all time steps. The table or graph can also be exported as tabular data in a text file.

The histogram data view shows the value distribution for the current time step.

#### Operations¶

As a prerequisite for the `Operations`

tool, there has to be selected or also created a window on which the operations are applied. Here, also more than one dataset can be selected by pressing the `Plus`

button. In this way the number of utilized datasets will be increased. The dataset, which should be manipulated, needs then to be specified by selecting the utilized datasets explicitly. The maximum number of possible datasets is 22 (single small letters used as variable names).

Basically, this function comprises a mathematical variation of a dataset. To each dataset belongs a parameter appearing as a letter. This parameter serves for a comparison between several datasets and is used entering mathematical commands. For example it can be squared. Clicking on `Help`

and then on `Command reference`

leads to an online list of possible calculations, which can be realized using DP MICRESS. It is important to know that these applications do not only consist of simple mathematical modules but also of mathematical functions like sine function or like connections from the field of logics.

The letters x,y,z, and t are not part of a possible parameter selection since they are already unambiguously defined variable names for the cell’s coordinates [millimeter] and time [s].

On the field 'File' the created operations can be exported by selecting 'Save' or imported into another data file by selecting 'Load'.

It is possible to watch the same data file from different time step perspectives: So the past in respect of the current time step, are negative values, the future is revealed hence by positive values.

Operations are evaluated cell by cell without taking the spacing into account (compare grid is `Cell based`

). This is a usual setting when operating on datasets with the same spacing. In the `scale based' mode, the spacing is multiplied to the cell coordinate. It is slower but different geometries can be handled.

The `Sub pixel rendering`

mode averages the participating cell values for each pixel in the resulting image. The default view shows the nearest cell value. It can be observed when opening e.g. a phase field data set with more cells than the screen resolution can show. The interfaces will not be shown as solid lines anymore.

The operation for comparing two datasets can be set up via the main menu `Compare datasets`

.

#### Show vectors¶

This tool is especially applied when working with vector files, i.e. files which contain one component of a vector each. For example in Figure 2, the X and Z components of the flow velocity (stored in the files vxCV and vzCV) are visualized as arrows in the fraction field. In this case, the length of the arrow indicates the vector length as a measure of the velocity strength (see next section ‘Vector Settings’).

###### Figure 2¶

Figure 2: The laminar flow visualized in the faction field

Settings | Image |
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#### Vector settings¶

The visualization density of the vectors can be configured by the 'Grid size', e.g. drawing a vector every 25 pixel.

Cutoffs filter the shown vectors by length. Vector being shorter or longer than the set cutoffs in pixel are filtered out.

There are two visualization modes available. Using the `arrow`

mode, the length of the visualized vector is corresponding to numerical vector length. The `lines`

mode is intended to show the trace of a flow. The cutoff limits are still applied but all lines have the same length.

###### Figure 3¶

Figure 3: The trace of the laminar flow shown in the fraction field

Settings | Image |
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#### Isoline settings¶

Isolines refer on areas, in which the same values prevail. So, in DP_MICRESS they reveal for example consistent concentration values or 0.5 phase fraction line as a representative of the diffuse interface.

It is possible to draw multiple isolines in one data set window. The respective iso value for each line can be chosen manually or by calculating an equidistant value for the currently displayed area of the data set by `normalize`

.

The 'Window/dataset relation' allows to define in which window an isoline of the used dataset should be drawn. A variation in this relation enables for example a 0.5 phase fraction isoline in a concentration field. In Figure 4.8, a 0.5 percent isoline will be drawn in the first window 'Delta_Gamm.conc2' using the dataset of the second concentration because this is the content of the current window.

`Line width`

and `Background transparency`

define common properties for all line. The coloring of each line can be set by the squared buttons beside the iso value. The left one defines the inner color of the line, the right the color of a thin border of the line.

`Preserve timesteps`

enables a multiline plot over time, i.e. while stepping through the time steps, already drawn lines will be preserved.

#### Morpology analysis (work in progress)¶

This tool provides a begin of a morphology analysis. It identifies areas in a result array which have one common property, i.e. values in a given range. These areas are counted, the surface (3D) or perimeter (2D), and the volume (3D) or surface (2D) are calculated and presented as a table. Additionally, surfaces of these areas can be exported as an STL files for further processing, e.g. to generate an FE volume mesh.

###### Figure 4¶

FCC fractions from example A002_AlCu_Temp1d

The analysis takes one result field into account which can be chosen by the `Window`

pull down menu (see Figure 5). Be aware that all time steps of the loaded result will be evaluated. It is recommended to reduce large data sets with the data export in the file menu before using the morphology analysis.

The **Region** choice is limited to the complete dataset at the moment, but will be enhanced to the zoomed areas in future.

`2D`

or `3D`

will determine the analysis algorithm to be used. In fact, 2D results can be handled by the 3D algorithm as 1 voxel layer, too.

The `minimum`

and `maximum values`

determine the value range of the area regions of interest. In Figure 5 for example, 0.5 indicates the middle of the interface between FCC phase and liquid.

The `Show minimum cells`

filter can be used to filter out smaller areas. Only areas which cover this minimum number of cells or more will be evaluated.

In 3D, the region can be set `fixed`

or `periodic`

. If the region is interpreted in a periodic way, areas ending at one side can continue at the opposite side. Such areas will be regarded as two separate areas in the fixed mode.

Having `continuous`

data allows linear interpolation at the area boundaries which results in a smoother surface and a better estimation of surface and volume. Interpolation is switched off for `discontinuous`

data.

If the `STL file`

option is enabled, the found area surfaces will be written as triangular elements to an STL file. Each time step will be written in a separate file and the resulting series of STL files can be easily visualized other viewers, e.g. Paraview. Volume mesher software packages can be used to generate a finite element volume mesh from this STL surface export, too.

###### Figure 5¶

Area identification of grains with phase FCC in 2D using the 0.5 contour

Settings | Results |
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The `Update`

button starts the evaluation. This may take some time depending on the number of time steps and the size of the RVE.

A resulting table shows all identified areas separately for each time step with the number of covered cells, the perimeter or surface, and the enclosed surface or volume. This table can be exported as a comma separated file for further evaluation.

#### Segregation analysis¶

This tool offers a segregation analysis of the concentration taking one component into account without knowledge about the other components of an alloy (see an example in Figure 6).

Each line in the segregation diagram represents one analysed `dataset`

, e.g. carbon concentration, at a chosen `time step`

.

`StepX, step Y, step Z,`

and an `offset`

define a regular analysis grid, i.e. values of voxel/pixel in an interval of size `StepX/Y/Z`

will be analysed. The offset can be used to translate this grid to another origin. For example, an offset of 5 and steps of 10 cells mean that the first data point is taken from the coordinate (5,5,5), next (15,5,5), etc.

The `Copy`

button allows to add new analysis configurations, i.e. add a line to the diagram.

`Apply`

starts the analysis.

`Close`

removes a configuration.

The concentration values at the nodes of the grid defined in the configuration sorted and plotted in an ascending order along the cumulative distribution (see segregation plot in Figure 6).

###### Figure 6¶

Cumulative distribution of carbon in the T016_GammaAlphaCementite example at time step 21

Carbon Concentration | Segregation Plot |
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