While these capabilities can be used independently of the Monte Carlo simulation explored in the previous article, this example builds on the concepts in, and output of, that example.
Scenario
Pole Resilience vs Wind Speed (continued)
This example takes a set of observations from a Monte Carlo simulation and plots it as a cumulative distribution function (CDF).
While it's possible to view the observations as a list in a Neara report, it's not possible to easily intuit the distribution from a list of (for example) 1000 numbers.
Visualizing the plot as a CDF makes it easier to see the probability that the difference is negative (i.e., a pole was damaged) and the probabilities of various levels of damage.
Methodology
To plot a list of samples in this manner in Neara, use a collection (or report) with the x values to plot, plus any series to plot against the x axis.
It may be helpful to think of the x axis as a field on a collection, and likewise for any series to be plotted
A collection to store the fields
Start by creating a collection to store the fields.
The length of the collection should correspond to the number of values to be plotted.
This example will plot a histogram with 100 bins. Create a formula field under Model in the schema called u_n_bins with this formula:
100
See the note in Monte Carlo simulation for an explanation of why a formula, rather than Integer value, field is used in this case
Create an index on each pole to populate the x and y data. Create a field under Pole in the schema called u_cdf_index:
range(
model().u_n_bins
)
Create a field to represent the x values of the bins. The range of the x axis should be the smallest value of my random variable samples to their largest value. To get these, it's easiest to sort the random variable samples.
Create a field under Pole called u_sorted_composite_variable:
sort(
c_sample_index[].u_composite_random_variable
)
If you have a collection c with a field f, c[].f returns the f values of the collection as a list
To get the minimum and maximum values of the list, create two fields under Pole in the schema.
u_var_min:
index(
u_sorted_composite_variable,
0
)
u_var_max:
index(
u_sorted_composite_variable,
model().u_n_samples - 1
)
Lists in Neara are indexed starting at 0 and ending at 1 less than the length of the list
The bin values themselves should be evenly spaced throughout this range. It will be helpful to compute the spacing between bins. Create a new field under Pole in the schema called u_bin_spacing:
(u_var_max - u_var_min) / (model().u_n_bins - 1)
To create the x values on the index, create a new field under c_cdf_index in the schema called u_x:
self.pole.u_var_min + (cdf_index_item) * self.pole.u_bin_spacing
To create the y values recall that the (sample) CDF is the proportion of samples below a certain value. So, for each u_x, filter the list of samples for those less than u_x and report what percentage of the samples these represent.
Create a new field under Pole on the schema called u_y:
(
len(
filter(
self.pole.u_sorted_composite_variable,
self.pole.u_sorted_composite_variable <= u_x
)
)
/
model().u_n_samples
)
* 100
Create a custom report for the chart data source
Neara charts require that the values to be plotted are represented in a report. In this example, a custom report will be created to house the chart source data.
Click the (+) to the right of any group of tabs, and on the popup select Create custom report in the New report section.
When prompted, select Poles as the data source, and give the report a unique name, for example Composite Variable:
In the upper right corner of the report, click the settings (gear) icon to view the report configuration:
Add c_cdf_index after the Model > Poles > item in the Report Data setup:
Click the (x) to close the report configuration.
On the report table, scroll to the last column on the right, and click the Remove all columns icon:
This will clear the default columns from this report. Click the Add column icon in the empty report:
On the column configuration that appears, set the Field to u_x:
Add a second column, and set its Field to u_y.
Finally, add a column that provides a reference for the pole itself. Add a third column, and set the Field to self:
Recall that this simulation has been performed once on each pole, and each pole will have its own distribution of values that a user will likely want to inspect individually.
Filter the report to a single pole by clicking the filter icon in the report's Self column, and entering a suitable filter value, using the Search option:
Plot the chart
With the source data now available in a report table and filtered to a single pole, it can be plotted using a chart type Dashboard Widget.
Click the (+) to the right of any group of tabs, and select Create Dashboard Widget under the Widgets section on the popup:
On the dialog, set the Widget Type to Bar chart, and give it a meaningful name:
The widget's configuration screen should be automatically shown. If not, click the settings (gear) icon on the widget to reveal it:
Set the following options:
Source report:
Table Report > Composite Variable(or the name of your custom report)Labels Column:
XSort by:
X
In the series table:
Label:
CDFSource column:
Y
Click the settings icon (gear) in the upper right to close the configuration screen and display the chart:
Customizing the chart
To learn more about configuring and styling charts in Neara, see Charts.
Next: Linear regression