Cross-Correlation

The Cross-Correlation option is accessed through the Material Statistics > Cross-Correlation dialog. It allows you to define correlation coefficients between any two random variables in any material. This is useful when you have different materials which have some properties which are correlated.

For example, It is known that Cohesion and Friction Angle are related in a general way, such that materials with low friction angles tend to have high cohesion, and materials with low cohesion tend to have high friction angles. If a Correlation Coefficient is defined, this means that when the statistical samples are generated for any two variables, they will be correlated. In this case, the value of Cohesion will be related to the value of Friction Angle and vice versa. This simulates the relationship between Cohesion and Friction Angle which exists in real materials. This can be extended to other random variables between materials which are defined through this same process. By default, when no correlation has been defined, variables are treated independently.

In general, this should provide more realistic analysis results, compared to running the analysis with no correlation of variables.

To use Cross-Correlation:

1. First, define the random variables as described in the Material Statistics topic.
2. Select the Cross-Correlation button in the Material Statistics dialog.
3. In the Cross-Correlation dialog, select the Add button for each pair of random variables that you would like to correlate. You can correlate between any of the available distribution types assigned to the random variable.
4. Use the Prop1 and Prop2 columns to select the random variables that you would like to correlate and enter a Correlation Coefficient for each pair. The allowable value of the Correlation Coefficient is – 1 to 1. A negative Correlation Coefficient simply means that as one variable decreases, the other variable is likely to increase
5. Select the Check Valid button. If there are any input errors you will see a warning message, indicating what corrections should be made.
6. When all input is valid, select OK in the Cross-Correlation dialog.

When the probabilistic analysis is run, the sampling of the random variables will be correlated according to your input. The actual correlation between two variables can be observed by viewing a Scatter Plot. The actual Correlation Coefficient (listed on the Scatter Plot) should be close to the value you have specified in the dialog. See the Slide2 Interpret help for more information about Scatter Plots.

See Tutorial 23 - Statistical Correlation for a demonstration of the Cross-Correlation option.