Curve Fitting Method

RocData provides three methods for fitting strength models to test data:

• Levenberg-Marquardt

• Simplex

• Linear Regression

The curve fitting method is selected from the dropdown menu in the upper left corner of every data analysis dialog. New parameters are calculated as soon as a curve fitting method is selected from the dropdown menu.

For each strength criterion in RocData there are at least two techniques available for fitting the criterion to test data. The following table summarizes the curve fitting methods available for the different strength models.

Levenberg-Marquardt

The Levenberg-Marquardt method is the default technique for fitting all strength criteria to data points. This robust algorithm has become the standard for non-linear regression. It is very reliable in practice, and has the ability to converge quickly from a wider range of initial guesses than other typical methods.

Simplex

Users can also fit strength models to data using the Simplex method. The Simplex method is one of the best curve fitting methods, and has a reputation for being very reliable.

Linear Regression

Linear Regression (linear least-squares) curve fitting is the third technique provided in RocData. It can only be used to fit the Hoek-Brown criterion for intact rock, and the Mohr-Coulomb strength model to lab data.

Residuals

The Residuals value is a measure of how well a strength criterion fits a given data set. It is equal to the sum of the square of the vertical distances of the given data points from the fitted curve. The goal of the curve fitting computation is to determine the strength envelope which minimizes the value of the Residuals. The Residuals value for the best fit strength envelope is displayed in the test data dialogs and the main RocData viewing screen.