You are hereMoment-Based Probability Modelling and Extreme Response Estimation: The FITS Routine
Moment-Based Probability Modelling and Extreme Response Estimation: The FITS Routine
This report documents the usage of the routine FITS, which provides automated fits of various analytical, commonly used probability models from input data.
This routine is intended to complement the previously distributed routine, FITTING, documented in RMS Report 14 (Winterstein et al, 1994). The FITTING routine implements relatively complex, four-moment distribution models, whose parameters are fit with numerical optimization routines. While these four-moment fits can be quite useful and faithful to the observed data, their complexity can make them difficult to automate within standard fitting algorithms.
In contrast, the routine FITS is intended to provide more robust (lower moment) fits of simpler, more conventional distribution forms. For each database of interest, the routine estimates the distribution of annual maximum response, based on the data values and the durati on, T ,over which they were recorded. To focus on upper tails of interest, the user can also
supply an arbitrary lower-bound threshold,Ιlow , above which a shifted distribution model-exponential or Weibull-is fit. (In estimating the annual maximum response, the program automatically adjusts for the decreasing rate of response events as the threshold Ιlow is raised.)
This report generalizes an earlier report (Stanford RMS Report 19; Winterstein , 1995), which introduced the FITS routine. The major extension included in this updated version is the inclusion of a new, "quadratic Weibull'' distribution. This distribution, fitted to the first three moments of a data set, has been found especially useful in modelling fatigue loads observed on wind
turbine blades (Lange and \Vinte rstein, 1996). At the same time, unlike the four-moment models from FITTING, the parameter fitting of the quadratic Weibull does not require numerical optimization. It also avoids the tendency
of four-moment models toward overfitting, when applied to positive variables such as load peaks (or ranges). This is demonstrated here through an additional example, applying FITS to a data set of observed wind turbine blade loads.