GPS-X Technical Reference

379 Optimizer
Figure 14-3 - Example GPS-X Output Graph Showing Measured Data (+ Markers)
and the Predicted Response (Continuous Line)
Probability Optimization
GPS-X also allows you to perform probability optimizations. This involves fitting the
cumulative probability of simulation results to the cumulative probability of real data.
The cumulative probability is the probability that values X will have a value less than or
equal to a specific value x. It is a cumulative sum of all probabilities less than or equal
to x.
Probability optimizations are designed primarily for analysis of long-term operation. The
data used in the optimization are time-averaged values and these will be compared to
time-averaged data generated in a simulation.
The data requirements for this type of optimization are substantial due to the need to
perform long-term simulations.
Minimizing the difference between cumulative probabilities for real data and simulation
results is achieved by reducing a special weighted error measure. Both real data and
simulation results are first ordered based on absolute magnitude. Differences are taken
between each pair of values in the ordered lists. The differences are then grouped on the
assumption that they are normally distributed and the average difference for the group is
weighted accordingly. For example, the highest 10 percent of the differences are assumed
to have a probability of occurrence less than about 13 percent. The sum of these weighted
differences serves as the objective function for the optimization. The net effect of the
optimization is to achieve a close fit between cumulative probability distributions for real
data and simulation results.
The model parameter values resulting from this type of optimization may differ
significantly from those obtained from a time series optimization.
GPS-X Technical Reference