Data Analysis for Process Modeling
How do I select a function to describe my process?
Synthesis of Process Information Necessary
Selecting a model of the right form to fit a set of data usually requires the
use of empirical evidence in the data, knowledge of the process and some
trial-and-error experimentation. As mentioned on the previous page, model building
is always an iterative process. Much of the need to iterate stems from the
difficulty in initially selecting a function that describes the data well.
Details about the data are often not easily visible in the data as originally
observed. The fine structure in the data can usually only be elicited by
use of model-building tools such as residual plots and repeated refinement
of the model form. As a result, it is important not to overlook any of the
sources of information that indicate what the form of the model should be.
Answer Not Provided by Statistics Alone
Sometimes the different sources of information that need to be integrated to
find an effective model will be contradictory. An open mind and a willingness
to think about what the data are saying is important. Maintaining balance and
looking for alternate sources for unusual effects found in the data are also
important. For example, in the load cell
calibration case study the statistical analysis pointed out that the model
initially thought to be appropriate did not account for all of the structure in
the data. A refined model was developed, but the appearance of an unexpected
result brings up the question of whether the original understanding of the
problem was inaccurate, or whether the need for an alternate model was due
to experimental artifacts. In the load cell problem it was easy to accept that
the refined model was closer to the truth, but in a more complicated case
additional experiments might have been needed to resolve the issue.
Knowing Function Types Helps
Another helpful ingredient in model selection is a wide knowledge of the
shapes that different mathematical functions can assume. Knowing something
about the models that have been found to work well in the past for different
application types also helps. A menu of different functions on the next page,
Section 184.108.40.206. (links provided below), provides one way to learn about the
function shapes and flexibility. Section 220.127.116.11. discusses how general
function features and qualitative scientific information can be combined to
help with model selection. Finally, Section 18.104.22.168. points to methods that
don't require specification of a particular function to be fit to the data, and
how models of those types can be refined.
- Incorporating Scientific Knowledge into Function Selection
- Using the Data to Select an Appropriate Function
- Using Methods that Do Not Require Function Specification