The Value of Educated Guessing
I would like to affirm the value of the article “Combine Dimensional Analysis with Educated Guessing,” by Gommes and Gilet in the February 2018 issue (pp. 49–54). I find dimensional analysis to be a powerful engineering tool. By contrast, it is usually underrepresented in the curriculum in favor of first-principles modeling or classic statistical polynomial series modeling. All approaches are important and valid, and one method may be more appropriate than another, depending on the application. The engineer should have all of the tools.
Here is one anecdote: In a product development application from my industrial career, the data from about 30 screening trials revealed seven variables that were important to the product; and desiring to optimize, we were seeking to model how each attribute affected the product. Using classic polynomial regression, they realized that several hundred trials would be needed to generate data to determine values for about a hundred model coefficients. This was a huge cost burden to the company. However, the similarity in data trends made me recall something about dimensionless groups, and one evening I used the Buckingham Pi method to create the groups, linearized the power-law relation, and used simple linear regression to develop a model. It was an excellent fit to my subset of 10 data points, and the next day, we discovered the same 4-coefficient model also provided an excellent fit to the other 20 data sets.
Further, the Gommes and Gilet article explicitly admits the need for educated guesses in the modeling process. With any modeling, a first try usually misses aspects that are revealed when the models are compared to data. Discovering what is missing or what is...
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