Strength of Concrete

Obeservational Data Sets

• Thus far this is what we have been working with, existing predictor data
• Often comes in the form of a large comprehensive data set

Designed Experiments

• Prefer a sequence of studies rather than one large data set
• Involves planning, designing and analyzing an experiment
• Here we will use predictive measures to identify ingredient proportions for further testing

• Methods used to plan the exact values of predictors (factors)
• Begin with a balanced design
• Sequential Experimentation is used to determine important factors
• Response Surface Experiments

Concrete is integral for the infrastructure of industrial societies. Its strength and the optimal makeup to improve that strength have been widely studied. We will look at the various proportions of mixture ingredients to maximize compressive strength.

The ingredients of interest are cement, fly ash, blast furnace slag, water, superplasticizer, coarse & fine aggregate. All at a scale of kg/m^3.

The predictors will enter the model as a proportion of the total mixture

• Built in dependency between the predictors
• Pairwise correlations were not found to be large
• Observations with duplicate measures have outcomes averaged

• Linear regression, partial least squares, and the elastic net
• Support vector machines (SVMs).
• Neural network
• MARS
• Regression trees, model trees (with and without rules), and Cubist

• Bagged and boosted regression trees & random forest models

• Will use 10-fold cross validation

###For MAC:
#library(doMC)
#registerDoMC(cores = 2)

###For Windows
library(parallel)
library(doParallel)

cluster <- makeCluster(detectCores() - 1) # convention to leave 1 core for OS
registerDoParallel(cluster)
#caret package functions will now use multiple cores
#turn off parallel processing
stopCluster(cluster)
#resume use of the sequential backend
registerDoSEQ()

Simple way to check speed improvements of code

library(tictoc)
tic(
Sys.sleep(3)
)
toc()

3 sec elapsed

Now that we know which models appear to be best at predicting, how do we find the improved mixtures?

A numerical search routine

• Search seven dimensional space using direct methods
• Two were used by the authors: Nelder Mead simplex method and simulated annealing
• Simplex search method had the best results

Once we determine potential improved mixtures, further experiments will be needed

• The search routines begin with intital starting values

• For Nelder-Mead multiple starting places should be used and results compared

  • Used values with age 15 - 28 days to generate starting points

• Values which are impractical or impossible are avoided by setting the amount

  • Water did not occur at a value of less than 5.1%, so this was set to a minimum of 5%

• Desirability functions can be used to account for other decision parameters
  • May want to establish cost or time preferences in a model
• Map those desirability measures to a 0 to 1 scale, 0 being undesirable
• Desirability measures are combined using a geometric mean
  • Multiplies values so if any one measure is completely undesirable it is 0
• Search procedure would then be used

• Determined the best models
• Used search routines to determine potential improvements in mixtures
• Experimentation needed to verify the results

The following link will bring you to the Applied Predictive Modeling textbook code:

https://github.com/cran/AppliedPredictiveModeling/tree/master/inst/chapters