Generate an average curve using optim

The user must decide on a single dependent variable (Y) and a single independent variable (X). The user will specify a function defining the relationship between the dependent and independent variables. For a data.frame containing stress-strain (or load-deflection) data for more than one coupon, the maximum value of X for each coupon is found and the smallest maximum value determines the range over which the curve fit is performed: the range is from zero to this value. Only positive values of X are considered. For each coupon individually, the data is divided into a user-specified number of bins and averaged within each bin. The resulting binned/averaged data is then used for curve fitting. The mean squared error between the observed value of Y and the result of the user-specified function evaluated at each X is minimized by varying the parameters par.

Usage

average_curve_optim(
  data,
  coupon_var,
  x_var,
  y_var,
  fn,
  par,
  n_bins = 100,
  method = "L-BFGS-B",
  ...
)

Arguments

data

a data.frame

coupon_var

the variable for coupon identification

x_var

the independent variable

y_var

the dependent variable

fn

a function defining the relationship between Y and X. See Details for more information.

par

the initial guess for the parameters

n_bins

the number of bins to average the data inside into before fitting

method

The method to be used by optim(). Defaults to "L-BFGS-B"

...

extra parameters to be passed to optim()

Value

an object of class average_curve_optim with the following content:

• data the original data provided to the function

• binned_data the data after the binning/averaging operation

• fn the function supplied

• fit_optim the results of the call to optim

• call the call

• n_bins the number of bins specified by the user

• max_x the upper end of the range used for fitting

• y_var the independent (Y) variable

• x_var the dependent (X) variable

Details

The function fn must have two arguments. The first argument must be the value of the independent variable (X): this must be a numeric value (of length one). The second argument must be a vector of the parameters of the model, which are to be varied in order to obtain the best fit. See below for an example.

See also

optim(), average_curve_lm(), print.average_curve_optim(), augment.average_curve_optim()

Examples

# using the `pa12_tension` dataset and fitting a cubic polynomial with
# zero intercept:
curve_fit <- average_curve_optim(
  pa12_tension,
  Coupon,
  Strain,
  Stress,
  function(strain, par) {
    sum(par * c(strain, strain^2, strain^3))
  },
  c(c1 = 1, c2 = 1, c3 = 1),
  n_bins = 100
)
## Range: ` Strain ` in  [ 0,  0.1409409 ]
##
## Call:
## average_curve_optim(data = pa12_tension, coupon_var = Coupon,
##                     x_var = Strain, y_var = Stress,
##                     fn = function(strain, par) {
##                       sum(par * c(strain, strain^2, strain^3))
##                     }, par = c(c1 = 1, c2 = 1, c3 = 1), n_bins = 100)
##
## Parameters:
##       c1        c2        c3
## 1174.372 -8783.106 20585.898