Chwirut2: Ultrasonic calibration data 2

In NISTnls: Nonlinear least squares examples from NIST

Description

The Chwirut2 data frame has nr rows and nc columns giving

Format

This data frame contains the following columns:

y

A numeric vector of ultrasonic response values.

x

A numeric vector of metal distance values.

Details

These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance.

Source

Chwirut, D., NIST (197?). Ultrasonic Reference Block Study.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Chwirut2)
Try(fm1 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
            start = c(b1 = 0.1 , b2 = 0.01, b3 = 0.02)))
Try(fm1a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
             start = c(b1 = 0.1 , b2 = 0.01, b3 = 0.02), alg = "port"))
Try(fm2 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
            start = c(b1 = 0.15 , b2 = 0.008, b3 = 0.01)))
Try(fm2a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
             start = c(b1 = 0.15 , b2 = 0.008, b3 = 0.01), alg = "port"))
Try(fm3 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE,
           start = c(b1 = 0.1, p3 = 2.), alg = "plinear"))
Try(fm4 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE,
           start = c(b1 = 0.15, p3 = 0.01/0.008), alg = "plinear"))

Example output

14794.79 :  0.10 0.01 0.02
1127.464 :  0.139981133 0.005210818 0.014326137
524.0564 :  0.166842519 0.005181954 0.011911595
513.0496 :  0.166542926 0.005165775 0.012147521
513.048 :  0.166574406 0.005165294 0.012150094
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(b2 + b3 * x)
   data: Chwirut2
      b1       b2       b3 
0.166574 0.005165 0.012150 
 residual sum-of-squares: 513

Number of iterations to convergence: 4 
Achieved convergence tolerance: 7.922e-06
  0:     7397.3951: 0.100000 0.0100000 0.0200000
  1:     1318.1367: -0.00677752 0.00677865 0.0132968
  2:     296.40201: 0.0845867 0.00400387 0.0149317
  3:     257.65300: 0.154787 0.00508727 0.0124167
  4:     256.52629: 0.165797 0.00515591 0.0121755
  5:     256.52402: 0.166540 0.00516483 0.0121513
  6:     256.52401: 0.166575 0.00516531 0.0121501
  7:     256.52401: 0.166577 0.00516533 0.0121500
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(b2 + b3 * x)
   data: Chwirut2
      b1       b2       b3 
0.166577 0.005165 0.012150 
 residual sum-of-squares: 513

Algorithm "port", convergence message: relative convergence (4)
1486.959 :  0.150 0.008 0.010
534.4129 :  0.141831871 0.004586793 0.013138455
513.091 :  0.164508979 0.005143257 0.012210244
513.0481 :  0.166473992 0.005163946 0.012153654
513.048 :  0.166571991 0.005165264 0.012150177
513.048 :  0.166576454 0.005165326 0.012150015
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(b2 + b3 * x)
   data: Chwirut2
      b1       b2       b3 
0.166576 0.005165 0.012150 
 residual sum-of-squares: 513

Number of iterations to convergence: 5 
Achieved convergence tolerance: 7.256e-07
  0:     743.47941: 0.150000 0.00800000 0.0100000
  1:     329.49026: 0.204207 0.00693095 0.00924971
  2:     257.91707: 0.158797 0.00517442 0.0122070
  3:     256.52510: 0.166019 0.00515822 0.0121690
  4:     256.52402: 0.166551 0.00516497 0.0121509
  5:     256.52401: 0.166575 0.00516531 0.0121500
  6:     256.52401: 0.166577 0.00516533 0.0121500
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(b2 + b3 * x)
   data: Chwirut2
      b1       b2       b3 
0.166577 0.005165 0.012150 
 residual sum-of-squares: 513

Algorithm "port", convergence message: relative convergence (4)
852.0762 :    0.1000   2.0000 165.1199
518.4111 :    0.1482451   2.4711552 196.6031152
513.0639 :    0.1652067   2.3665484 194.1067356
513.0481 :    0.166510   2.353067 193.630750
513.048 :    0.1665736   2.3522640 193.6000916
513.048 :    0.1665765   2.3522251 193.5985809
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(1 + p3 * x)
   data: Chwirut2
      b1       p3     .lin 
  0.1666   2.3522 193.5986 
 residual sum-of-squares: 513

Number of iterations to convergence: 5 
Achieved convergence tolerance: 1.012e-06
1098.89 :    0.1500   1.2500 133.8166
574.2242 :    0.1424199   2.1089886 177.3429804
513.3576 :    0.162387   2.374994 194.076385
513.0484 :    0.1663405   2.3552654 193.7154889
513.048 :    0.1665658   2.3523655 193.6040115
513.048 :    0.1665762   2.3522300 193.5987704
Nonlinear regression model
  model: y ~ exp(-b1 * x)/(1 + p3 * x)
   data: Chwirut2
      b1       p3     .lin 
  0.1666   2.3522 193.5988 
 residual sum-of-squares: 513

Number of iterations to convergence: 5 
Achieved convergence tolerance: 3.705e-06

NISTnls documentation built on May 2, 2019, 2:37 a.m.