R help - Dec 2013 - Fitting particle size analysis data

Hi all,

How do you fit a sieve analysis data to a statistical function?
I have many sieve analysis data of crushed rocks and I'd like to find out
which statistical distributions describe the particular particle size
distributions (PSD) the best. So basically I need to find fitted parameters
to statistical distributions (mostly weibull and truncated lognormal).
Here is an example of particle size (in microns) versus percent weight
retained.
Sieve size   Wt%  Cumulative passing%
+250           0.1         99.9
-250+180    2.9         97
-180+125    9.5          87.5
-125+90      21.2        66.3
-90+63        29.4        36.9
-63+45         26          10.9
-45               10.9

PSD<-data.frame(size=c(250,180,125,90,63,45,0),retained=c(0.1,2.9,9.5,21.2,29.4,26,10.9),cumulative=c(99.9,97,87.5,66.3,36.9,10.9,0))

The above example is truncated to 350micron and I can't have particles
with minus dimension. Any help will be greatly appreciated.

Thank you,

Zorig

	[[alternative HTML version deleted]]

Hi

I made a simple spredsheet for PSD using Rosin Rammler equation and I am lazy to
transform it to R. However for single purpose you can use nls.

Reverse your cumulative values

PSD$cum<-cumsum(PSD$ret)

plot(PSD$size, PSD$cum)

fit<-nls(cum~ exp(-((size/r)^gama))*100, data=PSD, start=c(r=80, gama=2))

summary(fit)

Formula: cum ~ exp(-((size/r)^gama)) * 100

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
r     88.9664     2.3360   38.09 2.35e-07 ***
gama   2.5435     0.2244   11.33 9.36e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Residual standard error: 3.411  on  5  degrees of freedom

Number of iterations to convergence: 7 
Achieved convergence tolerance: 1.612e-06

lines(PSD$size, predict(fit))

Regards
Petr

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Zorig Davaanyam
> Sent: Friday, December 20, 2013 2:01 AM
> To: r-help at r-project.org
> Subject: [R] Fitting particle size analysis data
> 
> Hi all,
> 
> How do you fit a sieve analysis data to a statistical function?
> I have many sieve analysis data of crushed rocks and I'd like to find
> out which statistical distributions describe the particular particle
> size distributions (PSD) the best. So basically I need to find fitted
> parameters to statistical distributions (mostly weibull and truncated
> lognormal).
> Here is an example of particle size (in microns) versus percent weight
> retained.
> Sieve size   Wt%  Cumulative passing%
> +250           0.1         99.9
> -250+180    2.9         97
> -180+125    9.5          87.5
> -125+90      21.2        66.3
> -90+63        29.4        36.9
> -63+45         26          10.9
> -45               10.9
> 
> PSD<-
> data.frame(size=c(250,180,125,90,63,45,0),retained=c(0.1,2.9,9.5,21.2,2
> 9.4,26,10.9),cumulative=c(99.9,97,87.5,66.3,36.9,10.9,0))
> 
> The above example is truncated to 350micron and I can't have particles
> with minus dimension. Any help will be greatly appreciated.
> 
> Thank you,
> 
> Zorig
> 
> 	[[alternative HTML version deleted]]
> 
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