fitFOM function

Fit a First-Order Model to Biogas or Other Data

fitFOM (FOM is for first order model) is a flexible function for fitting first-order models to batch biogas production data, typically from a biochemical methane potential (BMP) test.

fitFOM(dat, n.pool = 1, time.name = 'time.d', resp.name = 'cvCH4',
       fit.to = 'yield', method = 'Nelder-Mead', abs.err = FALSE, trans = TRUE,
       init = if (n.pool == 1) c(B = 'yield', k = 0.5) 
                else c(B = 'yield', f = 0.5, k1 = 0.01, k2 = 0.5), 
       fixed = NULL, fit.last = FALSE, lower = NULL, upper = NULL, lag.phase = FALSE)

Arguments

• dat: a data frame with columns for elapsed time and cumulative methane yield ("specific methane production" SMP) or another response variable.
• n.pool: Number of substrate pools to include in the model. 1 or 2. Length-one numeric vector.
• time.name: Name of the column in dat that has elapsed time. Length-one character vector.
• resp.name: Name of the column in dat that has response variable, typically cumulative methane yield ("specific methane production" SMP). Length-one character vector.
• fit.to: Should fitting be to cumulative yield ('yield', default) or the average production rate ('rate', calculated as its difference over time)? Length-one character vector.
• method: Method used to fit the model, i.e., to estimate best-fit parameter values. Default of 'Nelder-Mead' uses that method via the optim function. The other methods available for link{optim} are alternatives. A better option seems to be 'LM', which uses the nls.lm function from the minpack.lm package; this is not the default option only because it requires another package. Length-one character vector.
• abs.err: Should fitting be based on mean absolute error (TRUE) or sum of squares (FALSE, default). Length-one logical vector.
• trans: Should parameter values be transformed for fitting? If TRUE, the k parameter(s) are log10-transformed and (if relevant) f is transformed with the standard logistic function. This ensures logical values (positive k, f between 0 and 1) and may result in better estimates. Default is FALSE. Length-one logical vector.
• init: Vector of initial parameter estimates. See defaults for elements. For B parameter, set to 'yield' to take the initial estimate from the resp.name column. Length-two or -four named numeric vector.
• fixed: Fixed parameters that should be excluded from optimization. Named numeric vector.
• fit.last: Set to TRUE to force fit exactly through final measured observation. Not recommended. Length-one logical vector.
• lower: Optional lower parameter value limits. Only available with some methods. Named numeric vector.
• upper: Optional upper parameter value limits. Only available with some methods. Named numeric vector.
• lag.phase: Should the "lag phase" be excluded from fitting? This period is defined as all observations prior to maximum average production rate. Default of FALSE. Length-one logical vector.

Details

Use for fitting a first-order model (estimation of best-fit parameter values). Intended for extracting kinetic constants and maximum methane potential from biochemical methane potential (BMP) test measurements.

Returns

A list with parameter estimates and additional information. Most useful elements are coefs and coef.tab (best-fit parameter values), summ (a summary that includes model efficiency, error, and convergence information), and pred (model predicted or fitted values).

References

Hafner, S.D., Koch, K., Carrere, H., Astals, S., Weinrich, S., Rennuit, C. 2018. Software for biogas research: Tools for measurement and prediction of methane production. SoftwareX 7 205-210. tools:::Rd_expr_doi("10.1016/j.softx.2018.06.005")

Author(s)

Sasha D. Hafner

Examples

# First use example data to generate a specific methane potential (SMP) curve
library(biogas)
data('feedVol')
data('feedSetup')

# Cumulative biogas and CH4 production
cbg <- calcBgVol(feedVol, comp = 1, temp = 0, pres = 1,
                 interval = FALSE, data.struct = 'wide',
                 id.name = 'id', time.name = 'time.d', vol.name = '1', 
                 dry = TRUE)

# Get SMP
SMP <- summBg(vol = cbg, setup = feedSetup, time.name = 'time.d', 
               inoc.name = 'BK', inoc.m.name = 'm.inoc', when = 'meas',
               norm.name = 'm.sub.vs', show.obs = TRUE)

# Select bottle 9
s9 <- subset(SMP, id == 9)

# Fit model
mod1 <- fitFOM(s9, n.pool = 1, time.name = 'time.d', resp.name = 'cvCH4')

# View summary
mod1$summ

# Add model predictions
s9$cvCH4.pred <- mod1$pred

# And plot
plot(cvCH4 ~ time.d, data = s9, type = 'o')
lines(cvCH4.pred ~ time.d, data = s9, col = 'red')

# Fit to rates instead
mod1b <- fitFOM(s9, n.pool = 1, time.name = 'time.d', resp.name = 'cvCH4', fit.to = 'rate')
mod1b$summ

# Try 2 pools
mod2 <- fitFOM(s9, n.pool = 2, time.name = 'time.d', resp.name = 'cvCH4')
mod2$summ

# First pool effectively ignored in the fit
# Try different method (this one required minpack.lm package)
## Not run:

mod2 <- fitFOM(s9, n.pool = 2, time.name = 'time.d', resp.name = 'cvCH4', method = 'LM')
mod2$summ
## End(Not run)

# Unfortunately, here is a big effect of method on the result!

s9$cvCH4.pred2 <- mod2$pred

plot(cvCH4 ~ time.d, data = s9, type = 'o')
lines(cvCH4.pred ~ time.d, data = s9, col = 'red')
lines(cvCH4.pred2 ~ time.d, data = s9, col = 'blue')

# Drop (exclude) lag phase
mod3 <- fitFOM(s9, n.pool = 2, time.name = 'time.d', resp.name = 'cvCH4', lag.phase = TRUE)
mod3$summ
s9$cvCH4.pred3 <- mod3$pred

lines(cvCH4.pred3 ~ time.d, data = s9, col = 'darkgreen')