Full text of DOI:10.1002/j.2050-0416.2003.tb00589.x

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Eric J. Samp1,2, Dana Sedin1 and Alan Foster1
sugar profiles or laboratory scale fermentations are col-
lected on wort; however, the time to obtain results is typi-
J. Inst. Brew. 109(1), 16–26, 2003
cally a few days and making inference on how the process
An enhanced method for the calibration of Near Infra Red (NIR)
is running to design targets is not real time. This lack of
reflectance spectra to wort fermentability is proposed using a
real time feedback can be due to the batching of analyses
signal pre-processing algorithm called orthogonal signal correc-
on complex measurements such as High Performance Liq-
tion (OSC). Pre-processing NIR spectra prior to partial least
uid Chromatography (HPLC) or the time to complete tests
squares Project to Latent Structures (PLS) regression modelling
such as a rapid fermentability, which is typically 24
hours22. Nonetheless, real time feedback for process con-
trol is lacking in the traditional brewing environment that
would provide brewers the capability for process correc-
tions such as modifications to the saccharification steps in
the mash tun32.
is becoming commonplace in multivariate calibration. A set of
twenty wort samples subjected to a replicated 22 factorial design
with a centre point and nine production samples were used to
construct multivariate prediction models. The experimental de-
sign factors were the mash tun saccharification temperature and
time used to purposely provide a sample set with significant lev-
erage in the fermentability responses. Calibration PLS models
for both wort apparent degree of fermentation (ADF) and final
attenuation apparent extract (Final AE) values with and without
OSC corrected spectra were compared demonstrating significant
improvements in prediction capability with the prior (Q2 = 0.90
versus Q2 = 0.28). The OSC algorithm removed almost 60%
of the variance in the NIR spectra, which was independent or
orthogonal to the fermentability measures. By cleaning up the
spectra, the standard errors of prediction (SEP) for ADF and
Final AE were improved by 50 and 90%, respectively, illustrat-
ing not only the enhancement in calibration but also the aptness
for process control applications. Various model validation tests,
including an external validation example and random response
permutation, verify the validity of the models using OSC. Fur-
thermore, interpretation of the important wavelengths related to
wort fermentability is provided and demonstrates that some key
wavelengths are related to both carbohydrate overtones as well
as nitrogen functional groups. The application of OSC prior to
developing calibration models with NIR demonstrates promising
results for brewers interested in real time control of wort fer-
mentability.
The use of Near Infra Red (NIR) technology is becom-
ing more prevalent in brewing and other industries to pro-
vide quick and accurate quality control measures. Many
brewing related quality characteristics measured using
NIR techniques have been investigated. Some examples
include the measurement of barley and malt moisture,
nitrogen, and amino acid content2,18,38, whole hop cone
moistures, ␣ and ␤ acids, and oils23, wort extract con-
tent24,31, and fermentable sugars and free ␣-amino nitro-
gen8,10,24,29,32,34. Both Halsey24 and Sjoholm et al.31 studied
calibration models for fermentability and comment on
moderate success. Halsey24 incorporated multiple linear
regression (MLR) on selected wavelengths after first and
second differentiation of the spectra. In this study, only a
few wavelengths were selected for the regression model
and it is questionable what information in the NIR spectra
was naively removed. Sjöholm et al.31 incorporated PLS
modelling with an argument on the assumption of a bi-
linear relationship between wort fermentability measures
and NIR spectra is conveyed through the wort fermentable
carbohydrate profile. The application of multivariate cali-
bration techniques such as PLS25 has generally gained
acceptance over MLR or Principal Component Regression
(PCR). In situations where specific wavelengths have been
assigned to certain functional groups, some researchers opt
to using MLR18 ; however, due to potential collinearity is-
sues the MLR approach is not recommended.
Key words: Near Infra Red, orthogonal signal correction, pro-
jection to latent structures regression, wort fermentability.
-2863(9'8-32ꢀ
Fermentability control in brewing is paramount to final
product consistency. If wort is too fermentable, the final
beer will become thin due to the excess water required to
standardize the product’s alcohol content to required levels
in the package. Quite often, measures such as fermentable
Pre-processing spectra prior to calibration to remove
systematic noise is commonplace. The purpose of pre-
processing algorithms for NIR spectra is to remove sys-
tematic variation in the spectra such as base-line variation
and multiplicative scatter effects. The most common ap-
proaches include differentiation and signal correction. Dif-
ferentiation approaches are subjected to removing infor-
mation relative to the analytes of interest. Some of the
more popular signal correction approaches include Sa-
vitzky-Golay smoothing30, multiple signal correction19, and
1 Quality Research & Development, Coors Brewing Company,
Golden, CO 80401
2 Corresponding Author. E-mail: eric.samp@coors.com

baseline correction7. These methods suffer from the draw-
back that information in the spectra related to the analytes
of interest for calibration can be removed39.
sured using an Anton Paar DMA5000 (Anton Paar, Aus-
tria) and converted to °Plato original gravity (°Pog) follow-
ing the ASBC methods of Analysis5. A 350 mL aliquot of
the wort sample was transferred into a 600 mL beaker
with 55 g of yeast cake. Antifoam (Dow Corning, USA)
was added and the sample was stirred for 18 hours (the
yeast was completely suspended in solution). During the
18 hour fermentation, the temperature was maintained be-
tween 18°C–22°C. The beer was poured from the beaker,
centrifuged and decanted from the remaining yeast. The
sample was degassed following the ASBC Methods of
Analysis3. The beer density was measured using an Anton
Paar DMA 5000 (Anton Paar, Austria) and converted to
apparent extract (Final AE) following the ASBC methods
of Analysis4. The apparent degree of fermentation (ADF)
was calculated using the following equation:
A more novel approach is proposed called Orthogonal
Signal Correction39 (OSC). The elegance of the OSC ap-
proach is that noise in the X block, the spectral data set, is
removed that is near or exactly orthogonal to the informa-
tion in the Y block, analytical data set. With this filtering,
noise irrelevant to analyte concentrations is removed prior
to developing calibration models with the desire to improve
prediction capabilities. In the case of NIR spectra where
the vector containing individual wavelength responses is
typically much larger than the number of samples used for
calibration, exact orthogonal solutions are obtained by the
algorithm and guarantee removal of noise independent of
the analyte concentrations21.
Other methods of signal correction aimed at removal of
noise in the X block independent of the Y block have been
recently developed. These include Direct Orthogonal Sig-
nal Correction1,17,37, Modified OSC16, Net Analyte Pre-
processing20, and Orthogonal Projection to Latent Struc-
tures OPLS36. A detailed comparison of these methods is
reported33. Another novel approach considered neural net-
works to pre-process data to remove temperature effects
and demonstrated significant improvements in prediction
errors15. This paper will only consider evaluating the origi-
nal OSC39 algorithm to demonstrate the improvements in
calibration with this signal pre-processing.
The scope of this paper will be to evaluate the improve-
ment in calibration between data sets with and without
OSC and to provide an interpretation of the important
wavelengths as they relate to wort fermentability. A com-
parison to the work of others24,31 will be provided to dem-
onstrate improvements in this calibration approach.
[•Pog - FinalAE]
ADF =
*100%.
•Pog
For each sample, the bivariate responses of ADF and
Final AE were recorded.
NIR – Analysis. The NIR analysis was performed us-
ing a NIRSystems 6500 scanning instrument (FOSS NIR-
Systems Inc., Silver Spring, MD) configured for reflec-
tance. Samples were scanned at wavelengths from 400–
2498 nm at 2 nm segments using a cell with a 10 mm
path length. Each spectra was obtained by averaging 25
scans/sample, the data was expressed as absorbance (Abs
= log 1/R, where R = reflectance). Data was collected
using WINISI on a PC and the exported to a comma-
delimited file for statistical analysis. The spectrum of each
sample consisted of 1050 absorbance points. Samples
were scanned on an as is basis with no sample preparation
at ambient temperature (approx. 20°C). The spectra of all
twenty-nine samples were collected into a data matrix of
size 29 × 1050.
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Notation. All matrices will be denoted in bold face
capital letters. NIR spectral data matrices will be denoted
as X whereas fermentability response data matrices will
be denoted as Y. Sample information was stored row-wise
in these matrices. Small bold and underlined characters
will be used for column vectors and row vectors will be
expressed as transposed vectors, e.g. pЈ. For the sake of
consistency, other notation given by Wold et al.38 will be
followed. The term R2Y and Q2 represent the percent vari-
ance explained and predicted, respectively, by the model
on the fermentability measures. The term R2X represents
the percent variance used in the X space to predict the
fermentability responses.
Statistical model development. All statistical calcula-
tions and modelling was done using SIMCAP+ v10 soft-
ware [Umetrics, Kinnelon, NJ]. The NIR spectra and fer-
mentability measures, ADF and Final AE, were centred
and scaled to unit variance prior to any calibration work.
This is standard practice in multivariate analysis28. Prior to
development of models, a principal component analysis
(PCA) model was constructed on the standardized NIR
data to identify potential outliers. A Distance to the Model
in the X block (DMODX) versus Hotelling’s T2 plot was
constructed and any observations falling outside both re-
jection regions were omitted. Significant regions were de-
Wort samples. Twenty wort samples were produced
according to a 22 factorial design with centre point repli-
cated four times. The experimental factors were sacchari-
fication rest temperature and time. The details of the de-
sign are provided in Table I. The centre point is not pro-
vided here; however, that information is irrelevant and it is
common knowledge that these factors affect wort ferment-
ability.
Nine extra wort samples not part of the test design but
within the experimental design space given above were
also included in the initial calibration data set. Wort sam-
ples were collected at the wort cooler, split for both NIR
and forced fermentability tests. All samples were analysed
within 24 hours of being produced.
Forced fermentability tests. A solid yeast cake (Sac-
charomyces cerevisiae) was prepared by vacuum filtration
with 3 litres of yeast. A 500 mL wort sample was collected
and equilibrated to 20°C–22°C. The wort density was mea-
TABLE I. Details of the mash tun saccharification experimental design.
Factor
Units
Low
High
Saccharification rest temperature
Saccharification rest time
C
min
–1.5
–5
+1.5
+5

fined as the 99th percentile of the null distributions. For
the DMODX region, the significant region was determined
using the F-distribution26 and for Hotelling’s T2 the sig-
nificance region was determined using the distribution
Beta distribution35.
For orthogonal signal correction, the algorithm is pro-
vided in the Appendix. The corrected NIR spectra block,
Xosc,A is simply determined by removing A successive or-
thogonal components calculated from the OSC algorithm,
i.e.:
of times such that all observations are removed at least
once. A comparison of prediction error to the total sums of
squares is done using the PRESS statistic13,27 and is used
to determine the number of components to be used in the
PLS model. This approach has been demonstrated to be
effective in PLS model development9. Due to speculated
optimistic results of cross validation with OSC40 Random
Response Permutation Validation (RRPV)11 was used to
further validate the OSC model. This technique consists of
randomly permuting the rows of Y, keeping the rows of X
intact, develop a PLS model using cross validation with
the shuffled Y matrix, record R2Y and Q2 results, and re-
peat this process a number of times, say 100. This boot-
strapping-type approach can be used to compare the
model’s record R2Y and Q2 results to the distribution of
results obtained by RRPV. If the model’s R2Y and Q2 re-
sults are significantly lower than what was observed in the
original model, then one can feel confident about the
model’s validity for predicting new observations14. It does
not, however, provide model developers with the confi-
dence obtained by external validation with new samples.
For the prediction of new samples, signal correction of
new spectra, say xnew , is easily obtained by removal of the
A OSC components. First, the new signal is standardized
to create xnew,0 . Then, using weight, wosc,a , and loading
vectors, posc,a , from the OSC algorithm, the signal cor-
rected new spectra is determined as
A
Xosc,A = X -
t
osc,a pt
osc,a
Ê
0
a
1
Based on recommendations by practitioners39 only two
orthogonal components were removed to clean up noise
due to baseline and multiplicative effects. The PLS models
for non corrected, denoted as Xnon , and corrected spectra,
X
osc,A , were developed as follows:
Xosc,A = TPt + E
Yosc,A = UQt + F
Xnon = TPt + E
Ynon = UQt + F
Model development was carried out using the method
of internal cross validation to determine the number of
components in the PLS models. This technique removes a
subset of the observations from the model, fits a model
with the remaining data, uses the removed X-data to pre-
dict the respective Y results, and compares the predicted
results to the actual. This procedure is replicated a number
A
Î
Þ
xnew,osc = I -
p
wtosc,a xnew,0
,
Ê
Ï
Ð
ß
à
osc,a
a
1
Fig. 1. NIR reflectance plot for the twenty-nine wort samples.

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Fig. 2. Three-dimensional PCA model of DMODX (ordinate) versus T-Squared (abscissa)
plot illustrating one outlier existed in the original data set.
where I represents the identity matrix. The corrected spec-
in the Y-space. However, the model’s total prediction ca-
pability is 28.3%. In general, models capable of predicting
over 50% of the observed variance in the y-variables are
considered good. The prediction capability of these models
is less than adequate (Figs. 3 and 4).
tra, xnew,osc , is then fed into the PLS model for prediction.
To understand the important wavelengths associated
with the prediction of wort fermentability measures, Vari-
able’s Influence in Projection12 (VIP) plots can be con-
structed for the spectra to determine key regions associ-
ated with fermentability.
PLS results with OSC. The OSC corrected spectra re-
veals some interesting patterns visually (Fig. 5). For ex-
ample, as the OSC corrected signal becomes higher in
value towards the region of 1300 nms and greater, the less
fermentable the wort would be. In fact, for the signal that
appears the highest in the 1300–2500 nm range, the wort
ADF result was approximately 73% whereas those signals
towards the lower end ranged in the 79–81% ADF range.
Discussions provided later will demonstrate that this sub-
set of wavelengths contains important variables for the
PLS model. The OSC model parameters are provided
(Table III). Both components are orthogonal to the Y-space
as indicated by the ninety-degree angle. The OSC cor-
rected spectra only contains 41.5% of the original variance
in the X-block clearly demonstrating the amount of noise
filtered out.
6)79087ꢀ
The NIR reflectance spectra are graphed (Fig. 1). Vis-
ual inspection does not demonstrate any significant anom-
alies. However, a PCA analysis of the twenty-nine NIR
spectra revealed that one outlier existed. The PCA model
consisted of three components explaining over 95% of the
variability in the PCA model. The DMODX versus Hotel-
ling’s T-Squared statistic illustrates how the outlier falls
outside the statistical norm of both the PCA subspace re-
gion and the orthogonal complement (Fig. 2). This obser-
vation was removed prior to any PLS modelling and is
justified on the basis that the starting point of the OSC
algorithm for the score vector, tstart , is the major eigen-
vector of the standardized NIR data matrix, X0 (see appen-
dix). By keeping this vector in the calibration data set, the
OSC score and loading vectors, ta and pa , could be nega-
tively influenced.
The PLS algorithm extracted only 1 component, veri-
fied through cross validation, yet was capable of predict-
ing over 90% of the total cumulative observed variance
TABLE III. OSC parameters.
PLS results with no signal pre-processing. PLS re-
gression was applied to the spectra and the observed fer-
mentability results (Table II). Only 1 PLS component was
extracted through cross validation, using 69.6% of the
variation in the X-space to explain 36.6% of the variation
Angle
in degrees
Remaining SS
in %
Component
Eigenvalue
1
2
90.00
90.00
53.75
41.54
12.9502
3.41769
TABLE IV. Results of PLS with OSC.
TABLE II. Results of PLS without OSC.
R2X %
Eigenval
R2Y %
Q2 %
Dim
R2X %
Eigenval
R2Y %
Q2 %
Dim
1
79.3
22.2
91.5
90.0
1
69.6
20.173
36.6
28.3

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Fig. 3. Observed (ordinate) versus predicted (abscissa) plot for ADF without OSC.
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Fig. 4. Observed (ordinate) versus predicted (abscissa) plot for Final AE without OSC.
(Table IV). These prediction capabilities are considered to
be quite good by chemometric standards. To illustrate the
prediction capabilities for ADF and Final AE, observed
versus predicted plots are provided (Figs. 6 and 7) as well
as R2Y and Q2 statistics (Table V). A comparison of the
Standard Errors of Calibration (SEC) and Standard Errors
of Prediction (SEP) results from both models and results
from previous research is also provided (Table VI).
were replicated 100 times for both fermentability mea-
sures. The observed R2Y and Q2 results, shown to the far
upper right in the plots, are much greater than all 100
RRPV trials (Figs. 8 and 9). If there were some overlap,
say 5% of the RRPV values greater than the observed re-
sults, the model’s validity could be questionable11. The
results of RRPV trials also suggest that these models are
not being driven by spurious correlations simply due to the
fact that 1050 predictor variables are used. Simple proba-
bility arguments can be made that with these many predic-
tors, the chances of seeing significant correlation coeffi-
cients between dependent and predictor variables is high.
In an attempt to externally validate this model with lim-
ited calibration samples, six observations were removed
from the data set, OSC was applied again to the X-block
subtracting two components, a PLS model was developed,
and the removed spectra was then filtered using the OSC
Validation trials. Random response permutation trials
TABLE V. Comparison of R2 and Q2 statistics with and without OSC.
Without OSC
With OSC
Response
R2Y%
Q2 %
R2Y%
Q2 %
ADF
Final AE
30.6
40.6
21.9
32.1
83.6
99.5
80.7
99.3

Fig. 5. OSC corrected log(1/R) spectra of the twenty-eight calibration samples.
model developed. Once the filtered NIR spectra were ob-
tained, it was fed into the PLS model for predicting re-
sults. The observed versus predicted plot illustrate that
these external samples were well modelled (Fig. 10).
VIP results & OSC-PLS regression coefficients. The
important wavelengths in the NIR spectrum from the
OSC-PLS model can be grouped into three general re-
gions with VIP scores greater than 1.0: 1) between 560
and 640 nms, 2) between 1340 and 1500 nms, and 3)
greater than 1520 (Fig. 11). The first region corresponds to
an electronic transition and not an IR overtone. The VIP
correlation is strongest at approximately 640 nm, which
corresponds to the absorbance of red light. The absorb-
ance of red light will increase as the blue-green appear-
ance of the wort increases. This could lend itself to a
quick and simple method using ultra violet-visible absorb-
ance spectroscopy. A survey of all NIR methods on wort
fermentability24,31,32,34 finds that no calibration models used
wavelengths less than 1200 nms; however, it is hard to
ignore the significant VIP scores in this study with OSC
and it is recommended that future research consider this
region.
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Fig. 6. Observed (ordinate) versus predicted (abscissa) plot for ADF with OSC.

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Fig. 7. Observed (ordinate) versus predicted (abscissa) plot for Final AE with OSC.
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Fig. 8. RRPV trials for ADF. represent R2 results and the Ⅵ represent Q2 results. The ordinate represents the
RRPV R2 and Q2 trials. The abscissa represents the correlation coefficient between original order of the ADF data
and the shuffled ADF data. The model’s result is indicated at the upper right. The R2 and Q2 intercepts are –0.05
and –0.18, respectively. The results of the 100 RRPV trials being less than the model’s scores and low R2 and Q2
intercepts illustrate the validity of the model.
ᮡ
TABLE VI. Summary of both models standard error of calibration (SEC) and standard error of prediction (SEP) along with
previous work of Sjöholm et al.31 and Halsey24.
Without OSC
With OSC
Sjöholm et al.
Halsey
Response
SEC
SEP
SEC
SEP
SEC
SEP
SEC
SEP
ADF (%)
Final AE ( Plato)
1.427
0.285
1.484
0.299
0.698
0.027
0.744
0.030
1.034
n/a
1.106
n/a
1.6
n/a
1.5
n/a
The NIR spectra for the second and third regions have
wavelengths that correspond to alkane, alkene, alcohol,
amide, and amine functional groups. Specifically, the third
region, which spans a large spectrum, is probably related
to amino acids and complex longer chain carbohydrates,
i.e. non-fermentable sugars. Halsey24 reported a spectral
trough at 1664 nms common to dextrins and fermentable
sugars and suggested that discrimination between ferment-
able and non-fermentable sugars falls in 1410 and 1970
nm wavelengths. Sojholm et al.31 found that the key pre-

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2
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Fig. 9. RRPV trials for Final AE. represent R results and the Ⅵ represent Q results. The ordinate represents the
RRPV R2 and Q2 trials. The abscissa represents the correlation coefficient between original order of the Final AE
data and the shuffled Final AE data. The model’s result is indicated at the upper right. The R2 and Q2 intercepts are
–0.08 and –0.19, respectively. The results of the 100 RRPV trials being less than the model’s scores and low R2
and Q2 intercepts illustrate the validity of the model.
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Fig. 10. External validation trials. represent observed versus predicted results for model for 22 selected observa-
tions in the calibration model, Ⅵ represent observed versus predicted results of the six external samples predicted
from the model with 22 observations.
dictors for the amount of extract fermented in a laboratory
scale fermentation test fall in the 1500–1863 and 2050–
2400 nm regions; however, the signs on their PLS regres-
sion coefficients do not all agree with these findings.
As for nitrogen sources, class II aromatic amino acids
such as phenylalanine and tyrosine have been assigned to
1680 nm whereas glutamine, probably less important for
fermentation, has been assigned to 2170 nm18. Assign-
ments of N–H groups have been reported at 1528 nm and
2048 nm17 and a N–H stretch is assigned to 1982 nm6.
This third region is key to predicting fermentability as
manifested by the large VIP scores. The general pattern
seems to be the higher the absorbance values are in this
region, the less fermentable the wort is (Table VII). This
has an intuitive appeal because one can argue that as the
balance of wort carbohydrates consists of more malto-
dextrins as opposed to monomers, dimers, and trimers, the
less fermentable it will be. Hence, interpretation of the
regression coefficients in this region tends to support this
hypothesis (Fig. 12).
The region between 900 nms and 1100 nms exhibit a
low VIP score indicating that their relative contribution to

Fig. 11. VIP plot illustrating important wavelengths in the calibration model. Note that VIP scores greater than 1.0 are considered most
influential in the model.
predicting wort fermentability is low or unimportant. It
has been reported that simple sugars will absorb in this
region10; however water also has a strong absorbance in
this same range and it is clear that even with OSC cor-
rected spectra, this region was not useful for calibration.
predictive modelling was considered. Since all samples
used in the calibration work came from production scale
worts, variability in the original gravities may have influ-
enced the calibration.
The VIP plot provides an explanation of the NIR spec-
tra results and its relationship to fermentability. It ap-
pears that wavelengths greater than 1300 nms are key to
the model’s prediction capability and are probably related
to complex carbohydrates. It is well known that as non-
fermentable sugars such as maltotetraose and maltopenta-
ose increase, the wort fermentability decreases. This phe-
nomenon is the result of less saccharification probably
driven by ␣-amylase, ␤-amylase, mash Ca++ levels, sac-
charification time-temperature profiles, and the inexplicit
interactions between these variables. The elegance of us-
ing NIR to predict fermentability falls in the brewhouse’s
ability to potentially control fermentability in real time.
NIR technology requires very little training for operators.
Real time monitoring can be incorporated into a Statistical
Process Control (SPC) program in which predicted fer-
mentability results can be charted against process targets,
(-7'977-32ꢀ
The prediction improvement in applying orthogonal
signal correction to the model development is impressive.
Without OSC, the overall prediction capability was Q2 =
28.3% and the prediction capability is similar to what pre-
vious attempts reported23,30. However, with OSC the over-
all prediction capability improved to Q2 = 90.0% which is
excellent and illustrates how OSC cleans up the noise in
NIR spectra. In fact, about 60% of the noise in the NIR
spectra was removed prior to calibration. The prediction
capability of ADF was slightly lower than that of Final AE
(Q2 ADF = 80.7% vs Q2 Final AE = 99.3%). The reason
behind this difference may fall in the fact that ADF is also
a function of the original gravity of the wort, of which no
TABLE VII. Pearson correlation coefficients of linear maltodextrins, fermentable sugars, and wort fermentability measures from the experimental
trials. P-values are indicated in brackets below the correlation coefficients.
Malto-
heptaose
Malto-
hexaose
Malto-
pentaose
Malto-
tetraose
Malto-
triose
Maltose
Glucose
ADF
Malto-hexaose
Malto-pentaose
Malto-tetraose
Malto-triose
Maltose
.547 (.002)
.338 (.068)
.489 (.006)
.035 (.856)
–.191 (.313)
.097 (.612)
.916 (.000)
.842 (.000)
.224 (.235)
.059 (.758)
.146 (.440)
.874 (.000)
.332 (.073)
.210 (.265)
.169 (.373)
.432 (.017)
.246 (.190)
.218 (.247)
.960 (.000)
.535 (.002)
Glucose
.464 (.010)
ADF
Final AE
–.521 (.003) –.625 (.000) –.671 (.000) –.729 (.000) –.167 (.377) –.054 (.777)
.259 (.167) .383 (.037) .516 (.003) .618 (.000) .425 (.019)
.138 (.466)
.370 (.044) –.047 (.805) –.831 (.000)

Fig. 12. OSC-PLS regression coefficients. Line above abscissa represents coefficients for Final AE. Line below abscissa represents
coefficients for ADF.
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3VXLSKSREPꢀ7MKREPꢀꢀ
'SVVIGXMSRꢀ%PKSVMXLQꢀ
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1. Assume X0 and Y0 represent mean centered and scaled
to unit variance data matrices of the NIR spectra and
fermentability measures, respectively. Note X0 and Y0
arranged such that the spectra and fermentability re-
sults for one sample are placed row-wise, and the num-
ber of rows corresponds to the number of samples in
calibration set.
2. Let a = 1.
3. Let Xosc,a–1 = X0 .
4. Let tstart be the score vector associated with the major
eigenvector of Xosc,a–1
.
5. Project tstart into the orthogonal complement of the
column space of Y , L {Y0}. This can be accom-
0
plished by tnew = [I – Y (Yt Y0)–1Yt ]tstart
.
0
0
0
6. Determine a least squares solution for wosc,a , i.e.
Xosc,a–1 osc,a = tnew
The solution involves the Moore-Penrose generalized
w
.
inverse of Xosc,a–1 and is given as wosc,a = X–osc,a–1 tnew
7. Calculate tosc,a = Xosc,a–1 wosc,a
.
.
8. Check for convergence such that
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by simplified least squares procedures, Anal. Chem., 1964,
36(8), 1627–1632.
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S., Determination of fermentability and extract content of in-
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135–140.
tosc,a - tnew
< 10
6
.
tosc,a
If convergence is not attained, let tstart = tosc,a and go
back to step 3; otherwise, proceed to step 9.
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100(1), 11–15.
9. Compute loading vector posc,a using the following
ttosc,a Xosc,a
(ttosc,a tosc,a
1
pt
=
.
osc,a
)
10. Subtract signal correction from Xosc,a–1 to give Xosc,a
osc,a–1 – tosc,a ptosc,a
=
X
.
11. Let a = a + 1 and continue to extract as many compo-
nents as desired. Go back to step 3.
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nal signal correction, Chem. Intell. Lab. Sys., 2001, 56(1), 13–25.
12. Once the desired number of components are extracted
for signal correction, use Xosc,A for the PLS algorithm.
X
osc,A can be determined as
A
Xosc,A = X -
t
osc,a pt
.
osc,a
Ê
0
a
1