Determination of free amino nitrogen in beer mash with an inline NIR transflectance probe and data evaluation by machine learning algorithms

Abstract

Free amino nitrogen (FAN) concentrations in beer mash can be determined with machine learning algorithms from near-infrared (NIR) spectra. NIR spectroscopy is an alternative to a classical chemical analysis and allows for the application of inline process quality control. This study investigates the capabilities of different machine learning techniques such as Ordinary Least Squares (OLS) regression, Decision Tree Regressor (DTR), Bayesian Ridge Regression (BRR), Ridge Regression (RR), K-nearest neighbours (KNN)
regression as well as Support Vector Regression (SVR) to predict the FAN content in beer mash from NIR spectra. Various pre-processing strategies such as principal component analysis (PCA) and data standardization were used to process NIR data that were used to train the machine learning algorithms. Algorithm training was conducted with NIR data obtained from 16 beer mashes with varying FAN concentrations. The trained models were then validated with 4 beer mashes that were not used for model training. Machine learning algorithms based on linear regression showed the highest prediction accuracy on
unpre-processed data. BRR reached a root mean square error of calibration (RMSEC) of 2.58 mg/L (R2 = 0.96) and a prediction accuracy (RMSEP) of 2.81 mg/L (R2 = 0.96). The FAN concentration range of the investigated samples was between approx. 180 and 220 mg/L. Machine learning based NIR spectra analysis is an alternative to classical chemical FAN level determination methods and can also be used as inline sensor system.

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Authors
https://doi.org/10.23763/BrSc21-10wefing
P. Wefing, F. Conradi, J. Rämisch, P. Neubauer and J. Schneider
Determination of free amino nitrogen in
beer mash with an inline NIR transflectance
probe and data evaluation by machine
learning algorithms
Free amino nitrogen (FAN) concentrations in beer mash can be determined with machine learning algorithms
from near-infrared (NIR) spectra. NIR spectroscopy is an alternative to a classical chemical analysis and
allows for the application of inline process quality control. This study investigates the capabilities of
different machine learning techniques such as Ordinary Least Squares (OLS) regression, Decision Tree
Regressor (DTR), Bayesian Ridge Regression (BRR), Ridge Regression (RR), K-nearest neighbours (KNN)
regression as well as Support Vector Regression (SVR) to predict the FAN content in beer mash from NIR
spectra. Various pre-processing strategies such as principal component analysis (PCA) and data
standardization were used to process NIR data that were used to train the machine learning algorithms.
Algorithm training was conducted with NIR data obtained from 16 beer mashes with varying FAN
concentrations. The trained models were then validated with 4 beer mashes that were not used for model
training. Machine learning algorithms based on linear regression showed the highest prediction accuracy on
unpre-processed data. BRR reached a root mean square error of calibration (RMSEC) of 2.58 mg/L (R2 = 0.96)
and a prediction accuracy (RMSEP) of 2.81 mg/L (R2 = 0.96). The FAN concentration range of the investigated
samples was between approx. 180 and 220 mg/L. Machine learning based NIR spectra analysis is an alternative
to classical chemical FAN level determination methods and can also be used as inline sensor system.
Descriptors: mashing, NIR, machine learning, FAN
Patrick Wefing, Florian Conradi, Johannes Rämisch, Jan Schneider,
Technische Hochschule Ostwestfalen-Lippe, Institute of Food Technology,
NRW, Lemgo, Germany; Peter Neubauer, Technische Universität Berlin,
Department of Biotechnology, Bioprocess Engineering, Berlin, Germany;
corresponding author: patrick.wefing@th-owl.de
1 Introduction
Free amino nitrogen (FAN) is an important quality parameter in
the field of beer production [1–4]. It is generated during malting,
extracted during mashing and usually analysed in the laboratory
[3]. FAN compounds are the sum of di- and tripeptides, ammonium
ions and amino acids [4]. As they are the primary nitrogen substrate
for yeast during the later beer fermentation the FAN concentration
is a major quality parameter in the mashing process. Adequate
levels of FAN in wort ensure efficient yeast cell growth and, hence,
a desirable fermentation performance [3–6].
In literature, varying FAN levels in beer mash are reported depend-
ing on the malt-liquor ratio and the used type of malts. Studies
that used a comparable type of malt and malt-liquor ratio reported
FAN values in the range of circa 170 mg/L – 320 mg/L [7–9]. Ap-
proximately up to 70 % of FAN is produced during malting, where
higher nitrogen barley results in extracts that are carbohydrate
rich and lower nitrogen barley results in extracts that are rich in
carbohydrates [3, 10, 11]. During mashing, FAN is produced by
proteolysis [8, 9, 12]. Mashing time and mashing temperature
influence the levels of FAN produced during mashing [8, 9, 13].
Ninhydrin-based laboratory methods are commonly used for
FAN analysis [3, 5, 14–17]. In FAN analysis, ninhydrin is added
to a sample as an oxidizing agent that causes decarboxylation
of α-amino acids. The reduced ninhydrin reacts with unreduced
ninhydrin and liberates ammonia, forming a colour complex [17].
The FAN concentration is determined by measuring the intensity
of the colour complex against a standard solution in a spectro-
photometer. Additionally, high performance liquid chromatography
(HPLC) methods are available for the analysis of amino acids in
beer [18, 19]. HPLC methods rely on the ninhydrin method but
allow for a separation of specific amino acids [3]. Alternatively, a
gradient elution HPLC method using dansyl chloride as fluorogenic
reagent is available for the quantification of individual amino acids
in beer mash [3, 20].
In order to optimise the duration of the mashing process and the
mash quality it is important either to determine the malt quality
extensively prior to mashing or to measure mash quality during
the process [8]. So far ninhydrin based methods do not allow for
an inline FAN determination and are thus unlikely to be integrated

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into a process. Due to the significance of the FAN value as a qual-
ity parameter there is an increasing interest in the application of
faster and easier applicable methods. A continuous solution for the
prediction of FAN was already demonstrated by Mitzscherling et
al. [8], who used an array of different bypass sensors such as pH,
conductivity, ultrasonic velocity and viscosity. Multivariate statisti-
cal techniques (e.g. principal component regression, partial least
squares regression) were used for the calibration of that bypass
sensor array.
However, complex spectroscopic technologies, such as e.g. near-
infrared (NIR) or Raman, have to our knowledge not been used for
this analysis in an inline application. These methods are advanta-
geous, as they only need a single sensor that can be implanted
into the process. The application of NIR sensors has already been
widely demonstrated in the fields of food and beer production [21,
22, 31–34, 23–30]. Apart from NIR, Fourier-transform infrared (FTIR)
spectroscopy is also used for the laboratory analysis of FAN and
soluble nitrogen content in the field of beer production [35, 36].
NIR spectroscopy is a non-invasive measuring method, allowing
a quick real time analysis without the need for sample preparation
[29]. Therefore, NIR is especially suited for the application in food
and beer production. Used as an inline measurement system it
allows the real time analysis of FAN during mashing and therefore
enables a better understanding of the mashing process itself due
to a process monitoring. Also, if available in real-time, the qual-
ity parameter FAN could be used as a control parameter during
mashing for example by adapting the mashing time.
Photonic technologies such as NIR spectroscopy produce a large
number of data and since the signals cannot be directly attributed
to a specific substance, aside from common multivariate statistics
approaches for the interpretation of NIR spectra as e.g. Partial
Least Squares (PLS) regression, this is a field where machine
learning algorithms may have a considerable potential [37]. PLS
regression is established as the standard method for the analysis
of NIR spectra [38]. However, PLS belongs to the field of classical
statistics, aiming to formalise relations between independent and
non-independent variables [39, 40]. In contrast to that, the aim of
machine learning is the prediction itself than to find an explanation
for the prediction. Here, inference is replaced by validation through
testing the model with new data [39].
In this study, we investigate whether data from an inline NIR sen-
sor, evaluated by machine learning algorithms, can be used for
FAN level prediction in the field of beer production. Studies have
revealed that machine learning algorithms such as Ordinary Least
Squares (OLS), Ridge Regression (RR), Bayesian Ridge Regres-
sion (BRR), Decision Tree Regressor (DTR), K-nearest neighbours
(KNN) regression, and Support Vector Regression (SVR) can be
successfully applied to predict quality parameters from NIR spectra
such as extract levels in beer, sugar levels in fruits, acidity of palm
oil, moisture content of freeze dried products, and others [41–49].
NIR spectra contain a large number of indirect chemical informa-
tion of the measured matrix. Often excessive data pre-processing
steps are necessary to use the NIR spectra for quantification of
single components. NIR pre-processing methods that are often
applied individually or in combination are “first derivation of NIR
spectra”, “multiplicative scatter correction”, “mean centring”,
“spectra smoothing”, “Pareto scaling”, “standard normal variate”
and “Savitzky-Golay filter” [43, 45, 50–53]. This complicates the
industrial application of that technology and the inline implementa-
tion into processes. However, machine learning algorithms might
be able to determine the FAN concentration in beer mash with a
small or no data pre-processing step and high determination ac-
curacy. Additionally, the available number of algorithms make the
selection of an appropriate algorithm difficult.
This paper aims to compare different linear and non-linear ma-
chine learning regression strategies for the determination of FAN
in beer mash. Mashes with different FAN contents were analysed
by both, NIR spectroscopy and the ninhydrin assay as reference
measurement. NIR spectra and reference data were then used
to train machine-learning algorithms, which were validated with
external data.
2 Materials and Methods
2.1 Mash Preparation
Finely ground malt (Pilsner malt, Weyermann, Germany) was used
for the mashing experiments and demineralized water was used
as brewing liquor (reverse osmosis). The malt was grinded with
an impact mill (Millomat 100, Treffler Maschinenbau GmbH & Co.
KG, Germany) at the Max Rubner-Institut -Federal Research Insti-
tute for Nutrition and Food in Detmold, Germany. The sieve used
in that mill only allowed particles with a diamater dp ≤ 500 µm to
pass. After mixing with the brewing liquor, the malt-liquor ratio was
1 : 4. The malt analysis of the used substrate is given in table 1.
Two stock mash batches (stock batch A and stock batch B) were
prepared. Stock batch A consisted of a mash that was allowed to
react for 30 min at 65 °C. The brewing liquor temperature for that
batch before it was mixed with malt was 70 °C. It was heated up
to 80 °C afterwards to inactivate enzymes and then cooled down
rapidly to prevent further temperature induced degradation. Stock
batch B was kept at 20 °C and was therefore not allowed to e.g.
decompose starch into sugars.
Table 1 Malt analysis of Pilsner Malt
Type Pilsner Malt
Producer Weyermann (Germany)
Water Content 4.4 %
Extract Water Free 82.9 %
pH-value 5.88
Saccharification Time 10 – 15 min
Total Protein 10.6 %
Free Amino Acid 794 mg/100 g dry mass
Kolbach Index 41.4 %
Friability 88.4 %
Glassiness 1.2 %
Viscosity
(referred to 86 g kg-1 Extract) 1.51 m Pa s

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Subsequently the two stock batches were used to prepare 20
different mash batches with varying concentrations of FAN. The
mashes were blended at 20 °C and each batch had a volume of
approximately 1 L. The batch with the lowest FAN concentration
consisted only of mash from stock batch b (0 % A : 100 % B) that
was kept at 20 °C, while for the batch with the highest FAN concen-
tration only mash from stock batch A was used (100 % A : 0 % B) .
The other batches were blended using increasing concentrations
of stock batch A (5 % – 95 %). Of the 20 prepared mash batches
16 were used for training of machine learning algorithms and four
were used for validation purposes.
2.2 FAN Concentration Determination
FAN was measured using ninhydrin-based methods with the use
of the absorbance measurement at 450 nm (CADAS 100, Hach
Lange GmbH, Germany) according to the EBC-ninhydrin method
by spectrophotometry [14, 17] .
2.3 Computation of Data
Python 3.7 was used for all calculations. The open source cross
platform Spyder (MIT license) was applied as the programming
environment. Machine learning libraries from scikit-learn 0.23 were
utilized. A total of 1345 different NIR spectra were used in this study.
Each spectra consists of 256 individual variables, describing the
measured intensity at a different wavelength. The variables are
referred to as features. Feature standardization was conducted
by removing the mean and scaling the values to unit variance.
(Eq. 1)
Here, is the standard score of a sample, is the value of a single
feature and is the average of the feature values. The dataset
standard deviation is represented by .
Principal component analysis (PCA) was also applied on NIR
spectra. It is an unsupervised data dimension reduction technique
frequently applied on large spectral data [43]. Unsupervised ma-
chine learning techniques are concerned with finding patterns and
structures in unlabeled data, while supervised learning concerns
learning from labeled data (e.g. NIR data that are trained with
laboratory reference values as labels) [54, 55]. Each principal
component (PC) is a linear combination of the original data. Data
dimension reduction can lead to a simplification of the data set
whilst maintaining a significant proportion of the variance, when
the first few PCs can explain most of variance in the used data
[56]. The first PC is the direction along which the samples show
the largest variation, explaining the most amount of variance in the
original data. The second PC is the direction that is uncorrelated
(orthogonal) to the first component, but along which the samples
show the largest variation [57].
2.4 Measurement of NIR Spectra
NIR spectra were obtained in a 1 L stainless steel stirred reactor
(fill volume 500 mL) with a NIR process spectrometer (PSS 2120,
Polyetc GmbH, Germany) equipped with a quartz halogen lamp.
The mash was stirred during the measurement and the spectra
were recorded in absorption mode at 20 °C. This differs from tem-
peratures usually applied for the “protein rest” during mashing. In
practice, a wide variety of different mashing procedures is found
with different “protein rest” temperatures, that are e.g. 38 °C and
48 °C to 52 °C [58–60].
The enzymes involved in proteolysis are endo-proteinases, exo-
peptidases, and carboxypeptidases [12]. Aldred et al. demon-
strated that no decrease in protein levels in beer mash occurs (due
to enzymatic or physical protein degradation) below a temperature
of 45 °C [12]. Therefore, no further change in FAN concentrations
is expected at 20 °C. The chosen experimental setup (at 20 °C)
thus allows for acquiring inline NIR sensor data and ninhydrin
reference measurements at stable conditions.
The analysed wavelength range was 1100 – 2100 nm with a
resolution of 3.9 nm. Baseline correction was conducted with
demineralized water. An inline transflectance probe (Avantes BV,
The Netherlands) was used with an optical path length of 10 mm
(distance between optical fibre and reflecting mirror: 5 mm).
2.5 Statistical Evaluation
Model performance was judged by the root mean square error
(RMSE) and R2. The RMSE is used to measure the error of predic-
tions by comparing the predicted value with the expected value and
is frequently used for regression performance analysis [27, 41, 43,
44, 61–63]. This in contrast to the standard deviation, where the
spread of data around a mean value is measured.
(Eq. 2)
Here, is the vector of the FAN levels determined with reference
experiments (observed values) and is the vector of FAN levels
predicted with a machine algorithm (predicted values). Both, the
training performance of the machine learning algorithm and the
prediction performance of the trained model on independent and
external validation data was evaluated with RMSE. RMSE for the
training performance is referred to as root mean square error of
calibration (RMSEC). The RMSE for the prediction performance
of the trained model on validation data is referred to as root mean
square error of prediction (RMSEP). Criteria to evaluate fitting
accuracy are high R2 and low RMSE values [43, 62].
The coefficient of variation (CV) was used to describe the repeat-
ability and precision of the results obtained from FAN level predic-
tion with NIR spectroscopy. The CV is calculated as the ratio of
to the corresponding mean value .
(Eq. 3)
(Eq. 4)
The observed values are { 1, …, n } and is the mean of the
observed values. The sample size is demonstrated by the de-
nominator .

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Also, the standard error (SE) indicating the distance from a sample
mean to the mean of a population was calculated in this study for
the FAN reference measurements.
(Eq. 5)
Here, is the standard deviation and is the numer of samples.
2.6 Machine Learning Strategy
This study aims to present an easy hands-on approach using
machine learning for the determination of FAN in beer mash. FAN
concentrations corresponding to raw NIR spectra of measured beer
mashes were determined with laboratory experiments (reference
data). The data were processed as shown in figure 1.
2.6.1 Raw Data
The used machine learning algorithms were trained on “training
data” and validated on “validation data”. Both datasets consist
of NIR spectra, that were labelled with the corresponding FAN
reference values obtained from the ninhydrin assay. From the 20
generated batches of mash, 16 were used for model training and
4 were used for model validation.
2.6.2 Data Pre-processing
The NIR data were prepared with four different pre-processing
strategies that were used for independent approaches: (i) raw NIR
data; (ii) standardized NIR data; (iii) dimensionally reduced NIR
data by PCA (fist two components); (iv) standardized NIR data that
were dimensionally reduced by PCA (first two components). Those
steps were identical for training and validation data. Afterwards,
the training data order was randomly changed (shuffled) and the
data were split into a test and a training set (10 % test set, 90 %
training set). A similar ratio for test and training set has already
been reported in other studies [64–67]. Of note, the pre-processing
does not influence the labelling of data, i.e. NIR spectra and cor-
responding FAN reference values are always shuffled as a pair.
2.6.3 Application of Different Machine Learning Algorithms
Machine learning algorithm training was then performed with the
training set. Subsequently, the trained model was used to predict
FAN values from the test set and the validation data.
2.6.4 Evaluation
To evaluate the prediction performance in comparison with the FAN
reference values in terms of accuracy, the RMSEC and RMSEP
was used.
2.7 Machine Learning Modules
Linear machine learning algorithms for regression are applicable if
the target value is a linear combination of the individual features.
In linear regression, the vector of observed values (dependent
variable) is a linear function of the regressors (predictor variable).
(Eq. 6)
Here, w is the vector of the unknown population to be estimated.
Factors influencing other than are referred to as error and
are represented by . The FAN values are represented by and
Fig. 1 Data processing steps for the determination of FAN content in beer mash. ”Training Data” and “Validation Data” consist of NIR
spectra and FAN reference values from the ninhydrin assay. Pre-processing such as standardization and dimension reduction
with a PCA were only applied on the NIR data

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An estimator that shows a relatively small bias on the training
data and has a higher RMSE and/or R2 score than an unbiased
estimator is closer to the real value of the parameter [46]. If finally
the variance of the ridge estimator could be reduced, the
mean squared error tends to be lower compared to OLS [46].
BRR is a variant of RR that formulates linear regression problems
by the aid of probabilities.
(Eq. 12)
Here, the output vector is viewed as variable of which the ele-
ments ( , ) are distributed in a Gaussian distribution (…).
The variance of the distribution is given by . According to Bayes’
theorem, the posterior probability of the parameter is proportional
to likelihood and prior.
(Eq. 13)
The evidence term is commonly ignored in model fitting with Bayes
regression [69]. The posterior is defined as the revised probability
of an occurring event depending on the available data.
(Eq. 14)
Here, is the parameter used to impose a penalty on the size of the
coefficient similar to RR. Likelihood represents the distribution
of the observed data in relation to its parameters as probability.
(Eq. 15)
The output is assumed to form a Gaussian distribution around
∙ . The prior is the parameter distribution before the data are
observed.
(Eq. 16)
Estimation of the coefficient occurs during model fitting, while
the (regularisation) parameters and being updated by the “log
marginal likelihood” function as described by Tipping et al. [70].
Apart from the linear machine learning strategies mentioned
above, non-linear algorithms also exist. As demonstrated before,
also DTR is used for analysis of NIR spectroscopy data in this
work [42]. Building a decision tree (in terms of creating nodes) is
based on decisions (criteria) that are arranged in a flowchart-like
structure. Inside that structure nodes represent an attribute test
(e.g. whether a value is above or under a certain threshold). As
a result of that test, new nodes are created. The different node
paths are referred to as branches. The terminal end of the deci-
sion tree structure are leafs. The whole path beginning from the
root node and ending in the leaf represents the prediction rules
for the trained model.
However, various decision tree algorithms are available. In this
work, the classification and regression tree (CART) algorithm
that creates nodes based on binary decisions was used for model
training and FAN value prediction from NIR data. Growing trees
in CART implies recursive splitting of tree nodes into a left and a
the NIR data with 256 channels are represented by ( × 256).
Equation 6 can be rewritten as
(Eq. 7)
In this work we aim to (i) train a model on a vector of reference FAN
values and the corresponding NIR data matrix by estimating
the parameter vector . Then, we aim (ii) to predict FAN values
from NIR spectra measured inline. The criteria used to determine
is to minimize the residual .
(Eq. 8)
The sum of squared residuals (RSS) is used to minimize .
(Eq. 9)
Here, has the dimension 1 × and has the dimension × 1.
The calculation of the estimator vector by OLS is then given by
(Eq. 10)
describes the estimator vector of the regression coefficients
achieved by OLS regression and is the matrix consisting of the
features (NIR predictor variables). FAN reference values are the
observed values .
RR is an alternative to OLS. It allows regularisation of the estimator
by introducing the penalizing scalar parameter [47].
(Eq. 11)
Here, is the identity matrix. The application of a regularisation
parameter works by trading increased bias for reduced variance
[68], meaning that regularisation parameters reduce errors occur-
ring during function fitting (training) and avoid overfitting. The bias
represents the best possible fitting of an algorithm to a test data set
of infinitive size [54]. Therefore, a low bias represents a relatively
high correlation to the training data, while a high bias represents
a relatively low correlation to the training data [54]. If the variance
of a model to validation data is high while the bias to the test set
is low, overfitting occurs.
Overfitting results in a minor predictive capability of a machine
learning algorithm and often appears if a relatively small set of
data is used for model training, as noise in that relatively small
amount of data might be interpreted as real information [54]. This
is of particular interest in the field of beer/food production, as the
measurement of reference data is often time consuming and the
number of data are therefore limited.
The regularisation parameter aims to prevent overfitting by in-
creasing the bias to the test data set and decreasing the variance
from generated model to the validation data set at the same time,
changing the bias/variance trade-off of a machine learning model.
If = 0, the regularisation parameter shows no effect on RR and
the estimation results will be equal to OLS. Choosing a regularisa-
tion parameter > 0 mimizes and aims to reduce the error on
generalized or validation data, while the bias on OLS [47].

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right branch: a root node containing all the calibration data and two
children nodes (left and right) containing data observations [42].
The DTR uses the mean squared error (MSE) to decide how to
split a node in sub-nodes. CART algorithm divides training data
depending on the attributes (category) and (threshold for
category). Determination of and is accomplished by the loss
function ( , ):
(Eq. 17)
(Eq. 18)
(Eq. 19)
Here, is the subset of features and the mean squared error (MSE)
is used as optimization indicator.
The KNN algorithm was also used for the prediction of FAN levels
from NIR data. KNN allows for a non-linear observation of coher-
ences describing the relation between the NIR data and the FAN
reference values [71]. To predict values (e.g. FAN levels) from any
new data (e.g. NIR spectra), similarities between the training data
(e.g. FAN concertation and NIR spectra) and the data used for
prediction are determined. Therefore, prediction of a new value is
based on how closely the measured data (NIR spectra) resemble
the set of training data. The constant is used to define the num-
bers of neighbours used for the prediction. Here, the nearest five
neighbours ( = 5) were used, meaning that a value was predicted
from the five data points, with the most similar structure. To find the
closest neighbours a distance function calculating the difference
between two stances is used [43].
(Eq. 20)
In Equation 20, the distance between the vectors of a new observa-
tion and an observation used for model training is determined.
Non-linear regression based on Support Vector Machines (SVM)
was also tested. It is referred to as SVR [72]. SVM is based on the
calculation of hyper-planes in the input feature space to separate
classes with maximal margin. The closest samples to the decision
boundary defining the hyper-plane position are called support
vectors [1].
SVR uses a penalty parameter ( SVR) which allows for a selection of
prediction parameters within a certain range only. That channelizes
the available data into a tube, whereas small SVR values allow for
a reduced error tolerance and vice versa [55]. SVR formulates a
function approximation problem as an optimization problem that
attempts to find the narrowest tube possible centred around the
available data [55]. The support vectors used for prediction are
located at the boundary of the area defined by SVR.
However, SVR can apply a “kernel trick”, that allows the algorithm
to operate in a higher dimension without computing the coordinates
in that space. This can help to solve non-linear problems [73]. In
principal, the input data can be transformed ( maps) into a
higher -dimensional feature space: . E.g. a posi-
tive definite kernel is expressed as
(Eq. 21)
Then non-linear problems can be solved linearly [1, 73].
(Eq. 22)
Here, is the bias term. and are the coefficients and non-
linear transformations, respectively [1]. Commonly used kernel
functions that were also applied in this study are the linear kernel
and the Radial Basis Function kernel (rbf) [73].
(Eq. 23)
(Eq. 24)
(Eq. 25)
The spread of the rbf was controlled by , where is the number
of features and is the variance of . The quality of the estima-
tion is then measured by a loss function that is sensitive to SVR [1].
(Eq. 26)
(Eq. 27)
(Eq. 28)
(Eq. 29)
Here, is the number of inputs, and are the inputs and tar-
gets, and and are the slack variables defining if a prediction
lies above the space that is created by SVR. The cost parameter
> 0 determines the trade-off between the size of (a small is
desired) and up to which deviations larger than SVR are tolerated
[74]. In this work, was set to 1. Further information regarding
the application of SVR can be seen in the publication of Smola
et al. [74].
3 Results
FAN levels in beer mash were analysed with NIR spectroscopy and
machine learning algorithms. FAN reference values were obtained
from a ninhydrin assay. Samples from 20 different mashes with
varying FAN concentrations were prepared and analysed. 16 of
those samples were used for model training, 4 for model valida-
tion. The results of the FAN ninhydrin assay analysis are shown
in table 2 (see page 113).

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Table 2 Results of the FAN nynhidryn assay reference analysis. n = 6
Batch No. FAN
[mg/L]
s
[mg/L]
CV
[%]
SE
[mg/L] Training Validation
1 220.22 ± 1.29 ± 1.67 ± 0.53 Yes No
2 218.29 ± 1.77 ± 3.12 ± 0.72 No Yes
3 215.68 ± 1.41 ± 1.99 ± 0.58 Yes No
4 213.77 ± 1.14 ± 1.29 ± 0.46 Yes No
5 206.89 ± 2.48 ± 6.16 ± 1.01 Yes No
6 206.50 ± 1.19 ± 1.41 ± 0.48 No Yes
7 204.69 ± 1.66 ± 2.75 ± 0.68 Yes No
8 202.72 ± 1.53 ± 2.34 ± 0.62 Yes No
9 201.76 ± 1.41 ± 2.00 ± 0.58 Yes No
10 199.41 ± 1.85 ± 3.43 ± 0.76 Yes No
11 199.13 ± 2.30 ± 5.30 ± 0.94 No Yes
12 197.12 ± 1.72 ± 2.95 ± 0.70 Yes No
13 194.81 ± 1.12 ± 1.26 ± 0.46 Yes No
14 192.48 ± 1.72 ± 2.94 ± 0.70 Yes No
15 190.63 ± 1.91 ± 3.64 ± 0.78 Yes No
16 190.62 ± 1.33 ± 1.77 ± 0.54 Yes No
17 187.15 ± 0.88 ± 0.78 ± 0.36 Yes No
18 186.24 ± 1.44 ± 2.08 ± 0.59 No Yes
19 183.00 ± 2.26 ± 5.09 ± 0.92 Yes No
20 181.86 ± 0.97 ± 0.94 ± 0.40 Yes No
Fig. 2 Example of NIR spectra used for training of machine learning algorithms. A: raw
NIR spectra, B: standardized NIR spectra; For a better clearness only around 15 %
randomly chosen of the data are shown in this figure. FAN levels of the spectra
are indicated by the grey scale
The laboratory analysis showed that the FAN concentration of the
investigated mash samples was in a range of 181.86 mg/L (s =
± 0.97 mg/L) and 220.22 mg/L (s = ± 1.29 mg/L).
3.1 Spectra Presentation
The NIR spectra used for training of machine learning algorithms
are displayed in figure 2. Areas with high
noise levels were detected between 1400 nm
– 1500 nm and 1900 nm – 2100 nm in the
raw data sets. Those areas also clearly show
noise in the standardized spectra.
The noise areas correspond to the first and
second water overtone areas in NIR spectra.
Areas before and between the noise areas
are distinguishable in standardized and raw
NIR data. FAN level and absorbance do not
correlate. The position of the spectra in the
figure 2 shows a randomized behaviour rather
than an organized distribution induced by
different FAN levels. A determination of FAN
levels is not possible from NIR spectra in this
processing status.
3.2 Principal Component Analysis
of NIR Spectra
A dimensionality reduction of data was con-
ducted with a PCA. The data were transferred
from a space with 256 dimension to a space
with 2 dimensions (Fig. 3, see page 114). PCA
of raw NIR data showed an explained variance
of 13.94 % for the first and 5.93 % for the sec-
ond principal component. Standardized data
decomposition resulted in variances explaining
55.51 % (PC 1) and 20.77 % (PC2).
The PCA of raw NIR data does not permit the
separation into independent clusters. However,
it is visible that data representing a lower FAN
are oriented in the lower left segment of figure
3A and those for medium and higher FAN in
opposite direction. A separation between the
different concentrations is still not possible as
the sections (low, medium, high FAN) overlap
each other.
The PCA of standardized data resulted in fairly
separable clusters. The clusters only allow a
clear separation of spectra with relatively high
differences in FAN concentrations as shown
in figure 3 B. However, data representing the
highest FAN levels (darkest sports) are clus-
tered on the right and the left side of the plot
(Fig. 3 B), indicating that FAN levels are not
the main driver of separation of the observed
clusters in the direction of PC 1.
Other factors influencing the quality of the NIR spectra such as
gradually dropping absorbance levels during measurement were
not observed in this study.
3.3 Training of Machine Learning Algorithms
Machine learning algorithms were applied on the NIR spectra

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Training results of BRR and RR applied on
raw data showed the best fits relating to the
RMSEC and R2 scores. The results are shown
in figure 4. As indicated by the obtained scores
(Table 3), training with raw and standardized
data show a similar distribution of predicted
values (Fig. 4 A and B). Application of data
pre-processed with PCA and a combination
of PCA and standardization showed a lower
accuracy compared to the raw data and
standardized data for the BRR approach and
for all the other algorithms tested. Both the
results of fitting with PCA and a combina-
tion of PCA and standardized data showed
a similar distribution as displayed in figure 4
C and D as expected given the similar score
values in table 3.
The RR algorithm can be regularised by the
scalable parameter value (cf. Eq. 11) to
achieve a potentially lower bias on the training
set and a greater variance on the test set. A
high bias is prone to overfitting of the trained
model. In comparison with OLS, where the
bias cannot be controlled by an additional vari-
able imposed on the learning coefficients, only
slightly better RMSEC values were achieved
with an value of = 1 ∙ 10-6. Also, values
of 1 ∙ 10-2 and 1 were tested on the data, but
with worse prediction accuracy compared to
an value of 1 ∙ 10-6 (cf. Table 3).
Improved training results with standardized
data compared to raw data were found for SVR
(rbf and linear kernel), DTR and KNN (k = 5).
Training of data with PCA pre-processing
showed no RMSEC values below 9.70 mg/L,
regardless if the NIR data were standardized
before decomposing, or not.
Overall model training with DTR and stand-
ardized data provided the best results in terms
of the lowest RMSEC. The training results are
shown in figure 5, see page 115. Again, data
pre-processed with PCA and a combination
of PCA and standardization did not allow a
sufficient FAN prediction in the training stage
and were therefore not considered for valida-
tion on external data.
3.4 External Validation of Trained
Machine Learning Models for
the Determination of FAN
The trained machine learning models were validated with data
not included for the model training. Those data were provided by
independent experiments representing external data to the training
Fig. 3 PCA of (A) raw NIR data and (B) standardized NIR data. 100 % of the data are
shown. FAN levels of the individual spectra are displayed by the grey scale
Fig. 4 Training results with test data of BRR for the prediction of FAN from NIR data. A:
without pre-processing of training data ; B: with standardization of training data
before model training; C: with PCA of training data prior to model training; D: with
standardized data used for PCA prior to model training. The dashed line indicates
an ideal fit between predicted and reference values
gathered from mash samples. The best training results for raw NIR
spectra were obtained for OLS, DTR, RR and BRR. The complete
results of the investigated machine learning algorithms are shown
in table 3, see page 115.

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Table 3 Results of machine learning training; Range of investigated FAN values: approx. 180 mg/L to 220 mg/L
Algorithm without pre-processing with standardization with PCA with PCA and
standardization
RMSEC
[mg/L] R2RMSEC
[mg/L] R2RMSEC
[mg/L] R2RMSEC
[mg/L] R2
OLS 2.60 0.95 2.60 0.95 9.85 0.15 9.85 0.15
SVR
RBF 7.72 0.50 4.63 0.83 9.70 0.19 9.70 0.19
Linear 5.91 0.69 3.11 0.92 9.99 0.15 9.99 0.15
DTR 3.44 0.90 2.13 0.96 13.28 0.06 13.78 0.03
RR
α = 1 ∙ 10-6 2.58 0.95 2.60 0.95 9.85 0.15 9.85 0.15
α = 0.01 3.08 0.92 2.59 0.95 9.85 0.15 9.85 0.15
α = 1 4.76 0.80 2.75 0.94 9.85 0.15 9.85 0.15
KNN
k = 5 8.30 0.40 2.51 0.98 10.04 0.17 10.04 0.17
BRR 2.58 0.96 2.62 0.94 9.85 0.15 9.85 0.15
Fig. 5 Training results with test data of DTR for the prediction of FAN levels from NIR
data. A: without pre-processing of training data; B: with standardization of training
data before model training; C: with PCA of training data prior to model training;
D: with standardized data used for PCA prior to model training. The dashed line
indicates an ideal fit between predicted and reference values
stage. The validation results are shown in table 4, see page 116.
As seen already for the (internal) training evaluation OLS, BRR
and RR showed better results in terms of lower RMSEP values
(compared to the other three model types). However, the DTR
showed comparably high RMSEP values in
the external validation whereas in the train-
ing status a relatively low RMSEC value
was found. With standardized NIR data DTR
allowed the FAN prediction with the lowest
RMSEP of all tested algorithms. For all other
algorithms, models with standardized data
showed higher RMSEP values compared
with unpre-processed data. The correlation of
predicted FAN concentrations to the labora-
tory reference data was best with BRR when
using raw (unpre-processed) NIR data, as
shown in figure 6, see page 116.
The lowest CV was found for the BRR model
that was 1.03 % (220.73 mg/L ± 2.26 mg/L),
while the highest 1.26 % (200.33 mg/L
± 2.52 mg/L) indicating a good reproduc-
ibility of the regression model according to
the requirements of industrial practice (cf.
Fig. 6). Predicted FAN levels from 64 NIR
measurements were used to calculate the
coefficients of variation, each. The lowest
RMSEP value for validation with standardized
data was 7.53 mg/L found for DTR.
4 Discussion
In this study, the application of NIR spectros-
copy in combination with an inline probe for
FAN quantification in beer mash was shown
for the first time. NIR spectroscopy allows for
a chemical feedback based on infrared light absorption. Mitzscher-
ling et al. already have demonstrated the application of a sensor
array for FAN online monitoring using a bypass [8]. However, the
then used system concentrated on rather physical measurement
parameters such as ultrasonic and conductivity measurements

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addition, for inline NIR measurement only a single senor is needed,
simplifying the technical implementation.
4.1 Precision and robustness of the NIR FAN determi-
nation in comparison to the reference method
Reference laboratory data are the foundation for supervised
machine learning methods. Supervised learning relies on prior
knowledge about an example dataset to make predictions about
new data points, e.g. predicting the value of a response variable
on the basis of the input variables [75]. The quality and accuracy
of those data is essential for the machine learning performance.
The ninhydrin assay for the determination of FAN levels in beer
used in this paper was published by Lie and is the EBC/MEBAK
standard method [17]. Analysing 14 replicates Lie obtained a vari-
ation coefficient of 4 – 6 % in FAN level analysis [17].
The majority of FAN ninhydrin assay results obtained from labora-
tory experiments in this study were below a variation coefficient of
6 %, with an exception for the variation coefficient of a single batch
that was 6.61 %. In this study, 6 replicates were used. Compared
to Lie higher coefficients of variation were expected, since the CV
decreases with increasing sample size [76]. However, the obtained
variation coefficients were similar or lower than the previously
reported numbers proving that the employed assay has a high
level of precision and repeatability.
Correspondingly, the precision of the results from the ninhydrin as-
say used for the reference analytics in this work measured by the
standard deviation was higher compared to the results published by
Lie [17]. The quality of the reference values is also demonstrated
by the relatively low SE values, showing that the calculated mean
values are close to the theoretical mean values of the population.
A satisfactory RMSEP and R2 indicate that sample amount and
quality (precision and repeatability) were sufficient for an accurate
machine learning based prediction model. Unsatisfying RMSEP
values might be due to reference methods unable to perform
measurements in certain level of repeatability and precision or due
to an incongruous choice of machine learning algorithms.
Prediction of FAN levels from NIR spectra with BRR resulted in
even lower coefficients of variation than observed for the majority
of reference measurements (18 of 20). The reason for this is the
greater number of samples used for the validation measurement.
64 individual NIR spectra were taken from each of the four batches
used for validation, while 6 measurements were conducted to de-
termine FAN levels with the ninhydrin assay. As mentioned above,
the CV is unproportional to the number of samples and decreases
with increasing sample number [76].
Accuracy and precision measured by RMSEP (and R2) and the
CV suggest that the NIR inline setup is able to predict FAN levels
in a satisfying quality. However, the precision also depends on the
number of samples used to predict a certain value (cf. determina-
tion of the CV). In this study, 64 for samples in the validation stage
were used to calculate the CV. A lower number of samples might
lead to a lower CV value.
The question whether an analytical method is robust or which
Table 4 Model validation on external data; RMSEP values (range
of FAN values: approx. 180 mg/L to 220 mg/L) represent-
ing the accuracy of the machine learning model as devia-
tion from the original value. For RMSEP values, the lower
the value the better the prediction
Algorithm without pre-processing with standardization
RMSEP
[mg/L] R2RMSEP
[mg/L] R2
OLS 3.04 0.95 21.32 0.04
SVR
RBF 9.44 0.40 10.24 0.25
linear 7.81 0.58 12.15 0.21
DTR 11.17 0.12 7.53 0.79
RR
α = 1 ∙ 10-6 3.00 0.95 21.32 0.04
α = 0.01 3.19 0.95 21.35 0.04
α = 1 4.94 0.84 17.63 0.01
KNN
k = 5 10.08 0.37 12.86 0.05
BRR 2.81 0.96 20.03 0.02
Fig. 6 Validation results of BRR model with external data for the
inline prediction of FAN without pre-processing of training
data. Dashed line indicate an ideal fit between predicted
and reference values. Each cluster consists of 64 values.
reaching an accuracy (RMSEP) of 15.60 mg/L FAN using PLS
regression. In our current work, we evaluated the combination of
NIR measurements with machine learning algorithms. The best
FAN prediction models (R2 ≥ 0.95) were BRR, RR (α = 1 ∙ 10-6),
OLS, and RR (α = 0.01) with 2.81 mg/L, 3.00 mg/L, 3.04 mg/L,
and 3.16 mg/L, respectively.
Given the above, the FAN prediction performance of the NIR ma-
chine learning setup seems to be more advantageous compared
to the sensor array setup presented by Mitzscherling et al. [8]. In

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factors possibly compromise the robustness of a method will be
important if it comes to its application. The definition of robustness
is similar in the field of chemical analysis and machine learning. In
the field of chemical analysis, robustness of an analytical procedure
is a measure of its capacity to remain unaffected by variations in
the method parameters [77, 78]. Examples of such variations are
the stability of the analytical sample and temperature fluctuations.
In the field of machine learning, robustness means that an algo-
rithm delivers trustworthy output values even if the input data for
model training or data used for prediction from a model are e.g.
affected by some perturbations [79–81]. Among many reasons
for altered data are the precision of measurement instruments,
quantization errors and the presence of noise [79]. Furthermore,
a robust machine learning model is characterized by the reliable
prediction of values from new and unseen data that are similar to
the data used for training. Equally, both definitions of robustness
emphasise that a robust procedure is unaffected by disturbances.
Beer mash is composed of malt, a substance of natural origin.
Biological variations of the mash are unavoidable and will therefore
play a role in the industrial application of inline FAN NIR determina-
tion. Noise areas in the NIR spectra between 1400 nm – 1500 nm
and 1900 nm – 2100 nm resulted in a perturbation of the NIR data.
Furthermore, the quality of the FAN reference measurements are
crucial for the machine learning models, as those results are used
as input data for the training algorithms. Yet, the comparison of
BRR training (RMSEC = 2.58 mg/L) and validation (RMSEP =
2.81 mg/L) metrics demonstrated, that the investigated method is
able to perform inline FAN prediction of a trustworthy robustness.
Training and validation results of RR and OLS indicated a similar
level of robustness.
The machine learning algorithms were trained within a range of
approximately 180 mg/L – 220 mg/L. Therefore, the prediction of
FAN values are expected to have a high accuracy, precision and
stable robustness within the investigated FAN range.
The inline measurements in this study were conducted at 20 °C.
However, typical “protein rest” temperatures are e.g. 38 °C and
48 °C to 52 °C [58–60]. The chosen temperature prevented a
change of the investigated mash during the measurement. This
allowed for a judgement of the FAN determination performance
on a stable measurement matrix. At temperatures that are usually
employed for the “protein rest”, FAN levels would increase during
the measurement. This might have an influence on the accuracy
and robustness of the inline FAN determination by NIR.
4.2 Quality and speed of NIR FAN determination allows
for an industrial inline application
Quality parameters such as FAN can potentially be used as a
control parameter in an industrial process. High FAN prediction
performance and fast inline data availability can be provided by
NIR spectroscopy. In this study, the measurement time for one
NIR spectrum was 640 ms. The choice of algorithm selection for
data processing plays a deciding role for the exploitation of inline
NIR for FAN determination.
In terms of achieving a fast and reliable inline FAN determina-
tion with NIR, linear regression models without the application of
data pre-processing showed the greatest potential in this study.
Elaborate pre-processing is time consuming and prone to errors.
Apart from fast measurement times, high accuracy is required for
industrial sensor systems. Here also, the linear regression mod-
els demonstrated the most accurate prediction performance and
therefore a high potential for the industrial application. They allow
inline FAN determination from NIR data in the range of accuracy
of the reference laboratory method. Among the linear regression
algorithms, the Bayesian method showed the best prediction
performance, which is at least partly explainable.
RR and OLS showed only slightly worse performances. However,
OLS prevents utilization of regularization parameters and is therefore
strongly dependent on data quality and data pre-processing. RR
allows regularisation parameters but only to a limited extend, to
change the bias of the training data set. BRR in contrast provides
variable regularization parameters that can even further adapt to
a given data set allowing it to exceed the limits of the RR regu-
larisation parameters.
4.3 BRR allows for small datasets due to its flexibility
Concerning the practical application in industrial food and bever-
age production, the limited amount of data is generally an issue
as laboratory reference analysis are usually costly. Adaptability on
the circumstances in a production site is therefore necessary for an
application in an industrial process and that can be best achieved
by the application of the comparable flexible BRR.
BRR is applicable for use on small sets of data [82]. It is flexible
with its choice of prior density assigned to measurement related
data variabilities, and it allows the implementation of models that
estimate shrinkage and perform variable selection [83]. BRR ap-
plication on data sets of varying sizes collected with measuring
instruments of varying precision can still lead to satisfactory predic-
tion models due to the flexibility of the algorithm itself.
4.4 DTR showed overfitting
DTR performance on training data tend to show a misleading
indication of the algorithm’s true predictive capacity [65]. In this
study, DTR showed a high accuracy on training data and a far
worse performance on validation data, indicating an overfitting.
That probably resulted from the fitting of noise and peculiarities in
training data rather than finding a general predictive rule [84]. Much
effort on the general design of the decision tree would be necessary
for better and perhaps acceptable prediction result. However, the
costly and time-consuming preparation of such an elaborated and
sensible design is not suitable for an industrial inline application
requiring a certain degree of robustness.
4.5 Boundary conditions such as interaction of water
and NIR are unavoidable in mash
Boundary conditions are circumstances that are uninfluencable
e.g. due to technical limitations of the analytical equipment or the

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composition of a sample. In this study, the main component of the
mash samples analysed with NIR spectroscopy was water. Usually,
the malt-liquor ratio during mashing is 1 : 4 or 1 : 3 [58, 85–88]. In
this study, a ratio of 1 : 4 was used, whereby the influence of water
on the NIR spectra was expected to be greater than of a mash
with a malt-liquor ration of 1 : 3 due to the higher amount of water.
The NIR spectra obtained from mash samples showed two noise
areas in the first overtone region and in the combination band
region of water. The noisy areas were induced by the relatively
high water content of the mash samples. They resulted in artefact
values leading to reach the maximum capacity of the detector,
especially in the combination band region and have therefore a
deteriorating effect on the NIR data quality.
However, the high water content of the mash samples cannot be
avoided in an inline measurement. Therefore, a suitable machine
learning method for inline FAN determination from NIR data must
be able to adapt to the noisy areas either by the algorithm itself or
by the application of pre-processing methods.
4.6 Standardization of data
Data pre-processing, in general, has the potential to significantly
enhance the results of machine learning algorithms in terms of
accuracy [89]. On the other hand, pre-processing methods are
a complication of machine learning strategies due to an increas-
ing number of processing steps and can impair the results. A low
number of steps needed for a machine learning strategy might
lead to a less error prone and therefore more robust concept [55].
Therefore, only cost efficient pre-processing strategies such as
standardization and dimension reduction by PCA were applied
in this study.
Data standardization is one such a cost efficient method, that is
widely used in the field of machine learning and often used to
improve training performance [90]. The anticipated effect of utiliz-
ing data standardization is to change the ratio between relatively
high values from noisy areas of the NIR spectra and relatively
low values from non noisy areas towards more balanced values
compared to the raw data.
The standardization of data led to improved or similar training
accuracies for the tested algorithms compared to training on raw
data. Nevertheless, overfitting was observed for all algorithms
trained with standardized data at the validation stage. Therefore,
standardization of NIR data was demonstrated to be unsuitable
as data pre-processing method in this study.
4.7 Dimension reduction via PCA
The explained variances obtained from PCA of raw data indicate
that only a small amount of the original information of the data is
included in the dimensionally reduced dataset. Furthermore, a sepa-
ration of the data into clusters did not occur. A dimension reduction
with PCA aims to extract the important information concerning the
variation in the data, to represent them as a set of new orthogonal
variables called principal components, and to display the pattern
of similarity of the observations and of the variables [91, 92].
As no patterns of similarity were found, PCA is probably not suit-
able as data pre-processing step for the data obtained in this study.
The areas of noise in the NIR spectra probably have contributed
to that. Removing those areas and/or the application of spectral
pre-processiong steps such as Savitzky-Golay filter or smoothing
of the spectral data might be necessary if PCA is used. Accord-
ingly, PCA as a pre-processing strategy was not implemented for
the validation with external data.
5 Conclusion
NIR spectroscopy with an inline transflectance probe is able to
predict FAN levels in beer mash by the application of machine
learning algorithms. A variety of six different machine learning re-
gression algorithms were tested on mashing samples. The tested
machine learning models utilized linear and non-linear algorithms.
Linear algorithms showed the highest accuracy for the inline predic-
tion of FAN levels in beer mash in this study. Among them, BRR
showed the most promising results in terms of accuracy and preci-
sion. Different data pre-processing steps from the field of machine
learning were tested to increase the performance of the tested
algorithms. Neither of them contributed to an increased precision
and/or accuracy of the tested models. Omitting pre-processing
steps contributes to a reduced effort in the implementation of that
technology.
Acknowledgments
Financial support by the Federal Ministry of Education (BMBF),
project 13FH3I01IA, in the frame of smartFoodTechnologyOWL,
and the Ministry of Culture and Science of North Rhine-Westphalia
is gratefully acknowledged.
Declaration of Interests
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to
influence the work reported in this paper.
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of the Veritas laboratory in Zurich
of Doemens wba – Technikum GmbH in Graefelfi ng/Munich www.brauwissenschaft.de
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Received 29 June 2021, accepted 13 September 2021