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foods
Article
Effects of Morphology on the Bulk Density of Instant
Whole Milk Powder
Haohan Ding 1, Bing Li 1, Irina Boiarkina 2, David I. Wilson 3, Wei Yu 1,* and Brent R. Young 1
1Department of Chemical & Materials Engineering, University of Auckland, Auckland 1010, New Zealand;
hdin307@aucklanduni.ac.nz (H.D.); bing.li@auckland.ac.nz (B.L.); b.young@auckland.ac.nz (B.R.Y.)
2Fonterra Co-Operative Group Limited, Auckland 1010, New Zealand; Irina.Boiarkina@fonterra.com
3Electrical and Electronic Engineering Department, Auckland University of Technology,
Auckland 1010, New Zealand; david.wilson@aut.ac.nz
*Correspondence: w.yu@auckland.ac.nz
Received: 28 June 2020; Accepted: 29 July 2020; Published: 31 July 2020
Abstract:
The chemical and physical properties of instant whole milk powder (IWMP), such as
morphology, protein content, and particle size, can affect its functionality and performance.
Bulk density, which directly determines the packing cost and transportation cost of milk powder, is one
of the most important functional properties of IWMP, and it is mainly affected by physical properties,
e.g., morphology and particle size. This work quantified the relationship between morphology and
bulk density of IWMP and developed a predictive model of bulk density for IWMP. To obtain milk
powder samples with different particle size fractions, IWMP samples of four different brands were
sieved into three different particle size range groups, before using the simplex-centroid design (SCD)
method to remix the milk powder samples. The bulk densities of these remixed milk powder samples
were then measured by tap testing, and the particles’ shape factors were extracted by light microscopy
and image processing. The number of variables was decreased by principal component analysis
and partial least squares models and artificial neural network models were built to predict the bulk
density of IWMP. It was found that different brands of IWMP have different morphology, and the bulk
density trends versus the shape factor changes were similar for the different particle size range groups.
Finally, prediction models for bulk density were developed by using the shape factors and particle
size range fractions of the IWMP samples. The good results of these models proved that predicting
the bulk density of IWMP by using shape factors and particle size range fractions is achievable and
could be used as a model for online model-based process monitoring.
Keywords:
instant whole milk powder; bulk density; morphology; principal component analysis;
partial least squares; artificial neural networks
1. Introduction
Bulk density, also called packing density, represents the weight of powder per unit volume,
and could generally be stated in kg/m
3
or g/cm
3
[
1
,
2
]. Bulk density is vital for instant whole milk
powder (IWMP) because it affects the packing, transportation, and processing of IWMP, all of which
affects the profit of IWMP processing [
3
]. For example, when transporting milk powder over long
distances, high bulk density can reduce the cost of shipping and packaging materials, while when selling
milk powder, low bulk density can make a milk powder more competitive than other brands’ higher
density milk powder because it has larger volume per given weight [
2
]. Furthermore, bulk density is
an important parameter describing the flowability of milk powder [
4
]. Since agglomeration increases
the particle size, it significantly reduces the bulk density of milk powder [
2
,
5
]. Therefore, the bulk
density of instant whole milk powder is generally lower than the bulk density of regular whole milk
Foods 2020,9, 1024; doi:10.3390/foods9081024 www.mdpi.com/journal/foods
Foods 2020,9, 1024 2 of 19
powder. Additionally, since free-flowing property is improved by agglomeration [
2
], regular whole
milk powder always has a poorer flowability compared with agglomerated/instant whole powder.
Generally, there are four kinds of bulk density measured: compact bulk density, tapped bulk density,
loose bulk density, and aerated bulk density [
3
]. Since the relationship between tapped and loose bulk
density is an effective evaluation of cohesion, tapped and loose bulk density are the most basic and useful
terms in describing powder behaviour [
6
]. Tuohy [
7
] reported that the tapped bulk density of whole milk
powder, skim milk powder, and fat-filled milk powder varied between 0.44 to 0.85 g/cm
3
. At present,
multiple methods can measure the bulk density of milk powders [
2
]. Nijdam and Langrish [
8
] used
a graduated cylinder of 1 g of milk powder, then used the change of volume after tapping to calculate
the loose and tapped bulk densities, while Pugliese et al. [
1
] used a 100 mL calibrated cylinder of milk
powder, before using the change of weight to calculate the loose and tapped bulk densities. However,
all current bulk density measurement methods are post-production tests. The shortage of real-time
feedback makes the real time control of bulk density difficult. Additionally, bulk density is also crucial
for some other powders. For example, it is vital for pharmaceutical powders since it determines the
complexity of handling, storing and processing these powders [
9
]. What is more, bulk density is also
an important physical parameter for soil because it can estimate its water-related characteristics [10].
Many factors determine the bulk density of milk powder. For example, the relative humidity and
the drying temperature can affect milk powder’s bulk density [
6
,
8
]. Additionally, Pisecky [
2
] pointed
out that the density of solids, the amount of interstitial air, and the sphericity of the particles determine
the bulk density of milk powder. Furthermore, Pisecky [
2
] also indicated that interstitial air and particle
shape are the dominating factors determining the bulk density of agglomerated powders, while the
bulk density of non-agglomerated powders is controlled by particle size distribution. Since the
non-agglomerated particles are recycled from the spray dryer chamber and the rest are removed in the
fluid bed, IWMP mostly consists of agglomerated particles [
2
,
11
]. Therefore, the IWMP’s bulk density
is determined by the particle shape. Similarly, Bhandari [
5
] indicated that the agglomeration process
influences the bulk density, and Abdullah and Geldart [
6
] pointed out that particle shape affects the
aerated and tapped bulk density of powders. However, most papers qualitatively use scanning electron
microscopy (SEM), to visually analyze the morphology of powders. For example,
Gaiani et al. [12]
used SEM to study the surface differences between native phospho-caseinate powders and native
phosphor-caseinate powders with addition of lactose and ultrafiltrate, respectively, but they did not
find any visual differences between the powders. SEM was also used by Murrieta-Pazos et al. [
13
] to
investigate the morphological differences between regular whole milk powders and skim milk powders,
and it was found that the surface of whole milk powders is smooth and homogeneous while the surface
of skim milk powders is wrinkled. In these studies, morphological characteristics have not often been
the key focus but rather have merely been supporting information, and the qualitative descriptions
used could generally only be identified in powders with significant compositional differences such as
skim, whole, and instant whole milk powders.
This work explores a quantitative connection between the morphology and bulk density of a single
type of milk powder (IWMP) with the ultimate aim of achieving control of bulk density. To obtain
milk powder samples with various particle size fractions, different brands of IWMPs were sieved into
three particle size groups and then recombined by using the simplex-centroid design. The quantitative
information on different shape characteristics of the powders was gathered by light microscopy and
image processing, and the tapped and loose bulk density of each milk powder sample were measured
by tap testing. In order to confirm which shape factor mostly affects the bulk density of IWMP, principal
component analysis was used. Regression analyses using partial least squares (PLS) and artificial
neural networks (ANN) were used to assess the effectiveness of bulk density prediction using the
morphology of IWMP.
Foods 2020,9, 1024 3 of 19
2. Experiment
2.1. Experimental Procedure
2.1.1. Powder Preparation
Since it is difficult to divide milk powder into different groups by morphology, and different
industrial plants may produce milk powders which have different bulk density and morphology,
different brands of IWMP samples, denoted as Brands 1, 2, 3 and 4, were purchased. All of these milk
powders were bought offthe shelf in a local Auckland, NZ, supermarket. Additionally, although some
other properties may affect the bulk density of IWMP, e.g., moisture and oil content, the bulk density
of IWMP is mainly determined by particle shape and the amount of interstitial air [
2
]. The aim of this
work is to develop on-line or at-line sensors to predict the bulk density of IWMP; the effects of other
properties on the bulk density of IWMP will be studied in the future.
2.1.2. Sieving
In previous research, the particle size groups had different diameter ranges [
2
,
3
,
14
] and the
prediction performance of the model might have been affected by the range of the diameters. In this
research, a Retsch AS200 sieve shaker was used to divide the milk powders into different but consistent
particle size range groups: coarse particles (>355
µ
m), medium particles (180–355
µ
m) and fine particles
(<180
µ
m). 150 g samples of milk powder were shaken for 30 min before the powders were transferred
to foil bags to ensure stable moisture content. To minimize the breakdown of agglomerates, the sieve
shaker used was a vibratory type and the amplitude selected was low. It is worth mentioning that
the milk powder samples that were measured came from a packer and had already gone through
significant dense phase vacuum transport. Therefore, only the most robust powder is left behind at
this point, as everything else is crushed during transport [
15
]. Finally, the milk powders from different
particle size fractions were remixed following a simplex centroid design, discussed in Section 2.1.5.
2.1.3. Image Processing
Particle shape factors were obtained by light microscopy and image processing. Firstly, 0.08 g
IWMP was weighed out before dispersing into 16 mL canola oil, followed by stirring at 600 rpm for
10 s [
14
]. 1 mL of the oil and powder combination was then loaded by a pipette onto a clean microscope
slide. The photos of IWMP particles were taken by a light microscope which consisted of a
×
10 objective
lens and a
×
10 Moticam camera. For each slide, twenty photos were taken, and for repeatability three
slides were analysed for each sample. An example image of the agglomerated particles is presented in
Figure 1a. Lastly, a custom MATLAB function was used to process these images. The boundaries of
each milk powder particle were computed and extracted from images, as shown in Figure 1b. Although
there are some alternative microscopy techniques that can obtain particle shape information, such as
stereo microscope and confocal microscope, we used light microscopy since it is cheap and easy to
operate, and the best choice for at-line sensor development [11].
Foods 2020, 9, x FOR PEER REVIEW 3 of 19
2. Experiment
2.1. Experimental Procedure
2.1.1. Powder Preparation
Since it is difficult to divide milk powder into different groups by morphology, and different
industrial plants may produce milk powders which have different bulk density and morphology,
different brands of IWMP samples, denoted as Brands 1, 2, 3 and 4, were purchased. All of these milk
powders were bought off the shelf in a local Auckland, NZ, supermarket. Additionally, although
some other properties may affect the bulk density of IWMP, e.g., moisture and oil content, the bulk
density of IWMP is mainly determined by particle shape and the amount of interstitial air [2]. The
aim of this work is to develop on-line or at-line sensors to predict the bulk density of IWMP; the
effects of other properties on the bulk density of IWMP will be studied in the future.
2.1.2. Sieving
In previous research, the particle size groups had different diameter ranges [2,3,14] and the
prediction performance of the model might have been affected by the range of the diameters. In this
research, a Retsch AS200 sieve shaker was used to divide the milk powders into different but
consistent particle size range groups: coarse particles (>355 μm), medium particles (180–355 μm) and
fine particles (<180 μm). 150 g samples of milk powder were shaken for 30 min before the powders
were transferred to foil bags to ensure stable moisture content. To minimize the breakdown of
agglomerates, the sieve shaker used was a vibratory type and the amplitude selected was low. It is
worth mentioning that the milk powder samples that were measured came from a packer and had
already gone through significant dense phase vacuum transport. Therefore, only the most robust
powder is left behind at this point, as everything else is crushed during transport [15]. Finally, the
milk powders from different particle size fractions were remixed following a simplex centroid design,
discussed in Section 2.1.5.
2.1.3. Image Processing
(a)
Figure 1. Cont.
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Foods 2020, 9, x FOR PEER REVIEW 4 of 19
(b)
Figure 1. (a) Image of agglomerated milk powder particles; (b) Particle identification processed by
MATLAB.
2.1.4. Tap Testing
The bulk density of IWMP was obtained by tap testing. This test uses a Quantachrome Autotap
that is equipped with a moving platform and a hollow circular box whose mass and volume are
known. A clear plastic cylinder sits over this box that allows excess powder to be poured over the
volume limit. Powder was poured into the box, and excess powder removed by a flat ruler, before
weighing the total mass of powder and box to calculate the loose bulk density by Equation (1):
𝐷 = 𝑀 − 𝑀
𝑉
(1)
where DL is the loose bulk density, Mc represents the mass of the box, Ml represents the total mass of
powder and box before tapping, and Vc is the volume of the box.
Next, a clear plastic cylinder was fixed on the container, and more milk powder was poured into
this cylinder. The container was then tightened onto the auto tap machine. After tapping 1250 times
[2,16], the plastic cylinder was removed, and the excess powder was again removed by the flat ruler.
Finally, the container was weighed, and Equation (2) was used to compute the tapped bulk density
of IWMP:
𝐷 = 𝑀 − 𝑀
𝑉
(2)
where DT is the tapped bulk density and Mt represents the total mass of powder and container after
tapping.
2.1.5. Simplex-Centroid Design (SCD)
As the proportion of the component is determined by a mixture, simplex-centroid design (SCD)
can examine the relationship between a mixture component and response variables [17,18]. In this
research, the boundaries of the design factors were determined by the boundaries of components
[19]. The boundaries of the components were controlled by sieving results: fine particles occupied
20–40% of the IWMP, medium particles were 50–70% of the IWMP, and the boundaries of coarse
particle fraction ranged from 10% to 30%. Figure 2 shows the particle size fractions of the IWMP
samples. For example, in sample 6, coarse particles account for 10%, 70% of the particles are medium,
and fine particles account for 20%. Firstly, the milk powders were divided into pure coarse particles
(the first sample), pure medium particles (the second sample), and pure fine particles (the third
sample). The milk powders were then remixed by using the SCD to get the other seven samples. As
a result, each brand of milk powder has ten samples in total.
Figure 1.
(
a
) Image of agglomerated milk powder particles; (
b
) Particle identification processed
by MATLAB.
2.1.4. Tap Testing
The bulk density of IWMP was obtained by tap testing. This test uses a Quantachrome Autotap
that is equipped with a moving platform and a hollow circular box whose mass and volume are known.
A clear plastic cylinder sits over this box that allows excess powder to be poured over the volume limit.
Powder was poured into the box, and excess powder removed by a flat ruler, before weighing the total
mass of powder and box to calculate the loose bulk density by Equation (1):
DL=
Ml−Mc
Vc(1)
where D
L
is the loose bulk density, M
c
represents the mass of the box, M
l
represents the total mass of
powder and box before tapping, and Vcis the volume of the box.
Next, a clear plastic cylinder was fixed on the container, and more milk powder was poured
into this cylinder. The container was then tightened onto the auto tap machine. After tapping
1250 times [
2
,
16
], the plastic cylinder was removed, and the excess powder was again removed by the
flat ruler. Finally, the container was weighed, and Equation (2) was used to compute the tapped bulk
density of IWMP:
DT=
Mt−Mc
Vc(2)
where D
T
is the tapped bulk density and M
t
represents the total mass of powder and container
after tapping.
2.1.5. Simplex-Centroid Design (SCD)
As the proportion of the component is determined by a mixture, simplex-centroid design (SCD)
can examine the relationship between a mixture component and response variables [
17
,
18
]. In this
research, the boundaries of the design factors were determined by the boundaries of components [
19
].
The boundaries of the components were controlled by sieving results: fine particles occupied 20–40% of
the IWMP, medium particles were 50–70% of the IWMP, and the boundaries of coarse particle fraction
ranged from 10% to 30%. Figure 2shows the particle size fractions of the IWMP samples. For example,
in sample 6, coarse particles account for 10%, 70% of the particles are medium, and fine particles
account for 20%. Firstly, the milk powders were divided into pure coarse particles (the first sample),
pure medium particles (the second sample), and pure fine particles (the third sample). The milk
powders were then remixed by using the SCD to get the other seven samples. As a result, each brand
of milk powder has ten samples in total.
Foods 2020,9, 1024 5 of 19
Foods 2020, 9, x FOR PEER REVIEW 5 of 19
Figure 2. Different particle size fraction choices based on simplex-centroid design.
2.2. Morphology Analysis
2.2.1. Shape Factors
The boundaries of each milk powder particle in the images that were extracted by the custom
MATLAB functions were used to compute the shape factors of each IWMP particle. There are many
2-D shape factors [20], and generally one or two shape factors were chosen to describe the shape of
particles [21]. In this research, the shape factors used to describe milk powder particles were: 2-D
cross-sectional area, perimeter, equivalent diameter, elongation, solidity, convexity, circularity, and
maximum and minimum Feret diameters. The definitions and detailed explanations of these shape
factors were summarized by Ding et al. [11]. Figure 3 shows the detailed information on these shape
factors.
Figure 3. Shape factors that are used for model construction.
2.2.2. Statistical Analysis and Mathematical Modelling
Principal Component Analysis (PCA)
PCA is a useful technique to obtain important information from a data set that consists of many
interrelated dependent variables and uses a reduced set of new orthogonal variables (principal
Figure 2. Different particle size fraction choices based on simplex-centroid design.
2.2. Morphology Analysis
2.2.1. Shape Factors
The boundaries of each milk powder particle in the images that were extracted by the custom
MATLAB functions were used to compute the shape factors of each IWMP particle. There are many
2-D shape factors [
20
], and generally one or two shape factors were chosen to describe the shape
of particles [
21
]. In this research, the shape factors used to describe milk powder particles were:
2-D cross-sectional area, perimeter, equivalent diameter, elongation, solidity, convexity, circularity,
and maximum and minimum Feret diameters. The definitions and detailed explanations of these
shape factors were summarized by Ding et al. [
11
]. Figure 3shows the detailed information on these
shape factors.
Foods 2020, 9, x FOR PEER REVIEW 5 of 19
Figure 2. Different particle size fraction choices based on simplex-centroid design.
2.2. Morphology Analysis
2.2.1. Shape Factors
The boundaries of each milk powder particle in the images that were extracted by the custom
MATLAB functions were used to compute the shape factors of each IWMP particle. There are many
2-D shape factors [20], and generally one or two shape factors were chosen to describe the shape of
particles [21]. In this research, the shape factors used to describe milk powder particles were: 2-D
cross-sectional area, perimeter, equivalent diameter, elongation, solidity, convexity, circularity, and
maximum and minimum Feret diameters. The definitions and detailed explanations of these shape
factors were summarized by Ding et al. [11]. Figure 3 shows the detailed information on these shape
factors.
Figure 3. Shape factors that are used for model construction.
2.2.2. Statistical Analysis and Mathematical Modelling
Principal Component Analysis (PCA)
PCA is a useful technique to obtain important information from a data set that consists of many
interrelated dependent variables and uses a reduced set of new orthogonal variables (principal
Figure 3. Shape factors that are used for model construction.
2.2.2. Statistical Analysis and Mathematical Modelling
Principal Component Analysis (PCA)
PCA is a useful technique to obtain important information from a data set that consists of
many interrelated dependent variables and uses a reduced set of new orthogonal variables (principal
components) to represent this important information [
22
–
24
]. It has been widely used in various
scientific fields [25].
In this research, ten points (10% to 100% percentiles in increments of 10%) from an empirical
cumulative distribution function (ECDF) for each shape factor value (maximum Feret diameter,
circularity, elongation, etc.) were selected to construct the models. The variable size (90 variables) is
Foods 2020,9, 1024 6 of 19
much bigger than the sample size (40 samples), which means that the matrix for PCA analysis is ill
conditioned [
26
]. Therefore, three shape factors (maximum Feret diameter, circularity, and elongation)
were chosen by PCA to develop models. However, the variable size, which has 30 shape factor variables,
was still very big. So PCA was used again to reduce the number of shape factor variables. In the end
nine ECDF points were chosen, and the variable size is smaller than the sample size. These shape
factor variables were then used to develop the PLS and ANN models.
Partial Least Squares (PLS) Regression
PLS regression is a powerful technique of analysis because of the small limitation on variable
size, noise, and sample scales [
11
]. In particle analysis, PLS has been widely used [
27
–
29
] since it
can confirm the relationships between independent variables and dependent variables [
30
]. In this
research, PLS models were developed to predict the bulk density of IWMP by using shape factors and
particle size fractions. To avoid model overfitting, cross-validation was used to determine the number
of PLS components [
31
]. The samples were separated into five groups, and the R
2
(multiple correlation
coefficient) and Q2(the cross-validated R2) of the model were calculated as follows [11]:
R2=1−RSS
SS (3)
Q2=1−PRESS
SS (4)
where RSS is the sum of the squares of the fitted residuals, SS is the sum of the squares of the difference
between actual Y values and its mean values, and PRESS is the sum of squares of the differences
between the actual and predicted Y values for the selected data.
Artificial Neural Networks (ANNs)
An ANN is a multiple parallel computing system which contains a number of neurons in layers
which can fit the data while interconnecting with each other [
32
,
33
]. ANNs are very prevalent
in classification, prediction, optimization, and clustering because of their excellent performance in
processing nonlinear signals [
34
]. In this research, MATLAB was used to solve the fitting problem.
The network of the neural net fitting application was a two-layer feed-forward network which included
sigmoid hidden neurons and linear output neurons because this feed-forward neural network model
can use consistent data, and has enough neurons in its hidden layer to fit the multi-dimensional
mapping problems arbitrarily well. Additionally, the samples were divided into three subsets: training,
validation, and testing. The training subset accounts for 70%, the validation subset occupies 15%,
while the rest of the data were used for testing. After testing a different number of hidden neurons, it was
found that ten hidden neurons performed the best. The Levenberg-Marquardt algorithm which requires
more memory but less time was chosen to train the model and to avoid overfitting [
35
]. When the mean
squared error (MSE) of the validation samples stopped reducing, the training automatically ended.
3. Results and Discussion
3.1. Univariate Analysis
To study the link between morphology and bulk density of IWMP, the morphology of each
brand’s milk powders was compared. The ECDF values of the selected shape factors (maximum Feret
diameter, circularity, and elongation) from PCA results, were used to describe the morphology of
each milk powder sample. Table 1lists the bulk densities of each brand’s coarse, medium, and fine
particle samples. The mean value and standard deviation of three repeated experiment were computed.
From Table 1, it is clear that all coarse particle samples have the lowest bulk density while all fine
particle samples show the highest bulk density. The main reason is that coarse particles are more
irregular than medium particles and fine particles, while the fine particles are the most spherical [
11
],
Foods 2020,9, 1024 7 of 19
and the spherical shaped particles will lead to higher bulk density caused by the low interstitial air
content, while the irregular shaped particles will cause lower bulk density [2].
Table 1.
Tapped and loose bulk density of coarse, medium, and fine particles for four brands of
milk powders.
Brand 1 Brand 2 Brand 3 Brand 4
Loose bulk
density (kg/m3)
Coarse 397.99 ±3.67 339.40 ±0.43 337.76 ±1.11 333.17 ±1.05
Medium 433.97 ±8.17 417.79 ±6.84 409.95 ±4.22 422.88 ±2.83
Fine 494.41 ±2.23 466.90 ±5.36 440.84 ±5.82 467.74 ±7.62
Tapped bulk
density (kg/m3)
Coarse 421.81 ±4.76 386.03 ±1.48 395.28 ±0.95 382.98 ±0.39
Medium 529.88 ±3.75 508.21 ±2.01 521.54 ±1.31 520.94 ±0.40
Fine 632.73 ±3.12 613.60 ±1.36 600.41 ±3.20 617.45 ±0.95
3.1.1. Fine Particles
Figure 4shows the ECDF of maximum Feret diameter, circularity, and elongation for fine particle
samples from four different brands of IWMP. It is clear that the ECDF curves of elongation and
circularity for Brand 3 are higher than other brands, and the tapped and loose bulk density of Brand
3
0
s fine particles are significantly lower. In addition, the ECDF curves of elongation and circularity
for Brand 1 are lower than other brands, and the tapped and loose bulk density of Brand 1
0
s fine
particles are higher. Furthermore, the values of elongation and circularity of Brands 2 and 4 are similar,
and the tapped and loose bulk density of Brands 2 and 4 are also similar, indicating that circularity and
elongation can distinguish high bulk density from low bulk density in fine particle size fractions of
IWMP. But the maximum Feret diameter of four different brands is similar, therefore, the bulk density
of IWMP cannot be distinguished by maximum Feret diameter from the fine particle size fraction.
Foods 2020, 9, x FOR PEER REVIEW 7 of 19
particle samples. The mean value and standard deviation of three repeated experiment were
computed. From Table 1, it is clear that all coarse particle samples have the lowest bulk density while
all fine particle samples show the highest bulk density. The main reason is that coarse particles are
more irregular than medium particles and fine particles, while the fine particles are the most spherical
[11], and the spherical shaped particles will lead to higher bulk density caused by the low interstitial
air content, while the irregular shaped particles will cause lower bulk density [2].
Table 1. Tapped and loose bulk density of coarse, medium, and fine particles for four brands of milk
powders.
Brand 1 Brand 2 Brand 3 Brand 4
Loose bulk density (kg/m3)
Coarse 397.99 ± 3.67 339.40 ± 0.43 337.76 ± 1.11 333.17 ± 1.05
Medium 433.97 ± 8.17 417.79 ± 6.84 409.95 ± 4.22 422.88 ± 2.83
Fine 494.41 ± 2.23 466.90 ± 5.36 440.84 ± 5.82 467.74 ± 7.62
Tapped bulk density (kg/m3)
Coarse 421.81 ± 4.76 386.03 ± 1.48 395.28 ± 0.95 382.98 ± 0.39
Medium 529.88 ± 3.75 508.21 ± 2.01 521.54 ± 1.31 520.94 ± 0.40
Fine 632.73 ± 3.12 613.60 ± 1.36 600.41 ± 3.20 617.45 ± 0.95
3.1.1. Fine Particles
Figure 4 shows the ECDF of maximum Feret diameter, circularity, and elongation for fine particle
samples from four different brands of IWMP. It is clear that the ECDF curves of elongation and
circularity for Brand 3 are higher than other brands, and the tapped and loose bulk density of Brand 3′s
fine particles are significantly lower. In addition, the ECDF curves of elongation and circularity for
Brand 1 are lower than other brands, and the tapped and loose bulk density of Brand 1′s fine particles
are higher. Furthermore, the values of elongation and circularity of Brands 2 and 4 are similar, and the
tapped and loose bulk density of Brands 2 and 4 are also similar, indicating that circularity and
elongation can distinguish high bulk density from low bulk density in fine particle size fractions of
IWMP. But the maximum Feret diameter of four different brands is similar, therefore, the bulk density
of IWMP cannot be distinguished by maximum Feret diameter from the fine particle size fraction.
Figure 4. The empirical cumulative distribution function (ECDF) of shape factors for fine particles.
The mean values of maximum Feret diameter, elongation, and circularity for fine particles of
four different brands of IWMP versus their tapped and loose bulk density values are presented in
Figure 5. As circularity and elongation increase, the bulk density also increases, while as maximum
Feret diameter increases, the bulk density decreases. This may be because the milk powders with
more regular particle shape will cause low interstitial air content, which will lead to a high bulk
Figure 4. The empirical cumulative distribution function (ECDF) of shape factors for fine particles.
The mean values of maximum Feret diameter, elongation, and circularity for fine particles of
four different brands of IWMP versus their tapped and loose bulk density values are presented in
Figure 5. As circularity and elongation increase, the bulk density also increases, while as maximum
Feret diameter increases, the bulk density decreases. This may be because the milk powders with more
regular particle shape will cause low interstitial air content, which will lead to a high bulk density.
Figure 5also shows that the circularity, elongation, and bulk density of Brands 2 and 4 are very similar.
Foods 2020,9, 1024 8 of 19
Foods 2020, 9, x FOR PEER REVIEW 8 of 19
density. Figure 5 also shows that the circularity, elongation, and bulk density of Brands 2 and 4 are very
similar.
Figure 5. Tapped and loose bulk density from four different brands of instant whole milk powder
versus mean values of shape factors for fine particles.
3.1.2. Medium Particles
The ECDFs of maximum Feret diameter, elongation, and circularity are illustrated in Figure 6. It
is noticeable that the ECDF curves of elongation and circularity for Brand 1 are well separated from
the other three brands, and the tapped and loose bulk density of Brand 1′s medium sized particles
are also significantly higher in comparison. Additionally, the values of circularity and elongation of
Brand 3 is the highest while the loose bulk density of Brand 3 is the lowest. Consequently, in the
medium particle size group, the loose bulk density of IWMP can be differentiated by elongation and
circularity. However, the tapped bulk density of Brand 3 is higher than that for Brands 2 and 4, so
circularity and elongation cannot distinguish the tapped bulk density of IWMP in the medium
particle size group. Furthermore, since the values of maximum Feret diameter of Brands 1, 2, 3, 4 are
similar, the maximum Feret diameter also cannot distinguish the bulk density of IWMP for the
medium particle size fraction.
Figure 6. The empirical cumulative distribution function of shape factors for medium sized particles
from four different brands of instant whole milk powder (IWMP).
Bulk Density (kg/m3)
Figure 5.
Tapped and loose bulk density from four different brands of instant whole milk powder
versus mean values of shape factors for fine particles.
3.1.2. Medium Particles
The ECDFs of maximum Feret diameter, elongation, and circularity are illustrated in Figure 6.
It is noticeable that the ECDF curves of elongation and circularity for Brand 1 are well separated from
the other three brands, and the tapped and loose bulk density of Brand 1
0
s medium sized particles are
also significantly higher in comparison. Additionally, the values of circularity and elongation of Brand
3 is the highest while the loose bulk density of Brand 3 is the lowest. Consequently, in the medium
particle size group, the loose bulk density of IWMP can be differentiated by elongation and circularity.
However, the tapped bulk density of Brand 3 is higher than that for Brands 2 and 4, so circularity and
elongation cannot distinguish the tapped bulk density of IWMP in the medium particle size group.
Furthermore, since the values of maximum Feret diameter of Brands 1, 2, 3, 4 are similar, the maximum
Feret diameter also cannot distinguish the bulk density of IWMP for the medium particle size fraction.
Foods 2020, 9, x FOR PEER REVIEW 8 of 19
density. Figure 5 also shows that the circularity, elongation, and bulk density of Brands 2 and 4 are very
similar.
Figure 5. Tapped and loose bulk density from four different brands of instant whole milk powder
versus mean values of shape factors for fine particles.
3.1.2. Medium Particles
The ECDFs of maximum Feret diameter, elongation, and circularity are illustrated in Figure 6. It
is noticeable that the ECDF curves of elongation and circularity for Brand 1 are well separated from
the other three brands, and the tapped and loose bulk density of Brand 1′s medium sized particles
are also significantly higher in comparison. Additionally, the values of circularity and elongation of
Brand 3 is the highest while the loose bulk density of Brand 3 is the lowest. Consequently, in the
medium particle size group, the loose bulk density of IWMP can be differentiated by elongation and
circularity. However, the tapped bulk density of Brand 3 is higher than that for Brands 2 and 4, so
circularity and elongation cannot distinguish the tapped bulk density of IWMP in the medium
particle size group. Furthermore, since the values of maximum Feret diameter of Brands 1, 2, 3, 4 are
similar, the maximum Feret diameter also cannot distinguish the bulk density of IWMP for the
medium particle size fraction.
Figure 6. The empirical cumulative distribution function of shape factors for medium sized particles
from four different brands of instant whole milk powder (IWMP).
Bulk Density (kg/m3)
Figure 6.
The empirical cumulative distribution function of shape factors for medium sized particles
from four different brands of instant whole milk powder (IWMP).
Figure 7shows the mean values of shape factors (maximum Feret diameter, elongation,
and circularity) for medium particles of different brands versus their tapped and loose bulk density.
Foods 2020,9, 1024 9 of 19
Similarly to the fine particles, with a decrease in maximum Feret diameter and an increase in circularity
and elongation (more regular particle shape) the loose bulk density shows an overall upward trend
(low interstitial air content). Additionally, with a decline in maximum Feret diameter, the tapped bulk
density rises, but the trend of tapped bulk density versus the change of circularity and elongation
is unclear.
Foods 2020, 9, x FOR PEER REVIEW 9 of 19
Figure 7 shows the mean values of shape factors (maximum Feret diameter, elongation, and
circularity) for medium particles of different brands versus their tapped and loose bulk density.
Similarly to the fine particles, with a decrease in maximum Feret diameter and an increase in
circularity and elongation (more regular particle shape) the loose bulk density shows an overall
upward trend (low interstitial air content). Additionally, with a decline in maximum Feret diameter,
the tapped bulk density rises, but the trend of tapped bulk density versus the change of circularity
and elongation is unclear.
Figure 7. Tapped and loose bulk density of four different brands of instant whole milk powder versus
mean values of shape factors for medium sized particles.
3.1.3. Coarse Particles
Figure 8 presents the ECDF of maximum Feret diameter, elongation, and circularity for coarse
particle samples from four different brands of IWMP. The maximum Feret diameter of Brand 1 has
the highest ECDF curve, while the maximum Feret diameter of Brand 4 has the lowest ECDF curve,
and the bulk densities of Brand 1 are the highest, while Brand 4′s milk powders have the lowest
tapped and loose bulk density. Additionally, the ECDF values of circularity for Brand 1 are
significantly lower than the other three brands, while the bulk densities of Brand 1 are much higher
than the other three brands. Therefore, in the coarse particle size group, the tapped and loose bulk
density of IWMP can be distinguished by maximum Feret diameter and circularity. However, due to
the similar ECDF curves of elongation for four different brands, elongation cannot differentiate the
bulk density in the coarse particle size fraction.
190 200 210 220 230
Mean value of Maxferet ( m)
410
420
430
440
190 200 210 220 230
505
510
515
520
525
530
535
Bulk Density (kg/m3)
0.3 0.35 0.4 0.45
Mean value of Circularity
410
420
430
440
0.3 0.35 0.4 0.45
505
510
515
520
525
530
535
0.58 0.6 0.62 0.64 0.66 0.68
Mean value of Elongation
410
420
430
440
Brand 1 Medium
Brand 2 Medium
Brand 3 Medium
Brand 4 Medium
Loose Bulk Density
0.58 0.6 0.62 0.64 0.66 0.68
505
510
515
520
525
530
535
Brand 1 Medium
Brand 2 Medium
Brand 3 Medium
Brand 4 Medium
Tapped Bulk Density
Figure 7.
Tapped and loose bulk density of four different brands of instant whole milk powder versus
mean values of shape factors for medium sized particles.
3.1.3. Coarse Particles
Figure 8presents the ECDF of maximum Feret diameter, elongation, and circularity for coarse
particle samples from four different brands of IWMP. The maximum Feret diameter of Brand 1 has
the highest ECDF curve, while the maximum Feret diameter of Brand 4 has the lowest ECDF curve,
and the bulk densities of Brand 1 are the highest, while Brand 4
0
s milk powders have the lowest tapped
and loose bulk density. Additionally, the ECDF values of circularity for Brand 1 are significantly lower
than the other three brands, while the bulk densities of Brand 1 are much higher than the other three
brands. Therefore, in the coarse particle size group, the tapped and loose bulk density of IWMP can be
distinguished by maximum Feret diameter and circularity. However, due to the similar ECDF curves
of elongation for four different brands, elongation cannot differentiate the bulk density in the coarse
particle size fraction.
The mean values of maximum Feret diameter, elongation, and circularity of four different brands’
coarse particles versus their tapped and loose bulk density are illustrated in Figure 9. It is clear that
as maximum Feret diameter increases and the circularity decreases (more irregular particle shape),
the bulk density decreases (high interstitial air content). It is also notable that even though the brand
order for highest to lowest bulk density has changed from what was seen with fine particles, the trends
in tapped and loose bulk density have remained consistent with the particle circularity and maximum
Feret diameter. Additionally, when the elongation of coarse particles is around 0.61, the bulk density
of IWMP coarse particles is maximum.
Foods 2020,9, 1024 10 of 19
Foods 2020, 9, x FOR PEER REVIEW 10 of 19
Figure 8. The empirical cumulative distribution function of shape factors for coarse particles.
The mean values of maximum Feret diameter, elongation, and circularity of four different
brands’ coarse particles versus their tapped and loose bulk density are illustrated in Figure 9. It is
clear that as maximum Feret diameter increases and the circularity decreases (more irregular particle
shape), the bulk density decreases (high interstitial air content). It is also notable that even though
the brand order for highest to lowest bulk density has changed from what was seen with fine
particles, the trends in tapped and loose bulk density have remained consistent with the particle
circularity and maximum Feret diameter. Additionally, when the elongation of coarse particles is
around 0.61, the bulk density of IWMP coarse particles is maximum.
Figure 9. Tapped and loose bulk density from four different brands of instant whole milk powder
samples versus mean values of shape factors for coarse particles.
In conclusion, for the fine-sized particles, elongation and circularity can differentiate high bulk
density from low bulk density for the IWMP, but the maximum Feret diameter cannot. In the
medium-sized particle group, elongation and circularity can distinguish the loose bulk density of the
IWMP. However, they cannot differentiate the tapped bulk density, while the maximum Feret
diameter still cannot distinguish the tapped and loose bulk density of the IWMP. For the coarse-sized
particles, the maximum Feret diameter and circularity can differentiate the tapped and loose bulk
200 300 400 500 600 700
Mean value of Maxferet ( m)
340
360
380
400
200 300 400 500 600 700
380
390
400
410
420
430
Bulk Density (kg/m
3
)
0.2 0.25 0.3 0.35
Mean value of Circularity
340
360
380
400
0.2 0.25 0.3 0.35
380
390
400
410
420
430
0.56 0.58 0.6 0.62 0.64 0.66
Mean value of Elongation
340
360
380
400
Brand 1 Coarse
Brand 2 Coarse
Brand 3 Coarse
Brand 4 Coarse
Loose Bulk Density
0.56 0.58 0.6 0.62 0.64 0.66
380
390
400
410
420
430
Brand 1 Coarse
Brand 2 Coarse
Brand 3 Coarse
Brand 4 Coarse
Tapped Bulk Density
Figure 8. The empirical cumulative distribution function of shape factors for coarse particles.
Foods 2020, 9, x FOR PEER REVIEW 10 of 19
Figure 8. The empirical cumulative distribution function of shape factors for coarse particles.
The mean values of maximum Feret diameter, elongation, and circularity of four different
brands’ coarse particles versus their tapped and loose bulk density are illustrated in Figure 9. It is
clear that as maximum Feret diameter increases and the circularity decreases (more irregular particle
shape), the bulk density decreases (high interstitial air content). It is also notable that even though
the brand order for highest to lowest bulk density has changed from what was seen with fine
particles, the trends in tapped and loose bulk density have remained consistent with the particle
circularity and maximum Feret diameter. Additionally, when the elongation of coarse particles is
around 0.61, the bulk density of IWMP coarse particles is maximum.
Figure 9. Tapped and loose bulk density from four different brands of instant whole milk powder
samples versus mean values of shape factors for coarse particles.
In conclusion, for the fine-sized particles, elongation and circularity can differentiate high bulk
density from low bulk density for the IWMP, but the maximum Feret diameter cannot. In the
medium-sized particle group, elongation and circularity can distinguish the loose bulk density of the
IWMP. However, they cannot differentiate the tapped bulk density, while the maximum Feret
diameter still cannot distinguish the tapped and loose bulk density of the IWMP. For the coarse-sized
particles, the maximum Feret diameter and circularity can differentiate the tapped and loose bulk
200 300 400 500 600 700
Mean value of Maxferet ( m)
340
360
380
400
200 300 400 500 600 700
380
390
400
410
420
430
Bulk Density (kg/m
3
)
0.2 0.25 0.3 0.35
Mean value of Circularity
340
360
380
400
0.2 0.25 0.3 0.35
380
390
400
410
420
430
0.56 0.58 0.6 0.62 0.64 0.66
Mean value of Elongation
340
360
380
400
Brand 1 Coarse
Brand 2 Coarse
Brand 3 Coarse
Brand 4 Coarse
Loose Bulk Density
0.56 0.58 0.6 0.62 0.64 0.66
380
390
400
410
420
430
Brand 1 Coarse
Brand 2 Coarse
Brand 3 Coarse
Brand 4 Coarse
Tapped Bulk Density
Figure 9.
Tapped and loose bulk density from four different brands of instant whole milk powder
samples versus mean values of shape factors for coarse particles.
In conclusion, for the fine-sized particles, elongation and circularity can differentiate high bulk
density from low bulk density for the IWMP, but the maximum Feret diameter cannot. In the
medium-sized particle group, elongation and circularity can distinguish the loose bulk density of the
IWMP. However, they cannot differentiate the tapped bulk density, while the maximum Feret diameter
still cannot distinguish the tapped and loose bulk density of the IWMP. For the coarse-sized particles,
the maximum Feret diameter and circularity can differentiate the tapped and loose bulk density of the
IWMP, but elongation cannot. Additionally, for all the particle size fractions (fine particles, medium
sized particles, and coarse particles), as the maximum Feret diameter decreases or the circularity
increases, the bulk density of the IWMP increases, which may be because the milk powders with small
particle size and high circularity (more regular) will lead to low interstitial air content, which will
cause a high bulk density. However, with an increase in elongation, there is no clear trend for tapped
and loose bulk density. Furthermore, although the moisture and oil content may affect the bulk density
of IWMP [
5
], these are controlled very tightly during milk powder production [
2
], so the difference of
moisture and oil content between four different brands’ IWMP should not be appreciable.
Foods 2020,9, 1024 11 of 19
3.2. Principal Component Analysis
To decide which shape factor dominates the bulk density of IWMP, PCA was used. Figure 10a
shows the scores plot of PCA, in which variables 1 to 12 represent the four different brands’ coarse
particle, medium particle, and fine particle fractions. Since the coarse particle samples have the lowest
tapped and loose bulk density, and the fine particle samples have the highest tapped and loose bulk
density, therefore the samples were well classified by their bulk density along the axes in the PCA
scores plot. It is also clear that the first two principal components were enough to categorize the
bulk density of the IWMP because they account for 88% and 6% of the total variance, respectively.
Figure 10b presents the PCA loading plot. It is noticeable that the shape factors were divided into
two groups. One of them includes all the size metrics like minimum and maximum Feret diameter,
equivalent diameter, perimeter, and area. In contrast, the other group contains all the shape metrics
(circularity, solidity, convexity, and elongation). As in the same group the shape factors have similar
loadings, the maximum Feret diameter, elongation, and circularity, for which loadings were relatively
high, were chosen to train models to predict the bulk density of IWMP.
Foods 2020, 9, x FOR PEER REVIEW 11 of 19
density of the IWMP, but elongation cannot. Additionally, for all the particle size fractions (fine
particles, medium sized particles, and coarse particles), as the maximum Feret diameter decreases or
the circularity increases, the bulk density of the IWMP increases, which may be because the milk
powders with small particle size and high circularity (more regular) will lead to low interstitial air
content, which will cause a high bulk density. However, with an increase in elongation, there is no
clear trend for tapped and loose bulk density. Furthermore, although the moisture and oil content
may affect the bulk density of IWMP [5], these are controlled very tightly during milk powder
production [2], so the difference of moisture and oil content between four different brands’ IWMP
should not be appreciable.
3.2. Principal Component Analysis
To decide which shape factor dominates the bulk density of IWMP, PCA was used. Figure 10a
shows the scores plot of PCA, in which variables 1 to 12 represent the four different brands’ coarse
particle, medium particle, and fine particle fractions. Since the coarse particle samples have the lowest
tapped and loose bulk density, and the fine particle samples have the highest tapped and loose bulk
density, therefore the samples were well classified by their bulk density along the axes in the PCA
scores plot. It is also clear that the first two principal components were enough to categorize the bulk
density of the IWMP because they account for 88% and 6% of the total variance, respectively. Figure
10b presents the PCA loading plot. It is noticeable that the shape factors were divided into two
groups. One of them includes all the size metrics like minimum and maximum Feret diameter,
equivalent diameter, perimeter, and area. In contrast, the other group contains all the shape metrics
(circularity, solidity, convexity, and elongation). As in the same group the shape factors have similar
loadings, the maximum Feret diameter, elongation, and circularity, for which loadings were
relatively high, were chosen to train models to predict the bulk density of IWMP.
(a)
(b)
Figure 10. (a) Principal Component Analysis (PCA) scores plot of the first two principal components
distinguishing the twelve instant whole milk powder samples from their bulk density; (b) PCA
Figure 10.
(
a
) Principal Component Analysis (PCA) scores plot of the first two principal components
distinguishing the twelve instant whole milk powder samples from their bulk density; (
b
) PCA
loadings plot of the first two principal components distinguishing the relationships between different
shape factors.
For each shape factor, there are ten variables (shape factor
0.1
to shape factor
1.0
, where the ECDF
fraction is represented by a subscript). Hence, the data set has 30 shape factor variables and 12 samples.
Since the variable size is large, PCA was used to determine which shape factor variables most
significantly contribute to the bulk density of the IWMP. Figure 11a shows the PCA scores plot. It is
clear that PC1 and PC2 explain 75% and 10% respectively of the complete variance, and the milk powder
samples were well classified with their bulk density. The PCA loadings plot is presented in Figure 11b,
where the points branded 1 to 30 are the 30 shape factor variables (maximum Feret diameter
0.1
to
Foods 2020,9, 1024 12 of 19
maximum Feret diameter
1.0
, circularity
0.1
to circularity
1.0
, and elongation
0.1
to elongation
1.0
). Since the
loadings of some shape factor variables are similar, nine variables with relatively high loadings were
chosen to represent the shape factors of IWMP. Therefore, points 3 (maximum Feret diameter
0.3
),
7 (maximum Feret diameter
0.7
), 10 (maximum Feret diameter
1.0
), 13 (circularity
0.3
), 17 (circularity
0.7
),
19 (circularity
0.9
), 22 (elongation
0.2
), 23 (elongation
0.3
), and 27 (elongation
0.7
) were chosen to represent
the shape factors of the IWMP. From the shape factors’ ECDF curves, it is clear that at the selected points,
the differences between shape factors are considerable between the different brands’ milk powders.
Foods 2020, 9, x FOR PEER REVIEW 12 of 19
loadings plot of the first two principal components distinguishing the relationships between different
shape factors.
For each shape factor, there are ten variables (shape factor0.1 to shape factor1.0, where the ECDF
fraction is represented by a subscript). Hence, the data set has 30 shape factor variables and 12
samples. Since the variable size is large, PCA was used to determine which shape factor variables
most significantly contribute to the bulk density of the IWMP. Figure 11a shows the PCA scores plot.
It is clear that PC1 and PC2 explain 75% and 10% respectively of the complete variance, and the milk
powder samples were well classified with their bulk density. The PCA loadings plot is presented in
Figure 11b, where the points branded 1 to 30 are the 30 shape factor variables (maximum Feret
diameter0.1 to maximum Feret diameter1.0, circularity0.1 to circularity1.0, and elongation0.1 to
elongation1.0). Since the loadings of some shape factor variables are similar, nine variables with
relatively high loadings were chosen to represent the shape factors of IWMP. Therefore, points 3
(maximum Feret diameter0.3), 7 (maximum Feret diameter0.7), 10 (maximum Feret diameter1.0), 13
(circularity0.3), 17 (circularity0.7), 19 (circularity0.9), 22 (elongation0.2), 23 (elongation0.3), and 27
(elongation0.7) were chosen to represent the shape factors of the IWMP. From the shape factors’ ECDF
curves, it is clear that at the selected points, the differences between shape factors are considerable
between the different brands’ milk powders.
(a)
(b)
Figure 11. (a) PCA scores plot of the first two principal components allowing the discrimination of
the twelve instant whole milk powder samples from their bulk density; (b) PCA loadings plot of the
first two principal components allowing the determination of the relationships between different
shape factor variables.
3.3. Prediction of the Bulk Density
Each brand of IWMP was remixed into ten samples with varying fractions by using the simplex-
centroid design. Next, tap testing was used to measure the bulk density of each sample. Table 1 shows
the tapped and loose bulk density of the first three samples for each brand, while the bulk densities
Figure 11.
(
a
) PCA scores plot of the first two principal components allowing the discrimination of the
twelve instant whole milk powder samples from their bulk density; (
b
) PCA loadings plot of the first
two principal components allowing the determination of the relationships between different shape
factor variables.
3.3. Prediction of the Bulk Density
Each brand of IWMP was remixed into ten samples with varying fractions by using the
simplex-centroid design. Next, tap testing was used to measure the bulk density of each sample.
Table 1shows the tapped and loose bulk density of the first three samples for each brand, while the
bulk densities of the other seven samples for each brand are presented in Table 2. The proportion
of the different sized particles in each milk powder sample was determined by the simplex-centroid
design in Section 2.1.5. All experiments were repeated three times. The mean value with the standard
deviation of bulk density is listed in Table 2. Each milk powder sample has three particle size groups,
and there are nine shape factor variables for each particle size group. Therefore, there are 27 shape
factor variables for each sample. To predict the bulk density of the IWMP, the shape factor variables of
each particle size group were multiplied by their fraction to get the composite values, which were used
for the PLS and ANN analysis.
Foods 2020,9, 1024 13 of 19
Table 2. Tapped and loose bulk density of each sample class for the four different brands.
Sample Class Brand 1 Brand 2 Brand 3 Brand 4
Loose bulk
density (kg/m3)
4 457.35 ±8.25 424.42 ±0.91 405.29 ±3.53 412.36 ±2.50
5 466.00 ±6.66 449.95 ±1.74 423.75 ±2.09 436.35 ±1.86
6 456.31 ±6.82 429.58 ±2.18 418.49 ±1.38 421.91 ±1.23
7 453.90 ±2.71 428.94 ±1.26 418.29 ±6.68 428.17 ±2.33
8 456.65 ±5.33 434.00 ±3.51 424.02 ±1.36 428.14 ±2.73
9 451.02 ±2.76 421.98 ±5.31 411.96 ±1.68 414.67 ±1.68
10 446.50 ±1.84 428.07 ±1.89 418.89 ±3.10 435.14 ±2.55
Tapped bulk
density (kg/m3)
4 547.10 ±1.58 531.36 ±0.81 519.63 ±1.51 525.39 ±0.71
5 587.91 ±3.58 571.09 ±1.97 552.46 ±1.53 568.58 ±0.74
6 559.97 ±2.96 537.92 ±1.89 538.09 ±1.24 535.88 ±0.30
7 572.73 ±1.23 547.81 ±2.18 542.48 ±0.42 550.08 ±1.18
8 578.76 ±1.11 551.39 ±1.01 543.58 ±0.55 547.97 ±1.01
9 564.82 ±0.79 528.94 ±0.81 532.86 ±0.51 530.32 ±0.41
10 561.04 ±1.05 541.04 ±1.28 541.78 ±2.26 552.40 ±0.17
3.3.1. Partial Least Squares Models
Two PLS models were developed by using the shape factor variables selected in Section 3.2 to
predict the tapped and loose bulk density of IWMP, respectively. The results of the first PLS model
(for predicting loose bulk density) are shown in Figure 12a,b. Since the milk powder samples were
separated into five groups, there are eight samples in each group. The R
2
and Q
2
of the model were
computed by Equations (3) and (4). Figure 12a presents the change of R
2
and Q
2
with the growing
number of PLS components, and when the PLS model has four components, the Q
2
reached its
maximum value (0.87), and the corresponding R
2
is 0.94. In this condition, the PLS regression of the
actual loose bulk density versus the predicted loose bulk density is shown in Figure 12b, and the MSE
of the model is 65.51.
The second PLS model was constructed for predicting the tapped bulk density of IWMP. Figure 13a
shows the change of the R
2
and Q
2
of the model with an increasing number of PLS components.
A parsimonious solution was chosen when the number of PLS components is small (two) and Q
2
is
near maximum. For this, the R
2
value is 0.92, and the Q
2
is 0.91. The predicted tapped bulk density
versus actual tapped bulk density is presented in Figure 13b, and the MSE of the model is 227.49.
The PLS models are considered good as the R
2
of the models is high (0.94 and 0.92), and the mean
squared errors are reasonable.
Foods 2020, 9, x FOR PEER REVIEW 13 of 19
of the other seven samples for each brand are presented in Table 2. The proportion of the different
sized particles in each milk powder sample was determined by the simplex-centroid design in Section
2.1.5. All experiments were repeated three times. The mean value with the standard deviation of bulk
density is listed in Table 2. Each milk powder sample has three particle size groups, and there are
nine shape factor variables for each particle size group. Therefore, there are 27 shape factor variables
for each sample. To predict the bulk density of the IWMP, the shape factor variables of each particle
size group were multiplied by their fraction to get the composite values, which were used for the PLS
and ANN analysis.
Table 2. Tapped and loose bulk density of each sample class for the four different brands.
Sample Class Brand 1 Brand 2 Brand 3 Brand 4
Loose bulk density (kg/m3)
4 457.35 ± 8.25 424.42 ± 0.91 405.29 ± 3.53 412.36 ± 2.50
5 466.00 ± 6.66 449.95 ± 1.74 423.75 ± 2.09 436.35 ± 1.86
6 456.31 ± 6.82 429.58 ± 2.18 418.49 ± 1.38 421.91 ± 1.23
7 453.90 ± 2.71 428.94 ± 1.26 418.29 ± 6.68 428.17 ± 2.33
8 456.65 ± 5.33 434.00 ± 3.51 424.02 ± 1.36 428.14 ± 2.73
9 451.02 ± 2.76 421.98 ± 5.31 411.96 ± 1.68 414.67 ± 1.68
10 446.50 ± 1.84 428.07 ± 1.89 418.89 ± 3.10 435.14 ± 2.55
Tapped bulk density (kg/m3)
4 547.10 ± 1.58 531.36 ± 0.81 519.63 ± 1.51 525.39 ± 0.71
5 587.91 ± 3.58 571.09 ± 1.97 552.46 ± 1.53 568.58 ± 0.74
6 559.97 ± 2.96 537.92 ± 1.89 538.09 ± 1.24 535.88 ± 0.30
7 572.73 ± 1.23 547.81 ± 2.18 542.48 ± 0.42 550.08 ± 1.18
8 578.76 ± 1.11 551.39 ± 1.01 543.58 ± 0.55 547.97 ± 1.01
9 564.82 ± 0.79 528.94 ± 0.81 532.86 ± 0.51 530.32 ± 0.41
10 561.04 ± 1.05 541.04 ± 1.28 541.78 ± 2.26 552.40 ± 0.17
3.3.1. Partial Least Squares Models
Two PLS models were developed by using the shape factor variables selected in Section 3.2 to
predict the tapped and loose bulk density of IWMP, respectively. The results of the first PLS model
(for predicting loose bulk density) are shown in Figure 12a,b. Since the milk powder samples were
separated into five groups, there are eight samples in each group. The R2 and Q2 of the model were
computed by Equations (3) and (4). Figure 12a presents the change of R2 and Q2 with the growing
number of PLS components, and when the PLS model has four components, the Q2 reached its
maximum value (0.87), and the corresponding R2 is 0.94. In this condition, the PLS regression of the
actual loose bulk density versus the predicted loose bulk density is shown in Figure 12b, and the MSE
of the model is 65.51.
(a)
Figure 12. Cont.
Foods 2020,9, 1024 14 of 19
Foods 2020, 9, x FOR PEER REVIEW 14 of 19
(b)
Figure 12. (a) R2 and Q2 versus the number of partial least squares (PLS) components for the PLS
model of loose bulk density; (b) Predicted loose bulk density versus actual loose bulk density of
IWMP samples.
The second PLS model was constructed for predicting the tapped bulk density of IWMP. Figure
13a shows the change of the R2 and Q2 of the model with an increasing number of PLS components.
A parsimonious solution was chosen when the number of PLS components is small (two) and Q2 is
near maximum. For this, the R2 value is 0.92, and the Q2 is 0.91. The predicted tapped bulk density
versus actual tapped bulk density is presented in Figure 13b, and the MSE of the model is 227.49. The
PLS models are considered good as the R2 of the models is high (0.94 and 0.92), and the mean squared
errors are reasonable.
(a)
(b)
Figure 13. (a) R2 and Q2 versus the number of PLS components for the PLS model of tapped bulk
density; (b) Predicted tapped bulk density versus actual tapped bulk density of IWMP samples.
Figure 12.
(
a
) R2 and Q2 versus the number of partial least squares (PLS) components for the PLS
model of loose bulk density; (
b
) Predicted loose bulk density versus actual loose bulk density of
IWMP samples.
Foods 2020, 9, x FOR PEER REVIEW 14 of 19
(b)
Figure 12. (a) R2 and Q2 versus the number of partial least squares (PLS) components for the PLS
model of loose bulk density; (b) Predicted loose bulk density versus actual loose bulk density of
IWMP samples.
The second PLS model was constructed for predicting the tapped bulk density of IWMP. Figure
13a shows the change of the R2 and Q2 of the model with an increasing number of PLS components.
A parsimonious solution was chosen when the number of PLS components is small (two) and Q2 is
near maximum. For this, the R2 value is 0.92, and the Q2 is 0.91. The predicted tapped bulk density
versus actual tapped bulk density is presented in Figure 13b, and the MSE of the model is 227.49. The
PLS models are considered good as the R2 of the models is high (0.94 and 0.92), and the mean squared
errors are reasonable.
(a)
(b)
Figure 13. (a) R2 and Q2 versus the number of PLS components for the PLS model of tapped bulk
density; (b) Predicted tapped bulk density versus actual tapped bulk density of IWMP samples.
Figure 13.
(
a
) R2 and Q2 versus the number of PLS components for the PLS model of tapped bulk
density; (b) Predicted tapped bulk density versus actual tapped bulk density of IWMP samples.
3.3.2. Artificial Neural Network models
ANN models were also constructed for predicting the bulk density of IWMP. The shape factor
variables selected from PCA results were multiplied by their particle size fractions and introduced
into the ANN models. The first ANN model was constructed for predicting the loose bulk density of
IWMP. The validation of this ANN model is shown in Figure 14a where the MSE of the validation
model reached its minimum value for an epoch number of four. Therefore, four epochs were selected.
Foods 2020,9, 1024 15 of 19
Figure 14b presents the performance of the first model, and Table 3presents the results of this ANN
model. These results are discussed below.
Foods 2020, 9, x FOR PEER REVIEW 15 of 19
3.3.2. Artificial Neural Network models
ANN models were also constructed for predicting the bulk density of IWMP. The shape factor
variables selected from PCA results were multiplied by their particle size fractions and introduced
into the ANN models. The first ANN model was constructed for predicting the loose bulk density of
IWMP. The validation of this ANN model is shown in Figure 14a where the MSE of the validation
model reached its minimum value for an epoch number of four. Therefore, four epochs were selected.
Figure 14b presents the performance of the first model, and Table 3 presents the results of this ANN
model. These results are discussed below.
(a)
(b)
Figure 14. (a) Validation of the artificial neural networks (ANN) model of loose bulk density; (b)
Performance of the ANN model of loose bulk density.
Figure 14.
(
a
) Validation of the artificial neural networks (ANN) model of loose bulk density;
(b) Performance of the ANN model of loose bulk density.
Table 3. Results of the ANN model of loose bulk density.
Samples MSE R2
Training 28 10.80 0.98
Validation 6 34.26 0.98
Test 6 62.13 0.97
All 40 22.02 0.98
The second ANN model was constructed for the tapped bulk density of the IWMP. The validation
of the second ANN model is shown in Figure 15a, where we can see that when the epoch number
Foods 2020,9, 1024 16 of 19
was two, the MSE of the validation model reached its minimum value. So, two epochs were used.
Figure 15b shows the performance of this ANN model, and Table 4presents the results of this model.
Foods 2020, 9, x FOR PEER REVIEW 16 of 19
Table 3. Results of the ANN model of loose bulk density.
Samples MSE R2
Training 28 10.80 0.98
Validation 6 34.26 0.98
Test 6 62.13 0.97
All 40 22.02 0.98
The second ANN model was constructed for the tapped bulk density of the IWMP. The validation
of the second ANN model is shown in Figure 15a, where we can see that when the epoch number was
two, the MSE of the validation model reached its minimum value. So, two epochs were used. Figure
15b shows the performance of this ANN model, and Table 4 presents the results of this model.
(a)
(b)
Figure 15. (a) Validation of the ANN model of tapped bulk density; (b) Performance of the ANN
model of tapped bulk density.
Figure 15.
(
a
) Validation of the ANN model of tapped bulk density; (
b
) Performance of the ANN model
of tapped bulk density.
Table 4. Results of the ANN model of tapped bulk density.
Samples MSE R2
Training 28 53.04 0.98
Validation 6 19.38 0.98
Test 6 159.71 0.96
All 40 63.99 0.98
These two ANN models are considered good since the R
2
(0.98 and 0.98) of the models are high,
and the mean squared errors (22.02 and 63.99) are low. Since the performance of the ANN models
is better than the performance of the PLS models here, on this basis ANN could be considered as
potentially being useful for at-line prediction. However, due to the black-box characteristic of the
ANN models, the mechanism behind an ANN is rarely understood. Contrary to this, PLS ban be more
Foods 2020,9, 1024 17 of 19
easily interpreted to reflect fundamental changes that could be understood by operators and process
engineers. Therefore, PLS is recommended for use in the current industry [36].
In summary, the bulk density of IWMP mainly depends on powder morphology and particle size.
Furthermore, since these models only depend on the particle size fraction and shape factors of the
milk powder but are independent of the brand of the milk powder, using these models to predict the
bulk density of IWMP is applicable. Compared to traditional time-consuming and labor-intensive
off-line bulk density testing, using the PLS and ANN models developed in this work is potentially
helpful to build on-line or at-line sensors, which is necessary for industry 4.0. Additionally, Depree et
al. [
11
] used process variables (pressure, flow, temperature, etc.) and online quality variables (moisture,
fat, protein, etc.) to develop a partial least squares model for predicting the bulk density of IWMP.
However, the precision (R
2
is lower than 0.8) of using process variables to predict bulk density of
IWMP is much poorer than the precision (R
2
is about 0.94) of using morphology, which may be because
the bulk density of the agglomerated powders is mainly determined by particle shape [
2
]. Furthermore,
3D image processing technologies which can obtain more accurate information may be applied to these
smart sensors in the future.
4. Conclusions
By investigating the relationship between morphology/particle size and bulk density, the current
research aims to develop an on-line or at-line sensor for bulk density measurement. The proposed
methodology can improve plant efficiency and reduce operating costs as an alternative to the
traditional bulk density test. It was found that the shape factors (maximum Feret diameter, elongation,
and circularity) for different brands of IWMP are different. For different particle size groups, the trends
of the tapped and loose bulk density versus the changes of the shape factors (maximum Feret diameter,
elongation, and circularity) are similar. In addition, PCA could well classify the bulk density of IWMP
by their shape factors. Finally, two PLS models and two ANN models were developed using selected
shape factor variables to predict the tapped and loose bulk density of IWMP. The good results of
these models indicate that using the shape factors and particle size fractions of IWMP to predict the
bulk density of IWMP is applicable. Due to the black box limitations of ANN models, PLS models
are considered more useful to operators for indicating trends, although ANN models performed
marginally better than the PLS models.
Author Contributions:
Conceptualization, W.Y. and I.B.; methodology, H.D., B.L. and D.I.W.; software, H.D. and
I.B.; validation, H.D. and B.R.Y.; formal analysis, H.D. and W.Y.; investigation, H.D.; resources, H.D.; data curation,
H.D.; writing—original draft preparation, H.D.; writing—review and editing, H.D., B.R.Y., B.L., I.B., D.I.W. and
W.Y.; visualization, H.D. and D.I.W.; supervision, W.Y., B.R.Y. and B.L.; project administration, W.Y. and B.R.Y.
All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
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