Vol.4, No.5B, 21-27 (2013) Agricultural Sciences
Slight free falling impact test for assessing guava
Cheng-Chang Lien1, Ching-Hua Ting2*
1Department of Biomechatronic Engineering, National Chiayi University.
2Department of Mechanical and Energy Engineering, National Chiayi University;
*Corresponding Author: cting@mail.ncyu.edu.tw
Received 2013
A non-destructive method for assessing the
maturity of guava was developed based on the
mechanical properties of the fruit under the
slight falling impact test. The levels of maturity
were classified with cluster and discriminant
analyses on the primitive impact measurements
and their derivatives. The accuracy of classifi-
cation was improved with linear discriminant
analysis and the number of indices being proc-
essed was reduced with stepwise regression
analysis. The accurac y of classification is 84.21 %.
The performance shows that slight falling im-
pact together with linear discriminant analysis
provides a promising non-destructive approach
in assessing the maturity of guavas.
Keywords: Falling impact; Guava; Cluster Analysis;
Discriminating Analysis; S tepw ise Regression
Analysis; Fruit Maturity
Maturity grading of fruits in harvesting before delivery
to the market is beneficial for indicating the optimal time
for marketing or for optimisation of storage management
[1, 2]. The maturity of fruit is a qualitative measure, which
is difficult to identify. The firmness of a fruit is an index
of the mechanical, chemical and rheological properties of
the fruit. It is negatively proportional to the maturity of
the fruit and can hence be used as an alternative indicator
to maturity in fruit grading and sorting [3-4].
The compression and the penetration tests are reliable
and traditional methods used to estimate fruit firmness [5]
A force-deformation profile is obtained from the test and
accordingly, the firmness of the specimen is estimated in
reference to the geometrical information of the profile,
e.g. the proportional limit, bio-yield strength, and critical
strength [5-7]. Several devices related to the classical
penetrometer have been developed [8,9]. While many of
these proposed techniques result in reasonably accurate
and reproducible estimates, they are of a destructive nature,
represent mechanical properties at the point of measure-
ment only, and cannot be used as real-time monitoring for
fruit sorting.
There are several non-destructive, fast and objective
quality measures that have been proposed and some of
them are commercially available [4]. Some promising
dynamic methods for fruit quality evaluation are based
on measurement of fruit response to force vibration or
impact [6,9-12]. The use of mass impact [13], either by a
light rigid mass or fruit falling, has been widely applied
in the detection of fruit maturity. The material is either
dropped freely onto a force transducer or hammered with
an accelerating rigid mass. The impact responses are
interpreted in either the frequency or the time domain.
The impact indices show a strong correlation with the
firmness of vegetables and fruits [14,15] This method
has been used in the detection of the firmness of fruits
such as apples [9,16], mangoes [17-19], papayas [20],
peaches [13,18,19], and tomatoes [10,12].
Our previous work [12] and other work [18] demon-
strate falling impact together with statistical analyses is a
simple, effective, efficient fruit maturity assessing tech-
nique. Thus, the previous study was expanded for the
assessment of psidium guava maturity. A psidium guava
is a pear-shape tropical fruit with light green thin skin,
white flesh, and hard seeds. In Taiwan, it is consumed as
fruit or guava juice. The fruit is rich of proteins and vi-
tamins A and C. It contains vitamin C eight times more
than orange and 30 - 80 times more than watermelon or
pineapple. This feature makes it treated as a food in this
country. Salient features derived from force responses to
falling impact were used as the characterising parameters.
Significant characterising parameters are picked using
stepwise regression analysis. Results from destructive
penetration and compression tests are used as a calibrator.
In discriminant analysis, guavas of different maturity
classes based on days after fruit harvesting set are graded.
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C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27
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2.1. App aratus
Figure 1 illustrates the experimental system devel-
oped in the laboratory for investigation into the impact
reaction of fruit falling onto a load cell. The apparatus
consists of a pneumatic holding mechanism, a load cell
and transmitter, a digital oscilloscope, and a computer. A
fruit is held by a manually manipulated vacuum sucker
and released to fall freely from an adjustable height onto
the load cell. The surface of the load cell that receives the
impact of the fruit is stainless steel. The vacuum pressure
and the falling height are manually adjustable with the
rule of thumb of not incurring bruise damage to the fruit,
as inadequate mechanical impact may affect the firmness
of the guava [21-22].
The load cell (208C02, PCB Piezotronics, NY, USA)
is a piezoelectric transducer that generates an analogical
signal proportional to the applied force. Its signal is am-
plified with a 480A09 transmitter (PCB Piezotronics, NY,
USA). A digital oscilloscope (2827-02, Bruel&Kjaer,
Demark) digitizes and visualizes the amplified analogue
signal and then transmits it to the computer through RS-
232 serial communication. Data are stored on the com-
puter for subsequent off-line analysis.
2.2. Conceptual Impact Model
The mechanical behaviour of a fruitis best modelled
with viscoelastic characteristics. The impact of a viscoe-
lastic object onto a rigid obstacle is a complicated phe-
nomenon and could be studied by several different ap-
proaches [23]. An impacting fruit is deformable, hence
the impact behaviour can be characterised thorough the
impacting time, maximal deflection, and impacting forces
[24]. Special feature of viscoelastic impacting body is
that there exists hysteresis-like behaviour in force-dis-
placement diagram. Such behaviour was explained either
by nonlinear models or by use of the standard linear vis-
coelastic model [25].
Figure 2 demonstrates a typical force response of a
guava fruit subject to slight free falling test using the
apparatus of Figure 1. The re-bouncing, Dt, defines how
long the fruit collides with base structure. A fruits is of
viscoelastic characteristics and will deform when im-
pacting onto another subject. This phenomenon can be
described as the conversion between potential and kinetic
energies. A guava weighing m and falling from height h
has the following energy transformation:
mgh mv (1)
Where g is the gravitational acceleration and v is the
speed of the fruit before colliding.
Figure 1. The impact test rig[12].
Figure 2. Definitions of impact response.
It is unlikely practical to measure the height, the force,
and the velocity. An alternative approach is to character-
ise the collision through analysing the force response
profile. Accordingly, the following indices are proposed
for characterising the maturity of guava:
,12121 2
,121 2
to transcribe collision with reactive force and colliding
,12,12 /
,12,12 /
to involve the effect of fruit weight.
2.3. Falling Impact and Fruit Firmness
The fruit falling on the load cell produces a force that
causes a deformation on its flesh. To avoid incurring
bruise damage to the fruit, the falling height was adjusted
to a distance that does not cause inelastic deformation to
the fruit. This non-destructive procedure was validated
through the compression test which assures that the peak
impact force is far below the bio-yield point of the fruit.
The fall on the load cell represents a rheoelastic shock,
during which there is a transmission of a certain fraction
of the total energy of the fruit onto the surface of the
transducer. After the first impact, the fruit suffers a sec-
ond impact due to the rebound and a new transmission of
C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27 23
energy is produced. These energy fractions are directly
related with the firmness [26].
3.1. Fruit Materials
Psidium guavas were hand harvested from the same
farm at the same time on the day of test. Extremely large
and small guavas were rejected. Upon arrival at the
laboratory, the guavas were again inspected to ensure
that they were uniform, non-damaged and not attacked
by worms. The samples were categorised into 4 groups
according to the number of post-harvest days, ie. the 1st,
3rd, 5th, and 7th day. Hence samples of 4 different maturi-
ties were studied.
3.2. Experimental Procedures
Each guava sample was sized (precision 0.01 mm, 500
- 196, Mitutoyo, Japan) and weighed (precision 0.1 mg,
HR-200, A&D, Japan)immediately after harvesting.
Afterwards, the moisture content of some samples from
the 4 groups was evaluated. The slight impact test was
immediately conducted on the fruit using the apparatus
in Figure 1 at a falling height of 15 mm. The height is a
compromise between the ease of signal picking by the
load cell and causing no bruise damage to the fruit.
The impact measurements provide neither qualitative
nor quantitative information about firmness. Hence, the
measurements are correlated with the results of the pene-
tration test. The resultant penetration force reflects the
lumped mechanical properties of a bio-material [4,8] and
can therefore be used as a direct indicator of the firmness
of fruit flesh [18,27].
3.3. Texture Analysis
The penetration and compression tests were conducted
at room temperature on a TA-TX2 Texture Analyser
(Texture Technologies Corp., NY, USA). The analyser
was calibrated with a 5 kg weight prior to the first test. It
was equipped with a11mm diameter cylindrical stainless-
steel probe for the penetration test and an 80 mm diame-
ter plate for the compression test. Equipment settings
were as follows: test speed, 2 mm/s; distance, 10 mm
into the guava. Figure 3 is a typical force-distance re-
sponse curve of a guava under penetration test. The curve
characterises the firmness of the guava with peak force F
and stiffness K.
3.4. Moisture Content
The moisture content of a guava is determined by
placing the sample in an oven of 103℃ for 24 hours.
The moisture content is then calculated by
Figure 3. A typical response of penetration test.
%[()/ ]100
wd w
 (6)
where Ww is the weight of the guava before drying and
Wd is the weight of the guava after drying.
3.5. Data Anal ysis
Responses of the penetration test were used as a cali-
brator for the impact indices and the derivatives. Fruits
with various firmness (maturity) under the penetration
test were graded with the assistance of cluster analysis.
The analysis attempted to correlate the fruit's maturity
with its responsive penetration force.
3.5.1. Cluster Analysis
The penetration test only indicates the firmness of the
guavas samples. The ultimate goal of a sorting system is
to classify the guavas into several distinguishable quality
groups. Hence, cluster analysis (CA) was introduced to
classify the fruits, according to experimental measure-
ments, into different maturity groups (clusters). The
measurements in each group share some common traits
according to some defined distance measures. CA is used
to search for natural grouping trends among samples into
fourripeness levels (aka the number of post-harvest days).
The FASTCLU procedure of the SAS statistical software
(V8, SAS Institute Inc., NY, USA) was used.
3.5.2. Analy sis of Primitive Measurements
The primitive impact measurements give direct infor-
mation about the mechanical properties of the fruit. They
are determined by the firmness and the weight of the
fruit. These measurements may provide redundant or
insignificant information in identifying the level of ripe-
ness. Hence, the Scheffe test was used to compare the
significance of each variable among the four groups of
ripeness. The test determines which specific groups are
significantly different in statistics. The Scheffe test was
performed using the SAS ANOVA procedure.
3.5.3. Linear Discriminant Analysis
Linear discriminant analysis (LDA) is a statistical tech-
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C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27
nique to classify individuals or objects into mutually ex-
clusive and exhaustive groups on the basis of a set of
independent variables. LDA is used to find an optimum
linear combination of the independent variables that mini-
mises the probability of misclassifying fruits into their
respective groups. The variables used in computing the
linear discriminant functions are chosen in a stepwise
manner, both forward and backward, using the SAS
STEPDISC procedure. At each step, the variable that
adds most to the separation of the classes is entered into
(forward) or the variable that adds least is removed from
(backward) the discriminant function. The SAS DIS-
CRIM procedure was used to perform discriminant
analysis to classify the guavas into classes of test re-
sponse. If a fruit is classified into the same class of test
response and origin, e.g. a ripe guava (origin) is classi-
fied into the ripe class of test response, this guava is
identified as well classified.
4.1. Primitive Measurements
Table 1 summarises the physical properties of the
guava fruits examined immediately after harvesting. The
level of maturity can be characterised by the peak pene-
trating force, F, and the stiffness, K, as defined in Figure
3. The results of penetration test of guavas with different
maturities are shown in Ta b l e 2 . Clearly, the number of
days of post-harvest affects the maturity of guava sig-
nificantly. The penetration test is therefore used as a ref-
erence for calibrating the accuracy of maturity identifica-
tion using the impact test.
Table 1. Physical properties.
Average Diameter
Moisture Content
Samples 38 38 24
Average 323.86 83.87 87.69
Std. Dev. 79.97 3.67 1.40
Variancea 0.24 0.04 0.02
aVariance = standard deviation/average.
Table 2. Penetration measurements of guavas after days of
Day 1 Day 3 Day 5 Day 7
Samples 38 38 38 38
F 11747 ± 2228a 11548 ± 2450 a 10391 ± 3002 a 7853 ± 3448 b
K 2228 ± 493 a 1703 ± 389 b1204 ± 362 c 904 ± 378 d
Values are in mean ± SD. At the same row, values with different superscripts
aresignicantly different (P 0.05) in means by the Scheffé test.
4.2. Penetration Test as a Calibrator
All samples were classified into distinguishing clusters
with cluster analysis of the penetration force K. Tab le 3
lists the result of cluster analysis using the SAS FAST-
CLU procedure. It is understandable that a riper sample
can easily be penetrated with a smaller force, as matura-
tion causes a slight softening in such a guava than in a
less mature one [28]. The automated FASTCLU proce-
dure classified the samples into 6 distinguishing clusters.
However, the use of 6 levels of maturity is considered
too many and cumbersome in practice [12]. Thus, the 6
clusters are further transcribed to 3 groups by combining
any two clusters which have the closest mean penetration
forces. Table 4 summarises the information about the
transcribed three maturity groups.
4.3. Adequate Indices
Stepwise regression analysis (SAS STEPDISC) was
used to find out the most significant factors among the
bulky number of candidate indices in maturity classifica-
tion. The analysis revealed that 21
f ,12PW , and
are the three most dominant indices, with ana-
lytical results summarised in Table 5.
Table 3. Guavas in 6 clusters by cluster analysis of the stiffness
K (g/mm) from penetration test.
GroupSamplesMean Standard Deviation Closest Cluster
1 1 3516.4. 2
2 9 2743.57144.38 6
3 47 1572.15199.91 5
4 14 476.36148.19 5
5 48 1021.31153.93 4
6 33 2175.39172.44 2
Table 4. Guava in 3 groups of maturity transcribed from the 6
CA clusters from cluster analysis of the stiffness K (g/mm).
MaturitySamplesMean Standard DeviationCA clusters
A 62 898.26 275.14 4, 5
B 47 1572.15 199.91 3
C 43 2325.50 339.90 1, 2, 6
Table 5. Statistics of the most signicant impact indices by
stepwise regression analysis.
StepIndex PartialR-square FValue Pr > F
1 fP2/fP10.5271 83.03 < 0.0001
2 CPW,12
0.1706 15.22 < 0.0001
3 fP1 – fP2
0.0649 5.1 0.0072
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The three indices contain collision force, which has
significant difference in the mean values of all three
classes of maturity as shown in Table 6. The analysis
also reveals that the weight W is an important factor of
using falling impact test in estimation of guava maturity.
The methodology can arrive at an estimation accuracy of
77.4% using the three indices.
4.4. Validation with Post-harvest Ripening
The ripeness of a fruit is proportional to the number of
post-harvest days. Samples at 1st, 3rd, 5th, and 7th
post-harvest days should have 4 different maturities. Ta-
ble 7 lists the 5 most significant impact indices, obtained
through stepwise regression analysis, for identifying the
maturity of guava categorised by the number of post-
harvest days. The methodology can arrive at an estima-
tion accuracy of 84.21%, as shown in Table 8.
4.5. Assurance of Non-Destructive Test
Possible bruise damage by falling impact was in-
spected by visual inspection and mechanical analysis.
Guava samples of various post-harvest daywere ran-
domly selected for the compression test. The bio-yield
points of the four fruit maturities counted by post-harvest
days are all around 20000 g (196 N). The maximum im-
pact force shown is 88.45 Nfar below 196 N, the bio-
yield points. Hence, the impact test does not develop
inelastic deformation to the fruits.
5. Conclusions
The slight falling impact method is feasible in firm-
ness measurement and hence in classification of the
guava maturity in compliance with numbers of post-
harvestdays. The falling induces an impact force to the
fruit, which can be easily adjusted to such a level that
Table 6. Accuracies of tomato classication using derived impact indices.
MaturityA Maturity B Maturity C Total
62 47 43 152
fP2/fP1 48(77.42%) 23(48.94%) 32(74.42%) 103(66.92%)
fP2/fP1, CPW,12
42(67.74%) 31(65.96%) 38(88.37%) 111(74.02%)
43(69.35%) 35(74.47%) 38(88.37%) 115(77.40%)
Table 7. Statistics of the most signicant impact indices by stepwise regression analysis.
Index PartialR-square F Value Pr > F
fP2/fP1 0.772 167.05 < 0.0001
0.125 6.98 0.0002
0.069 3.61 0.015
0.097 5.17 0.002
tC2/tC1 0.172 9.93 < 0.0001
Table 8. Accuracies of guava classication using discriminant analysis of two re-bouncing reponses.
Samples (accuracy%) Day 1 Day 3 Day 5 Day 7 Total
fP2/fP1 31 (81.58%) 22 (57.89%) 25 (65.79%) 31 (81.58%) 109 (71.71%)
fP2/fP1, fP1fP2 35 (92.11%) 26 (68.42%) 27 (71.05%) 31 (81.58%) 119 (78.29%)
fP2/fP1, fP1fP2, ΔT 35 (92.11%) 25 (65.79%) 28 (73.68%) 32 (84.21%) 120 (78.95%)
fP2/fP1, fP1fP2, ΔT, CPW,12 36 (94.74%) 30 (78.95%) 30 (78.95%) 29 (76.32%) 125 (82.24%)
fP2/fP1, fP1fP2, ΔT, CPW,12, tC2/tC1 38 (100%) 30 (78.95%) 28 (73.68%) 32 (84.21%) 128 (84.21%)
C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27
does not damage the fruit. The primitive measurements
of impact test do not give substantial information about
the classification of guava maturity. The accuracy of
classification can be improved by performing CA and
LDA on derived indices. The accuracy reaches 77.4%
with the stiffness K as a calibrator from textural analysis
and 84.21% with post-harvest days as a calibrator. How-
ever, a method with an accuracy of classification better
than 75% is good enough for practical application [19].
Hence, this laboratory study encourages the use of fall.
This study is partially sponsored by National Science Council of
Taiwan under a grant no. NSC-101-2221-E-415-014.
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