Slight free falling impact test for assessing guava maturity

doi:10.4236/as.2013.45B004

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Vol.4, No.5B, 21-27 (2013) Agricultural Sciences

doi:10.4236/as.2013.45B004

Slight free falling impact test for assessing guava

maturity

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

ABSTRACT

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

1. INTRODUCTION

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.

C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27

2. MEASUREMENT OF FIRMNESS

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

()/

PPPP

Cfft





 (2)

,121 2

()

CPP

Cff/t





(3)

to transcribe collision with reactive force and colliding

time;

,12,12 /

PW P



(4)

,12,12 /

CW C

CCW



(5)

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. MATERIALS AND METHODS

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

wbWWW



 (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-

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. RESULTS AND DISCUSSION

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.

Weight

(g)

Average Diameter

(mm)

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

harvesting.

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

aresigniﬁcantly 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 signiﬁcant impact indices by

stepwise regression analysis.

StepIndex PartialR-square FValue Pr > F

1 fP2/fP10.5271 83.03 < 0.0001

2 CPW,12



0.1706 15.22 < 0.0001

3 fP1 – fP2



0.0649 5.1 0.0072

C.-C. Lien, C.-H. Ting / Agricultural Sciences 4 (2013) 21-27

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 classiﬁcation using derived impact indices.

MaturityA Maturity B Maturity C Total

Samples

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%)

fP1–fP2



43(69.35%) 35(74.47%) 38(88.37%) 115(77.40%)

Table 7. Statistics of the most signiﬁcant impact indices by stepwise regression analysis.

Index PartialR-square F Value Pr > F

fP2/fP1 0.772 167.05 < 0.0001

fP1–fP2



0.125 6.98 0.0002

tC1–tC2



0.069 3.61 0.015

CPW,12



0.097 5.17 0.002

tC2/tC1 0.172 9.93 < 0.0001

Table 8. Accuracies of guava classiﬁcation 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, fP1–fP2 35 (92.11%) 26 (68.42%) 27 (71.05%) 31 (81.58%) 119 (78.29%)

fP2/fP1, fP1–fP2, ΔT 35 (92.11%) 25 (65.79%) 28 (73.68%) 32 (84.21%) 120 (78.95%)

fP2/fP1, fP1–fP2, ΔT, CPW,12 36 (94.74%) 30 (78.95%) 30 (78.95%) 29 (76.32%) 125 (82.24%)

fP2/fP1, fP1–fP2, 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.

6. ACKNOWLEDGEMENTS

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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