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Orthogonal test design to optimize the acoustic vibration method for pear texture measurement
Postharvest Biology and Technology 107 (2015) 33–42
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Orthogonal test design to optimize the acoustic vibration method for pear texture measurement Wen Zhang, Di Cui, Yibin Ying * College of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 28 September 2014 Received in revised form 30 March 2015 Accepted 7 April 2015 Available online 15 May 2015
The test parameters for pear texture measurement using a laser Doppler vibrometer (LDV) were optimized. The pear was placed in the middle of the vibration stage and excited by swept sine wave signals with a constant frequency sweeping rate and acceleration amplitude. The response signals from the tops of the pears were measured using an LDV. First, 10 pear samples were tested under different test conditions in the single-factor experiment. The test parameters included the frequency sweeping mode and rate, acceleration amplitude, pear laying style, and LDV detection point. The results show that the frequency–response curves at the same detection point have good repeatability under all tested frequency sweeping rates (regardless of the linear or logarithmic frequency sweeping mode) and acceleration amplitudes. However, the frequency–response curves at different detection points have poor repeatability for each laying style. To find a better combination of test parameters, an L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, pear laying style, and their 2-way interactions was designed according to the results of the single-factor experiments. No significant 2-way interaction is found among the frequency sweeping rate, acceleration amplitude, and pear laying style on the repeatability of the frequency–response curves. The test parameter values required to obtain a better repeatability are as follows: frequency sweeping rate of 23.33 Hz/s with the linear frequency sweeping mode, acceleration amplitude of 1 g (g = 9.8 m/s2), and laying style that the pear is placed with its stem upward. After the optimization of the LDV method, a total of 118 pear samples were used to compare the LDV method with the destructive puncture test. The results show that the elasticity index (EI) is well correlated with the stiffness (Stif) of pears and that the correlation is not significantly affected by the pear laying style. In addition, the LDV method is superior to the puncture test in terms of repeatability and sensitivity. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Optimization Test parameter Texture Acoustic vibration Laser Doppler vibrometer
1. Introduction With the increasing demand for high-quality fruits, it is highly desirable to nondestructively detect the fruit quality (Wang et al., 2004). Fruit quality indices include appearance, shape, texture, acid content, soluble solid content, etc., among which, the texture is a key quality factor for consumers to decide whether the fruit is acceptable because this index is related to the maturity and taste of the fruit and can be used as an indicator for storage (De Ketelaere et al., 2006). The acoustic vibration method is an effective and commonly used nondestructive method for fruit texture detection. Abbott et al. (1968) used a stiffness coefficient, f2m, where f is the
* Corresponding author. Tel.: +86 571 88982885; fax: +86 571 88982885. E-mail addresses: [email protected] (W. Zhang), [email protected] (D. Cui), [email protected] (Y. Ying). http://dx.doi.org/10.1016/j.postharvbio.2015.04.002 0925-5214/ ã 2015 Elsevier B.V. All rights reserved.
resonance frequency and m is the mass of fruit, to describe the elastic properties of apples. They found that the stiffness coefficient was well correlated with the fruit firmness. Later, Cooke (1972) introduced a modified stiffness coefficient f2m2/3 for spherical fruits. Extensive studies about the acoustic vibration method for the texture measurement of spherical fruits based on the stiffness coefficient have been performed in recent decades. Sensors to measure vibration signals are classified into contact and non-contact sensors according to the signal-acquiring method (Taniwaki and Sakurai, 2010). Contact sensors are directly attached to the tested sample, such as the piezoelectric sensor (Gomez et al., 2005; Kadowaki et al., 2012) and accelerometer (Abbott et al., 1992). However, these sensors may affect the free vibration of the test sample. The microphone, a type of non-contact sensor, has been widely used in research and application (Molina-Delgado et al., 2009; Zude et al., 2006; Mendoza et al., 2012). However, the response signal obtained using a microphone is easily affected by environmental noise. The laser Doppler vibrometer (LDV), which is
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a type of optical detection method, overcomes the shortcomings of contact sensors and microphones and has drawn increasing attention in recently. The LDV method has been used to measure the vibration characteristics of watermelons (Abbaszadeh et al., 2013, 2014), kiwifruits (Terasaki et al., 2001, 2013), pears (Zhang et al., 2014a,b; Taniwaki et al., 2009), etc. The reliability of the acoustic vibration method for fruit quality evaluation significantly depends on whether repeatable parameters can be obtained. Therefore, extensive studies have been conducted on the factors that affect the vibration characteristics and repeatability of the vibration parameters. Yamamoto et al. (1980) studied the reliability of the acoustic impulse response method for the quality evaluation of apples and watermelons. The fruit was hit with a wooden ball pendulum, and the sound was detected by a microphone. Good repeatability was obtained for the resonance frequency but not for the damping factor and peak height. Armstrong et al. (1990) investigated the repeatability of the resonance frequency of apples by striking the fruit with a hammer and detecting the response signal with a microphone, and they found that the resonance frequency had a good repeatability. Chen et al. (1992) studied the effect of factors that affected the acoustic responses of apples. The results showed no significant difference in resonance frequencies obtained at different testing locations, impulse-generating methods, and fruitholding methods. However, these factors affected the amplitude at the resonance frequency. Wang et al. (2004, 2006) set up an experimental system to measure the resonance frequency of fruits and found that the excitation point, detection point, excitation intensity and impacting material did not significantly affect the dominant frequency for both pears and peaches. De Ketelaere et al. (2006) compared the repeatability of two commercially available sensors for firmness detection and found that the acoustic firmness sensor clearly outperformed the low-mass impact sensor. Tiplica et al. (2010) measured the elastic properties of apples using a method similar to that of Armstrong et al. (1990). The results showed that the vibration spectra varied, but the resonance frequency remained constant for repeated measurements on the same side of the same apple. However, few studies examined the factors that affected the measurement of the vibration characteristics using the LDV method. Therefore, the objectives of this investigation were as follows: (i) to investigate the vibration characteristics of pears measured by the LDV method under different test conditions, including the frequency sweeping mode and rate, acceleration amplitude, pear laying style, and detection point of the LDV; (ii) to find a good combination of test parameters for pear texture measurement using the LDV method; and (iii) to compare the LDV method with the traditional destructive method for texture evaluation. 2. Materials and methods 2.1. Pear samples Pear samples (Pyrus pyrifolia cv. ‘Hosui’) were purchased from a planting base in Shandong, China. First, 20 samples with uniform shape were selected to optimize the test parameters of the LDV method. The morphological properties of these samples are shown in Table 1. The first 10 samples were used for the single-factor experiment, and the remaining 10 samples were used for the orthogonal test. Then, 130 intact pear samples were used for the experiment to compare the LDV method with the destructive method for the pear texture evaluation. The fruits were stored in the laboratory at a room temperature of approximately 23 C and a relative humidity of approximately 50% for 7 d. The samples that spoiled during
Table 1 Morphological properties of the samples used to optimize the test parameters of the LDV method. Number
Mass (m, g)
Heighta (h, mm)
Diametera (d, mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
315.68 364.11 344.57 328.65 301.65 301.93 333.12 337.57 324.33 357.65 292.85 356.63 309.69 339.60 345.22 381.33 337.30 292.49 344.60 386.82
67.94 70.10 71.92 71.05 72.58 68.35 67.96 67.69 69.85 72.99 67.78 79.94 71.64 71.78 79.92 79.57 77.99 74.88 78.23 75.14
89.43 94.47 91.41 88.62 85.79 87.33 90.67 91.29 90.30 94.03 86.80 90.19 85.82 91.03 89.68 93.35 88.05 85.85 91.36 94.07
a
Average value of 3 measurements taken at evenly spaced interval of 120 .
storage were removed; finally, 118 fruit samples (Table 2) were used to measure their vibration characteristics and texture. The experiment was conducted every 2 d to obtain a wide range of texture. In this experiment, 30 samples were tested in each test on days 0, 2, and 4, and 28 samples were tested on day 6. 2.2. Vibration spectrum measurement The system to measure the vibration characteristics of pears was described in detail in our previous study (Zhang et al., 2014a,b). The pear was placed in the middle of the stage of the vibrator (ES-05; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) and excited by swept sine wave signals (200–2000 Hz) with a constant frequency sweeping rate and acceleration amplitude. An accelerometer (752A12; Meggitt’s Endevco Corporation, San Juan Capistrano, California, USA) and an LDV (LV-S01; Sunny Instruments Singapore Pte.-Ltd., Singapore) were used to measure the excitation signal (xin) and response signal (xout) from the top of the pear sample, respectively. The frequency responses, which include the amplitude-frequency response and phase-frequency response, were obtained after a fast Fourier transformation (FFT) was applied to the xin and xout data. The following vibration parameters were extracted from the frequency–response curves: the second resonance frequency (f2), amplitude at f2 (A2), and phase shifts at 400, 800, 1200 and 1600 Hz (P400, P800, P1200 and P1600). In addition, the elasticity index (EI) (Cooke, 1972; Terasaki et al., 2006) was calculated using Eq. (1): 2
EI ¼ f 2 m2=3
(1)
where m is the mass of the sample. The key test parameters of the LDV method are the frequency sweeping mode, frequency sweeping rate, acceleration amplitude, Table 2 Morphological properties of the pear samples (n = 118) used for the experiment to compare the LDV method with the destructive method for the pear texture measurement.
Mean Maximum Minimum Standard deviation a
Mass (m, g)
Heighta (h, mm)
Diametera (d, mm)
347.08 403.52 292.49 26.61
77.40 86.37 68.90 3.28
89.74 97.31 84.49 2.67
Average value of 3 measurements taken at evenly spaced interval of 120 .
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Fig. 1. Measurement of the vibration spectra of pears at different laying styles and detection points. The pear was placed in the middle part of the vibration stage. Laying style A: the pear was placed with its stem upward; laying style B: the pear was placed with its calyx upward and laying style C: the pear was placed with the stem-calyx horizontal. Three equivalent detection points were selected in each laying style.
pear laying style, and detection point of the LDV. The frequency sweeping modes and rates are critical for the detection speed. The acceleration amplitude is related to the excitation force for the test sample. The pear laying style and detection point of the LDV affect the elastic wave propagation from the vibration stage to the detection point of the LDV in the fruit tissue. 2.3. Texture measurement The puncture test was performed to measure the pear texture using a texture analyzer (TA-XT2i, Stable Micro System, Inc., England). Three peeled sites with equal intervals along the equatorial plane of the pear were selected. At each site, a 5-mm-diameter cylindrical probe was inserted into the sample to a depth of 8 mm at a speed of 1 mm/s. Three texture indices were extracted from the force–deformation (F–D) curve (Zhang et al., 2014a): maximum force (MF), flesh firmness (FF, average force after the rupture point), and stiffness (Stif, the slope of the F–D curve before the rupture point). The average values of each texture index at 3 sites were calculated and reported as the MF, FF, and Stif values of each sample. 2.4. Experimental procedure Ten samples (Table 1, No. 1–10) were used for the single-factor experiment. First, the vibration spectra of the pears were measured at different frequency sweeping modes and rates. The frequency sweeping modes include the linear mode and the logarithmic mode. Because the maximum linear frequency sweeping rate of the vibrator was 100 Hz/s, the selected levels of the linear frequency sweeping rate were 16.67, 33.33, 50, 66.67, 83.33, and 100 Hz/s. For approximately equal detection time, the selected levels of the logarithmic frequency sweeping rate were 0.033, 0.067, 0.1, 0.133, 0.167, and 0.2 octaves/s. Octave is defined by American National Standards Institute (ANSI) as the unit of frequency level when the base of the logarithm is two. Each test was repeated 3 times at the same detection point. Second, the vibration spectra were measured at different acceleration amplitudes. The vibrator produced a harsh noise when the acceleration amplitude was larger than 2 g (g = 9.8 m/s2) in the high-frequency region, so the tested levels of acceleration amplitudes in this study were 0.5 g, 1 g, 1.5 g, and 2 g. Each test was repeated 3 times at the same detection point. Third, the vibration spectra were measured
for 3 different laying styles. For each laying style, 3 equivalent detection points were selected (shown in Fig. 1). After the single-factor experiment, an orthogonal test was designed to obtain the optimal combination of test parameters. The orthogonal test is an effective measurement to assay the comprehensive effect of multiple factors (Wei et al., 2013). An L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, laying style, and their 2-way interactions was designed according to the results of the single-factor experiments. The first, second and fifth columns were assigned to the frequency sweeping rate, acceleration amplitude, and pear laying style, respectively. The remaining columns were assigned to the interactions. The detailed experimental design is shown in Table 3. All treatments were repeated 10 times. The data were
Table 3 L27(313) orthogonal test for the combinational effect trial. Treatments Factors 1 2 3 4 5 6 7 8 11 A B (A B)1 (A B)2 C (A C)1 (A C)2 (B C)1 (B C)2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
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analyzed using the analysis of variance. Then, multiple comparisons of the means were performed using Duncan’s new multiplerange test. After the optimization of the LDV method, 118 samples (Table 2) were used to compare the LDV method with the traditional destructive method. The vibration spectra of pears were first measured using the LDV method; then, the pear texture was immediately detected using the puncture test on each test day.
variance (ANOVA) was performed to analyze whether the repeatability was affected by the test parameters. 2.5.2. Analysis of sensitivity The sensitivity of the index is represented by its relative value loss (De Ketelaere et al., 2006; Shmulevich et al., 2003), which was calculated using Eq. (4): Relative value loss ¼
2.5. Statistical analysis 2.5.1. Analysis of repeatability The repeatability of a single index is represented by the measurement variability (MV) (Pan and Tu, 2004 De Ketelaere et al., 2006), which was defined as the standard deviation of repeated measurements divided by the mean value of the repeated measurements and multiplied by 100%. Generally, an MV value below 10% indicates good repeatability (De Ketelaere et al., 2006). The repeatability of the frequency–response curves was represented by the differentiation index (D) (Mouwen et al., 2011; Naumann, 2000). First, the correlation coefficient was calculated using Eq. (2): n X
y1i y2i ny1 y2
i¼1 ry1 y2 ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n n uP t y2 ny2 P y2 ny2 1 2 1i 2i i¼1
(2)
i¼1
where y1i and y2i are the values of the two frequency–response curves to be compared; n is the number of data points of the frequency–response curve in the range of 200–2000 Hz; and y1 and y2 are the arithmetic mean values of y1 and y2, respectively. Then, the differentiation index was defined according to Eq. (3): D ¼ ð1 ry1 y2 Þ 1000
(3)
The mean of 3 D values (between replicates 1–2, 2–3, and 1–3) was calculated and reported as the D value under each test condition. The differentiation indices for the amplitude–frequency curve (Da) and phase–frequency curve (Dp) were separately calculated. Generally, a D value below 10 indicates good repeatability (Mouwen et al., 2011).The one-way analysis of
V init V 100% V init
(4)
where Vinit is the initial value of the index and V is the value of the index after storage. A higher relative value loss indicates that the index is more sensitive to the storage time. 3. Results and discussion 3.1. Effects of the test parameters on the frequency–response characteristics of pears 3.1.1. Frequency–response characteristics at different frequency sweeping modes and rates Fig. 2 shows the typical amplitude–frequency and phase–frequency curves at different frequency sweeping modes and rates. The pear was placed on the middle of the vibration stage in laying style A and excited by swept sine wave signals with an acceleration amplitude of 1 g. The frequency–response curves at different frequency sweeping modes and rates almost overlapped, so the curves are offset for clarity in the figure. With the increase in frequency sweeping rate, the curve gradually became rougher, particularly for the amplitude-frequency curve. For the logarithmic frequency sweeping mode, the high-frequency region has a rougher curve than the low-frequency region, possibly because the increase in frequency per unit time increases with the increase in frequency of the logarithmic frequency sweeping mode, and as a result, fewer data are collected in the high-frequency region. Results of the one-way ANOVA show that Da is significantly affected by the linear frequency sweeping rate (P < 0.05) and logarithmic frequency sweeping rate (P < 0.01), whereas Dp is not. Fig. 3 shows Da at different frequency sweeping rates with the linear sweeping mode and logarithmic sweeping mode. Good repeatability was found for the amplitude–frequency curve under all tested frequency sweeping rates (Da < 10). However, Da generally increases with the increase in frequency sweeping rate,
Fig. 2. Typical amplitude-frequency (a) and phase-frequency (b) curves at different frequency sweeping modes and rates. The vertical scale applies to the bottom curve; all other curves are offset for clarity.
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Fig. 3. Differentiation index for amplitude–frequency curves (Da) at different frequency sweeping rates with the linear sweeping mode (a) and logarithmic sweeping mode (b). The linear sweeping rate was 16.67–100 Hz/s at an interval of 16.67 Hz/s, and the logarithmic sweeping rate was 0.033–0.2 octaves/s at an interval of 0.033 octaves/s. The bars represent the standard errors.
which indicates that the repeatability improves at a slower frequency sweeping rate. In general, the logarithmic sweeping mode obtains larger Da values than the linear sweeping mode. It may also be caused by the rapid increase in frequency in the highfrequency region because of the logarithmic frequency sweeping mode. Therefore, the linear frequency sweeping mode was considered better and chosen for the subsequent study. To further optimize the frequency sweeping rate with the linear sweeping mode, more frequency sweeping rates of approximately 33.33 Hz/s with an interval of 3.33 Hz/s were tested. Fig. 4 shows Da at these frequency sweeping rates. The result showed that the variation trend of Da was consistent with that in Fig. 3 (a) (initially decreasing and subsequently increasing), except for an abnormal point at the frequency of 46.67 Hz/s. The frequency sweeping rate of 23.33 Hz/s was found to have the minimum value of Da among the tested frequency sweeping rates.
3.1.2. Frequency–response characteristics at different acceleration amplitudes The pear was placed on the vibration stage in laying style A and excited by swept sine wave signals with a linear frequency sweeping rate of 23.33 Hz/s. The frequency–response curves at different acceleration amplitudes also almost overlapped (not shown). The one-way ANOVA results show that Da is significantly affected by the acceleration amplitude (P < 0.05), whereas Dp is not. Fig. 5 shows Da at different acceleration amplitudes. The values of Da were much less than 10, indicating that the repeatability was good for the 4 tested acceleration amplitudes. The multiplecomparison results show that Da at the acceleration amplitude of 0.5 g significantly differs from those at the acceleration amplitudes of 1 g, 1.5 g, and 2 g. However, no significant difference was found in Da for the acceleration amplitudes of 1 g, 1.5 g, and 2 g.
Fig. 4. Differentiation index for amplitude-frequency curves (Da) at different frequency sweeping rates with the linear frequency sweeping mode. The frequency sweeping rate was 16.67–50 Hz/s at an interval of 3.33 Hz/s. The bars represent the standard errors.
Fig. 5. Differentiation index for the amplitude–frequency curves (Da) at different acceleration amplitudes. The bars represent the standard errors, and g = 9.8 m/s2.
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Fig. 6. Typical amplitude-frequency (a) and phase-frequency (b) curves for different laying styles.
Fig. 7. Typical amplitude–frequency (a) and phase-frequency (b) curves at different detection points for the same laying style.
3.1.3. Frequency–response characteristics at different laying styles and detection points Figs. 6 and 7 show the typical amplitude–frequency and phase– frequency curves for different laying styles and different detection points with the same laying style, respectively. The pear was excited by swept sine wave signals with a linear frequency sweeping rate of 23.33 Hz/s and an acceleration amplitude of 1 g. It is clearly shown that the curves measured for different laying styles or different detection points with the same laying style were not consistent. Da and Dp at different detection points for each laying style are shown in Fig. 8. D values at different detection points for each laying style were obtained by calculating the mean value of 3 D values between detection points 1–2, 2–3, and 1–3. The mean values of Da at different detection points were above 100 for all laying styles. In addition, although the mean values of Dp at different detection points were below 10, the Dp values of some specific samples were above 10. Therefore, the repeatability of the frequency–response curves at different detection points was poor for each laying style. However, some vibration parameters were found to have good repeatability for different laying styles or different detection points, such as f2, as is clearly observed in Figs. 6 (a) and 7 (a). f2, which corresponds to the spherical mode (Blahovec et al., 2007,
Fig. 8. Differentiation index for the amplitude-frequency curves (Da) and phase– frequency curves (Dp) at different detection points for each laying style. The bars represent the standard errors.
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Table 4 Measurement variability (MV, %) of the vibration parameters for different laying styles.
Laying style A Laying style B Laying style C All detection points a b
f2a
A2 a
P400a
P800a
P1200a
P1600a
0.44 0.56b 0.73 1.43 1.95 2.12 2.09 1.44
34.53 18.26 32.25 23.18 74.00 25.19 52.26 13.08
72.47 38.14 71.72 87.55 19.85 21.45 60.89 29.33
10.29 6.16 7.71 6.59 9.21 10.97 14.66 10.27
12.37 7.30 13.61 8.39 7.26 6.19 18.82 5.97
13.76 11.83 15.04 6.99 5.83 4.94 21.47 6.25
f2: the resonance frequencies; A2: the amplitude at f2; P400,P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. Mean standard deviation.
3.2. Orthogonal test design
Table 5 Factors and levels of the orthogonal test. Levels Factors Frequency sweeping rate (Hz/s) Acceleration amplitude 1 2 3 a
1ga 1.5g 2g
20 23.33 26.67
Laying style A B C
g = 9.8 m/s2.
2008), was widely used in the LDV method to calculate the elasticity index of spherical fruits. The repeatability of some vibration parameters is summarized in Table 4. f2 has good repeatability and is much better than the other selected vibration parameters. P800, P1200, and P1600 show relatively good repeatability. However, P400 and A2 have poor repeatability. In addition, the f2 that was obtained for laying style A has a better repeatability than that recorded for the other laying styles. Good repeatability of the resonance frequency and poor repeatability of the amplitude at the resonance frequency were also observed in many other studies (Armstrong et al., 1990; Chen et al., 1992; Yamamoto et al., 1980; Tiplica et al., 2010), where the fruit was usually hit with a hammer or a pendulum. Armstrong et al. (1990) believed that the fruit had an uneven surface and that small differences in the hitting point or collision angle between the fruit and the striker significantly changed the amplitude of vibration. Tiplica et al. (2010) provided a possible explanation for this phenomenon, suggesting that the impact force of the hammer was not constant from one measurement to the next. In this study, the excitation signal to the fruit from the vibration stage remains identical for each test, and the frequency–response curves at the same detection point of repeated measurements almost overlap. Therefore, the difference in A2 is most likely attributable to the difference in the elastic wave propagation from the vibration stage to the detection point of the LDV in the fruit tissue, which may also account for the poor repeatability of the frequency– response curves that were measured at different detection points.
The L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, pear laying style, and their 2-way interactions was designed according to the results of the singlefactor experiments. Through the single-factor experiments, the linear sweeping mode was found to be better than the logarithmic sweeping mode in terms of repeatability. Therefore, the linear sweeping mode was chosen in the orthogonal test. Three levels of frequency sweeping rates of approximately 23.33 Hz/s, which has the minimum Da in the single-factor experiment, were selected. Similarly, 1 g, 1.5 g and 2 g were selected as the levels of acceleration amplitude because of the better repeatability for these values of acceleration amplitude. The factors and levels of the orthogonal test are listed in Table 5. The variance-of-analysis results are shown in Table 6. No significant 2-way interaction is found among the frequency sweeping rate, acceleration amplitude, and pear laying style on the repeatability of the frequency–response curves. As to the main effect, Da is significantly affected by the frequency sweeping rate, but Dp is not significantly affected by the frequency sweeping rate. In addition, the results show that both Da and Dp are not significantly affected by the acceleration amplitude and pear laying style. The pairwise comparison of the means of different levels of three test parameters for Da is shown in Table 7. It is concluded that 23.33 Hz/s is the optimal frequency sweeping rate among the selected values, which is consistent with the results of the singlefactor experiment. The repeatability of the frequency–response curves does not significantly vary for the acceleration amplitudes of 1 g, 1.5 g and 2 g. However, the noise and equipment wear increase as the acceleration amplitude increases, and as a result, a lower acceleration amplitude is suggested. Therefore, the acceleration amplitude of 1 g is recommended and was selected in the subsequent study. The laying style does not significantly affect the repeatability of the frequency–response curves. However, f2 shows a better repeatability at different detection points with laying style A. Therefore, laying style A was determined to be a better laying style.
Table 6 Analysis of variance for three test parameters of the LDV method. Source
SSDa a
Frequency sweeping rate (A) Acceleration amplitude (B) Laying style (C) AB AC BC Error Total variance
0.2290 0.0598 0.0151 0.0783 0.0572 0.0886 2.6499 3.1778
SSDp
dfa
MSDa a
MSDp
F Da
3.55 106 9.18 107 1.16 106 5.64 106 1.41 106 7.79 106 2.49 104 2.70 104
2 2 2 4 4 4 251 269
0.1145 0.0299 0.0075 0.0196 0.0143 0.0221 0.0106
1.77 106 4.59 107 5.81 107 1.41 106 3.53 107 1.95 106 9.92 107
10.84 2.83 0.72 1.86 1.35 2.10
Significance
F Dp
Significance
0.00** 0.06 0.49 0.12 0.25 0.08
1.79 0.46 0.59 1.42 0.36 1.96
0.17 0.63 0.56 0.23 0.84 0.10
a SS: sum of squares; df: degree of freedom; MS: mean square mean; Da and Dp: differentiation indices for the amplitude–frequency curve and the phase–frequency curve, respectively. ** P < 0.01.
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Table 7 Pairwise comparison of the mean of different levels of three test parameters.a Performance index
Means of different levels of each test parameter
Differentiation index for amplitude–frequency curves (Da) a b
Frequency sweeping rate (Hz/s)
Acceleration amplitude
Laying style
20 0.1187b
1gb 0.0911a
A 0.0801a
23.33 0.0478a
26.67 0.0898b
1.5g 0.0650a
2g 0.1001a
B 0.0801a
C 0.0960a
Values of the same factor superscripted with different small letters indicate significant differences (p < 0.05). g = 9.8 m/s2.
Table 8 Correlation coefficients between the vibration parameters and the texture indices for different laying styles. Stifb
MFb
FFb
Laying style A
a
EI A2 a P400a P800a P1200a P1600a
**
0.7776 0.0678 0.4348** 0.7002** 0.7245** 0.6750**
**
0.3902 0.1095 0.2289* 0.4116** 0.4144** 0.3584**
0.4919** 0.1195 0.2852** 0.5035** 0.5029** 0.4869**
Laying style B
EI A2 P400 P800 P1200 P1600
0.7744** 0.1029 0.4194** 0.6528** 0.7201** 0.7139**
0.3899** 0.0626 0.2325* 0.3933** 0.4273** 0.4824**
0.4910** 0.0547 0.2842** 0.4812** 0.5195** 0.5552**
Laying style C
EI A2 P400 P800 P1200 P1600
0.7627** 0.0132 0.4526** 0.6836** 0.6700** 0.6504**
0.3622** 0.1636 0.2477** 0.3948** 0.3488** 0.3123**
0.4616** 0.1164 0.3006** 0.4765** 0.4251** 0.3721**
a
EI: the elasticity index; A2: the amplitude at f2; P400, P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. MF: maximum force; FF: flesh firmness; Stif: stiffness. Significant difference (P < 0.05). ** Highly significant difference (P < 0.01). b *
A verification test was conducted to determine the optimized combination of test parameters. Three pears were measured at the frequency sweeping rate of 23.33 Hz/s with the linear frequency sweeping mode, acceleration amplitude of 1 g, and laying style A. The results show that the mean values of Da and Dp are 0.0459 and 0.0004, respectively, confirming the good repeatability of the frequency–response curves under this test condition. 3.3. Comparison of the acoustic vibration method and destructive method for the texture measurement of pears 3.3.1. Correlations between vibration parameters and texture parameters Table 8 shows the correlation coefficients between the vibration parameters and texture indices for different laying styles. Stif is well correlated with the vibration parameters except A2 and P400 for each laying style. In addition, EI has the highest correlation coefficient with Stif among these vibration parameters.
However, unlike Stif, the other texture indices exhibit poor correlations with the vibration parameters. The result is consistent with the finding in our previous study (Zhang et al., 2014a), where the pear was placed in laying style A. The vibration parameters are poorly correlated with MF or FF because they correspond to different physical properties, as discussed in detail by Zhang et al. (2014b). The elastic properties mainly depend on the turgor pressure of fruit cells, whereas MF is mainly related to the cell wall structure. The correlation coefficients between vibration parameters and texture indices for different laying styles are almost equal, which indicates that the laying style has no obvious effect on the pear texture detection by the LDV method in terms of correlation.
3.3.2. Comparison on repeatability Table 9 shows the repeatability of vibration parameters and texture indices on each test day. The results show that EI is the best
Table 9 Measurement variability (MV, %) of the vibration parameters and texture indices on each test day. Days
EIa
A2 a
P400a
P800a
P1200a
P1600a
Stifb
MFb
FFb
0 2 4 6
1.99 2.01c 2.88 3.16 2.20 1.57 2.45 2.02
72.20 28.45 53.95 28.76 66.92 32.37 64.16 35.15
81.62 35.74 66.02 38.56 40.41 32.61 49.19 39.87
7.05 9.09 6.12 5.46 7.97 6.11 6.80 5.09
7.67 5.30 6.68 3.96 8.43 5.85 9.49 8.14
8.12 4.80 8.13 4.76 12.91 8.27 15.14 9.21
14.08 6.46 11.83 7.19 11.06 6.64 11.46 5.79
9.11 5.20 12.55 5.67 11.48 5.19 11.86 8.26
8.06 5.12 10.30 6.22 9.04 4.98 9.97 7.16
a b c
EI: the elasticity index; A2: the amplitude at f2; P400, P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. MF: maximum force; FF: flesh firmness; Stif: stiffness. Mean standard deviation.
W. Zhang et al. / Postharvest Biology and Technology 107 (2015) 33–42
41
Table 10 Changes in elasticity index (EI) and texture indices during storage. Days
EIa (104 Hz2 kg2/3) Laying style A
Laying style B
Laying style C
0 2 4 6 Relative value loss
22.72 20.11 16.61 13.11 42.31%
22.66 19.97 16.42 12.93 42.92%
22.21 19.31 16.09 12.68 42.91%
a b
Stifb (N/mm)
MFb (N)
FFb (N)
10.85 10.18 9.12 7.97 26.56%
16.01 16.56 15.73 14.23 11.13%
11.97 12.19 11.52 10.41 13.08%
EI: the elasticity index. MF: maximum force; FF: flesh firmness; Stif: stiffness.
index in terms of repeatability (MV < 3%) among all indices and that it has much lower MV values than the texture indices. The texture indices have better repeatability than A2 and P400 but worse repeatability than P800, P1200, and EI. The poor repeatability of A2 and P400 may account for their poor correlation with the texture indices. The fruit texture at different sites measured by the puncture test varied because of the non-homogeneous and anisotropic properties of fruits (Abbott and Lu, 1996). However, the resonance frequency, which describes the overall elasticity characteristics of pears, is not significantly affected by the detection point and laying style. The better repeatability of EI than the texture indices indicates that the LDV method is superior to the destructive puncture test in terms of repeatability.
method is superior to the destructive puncture test in terms of repeatability and sensitivity. Acknowledgements The authors gratefully acknowledge the support of this program by theNational Natural Science Foundation of China (Grant No. 31201132). Any opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of Zhejiang University. The trade and manufacturers’ names are necessary to report factually on the available data. References
3.3.3. Comparison on sensitivity Table 10 shows the changes in EI and texture indices during storage. A2 does not have an obvious variation trend, and the phase shifts at selected frequencies increase during storage, so they are not listed in this table. EI and the texture indices gradually decrease during storage. The relative value losses of EI for different laying styles are almost equal, which indicates that the sensitivity of EI is not affected by the laying style. Stif shows the highest sensitivity among the texture indices, but its sensitivity remains lower that of EI. The higher sensitivity of EI compared to the texture indices indicates that the LDV method is also more advantageous than the destructive puncture test in terms of sensitivity, which is consistent with Shmulevich et al. (2003), who found that the acoustic firmness was more sensitive than the Magness-Taylor firmness for apples during their shelf life, and Murayama et al. (2006), who found that EI of “La France” pears always decreased immediately after harvest, whereas the flesh firmness decreased after an initial lag time. 4. Conclusion The test parameters of the pear texture measurement using the LDV method were optimized in this paper. A good repeatability of the vibration spectrum or vibration parameters is the basis for further texture evaluation using the LDV method. Therefore, the test parameters in this study were mainly optimized based on the repeatability of frequency–response curves under different test conditions. Better test parameter values for the pear texture measurement are as follows: frequency sweeping rate of 23.33 Hz/ s with the linear frequency sweeping mode, acceleration amplitude of 1 g, and laying style A. In addition to the correlation, a combination of repeatability and sensitivity is recommended to compare the performance of a new method with the traditional method. The comparison between the LDV method and the destructive puncture test shows that EI is well correlated with the Stif of pears. In addition, the LDV
Abbaszadeh, R., Rajabipour, A., Mahjoob, M., Delshad, M., Ahmadi, H., 2013. Evaluation of watermelons texture using their vibration responses. Biosyst. Eng. 115 (1), 102–105. Abbaszadeh, R., Rajabipour, A., Sadrnia, H., Mahjoob, M.J., Delshad, M., Ahmadi, H., 2014. Application of modal analysis to the watermelon through finite element modeling for use in ripeness assessment. J. Food Eng. 127, 80–84. Abbott, J.A., Lu, R., 1996. Anisotropic mechanical properties of apples. Trans. ASAE 39 (4), 1451–1459. Abbott, J.A., Bachman, G.S., Childers, R.F., Fitzgera, J.V., Matusik, F.J., 1968. Sonic techniques for measuring texture of fruits and vegetables. Food Technol. 22 (5), 101–112. Abbott, J.A., Affeldt, H.A., Liljedahl, L.A., 1992. Firmness measurement of stored delicious apples by sensory methods, Magness-Taylor, and sonic transmission. J. Am. Soc. Hortic. Sci. 117 (4), 590–595. Armstrong, P., Zapp, H.R., Brown, G.K., 1990. Impulsive excitation of acoustic vibrations in apples for firmness determination. Trans. ASAE 33 (4), 1353–1359. Blahovec, J., Akimoto, H., Sakurai, N., 2007. Laser Doppler forced vibrology of soft agricultural products. Appl. Rheol. 17 (2), 25111 (1–7). Blahovec, J., Kuroki, S., Sakurai, N., 2008. Precise correction in laser Doppler forced vibrology of soft products. Biosyst. Eng. 99 (1), 156–160. Chen, P., Sun, Z., Huarng, L., 1992. Factors affecting acoustic responses of apples. Trans. ASAE 35 (6), 1915–1920. Cooke, J.R., 1972. An interpretation of the resonant behavior of intact fruits and vegetables. Trans. ASAE 15, 1075–1080. De Ketelaere, B., Howarth, M.S., Crezee, L., Lammertyn, J., Viaene, K., Bulens, I., De Baerdemaeker, J., 2006. Postharvest firmness changes as measured by acoustic and low-mass impact devices: a comparison of techniques. Postharvest Biol. Technol. 41 (3), 275–284. Gomez, A.H., Wang, J., Pereira, A.G., 2005. Impulse response of pear fruit and its relation to Magness-Taylor firmness during storage. Postharvest Biol. Technol. 35 (2), 209–215. Kadowaki, M., Nagashima, S., Akimoto, H., Sakurai, N., 2012. Detection of core rot symptom of Japanese pear (Pyrus pyrifolia cv. Kosui) by a nondestructive resonant method. J. Japn. Soc. Hortic. Sci. 81 (4), 327–331. Mendoza, F., Lu, R.F., Cen, H.Y., 2012. Comparison and fusion of four nondestructive sensors for predicting apple fruit firmness and soluble solids content. Postharvest Biol. Technol. 73, 89–98. Molina-Delgado, D., Alegre, S., Puy, J., Recasens, I., 2009. Relationship between acoustic firmness and Magness-Taylor firmness in Royal Gala and Golden Smoothee apples. Food Sci. Technol. Int. 15 (1), 31–40. Mouwen, D.J.M., Horman, A., Korkeala, H., Alvarez-Ordonez, A., Prieto, M., 2011. Applying Fourier-transform infrared spectroscopy and chemometrics to the characterization and identification of lactic acid bacteria. Vib. Spectrosc. 56 (2), 193–201. Murayama, H., Konno, I., Terasaki, S., Yamamoto, R., Sakurai, N., 2006. Nondestructive method for measuring fruit ripening of ‘La France’ pears using a laser Doppler vibrometer. J. Japn. Soc. Hortic. Sci. 75 (1), 79–84.
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Naumann, D., 2000. Infrared spectroscopy in microbiology. In: Meyers, R.A. (Ed.), Encyclopedia of Analytical Chemistry. John Wiley & Sons Ltd., Chichester, pp. 1–29. Pan, X.J., Tu, K., 2004. Measurement of firmness changes of harvested Fuji apples with destructive and nondestructive method. J. Northwest A & F Univ. (Nat. Sci. Ed.) 32 (09), 38–42. Shmulevich, I., Ben-Arie, R., Sendler, N., Carmi, Y., 2003. Sensing technology for quality assessment in controlled atmospheres. Postharvest Biol. Technol. 29 (2), 145–154. Taniwaki, M., Sakurai, N., 2010. Evaluation of the internal quality of agricultural products using acoustic vibration techniques. J. Japn. Soc. Hortic. Sci. 79 (2), 113–128. Taniwaki, M., Hanada, T., Tohro, M., Sakurai, N., 2009. Non-destructive determination of the optimum eating ripeness of pears and their texture measurements using acoustical vibration techniques. Postharvest Biol. Technol. 51 (3), 305–310. Terasaki, S., Wada, N., Sakurai, N., Muramatsu, N., Yamamoto, R., Nevins, D.J., 2001. Nondestructive measurement of kiwifruit ripeness using a laser Doppler vibrometer. Trans. ASAE 44 (1), 81–87. Terasaki, S., Sakurai, N., Zebrowski, J., Murayama, H., Yamamoto, R., Nevins, D.J., 2006. Laser Doppler vibrometer analysis of changes in elastic properties of ripening ‘La France’ pears after postharvest storage. Postharvest Biol. Technol. 42 (2), 198–207. Terasaki, S., Sakurai Kuroki, N.S., Yamamoto, R., Nevins, D.J., 2013. A new descriptive method for fruit firmness changes with various softening patterns of kiwifruit. Postharvest Biol. Technol. 86, 85–90.
Tiplica, T., Vandewalle, P., Verron, S., Grémy-Gros, C., Mehinagic, E., 2010. Identification of apple varieties using acoustic measurements. Paper read at Conférence Internationale en Métrologie, CAFMET'10. Wang, J., Teng, B., Yu, Y., 2004. Pear dynamic characteristics and firmness detection. Eur. Food Res. Technol. 218 (3), 289–294. Wang, J., Teng, B., Yu, Y., 2006. The firmness detection by excitation dynamic characteristics for peach. Food Control 17 (5), 353–358. Wei, L., Huang, X., Huang, Z., Zhou, Z., 2013. Orthogonal test design for optimization of lipid accumulation and lipid property in Nannochloropsis oculata for biodiesel production. Bioresour. Technol. 147, 534–538. Yamamoto, H., Iwamoto, M., Haginuma, S., 1980. Acoustic impulse response method for measuring natural frequency of intact fruits and preliminary applications to internal quality evaluation of apples and watermelons. J. Texture Stud. 11 (2), 117–136. Zhang, W., Cui, D., Ying, Y., 2014a. Nondestructive measurement of pear texture by acoustic vibration method. Postharvest Biol. Technol. 96, 99–105. Zhang, W., Cui, D., Ying, Y., 2014b. Analysis of vibration characteristic of ‘Huangguan’ pears and its relation to firmness during storage. Trans. ASABE 57 (5), 1407–1413. Zude, M., Herold, B., Roger, J.M., Bellon-Maurel, V., Landahl, S., 2006. Nondestructive tests on the prediction of apple fruit flesh firmness and soluble solids content on tree and in shelf life. J. Food Eng. 77 (2), 254–260.
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Postharvest Biology and Technology journal homepage: www.elsevier.com/locate/postharvbio
Orthogonal test design to optimize the acoustic vibration method for pear texture measurement Wen Zhang, Di Cui, Yibin Ying * College of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 28 September 2014 Received in revised form 30 March 2015 Accepted 7 April 2015 Available online 15 May 2015
The test parameters for pear texture measurement using a laser Doppler vibrometer (LDV) were optimized. The pear was placed in the middle of the vibration stage and excited by swept sine wave signals with a constant frequency sweeping rate and acceleration amplitude. The response signals from the tops of the pears were measured using an LDV. First, 10 pear samples were tested under different test conditions in the single-factor experiment. The test parameters included the frequency sweeping mode and rate, acceleration amplitude, pear laying style, and LDV detection point. The results show that the frequency–response curves at the same detection point have good repeatability under all tested frequency sweeping rates (regardless of the linear or logarithmic frequency sweeping mode) and acceleration amplitudes. However, the frequency–response curves at different detection points have poor repeatability for each laying style. To find a better combination of test parameters, an L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, pear laying style, and their 2-way interactions was designed according to the results of the single-factor experiments. No significant 2-way interaction is found among the frequency sweeping rate, acceleration amplitude, and pear laying style on the repeatability of the frequency–response curves. The test parameter values required to obtain a better repeatability are as follows: frequency sweeping rate of 23.33 Hz/s with the linear frequency sweeping mode, acceleration amplitude of 1 g (g = 9.8 m/s2), and laying style that the pear is placed with its stem upward. After the optimization of the LDV method, a total of 118 pear samples were used to compare the LDV method with the destructive puncture test. The results show that the elasticity index (EI) is well correlated with the stiffness (Stif) of pears and that the correlation is not significantly affected by the pear laying style. In addition, the LDV method is superior to the puncture test in terms of repeatability and sensitivity. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Optimization Test parameter Texture Acoustic vibration Laser Doppler vibrometer
1. Introduction With the increasing demand for high-quality fruits, it is highly desirable to nondestructively detect the fruit quality (Wang et al., 2004). Fruit quality indices include appearance, shape, texture, acid content, soluble solid content, etc., among which, the texture is a key quality factor for consumers to decide whether the fruit is acceptable because this index is related to the maturity and taste of the fruit and can be used as an indicator for storage (De Ketelaere et al., 2006). The acoustic vibration method is an effective and commonly used nondestructive method for fruit texture detection. Abbott et al. (1968) used a stiffness coefficient, f2m, where f is the
* Corresponding author. Tel.: +86 571 88982885; fax: +86 571 88982885. E-mail addresses: [email protected] (W. Zhang), [email protected] (D. Cui), [email protected] (Y. Ying). http://dx.doi.org/10.1016/j.postharvbio.2015.04.002 0925-5214/ ã 2015 Elsevier B.V. All rights reserved.
resonance frequency and m is the mass of fruit, to describe the elastic properties of apples. They found that the stiffness coefficient was well correlated with the fruit firmness. Later, Cooke (1972) introduced a modified stiffness coefficient f2m2/3 for spherical fruits. Extensive studies about the acoustic vibration method for the texture measurement of spherical fruits based on the stiffness coefficient have been performed in recent decades. Sensors to measure vibration signals are classified into contact and non-contact sensors according to the signal-acquiring method (Taniwaki and Sakurai, 2010). Contact sensors are directly attached to the tested sample, such as the piezoelectric sensor (Gomez et al., 2005; Kadowaki et al., 2012) and accelerometer (Abbott et al., 1992). However, these sensors may affect the free vibration of the test sample. The microphone, a type of non-contact sensor, has been widely used in research and application (Molina-Delgado et al., 2009; Zude et al., 2006; Mendoza et al., 2012). However, the response signal obtained using a microphone is easily affected by environmental noise. The laser Doppler vibrometer (LDV), which is
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W. Zhang et al. / Postharvest Biology and Technology 107 (2015) 33–42
a type of optical detection method, overcomes the shortcomings of contact sensors and microphones and has drawn increasing attention in recently. The LDV method has been used to measure the vibration characteristics of watermelons (Abbaszadeh et al., 2013, 2014), kiwifruits (Terasaki et al., 2001, 2013), pears (Zhang et al., 2014a,b; Taniwaki et al., 2009), etc. The reliability of the acoustic vibration method for fruit quality evaluation significantly depends on whether repeatable parameters can be obtained. Therefore, extensive studies have been conducted on the factors that affect the vibration characteristics and repeatability of the vibration parameters. Yamamoto et al. (1980) studied the reliability of the acoustic impulse response method for the quality evaluation of apples and watermelons. The fruit was hit with a wooden ball pendulum, and the sound was detected by a microphone. Good repeatability was obtained for the resonance frequency but not for the damping factor and peak height. Armstrong et al. (1990) investigated the repeatability of the resonance frequency of apples by striking the fruit with a hammer and detecting the response signal with a microphone, and they found that the resonance frequency had a good repeatability. Chen et al. (1992) studied the effect of factors that affected the acoustic responses of apples. The results showed no significant difference in resonance frequencies obtained at different testing locations, impulse-generating methods, and fruitholding methods. However, these factors affected the amplitude at the resonance frequency. Wang et al. (2004, 2006) set up an experimental system to measure the resonance frequency of fruits and found that the excitation point, detection point, excitation intensity and impacting material did not significantly affect the dominant frequency for both pears and peaches. De Ketelaere et al. (2006) compared the repeatability of two commercially available sensors for firmness detection and found that the acoustic firmness sensor clearly outperformed the low-mass impact sensor. Tiplica et al. (2010) measured the elastic properties of apples using a method similar to that of Armstrong et al. (1990). The results showed that the vibration spectra varied, but the resonance frequency remained constant for repeated measurements on the same side of the same apple. However, few studies examined the factors that affected the measurement of the vibration characteristics using the LDV method. Therefore, the objectives of this investigation were as follows: (i) to investigate the vibration characteristics of pears measured by the LDV method under different test conditions, including the frequency sweeping mode and rate, acceleration amplitude, pear laying style, and detection point of the LDV; (ii) to find a good combination of test parameters for pear texture measurement using the LDV method; and (iii) to compare the LDV method with the traditional destructive method for texture evaluation. 2. Materials and methods 2.1. Pear samples Pear samples (Pyrus pyrifolia cv. ‘Hosui’) were purchased from a planting base in Shandong, China. First, 20 samples with uniform shape were selected to optimize the test parameters of the LDV method. The morphological properties of these samples are shown in Table 1. The first 10 samples were used for the single-factor experiment, and the remaining 10 samples were used for the orthogonal test. Then, 130 intact pear samples were used for the experiment to compare the LDV method with the destructive method for the pear texture evaluation. The fruits were stored in the laboratory at a room temperature of approximately 23 C and a relative humidity of approximately 50% for 7 d. The samples that spoiled during
Table 1 Morphological properties of the samples used to optimize the test parameters of the LDV method. Number
Mass (m, g)
Heighta (h, mm)
Diametera (d, mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
315.68 364.11 344.57 328.65 301.65 301.93 333.12 337.57 324.33 357.65 292.85 356.63 309.69 339.60 345.22 381.33 337.30 292.49 344.60 386.82
67.94 70.10 71.92 71.05 72.58 68.35 67.96 67.69 69.85 72.99 67.78 79.94 71.64 71.78 79.92 79.57 77.99 74.88 78.23 75.14
89.43 94.47 91.41 88.62 85.79 87.33 90.67 91.29 90.30 94.03 86.80 90.19 85.82 91.03 89.68 93.35 88.05 85.85 91.36 94.07
a
Average value of 3 measurements taken at evenly spaced interval of 120 .
storage were removed; finally, 118 fruit samples (Table 2) were used to measure their vibration characteristics and texture. The experiment was conducted every 2 d to obtain a wide range of texture. In this experiment, 30 samples were tested in each test on days 0, 2, and 4, and 28 samples were tested on day 6. 2.2. Vibration spectrum measurement The system to measure the vibration characteristics of pears was described in detail in our previous study (Zhang et al., 2014a,b). The pear was placed in the middle of the stage of the vibrator (ES-05; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) and excited by swept sine wave signals (200–2000 Hz) with a constant frequency sweeping rate and acceleration amplitude. An accelerometer (752A12; Meggitt’s Endevco Corporation, San Juan Capistrano, California, USA) and an LDV (LV-S01; Sunny Instruments Singapore Pte.-Ltd., Singapore) were used to measure the excitation signal (xin) and response signal (xout) from the top of the pear sample, respectively. The frequency responses, which include the amplitude-frequency response and phase-frequency response, were obtained after a fast Fourier transformation (FFT) was applied to the xin and xout data. The following vibration parameters were extracted from the frequency–response curves: the second resonance frequency (f2), amplitude at f2 (A2), and phase shifts at 400, 800, 1200 and 1600 Hz (P400, P800, P1200 and P1600). In addition, the elasticity index (EI) (Cooke, 1972; Terasaki et al., 2006) was calculated using Eq. (1): 2
EI ¼ f 2 m2=3
(1)
where m is the mass of the sample. The key test parameters of the LDV method are the frequency sweeping mode, frequency sweeping rate, acceleration amplitude, Table 2 Morphological properties of the pear samples (n = 118) used for the experiment to compare the LDV method with the destructive method for the pear texture measurement.
Mean Maximum Minimum Standard deviation a
Mass (m, g)
Heighta (h, mm)
Diametera (d, mm)
347.08 403.52 292.49 26.61
77.40 86.37 68.90 3.28
89.74 97.31 84.49 2.67
Average value of 3 measurements taken at evenly spaced interval of 120 .
W. Zhang et al. / Postharvest Biology and Technology 107 (2015) 33–42
35
Fig. 1. Measurement of the vibration spectra of pears at different laying styles and detection points. The pear was placed in the middle part of the vibration stage. Laying style A: the pear was placed with its stem upward; laying style B: the pear was placed with its calyx upward and laying style C: the pear was placed with the stem-calyx horizontal. Three equivalent detection points were selected in each laying style.
pear laying style, and detection point of the LDV. The frequency sweeping modes and rates are critical for the detection speed. The acceleration amplitude is related to the excitation force for the test sample. The pear laying style and detection point of the LDV affect the elastic wave propagation from the vibration stage to the detection point of the LDV in the fruit tissue. 2.3. Texture measurement The puncture test was performed to measure the pear texture using a texture analyzer (TA-XT2i, Stable Micro System, Inc., England). Three peeled sites with equal intervals along the equatorial plane of the pear were selected. At each site, a 5-mm-diameter cylindrical probe was inserted into the sample to a depth of 8 mm at a speed of 1 mm/s. Three texture indices were extracted from the force–deformation (F–D) curve (Zhang et al., 2014a): maximum force (MF), flesh firmness (FF, average force after the rupture point), and stiffness (Stif, the slope of the F–D curve before the rupture point). The average values of each texture index at 3 sites were calculated and reported as the MF, FF, and Stif values of each sample. 2.4. Experimental procedure Ten samples (Table 1, No. 1–10) were used for the single-factor experiment. First, the vibration spectra of the pears were measured at different frequency sweeping modes and rates. The frequency sweeping modes include the linear mode and the logarithmic mode. Because the maximum linear frequency sweeping rate of the vibrator was 100 Hz/s, the selected levels of the linear frequency sweeping rate were 16.67, 33.33, 50, 66.67, 83.33, and 100 Hz/s. For approximately equal detection time, the selected levels of the logarithmic frequency sweeping rate were 0.033, 0.067, 0.1, 0.133, 0.167, and 0.2 octaves/s. Octave is defined by American National Standards Institute (ANSI) as the unit of frequency level when the base of the logarithm is two. Each test was repeated 3 times at the same detection point. Second, the vibration spectra were measured at different acceleration amplitudes. The vibrator produced a harsh noise when the acceleration amplitude was larger than 2 g (g = 9.8 m/s2) in the high-frequency region, so the tested levels of acceleration amplitudes in this study were 0.5 g, 1 g, 1.5 g, and 2 g. Each test was repeated 3 times at the same detection point. Third, the vibration spectra were measured
for 3 different laying styles. For each laying style, 3 equivalent detection points were selected (shown in Fig. 1). After the single-factor experiment, an orthogonal test was designed to obtain the optimal combination of test parameters. The orthogonal test is an effective measurement to assay the comprehensive effect of multiple factors (Wei et al., 2013). An L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, laying style, and their 2-way interactions was designed according to the results of the single-factor experiments. The first, second and fifth columns were assigned to the frequency sweeping rate, acceleration amplitude, and pear laying style, respectively. The remaining columns were assigned to the interactions. The detailed experimental design is shown in Table 3. All treatments were repeated 10 times. The data were
Table 3 L27(313) orthogonal test for the combinational effect trial. Treatments Factors 1 2 3 4 5 6 7 8 11 A B (A B)1 (A B)2 C (A C)1 (A C)2 (B C)1 (B C)2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
36
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analyzed using the analysis of variance. Then, multiple comparisons of the means were performed using Duncan’s new multiplerange test. After the optimization of the LDV method, 118 samples (Table 2) were used to compare the LDV method with the traditional destructive method. The vibration spectra of pears were first measured using the LDV method; then, the pear texture was immediately detected using the puncture test on each test day.
variance (ANOVA) was performed to analyze whether the repeatability was affected by the test parameters. 2.5.2. Analysis of sensitivity The sensitivity of the index is represented by its relative value loss (De Ketelaere et al., 2006; Shmulevich et al., 2003), which was calculated using Eq. (4): Relative value loss ¼
2.5. Statistical analysis 2.5.1. Analysis of repeatability The repeatability of a single index is represented by the measurement variability (MV) (Pan and Tu, 2004 De Ketelaere et al., 2006), which was defined as the standard deviation of repeated measurements divided by the mean value of the repeated measurements and multiplied by 100%. Generally, an MV value below 10% indicates good repeatability (De Ketelaere et al., 2006). The repeatability of the frequency–response curves was represented by the differentiation index (D) (Mouwen et al., 2011; Naumann, 2000). First, the correlation coefficient was calculated using Eq. (2): n X
y1i y2i ny1 y2
i¼1 ry1 y2 ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n n uP t y2 ny2 P y2 ny2 1 2 1i 2i i¼1
(2)
i¼1
where y1i and y2i are the values of the two frequency–response curves to be compared; n is the number of data points of the frequency–response curve in the range of 200–2000 Hz; and y1 and y2 are the arithmetic mean values of y1 and y2, respectively. Then, the differentiation index was defined according to Eq. (3): D ¼ ð1 ry1 y2 Þ 1000
(3)
The mean of 3 D values (between replicates 1–2, 2–3, and 1–3) was calculated and reported as the D value under each test condition. The differentiation indices for the amplitude–frequency curve (Da) and phase–frequency curve (Dp) were separately calculated. Generally, a D value below 10 indicates good repeatability (Mouwen et al., 2011).The one-way analysis of
V init V 100% V init
(4)
where Vinit is the initial value of the index and V is the value of the index after storage. A higher relative value loss indicates that the index is more sensitive to the storage time. 3. Results and discussion 3.1. Effects of the test parameters on the frequency–response characteristics of pears 3.1.1. Frequency–response characteristics at different frequency sweeping modes and rates Fig. 2 shows the typical amplitude–frequency and phase–frequency curves at different frequency sweeping modes and rates. The pear was placed on the middle of the vibration stage in laying style A and excited by swept sine wave signals with an acceleration amplitude of 1 g. The frequency–response curves at different frequency sweeping modes and rates almost overlapped, so the curves are offset for clarity in the figure. With the increase in frequency sweeping rate, the curve gradually became rougher, particularly for the amplitude-frequency curve. For the logarithmic frequency sweeping mode, the high-frequency region has a rougher curve than the low-frequency region, possibly because the increase in frequency per unit time increases with the increase in frequency of the logarithmic frequency sweeping mode, and as a result, fewer data are collected in the high-frequency region. Results of the one-way ANOVA show that Da is significantly affected by the linear frequency sweeping rate (P < 0.05) and logarithmic frequency sweeping rate (P < 0.01), whereas Dp is not. Fig. 3 shows Da at different frequency sweeping rates with the linear sweeping mode and logarithmic sweeping mode. Good repeatability was found for the amplitude–frequency curve under all tested frequency sweeping rates (Da < 10). However, Da generally increases with the increase in frequency sweeping rate,
Fig. 2. Typical amplitude-frequency (a) and phase-frequency (b) curves at different frequency sweeping modes and rates. The vertical scale applies to the bottom curve; all other curves are offset for clarity.
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Fig. 3. Differentiation index for amplitude–frequency curves (Da) at different frequency sweeping rates with the linear sweeping mode (a) and logarithmic sweeping mode (b). The linear sweeping rate was 16.67–100 Hz/s at an interval of 16.67 Hz/s, and the logarithmic sweeping rate was 0.033–0.2 octaves/s at an interval of 0.033 octaves/s. The bars represent the standard errors.
which indicates that the repeatability improves at a slower frequency sweeping rate. In general, the logarithmic sweeping mode obtains larger Da values than the linear sweeping mode. It may also be caused by the rapid increase in frequency in the highfrequency region because of the logarithmic frequency sweeping mode. Therefore, the linear frequency sweeping mode was considered better and chosen for the subsequent study. To further optimize the frequency sweeping rate with the linear sweeping mode, more frequency sweeping rates of approximately 33.33 Hz/s with an interval of 3.33 Hz/s were tested. Fig. 4 shows Da at these frequency sweeping rates. The result showed that the variation trend of Da was consistent with that in Fig. 3 (a) (initially decreasing and subsequently increasing), except for an abnormal point at the frequency of 46.67 Hz/s. The frequency sweeping rate of 23.33 Hz/s was found to have the minimum value of Da among the tested frequency sweeping rates.
3.1.2. Frequency–response characteristics at different acceleration amplitudes The pear was placed on the vibration stage in laying style A and excited by swept sine wave signals with a linear frequency sweeping rate of 23.33 Hz/s. The frequency–response curves at different acceleration amplitudes also almost overlapped (not shown). The one-way ANOVA results show that Da is significantly affected by the acceleration amplitude (P < 0.05), whereas Dp is not. Fig. 5 shows Da at different acceleration amplitudes. The values of Da were much less than 10, indicating that the repeatability was good for the 4 tested acceleration amplitudes. The multiplecomparison results show that Da at the acceleration amplitude of 0.5 g significantly differs from those at the acceleration amplitudes of 1 g, 1.5 g, and 2 g. However, no significant difference was found in Da for the acceleration amplitudes of 1 g, 1.5 g, and 2 g.
Fig. 4. Differentiation index for amplitude-frequency curves (Da) at different frequency sweeping rates with the linear frequency sweeping mode. The frequency sweeping rate was 16.67–50 Hz/s at an interval of 3.33 Hz/s. The bars represent the standard errors.
Fig. 5. Differentiation index for the amplitude–frequency curves (Da) at different acceleration amplitudes. The bars represent the standard errors, and g = 9.8 m/s2.
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Fig. 6. Typical amplitude-frequency (a) and phase-frequency (b) curves for different laying styles.
Fig. 7. Typical amplitude–frequency (a) and phase-frequency (b) curves at different detection points for the same laying style.
3.1.3. Frequency–response characteristics at different laying styles and detection points Figs. 6 and 7 show the typical amplitude–frequency and phase– frequency curves for different laying styles and different detection points with the same laying style, respectively. The pear was excited by swept sine wave signals with a linear frequency sweeping rate of 23.33 Hz/s and an acceleration amplitude of 1 g. It is clearly shown that the curves measured for different laying styles or different detection points with the same laying style were not consistent. Da and Dp at different detection points for each laying style are shown in Fig. 8. D values at different detection points for each laying style were obtained by calculating the mean value of 3 D values between detection points 1–2, 2–3, and 1–3. The mean values of Da at different detection points were above 100 for all laying styles. In addition, although the mean values of Dp at different detection points were below 10, the Dp values of some specific samples were above 10. Therefore, the repeatability of the frequency–response curves at different detection points was poor for each laying style. However, some vibration parameters were found to have good repeatability for different laying styles or different detection points, such as f2, as is clearly observed in Figs. 6 (a) and 7 (a). f2, which corresponds to the spherical mode (Blahovec et al., 2007,
Fig. 8. Differentiation index for the amplitude-frequency curves (Da) and phase– frequency curves (Dp) at different detection points for each laying style. The bars represent the standard errors.
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Table 4 Measurement variability (MV, %) of the vibration parameters for different laying styles.
Laying style A Laying style B Laying style C All detection points a b
f2a
A2 a
P400a
P800a
P1200a
P1600a
0.44 0.56b 0.73 1.43 1.95 2.12 2.09 1.44
34.53 18.26 32.25 23.18 74.00 25.19 52.26 13.08
72.47 38.14 71.72 87.55 19.85 21.45 60.89 29.33
10.29 6.16 7.71 6.59 9.21 10.97 14.66 10.27
12.37 7.30 13.61 8.39 7.26 6.19 18.82 5.97
13.76 11.83 15.04 6.99 5.83 4.94 21.47 6.25
f2: the resonance frequencies; A2: the amplitude at f2; P400,P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. Mean standard deviation.
3.2. Orthogonal test design
Table 5 Factors and levels of the orthogonal test. Levels Factors Frequency sweeping rate (Hz/s) Acceleration amplitude 1 2 3 a
1ga 1.5g 2g
20 23.33 26.67
Laying style A B C
g = 9.8 m/s2.
2008), was widely used in the LDV method to calculate the elasticity index of spherical fruits. The repeatability of some vibration parameters is summarized in Table 4. f2 has good repeatability and is much better than the other selected vibration parameters. P800, P1200, and P1600 show relatively good repeatability. However, P400 and A2 have poor repeatability. In addition, the f2 that was obtained for laying style A has a better repeatability than that recorded for the other laying styles. Good repeatability of the resonance frequency and poor repeatability of the amplitude at the resonance frequency were also observed in many other studies (Armstrong et al., 1990; Chen et al., 1992; Yamamoto et al., 1980; Tiplica et al., 2010), where the fruit was usually hit with a hammer or a pendulum. Armstrong et al. (1990) believed that the fruit had an uneven surface and that small differences in the hitting point or collision angle between the fruit and the striker significantly changed the amplitude of vibration. Tiplica et al. (2010) provided a possible explanation for this phenomenon, suggesting that the impact force of the hammer was not constant from one measurement to the next. In this study, the excitation signal to the fruit from the vibration stage remains identical for each test, and the frequency–response curves at the same detection point of repeated measurements almost overlap. Therefore, the difference in A2 is most likely attributable to the difference in the elastic wave propagation from the vibration stage to the detection point of the LDV in the fruit tissue, which may also account for the poor repeatability of the frequency– response curves that were measured at different detection points.
The L27(313) orthogonal test probing the frequency sweeping rate, acceleration amplitude, pear laying style, and their 2-way interactions was designed according to the results of the singlefactor experiments. Through the single-factor experiments, the linear sweeping mode was found to be better than the logarithmic sweeping mode in terms of repeatability. Therefore, the linear sweeping mode was chosen in the orthogonal test. Three levels of frequency sweeping rates of approximately 23.33 Hz/s, which has the minimum Da in the single-factor experiment, were selected. Similarly, 1 g, 1.5 g and 2 g were selected as the levels of acceleration amplitude because of the better repeatability for these values of acceleration amplitude. The factors and levels of the orthogonal test are listed in Table 5. The variance-of-analysis results are shown in Table 6. No significant 2-way interaction is found among the frequency sweeping rate, acceleration amplitude, and pear laying style on the repeatability of the frequency–response curves. As to the main effect, Da is significantly affected by the frequency sweeping rate, but Dp is not significantly affected by the frequency sweeping rate. In addition, the results show that both Da and Dp are not significantly affected by the acceleration amplitude and pear laying style. The pairwise comparison of the means of different levels of three test parameters for Da is shown in Table 7. It is concluded that 23.33 Hz/s is the optimal frequency sweeping rate among the selected values, which is consistent with the results of the singlefactor experiment. The repeatability of the frequency–response curves does not significantly vary for the acceleration amplitudes of 1 g, 1.5 g and 2 g. However, the noise and equipment wear increase as the acceleration amplitude increases, and as a result, a lower acceleration amplitude is suggested. Therefore, the acceleration amplitude of 1 g is recommended and was selected in the subsequent study. The laying style does not significantly affect the repeatability of the frequency–response curves. However, f2 shows a better repeatability at different detection points with laying style A. Therefore, laying style A was determined to be a better laying style.
Table 6 Analysis of variance for three test parameters of the LDV method. Source
SSDa a
Frequency sweeping rate (A) Acceleration amplitude (B) Laying style (C) AB AC BC Error Total variance
0.2290 0.0598 0.0151 0.0783 0.0572 0.0886 2.6499 3.1778
SSDp
dfa
MSDa a
MSDp
F Da
3.55 106 9.18 107 1.16 106 5.64 106 1.41 106 7.79 106 2.49 104 2.70 104
2 2 2 4 4 4 251 269
0.1145 0.0299 0.0075 0.0196 0.0143 0.0221 0.0106
1.77 106 4.59 107 5.81 107 1.41 106 3.53 107 1.95 106 9.92 107
10.84 2.83 0.72 1.86 1.35 2.10
Significance
F Dp
Significance
0.00** 0.06 0.49 0.12 0.25 0.08
1.79 0.46 0.59 1.42 0.36 1.96
0.17 0.63 0.56 0.23 0.84 0.10
a SS: sum of squares; df: degree of freedom; MS: mean square mean; Da and Dp: differentiation indices for the amplitude–frequency curve and the phase–frequency curve, respectively. ** P < 0.01.
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Table 7 Pairwise comparison of the mean of different levels of three test parameters.a Performance index
Means of different levels of each test parameter
Differentiation index for amplitude–frequency curves (Da) a b
Frequency sweeping rate (Hz/s)
Acceleration amplitude
Laying style
20 0.1187b
1gb 0.0911a
A 0.0801a
23.33 0.0478a
26.67 0.0898b
1.5g 0.0650a
2g 0.1001a
B 0.0801a
C 0.0960a
Values of the same factor superscripted with different small letters indicate significant differences (p < 0.05). g = 9.8 m/s2.
Table 8 Correlation coefficients between the vibration parameters and the texture indices for different laying styles. Stifb
MFb
FFb
Laying style A
a
EI A2 a P400a P800a P1200a P1600a
**
0.7776 0.0678 0.4348** 0.7002** 0.7245** 0.6750**
**
0.3902 0.1095 0.2289* 0.4116** 0.4144** 0.3584**
0.4919** 0.1195 0.2852** 0.5035** 0.5029** 0.4869**
Laying style B
EI A2 P400 P800 P1200 P1600
0.7744** 0.1029 0.4194** 0.6528** 0.7201** 0.7139**
0.3899** 0.0626 0.2325* 0.3933** 0.4273** 0.4824**
0.4910** 0.0547 0.2842** 0.4812** 0.5195** 0.5552**
Laying style C
EI A2 P400 P800 P1200 P1600
0.7627** 0.0132 0.4526** 0.6836** 0.6700** 0.6504**
0.3622** 0.1636 0.2477** 0.3948** 0.3488** 0.3123**
0.4616** 0.1164 0.3006** 0.4765** 0.4251** 0.3721**
a
EI: the elasticity index; A2: the amplitude at f2; P400, P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. MF: maximum force; FF: flesh firmness; Stif: stiffness. Significant difference (P < 0.05). ** Highly significant difference (P < 0.01). b *
A verification test was conducted to determine the optimized combination of test parameters. Three pears were measured at the frequency sweeping rate of 23.33 Hz/s with the linear frequency sweeping mode, acceleration amplitude of 1 g, and laying style A. The results show that the mean values of Da and Dp are 0.0459 and 0.0004, respectively, confirming the good repeatability of the frequency–response curves under this test condition. 3.3. Comparison of the acoustic vibration method and destructive method for the texture measurement of pears 3.3.1. Correlations between vibration parameters and texture parameters Table 8 shows the correlation coefficients between the vibration parameters and texture indices for different laying styles. Stif is well correlated with the vibration parameters except A2 and P400 for each laying style. In addition, EI has the highest correlation coefficient with Stif among these vibration parameters.
However, unlike Stif, the other texture indices exhibit poor correlations with the vibration parameters. The result is consistent with the finding in our previous study (Zhang et al., 2014a), where the pear was placed in laying style A. The vibration parameters are poorly correlated with MF or FF because they correspond to different physical properties, as discussed in detail by Zhang et al. (2014b). The elastic properties mainly depend on the turgor pressure of fruit cells, whereas MF is mainly related to the cell wall structure. The correlation coefficients between vibration parameters and texture indices for different laying styles are almost equal, which indicates that the laying style has no obvious effect on the pear texture detection by the LDV method in terms of correlation.
3.3.2. Comparison on repeatability Table 9 shows the repeatability of vibration parameters and texture indices on each test day. The results show that EI is the best
Table 9 Measurement variability (MV, %) of the vibration parameters and texture indices on each test day. Days
EIa
A2 a
P400a
P800a
P1200a
P1600a
Stifb
MFb
FFb
0 2 4 6
1.99 2.01c 2.88 3.16 2.20 1.57 2.45 2.02
72.20 28.45 53.95 28.76 66.92 32.37 64.16 35.15
81.62 35.74 66.02 38.56 40.41 32.61 49.19 39.87
7.05 9.09 6.12 5.46 7.97 6.11 6.80 5.09
7.67 5.30 6.68 3.96 8.43 5.85 9.49 8.14
8.12 4.80 8.13 4.76 12.91 8.27 15.14 9.21
14.08 6.46 11.83 7.19 11.06 6.64 11.46 5.79
9.11 5.20 12.55 5.67 11.48 5.19 11.86 8.26
8.06 5.12 10.30 6.22 9.04 4.98 9.97 7.16
a b c
EI: the elasticity index; A2: the amplitude at f2; P400, P800, P1200 and P1600: phase shifts at 400, 800, 1200 and 1600 Hz, respectively. MF: maximum force; FF: flesh firmness; Stif: stiffness. Mean standard deviation.
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Table 10 Changes in elasticity index (EI) and texture indices during storage. Days
EIa (104 Hz2 kg2/3) Laying style A
Laying style B
Laying style C
0 2 4 6 Relative value loss
22.72 20.11 16.61 13.11 42.31%
22.66 19.97 16.42 12.93 42.92%
22.21 19.31 16.09 12.68 42.91%
a b
Stifb (N/mm)
MFb (N)
FFb (N)
10.85 10.18 9.12 7.97 26.56%
16.01 16.56 15.73 14.23 11.13%
11.97 12.19 11.52 10.41 13.08%
EI: the elasticity index. MF: maximum force; FF: flesh firmness; Stif: stiffness.
index in terms of repeatability (MV < 3%) among all indices and that it has much lower MV values than the texture indices. The texture indices have better repeatability than A2 and P400 but worse repeatability than P800, P1200, and EI. The poor repeatability of A2 and P400 may account for their poor correlation with the texture indices. The fruit texture at different sites measured by the puncture test varied because of the non-homogeneous and anisotropic properties of fruits (Abbott and Lu, 1996). However, the resonance frequency, which describes the overall elasticity characteristics of pears, is not significantly affected by the detection point and laying style. The better repeatability of EI than the texture indices indicates that the LDV method is superior to the destructive puncture test in terms of repeatability.
method is superior to the destructive puncture test in terms of repeatability and sensitivity. Acknowledgements The authors gratefully acknowledge the support of this program by theNational Natural Science Foundation of China (Grant No. 31201132). Any opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of Zhejiang University. The trade and manufacturers’ names are necessary to report factually on the available data. References
3.3.3. Comparison on sensitivity Table 10 shows the changes in EI and texture indices during storage. A2 does not have an obvious variation trend, and the phase shifts at selected frequencies increase during storage, so they are not listed in this table. EI and the texture indices gradually decrease during storage. The relative value losses of EI for different laying styles are almost equal, which indicates that the sensitivity of EI is not affected by the laying style. Stif shows the highest sensitivity among the texture indices, but its sensitivity remains lower that of EI. The higher sensitivity of EI compared to the texture indices indicates that the LDV method is also more advantageous than the destructive puncture test in terms of sensitivity, which is consistent with Shmulevich et al. (2003), who found that the acoustic firmness was more sensitive than the Magness-Taylor firmness for apples during their shelf life, and Murayama et al. (2006), who found that EI of “La France” pears always decreased immediately after harvest, whereas the flesh firmness decreased after an initial lag time. 4. Conclusion The test parameters of the pear texture measurement using the LDV method were optimized in this paper. A good repeatability of the vibration spectrum or vibration parameters is the basis for further texture evaluation using the LDV method. Therefore, the test parameters in this study were mainly optimized based on the repeatability of frequency–response curves under different test conditions. Better test parameter values for the pear texture measurement are as follows: frequency sweeping rate of 23.33 Hz/ s with the linear frequency sweeping mode, acceleration amplitude of 1 g, and laying style A. In addition to the correlation, a combination of repeatability and sensitivity is recommended to compare the performance of a new method with the traditional method. The comparison between the LDV method and the destructive puncture test shows that EI is well correlated with the Stif of pears. In addition, the LDV
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