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Nondestructive measurement of pear texture by acoustic vibration method
Postharvest Biology and Technology 96 (2014) 99–105
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Postharvest Biology and Technology journal homepage: www.elsevier.com/locate/postharvbio
Nondestructive measurement of pear texture by acoustic vibration method Wen Zhang 1 , Di Cui ∗ , Yibin Ying 2 School of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, 310058 Hangzhou, PR China
a r t i c l e
i n f o
Article history: Received 10 January 2014 Accepted 1 May 2014 Keywords: Nondestructive measurement Texture Acoustic vibration Laser Doppler vibrometer Shape index
a b s t r a c t Texture is a key attribute for the assessment of pear quality, and a nondestructive texture detection method was investigated. Each pear fruit was excited by a swept sine wave signal (xin ), and the response signal from the top of the pear (xout ) was detected by a laser Doppler vibrometer (LDV). The vibration spectrum was acquired after a fast Fourier transform was applied to the xin and xout data. Six vibration parameters, including the second resonance (f2 ), the amplitude at f2 (A2 ), and the phase shifts at 400, 800, 1200 and 1600 Hz (P400 , P800 , P1200 and P1600 ) were extracted from the vibration spectrum, and the elasticity index (EI) was determined by the formula EI = f22 m2/3 . The fruit texture was then measured by a puncture test. Three texture indices were extracted from the force–deformation curve, in which the stiffness (Stif) was found to be more suitable for representing fruit quality. The multiple linear regression (MLR) method was applied to evaluate the importance of each vibration parameter for predicting Stif, and the following order of importance was found: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . A texture prediction model was built by the stepwise multiple linear regression (SMLR) method and modified through the introduction of the pear shape index (SI). The performance of the prediction model was improved after modification; the value of the correlation coefficient for the calibration and validation sample sets (rc and rp ) increased by 0.4% and 2.1%, respectively, while the root mean square errors of calibration and prediction (RMSEC and RMSEP) decreased by 0.6% and 3.3%, respectively. Highly significant results (P < 0.01) for both the initial and modified prediction models proved that the evaluation of pear texture by a combination of the LDV method and the proposed approach was feasible. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Pear fruit continue to ripen and eventually develop into juicy fruit with a buttery texture (Kondo and Takano, 2000). The gross texture of fruit is associated with the characteristics of their cells, such as cell size, cell wall thickness and strength, and cell turgor pressure (Harker et al., 1997). Consumers evaluate fruit texture by chewing or touching, considering it a major factor when purchasing because it represents the ripeness, freshness and edibility of the fruit. Therefore, texture is a key quality attribute, and it is widely used to assess product quality and acceptability in the fresh and processed food industry (Chen and Opara, 2013a).
∗ Corresponding author. Tel.: +86 571 88982820. E-mail addresses: [email protected] (W. Zhang), [email protected] (D. Cui), [email protected] (Y. Ying). 1 Tel.: +86 188 68817192. 2 Tel.: +86 571 88982885. http://dx.doi.org/10.1016/j.postharvbio.2014.05.006 0925-5214/© 2014 Elsevier B.V. All rights reserved.
The evaluation of fruit texture can be divided into subjective and objective analyses (Chen and Opara, 2013a). Subjective analysis, often referred to as sensory evaluation, is time-consuming and expensive. Among objective analysis techniques, the puncture test, which is based on the force–deformation (F–D) characteristics of the fruit, is one of the mostly widely used destructive methods. Many indicators of texture can be extracted from the F–D curve: (i) the maximum force during penetration (Gomez et al., 2005; Mendoza et al., 2012); (ii) the flesh firmness which is the mean force during the period after rupture (Duprat et al., 1997; Wang et al., 2005); and (iii) the stiffness, based on the slope of the F–D curve (Pitt and Davis, 1984; Benedito et al., 2000; Camps et al., 2005). The acoustic technique is the most commonly used nondestructive detection method for evaluation of the texture of agro-products. Abbott et al. (1968) proposed a stiffness coefficient, f2 m, for spherical fruit, where f is the dominant frequency and m is the mass of the sample. Later, Cooke (1972) proposed a modified elasticity coefficient, f2 m2/3 1/3 , where is the density of the sample. This index is typically simplified to f2 m2/3 for small differences in (Molina-Delgado et al., 2009; Chen and Opara, 2013b). Many
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studies have shown that the stiffness coefficient or elasticity coefficient is strongly correlated with fruit texture (Duprat et al., 1997; Terasaki et al., 2001; Gomez et al., 2005; Mendoza et al., 2012). General methods for fruit vibration detection mainly include piezoelectric sensors, acceleration pickups and microphones (Taniwaki and Sakurai, 2010). However, the attachment of piezoelectric sensors or acceleration pickups to the fruit would prevent its free vibration. Methods that use microphones would be easily affected by ambient noise. The laser Doppler vibrometer (LDV) method is an acoustic vibration technique proposed for the quality inspection of agro-products since the 1990s (Muramatsu et al., 1997). It has the advantages of being contact-free and unaffected by ambient noise. Muramatsu et al. (1999) did a preliminary study on the detection of pear texture by the LDV method and found that the displacement force was correlated with the phase shift. Their results suggested that this method had the potential for the evaluation of pear firmness and maturity. Terasaki et al. (2006) applied this technique to monitor changes in the elastic properties of ‘La France’ pears and develop a reciprocal modal to simulate the ripening process. However, the relationship between the vibration properties and the texture of the pears was not investigated. Taniwaki et al. (2009a) measured pear texture by an improved self-designed device and determined the optimum eating ripeness of pears according to the relations between the overall acceptability assessed by a sensory test and the elasticity index calculated from the second resonance frequency acquired by the LDV method. However, few studies have considered fruit shape in the nondestructive determination of agro-product quality based on vibration characteristics acquired by the LDV method. Therefore, the objectives of this investigation were (i) to monitor changes in the texture indices of pears based on their F–D curves during storage, (ii) to evaluate the feasibility of the LDV method for nondestructive detection of pear texture, and (iii) to investigate the influence of pear shape on the performance of the texture prediction model.
2. Materials and methods Symbols and abbreviations used in this paper are shown in Table 1.
2.1. Pear samples More than 300 fruit (Pyrus bretschneideri Rehd. cv. Huangguan) were purchased from a local fruit market and immediately transported to the laboratory at Zhejiang University in Hangzhou, China. After weighing, fruit whose mass were greater than 320 g or less than 220 g were removed, and the remaining 160 samples (274.35 ± 21.57 g) were stored in a manual climatic box (PRX-1500A, Haishusaifu Instrument Co., Ltd., Ningbo, China) at a temperature of 20 ◦ C and a relative humidity of 50% for 54 days. Fruit that spoiled during storage were removed, and a total of 135 fruit samples were finally used for the experiment. During storage, the vibration spectra and texture of 7–12 samples were measured every 3 days during the first 18 days and every 6 days thereafter by the following methods. In each test, fruit were placed in the experimental environment for 12 h, then they were numerically coded and their morphological properties were measured. Morphological properties included the mass (m), height (h), and diameter along the equatorial plane (d). Fruit shape was characterized by the shape index (SI) defined as h/d. Table 2 shows the basic morphological properties of the tested pear samples.
Table 1 Symbols and abbreviations. A2 d EI f2 F–D FF FFT h LDV m MF MLR P400 P800 P1200 P1600 r rc rp RMSEC RMSEP SI SMLR Stif xin xout F d
Amplitude at the second resonance frequency Diameter of the sample Elasticity index Second resonance frequency Force–deformation Flesh firmness Fast Fourier transform Height of the sample Laser Doppler vibrometer Mass of the sample Maximum force during penetration Multiple linear regression Phase shift at 400 Hz Phase shift at 800 Hz Phase shift at 1200 Hz Phase shift at 1600 Hz Correlation coefficient Correlation coefficient for the calibration sample set Correlation coefficient for the validation sample set Root mean square error of calibration Root mean square error of prediction Shape index Stepwise multiple linear regression Stiffness Excitation signal for the sample Response signal at the top of the sample Force at the rupture point Penetration distance at the rupture point
2.2. Vibration spectrum measurement The experimental set-up used to measure the vibration spectra of pears was similar to that used by Terasaki et al. (2001) and Abbaszadeh et al. (2013). The measurement system consisted of two parts: the control element and the signal acquisition element. For the control element, the vibrator (ES-05; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) was excited by swept sine wave signals (ranging from 100 to 2000 Hz at a linear sweep rate of 600 Hz/min), which were generated by a PC (Dell Inc., Round Rock, TX, USA) and amplified by a power amplifier (PA-1200; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China). Actual vibration signals of the stage (xin ) were sensed by the accelerometer 1 (DL-24100, Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) and sent back to the vibration controller (Amber; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) to obtain closedloop control. For signal acquisition, fruit were placed vertically on the vibration stage, and the response signal at the top of each sample (xout ) was measured by a LDV (LV-S01; Sunny Instruments Singapore Pte., Ltd., Singapore); the xin was simultaneously monitored by the accelerometer 2 (LC0159; Lance Technologies Inc., Akron, USA) which was attached to the stage. Both xin and xout were acquired by a signal acquisition module (USB-4431; National Instrument, Austin, USA) and delivered to the PC. The frequency response of fruit consisted of the amplitude–frequency response and phase–frequency response, which were obtained after a fast Fourier transform (FFT) algorithm was applied to the xin and xout data. Representative examples Table 2 Morphological properties of the tested pear samples (n = 135).
Mass (m, g) Heighta (h, mm) Diametera (d, mm) Shape index (SI) a
Average
Maximum
Minimum
Standard deviation
262.25 73.98 78.78 0.94
309.52 81.66 84.17 1.03
203.29 66.40 72.22 0.85
23.55 3.35 2.41 0.04
Average value of three measurements taken at evenly spaced intervals of 120◦ .
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Fig. 1. Representative examples of (a) amplitude–frequency response and (b) phase–frequency response of two pears with different textures. The second resonance frequency (f2 ) was used for determining the elasticity index (EI).
of the frequency responses of two pears with different textures are presented in Fig. 1. After frequency response evaluation, six vibration parameters were extracted: the second resonance frequency (f2 ); the amplitude at f2 (A2 ); and the phase shifts at 400, 800, 1200 and 1600 Hz (P400 , P800 , P1200 and P1600 ). Additionally, the elasticity index (EI) (Cooke, 1972; Taniwaki et al., 2009a,b) was calculated by Eq. (1): EI = f22 m2/3
(1)
where m is mass of the sample.
Correlation analysis was then performed among the vibration parameters, and the multiple linear regression (MLR) method was chosen to fit the experimental data to evaluate the importance of each vibration parameter. In the MLR model, the contribution of each factor for determining the dependent variable can be evaluated by the absolute values of the standardized regression coefficients. The MLR model is shown in Eq. (3). Y = a0 +
7
ai xi
(3)
i=1
2.3. Texture measurement After the vibration spectrum was measured, the fruit texture was measured by the puncture test, which was performed with a texture analyzer (TA-XT2i, Stable Micro System, Inc., England) at four sites at evenly spaced intervals along the equatorial plane. At each site, a piece of peel was removed, and a cylindrical probe with a diameter of 5 mm was inserted into the sample to a penetration depth of 10 mm, at a loading speed of 60 mm/min. A typical puncture F–D curve of a site is shown in Fig. 2. Three texture indices, including the maximum force (MF) during penetration, flesh firmness (FF, average force between 3 mm and 10 mm distance), and stiffness (Stif, the slope of F–D curve before the rupture point), were determined from the F–D curve. The value of Stif was calculated by Eq. (2): Stif =
F d
where Y is the texture index, a0 –a7 are the regression coefficients, and x1 –x7 are f2 , A2 , P400 , P800 , P1200 , P1600 , and EI, respectively. Finally, the seven vibration parameters (f2 , A2 , P400 , P800 , P1200 , P1600 , and EI) and SI were taken as independent variables to build the texture prediction model. Prior to modeling, atypical values were removed by the Chauvenet testing method. All remaining samples were sorted in order of the texture index and then divided into two sample sets: calibration and validation. Samples with the
(2)
where F is the force at rupture point and d is the penetration distance at rupture point. All of these texture indices were calculated automatically by the Exponent 6.0 software (Stable Micro System Inc., England). The average value of each texture index at four sites was calculated and reported as the MF, FF, and Stif value of each sample. 2.4. Statistical analysis Firstly, changes in the texture indices were analyzed, and correlation analysis between the texture indices and the vibration parameters was performed. Stif was chosen for further analysis because of its variation trend and correlations with the vibration parameters.
Fig. 2. A typical puncture force–deformation (F–D) curve for a single site along the equatorial plane. Three texture indices, including the maximum force (MF), flesh firmness (FF, average force between 3 mm and 10 mm distance), and stiffness (Stif, the slope of F–D curve before the rupture point), were determined from the F–D curve.
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Fig. 3. Time–course changes in (a) maximum force (MF), flesh firmness (FF), and (b) stiffness (Stif) determined by the puncture test during storage. The bars represent the standard error.
maximum and minimum texture indices were put into the calibration sample set. Then, three out of four samples were put into the calibration sample set in order, and the remainders were used for validation. Calibration models were established according to two steps. In Step 1, a stepwise multiple linear regression (SMLR) method was used to extract feature parameters and build an initial texture prediction model (Eq. (4)).
where Y is the modified prediction value of the texture index and C0 –C2 are the regression coefficients. The performance of the models was assessed in terms of the correlation coefficients for the calibration and validation sample sets (i.e., rc and rp ) and the root mean square errors of calibration and prediction (i.e., RMSEC and RMSEP).
Y = g1 (x1 , x2 , . . ., xn )
3. Results
(4)
where Y is the prediction value of the texture index and x1 –xn are the extracted feature parameters. In Step 2, SI was introduced to modify the model. The modified model is shown in Eq. (5). Y = C0 g1 (x1 , x2 , . . ., xn ) + C1 SI + C2
(5)
3.1. Changes in texture during storage Fig. 3 shows the time-course changes in MF, FF, and Stif during storage. All three texture indices exhibited a declining trend overall. A similar trend was observed in MF and FF; relatively stable levels were observed for both before day 24, and they then decreased
Table 3 Correlations between the texture indices and the vibration parameters.
Maximum force (MF) Flesh firmness (FF) Stifness (Stif) * ** ***
Second resonance frequency (f2 )
Amplitude at the second resonance frequency (A2 )
Phase shift at 400 Hz (P400 )
Phase shift at 800 Hz (P800 )
Phase shift at 1200 Hz (P1200 )
Phase shift at 1600 Hz (P1600 )
Elasticity index (EI)
−0.004 0.203* 0.738**
0.144 0.075 0.364**
0.095 −0.114 −0.604**
0.135 −0.113 −0.641**
0.177* −0.087 −0.593**
0.184* −0.079 −0.581**
0.042 0.235** 0.756**
P < 0.05. P < 0.01. P < 0.001.
Table 4 Statistical results of the multiple linear regression (MLR) model for determining Stiffness (Stif) of the pears. y
x
Non-standardized coefficients
Standardized coefficients
Significance
Stiffness (Stif, N/mm)
Second resonance frequency (f2 , Hz) Amplitude at the second resonance frequency (A2 , dB) Phase shift at 400 Hz (P400 , -deg) Phase shift at 800 Hz (P800 , -deg) Phase shift at 1200 Hz (P1200 , -deg) Phase shift at 1600 Hz (P1600 , -deg) Elasticity index (EI, Hz2 kg2/3 ) Constant
−0.008 0.038 −0.006 0.000 0.000 0.001 0.000 4.312
−1.1902 0.0557 −0.4313 −0.1895 0.0976 0.3544 1.8111
0.023* 0.401 0.016* 0.514 0.700 0.088 0.000** 0.002**
The superscripted numbers represent the sequence of absolute value of standardized coefficient from the highest to the lowest. * ** ***
P < 0.05. P < 0.01. P < 0.001.
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Table 5 Correlation coefficient matrix of the vibration parameters. Second resonance frequency (f2 ) Second resonance frequency (f2 ) Amplitude at the second resonance frequency (A2 ) Phase shift at 400 Hz (P400 ) Phase shift at 800 Hz (P800 ) Phase shift at 1200 Hz (P1200 ) Phase shift at 1600 Hz (P1600 ) Elasticity index (EI) * ** ***
1 0.358** −0.813** −0.901** −0.886** −0.878** 0.985**
Amplitude at the second resonance frequency (A2 )
Phase shift at 400 Hz (P400 )
Phase shift at 800 Hz (P800 )
Phase shift at 1200 Hz (P1200 )
Phase shift at 1600 Hz (P1600 )
Elasticity index (EI)
1 0.932** 0.863** 0.816** −0.735**
1 0.954** 0.924** −0.847**
1 0.960** −0.841**
1 −0.849**
1
1 −0.115 −0.149 −0.163 −0.206* 0.412**
P < 0.05. P < 0.01. P < 0.001.
gradually. Stif declined more regularly over time throughout the entire storage period, excluding an abnormal point on day 6. MF, FF, and Stif decreased by −0.2%, 7.0% and 33.9%, respectively, in the first 24 days, and by 29.5%, 18.4% and 47.3%, respectively, during the entire storage period. It was clear that Stif was more appropriate to represent the fruit quality because of its regular variation trend and large range of variation.
correlation coefficients with Stif (Table 3). The significant vibration parameters were EI, f2 , and P400 . The correlation coefficient matrix of the vibration parameters is shown in Table 5, in which highly significant correlations were observed among the vibration parameters, excluding that between A2 and the phase shift at selected frequencies. The value of r between EI and f2 was the highest (r = 0.985).
3.2. Relationship between the texture indices and the vibration parameters
3.3. Texture prediction model
Correlations between the texture indices and the vibration parameters are shown in Table 3. All correlation coefficients (r) between MF, FF and the vibration parameters were too low; the highest was only 0.235. Stif was highly correlated with all the vibration parameters (P < 0.01), and the correlation coefficients were much larger than those of MF and FF. Because MF and FF did not correlate well with the vibration parameters and Stif was more appropriate to represent fruit quality during the storage time, Stif was the texture index chosen for further analysis. Statistical results of the MLR model for determining Stif of the pears are presented in Table 4. The sequence of vibration parameters according to their importance, based on the standardized coefficients, was as follows: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . EI and A2 had the highest and lowest contribution, respectively, supporting the finding that they had the maximum and minimum
At first, one sample was removed by the Chauvenet testing method. Then, 101 samples were chosen for the calibration sample set, and 33 samples were selected for the validation sample set. Table 6 and Table 7 show the statistical results of the initial texture prediction model and the modified texture prediction model, respectively. The significance test showed that both models were highly significant (P < 0.01). The three vibration feature parameters extracted from the initial texture prediction model, in order of importance, were EI, P1600 , and P400 . All of these vibration feature parameters were highly significant in the initial texture prediction model. However, SI was not significant in the modified texture prediction model. Table 8 shows the comparison of the performance of the initial and modified models. Higher rc and rp , and lower RMSEC and RMSEP were observed after modification. Clearly, the performance of the model improved after introducing SI. The actual and
Table 6 Statistical results of the initial texture prediction model. y
x
Stiffness (Stif, N/mm)
Phase shift at 400 Hz (P400 , -deg) Phase shift at 1600 Hz (P1600 , -deg) Elasticity index (EI, Hz2 kg2/3 ) Constant
* ** ***
Non-standardized coefficients −0.009 0.002 3.057 × 10−5 1.163 F = 62.731 (P < 0.01)
Standardized coefficients
Significance
−0.302 0.529 0.998
0.005** 0.000** 0.000** 0.188
P < 0.05. P < 0.01. P < 0.001.
Table 7 Statistical results of the modified texture prediction model. y
x
Stif (N/mm)
g1 Shape index (SI) Constant
* ** ***
P < 0.05. P < 0.01. P < 0.001.
Non-standardized coefficients 0.989 2.884 −2.633 F = 96.678 (P < 0.01)
Standardized coefficients
Significance
0.804 0.062
0.000** 0.298 0.308
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Table 8 Comparison of the performance of the initial and modified prediction models. Models
Initial texture prediction model Modified texture prediction model
Calibration
Validation
rc
RMSEC (N/mm)
rp
RMSEP (N/mm)
0.812 0.815
1.048 1.042
0.717 0.732
1.243 1.202
predicted Stif values of the modified model in the calibration and validation sample sets are shown in Fig. 4. 4. Discussion Swept sine wave excitation, which is the most commonly used excitation method in LDV detection, was chosen in our research (Terasaki et al., 2001; Taniwaki et al., 2009a,b; Abbaszadeh et al., 2013). The swept sine wave method is advantageous in terms of its repeatability, and can measure the vibration characteristic more accurately than the impact method because it can concentrate the excitation energy within a small frequency band at a certain time (Taniwaki et al., 2009a; Taniwaki and Sakurai, 2010). As for the pear texture measurement, MF and FF maintained a relatively stable level during the first 24 days and then decreased gradually. However, the fruit appearance changed visibly over time. Stif, by contrast, exhibited a declining trend during the entire storage period, which was consistent with the fruit quality change. Additionally, the variation range of Stif was much larger than those of MF and FF during the storage period. Therefore, it would be easier to distinguish fruit at different storage times by Stif. Consequently, the value of Stif may be a more suitable index than MF and FF for evaluating fruit quality. In addition, sensory evaluations will be needed to validate the relationships between these texture indices and sensory scores because texture is ultimately a subjective sensation (Taniwaki and Sakurai, 2010). The vibration parameters had higher correlation coefficients with Stif than MF or FF (Table 3). Similar results were observed for ‘Dangshan’ pears (Pan and Tu, 2004a) and ‘Fuji’ apples (Pan and Tu, 2004b). A possible cause of this result was that both force and deformation were involved in Stif. Therefore, Stif may reflect the mechanical properties of fruit more accurately, better reflecting the fruit texture changes. The vibration parameters were all strongly correlated with Stif (Table 3); however, not all the regression coefficients were significant in the MLR model, according to the significance test
(Table 4). The non-significant regression coefficients of some vibration parameters in the MLR model and some highly significant correlations among the vibration parameters indicated that multicollinearity existed in this model. Therefore, the SMLR method was used to eliminate the unnecessary variables for a prediction model with high robustness. Three vibration parameters with high contribution were extracted: EI, P1600 , and P400 . The r value (0.812) observed between the actual Stif and the predicted Stif obtained by the SMLR model (Table 8) was higher than that between Stif and the vibration parameters (the highest was 0.756, as shown in Table 3), suggesting that the combination of multiple vibration parameters provided more information about the texture than a single vibration parameter. Vibration characteristics of fruit are affected by their texture, mass, geometric shape, size, among other properties (Duprat et al., 1997). Thus, fruit shape was taken into consideration in our model, and a shape index was calculated to describe the geometric shape of the pears. rc and rp increased by 0.4% and 2.1%, respectively, while RMSEC and RMSEP decreased by 0.6% and 3.3%, respectively (Table 8). It is clear that the performance of the model was improved. However, the improvement of the model performance was limited, and SI was not significant in the modified texture prediction model. There may be two reasons for this result: (i) the method used to describe pear shape was crude, and the pear shape could not be described well through the h/d ratio alone; (ii) the difference in SI among the pear samples in this study was relatively small. Therefore, a more precise description method for fruit shape and samples with a wide range of shapes will be needed in future research. A significant influence of shape on vibration properties was also found in apples, pears, potatoes and some other agro-products (Chen and Debaerdemaeker, 1993; Jancsok et al., 2001; Blahovec et al., 2007). The results of the significance tests of both the initial and modified prediction models (Tables 6 and 7) showed that the models were feasible for the evaluation of pear texture by the LDV method.
Fig. 4. Correlations between the predicted stiffness (Stif) determined by the modified model and the actual stiffness in the (a) calibration sample set and (b) validation sample set. The solid line is the regression line.
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5. Conclusion In this paper, three texture indices (MF, FF and Stif) and seven vibration parameters (f2 , A2 , P400 , P800 , P1200 , P1600 , and EI) of the pears were selected. Stif was found to be a more suitable index for evaluating fruit quality, and correlate well with the vibration parameters than MF and FF. The sequence of vibration parameters for predicting Stif, according to the standardized coefficients of the MLR model, was as follows: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . Three vibration feature parameters, EI, P1600 , and P400 , were extracted by the SMLR method, and an initial texture prediction model was built. The results showed that multiple vibration parameters provided more information for texture prediction than a single vibration parameter. After modification by the introduction of SI, the performance of the prediction model was improved. The results of the significance tests of both the initial and modified prediction models proved that the evaluation of pear texture by a combination of the LDV method and the proposed modeling approach was feasible. Acknowledgements The authors gratefully acknowledge the support of this program by National High Technology Research and Development Program of China (2012AA10A504). Any opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of Zhejiang University. Trade and manufacturer’s names are necessary to report factually on available data. References Abbaszadeh, R., Rajabipour, A., Mahjoob, M., Delshad, M., Ahmadi, H., 2013. Evaluation of watermelons texture using their vibration responses. Biosyst. Eng. 115, 102–105. 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, 101–112. Benedito, J., Carcel, J.A., Sanjuan, N., Mulet, A., 2000. Use of ultrasound to assess Cheddar cheese characteristics. Ultrasonics 38, 727–730. Blahovec, J., Kuroki, S., Sakurai, N., 2007. Cooking kinetics of potato tubers determined by vibration techniques. Food Res. Int. 40, 576–584. Camps, C., Guillermin, P., Mauget, J.C., Bertrand, D., 2005. Data analysis of penetrometric force/displacement curves for the characterization of whole apple fruits. J. Texture Stud. 36, 387–401. Chen, H., Debaerdemaeker, J., 1993. Effect of apple shape on acoustic measurements of firmness. J. Agric. Eng. Res. 56, 253–266.
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Chen, L., Opara, U.L., 2013a. Texture measurement approaches in fresh and processed foods. Food Res. Int. 51, 823–835. Chen, L., Opara, U.L., 2013b. Approaches to analysis and modeling texture in fresh and processed foods – a review. J. Food Eng. 119, 497–507. Cooke, J.R., 1972. An interpretation of the resonant behavior of intact fruits and vegetables. Trans. ASAE 15, 1075–1080. Duprat, F., Grotte, M., Pietri, E., Loonis, D., 1997. The acoustic impulse response method for measuring the overall firmness of fruit. J. Agric. Eng. Res. 66, 251–259. 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, 209–215. Harker, F.R., Redgwell, R.J., Hallett, I.C., Murray, S.H., Carter, G., 1997. Texture of fresh fruit. Hortic. Rev. 20, 121–224. Jancsok, P.T., Clijmans, L., Nicolai, B.M., De Baerdemaeker, J., 2001. Investigation of the effect of shape on the acoustic response of ‘conference’ pears by finite element modelling. Postharvest Biol. Technol. 23, 1–12. Kondo, S., Takano, Y., 2000. Cell wall metabolism and induction of ripening capacity in ‘La France’ pear as influenced by 2, 4-DP. J. Am. Soc. Hortic. Sci. 125, 242–247. 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., Barreiro, P., Valero, C., Ruiz-Altisent, M., Recasens, I., 2009. Addressing potential sources of variation in several non-destructive techniques for measuring firmness in apples. Biosyst. Eng. 104, 33–46. Muramatsu, N., Sakurai, N., Wada, N., Yamamoto, R., Takahara, T., Ogata, T., Tanaka, K., Asakura, T., Ishikawa-Takano, Y., Nevins, D.J., 1999. Evaluation of fruit tissue texture and internal disorders by laser Doppler detection. Postharvest Biol. Technol. 15, 83–88. Muramatsu, N., Tanaka, K., Asakura, T., Ishikawa-Takano, Y., Sakurai, N., Wada, N., Yamamoto, R., Nevins, D.J., 1997. Critical comparison of an accelerometer and a laser Doppler vibrometer for measuring fruit firmness. HortTechnology 7, 434–438. Pan, X.J., Tu, K., 2004a. Nondestructive measurement of texture changes of pear fruit with acoustic impulse response technique. J. Nanjing Agric. Univ. 27, 94–98. Pan, X.J., Tu, K., 2004b. Measurement of firmness changes of harvested Fuji apples with destructive and nondestructive method. J. Northwest A & F U. (Nat. Sci.) 32, 38–42. Pitt, R.E., Davis, D.C., 1984. Finite-element analysis of fluid-filled cell response to external loading. Trans. ASAE 27, 1976–1983. Taniwaki, M., Hanada, T., Tohro, M., Sakurai, N., 2009a. Non-destructive determination of the optimum eating ripeness of pears and their texture measurements using acoustical vibration techniques. Postharvest Biol. Technol. 51, 305–310. Taniwaki, M., Hanada, T., Sakurai, N., 2009b. Postharvest quality evaluation of Fuyu and Taishuu persimmons using a nondestructive vibrational method and an acoustic vibration technique. Postharvest Biol. Technol. 51, 80–85. Taniwaki, M., Sakurai, N., 2010. Evaluation of the internal quality of agricultural products using acoustic vibration techniques. J. Jpn. Soc. Hortic. Sci. 79, 113–128. 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, 198–207. 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, 81–87. Wang, X., LI, J.Q., Ren, L.Q., Ma, Z.S., 2005. Mensuration and changes on firmness of tomato fruits during the post-harvest storage. Trans. CSAM 36, 65–67.
Contents lists available at ScienceDirect
Postharvest Biology and Technology journal homepage: www.elsevier.com/locate/postharvbio
Nondestructive measurement of pear texture by acoustic vibration method Wen Zhang 1 , Di Cui ∗ , Yibin Ying 2 School of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, 310058 Hangzhou, PR China
a r t i c l e
i n f o
Article history: Received 10 January 2014 Accepted 1 May 2014 Keywords: Nondestructive measurement Texture Acoustic vibration Laser Doppler vibrometer Shape index
a b s t r a c t Texture is a key attribute for the assessment of pear quality, and a nondestructive texture detection method was investigated. Each pear fruit was excited by a swept sine wave signal (xin ), and the response signal from the top of the pear (xout ) was detected by a laser Doppler vibrometer (LDV). The vibration spectrum was acquired after a fast Fourier transform was applied to the xin and xout data. Six vibration parameters, including the second resonance (f2 ), the amplitude at f2 (A2 ), and the phase shifts at 400, 800, 1200 and 1600 Hz (P400 , P800 , P1200 and P1600 ) were extracted from the vibration spectrum, and the elasticity index (EI) was determined by the formula EI = f22 m2/3 . The fruit texture was then measured by a puncture test. Three texture indices were extracted from the force–deformation curve, in which the stiffness (Stif) was found to be more suitable for representing fruit quality. The multiple linear regression (MLR) method was applied to evaluate the importance of each vibration parameter for predicting Stif, and the following order of importance was found: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . A texture prediction model was built by the stepwise multiple linear regression (SMLR) method and modified through the introduction of the pear shape index (SI). The performance of the prediction model was improved after modification; the value of the correlation coefficient for the calibration and validation sample sets (rc and rp ) increased by 0.4% and 2.1%, respectively, while the root mean square errors of calibration and prediction (RMSEC and RMSEP) decreased by 0.6% and 3.3%, respectively. Highly significant results (P < 0.01) for both the initial and modified prediction models proved that the evaluation of pear texture by a combination of the LDV method and the proposed approach was feasible. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Pear fruit continue to ripen and eventually develop into juicy fruit with a buttery texture (Kondo and Takano, 2000). The gross texture of fruit is associated with the characteristics of their cells, such as cell size, cell wall thickness and strength, and cell turgor pressure (Harker et al., 1997). Consumers evaluate fruit texture by chewing or touching, considering it a major factor when purchasing because it represents the ripeness, freshness and edibility of the fruit. Therefore, texture is a key quality attribute, and it is widely used to assess product quality and acceptability in the fresh and processed food industry (Chen and Opara, 2013a).
∗ Corresponding author. Tel.: +86 571 88982820. E-mail addresses: [email protected] (W. Zhang), [email protected] (D. Cui), [email protected] (Y. Ying). 1 Tel.: +86 188 68817192. 2 Tel.: +86 571 88982885. http://dx.doi.org/10.1016/j.postharvbio.2014.05.006 0925-5214/© 2014 Elsevier B.V. All rights reserved.
The evaluation of fruit texture can be divided into subjective and objective analyses (Chen and Opara, 2013a). Subjective analysis, often referred to as sensory evaluation, is time-consuming and expensive. Among objective analysis techniques, the puncture test, which is based on the force–deformation (F–D) characteristics of the fruit, is one of the mostly widely used destructive methods. Many indicators of texture can be extracted from the F–D curve: (i) the maximum force during penetration (Gomez et al., 2005; Mendoza et al., 2012); (ii) the flesh firmness which is the mean force during the period after rupture (Duprat et al., 1997; Wang et al., 2005); and (iii) the stiffness, based on the slope of the F–D curve (Pitt and Davis, 1984; Benedito et al., 2000; Camps et al., 2005). The acoustic technique is the most commonly used nondestructive detection method for evaluation of the texture of agro-products. Abbott et al. (1968) proposed a stiffness coefficient, f2 m, for spherical fruit, where f is the dominant frequency and m is the mass of the sample. Later, Cooke (1972) proposed a modified elasticity coefficient, f2 m2/3 1/3 , where is the density of the sample. This index is typically simplified to f2 m2/3 for small differences in (Molina-Delgado et al., 2009; Chen and Opara, 2013b). Many
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studies have shown that the stiffness coefficient or elasticity coefficient is strongly correlated with fruit texture (Duprat et al., 1997; Terasaki et al., 2001; Gomez et al., 2005; Mendoza et al., 2012). General methods for fruit vibration detection mainly include piezoelectric sensors, acceleration pickups and microphones (Taniwaki and Sakurai, 2010). However, the attachment of piezoelectric sensors or acceleration pickups to the fruit would prevent its free vibration. Methods that use microphones would be easily affected by ambient noise. The laser Doppler vibrometer (LDV) method is an acoustic vibration technique proposed for the quality inspection of agro-products since the 1990s (Muramatsu et al., 1997). It has the advantages of being contact-free and unaffected by ambient noise. Muramatsu et al. (1999) did a preliminary study on the detection of pear texture by the LDV method and found that the displacement force was correlated with the phase shift. Their results suggested that this method had the potential for the evaluation of pear firmness and maturity. Terasaki et al. (2006) applied this technique to monitor changes in the elastic properties of ‘La France’ pears and develop a reciprocal modal to simulate the ripening process. However, the relationship between the vibration properties and the texture of the pears was not investigated. Taniwaki et al. (2009a) measured pear texture by an improved self-designed device and determined the optimum eating ripeness of pears according to the relations between the overall acceptability assessed by a sensory test and the elasticity index calculated from the second resonance frequency acquired by the LDV method. However, few studies have considered fruit shape in the nondestructive determination of agro-product quality based on vibration characteristics acquired by the LDV method. Therefore, the objectives of this investigation were (i) to monitor changes in the texture indices of pears based on their F–D curves during storage, (ii) to evaluate the feasibility of the LDV method for nondestructive detection of pear texture, and (iii) to investigate the influence of pear shape on the performance of the texture prediction model.
2. Materials and methods Symbols and abbreviations used in this paper are shown in Table 1.
2.1. Pear samples More than 300 fruit (Pyrus bretschneideri Rehd. cv. Huangguan) were purchased from a local fruit market and immediately transported to the laboratory at Zhejiang University in Hangzhou, China. After weighing, fruit whose mass were greater than 320 g or less than 220 g were removed, and the remaining 160 samples (274.35 ± 21.57 g) were stored in a manual climatic box (PRX-1500A, Haishusaifu Instrument Co., Ltd., Ningbo, China) at a temperature of 20 ◦ C and a relative humidity of 50% for 54 days. Fruit that spoiled during storage were removed, and a total of 135 fruit samples were finally used for the experiment. During storage, the vibration spectra and texture of 7–12 samples were measured every 3 days during the first 18 days and every 6 days thereafter by the following methods. In each test, fruit were placed in the experimental environment for 12 h, then they were numerically coded and their morphological properties were measured. Morphological properties included the mass (m), height (h), and diameter along the equatorial plane (d). Fruit shape was characterized by the shape index (SI) defined as h/d. Table 2 shows the basic morphological properties of the tested pear samples.
Table 1 Symbols and abbreviations. A2 d EI f2 F–D FF FFT h LDV m MF MLR P400 P800 P1200 P1600 r rc rp RMSEC RMSEP SI SMLR Stif xin xout F d
Amplitude at the second resonance frequency Diameter of the sample Elasticity index Second resonance frequency Force–deformation Flesh firmness Fast Fourier transform Height of the sample Laser Doppler vibrometer Mass of the sample Maximum force during penetration Multiple linear regression Phase shift at 400 Hz Phase shift at 800 Hz Phase shift at 1200 Hz Phase shift at 1600 Hz Correlation coefficient Correlation coefficient for the calibration sample set Correlation coefficient for the validation sample set Root mean square error of calibration Root mean square error of prediction Shape index Stepwise multiple linear regression Stiffness Excitation signal for the sample Response signal at the top of the sample Force at the rupture point Penetration distance at the rupture point
2.2. Vibration spectrum measurement The experimental set-up used to measure the vibration spectra of pears was similar to that used by Terasaki et al. (2001) and Abbaszadeh et al. (2013). The measurement system consisted of two parts: the control element and the signal acquisition element. For the control element, the vibrator (ES-05; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) was excited by swept sine wave signals (ranging from 100 to 2000 Hz at a linear sweep rate of 600 Hz/min), which were generated by a PC (Dell Inc., Round Rock, TX, USA) and amplified by a power amplifier (PA-1200; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China). Actual vibration signals of the stage (xin ) were sensed by the accelerometer 1 (DL-24100, Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) and sent back to the vibration controller (Amber; Dongling Vibration Test Instrument Co., Ltd., Suzhou, China) to obtain closedloop control. For signal acquisition, fruit were placed vertically on the vibration stage, and the response signal at the top of each sample (xout ) was measured by a LDV (LV-S01; Sunny Instruments Singapore Pte., Ltd., Singapore); the xin was simultaneously monitored by the accelerometer 2 (LC0159; Lance Technologies Inc., Akron, USA) which was attached to the stage. Both xin and xout were acquired by a signal acquisition module (USB-4431; National Instrument, Austin, USA) and delivered to the PC. The frequency response of fruit consisted of the amplitude–frequency response and phase–frequency response, which were obtained after a fast Fourier transform (FFT) algorithm was applied to the xin and xout data. Representative examples Table 2 Morphological properties of the tested pear samples (n = 135).
Mass (m, g) Heighta (h, mm) Diametera (d, mm) Shape index (SI) a
Average
Maximum
Minimum
Standard deviation
262.25 73.98 78.78 0.94
309.52 81.66 84.17 1.03
203.29 66.40 72.22 0.85
23.55 3.35 2.41 0.04
Average value of three measurements taken at evenly spaced intervals of 120◦ .
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Fig. 1. Representative examples of (a) amplitude–frequency response and (b) phase–frequency response of two pears with different textures. The second resonance frequency (f2 ) was used for determining the elasticity index (EI).
of the frequency responses of two pears with different textures are presented in Fig. 1. After frequency response evaluation, six vibration parameters were extracted: the second resonance frequency (f2 ); the amplitude at f2 (A2 ); and the phase shifts at 400, 800, 1200 and 1600 Hz (P400 , P800 , P1200 and P1600 ). Additionally, the elasticity index (EI) (Cooke, 1972; Taniwaki et al., 2009a,b) was calculated by Eq. (1): EI = f22 m2/3
(1)
where m is mass of the sample.
Correlation analysis was then performed among the vibration parameters, and the multiple linear regression (MLR) method was chosen to fit the experimental data to evaluate the importance of each vibration parameter. In the MLR model, the contribution of each factor for determining the dependent variable can be evaluated by the absolute values of the standardized regression coefficients. The MLR model is shown in Eq. (3). Y = a0 +
7
ai xi
(3)
i=1
2.3. Texture measurement After the vibration spectrum was measured, the fruit texture was measured by the puncture test, which was performed with a texture analyzer (TA-XT2i, Stable Micro System, Inc., England) at four sites at evenly spaced intervals along the equatorial plane. At each site, a piece of peel was removed, and a cylindrical probe with a diameter of 5 mm was inserted into the sample to a penetration depth of 10 mm, at a loading speed of 60 mm/min. A typical puncture F–D curve of a site is shown in Fig. 2. Three texture indices, including the maximum force (MF) during penetration, flesh firmness (FF, average force between 3 mm and 10 mm distance), and stiffness (Stif, the slope of F–D curve before the rupture point), were determined from the F–D curve. The value of Stif was calculated by Eq. (2): Stif =
F d
where Y is the texture index, a0 –a7 are the regression coefficients, and x1 –x7 are f2 , A2 , P400 , P800 , P1200 , P1600 , and EI, respectively. Finally, the seven vibration parameters (f2 , A2 , P400 , P800 , P1200 , P1600 , and EI) and SI were taken as independent variables to build the texture prediction model. Prior to modeling, atypical values were removed by the Chauvenet testing method. All remaining samples were sorted in order of the texture index and then divided into two sample sets: calibration and validation. Samples with the
(2)
where F is the force at rupture point and d is the penetration distance at rupture point. All of these texture indices were calculated automatically by the Exponent 6.0 software (Stable Micro System Inc., England). The average value of each texture index at four sites was calculated and reported as the MF, FF, and Stif value of each sample. 2.4. Statistical analysis Firstly, changes in the texture indices were analyzed, and correlation analysis between the texture indices and the vibration parameters was performed. Stif was chosen for further analysis because of its variation trend and correlations with the vibration parameters.
Fig. 2. A typical puncture force–deformation (F–D) curve for a single site along the equatorial plane. Three texture indices, including the maximum force (MF), flesh firmness (FF, average force between 3 mm and 10 mm distance), and stiffness (Stif, the slope of F–D curve before the rupture point), were determined from the F–D curve.
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Fig. 3. Time–course changes in (a) maximum force (MF), flesh firmness (FF), and (b) stiffness (Stif) determined by the puncture test during storage. The bars represent the standard error.
maximum and minimum texture indices were put into the calibration sample set. Then, three out of four samples were put into the calibration sample set in order, and the remainders were used for validation. Calibration models were established according to two steps. In Step 1, a stepwise multiple linear regression (SMLR) method was used to extract feature parameters and build an initial texture prediction model (Eq. (4)).
where Y is the modified prediction value of the texture index and C0 –C2 are the regression coefficients. The performance of the models was assessed in terms of the correlation coefficients for the calibration and validation sample sets (i.e., rc and rp ) and the root mean square errors of calibration and prediction (i.e., RMSEC and RMSEP).
Y = g1 (x1 , x2 , . . ., xn )
3. Results
(4)
where Y is the prediction value of the texture index and x1 –xn are the extracted feature parameters. In Step 2, SI was introduced to modify the model. The modified model is shown in Eq. (5). Y = C0 g1 (x1 , x2 , . . ., xn ) + C1 SI + C2
(5)
3.1. Changes in texture during storage Fig. 3 shows the time-course changes in MF, FF, and Stif during storage. All three texture indices exhibited a declining trend overall. A similar trend was observed in MF and FF; relatively stable levels were observed for both before day 24, and they then decreased
Table 3 Correlations between the texture indices and the vibration parameters.
Maximum force (MF) Flesh firmness (FF) Stifness (Stif) * ** ***
Second resonance frequency (f2 )
Amplitude at the second resonance frequency (A2 )
Phase shift at 400 Hz (P400 )
Phase shift at 800 Hz (P800 )
Phase shift at 1200 Hz (P1200 )
Phase shift at 1600 Hz (P1600 )
Elasticity index (EI)
−0.004 0.203* 0.738**
0.144 0.075 0.364**
0.095 −0.114 −0.604**
0.135 −0.113 −0.641**
0.177* −0.087 −0.593**
0.184* −0.079 −0.581**
0.042 0.235** 0.756**
P < 0.05. P < 0.01. P < 0.001.
Table 4 Statistical results of the multiple linear regression (MLR) model for determining Stiffness (Stif) of the pears. y
x
Non-standardized coefficients
Standardized coefficients
Significance
Stiffness (Stif, N/mm)
Second resonance frequency (f2 , Hz) Amplitude at the second resonance frequency (A2 , dB) Phase shift at 400 Hz (P400 , -deg) Phase shift at 800 Hz (P800 , -deg) Phase shift at 1200 Hz (P1200 , -deg) Phase shift at 1600 Hz (P1600 , -deg) Elasticity index (EI, Hz2 kg2/3 ) Constant
−0.008 0.038 −0.006 0.000 0.000 0.001 0.000 4.312
−1.1902 0.0557 −0.4313 −0.1895 0.0976 0.3544 1.8111
0.023* 0.401 0.016* 0.514 0.700 0.088 0.000** 0.002**
The superscripted numbers represent the sequence of absolute value of standardized coefficient from the highest to the lowest. * ** ***
P < 0.05. P < 0.01. P < 0.001.
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Table 5 Correlation coefficient matrix of the vibration parameters. Second resonance frequency (f2 ) Second resonance frequency (f2 ) Amplitude at the second resonance frequency (A2 ) Phase shift at 400 Hz (P400 ) Phase shift at 800 Hz (P800 ) Phase shift at 1200 Hz (P1200 ) Phase shift at 1600 Hz (P1600 ) Elasticity index (EI) * ** ***
1 0.358** −0.813** −0.901** −0.886** −0.878** 0.985**
Amplitude at the second resonance frequency (A2 )
Phase shift at 400 Hz (P400 )
Phase shift at 800 Hz (P800 )
Phase shift at 1200 Hz (P1200 )
Phase shift at 1600 Hz (P1600 )
Elasticity index (EI)
1 0.932** 0.863** 0.816** −0.735**
1 0.954** 0.924** −0.847**
1 0.960** −0.841**
1 −0.849**
1
1 −0.115 −0.149 −0.163 −0.206* 0.412**
P < 0.05. P < 0.01. P < 0.001.
gradually. Stif declined more regularly over time throughout the entire storage period, excluding an abnormal point on day 6. MF, FF, and Stif decreased by −0.2%, 7.0% and 33.9%, respectively, in the first 24 days, and by 29.5%, 18.4% and 47.3%, respectively, during the entire storage period. It was clear that Stif was more appropriate to represent the fruit quality because of its regular variation trend and large range of variation.
correlation coefficients with Stif (Table 3). The significant vibration parameters were EI, f2 , and P400 . The correlation coefficient matrix of the vibration parameters is shown in Table 5, in which highly significant correlations were observed among the vibration parameters, excluding that between A2 and the phase shift at selected frequencies. The value of r between EI and f2 was the highest (r = 0.985).
3.2. Relationship between the texture indices and the vibration parameters
3.3. Texture prediction model
Correlations between the texture indices and the vibration parameters are shown in Table 3. All correlation coefficients (r) between MF, FF and the vibration parameters were too low; the highest was only 0.235. Stif was highly correlated with all the vibration parameters (P < 0.01), and the correlation coefficients were much larger than those of MF and FF. Because MF and FF did not correlate well with the vibration parameters and Stif was more appropriate to represent fruit quality during the storage time, Stif was the texture index chosen for further analysis. Statistical results of the MLR model for determining Stif of the pears are presented in Table 4. The sequence of vibration parameters according to their importance, based on the standardized coefficients, was as follows: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . EI and A2 had the highest and lowest contribution, respectively, supporting the finding that they had the maximum and minimum
At first, one sample was removed by the Chauvenet testing method. Then, 101 samples were chosen for the calibration sample set, and 33 samples were selected for the validation sample set. Table 6 and Table 7 show the statistical results of the initial texture prediction model and the modified texture prediction model, respectively. The significance test showed that both models were highly significant (P < 0.01). The three vibration feature parameters extracted from the initial texture prediction model, in order of importance, were EI, P1600 , and P400 . All of these vibration feature parameters were highly significant in the initial texture prediction model. However, SI was not significant in the modified texture prediction model. Table 8 shows the comparison of the performance of the initial and modified models. Higher rc and rp , and lower RMSEC and RMSEP were observed after modification. Clearly, the performance of the model improved after introducing SI. The actual and
Table 6 Statistical results of the initial texture prediction model. y
x
Stiffness (Stif, N/mm)
Phase shift at 400 Hz (P400 , -deg) Phase shift at 1600 Hz (P1600 , -deg) Elasticity index (EI, Hz2 kg2/3 ) Constant
* ** ***
Non-standardized coefficients −0.009 0.002 3.057 × 10−5 1.163 F = 62.731 (P < 0.01)
Standardized coefficients
Significance
−0.302 0.529 0.998
0.005** 0.000** 0.000** 0.188
P < 0.05. P < 0.01. P < 0.001.
Table 7 Statistical results of the modified texture prediction model. y
x
Stif (N/mm)
g1 Shape index (SI) Constant
* ** ***
P < 0.05. P < 0.01. P < 0.001.
Non-standardized coefficients 0.989 2.884 −2.633 F = 96.678 (P < 0.01)
Standardized coefficients
Significance
0.804 0.062
0.000** 0.298 0.308
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Table 8 Comparison of the performance of the initial and modified prediction models. Models
Initial texture prediction model Modified texture prediction model
Calibration
Validation
rc
RMSEC (N/mm)
rp
RMSEP (N/mm)
0.812 0.815
1.048 1.042
0.717 0.732
1.243 1.202
predicted Stif values of the modified model in the calibration and validation sample sets are shown in Fig. 4. 4. Discussion Swept sine wave excitation, which is the most commonly used excitation method in LDV detection, was chosen in our research (Terasaki et al., 2001; Taniwaki et al., 2009a,b; Abbaszadeh et al., 2013). The swept sine wave method is advantageous in terms of its repeatability, and can measure the vibration characteristic more accurately than the impact method because it can concentrate the excitation energy within a small frequency band at a certain time (Taniwaki et al., 2009a; Taniwaki and Sakurai, 2010). As for the pear texture measurement, MF and FF maintained a relatively stable level during the first 24 days and then decreased gradually. However, the fruit appearance changed visibly over time. Stif, by contrast, exhibited a declining trend during the entire storage period, which was consistent with the fruit quality change. Additionally, the variation range of Stif was much larger than those of MF and FF during the storage period. Therefore, it would be easier to distinguish fruit at different storage times by Stif. Consequently, the value of Stif may be a more suitable index than MF and FF for evaluating fruit quality. In addition, sensory evaluations will be needed to validate the relationships between these texture indices and sensory scores because texture is ultimately a subjective sensation (Taniwaki and Sakurai, 2010). The vibration parameters had higher correlation coefficients with Stif than MF or FF (Table 3). Similar results were observed for ‘Dangshan’ pears (Pan and Tu, 2004a) and ‘Fuji’ apples (Pan and Tu, 2004b). A possible cause of this result was that both force and deformation were involved in Stif. Therefore, Stif may reflect the mechanical properties of fruit more accurately, better reflecting the fruit texture changes. The vibration parameters were all strongly correlated with Stif (Table 3); however, not all the regression coefficients were significant in the MLR model, according to the significance test
(Table 4). The non-significant regression coefficients of some vibration parameters in the MLR model and some highly significant correlations among the vibration parameters indicated that multicollinearity existed in this model. Therefore, the SMLR method was used to eliminate the unnecessary variables for a prediction model with high robustness. Three vibration parameters with high contribution were extracted: EI, P1600 , and P400 . The r value (0.812) observed between the actual Stif and the predicted Stif obtained by the SMLR model (Table 8) was higher than that between Stif and the vibration parameters (the highest was 0.756, as shown in Table 3), suggesting that the combination of multiple vibration parameters provided more information about the texture than a single vibration parameter. Vibration characteristics of fruit are affected by their texture, mass, geometric shape, size, among other properties (Duprat et al., 1997). Thus, fruit shape was taken into consideration in our model, and a shape index was calculated to describe the geometric shape of the pears. rc and rp increased by 0.4% and 2.1%, respectively, while RMSEC and RMSEP decreased by 0.6% and 3.3%, respectively (Table 8). It is clear that the performance of the model was improved. However, the improvement of the model performance was limited, and SI was not significant in the modified texture prediction model. There may be two reasons for this result: (i) the method used to describe pear shape was crude, and the pear shape could not be described well through the h/d ratio alone; (ii) the difference in SI among the pear samples in this study was relatively small. Therefore, a more precise description method for fruit shape and samples with a wide range of shapes will be needed in future research. A significant influence of shape on vibration properties was also found in apples, pears, potatoes and some other agro-products (Chen and Debaerdemaeker, 1993; Jancsok et al., 2001; Blahovec et al., 2007). The results of the significance tests of both the initial and modified prediction models (Tables 6 and 7) showed that the models were feasible for the evaluation of pear texture by the LDV method.
Fig. 4. Correlations between the predicted stiffness (Stif) determined by the modified model and the actual stiffness in the (a) calibration sample set and (b) validation sample set. The solid line is the regression line.
W. Zhang et al. / Postharvest Biology and Technology 96 (2014) 99–105
5. Conclusion In this paper, three texture indices (MF, FF and Stif) and seven vibration parameters (f2 , A2 , P400 , P800 , P1200 , P1600 , and EI) of the pears were selected. Stif was found to be a more suitable index for evaluating fruit quality, and correlate well with the vibration parameters than MF and FF. The sequence of vibration parameters for predicting Stif, according to the standardized coefficients of the MLR model, was as follows: EI, f2 , P400 , P1600 , P800 , P1200 , and A2 . Three vibration feature parameters, EI, P1600 , and P400 , were extracted by the SMLR method, and an initial texture prediction model was built. The results showed that multiple vibration parameters provided more information for texture prediction than a single vibration parameter. After modification by the introduction of SI, the performance of the prediction model was improved. The results of the significance tests of both the initial and modified prediction models proved that the evaluation of pear texture by a combination of the LDV method and the proposed modeling approach was feasible. Acknowledgements The authors gratefully acknowledge the support of this program by National High Technology Research and Development Program of China (2012AA10A504). Any opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of Zhejiang University. Trade and manufacturer’s names are necessary to report factually on available data. References Abbaszadeh, R., Rajabipour, A., Mahjoob, M., Delshad, M., Ahmadi, H., 2013. Evaluation of watermelons texture using their vibration responses. Biosyst. Eng. 115, 102–105. 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, 101–112. Benedito, J., Carcel, J.A., Sanjuan, N., Mulet, A., 2000. Use of ultrasound to assess Cheddar cheese characteristics. Ultrasonics 38, 727–730. Blahovec, J., Kuroki, S., Sakurai, N., 2007. Cooking kinetics of potato tubers determined by vibration techniques. Food Res. Int. 40, 576–584. Camps, C., Guillermin, P., Mauget, J.C., Bertrand, D., 2005. Data analysis of penetrometric force/displacement curves for the characterization of whole apple fruits. J. Texture Stud. 36, 387–401. Chen, H., Debaerdemaeker, J., 1993. Effect of apple shape on acoustic measurements of firmness. J. Agric. Eng. Res. 56, 253–266.
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