Internal Defect Detection of Pears by Impulse Response Method

Pál T. Jancsók, Katholieke Universiteit Leuven, Laboratorium for Agro- Machinery and Processing Kasteelpark Arenberg 30, B-3001 Leuven Tel: +3216321470 Fax: +3216321994 email:[email protected] Internal Defect Detection of Pears by Impulse Response Method Pál T. Jancsók1, Jeroen Lammertyn2, Bart M. Nicolaï2, Josse De Baerdemaeker1. 1

Laboratorium for Agro- Machinery and Processing, Katholieke Universiteit Leuven

Kasteelpark Arenberg 30, B-3001 Leuven, Belgium. 2

Laboratory/FlandersCentre of Postharvest Technology, Katholieke Universiteit Leuven,

Willem de Croylaan 42, B-3001 Leuven, Belgium Email: [email protected] Abstract In Europe, pears are the most important fruit besides apples. The impulse response method is often used to measure firmness of fruits. In this method the fruit is excited using an impact hammer and the response signal is captured using a microphone and analysed. The non-optimal picking dates and storage conditions can cause development of cavities inside the Conference pear. The disorder (core breakdown) starts with softening and discoloration of the tissue and later cavities can develop. The aim of this work is to examine the possibility to detect such internal defects by the impulse response method. Pears with cavities were produced by storing them in a disorder inducing environment. Then X-ray CT scans were taken and evaluated to measure the position and the size of the holes. Based on the CT scans and on calibrated images of the pears taken from different directions finite element (FE) meshes were created. The resonance frequencies were calculated by FE modal analysis with and without the hole. Vibration measurements were also carried out on the hollow pears. The pears were excited by a small hammer at 3 different positions and from several directions. In case of an out of symmetry cavity the consecutive measurements showed different pattern. The FE model is validated and the results of the simulations are compared.

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Introduction In Europe, pears (Pyrus communis) are the most important fruit besides apples. Among the different varieties the most widely produced one is the ‘Conference’. The quality of pears is determined by several internal and external factors. External factors like shape and colour, can be measured easily, but internal attributes such as firmness, the absence or presence of internal defects are more difficult to assess. The impulse response method is often used to measure firmness of spherical fruits and vegetables (Abbott et al., 1997; De Belie et al. 2000) In this method the fruit is excited using an impact hammer and the response signal is captured using a microphone. This vibration response is subsequently analysed and related to the firmness of the fruit. Recently this method is extended to measure properties of non-spherical fruits (Jancsok et al. 2001). The non-optimal picking dates and storage conditions (cooling program, CO2 concentration, etc) can cause development of cavities inside a Conference pear. The disorder (core breakdown) starts with softening and discoloration of the tissue and later cavities develop (Lammertyn et al. 2000). In Belgium and in the Netherlands those hollow pears can cause large economic losses. This quality problem cannot be detected by the consumer from outside. The aim of this work is to examine the possibility to detect such internal defects by the impulse response method. Materials and methods Pears In order to be able to investigate the defected fruits, Conference pears (Pyrus communis cv Conference) with the cavities were produced. The pears were harvested and stored in a special, disorder inducing controlled atmosphere at 1 °C for 10 months. The storing conditions were determined according to Lammertyn (2000). The presence of the cavities was checked by means of X-ray imaging. 13 different pears with different internal cavities were selected for the measurements. Vibration measurements For the acoustic measurements the pears were put into a holder where a rubber membrane held the fruit. This setup allows free vibration. By exciting the pear at 2

different positions different vibration modes are active. In this research 3 different vibration modes were used, namely the compression, the bending and the oblate-prolate modes. In compression mode the whole body of the pear is vibrating in longitudinal direction. It becomes shorter and longer as the pear is compressed and elongated. In bending mode, the top part of the pear is deformed and bended. In oblate -prolate mode the bottom part of the pear becomes flatter in one direction and wider in the perpendicular direction. The pears were excited by a small plastic hammer several times in 3 different positions and from 5 different directions: at the end of the conical part of the pears parallel to the axis of the fruits, at the side of the conical part perpendicular to the axis of the fruit around the pear and at the side of the bottom part of the pears perpendicular to the axis around the fruit. The vibration pattern was captured by the microphone placed at the other side of the fruit. The signal of the microphone is digitised by the sound card of the computer. From the time domain signal the frequency spectrum was calculated by Fourier Transformation. The amplitude of the frequency signal is normalised to have the maximum amplitude equal to 1. Finite element modelling To simulate the vibration behaviour of such defected pears, finite element models were developed. The finite element meshes are based on shape measurements of real hollow fruits. First the X-ray CT scans of hollow pears were taken by a microfocus Computer Tomography AEA Tomahowk system at the Dept. Metallurgy and Materials Engineering, Katholieke Universiteit Leuven. The contour information of the cavities were extracted from the CT scans and three dimensional geometrical models were constructed. During the processing first periodic (closed) spline curves are fitted to the contour lines and then the splines are combined together to form a surface by a skinning algorithm (Jeong et al.,1999). If the cavity had two or more branches they were handled separately. Due to the limitations of the X ray imaging system it was not possible to take a full image of the outer contour of the pear. The outer shape of the pears therefore was measured by a conventional image processing system. The image processing system takes several calibrated images of the standing pear from different directions. The contour information of the pears were extracted and a 3D geometrical model was created. (Jancsok et al 1998) The internal shape information (the cavity) was combined with the outer pear

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shape and a finite element mesh was created. (Fig. 1). With the ANSYS commercial finite element program the resonance frequencies were calculated by finite element modal analysis. The following material properties were used: dynamic E modulus: 6MPa; density: 990 kgm-3; Poisson ratio: 0.3 (Jancsok et al 2001). The finite element meshes then were modified and the cavities were removed from the models. Because the mass influences the resonance frequencies in a large extent, the resonance frequencies calculated with different mass were made comparable by applying the following equation: f r =  m   mr 

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⋅f

where f r , mr are the reference frequency and

mass. Results and Discussions X-ray CT From the examination of the X-ray CT images different kinds of damage can be seen. There are pears where there is one big cavity in the middle of the pear out of the symmetry axis. There are pears where several small cavities are developed spread out in the pear and there are pears where there is a big cavity in the middle of the pear around the clock house. Finite element modelling First the finite element (FE) model is validated. The resonance frequencies of the FE model corresponds well with the ones from measurements. (Table 1.) There are modes where the finite element calculation gives two results. This means that the resonant frequency is calculated for two different axis. Such modes are the bending and the oblate-prolate modes. Using the validated finite element model the resonance frequencies of the models with and without the cavities. The aim was to examine the effect of the cavity on the resonant frequencies. The mode shapes were identified by examining the deformations. The results for the model with the biggest cavity are summarised in Table 2. The three main modes are indicated by their name. The difference between the resonance frequencies are small. This means that it is almost impossible to distinguish between the hollow and not hollow pears just based on the resonant frequencies. However the difference between frequencies of the hollow and not hollow pears are not the same for all the 4

modes. Even the difference between the coupled modes are not the same. This possibly allows us to detect the cavities. Further the complex modes (indicated by their Mode Nr) shows high difference. Those modes can not be measured accurately, but surely responsible for the form of the vibration spectrum. Vibration measurements In the vibration measurements the pattern of consecutive impact at different sides of the pear are compared. In case of a symmetric pear the patterns of the spectrum of the impact from different directions should be the same. If there is a hole inside the fruit which breaks the symmetry the patterns will be different. In the left side of figure 2 the vibration patterns of a otherwise symmetric pear can be seen. Inside there is a hole which is long and out of symmetry. If the cavity is exactly in the centrum then it is hard to detect (Fig. 2b). The cavity in the bottom part of the pear can cause that the consecutive impacts at different positions are not the same in the oblate prolate mode. (Fig. 2c) Conclusions Based on pears with core breakdown defect, finite element meshes were made by Xray CT and image processing methods. The finite element models were validated by acoustic impulse measurements. FE simulation were performed to calculate the effect of the cavities. It was found that even a bigger hole influences the resonant frequencies in a small extent, but differently in different mode shapes. From the vibration measurements it was found that it may be possible to detect cavities if they modifiy the symmetry properties of the pear. In this case the consecutive impacts on the different sides of the pear result in different spectra. Literature Cited Abbott AJ, Lu R, Upchurch LB, Stroshine LR (1997). Technologies for non-destructive quality evaluation of fruits and vegetables. Hortic. Rev. 20: 1-120. Jancsók P, Nicolaï B, Coucke P, De Baerdemaeker J, (1997) 3D Finite Element Model generation of fruits based on image processing. In: Munack A, Tantau H, Eds, Mathematical and Control Application in Agriculture and Horticulture. Sept. 28 - Oct. 2 1997, Hannover, Germany, pp 131-135. Jeong J, Kim K, Park H, Cho H, Jung M (1999) B-spline surface approximation to crosssections using distance maps. Int J Adv Manuf Technol 15: 876-855.

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De Belie N, Schotte S, Coucke P, De Baerdemaeker J, (2000) Development of an automated monitoring device to quantify changes in firmness of apples during storage. Postharvest Biol Technol 18: 1-8. Lammertyn J, Aerts M, Verlinden BE, Schotsmans W, Nicolaï BM (2000). Logistic regression analysis of factors influencing core breakdown in ‘Conference’ pears. Postharvest Biol and Tec 20: 25-37. Jancsók PT, Clijmans L, Nicolai BM, De Baerdemaeker J (2001) Investigation of the effect of shape on the acoustic response of conference pears by finite element modelling. Postharvest Biol and Tec 23(1):1-12 (in print) Figure captions and legends Figure 1. Finite element mesh of a hollow pear. Figure 2. Typical vibration spectra of 3 hollow pears with asymmetrical long hole (a), symmetric holes in the middle (b) and asymmetric holes in the lower part (c). Tables Table 1. Validation of the finite element model. The calculated and the measured resonance frequencies. Name

Bending Min

Max

Measured [Hz]

210

226

Calculated [Hz]

209,6

222,8

Compression

Oblate Prolate

Min

Min

Max

359

382

369,9

Max

585

617

581,7

598,9

Table 2. Calculated resonance frequencies [Hz] with and without the cavity. Mode

Bend. Bend No3

Com. No5

No6

No7

No8

No9

No10 O-P

O-P

With

220,7 230,8 320,5 389,5 419,8 428,1 531,6 592,5 612,3 637,5 651,0 652,6

Without 223,8 231,9 325,1 398,8 430,0 440,4 536,9 594,2 614,0 646,6 663,2 667,3 Diff %

1,4

0,4

1,4

2,3

2,4

2,8

0,9

0,2

0,2

1,4

1,8

2,2

Bend=Bending mode;Com=Compression mode;O-P= Oblate Prolate mode.

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Figures

Figure 1. Finite element mesh of a hollow pear. Pear No23 vibration pattern 1

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Pear No36 vibration pattern 1

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(c) Figure 2. Typical vibration spectra of 3 hollow pears with asymmetrical long hole (a), symmetric holes in the middle (b) and asymmetric holes in the lower part (c) 7