Detection of Eggshell Cracks by Means of Acoustic Frequency Analysis

Copyright © IFAC Mathematical and Control Applications in Agriculture and Horticulture, Hannover, Germany, 1997

DETECTION OF EGGSHELL CRACKS BY MEANS OF ACOUSTIC FREQUENCY ANALYSIS

P.

Coucke, B. De Ketelaere, and J. De Baerdemaeker

Department ofAgro-engineering alld -economics Kaiholieke Uni versiieit Leuven Kardinaal Mercierlaan 92, 3001 Heverlee

Abstract: The visual inspection by persons of the eggshell integrity is an important bottleneck in the automation of egg grading machines. The inspection rate is slow and manual inspection is subjective. This research forms a basis for a new crack detection system. Based on the results of experimental modal tests on chicken eggs a novel eggshell crack detector is designed. An egg is subjected to a light impact excitation. The acoustically measured frequency response spectrum is used as input in a classification algorithm. Improving accuracy can be achieved using multiple measurements per egg.

Keywords: Quality control, Vibration Measurement, Mode analysis, Bio control, Fourier analysis

visible and thin, translucent shell areas in an intact eggshell are detected as cracks.

1. INTRODUCTION Eggshell crack detection is an important aspect in the quality control process of consumption eggs. The intact eggshell forms a physical barrier for the transmission of harmful micro-organisms (Bain, 1990). Traditionally eggs are inspected visually by candlers prior to packing. A bright light is sent through the eggs in order to assess external and internal egg quality visually. However, this human quality inspection is too slow. Technically, modern, electronic grading machines can handle more than 36 eggs per second, but candling is the bottleneck. Furthermore, the manual inspection is subjective (Overfield, 1988). Fine fresh cracks are not visible and candlers remove eggs with no faults. Therefore research in automatic, high accuracy inspection methods is necessary.

The second group of techniques are based on the measurement of the elasticity of the eggshell on a local shell area. An intact eggshell area will react by an elastic rebound while a cracked shell area will damp the vibration heavily. This technique is currently used in commercial crack detectors (Diamond Systems 1992 ; MOBA b.v., 1996). A main disadvantage of this measurement technique is the large number (12 to 36) of measurements per egg required for acceptable detection rates. In this research the feasibility of a new inspection method is tested. The technique is based on the analysis of the dynamic, mechanical behaviour of the whole egg during vibration. The frequency response signal forms a fingerprint of the mechanical integrity of the total structure. The technique of resonant frequency analysis is commonly used in the quality control procedure of geometrically simple (bar, cylinder) finished parts made in metals, alloys, ceramics and composites (Lemmens, 1990). For these objects the selection of optimal places for

Recent research is focused on optical and mechanical detection principles. Optical techniques are based on machine vision (Worley and Goodrum, 1996 ; Goodrum and Elster, 1992) and laser scanning systems (Bol, 1984). Fresh hairline cracks are not

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signal. The resolution of the measurement is 32 Hz. An average frequency response function (FRF) is calculated from 5 measurements at each point. This complex FRF function is a ratio of the output signal divided by the input signal. It describes the dynamic, mechanical system characteristics for each combination of excitation and response position.

excitation and response measurement and the interpretation of the response signal is straightforward and based on the mathematical relationships that describe the mode shapes and corresponding resonant frequencies. However the determination of these dynamic properties for objects with more complex shape and non homogeneous material properties as chicken eggs, is not obvious. Therefore an experimental set of modal tests are performed in order to establish the dynamic mechanical behaviour of an intact egg. The next step in the research is to interprete the acoustically measured frequency response spectra. Based on these results a novel concept for a crack detector and suitable sorting algorithm are built and validated.

A modal model is built using Compter Aided Dynamic Analysis software (CADA-PC, LMS International Belgium). A sum-FRF can be built (Figure 2) based on the FRF calculations in the 42 points.

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2. EXPERIMENTAL MODAL TESTS In order to better understand the dynamic mechanical behaviour of an egg, an experimental modal test is performed. In this test 42 measurement places are marked on the eggshell. of an intact egg. These points are equally distributed over the eggshell surface (top and bottom of the egg and 5 rings of 8 measurement points). Figure 1 shows a representation of the modeled egg structure.

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Fig. 2 : Sum FRF of 42 measurements Parameter estimation techniques are used to identify a modal model and to estimate the values for the resonant frequencies, damping factors and mode shapes. The identification technique is based on a least squares approximation in the frequency domain. Validation of the modal model is done by graphic visualisation of the modes in an animated display. Figure 3 a and b and figure4 a and b are respectively two front and' top views of the vibrating egg at its first flexural spherical mode. The bold line is the undeformed egg shape and the thin line is the deformed egg shape.

Fig. 1 Graphical representation of the egg model used in the modal analysis tests.

The mode shape of the first flexural mode shows an elliptic deformation. The two anti-nodal lines are running through the positions (0°,180) and (90 0 270°) on the equator. Their magnitude is maximum at the equator zone and decreases towards the small and blunt end of the egg. The anti-nodal points located at 0° and 180° on the equator move in phase A similar observation exists for the points at 90° and 270 0 on the equator of the second anti-nodal line. The two nodal lines are going from pole to pole through positions (45°_25°) and (135°-315°) on the equator. This mode is also called the oblate-prolate mode.

The egg is suspended with an elastic string. The string is glued to the eggshell at the top (sharp pole). A small impact hammer (pCB type 086C80) is used to excite the object in all 42 measurement points. The sensitivity of the force cell is 10 mVIN. The response is captured using a miniature accelerometer (Dytran . 3225C type) of 0.5 grams. This accelerometer is attached to the shell with petrowax at position 3 1. This measurement point is on the equator ring, that is where the minor axis of the egg is maximum. Excitation and measurement detection are orthogonal to the shell surface. The data aquisition is controlled using a Dynamic Signal Analyser (HP 35665). The input signal is filtered by a force window. An exponentially decay window filters the response

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Fig. 3a : Momentary front view of the mode shape of the first flexural spherical mode (RF : 4074 Hz ; damping ratio: 2.58 %).

Fig. 4 b : Momentary top view of the mode shape of the first flexuraI spherical mode (RF : 4074 Hz ; damping ratio: 2.58 %).

Figures 5 a and b and Figures 6 a and b are representations of respectively the front and top view of the mode shape of the second flexural spherical mode. A triangular shape can be recognised. Modes at higher frequency have geometrically more complex mode shapes. Three anti-nodal lines can be identified going through locations (0°_180°) for anti-nodal line 1, (60°-240°) for anti-nodal line 2 and (120°-300°) for anti-nodal line 3. The anti-nodal points on the equator of each anti-nodal line move in anti-phase. The nodal points on the equator of each nodal line are situated at positions (40°-220°) for nodal line 1, (90°-270°) for nodal line 2 and (140°-320°) for nodal line 3. However, more measurements points are required to determine these locations more accuratiy.

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Fig. 3b : Momentary front view of the mode shape of the first flexural spherical mode (RF : 4074Hz ; damping ratio : 2.58 %).

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Fig. 5 a : Momentary front view of the mode shape of the second flexural mode (RF : 4670 Hz ; damping ratio : 2.33 %).

Fig. 4a : Momentary top view of the mode shape of the first flexural spherical mode (RF : 4074Hz ; damping ratio: 2.58 %).

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to detennine the correlation between succesive measurements on the same egg. Z I

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3.1. Excitation and response measurement

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The small impact hammer used in the modal tests is built into an electromagnetic excitation device (Figure 7). The activation of the magnet is contolled by an optical sensor that detects the presence of an egg on the conveyor. The ideal excitation for impact tests is a Dirac impulse. In this way a constant energy distribution is achieved in the frequency domain. Practically, . the energy of the impact is mainly concentrated is two or more frequency ranges designated as lobes. In this practical set-up the first lobe corresponds to the frequency value up to 65006800 Hz. A sharp decrease in magnitude of this lobe is observed towards this first minimum. The resonant frequencies of the first (dominant) and second spherical mode of normal intact chicken eggs are situated in this frequency band.

Fig. 5 b : Momentary front view of the mode shape of the second tlexural mode (RF : 4670 Hz ; damping ratio : 2.33 %).

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Optimal places for excitation and response measurements for both the first and second tlexural spherical modes are at 0° and 180° on the equator. These locations correspond with anti-nodal lines of both modes. In order to protect the impact and response sensors from leaking eggs the excitation and response measurement place are selected at position 0°.

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Fig. 6 a : Momentary top view of the mode shape of the second tlexural mode (RF : 4670 Hz ; damping ratio: 2.33 %).

A small condenser microphone (type ECM 2005, Monacor) is used as response sensor. Each egg is measured six times, every 60° around the equator (points 1-6 on Figure 7).

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Fig. 6 b : Momentary top view of the mode shape of the second tlexural mode (RF : 4670 Hz ; damping ratio : 2.33 %). e~

3. PROTOTYPE DESIGN

conveyor with diabolic shaped rollcn

Fig. 7 : Practical test setup for in-line measurements

Based on the results of these experimental tests a procedure for crack detection is set up. The method consist of an excitation step, in which the test object is mechanically impacted, a detection step during which the vibration is captured and an analysis step,

3.2 Egg support The egg is supported in the area of the location of the nodal lines of the first and second tlexural spherical mode. Rubber diabolo shaped rollers are

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used for egg support. In this way the free vibration of the egg is guaranteed.

the Pearson correlation coefficient between two vectors of data measured on the same egg.

3.3. Signal analysis

4. RESULTS AND DISCUSSION

The input signal generated by the automatic impactor can be very well repeated on an individual egg. Hence; there is no need to calculate FRF functions and only the time signal of the response is measured at a sample frequency of 30 kHz. A Fast Fourier Transfonnation converts this signal to a power spectrum in the frequency range 500 Hz-13300 Hz.. The frequency resolution is 64 Hz. No further preprocessing is done on this signal.

The evaluation of the technical performances of the crack detector is done on a sample of 400 intact eggs (class 1), 400 eggs with hairline gracks (class 2) and 170 open breakage eggs (class3). As each egg is tapped six times around its equator, an evaluation of several combinations of correlation calculations is possible. Pearson correlation coefficients between two measurements on one egg are calculated and the detection percentages are calculated for different treshold values and excitation/response combinations. Two classification algorithms are tested. In a first algorithm (Table 1) the detection percentages are calculated for each class. The correlation calculation is based on two measurements, opposite to each other, per egg. The three possible combinations are : 1-4,2-5 and 3-6. In Table 2 three measurements are used per egg. The measurement places are 1200 from each other along the equator. In this case three possible combinations for correlation calculation are used. The treshold values must be satisfied in every combination in order to accept the egg as intact.

3.4. Co"eiation analysis Due to the axial symmetry of an intact egg along its major axis, the responses measured at several places around the equator arevery similar (Figure 8).

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Table 1 Detection percentages of two measurements per egg for several threshold values of Pearson correlation coefficients

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Fig. 8: Powerspectra of six measurements on a class 1 egg

2 measurements

class

cor > 0.7

cor > 0.75

cor > 0.80

cor > 0.85

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99.7 14.5 3.53 99.7 13 ,6 3.5 99 12 .4 5.3

99.7 11.7 2.35 99.7 11.9 1.18 98.8 10.1 4.12

99.3 10.3 \.20 99.3 8.90 0.59 98.6 8.20 2.94

98,6 7.5 1.20 98.8 7.96 0.00 97.6 5,85 1.18

per egg

Cracked eggs however have lost their symmetry and will respond differently depending of the relative position of the crack towards the place of exitation (Figure 9).

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99.7 7.73 1.18 99.5 6.79 1.75

99.2 6.32 1.18 98.8 5.62 ]]8

99.2 4.69 1.18 98.6 4.92 0.59

98.3 4.45 0.59 98,3 3.75 0.59

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Fig. 9 : Power spectra of six measurements on a class 2 egg This phenonomen forms the basis of a simple classification algorithm based on the calculation of

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The evaluation of the new detection technique is based on a comparaison of the technical performances for each quality class between several crack detection techniques. Overfield (1987) reports that in traditional candling 2% to 3 % of the intact eggs are downgraded. Commercially available automatic crack detectors based on local stiffuess evaluation on 24 places per egg achieve 99.7 % accuracy for the detection of intact eggs (personal communication, 1997).

The variable treshold value for the correlation allows a fine tuning for the desired detection accuracy according to the legal requirements and the consumer needs.

ACKNOWLEDGEMENT The authors gratefully acknowlegde the Flemish Institutre for Scientific and Technological Research in the Industry for their financial support by doctoral grant nO 942019.

The crack detector proposed here has a false reject percentage between 2.4 % (cor >0.85 and 2 measurements) and 0.3 % (cor >0.7 and 2 measurements per egg) depending on the threshold value. Correlation calculations based on three measurements per egg result in a false reject of 0.3 % to 1.7 %.

REFERENCES Bain, M . (1990). Eggshell Strength A mechanical/ultrastructural evaluation Ph.D. Thesis Faculty of Veterinary Medicine, University of Glasgow.

The detection percentages for class 2 eggs ranges from 85 % (cor >0.7; 2 measurements per egg) to 94 % (cor> 0.85; 2 measurements per egg) for this new crack detection technique. The extension to three measurements allows an average improvement of 50% in the detection rates of class 2 eggs but increases slightly the false reject percentages. Worley (1995) reports a 90 % accuracy for crack detection based on machine vision. Commercially available detection techniques based on local stiffuess measurement achieve a 85 % to 90 % accuracy (personal communication, 1997).

Bol, 1. (1984). Laser scanning system for the automated inspection of eggs for haircracks. In : Quality of Eggs Proceedings of the First EuropeanSymposium. (G. Beuving, C.W. Scheele and P.C.M. Simons (Ed.» 84-93. Spelderholt Institute for Poultry Research,Wageningen. Diamond Systems (1992) Leaflet on Electronic crack detection. LMS CADA-PC Manual. (1992) Leuven Measurement Systems Int., Interleuvenlaan 68,Belgium.

Class 3 eggs can be detected with high accuracy. Three measurements per egg allow a higher accuracy than two measurements per egg for this class.

Goodrurn, J. W. and R. T. Elster (1992) Machine vision for crack detection in rotating eggs. Transactions of the American Society of Agricultural Engineering VoI35(4), 1323-1328.

5. CONCLUSIONS The application of acoustic resonant frequency analysis for mechanical integrity inspection is a technique that can also be used for biological products, as chicken eggs. However they have a large variability in material and geometrical properties. The interpretation of the frequency response spectrum is not straightforward. Based on experimental modal tests the dynamic mechanical behaviour is analysed. Several flexural spherical modes are detected. Because of the axial symmetry of the intact egg the dynamic mechanical response behaviour is very similar when measured on different places on the equator. This property offers an interesting tool for differentation between intact and cracked eggs based on a correlation calculation between two or three consequtive measurements. This new technique achieves the same detection rates as commercially available crack detectors but with only two to three measuremetns per egg.

Lemmens, J.W. (1990) Impulse eXCitatIOn : a technique for dynamic modulus measurement. In : Dynamic Elastic Modulus Measurements in Materials. (Alan Woljenden (ed)). American Society for Testing and Materials. MOBA (1996) Brochure of the description of Omnia 250/330 electronic grading machine and optional apparatus. Overfield, N.D. (1987). Egg grading as form of quality control. Poultry Misset AprillMay 10-14. Worley, J.w. and J.W Goodrum (1996) Strobe versus incandescent lighting for egg crack detection using machine vision. Applied Engineering in Agriculture Vol. 11(4), 549-554.

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