Experimental Modal Analysis of fruit: A starting point of objectivelycharacterizing the degree of ripeness.

M. Guettler, M. Gatt, and S. MarburgInstitute of Vibroacoustics of Vehicles and Machines

Technische Universität München, Germany

ABSTRACTIn the food industry, objectively characterizing the degree of ripeness of fruit and vegetables is often crucial tomaintain quality standards. Buying these products at a typical food market, the customer has to trust his ownsenses such as smell, touch or visual impression in order to determine the right degree of ripeness. Occasion-ally, one can find very experienced customers who use the sound a certain fruit creates when knocking againstit. This "hearing of fruits’ sound" gives rise to develop new methods for objectively determining the degreeof ripeness. Many interesting facts and relations can be recognized. First, it is possible to excite a structuresuch as a fruit. Second, the excitation is strong enough to create a structural response and third, the structuralresponse is effective enough to create an audible sound to the human ear. In this paper, two examples of fruit,a canary melon and an apple, are excited with a shaker and the structural response is measured utilizing a2D-Laser-Scanning-Vibrometer. The subsequent experimental modal analysis reveals natural eigenfrequen-cies and mode shapes of the test samples. With this information novel objective criteria can be developed toimprove the ability to reliably characterize the degree of ripeness.

Keywords: Experimental Modal Analysis, Fruit, Damage detectionI-INCE Classification of Subjects Number: 21.2.1

1. INTRODUCTION

In recent years, due to a tremendous rise in welfare diseases such as adiposity and diabetes which are asso-ciated to an unhealthy life style of the modern society, the desire for proper and more healthy food as part ofa balanced diet has reached a new level of awareness [1]. The global trade allows us to choose from variousarticles of food every day while at the same time the commercial industry communicates a standard of highquality products. Therefore, a sufficient product quality management is desirable to ensure that customersare not faced with the question whether the product is of high quality or not. A particular challenge in thiscontext is the quality assurance of fruit. Often long commercial routs between cultivation areas and the finalcustomer lead to a reduced quality due to natural aging. Taking bananas as an example, the supplier is facingthe compromise between picking the fruit in an early stage of ripeness and let the fruit ripen during the travelwith a limited taste quality or picking the fruit when full ripeness is achieved and the possibility that the fruitcontinues aging to a stage where it is not possible to sell it as a high quality product anymore. Often, it isdifficult to conclude the inner ripeness just by visual observation without oping or damaging the fruit itself.Therefore, an intense demand exists for non-destructive testing together with the evaluation of objective cri-teria in the field of quality management of fruit and similar food products. Stache et al.[2] utilized modaldate as a basis for a non-destructive damage identification algorithm in order to locate structural weak spotsin form of predefined cracks in slender structures.In this work, methods of Experimental-Modal-Analysis[3, 4] for solid structures are applied to the dynamicbehavior of fruit. It is possible to identify the modal properties of the test samples and possibly use thisdata as a basis for characterizing the quality of the product. The excitation of the fruit is realized with ashaker applying a periodic force input to the sample, namely a canary melon and an apple of Ambrosia kindoff-the-shelf is used. The structural vibration forced by the excitation is measured with a Scanning-Laser-Doppler-Vibrometer. A subsequent modal analysis reveals the characteristic dynamic behavior in terms ofmode shapes and associated eigenfrequencies.

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2. EXPERIMENTS

The experiments where conducted at the facilities of the Universität der Bundeswehr München. Since theconfiguration is similar for the setup of both test samples the following elaboration is restricted to the setupof the canary melon.Figure 1 shows the general setup where the test sample is placed on acoustic foam, cf. Figure 1(a). Theexcitation is realized utilizing a shaker together with a force transducer (B&K Typ 8200) and a rubber tipof an impulse hammer. Beeswax is used to attach the force transducer to the sample, cf. Figure 1(b). AScanning-Laser-Doppler-Vibrometer (LDV; PSV-400; Polytec) measures the structural vibration in terms ofsurface velocities in the direction of the incident laser beam consecutively at different measuring points. Amirror configuration ensures the optical access to all significant sides of the test sample. The red dot in Figure1(a) visualizes the laser beam generated by the LDV.

(a) Mirror configuration (b) Force transducer

Figure 1 – Experimental setup: canary melon

3. RESULTS

From the measurements of the surface velocity and the force put into the structure, Frequency-Response-Functions (FRF) are calculated and further handled to do an Experimental-Modal-Analysis (EMA) usingME’scope as the post processing software. Furthermore, the number of FRFs are squared averaged in orderto obtain a representative FRF for the whole structure. Figure 2 displays the averaged FRF of the canary

Figure 2 – Averaged FRF-spectrum of canary melon test

melon test in a frequency range up to fmax = 500Hz. The EMA allows to visualize the typical mode shapeswith the associate eigenfrequencies. Despite measurements where realized up to a frequency of ftot = 3kHz,data only up to fmax = 500Hz was useful. The authors can find two explanations. First, the shaker is notcapable of exciting the structure at higher frequencies and second, the material damping of this kind of fruitis rising with frequency so no structural vibration can be noticed for higher frequencies. Since the measureddata over fmax remained under the noise level of the LDV, this data is discarded.

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(a) Mode1: f1 = 175Hz (b) Mode3: f3 = 235Hz

Figure 3 – Mode shapes of canary melon

Exemplarily Figure 3 presents such an animation of the first and third mode of the canary melon1. Thesemodes are identified at f1 = 175Hz and f3 = 235Hz. In all animations the y-axis connects top and bottomof the test samples.If one simply knocks against the melon with a finger a typical sound can be noticed which mainly correspondsto the frequency of the first mode. In analogy to common structural dynamics of a sphere and simplifiedsources, the first structural mode corresponds to a quadrupol type of deformation. Investigating the structural

Figure 4 – Averaged FRF-spectrum of apple test

dynamics of the apple, structural vibration in higher frequencies compared to the results of the canary meloncan be noticed, cf. Figure 4. Below f = 500Hz no structural modes can be identified. Above f = 2kHz

the data drops below the noise lever of the LDV and is discarded. From the list of modes which can be clearlyidentified, i.e. a Modal-Phase-Correlation number higher than 0, 85, Figure 5 shows the animations of thetwo modes associated to the first and third eigenfrequencies at f = 733Hz and f = 1024Hz.These kind of results and that the presented structural vibration can actually be measured is rarely found inthe literature but to some extent discussed in [5–7].

1For animating the Adobe Flash Player is necessary.

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(a) Mode1: f = 733Hz (b) Mode3: f = 1024Hz

Figure 5 – Mode shapes of apple

4. SUMMARY AND CONCLUSION

The purpose of this analysis was to show that the EMA is a powerful tool for finding objective criteria inthe field of quality management of fruit and similar food products. An important advantage of the suggestedmethod is the non-destructive testing of the test samples.In summary a canary melon and an apple of Ambrosia kind was investigated off-the-shelf. For both test sam-ples, typical modal parameters such as eigenfrequencies and mode shapes where identified. These objectivecharacteristics of structures can be used in quality management. Further investigations will include the de-pendency of the modal parameters due to environmental influences. In addition, statistics of a larger numberof test samples is required to ensure the results’ reliability.

REFERENCES

[1] Lemke H. Ethik des Essens. Eine Einführung in die Gastrosophie. Akademie; 2007.

[2] Stache M, Guettler M, Marburg S. A precise non-destructive damage identification technique of long andslender structures based on modal data. Journal of Sound and Vibration. 2016;365:89–101.

[3] Ewins DJ. Modal Testing: Theory, Practice and Application. (second edition). Research Studies PressLtd.; 2000.

[4] Magnus K, Popp K. Schwingungen. B.G. Teubner; 2005.

[5] Chen H, De Baerdemaeker J. Modal-analysis of the dynamic behavior of pineapples and its relation tofruit firmness. Transactions of the ASAE. 1993;36:1439–1444.

[6] Diezma-Iglesias B, Ruiz-Altisent M, Barreiro P. Detection of Internal Quality in Seedless Watermelonby Acoustic Impulse Response. Biosystems Engineering. 2004;88:221–230.

[7] Zude M, Herold B, Roger JM, Bellon-Maurel V, Landahl S. Non-destructive tests on the prediction ofapple fruit flesh firmness and soluble solids content on tree and in shelf life. Journal of Food Engineering.2006;77:254–260.

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