Prediction of Poultry Egg Freshness Using Vis-Nir Spectroscopy with Maximum Likelihood Method

Abstract

Crucial physio-chemical changes occuring in eggs during storage after laying lead to loss of egg freshness. In this research, a new method for prediction of egg freshness using transmission visible near infrared spectroscopy was investigated. For this purpose 300 eggs were stored at two control conditions: refrigerator (4–5°C, 75%RH) and room (24–25°C, 40%RH) then by special egg holder, transmission spectroscopy was measured. For two eggs groups, 25 eggs in each group, in six days were tested by spectroscopy, after that Haugh unit and air cell height was measured directly. The non-destructive visible near infrared spectroscopy spectral measurements from 300 to 1100 nm (832 length of wave) were done as well as Haugh unit, air cell height for each egg and created the database for both environments. Finally a maximum likelihood latent root regression algorithm was developed to predict Haugh unit and air cell height by spectrum observation. The database was randomly divided into two parts. Training data, was used for maximum likelihood latent root regression parameter tuning and training of the model and testing data, was used just for model evaluation. Results indicated that maximum likelihood latent root regression method showed good prediction ability with coefficient of determination (R²) value up to 0.82 and 0.86 for Haugh unit and air cell height, respectively for testing data set. The results showed this method was better in comparison with partial least square regression (R² up to 0.79 and 0.72 for air cell height and Haugh unit) which was already used for this prediction.

Keywords:

• Vis-NIR Spectroscopy
• Egg freshness
• Haugh Unit
• Air cell
• MLLR

INTRODUCTION

Prediction of important changes occuring in eggs during storage is critical in order to monitor egg freshness. The internal quality change during storage is based on air cell size, albumen quality, yolk quality, and the presence of blood or meat spots. One of the most important interior egg qualities is the albumen height. Albumen (egg white) accounts for most of an egg’s liquid weight, about 67%. Albumen quality can also give an indication of food safety. When a freshly laid egg is broken onto a smooth flat surface, the yolk is generally in a central position surrounded by thick albumen. However, the thick albumen becomes thinner with time resulting in a larger area displacing the yolk placement to one side.[¹²] The rate at which these changes occur during storage depends on storage duration, relative humidity, temperature, and hen age and strain.[³⁵] Studies carried out in order to set up techniques for on-line prediction of the days of storage and the assessment of the egg freshness parameters concerned the dielectric properties analyses, the use of an electronic nose-based system and the Vis-NIR spectroscopy.[^6–11] A predictive model of thick albumen height was obtained with a determination coefficient of 0.78 by means of diffuse reflectance Fourier Transform (FT-NIR) spectroscopy.[¹²] Spectroscopy is the study of the interaction between matter and optic radiated energy. It is a new non-destructive method where the optic light was radiated to the poultry egg in one side and in the other side the energy of each wavelength was measured. It has the advantage of fast and non-contact method. The egg was affected like an optic filter and this energy is changed under the influence quality of poultry egg. The success of this technique is due to the continuous improvements of the sensors and instrumentations capable of supporting complex calculations based on multivariate statistical methods such as principal components analysis (PCA) and partial least squares regression (PLS).[¹³¹³] The advantage of optical measurements is that their nature is non-destructive, non-contact, and fast.

The PLS algorithm could consider simultaneously the variable matrix Y (Haugh unit [HU], air cell height) and the variable matrix X (power spectrum). To reduce the dimension and compress the original spectral data, the PCA were considered as new eigenvectors of the original spectra. In the development of PLS model, was used full cross-validation to evaluate the quality and prevent over fitting of calibration model. The number of PLS components (i.e., PCs) can affect the performance of PLS model, and it should be optimized by cross-validation in model calibration.

Maximum likelihood latent root regression (MLLRR) has also significantly demonstrated marginal improvements over maximum likelihood principal components regression (MLPCR), but this will depend on the error structure, particularly as it pertains to the errors in outputs data. MLPCR has demonstrated significant improvement over principle component regression (PCR) and PLS under the right error conditions. An important feature of MLLRR is its tremendous versatility in terms of the error structures that can be accommodated. In some ways, the relationship between MLPCR and MLLRR can be considered analogous to the relationship between PCR and PLS, the latter using the information in output data to obtain a more condensed representation of the factor space better suited for prediction. The analogy is not exact, however, since PLS uses a somewhat different modeling philosophy.[¹⁸,¹⁹] The objective of this research was to introduce MLLRR method for prediction of egg freshness in terms of internal egg quality of HU and air cell height. This experiment aimed to improve the technique’s reliability.

MATERIALS AND METHODS

Samples

Tests were carried out on 300 medium-sized commercial eggs collected from 33-week-old Boris Brown hens from the Kei farm (Kyoto, Japan) on the day the eggs were laid. On arrival at the laboratory, 50 eggs were analyzed, and the rest were stored under controlled conditions. One group was kept at refrigerator condition (4–5°C, 75% relative humidity), the another group was kept at room condition (24 ± 1°C, 40% relative humidity) in order to cause a variation in HU and air cell height. Twenty-five eggs from each group were selected for analysis every six days over a five-week storage period.

Quality Egg Parameters

The quality parameters considered were: temperature (°C) and humidity (%), air cell height (mm), thick albumen height (mm), and HU. The air cell height is measured from the base of the shell in three equidistant points on the circumference described by the contact line of the membrane to the shell, and at the middle point of the same membrane. The air cell height was obtained averaging the values of these four points. The thick albumen was measured by averaging three measurements carried out at different points of the thick albumen at the distance of 10 mm from the yolk. The HU was calculated by using the following formula[¹³]:

(1)

where, H is the albumen height (average) in millimeters, G is 32.2 (gravitational constant), and W is the mass of the egg in grams.

Vis-NIR spectroscopic data

Vis-NIR transmission data of 300 Borris Brown hen eggs of the same flock fed with a standard ration for each egg were obtained using spectroscope in 832 wavebands. The set up transmittance measured at wavelengths from 300–1100 nm with 1 nm increments. For this purpose a special egg holder was used to hold eggs between incident and transmitted light (Fig. 1). The egg is placed on a foam ring with its blunt end pointed upwards. This configuration was chosen in order to reproduce the typical egg orientation in a grading machine. An optical fiber is placed on one side of the egg and transports the transmitted light into an Avaspec-2048 spectrophotometer (Avantes, Eerbeek, The Netherlands). A xenon lamp was used as a light source and a Teflon block was used for calibration. Because light is not molecularly absorbed and scattered when it passes Teflon, the transmission spectrum of Teflon is nearly flat in the visible and NIR range. This makes it suitable as a reference measurement.

Figure 1  Experimental set-up for the measurements of transmission spectroscopy (LAX-Cute, 100W Xenon light source, Asahi Spectra).

For each egg, a non-destructive spectral transmission measurement and then determination of destructive freshness parameters (HU and air cell height) were performed. The spectral data of each egg was obtained by averaging three measurements and the acquisition time for each measurement was 250 ms. After spectra measurment the eggs were weighed (± 0.01 g) and broken. The albumen height was determined (± 0.25 mm) by means of a vertically mounted micrometer. Based on these measurements, the HU was determined by formula (1). Typically wavelength to response attitude for two random data illustrated in Fig. 2.

Figure 2  Wavelength response attitude for two random data.

Data Processing

The goal of the identification is finding the best function between HU, air cell height, and the Vis-NIR spectroscopy data which already obtained from stored eggs in room and refrigerator conditions. There are 832 wavelengths, which is known as regressor, from Vis-NIR spectroscopy, the air cell height and HU for each egg. In other words, the aim of identification is finding the best two mappings between 832 regressors in one hand and HU and air cell height in the other hand. Sample points and numbers of eggs, is less than the regressors number and so the following parts must be done in this case:

• Subset selection: In this part the number of regressors must be reduced by eliminating regressors which has non-significant effect or finding a linear mapping matrix, to reduce the size of regressors data.

• Finding a map between reduced regressors, air cell and HU, using MLLRR¹ method.

Subset Selection

For this part SVD² the composition is used for regressors reduction by defining a new parameters, λ, which is used for control of number of regressors. Singular value decomposition of an m × n real or complex matrix M is a factorization of the form.

(2)

where, U is an m × m real or complex unitary matrix, ∑ is an m × n rectangular diagonal matrix with non-negative real numbers on the diagonal, and V* (the conjugate transpose of V) is an n × n real or complex unitary matrix. The diagonal entries ∑ii of ∑ are known as the singular values of M and sorted. Absolute value of singular values shown the importance of the regressors. So the singular value is normalized and sorted and accepted if the singular values are less than λ. Then inverse of SVD is applied and M will be down sized.

MLLRR

If the statistical characteristic of measured data was known the maximum likelihood method is best estimator because this method searches for best match model. The result of this method is the same as the result of least square (LS) method in this saturation. Parameter estimation methods are widely used because of their desirable statistical characteristics. By this method the parameters determined for the model are the ones most likely to give rise to the observed data, given the statistical characteristics of the measurement uncertainties.[²] In this research the MLLRR was used for pure approach. With this technique, the original calibration matrix of response variables is augmented by the corresponding concentration vector(s). In this way, the reduction of dimensionality and the determination of the calibration model are performed simultaneously. For a single component there is:

(3)

which, X is a matrix of m spectra measured at n wavelengths, y is an m × 1 vector of concentrations for the component of interest, and the tilde indicates that the SVD results are truncated to pseudorank p. If (which now has dimensions( (n + 1) × p) is partitioned into the upper (n × p) and lower (1 × p), then the regression vector will be given by:

(4)

MLLRR is more general in its treatment of measurement errors than other method that it includes uncertainties in the concentration values. It is an optimal modeling method in the maximum likelihood sense, subject to the usual restrictions (linear model of known pseudorank, normally distributed errors with a known covariance structure). All algorithms were implemented in Matlab V7.0 (Mathworks,USA) under Windows XP.

RESULTS AND DISCUSSION

Egg Freshness and Storage Time

Egg freshness mainly includes two indexes: HU and air cell height. In order to build the inspection freshness model with optical properties, a tracing test of the egg freshness had also been done for five weeks. Figure 3 shows the relationship between HU and air cell height under the controlled storage conditions. Since egg aging coincides with an increase in air cell height on the one hand and a decrease in the HU on the other hand, a similar but reverse interpretation can be given for the variations of these two parameters. The main reason for liquefaction of thick white is that amino acid based proteins, which are one of the building materials for thick whites, are influenced by aging eggs.

Figure 3 Changes in Haugh Unit and air cell height under different storage conditions.

Destructive Analysis

Data analysis

Significant differences (p < 0.05) between mean values of the freshness parameters (air cell, thick albumen heights, and HU) at different storage durations were explored using ANOVA; Duncan’s multiple range test was used if significant differences emerged between variance means (SAS 9.1 for windows). Mean value of freshness parameters measured for each sample are summarized in Table 1 for different storage conditions.

Table 1  Mean values of main physical attributes of 25 eggs measured at different storage condition

Refrigerator (4–5°C and 75% humidity)*			Room (24–25°C and 40% humidity)*
Storage (day)	Thick albumen height (mm	HU	Air cell height (mm)	Thick albumen height (mm)	HU	Air cell height (mm)
1	8.4a (0.8)	95.9a (3.2)	3.5a (0.2)	7.78a (1.0)	93.4a (8.0)	3.6a (0.5)
6	6.5b (0.5)	80.1b (3.8)	4.3b (0.4)	5.1b (0.75)	69.3b (6.1)	5.6b (0.4)
12	6.2cb (0.6)	76.2c (5.0)	4.9c (0.4)	4.8b (1.2)	64.7d (7.2)	6.7c (0.4)
18	5.9c (0.2)	73.5dc (2.0)	5.0c (0.3)	3.5c (0.65)	51.8c (8.1)	7.6d (0.6)
24	5.4d (0.4)	69.6e (3.1)	5.3d (0.5)	3.2c (0.91)	48.4c (6.2)	9.3e (0.6)
30	5.0e (0.3)	67.3e (4.0)	5.6d (0.4)	2.9d (0.7)	43.1d (7.2)	12.8f (1.5)

*Differences between means with the same letter within a column are not significant at p < 0.05.

Values in parentheses are standard deviation for 25 samples.

Relation Between Transmission Spectra and Destructive Freshness Parameters

Partial least square (PLS)

Consider the general model as follows:

(5)

(6)

where, X is an n × m matrix for prediction, T and U are n × l matrices that are respectively the projection of X and Y, Y is an n × p matrix of response, P and Q are respectively m × l and p × l, orthogonal loading matrices and E and F are error terms and assumed to be identically independent. There are some algorithms for calculation of T, P, and Q. In this research the MLRR was introduced and R² values compared with PLS method. The result of the PLS implementation are shown in Table 2

Table 2  R² value for egg quality indices at different storage conditions

Egg quality indices	R^2 value	Storage condition
HU	0.68	Room (24–25°C)
	0.72	Refrigerator (4–5°C)
Air cell height	0.77	Room (24–25°C)
	0.79	Refrigerator (4–5°C)

Spectrum Data

All spectrum data were divided into two subsets. The first subset was used to train, the model build its structure and determine the model parameters. The second set, which was not included in the first set, was used to test the robustness and the generation power of the model. The training set contained 80% of all data where the remaining 20% was kept as test data. In this case there are many input data (830 regressors) which must be selected using subset selection algorithm as mentioned before. For air cell height and HU prediction, two separate models are proposed. So the first simulation for the different value of λ was run and R² value of HU for training and testing data were calculated and shown in Fig. 4a. Similarly, the air cell height model was simulated and R² values of air cell for both subsets were calculated and shown in Fig. 4b. The best value of λ and the number of regressors are reported in Table 3. An improvement in prediction of egg quality indices with 14 and 54 regressors compared to full spectrum was found. By eliminating less informative wavelengths and selecting the best regressors, MLLRR can improve the accuracy of model prediction. The difference between this study and previous work can be attributed to different predictive model and development of new experimental setup. According to Table 3, an extra test was run for room and refrigerator test data and R² value was reported in Table 4.

Table 3  Best value for λ and number of regressors in train data

λ Value	Number of regressors
0.9615	14	HU
0.986	54	Air cell height

Table 4  R² and λ value for HU and air cell height at different storage conditions

Egg quality indices	λ	R^2 value	Storage condition
HU	0.986	0.834	Room (24–25°C)
	0.986	0.823	Refrigerator (4–5°C)
Air cell height	0.961	0.887	Room (24–25°C)
	0.961	0.857	Refrigerator (4–5°C)

Figure 4  R² value for train and test HU (a) and air cell height (b) versus tuning parameter λ.

For data of eggs stored in different storage conditions, train and test data a simulation was run and showed the value of HU and air cell height. Results were illustrated in Figs. 5 and 6. Albumen becomes thinner over time which leads to a change in the transmitted spectra. NIR spectra correspond to vibrational modes involving O-H chemical bonds.[¹⁰]

Figure 5  value of estimation and measured (real) air cell for train and test data in room condition (25°C).

Figure 6  Value of estimation and measured (real) HU for train and test data in refrigerator condition (5°C).

Regresion Model Between Measured and Estimated Values

Figure 7 shows the predicted value by the model versus the measured value of HU and air cell height in room condition by performing the cross-validation of the non-destructive measurements of spectral transmittance. The validation was carried out in the full range of spectra. The predictive model produced satisfactory results with a high coefficient of determination between transmittance spectra and egg quality indices (R² = 0.834, 0.88 for HU and air cell height, respectively). Also a similar trend can be found for eggs stored in refrigerated conditions as presented in Fig. 8.

Figure 7  Relation between estimated and measured HU and air cell height for egg stored in room condition (25°C).

CONCLUSIONS

This work showed that the Vis-NIR transmission of an egg provides quantitative information about egg quality. PLS and MLLR models were built in order to predict the HU and air cell height with non-destructive spectral measurements. For the HU and air cell height the results showed an improvement in prediction with 14 and 54 wavelengths, respectively compared to those obtained with full spectrum. The developed model was used to relate the spectral data to HU and air cell height. For MLLR predictor, the R² for the validation set were 0.823, 0.857 for HU and air cell height, respectively and values of 0.72, 0.79 for the same in PLS model. R² value using maximum likelihood method compared to PLS illustrated MLLR method is better for prediction of egg freshness. In conclusion, the MLLR model can improve the predictive ability, decrease the model complexity and reduce the time of analysis.

Figure 8  Relation between estimated and measured HU and air cell height for egg stored in refrigerator condition (5°C).

ACKNOWLEDGMENT

The authors would like to thank the laboratory of Agriculture Process Engineering, Kyoto University for their technical support.

Notes

2. ¹Maximum Likelihood Latent Root Regression

3. ²Singular Value Decomposition