3.1 White yam (Discorea rotundata)
Results of the entire discriminant analysis for detection evaluation of white yam, for the developed devices on software generation-technique and surface impact generation-technique, are displayed in Table S3 and S4 (tables too large for manuscript) submitted as a supplementary document. These tables also show predicted white yam quality by the discriminant software using the discriminant score functions (equations). These score functions (equations) were used to determine the probability that the predicted quality belongs to either quality class 1 (good), class 2 (diseased damaged), or class 3 (insect-damaged). Table 1 shows the mean and standard deviation of acoustic properties obtained during the evaluation of white yam for the developed devices. The mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), intensity (db), period (s), velocity (m/s) and wavelength (m) were 270.621 ± 14.125, 200 ± 0, 4333 ± 21906, 5 ± 0, 25 ± 0, 0.125 ± 0 for good yams respectively using the software sound generation technique. Similarly, 147.573 ± 27.765, 155.714 ± 11.506, 1448 ± 247, 2.32 ± 0.49, 16 ± 0, 0.101 ± 0.013 respectively were values obtained for good white yam using the surface impact sound generation technique. These results show that the acoustic properties of good white yams were higher in values for the software sound generation-technique than for the surface impact sound generation technique. This phenomenon can be attributed to the sound generation frequency of the software sound generation-technique being constant; while that of the surface impact sound generation-technique was not fixed but depended on sample impact. Looking at the statistical behavior of the obtained results, the acoustic property having the highest deviation from the mean for both techniques is the intensity of the sound. This is because according to Figura and Teixeira (2007) the intensity of the sound measured through solid material depends on the area of the sample that sound must travel through. So, since these white yam samples were not of the same size, the amount of sound going through them will defer notwithstanding the technique used. The mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), intensity (db), period (s), velocity (m/s) and wavelength (m) were 307.764 ± 8.24, 200 ± 0, 2462 ± 65.916, 5 ± 0, 25 ± 0, and 0.125 ± 0 for diseased damaged white yams respectively using the software sound generation technique. Similarly, 72.907 ± 9.309, 83.54 ± 9.446, 800.876 ± 314.904, 1.01 ± 0.1, 8 ± 0 and 0.094 ± 0.012 respectively were values obtained for diseased damaged white yams using surface impact sound generation technique. These results show that the acoustic properties of diseased damaged white yams were higher for the software sound generation-technique than for the surface impact sound generation technique. This same explanation given for good white yam can also be used to explain this phenomenon. The acoustic property having the highest deviations from the mean for both techniques is the intensity of the sound for diseased damaged white yams. Again, the same explanation given for good white yams can also be used to explain this phenomenon in diseased damaged yams. The insect-damaged result mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), intensity (db), period (s), velocity (m/s) and wavelength (m) were 285.566 ± 11.599, 200 ± 0, 2290 ± 92.681, 5 ± 0, 25 ± 0 and 0.125 ± 0 for software sound generation technique. Similarly, 143.055 ± 9.576, 153.772 ± 9.415, 1369 ± 225.5, 2.24 ± 0.429, 16 ± 0 and 0.102 ± 0.009 respectively were values obtained for insect-damaged white yams using surface impact sound generation technique. The same explanation given for white good yams is applicable here as well. The descriptive statistic alone can not give us an in-depth explanation of how these acoustic properties affect the choice for detecting these white yam qualities. So, we take a look at the test for equality of variance, group means and covariance matrices for the two acoustic techniques.
Table 1
Descriptive statistic on the performance of two acoustic techniques used in detecting white yam quality
White Yam
|
Software Sound generation technique
|
Surface impact sound generation technique
|
Yam Quality
|
Acoustic Property
|
N
|
Mean
|
Std. Deviation
|
Mean
|
Std. Deviation
|
Good
|
Amplitude (db)
|
100
|
270.621
|
14.125
|
147.573
|
27.765
|
Frequency (Hz)
|
100
|
200.000
|
0.000
|
155.714
|
11.506
|
Intensity (db)
|
100
|
4333.156
|
21906
|
1448
|
247
|
Period (s)
|
100
|
5.000
|
0.000
|
2.320
|
0.490
|
Velocity (m/s)
|
100
|
25.000
|
0.000
|
16.000
|
0.000
|
Wavelength (m)
|
100
|
0.125
|
0.000
|
0.101
|
0.013
|
Disease damaged
|
Amplitude (db)
|
100
|
307.764
|
8.240
|
72.907
|
9.309
|
Frequency (Hz)
|
100
|
200.000
|
0.000
|
83.540
|
9.446
|
Intensity (db)
|
100
|
2462
|
65.916
|
800.876
|
314.904
|
Period (s)
|
100
|
5.000
|
0.000
|
1.010
|
0.100
|
Velocity (m/s)
|
100
|
25.000
|
0.000
|
8.000
|
0.000
|
Wavelength (m)
|
100
|
0.125
|
0.000
|
0.094
|
0.012
|
Insect Damaged
|
Amplitude (db)
|
100
|
285.566
|
11.599
|
143.055
|
9.576
|
Frequency (Hz)
|
100
|
200.000
|
0.000
|
153.772
|
9.415
|
Intensity (db)
|
100
|
2290
|
92.681
|
1369
|
225.561
|
Period (s)
|
100
|
5.000
|
0.000
|
2.240
|
0.429
|
Velocity (m/s)
|
100
|
25.000
|
0.000
|
16.000
|
0.000
|
Wavelength (m)
|
100
|
0.125
|
0.000
|
0.102
|
0.009
|
Total
|
Amplitude (db)
|
300
|
287.984
|
19.150
|
121.178
|
38.558
|
Frequency (Hz)
|
300
|
200.000
|
0.000
|
131.009
|
35.125
|
Intensity (db)
|
300
|
3028
|
12639
|
1206
|
391.775
|
Period (s)
|
300
|
5.000
|
0.000
|
1.857
|
0.710
|
Velocity (m/s)
|
300
|
25.000
|
0.000
|
13.333
|
3.778
|
Wavelength (m)
|
300
|
0.125
|
0.000
|
0.099
|
0.012
|
N is the experimental observation number |
The test for equality of variance, group means and covariance matrices are statistical properties that show if the acoustic data obtained can be discriminated against using discriminant analysis. These tests are displayed in Table S5 submitted in the supplementary document. The first test on the table is the test of equality of yam quality groups means. This test is a univariate ANOVA test, using ‘Wilks' Lambda’ and ‘Fisher (F)’ values. Lower wilks’ lambda and F values mean that the variable had effects on the detection classification. In the software sound generation-technique, the test shows that among the five acoustic properties tested only amplitude and Intensity can be tested while the remaining variables (frequency, period, velocity and wavelength) can not be tested because they do not show any variation among it data sets. Now, between amplitude and intensity that were tested, only amplitude was found to have an effect while intensity does not have any effect on detecting white yam quality. This decision was taken because, the amplitude has a low wilks’ lambda value of 0.363 and f value of 4.24E-66, while Intensity has a higher wilks’ lambda value of 0.995 and f value of 4.49E-01. This means that in using the software sound generation-technique only one acoustic property or variable (amplitude) is required. Therefore, this makes the software-technique less expensive and an easy acoustic form of detecting yam quality. In the surface impact sound generation technique, the test of equality shows that among the five acoustic properties tested, variables like amplitude, frequency, period, wavelength and Intensity can be tested; while only sound velocity can not be tested because velocity data do not have many variations. In this impact technique, it was found that: amplitude, frequency, intensity, period and wavelength were affecting the detection of white yam quality. The decision was taken because their wilks’ lambda values were 0.211, 0.083, 0.456, 0.285 and 0.927 while their F values were 6.07E-101, 4.89E-161, 2.45E-51, 1.11E-81 and 1.21E-05 respectively. This means that the surface impact sound generation-technique requires five acoustic properties (variables) to detect white yam quality, unlike the software sound generation-technique that requires just one. Another statistical test conducted was the box's tests of equality of covariance matrices. It tests the homogeneity of variances and covariances within the white yam quality groups. So, to show that the covariance matrices are the same for data of all-white yam quality groups the log determinant was found. The equal log determinant shows equal covariance matrices among the quality groups. Log determinants for good, diseased damage and insect damage in the software sound generation-technique were 25.283, 3.781 and 12.435. These values are not equal, therefore, violating the assumption that the quality group covariance matrices must be equal. Nevertheless, ‘Box M; value can still be calculated to see if it has an effect. Non-significant 'Box M; value with an unequal log determinant still proves that the quality group covariance matrices are equal, this situation always occurs when data are large. The ‘Box M value calculated was 2956.271 with an F value of 487.918. This also violates the assumption that the quality group covariance matrices are equal but the analysis can continue because these can also occur when data are large. Log determinants for good, diseased damage and insect damage in the surface impact sound generation-technique were 9.486, 1.574, and 1.344. The calculated ‘Box M value was 1244 with an F value of 40.497. This also violates the assumption that the quality group covariance matrices are equal but the analysis can continue because these can also occur when data are large. Despite the drawback of the 'Box M' test, the test of the discriminant score functions will give a better insight into the discriminant analysis.
A summary of canonical discriminant score functions of white yam for both acoustic techniques is shown in table S6 (submitted in the supplementary document). The discriminant score functions are equations that will be used to determine the probability of a case belonging to a quality group. In this analysis, two discriminant score functions (equations) were developed for the software sound generation-technique and another two for the surface impact sound-generating technique. In the software sound generation technique, the first and the second discriminant score functions (equations) developed had Eigenvalue, % of the variance, cumulative % and canonical correlation of 1.766, 99.87, 99.87, 0.799 and 0.002, 0.13, 100, 0.048 respectively. The eigenvalue is the ratio between and within quality groups sum of squares and a higher value makes a discriminant score function (equation) a better predictor. So, for the software sound generation-technique, the first discriminant score function (Eq. 3) was chosen because it has a higher eigenvalue and higher canonical correlation value than the second function (Eq. 4). These equations (functions) are also displayed in Table S6 (submitted in the supplementary document). In the surface impact sound-generating technique the first and the second discriminant score functions (equations) developed had Eigenvalue, % of the variance, cumulative % and canonical correlation of 21.669, 99.91, 99.91, 0.978 and 0.02, 0.09, 100, 0.139 respectively. So, for the impact sound-generating technique the first discriminant score function (Eq. 5) was chosen because it has a higher eigenvalue and higher canonical correlation value than the second function (Eq. 6). These equations (functions) are also displayed in table S6 (submitted in the supplementary document). Wilks’ lambda test was also done to the discriminant score functions (equations) for both techniques. The test shows that for the software sound generation-technique the wilks' lambda value, chi-square value, degree of freedom and P-value for the two developed discriminant score functions (equations) were 0.361, 302.369, 4, 3.34E-64 and 0.998, 0.68, 1, 0.41 respectively. The first discriminant score function (Eq. 3) was again chosen over the second because it has a lower wilks' lambda value. Also, this same wilks’ lambda test for the surface impact sound-generating technique shows the wilks' lambda value, chi-square value, degree of freedom and P-value for the two developed discriminant score functions (equations) were 0.043, 926.42, 10, 1.31E-192 and 0.981, 5.722, 4, 0.221 respectively. The first discriminant score function (Eq. 5) was again chosen over the second (Eq. 6) because it has a lower wilks' lambda value. Another test called the standardized discriminant score function coefficients test” was done for functions (equations) developed for both techniques. This test shows the importance of the coefficients to the developed functions (equations). In the software sound generation technique, only the amplitude and intensity of sound variables were considered. The choices of these two variables were the same as explained for the test of equality of variance. The importance of the values of the coefficients for amplitude (db) and intensity (db) were 1, 0.042 and − 0.078, 0.998 for the first and second discriminant score functions (equations 3 and 4) developed respectively. These values show that only the coefficient of amplitude and intensity in the first developed function (Eq. 3), was important to it. In the surface impact sound-generating technique only the amplitude, frequency, intensity, period and wavelength variables were considered. The choices of these five variables were the same as explained for the test of equality of variance Their importance of the values of the coefficients for amplitude (db), frequency (Hz), intensity (db), period (s) and wavelength (m) were 0.042, 1.318, 0.094, -0.104, 0.948 and 0.266, -0.822, 1.152, 0.542, 0.368 for the first and second discriminant score function (Eqs. 4 and 5) developed respectively. These values show that for the first developed function (Eq. 5), only the coefficient of the period has negative importance while in the second discriminant score function (Eq. 6) developed, only the coefficient of frequency has negative importance ( see table S6 submitted in the supplementary document). These phenomena can be attributed to the difference in weights of the different yam samples used for the surface impact experiments. Also, a further statistical test was carried out on the functions (equations) developed. This further test was called the “structure matrix test” and was carried out for the function developed for both techniques. The structure matrix test tells the correction between the acoustic properties variable and the developed functions (equations). In the software sound generation technique, only the intensity and amplitude of sound variables were considered as explained by the equality of variance test, for the two developed functions (equations 3 and 4). The values of intensity (db) and amplitude (db) for the test obtained were − 0.042, 0.997 and 0.999, 0.078 respectively for the two developed functions (equations). This again shows that the intensity of the sound did not contribute to the prediction of yam quality. This phenomenon was caused by using a constant frequency of sound. In the surface impact sound-generating technique only the amplitude, frequency, intensity, period and wavelength variables were considered as explained by the equality of variance test, for the two developed functions (equations 5 and 6). The values of amplitude (db), frequency (Hz), intensity (db), period (s) and wavelength (m) for the test obtained were 0.713, 0.233, 0.415, 0.34, 0.06 and 0.154, 0.746, 0.509, 0.423, -0.265 respectively for the two developed functions (equations 5 and 6). This again shows the superiority of the first function (Eq. 5) over the second function (Eq. 6). The developed discriminant score functions (equations) for both techniques are displayed from equations 3–6 (also see table S6 in the supplementary document).
Software sound generation technique
DSF1 = 0.086 A − 6.149 I − 24.855 3
DSF2 = 0.004 A + 7.888 E-5 I − 1.284 4
Surface impact sound generation technique
DSF1 = 0.002 A + 0.130 F + 3.55E-4 I − 0.273 T + 82.855 W − 25.374 5
DSF2 = 0.015 A − 0.081 F + 0.004 I + 1.425 T + 32.153 W − 2.287 6
Where
DSF1 is the discriminant score function (equation) for the first developed function (equation)
DSF2 is the discriminant score function (equation) for the second developed function (equation)
A = amplitude (db), F = frequency (Hz), I = intensity (db), T = period (s) and W = wavelength (m)
The first discriminant score function (equations 3 and 5) was chosen in either technique for white yam quality detection classification
The detection classification or confusion matrix results for the discriminant analysis detection of white yam quality, for both acoustic techniques used in the study are displayed in Table 2. This table shows that two experimental classifications were carried out for both acoustic techniques used in the study. These detection classifications were called original classification and validated classification. In the software sound generation technique, the actual detection classification result shows that out of the 100 good white yams used for the detection. A total of 69% of them were correctly detected and classified as good yams, 31% were wrongly detected and classified as insect damage yams while no good yams were wrongly classified as diseased damaged yams. Still on the original classification, out of the 100 diseased damaged white yams used for the detection. 97% were correctly detected and classified as diseased damaged yams while 1% were wrongly detected and classified as good yams and 2% were wrongly detected and classified as insect-damaged yams. Again, still on the original classification, out of the 100 insect-damaged white yams used for the detection. A total of 73% were correctly detected and classified as insect-damaged yams. While 19% were wrongly detected and classified as good yams and 8% were wrongly detected and classified as diseased damaged yams. The overall original performance of correctly detecting the classification of all-white yam quality considered in this study using the software sound generation-technique for the original detection classification experiment was 79.7%. A cross-validation detection classification experiment was done again to confirm the original result. In the cross-validation detection and classifications done, out of the 100 good white yams used for the detection and classifications. A total of 68% of them were correctly detected and classified as good yams, 31% were wrongly detected and classified as insect damage yams and 1% were wrongly classified as diseased damaged yams. Still on the validation classification, out of the 100 diseased damaged white yams used for the detection. A total of 97% were correctly detected and classified as diseased damaged yams. In comparison, 1% were wrongly detected and classified as good yams and 2% were wrongly detected and classified as insect-damaged yams. Again, still on the validation classification, out of the 100 insect-damaged white yams used for the detection. A total of 73% were correctly detected and classified as insect-damaged yams. In comparison, 19% were wrongly detected and classified as good yams and 9% were wrongly detected and classified as diseased damaged yams. The overall cross-validated performance of correctly detecting all-white yam quality considered in this study using the software sound generation-technique was 79%. In the surface impact sound-generating technique, the actual detection classification result shows that out of the 100 good white yams used for the detection. A total of 37% of them were correctly detected and classified as good yams, 62% were wrongly detected and classified as insect damage yams and 1% were wrongly classified as diseased damaged yams. Still on the original classification, out of the 100 diseased damaged white yams used for the detection. A total of 100% was correctly detected and classified as diseased damaged yams while none was wrongly detected and classified as neither good yams nor insect-damaged yams. Again, still on the original classification, of the 100 insect-damaged white yams used for the detection. 74% were correctly detected and classified as insect-damaged yams while 26% were wrongly detected and classified as good yams and none were wrongly detected and classified as diseased damaged yams. The overall original performance classification of correct detections of all-white yam quality considered in this study using the surface impact sound-generating technique was 70.3%. Cross-validation detection was done again to confirm the original result. In the cross-validation detection and classifications done, out of the 100 good white yams used for the detection and classifications. A total of 35% were correctly detected and classified as good yams, 64% were wrongly detected and classified as insect damage yams and 1% were wrongly classified as diseased damaged yams. Still on the cross-validation classification, out of the 100 diseased damaged white yams used for the detection. A total of 100% was correctly detected and classified as diseased damaged yams while none was wrongly detected and classified as neither good yams nor insect-damaged yams. Again, still on the cross-validation classification, out of the 100 insect-damaged white yams used for the detection. A total of 71% were correctly detected and classified as insect-damaged yams. In comparison, 29% were wrongly detected and classified as good yams and none were wrongly detected and classified as diseased damaged yams. The overall cross-validated performance of correct detections of all-white yam quality considered in this study using the surface impact sound-generating technique was 68.7%. Comparing both acoustic techniques, the software sound generation-technique detected more good yams while the surface impact sound-generating technique detects more diseased damaged yams. Both acoustic techniques detect insect-damaged yams equally well. The reason for the high detection of good yams by the software sound generation-technique could be due to the lack of interference with the transmission of a sound wave through the yam tubers. Also, the uniform texture of the sound transmission material can account for the high detection of good yams. The poor detection of diseased and insect damage in the sound generation-technique could be due to differences in texture within the yam tubers. These differences in texture hinder the smooth transmission of sound through the yam tubers. The reason for the high detection of diseased yams than good yams in the surface impact sound-generating technique could be attributed to the difference in yam tuber tissue texture (deformation) as well. Tissue deformation could have softened the yam tubers; therefore making them produce low-frequency sounds upon impact with any solid surface than good yam tubers. Though, the overall performance of white yam quality detection was higher in the software sound generation technique. The surface impact sound-generating technique is the best to use when the goal of the detection was to detect diseased damaged white yams.
Table 2
Classification or confusion matrix results for the discriminant analysis detection of white yam quality for both acoustic techniques
Yam quality
|
Software Sound generation technique
|
Surface Impact sound-generating technique
|
Predicted Group Membership
|
Total
|
Predicted Group Membership
|
Total
|
Good
|
Disease damaged
|
Insect Damaged
|
Good
|
Disease damaged
|
Insect Damaged
|
Original
|
Count
|
Good
|
69
|
0
|
31
|
100
|
37
|
1
|
62
|
100
|
Disease damaged
|
1
|
97
|
2
|
100
|
0
|
100
|
0
|
100
|
Insect Damaged
|
19
|
8
|
73
|
100
|
26
|
0
|
74
|
100
|
%
|
Good
|
69
|
0
|
31
|
100
|
37
|
1
|
62
|
100
|
Disease damaged
|
1
|
97
|
2
|
100
|
0
|
100
|
0
|
100
|
Insect Damaged
|
19
|
8
|
73
|
100
|
26
|
0
|
74
|
100
|
Cross-validated
|
Count
|
Good
|
68
|
1
|
31
|
100
|
35
|
1
|
64
|
100
|
Disease damaged
|
1
|
97
|
2
|
100
|
0
|
100
|
0
|
100
|
Insect Damaged
|
19
|
9
|
72
|
100
|
29
|
0
|
71
|
100
|
%
|
Good
|
68
|
1
|
31
|
100
|
35
|
1
|
64
|
100
|
Disease damaged
|
1
|
97
|
2
|
100
|
0
|
100
|
0
|
100
|
Insect Damaged
|
19
|
9
|
72
|
100
|
29
|
0
|
71
|
100
|
Overall White yam quality detection
|
79.7% of original cases were correctly classified.
|
70.3% of original cases were correctly classified.
|
79.0% of cross-validated cases were correctly classified.
|
68.7% of cross-validated cases were correctly classified.
|
3.2 Yellow yam (Dioscorea Cayanensis)
Results of discriminant analysis for detection evaluation of yellow yam for the developed devices for software generation-technique and surface impact generation-technique are displayed in Table S7 and S8 (tables too large for manuscript) submitted as a supplementary document. These tables also show predicted yellow yam quality by the discriminant software using either the first or second discriminant score function (equation). The discriminant score function then was used to determine the probability that the predicted quality belongs to either quality class 1 (good), class 2 (diseased damaged), or class 3 (insect-damaged). Table 3shows the mean and standard deviation of acoustic properties obtained during the evaluation of yellow yam for the developed devices. The mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), velocity (m/s), wavelength (m), period (s), and intensity (db) were 2907 ± 26188, 150.83 ± 7.841, 125666 ± 47947, 49839 ± 213523, 0.005 ± 0, 56447 ± 30494 for good yams respectively using the software sound generation technique. Similarly, 318.391 ± 1726.894, 0.006 ± 0.001, 166.78 ± 39.061, 1045 ± 245.458, 175420 ± 101794 and 45308 ± 221269 respectively were values obtained for good yellow yam using surface impact sound generation technique. These results show that the acoustic properties of good yellow yams were higher in values for the software sound generation-technique than for the surface impact sound generation technique. This phenomenon can be attributed to the sound generation frequency of the software sound generation-technique being fixed; while that of the surface impact sound generation-technique was not fixed but was based on sample impact. The acoustic property having the highest deviations from the mean for both techniques is the intensity of the sound. This is because the intensity of the sound measured depends on the area of the sample. So, since these yellow yam samples were not of the same size, the amount of sound going through them will defer notwithstanding the technique used. The mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), velocity (m/s), wavelength (m), period (s), and intensity (db) was 3429 ± 25953, 156.48 ± 9.215, 1067 ± 951, 152997 ± 22924, 0.005 ± 0, 486381 ± 1808198, for diseased damaged yams respectively using the software sound generation technique. Similarly, 134.399 ± 22.364, 0.006 ± 0.001, 151.81 ± 36.975, 5311 ± 21512, 153308 ± 76012 and 18469 ± 6472 respectively were values obtained for diseased damaged yams using the surface impact sound generation technique. These results show that the acoustic properties of diseased damaged yellow yams were higher for the software sound generation-technique than for the surface impact sound generation technique. This same explanation given for good yellow yam can also be used to explain this phenomenon. The acoustic property having the highest deviations from the mean for both techniques was the intensity of the sound for diseased damaged yellow yams. Again, the same explanation given for good yellow yam can also be used to explain this phenomenon. The mean and standard deviation values of acoustic properties like amplitude (db), frequency (Hz), velocity (m/s), wavelength (m), period (s), and intensity (db) were 296.266 ± 17.016, 175.677 ± 19.82, 12912 ± 117991, 208022 ± 164412, 0.005 ± 0, 178253 ± 934925, for insect-damaged yellow yams respectively using the software sound generation technique. Similarly, 1664 ± 15287, 0.014 ± 0.014, 87.88 ± 15.844, 4933 ± 43863, 146105 ± 649042, and 18523 ± 4896, respectively were values obtained for insect-damaged yellow yams using surface impact sound generation technique. The same explanation given for good yellow yams is applicable here. The descriptive statistic can not give us an in-depth explanation of how these acoustic properties affect the choice for detecting these yellow yam qualities. So, we take a look at the test for equality of variance, group means and covariance matrices for the two acoustic techniques.
Table 3
Descriptive statistic on the performance of two acoustic techniques used in detecting yellow yam quality
White Yam
|
Software Sound generation technique
|
Surface impact sound generation technique
|
Yam Quality
|
Acoustic Property
|
N
|
Mean
|
Std. Deviation
|
Mean
|
Std. Deviation
|
Good Yam
|
Amplitude (db)
|
100
|
2907
|
26188.
|
318.391
|
1726
|
Frequency (Hz)
|
100
|
150.830
|
7.841
|
0.006
|
0.001
|
Velocity (v/s)
|
100
|
125666
|
47947
|
166.780
|
39.061
|
Wavelength (m)
|
100
|
49839
|
213523
|
1045
|
245.458
|
Period (s)
|
100
|
0.005
|
0.000
|
175420
|
101794
|
Intensity (db)
|
100
|
56447
|
30494
|
45308
|
221269
|
Insect damaged Yam
|
Amplitude (db)
|
100
|
3429
|
25953
|
134.399
|
22.364
|
Frequency (Hz)
|
100
|
156.480
|
9.215
|
0.006
|
0.001
|
Velocity (v/m)
|
100
|
1067
|
951.832
|
151.810
|
36.975
|
Wavelength (m)
|
100
|
152997
|
22924
|
5311
|
21512
|
Period (s)
|
100
|
0.005
|
0.000
|
153308
|
76012
|
Intensity (db)
|
100
|
486381
|
1808198
|
18469
|
6472
|
Diseased damaged Yam
|
Amplitude (db)
|
100
|
296.266
|
17.016
|
1664.229
|
15287.966
|
Frequency (Hz)
|
100
|
175.677
|
19.820
|
0.014
|
0.014
|
Velocity (m/s)
|
100
|
12912
|
117991
|
87.880
|
15.844
|
Wavelength (m)
|
100
|
208022
|
164412
|
4933.341
|
43863.637
|
Period (s)
|
100
|
0.005
|
0.000
|
146105.648
|
649042.884
|
Intensity (db)
|
100
|
178253
|
934925
|
18523.229
|
4896.031
|
Total
|
Amplitude (db)
|
300
|
2211
|
21260
|
705.673
|
8879
|
Frequency (Hz)
|
300
|
160.996
|
17.088
|
0.009
|
0.009
|
Velocity (m/s)
|
300
|
46549
|
92383
|
135.490
|
47.070
|
Wavelength (m)
|
300
|
136953
|
168918
|
3763
|
28178
|
Period (s)
|
300
|
0.005
|
0.000
|
158277
|
380762
|
Intensity (db)
|
300
|
240360
|
1185384
|
27433
|
128035
|
The test for equality of variance, group means and covariance matrices are statistical properties that show if the acoustic data obtained can be discriminated against using discriminant analysis. These tests are displayed in Table S9 for yellow yam (table too large for manuscript) submitted as a supplementary document. The first test on the table is the test of equality of yam quality groups' means of yellow yam. This test is a univariate ANOVA test, using ‘Wilks' Lambda’ and ‘Fisher (F)’ values. Lower wilks’ lambda value and F value means that the variable is affecting the detection. In the software sound generation-technique for yellow yam, the test shows that all six acoustic properties can be tested, unlike the white yam test. So, for all the six acoustic properties tested frequency, intensity, period and wavelength were found to be affecting the detection with low wilks’ lambda values of 0.611, 0.629, 0.849, and 0.977 respectively. This means that only these four acoustic properties were used to decide the quality of yellow yam. This phenomenon occurs because unlike the white yam the frequency of the sound generated was not constant but varied slightly. This variation was responsible for more sound properties being involved in the determination of yellow quality. Acoustic properties like amplitude and velocity were found to not have any effect on the detection with high wilks’ lambda values of 0.996 and 1.000 respectively. So, these two acoustic properties do not play any part in deciding the quality properties of yellow yam. In the surface impact sound generation technique, the test shows that among the six acoustic properties tested, variables like amplitude, frequency, intensity and wavelength were found to be affecting the detection with low wilks’ lambda values of 0.994, 0.844, 0.47 and 0.99 respectively; while velocity and period were found to be no effect on the detection with high wilks’ lambda values of 0.995 and 0.999 respectively. This means that only acoustic properties like amplitude, frequency, intensity and wavelength are important in deciding the quality of yellow yam using the surface impact sound generation-technique while velocity and period were not. This could be attributed to the low sound produced by the yam impacts on the surface. The box's tests of equality of covariance matrices test the homogeneity of variances and covariances within the yellow yam quality groups. So, to show that the covariance matrices are the same for data of all yellow yam quality groups the log determinant was found. The equal log determinant shows equal covariance matrices among the quality groups. Log determinants for good, diseased damage and insect-damaged in the software sound generation-technique were 90.789, 86.235 and 86.494. These values are not equal therefore violating the assumption that the quality group covariance matrices must be equal. Nevertheless, ‘Box M; value can still be calculated to see if it has an effect. A non-significant 'Box M; value with an unequal log determinant still proves that the quality group covariance matrices are equal, this situation always occurs when data are large. ‘Box M value was 3425 with an F value of 111.43. This also violates the assumption that the quality group covariance matrices are equal but the analysis can continue because these can also occur when data are large. Log determinants for good, diseased damage and insect damage in the surface impact sound generation-technique were 60.103, 54.137 and 81.392. ‘Box M value is 5958 with an F value of 137.793. This also violates the assumption that the quality group covariance matrices are equal but the analysis can continue because these can also occur when data are large. Despite this drawback with the ‘Box M’ test, the test of the discriminant score functions will give a better insight into the discriminant analysis.
A summary of canonical discriminant score functions of yellow yam for both acoustic techniques is shown in table S10 (table too large for manuscript) and submitted as a supplementary document. The discriminant score functions (equations) are equations that will be used to determine the probability of a case belonging to a quality group. In this analysis, two discriminant score functions (equations) were developed for the software sound generation-technique and another two for the surface impact sound-generating technique. In the software sound generation technique, the first and the second discriminant score functions (equations) developed had Eigenvalue, % of the variance, cumulative % and canonical correlation of 1.134, 82.2, 82.2 0.73 and 0.246, 17.8, 100, 0.44 respectively. The eigenvalue is the ratio between and within quality groups sum of squares and a higher value makes a discriminant score function (equation) a better predictor. So, for the software sound generation-technique first, the discriminant score function (equation) was chosen because it has a higher eigenvalue and higher canonical correlation value than the second function (equation). These equations (functions) are displayed in table S10. In the surface impact sound-generating technique the first and the second discriminant score functions (equations) developed had Eigenvalue, % of the variance, cumulative % and canonical correlation of 1.32, 98.969, 98.969, 0.754 and 0.014, 1.031, 100, 0.116 respectively. The eigenvalue is the ratio between and within quality groups sum of squares and a higher value makes a discriminant score function (equation) a better predictor. So, for the impact sound-generating technique the first discriminant score function (equation) was chosen because it has a higher eigenvalue and higher canonical correlation value than the second function (equation). These equations (functions) are also displayed in table S10 (table too large for manuscript) submitted as a supplementary document. Wilks’ lambda test was also done to the discriminant score functions (equations) for both techniques. This test shows that for the software sound generation-technique the wilks' lambda value, chi-square value, degree of freedom and P-value for the two developed discriminant score functions (equations) were 0.38, 288.421, 10, 4.35E-56 and 0.8, 64.833, 4, 2.79E-13 respectively. The first discriminant score function (equation) was chosen over the second because it has a lower wilks' lambda value and is affect the detection. Also, this test for the surface impact sound-generating technique shows the wilks' lambda value, chi-square value, degree of freedom and P- value for the two developed discriminant score functions (equations) was 0.425, 251.814, 12, 5.72E-47 and 0.986, 4.023, 5, 0.546 respectively. The first discriminant score function (equation) was chosen over the second because it has a lower wilks' lambda value and is affecting the detection classification. The standardized discriminant score function coefficients test was done for functions (equations) developed for both techniques. This test shows the importance of the coefficients to the developed functions (equations). In the software sound generation-technique five acoustic properties, amplitude, frequency, velocity, wavelength and intensity were considered. Their importance of the coefficients values for were − 0.013, 0.701, -0.662, 0.247, 0.047and − 0.107, 0.646, 0.655, -0.008, -0.292 for the first and second discriminant score function (equation) developed respectively. These values show that only five of the coefficient of all-acoustic properties studied in the first developed function (equation) was important to it. In the surface impact sound-generating techniques all six acoustic properties studied which were amplitude (db), frequency (Hz)), velocity (m/s), wavelength (m), intensity (db) and period (s) were considered. These coefficients values were − 0.062, 0.938, -0.135, -0.052, 0.063, -0.34 and 0.184, 0.158, 0.134, -0.478, 0.658, 0.512 for the first and second discriminant score function (equation) developed respectively. These values show that for the first developed function (equation) some of the values of the coefficients have negative importance while in the second discriminant score function (equation) developed only the coefficient of wavelength has negative importance (table S10) (tables too large for manuscript) submitted as a supplementary document. These phenomena can be attributed to the difference in weights of the different yam samples used for the surface impact experiments. A structure matrix test was also carried out for the function developed for both techniques. The structure matrix test tells the correction between the acoustic properties variable and the developed functions (equations). In the software sound generation technique, only five of the six acoustic properties were important to the two functions (equations) developed. In the surface impact sound-generating technique, all six acoustic properties were important to the two functions (equations) developed. The developed discriminant score functions (equations) for both techniques are displayed in equations 7–10 (see table S10 in the supplementary document).
Software sound generation technique
DSF1 = − 6.038E-07 A + 5.227E-02 F − 8.996E-06 V + 1.584E-06 W + 3.962E-08 I − 8.222 7
DSF2 = -5.045E-06 A + 4.817E-02 F + 8.912E-06 V − 4.866E-08 W − 2.484E-07 I − 8.093 8
Surface impact sound generation technique
DSF1 = − 7.034E-06 A − 4.033E + 01 T + 2.898E-02 F − 1.838E-06 W − 3.546E-07 V + 4.931E-07 I − 3.517 9
DSF2 = 2.072E-05 A + 6.062E + 01 T + 4.890E-03 F − 1.695E-05 W + 3.510E-07 V + 5.146E-06 I − 1.345E 10
Where
DSF1 is the discriminant score function (equation) for the first developed function (equation)
DSF2 is the discriminant score function (equation) for the second developed function (equation)
A = amplitude, F = frequency, I = intensity, T = period and W = wavelength, V = velocity
The first discriminant score function (equation) was chosen in either technique for yellow yam quality detection classification.
The detection classification or confusion matrix result for the discriminant analysis detection of yellow yam quality, for both acoustic techniques used in this study is displayed in Table 4. This table shows that two experimental classifications were carried out for both acoustic techniques used in this study. These detection classifications were called original classification and validated classification. In the software sound generation technique, the actual detection classification result shows that of the 100 good yellow yams used for the detection. 87% of them were correctly detected and classified as yellow good yams, 10% were wrongly detected and classified as diseased damaged yellow yams and 3% were wrongly classified as insect-damaged yellow yams. Still on the original classification, of the 100 diseased damaged yellow yams used for the detection. 75% were correctly detected and classified as diseased damaged yellow yams. In comparison, none was wrongly detected and classified as good yellow yam and 25% were wrongly detected and classified as insect-damaged yellow yams. Again, still on the original classification, of the 100 insect-damaged yellow yams used for the detection. 87% were correctly detected and classified as insect-damaged yellow yams while 2% were wrongly detected and classified as good yellow yams and 11% were wrongly detected and classified as diseased damaged yams. The overall original classification performance of correct detections of all yellow yam quality considered in this study using the software sound generation-technique for the original detection classification experiment was 83%. A validation detection experiment classification was done again to confirm the original result. In the validation detection and classifications experiment, of the 100 good yellow yams used for the detection and classifications. 86% were correctly detected and classified as good yellow yams, 11% were wrongly detected and classified as diseased damaged yellow yams and 3% were wrongly classified as insect-damaged yellow yams. Still on the validation classification, of the 100 diseased damaged yellow yams used for the detection. 74% were correctly detected and classified as diseased damaged yellow yams. In comparison, 1% were wrongly detected and classified as good yellow yams and 25% were wrongly detected and classified as insect-damaged yellow yams. Again, still on the validation classification, of the 100 insect-damaged yellow yams used for the detection. 87% were correctly detected and classified as insect-damaged yellow yams. In comparison, 2% were wrongly detected and classified as good yellow yams and 11% were wrongly detected and classified as diseased damaged yellow yams. The overall validated performance of correct detections and classification of all yellow yam quality considered in this study using the software sound generation-technique was 82.3%. In the surface impact sound-generating technique, the actual detection classification result shows that of the 100 good yellow yams used for the detection. 47% of them were correctly detected and classified as good yellow yams, 48% were wrongly detected and classified as diseased damaged yellow yams and 5% were wrongly classified as insect-damaged yams. Still on the original classification, of the 100 diseased damaged yellow yams used for the detection. 61% were correctly detected and classified as diseased damaged yellow yams, 31% were wrongly detected and classified as good yellow yams and 8% were wrongly classified as insect-damaged yams. Again, still on the original classification, of the 100 insect-damaged yellow yams used for the detection. 100% were correctly detected and classified as insect-damaged yams while none were wrongly detected and classified as neither good yams nor diseased damaged yellow yams. The overall original performance classification of correct detections of all yellow yam quality considered in this study using the surface impact sound-generating technique was 69.3%. A validation detection experiment was done again to confirm the original result. In the validation detection and classifications experiment, of the 100 good yellow yams used for the detection and classifications. 47% were correctly detected and classified as good yellow yams, 48% were wrongly detected and classified as diseased damaged yellow yams and 5% were wrongly classified as insect-damaged yams. Still on the validation classification, of the 100 diseased damaged yellow yams used for the detection. 61% were correctly detected and classified as diseased damaged yellow yams, 31% were wrongly detected and classified as good yellow yams and 8% were wrongly classified as insect-damaged yams. Again, still on the validation classification, of the 100 insect-damaged yellow yams used for the detection. 98% were correctly detected and classified as insect-damaged yams while 1% were wrongly detected and classified as good yellow yams and 1% were wrongly detected and classified as diseased damaged yellow yams. The overall validated performance of classification of correct detections of all yellow yam quality considered in this study using the surface impact sound-generating technique was 68.7%. Comparing both acoustic techniques, the software sound generation-technique detected more good yellow yams while the surface impact sound-generating technique detects more insect-damaged yellow yams. Both acoustic techniques detect diseased damaged yams equal well. Though, the overall performance of yellow yam quality detection was higher in the software sound generation technique. The surface impact sound-generating technique is the best to use when the goal of the detection was to detect insect damage to yellow yams.
Table 4
Classification or confusion matrix results for the discriminant analysis detection of yellow yam quality for both acoustic techniques
Yam quality
|
Software Sound generation technique
|
Surface Impact sound-generating technique
|
Predicted Group Membership
|
Total
|
Predicted Group Membership
|
Total
|
Good
|
Disease damaged
|
Insect Damaged
|
Good
|
Disease damaged
|
Insect Damaged
|
Original
|
Count
|
Good
|
87
|
10
|
3
|
100
|
47
|
48
|
5
|
100
|
Disease damaged
|
0
|
75
|
25
|
100
|
31
|
61
|
8
|
100
|
Insect Damaged
|
2
|
11
|
87
|
100
|
0
|
0
|
100
|
100
|
%
|
Good
|
87
|
10
|
3
|
100
|
47
|
48
|
5
|
100
|
Disease damaged
|
0
|
75
|
25
|
100
|
31
|
61
|
8
|
100
|
Insect Damaged
|
2
|
11
|
87
|
100
|
0
|
0
|
100
|
100
|
Cross-validated
|
Count
|
Good
|
86
|
11
|
3
|
100
|
47
|
48
|
5
|
100
|
Disease damaged
|
1
|
74
|
25
|
100
|
31
|
61
|
8
|
100
|
Insect Damaged
|
2
|
11
|
87
|
100
|
1
|
1
|
98
|
100
|
%
|
Good
|
86
|
11
|
3
|
100
|
47
|
48
|
5
|
100
|
Disease damaged
|
1
|
74
|
25
|
100
|
31
|
61
|
8
|
100
|
Insect Damaged
|
2
|
11
|
87
|
100
|
1
|
1
|
98
|
100
|
Overall White yam quality detection
|
83.0 % of original cases were correctly classified.
|
69.3 % of original cases were correctly classified.
|
82.3 % of cross-validated cases were correctly classified.
|
68.7 % of cross-validated cases were correctly classified.
|