Acoustic-Vibration Detection Method for The Apple Moldy Core Disease Based on D-S Evidence Theory

doi:10.12133/j.smartag.SA202505032

Abstract

Abstract:

[Objective] Moldy core disease is a common internal disease of the apple and is highly infectious. In the early storage stage, the mold symptoms are confined to the interior of the core. The apple tissue is in a sub-healthy state and still has commercial value, so early detection of moldy-core apples is critical. [Methods] In this study, a non-destructive acoustic vibration detection system was used to acquire acoustic vibration response signals. Symmetrized dot pattern (SDP), gramian angular field (GAF), and stockwell transform (ST) were applied to obtain multi-domain acoustic vibration spectra, including SDP images, gramian angular summation field (GASF) images, gramian angular difference field (GADF) images, and ST images. These images were uniformly converted to grayscale, transforming the time-domain signals into multi-domain visual spectra to facilitate subsequent feature analysis and recognition. Uniform local binary pattern (ULBP) and gray-level-gradient co-occurrence matrix (GLGCM) methods were used to extract handcrafted features from the multi-domain visualized images. Subsequently, the maximum relevance and minimum redundancy (mRMR) criterion was applied to select the dominant features from each analysis domain that were sensitive to early disease information. Principal component analysis (PCA) was employed to reduce the dimensionality of the multi-domain spectral ULBP texture features. From the statistical features extracted from one-dimensional acoustic-vibration signals in the time and frequency domains, and the GLGCM texture features extracted from two-dimensional images in each domain, 5 to 8 features sensitive to early moldy core detection were selected. From the high-dimensional sensitive ULBP texture features extracted from each domain, 3 to 7 principal components were obtained through dimensionality reduction using principal component analysis. This selection aimed to maximize the relevance between features and class labels while minimizing redundancy among features, thereby identifying the most informative features for early mold core apple detection in each domain. Meanwhile, a ResNet50 feature extractor improved with a convolutional attention mechanism module and the Adam optimizer (Adam-IResNet50) was designed to automatically extract deep features from visualized images in each domain. The optimal shallow features were used to train a multiple support vector machine (MSVM) classifier, while the optimal deep features were used to train an extreme learning machine (ELM) classifier. The Adam-IResNet50 network was employed as a feature extractor. The deep features extracted from the time-domain and frequency-domain GADF images, as well as time-frequency images, resulted in higher sample matching scores (SC) and cluster compactness (CHS) values, along with lower inter-class overlap (DBI) values for the three apple categories. These results clearly indicate that the deep features extracted by the Adam-IResNet50 model from multi-domain images exhibit strong capability in identifying subhealth and moldy core apples. The preliminary outputs of the two classifiers were converted into basic probability assignments for independent evidence bodies. Dempster's combination rule and the associated decision criterion of Dempster-Shafer (D-S) theory were then applied to yield the final decision on early-stage moldy apples. Consequently, a decision-level fusion model was established for both shallow and deep features of the acoustic-vibration multi-domain spectra. [Results and Discussions] The constructed Adam-IResNet50-IPSO-ELM-DS model based on D-S evidence theory achieved a Kappa coefficient and Matthews Correlation Coefficient (MCC) slightly below 90% for multi-class classification of apples from known origins. The F₁-Score and Overall Accuracy (OA) reached 93.01% and 93.22%, respectively. The classification accuracy for sub-healthy apples was 87.37%, while the misclassification rate for diseased apples was 8.33%. These results indicate that the model maintains a balanced precision and recall while achieving high detection accuracy for three classes of apples from unknown origins. After decision fusion, the IPSO-MSVM-DS and Adam-IResNet50-IPSO-ELM-DS models demonstrated significant performance improvements. Among them, the Adam-IResNet50-IPSO-ELM-DS model achieved an accuracy of 93.22%, which was significantly higher than that of other methods. This demonstrates that decision-level fusion could effectively enhance the model's discriminative ability and further improve classification performance. [Conclusions] The proposed acoustic vibration detection method for mold core apples, based on Dempster-Shafer evidence theory, provides technical support for future online batch detection of early mold core apples. Early screening of sub-healthy apples is of great significance for quality control during postharvest storage. In future work, the model will be further optimized to develop a rapid acoustic vibration-based prediction method for early detection of mold core, providing technical support for quality control during apple distribution.

Key words: acoustic vibration technology, sub-healthy apple, decision fusion, non-destructive detection

CLC Number:

TP274.5

LIU Jie, ZHAO Kang, ZHAO Qinjun, SONG Ye. Acoustic-Vibration Detection Method for The Apple Moldy Core Disease Based on D-S Evidence Theory[J]. Smart Agriculture, 2025, 7(4): 119-131.

Figures/Tables 17

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Table 1

Textural feature parameters of vibro-acoustic multi-domain images and the corresponding formulas

序号	特征参数	计算公式	序号	特征参数	计算公式
1	小梯度优势	$G 1 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j) / (j + 1) 2 ∑ i = 0 l f - 1 ∑ i = 0 l g - 1 H (i, j)$ （1）	9	梯度均方差	$G 9 = ∑ j = 0 l g - 1 (j - G 7) 2 ∑ i = 0 l f - 1 P (i, j) 12$ （9）
2	大梯度优势	$G 2 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j) j 2 ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j)$ （2）	10	相关性	$G 10 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 (i - G 6) (j - G 7) P (i, j)$ （10）
3	灰度分布不均匀性	$G 3 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j) 2 ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j)$ （3）	11	灰度熵	$G 11 = - ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 P (i, j) l o g ∑ j = 0 l g - 1 P (i, j)$ （11）
4	梯度分布不均匀性	$G 4 = ∑ j = 0 l g - 1 ∑ i = 0 l f - 1 H (i, j) 2 ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 H (i, j)$ （4）	12	梯度熵	$G 12 = - ∑ j = 0 l g - 1 ∑ i = 0 l f - 1 P (i, j) l o g ∑ i = 0 l - f 1 P (i, j)$ （12）
5	角二阶距	$G 5 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 [P (i, j)] 2$ （5）	13	混合熵	$G 13 = - ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 P (i, j) l o g P (i, j)$ （13）
6	灰度均值	$G 6 = ∑ i = 0 l f - 1 i ∑ j = 0 l g - 1 P (i, j)$ （6）	14	惯性矩	$G 14 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 (i - j) 2 H ∧ (i, j)$ （14）
7	梯度均值	$G 7 = ∑ j = 0 l g - 1 j ∑ i = 0 l f - 1 P (i, j)$ （7）	15	逆差矩	$G 15 = ∑ i = 0 l f - 1 ∑ j = 0 l g - 1 P (i, j) 1 + (i - j) 2$ （15）
8	灰度均方差	$G 8 = ∑ i = 0 l f - 1 (i - G 6) 2 ∑ j = 0 l g - 1 P (i, j) 12$ （8）

Table 1

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Table 2

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Table 3

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Table 4

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Table 6

Fig. 8

Fig. 9

Table 7

Table 8

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数据集类型		筛选的敏感特征参数	数据集类型		筛选的敏感特征参数
时域信号统计特征		TD ₂、TD ₇、TD ₁₈、TD ₅ 、 TD ₉、TD ₁₁、TD ₁₀、TD ₆	频域信号统计特征		FD ₇、FD ₂、FD ₃、FD ₈
时域 SDP图	GLGCM	TD _G9、TD _G13、TD _G6 、 TD _G15、TD _G10、TD _G7	频域GASF图	GLGCM	FD _G6、FD _G9、FD _G13 、 FD _G1、FD _G11、FD _G14
时域 SDP图	ULBP	TD _U6、TD _U28、TD _U13、TD _U9、TD _U30、TD _U52、TD _U24、TD _U16、TD _U12、TD_U ₃₆、TD _U7、TD _U46、TD _U42、TD _U25、TD _U10	频域GASF图	ULBP	FD _U10、FD_U ₃₃、FD _U20、FD _U49、FD _U35、FD _U18、FD _U24、FD _U28、FD _U45、FD _U11、FD _U54、FD _U32、FD _U6、FD _U15 、FD _U39、FD _U13、FD _U2
时域GASF图	GLGCM	TD _G8、TD _G14、TD _G11 、 TD _G9、TD _G10	频域GADF图	GLGCM	FD _G6、FD _G9、FD _G13 、 FD _G11、FD _G14、FD _G1
时域GASF图	ULBP	TD _U12、TD _U3、TD _U21、TD _U6、TD _U35、TD _U22、TD _U15、TD _U38、TD _U26、TD _U10、TD _U42、TD _U14、TD _U33、TD _U50	频域GADF图	ULBP	FD _U16、FD _U25、FD _U8、FD _U32、FD _U20、FD _U7、FD _U43、FD _U50、FD _U21、FD _U5、FD _U12、FD _U38、FD _U23、FD _U44、FD _U15、FD _U31
时域GADF图	GLGCM	TD _G8、TD _G14、TD _G9 、 TD _G1、TD _G13	时频域ST图	GLGCM	TFD _G10、TFD _G13、TFD _G5、TFD _G15、TFD _G6、TFD _G4、TFD _G14
时域GADF图	ULBP	TD _U3、TD _U20、TD _U15、TD_U ₂₃、TD _U8、TD _U27、TD _U53、TD _U19、TD _U24、TD _U45、TD _U7、TD _U13、TD _U36、TD _U42	时频域ST图	ULBP	TFD _U9、TFD _U23、TFD _U16、TFD _U32、TFD _U14、TFD _U43、TFD _U38、TFD _U11、TFD _U25、TFD _U58、TFD _U12、TFD _U30、TFD _U44、TFD _U52、TFD _U27、TFD _U8、TFD _U2、TFD _U15、TFD _U46、TFD _U6

特征		分类准确率/%
时域特征	统计特征	75.75
	TD-SDP-GLGCM	79.42
	TD-SDP-ULBP-PC	76.83
	TD-GASF-GLGCM	80.03
	TD-GASF-ULBP-PC	78.34
	TD-GADF-GLGCM	81.62
	TD-GADF-ULBP-PC	85.20
频域特征	统计特征	78.31
	FD-GASF-GLGCM	75.27
	FD-GASF-ULBP-PC	80.59
	FD-GADF-GLGCM	83.20
	FD-GADF-ULBP-PC	88.94
时频域特征	TFD-ST-GLGCM	93.53
时频域特征	TFD-ST-ULBP-PC	91.62

分类器	各单一域深层特征（V_i ）	总体分类准确率（A_i ）/%
ELM	TD-GADF	89.05
	FD-GADF	91.27
	TFD-ST	95.49

特征类型	特征名称	分类器	证据体	各证据体的基本概率分配值m_i （L_j ）
特征类型	特征名称	分类器	证据体	L ₁	L ₂	L ₃	Θ
浅层特征	TD-GADF-ULBP-PC	MSVM	E ₁₁	0.295	0.273	0.306	0.126
	FD-GADF-ULBP-PC		E ₁₂	0.300	0.292	0.323	0.085
	TFD-ST-GLGCM		E ₁₃	0.312	0.306	0.351	0.031
深层特征	TD-GADF	ELM	E ₂₁	0.298	0.286	0.314	0.102
	FD-GADF		E ₂₂	0.312	0.294	0.366	0.028
	TFD-ST		E ₂₃	0.319	0.298	0.382	0.001

分类模型	模型参数							分类准确率/%
分类模型	α	c	σ	d	l	ω_j	b_j	分类准确率/%
IPSO-MSVM-DS	0.638	68.325	9.651	2	—	—	—	98.52
Adam-IResNet50-IPSO-ELM-DS	—	—	—	—	10	2.542	0.121	99.36