基于Logistic生长模型的多指标钦蜜9号百香果成熟阶段的判别

林钒; 陈登捷; 张德晖; 何金成

基于Logistic生长模型的多指标钦蜜9号百香果成熟阶段的判别

林钒^1,,
陈登捷¹,
张德晖^{1, 2},
何金成^{1, 2, ,}

1.
福建农林大学机电工程学院，福建　福州　350002
2.
现代农业装备福建省高校工程研究中心，福建　福州　350002

基金项目: 福建省星火计划（2020S0002）；福建农林大学科技创新专项（KFA17024A）

详细信息

作者简介:
林钒（1999 —），男，硕士研究生，主要从事农业工程研究，E-mail：13665084036@163.com

通讯作者:
何金成(1973 —)，男，博士，教授，主要从事农业机械设计与性能测试研究，E-mail：bighjc@163.com

中图分类号: S66
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- 被引次数: 0
出版历程
- 收稿日期: 2024-03-22
- 修回日期: 2024-04-28
- 网络出版日期: 2024-08-15

Passion Fruit Ripening Stages Divided by Logistic Growth Model with Multiple Quantifiable Indicators

LIN Fan^1
,,
CHEN Dengjie¹,
ZHANG Dehui^{1, 2},
HE Jincheng^{1, 2
, ,}

1.
College of Mechanical and Electrical Engineering, Fujian Agriculture & Forestry University, Fuzhou, Fujian　350002, China
2.
Modern Agricultural Equipment Engineering Research Center of Fujian Universities, Fuzhou, Fujian　350002, China

摘要

摘要: 目的为探究夏季百香果的生长发育与品质形成规律，并对百香果成熟阶段进行判别。方法采用钦蜜9号百香果作为试材，测定其横径、纵径、固酸比、可食率、果皮厚度、硬度等理化指标，利用Logistic生长模型分析理化指标随有效积温增长的变化规律，并应用因子分析法对百香果成熟度进行定量评价，最终划分成熟阶段。结果通过观测并记录百香果生长过程，发现其纵径、横径变化趋势符合“慢-快-慢”的生长曲线，分析得出百香果在有效积温达到440 ℃·d时，基本完成果实膨大。随后以固酸比、可食率、果皮厚度、硬度为品质指标，其中固酸比与可食率指标呈现S型增长趋势，果皮厚度与硬度呈现三次函数下降趋势，并且品质指标与有效积温之间存在显著的相关性。利用因子分析方法构建百香果成熟度评价指标I_M，采用Logistic生长函数建立百香果成熟度数学模型，模型拟合优度达99.25%，计算得出t₁、t₂、t₃三个生长分界点。最终确定有效积温为475～736 ℃·d时，果实处于果肉增重阶段；有效积温为736～997 ℃·d时，果实处于转色阶段；有效积温为997～1200 ℃·d时，果实处于成熟阶段。结论本研究量化分析了百香果成熟度，能够较好划分果肉增重期、转色期、成熟期三个成熟阶段，为百香果适时机械化采摘与贮藏管理提供研究基础。
- 有效积温 /
- 理化指标 /
- 成熟阶段 /
- Logistic生长模型 /
- 钦蜜9号百香果
Abstract: Objective To effectively determine the summer growth and development as well as the fruit formation and maturation of passion fruits applying logistic model was studied. Method Physiochemical parameters including transverse and longitudinal diameters, solid to acid ratio, pulp percentage, pericarp thickness, and firmness of Qinmi No. 9 passion fruits were monitored as the plant grew and fruits developed. A logistic growth model incorporating those quantifiable indicators was evaluated to classify the fruit maturity stages by a factor analysis. Result In terms of longitudinal and transverse diameters, the passion fruits grew in a slow-fast-slow pattern. Once the effective accumulated temperature in growth degree days (GDDs) reached 440 ℃·d, the fruits essentially had completed the enlargement stage. Thereafter, the solid to acid ratio and pulp yield of the fruits were in an S-shape trend, while the peel thickness and fruit firmness in a declining cubic function. A significant correlation was observed between the indicators and GDD. With the factor analysis-generated assessment index, I_M, the mathematic model built with the logistic growth function showed a high fitting of 99.25% on fruit maturity. Three growth transition points, t₁, t₂, and t₃, distinctively separated the fruits development into (A) the pulp weight gaining stage with a GDD of 475-736 ℃·d, (B) the color-changing stage with a GDD of 736-997 ℃·d, and (C) the ripening stage with a GDD of 997-1,200 ℃·d. Conclusion The analysis based on the selected quantitative physiochemical indicators effectively divided the maturation of Qinmi No. 9 passion fruits into the pulp weight gaining, color-changing, and ripening stages. The result would facilitate the design of automated fruit picking and storage management.
- growth degree days /
- physicochemical indicators /
- maturity /
- Logistic growth model /
- ‘Qinmi No. 9’ passion fruit

HTML全文

图 1 有效积温与百香果外形指标变化关系

Figure 1. Relationship between GDD and changes in passion fruit appearance indicators

下载: 全尺寸图片幻灯片

图 2 400～1200 ℃·d有效积温黄金百香果外、内部动态变化

图中编号1—9分别表示400～1200 ℃·d有效积温。

Figure 2. External and internal dynamic changes of golden passion fruit with GDD of 400-1200 ℃·d

Numbers 1—9 in the figure represent the GDD of 400～1200 ℃·d respectively.

下载: 全尺寸图片幻灯片

图 3 有效积温与品质指标变化的关系

Figure 3. Relationship between GDD and changes in quality indicators

下载: 全尺寸图片幻灯片

图 4 有效积温与百香果成熟度评价指标变化的关系

Figure 4. Relationship between GDD and changes in evaluation indicators of passion fruit maturity

下载: 全尺寸图片幻灯片

表 1 外形指标模型各参数取值

Table 1. Values of various parameters in the appearance index model

参数 Parameters	参数 Parameters			分界点 Boundary point
参数 Parameters	a	b	k	t₁	t₂	t₃
横径 Transverse diameter	5.3231 ± 1.95	0.02008 ± 0.39×10^-3	56.73 ± 5.38	17.682	83.27	148.857
纵径 Longitudinal diameter	3.9525 ± 1.26	0.02111 ± 0.48×10^-3	58.52 ± 5.35	2.717	65.104	127.492

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表 2 百香果品质指标拟合情况

Table 2. Fitting of quality indicators of passion fruit

参数 Parameters	拟合方程 Fitted equation	R²	调整后R² Adjusted R²
可食率 Pulp percentage	$ y=\dfrac{0.56}{1+33.29{e}^{-0.006x}} $	0.985	0.980
固酸比 Solid acid ratio	$ y=\dfrac{18.24}{1+90.09{e}^{-0.004x}} $	0.986	0.981
果皮厚度 Pericarp thickness	y=29.40−0.07x+7.79×10⁻⁵x²−2.82×10⁻⁸x³	0.942	0.908
硬度 Firmness	y=202.35−0.11x−2.92×10⁻⁴x²+1.47×10⁻⁷x³	0.989	0.982

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表 3 品质指标的相关性分析

Table 3. Correlation analysis of quality indicators

品质指标 Quality indicators	有效积温 GDD	可食率 Pulp percentage	固酸比 Solid acid ratio	果皮厚度 pericarp thickness	硬度 firmness
有效积温 GDD	1
可食率 Pulp percentage	0.849^*	1
固酸比 Solid acid ratio	0.960^*	0.822^*	1
果皮厚度 Pericarp thickness	−0.587^*	−0.714^*	−0.531^*	1
硬度 Firmness	−0.874^*	−0.823^*	−0.866^*	0.542^*	1
提取方法为主成分分析法。表中主成分F₁-F₄分别表示原始变量线性变换后得到的新变量。 The extraction method is mainly based on component analysis. The principal components F₁-F₄ in the table represent the new variables obtained from the linear transformation of the original variables, respectively.

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表 4 成分载荷矩阵和贡献率

Table 4. Component load matrix and contribution rate

指标 Index	载荷值 Load value
指标 Index	F₁	F₂	F₃	F₄
初始特征值 Initial eigenvalue	3.166	0.561	0.140	0.133
方差贡献率/% Variance contribution rate	79.151	14.024	3.492	3.333
累计方差贡献率/% Cumulative variance contribution rate	79.151	93.174	96.667	100.000
可食率 Pulp percentage	0. 948	−0. 039
固酸比 Solid acid ratio	0. 915	0. 292
果皮厚度 Pericarp thickness	−0. 767	0. 631
硬度 Firmness	−0. 918	−0. 276

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表 5 不同成熟阶段品质指标数据

Table 5. Quality indicator data for different maturity levels

不同成熟阶段 Different maturity stages	可食率 Pulp percentage	固酸比 Solid acid ratio	果皮厚度 Pericarp thickness	硬度 Firmness
果肉增重期 Pulp weight gain period	0.224±0.117c	1.471±0.485c	8.859±2.77a	196.4±7.1a
转色期 Color-changed period	0.426±0.074b	5.724±1.806b	7.173±0.89b	171.1±9.6b
成熟期 Ripeness period	0.543±0.029a	10.217±1.234a	6.234±0.60b	161.2±3.8c

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