An experimental modal test system was established to extract the natural frequencies of "Golden Delicious" apple, after which the elasticity index was calculated to predict the apple quality parameters based on the orthogonal polynomials method. The elasticity index in every vibration mode changed dramatically (P = 0.01) along time revolution. The multivariate regression methods were used to model the predictive relationship between the elasticity index and the apple quality parameters. The models of the apple juice pH based on support vector regression presented adequate determination coefficients of calibration set (Q2 = 0.68) and prediction set (R2 = 0.55), respectively. The models based on partial least squares regression could be used for predicting the apple firmness parameter offset gradient (Q2 = 0.76 and R2 = 0.72). It helped understanding the fruit dynamic properties of the fruit and spontaneously obtaining the fruit chemical parameters. A nondestructive and portable device was viable for fruit quality estimation by the modal test system during storage, transport, and even growth on the tree. PRACTICAL APPLICATION A nondestructive and portable device was provided for fruit quality detection during storage, transport and even growth based on experimental modal analysis. A systematic statistical analysis method about outlier detection, data set partitioning, parameter optimization, and multiple regression models were provided.

中文翻译：

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基于模态分析的弹性指数预测“金冠”苹果的硬度和pH值

建立实验模态测试系统，提取“金冠”苹果的固有频率，然后计算弹性指数，基于正交多项式法预测苹果品质参数。每种振动模式下的弹性指数随着时间的推移发生显着变化（P = 0.01）。采用多元回归方法对弹性指数与苹果品质参数之间的预测关系进行建模。基于支持向量回归的苹果汁 pH 模型分别提供了足够的校准集（Q2 = 0.68）和预测集（R2 = 0.55）的确定系数。基于偏最小二乘回归的模型可用于预测苹果硬度参数偏移梯度（Q2 = 0.76 和 R2 = 0.72）。它有助于了解果实的果实动态特性，并自发获得果实化学参数。在储存、运输甚至在树上生长过程中，模态测试系统对水果质量进行评估是一种非破坏性和便携式设备是可行的。实际应用基于实验模态分析，提供了一种无损便携式设备，用于水果在储存、运输甚至生长过程中的品质检测。提供了异常值检测、数据集划分、参数优化和多元回归模型的系统统计分析方法。运输，甚至在树上生长。实际应用基于实验模态分析，提供了一种无损便携式设备，用于水果在储存、运输甚至生长过程中的品质检测。提供了异常值检测、数据集划分、参数优化和多元回归模型的系统统计分析方法。运输，甚至在树上生长。实际应用基于实验模态分析，提供了一种无损便携式设备，用于水果在储存、运输甚至生长过程中的品质检测。提供了异常值检测、数据集划分、参数优化和多元回归模型的系统统计分析方法。