Prediction of Soluble Solid Contents in Apples Using Vis-NIRS and
Functional Linear Regression Model
HUANG Hua1, LIU Ya2, MA Yi-hang1, XIANG Si-han1, HE Jia-ning1, WANG Shi-ting1, GUO Jun-xian3*
1. College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi 830052, China
2. Comprehensive Testing Ground, Xinjiang Academy of Agricultural Sciences, Urumqi 830013, China
3. Mechanical and Traffic College, Xinjiang Agricultural University, Urumqi 830052, China
Abstract：Soluble solid contents (SSC) are an important indicator of apple quality and maturation and can be used for quality analysis and ripeness prediction. In this paper, 552 samples of Sugar Core Red Fuji apples from Aksu of Xinjiang Province were picked at equal intervals of three days from the fruit swelling and setting stage to the complete mature stage, the visible near-infrared spectroscopy (vis-NIRS) of the samples at 380 to 1 110 nm were collected respectively, and the SSC were measured. Then, the collected discrete data of vis-NIRS were transformed into spectral curves using the basis function smoothing method, i. e., function-type data, and respectively, the functional linear regression model was established with Vis-NIRS curves, first-order derivative curves, and second-order derivative curves as functional explanatory variables and SSC as scalar response variables. To confirm and analyze the performance of the model, partial least squares regression (PLSR), kernel support vector machine (KSVM), random forest (RF), gradient boosting tree (GBM) and deep neural network (DeepNN) were established by the original spectral discrete data after moving smooth, first-order derivative and second-order derivative pre-processing. The results show that among the 18 models, for the training set, the PLSR-dNIRmodel, KSVM-dNIR model, RF-dNIR model, GBM-dNIR model, and Deep NN-d2NIR model were outperformed the FunLR-NIR model, FunLR-dNIR model and FunLR-d2NIR model, and the Deep NN-d2NIR model was optimal (rc=0.999 6, R2c=0.998 6, RMSEC=0.074 0, RPDC=27.436 6). For the test set, the FunLR-NIR model, FunLR-dNIR model, and FunLR-d2NIR model outperformed all other models, and the FunLR-NIR model was optimal (rv=0.953 4, R2v=0.907, RMSEV=0.585 6, RPDV=3.301 7). The results of the training sets and test sets show that the kernel support vector machine model, random forest model, gradient boosting tree model, and deep neural network model are prone to overfitting. In contrast, the functional linear regression model has better generalizability. Besides, the prediction results of the three functional linear regression models (FunLR-NIR model, FunLR-dNIR model, and FunLR-d2NIR model) showed that all the models have good robustness and high prediction accuracy. The experimental results showed that the functional linear regression models combined with vis-NIR spectroscopy and functional data analysis could successfully and effectively achieve the prediction of soluble solid contents of apples at the ripening stage.
Key words：Apple; Soluble solid content; Visible near-infrared spectroscopy; Functional data analysis; Functional linear regression model
黄 华，刘 亚，马毅航，向思函，何佳宁，王诗婷，郭俊先. 基于可见/近红外光谱和函数型线性回归模型的成熟期苹果可溶性固形物含量预测[J]. 光谱学与光谱分析, 2024, 44(07): 1905-1912.
HUANG Hua, LIU Ya, MA Yi-hang, XIANG Si-han, HE Jia-ning, WANG Shi-ting, GUO Jun-xian. Prediction of Soluble Solid Contents in Apples Using Vis-NIRS and
Functional Linear Regression Model. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(07): 1905-1912.
[1] Pavlina D D, Georgios P. Scientia Horticulturae, 2011, 129(4): 752.
[2] Patricia P, María-Teresa S, Dolores P, et al. Computers and Electronics in Agriculture, 2009, 69(1): 24.
[3] Ma T, Xia Y, Inagaki T, et al. Postharvest Biology and Technology, 2021, 173: 111417.
[4] Ma T, Zhao J, Inagaki T, et al. Postharvest Biology and Technology, 2022, 186: 111841.
[5] Maii M N, Wang S, Mohamed A F. Trends in Food Science & Technology, 2022, 123: 290.
[6] Olga M, Nils K A, Svein H K, et al. Postharvest Biology and Technology, 2021, 180: 111620.
[7] LIU Yan-de, WANG Jun-zheng, JIANG Xiao-gang, et al(刘燕德, 王军政, 姜小刚, 等). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2021, 41(7): 2064.
[8] MENG Qing-long, SHANG Jing, HUANG Ren-shuai, et al(孟庆龙，尚 静，黄人帅，等). Storage and Process(保鲜与加工), 2020, 20(5): 185.
[9] Wang F, Zhao Y, Zheng J, et al. Computers and Electronics in Agriculture, 2021, 191: 106492.
[10] RAO Li-bo, CHEN Xiao-yan, PANG Tao(饶利波, 陈晓燕, 庞 涛). Chinese Journal of Luminescence(发光学报), 2019, 40(3): 389.
[11] Guo Z, Wang M, Agyekum A A, et al. Journal of Food Engineering, 2020, 279: 109955.
[12] Zhao X, Zhao X, Huang M. Chemometrics and Intelligent Laboratory Systems, 2021, 217: 104426.
[13] Xia Y, Fan S, Li J, et al. Chemometrics and Intelligent Laboratory Systems, 2020, 201: 104017.
[14] Zhang D, Xu Y, Huang W, et al. Infrared Physics & Technology, 2019, 98: 297.
[15] Zhang M, Zhang B, Li H, et al. Infrared Physics & Technology, 2020, 111: 103529.
[16] Lee A, Shim J, Kim B, et al. Journal of Food Engineering, 2022, 321: 110945.
[17] Huang Y, Wang J, Li N, et al. Pattern Recognition Letters, 2021, 151: 76.
[18] Bai Y, Xiong Y, Huang J, et al. Postharvest Biology and Technology, 2019, 156: 110943.
[19] Tian X, Fan S, Li J, et al. Biosystems Engineering, 2020, 197: 64.
[20] Ramsay J O, Silverman B W. Functional Data Analysis, 2nd ed., New York: Springer, 2006.
[21] Reiss P T, Ogden R T. Journal of the American Statistical Association, 2007, 102(479): 984.
[22] Goldsmith J, Bobb J, Crainiceanu C, et al. Journal of Computational and Graphical Statistics, 2011, 20(4): 830.
[23] Goldsmith J, Crainiceanu C, Caffo B, et al. Journal of the Royal Statistical Society Series C: Applied Statistics, 2012, 61(3): 453.
[24] Febrero-Bande M, Oviedo de la Fuente M. Journal of Statistical Software, 2012, 51(4): 1.
[25] McLean M W, Hooker G, Staicu A M, et al. Journal of Computational and Graphical Statistics, 2014, 23: 249.
[26] Brockhaus S, Scheipl F, Hothorn T, et al. Statistical Modelling, 2015, 15: 279.
