**1. Introduction**

Containing various types of ingredients (such as sugars, vitamin C, and minerals), "Huping" jujube has high nutritional and medicinal values. The content of soluble solids (SSC) is an important evaluation index for the internal quality of fruit and vegetables, which is closely related to improving the added value of products and meeting consumer needs [1,2]. In traditional detection of SSC, destructive or invasive methods (e.g., refractometers) were used, which damaged the integrity of the sample and were cumbersome, time-consuming, and laborious to perform. This destructive approach is unfavorable for large-scale collection, implementation assessment, and industrial applications. Therefore, it is important to achieve rapid, non-destructive detection of SSCs to support the quality assessment and grading of agricultural products.

Visible/near infrared spectroscopy (VIS/NIR) [3,4] uses absorption characteristics of the frequency doubling and combined frequency absorption of hydrogen-containing groups (such as C-H, N-H, and O-H) to obtain characteristic information of samples, which realizes the detection of key chemical components and physical properties. Compared with traditional detection methods, VIS/NIR technology requires little or no sample preparation and has the characteristics of rapidity, non-destructiveness, real-time application, and low cost. It has been widely applied in the quality detection of agricultural products, such as fruits [5], vegetables [6], cereals [7], and pulses [8]. VIS/NIR spectroscopy is multivariate and contains multiple overlapping peaks related to compounds such as water,

**Citation:** Sun, H.; Zhang, S.; Ren, R.; Xue, J.; Zhao, H. Detection of Soluble Solids Content in Different Cultivated Fresh Jujubes Based on Variable Optimization and Model Update. *Foods* **2022**, *11*, 2522. https://doi.org/10.3390/ foods11162522

Academic Editors: Zhiming Guo, Zhao Zhang and Dong Hu

Received: 6 July 2022 Accepted: 18 August 2022 Published: 20 August 2022

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sugars, and proteins. The prediction accuracy of the VIS/NIR model was affected by some conditions such as samples (for example, maturity, variety, season, year, and batch) [9–11], instruments [12,13], and environment (for example, temperature) [14,15]. Developed models based on VIS/NIR spectral data were generally applicable to the quality detection of samples in a single condition. There is some variability in measured values under the new conditions. Modeling based on the data from the first condition does not involve this variability, and these models are usually not robust for the actual variability. For samples of different conditions, models built with a single condition perform poorly, and the bias and error are generally high.

The damage [16], pest [17], crack [18], SSC [19], and hardness [20] have been carried out in the quality detection of fresh jujubes using VIS/NIR spectroscopy. Those quality detections were implemented in the open-field cultivation mode, and the predicted samples had similar characteristics to those modeling samples. In addition to the open-field cultivation mode, there is also a rain-shelter cultivation mode that adopts the method of building a rainproof shed in the actual "Huping" jujube cultivation [21]. The rain-shelter method can avoid direct contact between rainwater and jujube fruit; reduce the impact of cracking, diseases, and insect pests on jujubes; and have good ventilation performance. Due to the differences in temperature, humidity, and solar radiation between rain-shelter and open-field cultivation, various internal component contents of different cultivated fruit are different, such as pear [22,23], cherry [24], and grape [25]. Inside the samples, the chemical composition is related to its optical absorption properties, and the physical structure is related to its scattering properties. Changes in the texture and internal component contents lead to different optical responses, which would affect the performance of the model built in spectral detection [26,27]. In the above studies of quality detection, spectral detection models were mainly developed for samples cultivated in open fields. However, the analysis of this model prediction performance for fresh jujubes from different cultivation modes is rarely reported.

Several studies have been reported to address the poor performance of models constructed from a single condition. Mishra et al. [28] updated the NIR detection models of the moisture content and SSC for pears, which significantly improved the prediction results for samples of different batches. Sun et al. [29] pointed out that temperature had an influence on the spectral detection model of mango dry matter content and established a robust prediction model using the method of temperature correction. For mango dry matter content based on multi-season, multi-variety, and multi-growing regions, Anderson et al. [30] established a robust prediction model. In order to reduce the influence of instruments, seasons, and temperature changes on the fruit NIR detection model in the study of Mishra et al. [31], calibration models that preserved performance under new conditions were established. The above studies showed that reference measurements from new conditions were generally required in order to compensate for external influences. Model updating was an important method of resolving poor performance when the VIS/NIR model was applied to new conditions. New samples were required in the model update, and the method for determining the number of new samples needed to be investigated. In addition, a reasonable selection of variables could reduce the influence of interfering information and improve model performance due to the high dimensionality and overlapping peaks of VIS/NIR data. There are few studies incorporate wavelength offset properties into the selection of variables.

Therefore, the objective of this study was to develop a robust model for the SSC detection of fresh jujubes from different cultivation modes based on VIS/NIR spectroscopy. To achieve this aim in this study, the IRIV-SPA was used to select characteristic wavelengths, and a new combination of variables was established in combination with wavelength position offset properties. A model update using wavelength fusion-Euclidean distance was proposed to re-calibrate the SSC model. The proposed method achieves the SSC prediction of fresh jujubes from different cultivation modes and improves the generalizability and stability of the model.
