A total of 360 cherries of Prunus avium cv. 'Chelan' cultivated on a commercial farm were collected in three different years: Season 1 (year 2011), Season 2 (year 2012) and Season 3 (year 2016). The farm is located at the boundary of La Almunia de Doña Godina (Zaragoza, Spain) (UTM: 41.500581, -1.324072). The trees were planted in the year 2000, on a planting grid of 5 × 3 m. Drip irrigation was applied at a rate of 25,000 L ha ^-1 h ^-1 . The cherries were collected weekly during the harvest period (May-June) in the first season, at a rate of 50 cherries/week. In the second year, 35 samples were harvested per collection day every three days for two weeks (May-June). In 2016 (June), 78 cherries were collected in optimal harvest dates ( i.e. , when fruits have ripeness parameters - SSC, firmness - within commercialization range). All samples were immediately transported to the analysis laboratory and underwent near-infrared spectroscopy. After collecting Vis/NIR spectra, the SSC was determined for each fruit at the exact same points used for NIR analysis.

The equipment used was QualitySpec Pro 2600 mo­dular reflectance equipment (Analytical Spectral Devices, INC. Colorado, USA) (Figure 1). Fast-scanning spectro­photometry was performed with a measuring range of 350-2500 nm, spectral resolution of 1 nm and a tungsten halogen lamp (12V/45W) as light source. The detection system consists of a monochromator, with a double InGaAs detector. The scanning speed was 10 scans/sec. The light energy was collected through a bundle of specially formulated optical fibres. The fibre-optic cable has a conical view subtending a full angle of approximately 25 degrees. Spectrometer was calibrated using dark and white spectral energy ( Alamar et al ., 2007 ).

The equipment measures the reflection spectra in units of optical density (D.O=log1/Reflectance). Two spectral measurements were made per fruit at two opposing fixed positions at the equator of the fruit, using the mean of the two spectra for the calibration processes. The initial and final parts of the spectra were removed to reduce noise, so the working range was 400-2420 nm.

The total SSC were calculated using a digital refractometer (ATAGO PR-101 Co. Model, Tokyo, Japan). The determined refractive index accuracy was ± 0.2 and the °Brix (%) range 0-53% with automatic temperature compensation. Two SSC values were re­corded for each sample. Firstly, a piece of peel was removed and then a piece of flesh was extracted. Then the flesh tissue was squeezed to extract the juice. The measurement was performed on a drop of cherry juice, running the analysis twice. The same experienced user performed all SSC determinations.

The calibration equations were formulated using two methods of multivariate analysis: PLS and LS-SVM. The software used was Matlab R2014a (The MathWorks, Natick, USA), with its corresponding programming.

Different pretreatments were tested on the study spectra before establishing the calibration models: stan­dard normal variate (SNV), multiplicative scatter co­rrection (MSC), derivative in first and second order, and normalization. Finally, normalization was applied to each of the variables of the spectrum, using mean zero and standard deviation (SD) one. This type of normalization was applied individually to each variable considered, whether it be spectral or otherwise ( Rossi et al ., 2006 ).

In the model calibration, the samples were divided into subsets: calibration and validation groups. The calibration group was used to develop the calibration model and included data from fruit samples belonging to first and second season (years 2011 and 2012). The validation group included data from fruit samples be­longing only to year 2016. The samples were divided according to the ratio 2:1.

For both PLS and LS-SVM methods, the cali­bration models were tested to predict SSC of the samples within the validation set. The best calibration models were selected based on the highest coefficient of deter­mination for cross validation ( R _cv ² ), together with the lowest standard error of cross validation (SECV) ( Williams, 2001 ).

Additionally, the residual predictive deviation (RPD) statistic parameter, calculated as the ratio of the SD of the reference data to the SECV ( Williams, 2001 ) was used. This latter statistic enables SECV to be standardized, facilitating the comparison of results found with sets of different means ( Williams, 2001 ). Williams (2001) points out that RPD values between 3 and 5 indicate a good Vis/NIR prediction efficiency.

With respect to the validation, the effect of the di­fferent settings on the performance of the model was evaluated by comparing the root mean square error of prediction (RMSEP) and the coefficient of external validation ( r ² _p ).

Different spectral ranges were checked to develop calibration models, such as full spectrum, 400-700 nm, 700-1060 nm, 700-2420 nm. In terms of R _cv ² and SECV, the spectral range of 700-1060 nm provided the best results. The selection of this specific spectral range is in agreement with previous studies ( Carlini et al ., 2000 ; Zude et al ., 2006 ; Nicolaï et al ., 2008 ; Travers et al ., 2014 ; Escribano et al ., 2017 ).

Very similar performance results were obtained by the application of both regression models (PLS and LS-SVM) when determining SSC (respectively R _cv ² = 0.97 vs 0.98, SECV=0.86 ºBrix vs 1.03 ºBrix) (Table 2). The RPD values ranged between 4.5 and 5.5. R _cv ² values were very similar, whereas SECV and RPD values were better for the PLS method, as SECV was 0.86º Brix, lower than for LS-SVM method. RPD-PLS was one point above RPD LS-SVM, showing a better calibration for PLS. These results are consistent with studies such us Carlini et al . (2000) that obtained models with high accuracy ( R ² _c =0.97, SEC (standard error of calibration = 0.49). Similarly, Lu (2001) developed very robust models for two cherry varieties; their model R _c ranged from 0.83 to 0.94. When compared with these studies, we registered improved R _cv ² values. However, the fact that a different cherry variety ('Hedelfinger' and 'Sam' cherries) was used in these studies, might also contribute to the differences found.

The correlation coefficients were used for weighing the sensitivity of each wavelength regarding the fruit quality parameter SSC. The sensitive wavelengths iden­tified appeared in one wavelength region, which was 940-980 nm. Model performance was established using these 40 wavelengths ( r ² _p =0.88). Similar results were reported by Qing et al . (2007) , Travers et al . (2014) and Escribano et al . (2017) with a similar range of variables.

Validation is necessary to ensure an independent measurement of the precision for the calibration models through RMSEP and r _p ² . Figure 3 shows the prediction statistics for SSC of the set of cherries from the third season using Vis/NIR calibrations.

The predictive ability of different models was vali­dated by RMSEP and r ² _p , using validation data coming from a different season. The validation sta­tistics were similar for both regression methods, though somewhat better for the linear method (PLS) when estimating the total SSC. RPD _v values were greater (2.78) for PLS than LS-SVM (2.52), pointing to a linear relationship between SSC and spectra. RMSEP for PLS model was lower than for LS-SVM prediction (1.15 ºBrix and 1.27 ºBrix, respectively). Besides RPD _v values were better to PLS model (RPD _v =2.78 in PLS vs RPD _v =2.52 in LS-SVM), which translates into a greater prediction accuracy (Fig. 3). A similar study ( Escribano et al ., 2017 ) analysing the same cherry variety (Chelan) developed a model which reached an RMSEP = 1.01 ºBrix, rp ² = 0.69, RPD _v = 1.28. The difference in re­sults could be due to the use of a different selection of variables (729-975 nm). Accurate and robust pre­dictions might be declined by using noisy regions of the spectra.

In conclusion, NIRS technology using different re­gression strategies provided highly effective models for the prediction of SSC in 'Chelan' cherry. The development of this methodology is of great interest to the fruit sector in the area, facilitating the harvest for future seasons. In this study we developed pre­dictive models to determine SSC in Prunus Avium cv. 'Chelan' via NIR spectroscopy using linear (PLS) and non-linear (LS-SVM) regression methods. The use of non-linear regression methods (LS-SVM) show­ed to be similar to PLS, as they got similar results. An important outcome of this work is the use of data from samples belonging to a different harvest season to build the validation test, and results show that a powerful prediction of SSC can be attained using calibration methods designed with data from previous season. Finally, the selection of variables (940-980 nm) reduced the number of wavelengths to ~ 40, with similar results to those corresponding to the entire interval. This enables the development of much simpler equipment for determining the maturity index of the cherry. Further work is needed on the development of the NIRS methodology and on new calibration equations for other varieties of cherry and other species.