Near-Infrared Model and Its Robustness as Affected by Fruit Origin for ‘Dangshan’ Pear Soluble Solids Content and pH Measurement

Abstract

Soluble solid content (SSC) and acidity (pH) are two important factors indicating the fruit quality of pears and can be measured by near-infrared spectroscopy (NIRS). However, the robustness of these measurements as affected by different origins of pears remains largely unknown. In this study, we developed an NIRS method to measure ‘Dangshan’ pear (Pyrus spp.) SSC and pH and evaluated the robustness of this non-destructive detection method by examining the effects of pears from three different origins in 2019 and 2020. First, the Kennard–Stone method was used to divide the calibration set of the 2020 pear samples from different orchards. The partial least squares (PLS) model was used to establish the local origin and hybrid origin models to predict the pears’ SSC and pH. Second, a combination of competitive adaptive reweighted sampling (CARS), successive projections algorithm (SPA), and uninformative variable elimination (UVE) was implemented to construct spectral prediction models based on effective variables for assessing the pears’ SSC and pH from local and hybrid origins. The results showed that the local origin detection model produced large errors in predicting the SSC and pH of pears from different origins, and the model, established based on the pear samples of three origins, performed better than the local origin and other hybrid origin models. Finally, the model could be effectively simplified using 70 and 52 characteristic variables selected by the CARS method. Pear samples harvested from three different orchards in 2019 were used as an independent set to verify the validity of the selected characteristic variables. The results showed that the predicted R²_p for the SSC and pH measurements of pears of three different origins were more than 0.9 and 0.85, respectively. This finding indicates that the difference in the origin of pears has an important influence on the quantitative inversion of pear SSC and pH measurements, and the combination of the hybrid origin model constructed based on the characteristic variables can improve the prediction accuracy. These findings provide an important theoretical basis for the development of rapid detection devices for the measurements of pears’ SSC and pH.

1. Introduction

Pears are one of the most widely consumed fruits in the world [1]. They are crispy and juicy and have a good combination of sweetness and sourness. Pears are rich in malic acid, citric acid, glucose, fructose, calcium, phosphorus, iron, vitamins, and other nutrients. China is ranked number one in global pear production, with approximately 1731 tons of pears harvested in 2019 [2]. However, the technologies used for pear quality testing and grade classification in China are evidently lagging compared to most developed countries. With an increasing demand for high-quality products in the fresh fruit market, one of the main goals of the current fruit industry is to provide the market with products that are not only good-looking but also have a high-quality taste [3]. Fruit acidity (pH) and soluble solids content (SSC) are two important factors that affect the taste and quality of pears and directly influence consumers’ desire to consume pears. Most traditional methods for fruit pH and SCC measurements are destructive, inefficient, and time-consuming [4]. Therefore, developing non-destructive, efficient, and convenient assessment methods for the fruit pH and SSC can help further promote the development of China’s pear fruit industry.

The use of hyperspectral imaging (HSI) to detect the internal quality of fruit has been developed very rapidly in recent years. The HSI has the advantage of combining traditional imaging and spectroscopic techniques. Peng and Lu [5] used hyperspectral scattering for non-destructive detection of various quality attributes of apples. They evaluated and compared different mathematical models to describe hyperspectral scattering profiles in the 450–1000 nm spectral region, and successfully selected the best model to predict apple hardness and SSC. Li and Chen [6] examined hyperspectral imaging in the visible and near-infrared (NIR) spectral range (400–1000 nm) to determine each SSC non-invasively. They developed a more robust and accurate model based on multi-regional information. Fan et al. [7] studied the SSC and hardness of pears using hyperspectral imaging and constructed a partial least squares (PLS) prediction model based on the CARS-SPA algorithm to select the characteristic variables. The correlation coefficient (R_pre) of 0.876 for SSC and 0.867 for hardness demonstrated that the hyperspectral imaging system and the CARS-SPA-PLS model can be used as rapid and potential methods for the SSC and hardness determination of pears. However, hyperspectral imaging techniques contain large hyperspectral data cubes that require much higher hardware speed to accommodate data acquisition and analysis [8]. Relatively, the non-imaging spectral data selected for the current study requires lower CPU, memory, and display functions that facilitate processing [9].

Near-infrared spectroscopy (NIR) is a low-cost optical detection technique with the advantages of non-destructiveness, rapidity, precision, control, accuracy, repeatability, and reproducibility [10]. Its main principle is to analyze the spectral responses of different chemical bonds in organic matter in the near-infrared interval of the electromagnetic spectrum. The organic matter in the sample has different spectral fingerprints, such as C-H, N-H, and especially O-H, due to the different specific vibrational frequencies of the chemical bonds [11]. The wealth of information absorbed by these chemical bond vibrations helps in the construction of multi-variate calibration models for food quality analysis [12]. In recent years, NIR technology has been widely used in the non-destructive testing of pears. Sun et al. [13] established a non-destructive detection method for the determination of the internal blackheart and SSC of pears and demonstrated that the online detection of internal blackheart and SSC of pears using non-imaging NIR spectroscopy was feasible. Wang et al. [14] used a portable non-imaging visual NIR spectrometer (model K-BA100R; Kubota Co., Osaka, Japan) to demonstrate the feasibility of a multi-species model for the in-situ determination of the internal quality of European pears. The MLR SSC prediction model was developed with the best R² of 0.87 and an RMSEP of 0.45. Sun et al. [15] used non-imaging Vis/NIR spectroscopy to accurately predict the SSC of “Cuiguan” pear online. The developed SSC-PLS calibration model had a coefficient of determination (R²) and a root mean square error of prediction (RMSEP) of 0.916 and 0.530, respectively.

Non-imaging spectrometers can obtain large amounts of spectral data that suffer from severe covariance problems and inevitably contain interference and useless information. If the Partial least squares (PLS) model is built based on the full wavelength, it will not only increase the complexity of the model, but even decrease the prediction performance of the model [16]. Therefore, it becomes necessary to screen the effective feature wavelengths. Travers et al. [17] developed regression models for measuring pre-harvest dry matter and SSC in the spectral ranges of 680–1000 nm and 1100–2350 nm for pears. They demonstrated that both spectra in the two band intervals were good detectors of dry matter and SSC. They also found that the internal quality detection model of pears using the spectral range of 1100–2350 nm performed better. Xu et al. [18] compared four wavelength variable screening methods, and the results showed that the accuracy of vis-NIR spectroscopy for quantitative analysis of pear saccharinity could be improved by selecting the appropriate wavelength. Li et al. [19] used visible-NIR spectroscopy combined with PLS, LV-LS-SVM, and EW-LS-SVM models to successfully determine pear SSC, pH, and hardness; the EW-LS-SVM model has better robustness and reliability. PLS and LS-SVM models constructed in the 400–1800 nm spectral range were found to be more suitable for SSC, pH, and hardness prediction than those in the 400–780 nm and 781–1800 nm spectral ranges.

In these studies, each of the testing models or methods has unique advantages and characteristics and achieves expected testing results. However, there are at least four limitations to these studies. First, the samples used in these studies were mostly purchased from the fruit market, and thus the picking time and storage time are unclear. The storage time affects the internal quality detection results of pears. Second, the origin or source of the fruit samples used in those studies is unclear, and almost none of the studies involve hybrid pear varieties, an important origin of pears. Third, most of the studies examine pear samples collected from a single year, and no research has been conducted on pear samples obtained from multiple years. Fourth, most studies lack independent validation or robustness verification. The introduction of multiple years or batches of data is crucial for validating the model’s robustness [20]. Model verification should be performed to examine the stability and robustness of the models.

The objectives of this research are to (1) test whether NIRS has a good ability to predict the SSC and pH of ‘Dangshan’ pears (cv. Dangshan), (2) identify the effective characteristic wavelength variables for predicting pear SSC and pH, (3) develop models and evaluate their performance for predicting the SSC and pH in local and hybrid pear origins by using full and effective variables, and (4) test the stability and accuracy of the models using independent validation pear sample sets from different years.

2. Materials and Methods

2.1. Experimental Pear Samples

Sample group 1: Production management practice and location significantly affected the yield and quality of pear. To increase the diversity of pear internal quality on pH and SSC, 496 pear samples without visual defects (e.g., scars, cuts, and wrinkles) were collected from three different orchards with different farming management practices (

Table 1. Pear production management practices used in three different orchards.

Origin *	Production Management Practices
TZ	Rough farming management
LSW	Rough and fine combined farming management
YH	Modern management

Note: * Tangzhai (TZ), Lishuangwang (LSW), and Yihao (YH).

). The samples were obtained in September 2020 from Tangzhai (TZ), Lishuangwang (LSW), and Yihao (YH) orchards in Dangshan County, Suzhou City, Anhui Province, China (Figure 1).

Sample group 2: A total of 450 pear samples were collected in 2019 from Lishuwang 1 (LSW1), Huanghegudao Farm (HHGD), and Lishuwang 2 (LSW2) orchards. These pear samples were used as an independent validation data set to test the robustness of the proposed model that detected the internal quality (pH and SSC) of pears.

All pear samples were cleaned and placed at a constant temperature (20 °C) for 24 h before they were used to reduce the effect of temperature on the accuracy of the pH and SSC prediction models [21]. Three areas with a diameter of 3 cm were marked as measurement points near the equator of each pear by taking a point at an interval of 120 degrees.

2.2. Spectral Data Acquisition

Spectral reflectance data for all the pear samples in this study were obtained using measurements with a PSR+3500 non-imaging portable spectrometer (Spectral Evolution, Haverhill, MA, USA) equipped with a 25° viewing angle fiber. This spectrometer has a spectral measurement range of 350–2500 nm and a spectral resolution between 3 and 8 nm. All spectral data acquisition was performed in a dark room to reduce the influence of external light on the observed spectra. In this case, the illumination system, which consisted of two 350 W halogen lamps, was placed at an angle of 45° on either side of the console and 40 cm from the carrier table to ensure light coverage of the entire pear. During the spectroscopic measurements, the fiber optic probe was fixed at the appropriate position, and the pear samples were placed 7 cm below the lens to ensure that the measurement environment was consistent for each sample. This distance was determined by Equation (1), as follows:

$$\mathrm{H}=\frac{\tan \mathsf{\alpha }}{\mathrm{R}}$$

(1)

where H is the distance from the fiber optic lens to the target nucleus, α is the fiber optic field of view angle, and R is the field of view radius. The spectral acquisition system is shown in Figure 2.

Calibration set and prediction set partitioning using the Kennard–Stone method can remarkably improve the accuracy of model predictions; it is widely used in the field of qualitative analysis of spectral data [22]. In the present study, the Kennard–Stone method was used to divide the calibration and prediction sets of pear samples from different production areas at a ratio of 3 to 1.

2.3. Measurement of pH and SSC

After the spectral data collection was completed, the pH and SSC of ‘Dangshan’ pears were measured using a portable pH tester (Testo 206 PH1) and a digital display saccharimeter (CHT65), respectively. A 10-mm skinned pulp from the equatorially marked part of the collection point was taken and filtered by manually pressing on gauze. Then, half of the pear juice was poured into the sample slot of the digital display saccharimeter, and a measured SSC value was recorded. A portable pH tester probe was inserted into the test tube containing the remaining pear juice, and the measured pH value was recorded.

2.4. Data Analysis

2.4.1. Spectral Pre-Processing

During the spectral data acquisition, disturbances, such as external stray light, sample background, electronic sources, and instrument performance, can cause baseline translation and rotation as well as spectral scattering [23]. The original reflectance spectra should be pre-processed to eliminate or attenuate the effects of non-target factors, and thus build a stable detection model. The original reflectance spectral data were pre-processed using multiple scattering correction (MSC) [24], standard normal variables (SNV) [25], Suavity–Golay smoothing [26], first-order derivatives, second-order derivatives [27], and maximum normalization.

2.4.2. Effective Variables Selection

The full-band spectral data were pre-processed to remove some noise information. However, they still contained excessive wavelength information variables. The PSR+3500 spectrometer contains more than 2000 wavelengths. If the full spectral bands are used for modeling and analysis, then the cost of equipment computing and running time increases. More importantly, the covariance problem of spectral data and the large number of wavelength variables are unrelated to the detected object, thereby affecting the prediction accuracy and stability of the model [16]. Therefore, selecting effective information variables from the full wavelength band is important. Several commonly used methods for effective wavelength selection are described in the following section.

(1)

Competitive adaptive reweighted sampling (CARS)

The CARS algorithm is a wavelength selection method proposed by Li et al. that can select the optimal combination of wavelengths in the full spectrum [28]. The most important evaluation metric for CARS variable selection is the absolute value of the PLS model regression coefficients. CARS uses an iterative competitive approach to sequentially select a subset of N variables from N Monte Carlo sampling runs. The number of wavelengths selected for each sample is then determined by an exponentially decreasing function (EDF) and adaptive reweighted sampling (ARS). Finally, the most critical variable for the prediction target is selected on the basis of the minimum root mean square error of each subset cross-validation (RMSECV). The PLS subset model is selected using 10 cross-validations, and the number of Monte Carlo samples is set to 50. When the RMSECV reaches its minimum value, the corresponding subset is the optimal variable subset [29].

(2)

Successive projections algorithm (SPA)

The SPA algorithm can effectively select spectral feature variables. The smallest combination of redundant information variables is screened in the spectral information by using vector projection analysis to reduce the number of modeled variables by minimizing the covariance between them [30]. The principle of the SPA algorithm for screening variables is to initially create a subset of candidate variables with the smallest covariance as a result of a projection operation on the columns of the spectral matrix that could be used in the training data. Then, the results of the multiple linear regression model are evaluated using cross-validation or by applying the results of a separate validation set. Finally, uninformative variables that contribute to the loss of predictive power are eliminated [31,32].

(3)

Uninformative variable elimination (UVE)

The UVE algorithm is a variable screening method commonly used to process spectral data. The method initially evaluates the reliability of each variable in the model by means of variable selection criteria, it assesses the stability of each variable. Then, variables containing redundant information in the spectral information are eliminated [33]. Modeling with the variables selected by UVE could effectively solve the over-fitting problem and improve the predictive power of the model [34]. UVE could not only eliminate redundant information variables when processing spectral data but also reduce the computing time [35].

2.4.3. Model Building

PLS is a multi-variate statistical method that is sensitive to non-collinear variables. It can handle data sets with a large number of variables and is widely used in regression model construction because of its simplicity of use, stability of performance, and ease of access. PLS was used to identify the fundamental relationship between two matrices (X and Y), the spectral matrix (X) and the target chemical composition matrix (Y), and to search for a set of latent variables (LVs) to perform X and Y decomposition [36]. PLS was used to filter spectral data LVs. The optimal number of LVs was determined by the minimum of the sum of squared errors, thereby eliminating redundant information and random errors in the original data. The ideal model should have a low RMSEC and RMSE of validation or prediction (RMSEP) [37].

The effects of appellation and year differences on the NIR spectral detection of SSC and pH values of ‘Dangshan’ pears were investigated comprehensively. Spectral prediction models for SSC and PH values of pear from local origin models (Case a) and hybrid origin models (Case b) were developed (Figure 3). First, the PLS models for three different origins were established with the calibration set data of pear samples from Pear King Orchard, Pear One Orchard, and Tangzhai Town Farm in 2020, respectively, and the SSC and pH of pears produced by each of the three origins were predicted. Then the PLS models of each origin were validated using the validation set data of the three origins in 2020, respectively (Case a). The calibration set samples from the three production locations were then mixed to create an integrated hybrid origin model to predict the SSC and pH of pears of different origins (Case b I). The model was verified and further observed to see whether it was affected by pear origin and test year. The validity of this model was verified using the spectral information of 450 pear samples obtained in 2019 from Pear King No.1 Orchard (LSW1), Yellow River Gorge Farm (HHGD), and Pear King No.2 Orchard (LSW2); these data were used as the prediction set (Case b II). The performance of the two detection models was compared, and the more accurate and robust model was selected for further analysis.

2.4.4. Model Evaluation

The coefficient of determination (R²_c and R²_p) and the RMSE (RMSEC and RMSEP) were used to evaluate the performance of the model. In general, a good model has high R²_c and R²_p values and low RMSEC and RMSEP values [38,39,40]. The R²_c and R²_p values should be close to 1, and the RMSEC and RMSEP values should be connected to 0. The formulae for calculating R²_c and R²_p, RMSEC, and RMSEP are as follows:

$${\mathrm{R}}_{\mathrm{c}}^2=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{c}}}{\left(\widehat{{\mathrm{y}}_{\mathrm{i}}}- \mathrm{y} ¯\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{c}}}{\left({\mathrm{y}}_{\mathrm{i}}- \mathrm{y} ¯\right)}^2}$$

(2)

$${\mathrm{R}}_{\mathrm{p}}^2=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{p}}}{\left(\widehat{{\mathrm{y}}_{\mathrm{i}}}- \mathrm{y} ¯\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{p}}}{\left({\mathrm{y}}_{\mathrm{i}}- \mathrm{y} ¯\right)}^2}$$

(3)

$$\mathrm{RMSEC}={(\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{c}}}{\left({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}}\right)}^2)}^{\frac{1}{2}}$$

(4)

$$\mathrm{RMSEP}={(\frac{1}{\mathrm{N}}{{\displaystyle \sum }}_{\mathrm{i}-1}^{{\mathrm{N}}_{\mathrm{p}}}{\left({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}}\right)}^2)}^{\frac{1}{2}}$$

(5)

where y indicates the data to be fitted with a mean value of $\overline{\mathrm{y}}$ and predicted value of $\hat{\mathrm{y}}$; and N is the total number of predicted samples.

3. Results

3.1. Spectral Characterization of Pear of Different Origins

Figure 4a shows the original reflectance spectral information of 496 pear samples collected in 2020 in the wavelength range of 350–2500 nm. Sample reflectance showed very distinct peaks near 400, 680, 1150, and 1550 nm. The absorption peak at approximately 400 nm was associated with the absorption of carotenoids, such as lutein and β-carotene [41]. The absorption peak near 680 nm might be related to the absorption band of chlorophyll [42]. The absorption peak at approximately 1150 nm was related to the first overtone of the O-H band in water [36]. The absorption peak at approximately 1550 nm was related to the stretching and bending of O-H [30]. The average spectral curves of the pear samples from the three origins are shown in Figure 4b. The figure shows that the spectral curves had similar trends, but the reflectance intensities were different at different wavelengths. This finding indicates that the different pear internal substances were the same, but the content of each compound was different. The difference in spectral reflectance intensities is a prerequisite for building the regression model [43].

After the analysis and comparison of the preprocessing algorithms, the preprocessed spectra by the SNV method were used for subsequent variable selection and modeling in this study. The original spectral profile (Figure 4a) and the SNV preprocessed spectral profile (Figure 5) were observed. The results showed significant bursts in the visible (959–985 nm) and NIR (1842–1859 nm) band ranges. Therefore, only 2004 wavelength points in the 400–958, 986–1841, and 1859–2450 nm spectral ranges were used for the analyses.

3.2. Analysis of SSC and pH of Pear of Different Origins

The test sample calibration set and prediction set were divided into a ratio of three to one, and the results of the division of the actual measured values of pH and SSC of ‘Dangshan’ pear samples from four different locations are shown in

Table 2. Measured values of acidity (pH) in ‘Dangshan’ pear in the calibration and prediction data sets of four different origins.

Origin *	Sample Set	No. of Samples	Min	Max	Mean	Standard Deviation
LSW	Calibration set	90	4.90	6.22	5.24	0.17
	Prediction set	32	5.16	5.55	5.31	0.07
TZZ	Calibration set	114	4.77	5.64	5.33	0.10
	Prediction set	37	5.10	5.55	5.39	0.15
YH	Calibration set	168	4.85	5.53	5.30	0.10
	Prediction set	55	5.13	5.47	5.29	0.09
hybrid	Calibration set	372	4.77	6.34	5.31	0.14
	Prediction set	124	4.85	5.53	5.30	0.10

Note: * Lishuangwang (LSW), Tangzhai (TZ), and Yihao (YH).

and

Table 3. Measured values of soluble solids content (SSC/%) in ‘Dangshan’ pear in the calibration and prediction data sets of four different origins.

Origin *	Sample Set	No. of Samples	Min	Max	Mean	Standard Deviation
LSW	Calibration set	90	7.23	10.63	9.36	0.61
	Prediction set	32	8.13	10.47	9.15	0.47
TZZ	Calibration set	114	6.57	11.20	8.86	0.74
	Prediction set	37	6.97	10.90	8.69	0.98
YH	Calibration set	168	7.23	11.97	9.73	0.90
	Prediction set	55	8.27	11.33	9.89	0.76
hybrid	Calibration set	372	6.57	11.97	9.02	0.78
	Prediction set	124	7.23	11.20	9.84	0.86

Note: * Lishuangwang (LSW), Tangzhai (TZ), and Yihao (YH).

. The maximum value, minimum value, mean value, standard deviation, and range of values of SSC and pH of ‘Dangshan’ pears in different locations were different. The statistical values indicate that the mean pH values of pear in the four different locations were between 5.24 and 5.39, indicating that the pH of pear does not vary remarkably with pear origin and is relatively stable. For SSC, the highest average value (9.89) was found in pears from Yihao Orchard, whereas the lowest average value (8.69) was found in pears from Tangzhai Farm, which is 12% lower than that of the former. This difference could be attributed to the differences in fertilization and cultivation management practices between the two locations. Tangzhai Farm and Lishuwang Orchard were considered to have rough farming practices and rough-to-fine farming practices in terms of fertilization and agronomical management. In these orchards, applications of chemical and organic fertilizers were not based on soil testing recommendations, but on personal experience. In contrast, Yihao Orchard adopted modern production management practices and made balanced applications of chemical, farmyard manure, and biological fertilizers via soil and foliar treatments based on soil testing recommendations to meet the needs of pear plant growth. In addition, other modern techniques, such as proper pruning and effective disease and weed and insect pest management, were adopted. These modern farming practices contributed to the improvement of pear quality [22]. The differences in farming practice also contributed, to some extent, to the significant differences observed in pear spectra among the four different orchards.

The results also showed that the ranges of pH and SSC in the prediction data sets were all within the ranges of pH and SSC in the calibration data sets (Table 2 and Table 3). These findings indicate that the developed pH and SSC prediction models can be applied to predict the pH and SCC in pears. This creates a condition that can help construct a more stable and reliable prediction model.

3.3. Modeling Analysis of pH and SSC of Pear of Different Origins

3.3.1. Local Model

The PLS models for three local pear origins were developed to predict the SSC and pH of pears produced by Lishuwang Orchard, Yihao Orchard, and Tangzhai Farm, and were validated with the pear samples from the calibration sets of different origins. The prediction results of the full spectrum-based PLS model based on the different prediction data sets are shown in

Table 4. Prediction results of the soluble solids content (SSC) and acidity (pH) detection models for local pear origins.

Parameters	Calibration Set *	Prediction Set
		LSW		TZ		YH
		R2p	RMSEP	R2p	RMSEP	R2p	RMSEP
SSC	LSW	0.913	0.201	0.803	0.330	0.843	0.268
	TZ	0.831	0.279	0.896	0.218	0.880	0.243
	YH	0.899	0.218	0.774	0.418	0.930	0.175
pH	LSW	0.914	0.026	0.790	0.046	0.836	0.039
	TZ	0.693	0.058	0.880	0.030	0.742	0.056
	YH	0.898	0.028	0.749	0.051	0.914	0.025

Note: * Lishuangwang (LSW), Tangzhai (TZ), and Yihao (YH).

. All the PLS models could effectively predict the pear SSC and pH. The local model based on the calibration set of pear samples of the same origin achieved a better prediction for all the samples in the prediction set of the same origin.

In the actual production situation, if the SSC or pH value models were constructed separately for each pear origin, the workload would be massive even when the detection results were improved. This condition is not favorable for practical application. For SSC and pH prediction of unknown origin samples, initially determining their origin information based on spectral information is necessary. Subsequently, the SSC and pH values are predicted based on the model under the corresponding origin; otherwise, the model prediction accuracy is affected [44]. However, this process is excessively tedious in accordance with the appellation determination results in the first step. Therefore, the established local origin model was applied to the prediction set samples from other pear production locations, and the results are shown in Table 4. The results show that the detection model with a local origin produced large errors when predicting the SSC and pH of pears from different origins. For example, using the proposed models, the RMSEP of the Lishuwang origin was 0.279 and 0.218, which was significantly greater than the 0.201 corresponding to the model built for the Lishuwang calibration set. The prediction coefficients of determination were also reduced to a varying degree. Similar conclusions could be drawn for the predictions of pears from all other locations. All exhibited a decrease in R²_p and an increase in RMSEP values. There was a maximum difference of 0.156 for R²_p and 0.243 for RMSEP in the SSC prediction, and a maximum difference of 0.187 for R²_p and 0.028 for RMSEP in the pH prediction. Therefore, the SSC and pH detection models for a local origin cannot satisfy the actual production requirements, and establishing a comprehensive model for hybrid (multiple) pear origins is needed for practical application.

3.3.2. Integrated Model for Hybrid Pear Origins

The calibration set of pear samples of different origins was combined, two-by-two, to establish a mixed NIR spectral detection model for pH and SSC of pears from two locations to further characterize the effect of pear origin on the pH and SSC spectral detection model. Then, the calibration set of pear samples from three locations was integrated to establish a comprehensive hybrid origin model, and the results are shown in

Table 5. Predicted results of the soluble solids content (SSC) and acidity (pH) detection model for hybrid (mix) pear origins.

Parameters	Calibration Set	Prediction Set
		LSW		TZ		YH
		R2p	RMSEP	R2p	RMSEP	R2p	RMSEP
SSC	LSW-TZ	0.906	0.202	0.873	0.261	0.885	0.228
	LSW-YH	0.890	0.224	0.802	0.332	0.913	0.201
	TZ-YH	0.845	0.265	0.901	0.215	0.913	0.201
	LSW-TZ-YH	0.919	0.180	0.906	0.202	0.921	0.178
pH	LSW-TZ	0.903	0.027	0.851	0.036	0.897	0.030
	LSW-YH	0.887	0.030	0.780	0.049	0.855	0.032
	TZ-YH	0.810	0.044	0.824	0.044	0.838	0.039
	LSW-TZ-YH	0.935	0.019	0.850	0.038	0.918	0.020

.

The prediction accuracy of the model continued to improve as the spectral information of pear samples from more origins was combined in the calibration set. The model built by integrating spectral information of pears from three origins was significantly better than that built by combining spectral information of pears from two origins. Moreover, the model built by combining the calibration sets of all three pear origins achieved better detection results for the prediction set of pear samples from the three origins. Therefore, when the calibration set contained more spectral information about pears from different origins, the constructed models achieved better predictions of SSC and pH values for pear samples from different origins. Thus, the influence of the pear origin on the spectral detection models of pH and SSC decreased. However, the full-band NIR spectra had 2004 wavelength variables, and the covariance between wavelengths and redundant information resulted in a more complex model; the PLS modeling time increases linearly with the increase in variables [45]. Therefore, to further simplify the detection model, an attempt was made to preferentially select the characteristic wavelengths used for assessing SSC and pH using CARS, SPA, and UVE methods to select characteristic wavelength-based prediction models for SSC and pH values.

3.3.3. Integrated Models for Different Pear Origins Based on Characteristic Wavelengths

The results of the CARS algorithm in selecting the effective variables of SSC and pH values of pear are shown in Figure 6. The results show that the number of selected variables decreased continuously with the increase in sampling size, and the rate of decrease appeared to change from fast to slow as a result of the exponential decay function (EDP) (Figure 6aI, bI). This finding indicates that the CARS algorithm uses a screening scheme that combines coarse and fine selection, which greatly improves the efficiency of variable selection. Figure 6aII, bII show the variation curves of RMSECV versus the number of variables. The RMSECV showed a slight decrease with the increase in the number of samples. When the number of samples was 25, the RMSECV reached its lowest point and then started to increase. This process was the result of eliminating the wavelengths that carried redundant information. The optimal set of variables was selected when the sampling number was 25 and the RMSECV was minimal. CARS selected 70 and 52 variables as valid variables for predicting SSC and pH values of ‘Dangshan’ pear, respectively.

A clear relationship was found between the number of wavelengths selected by SPA and the RMSEP value. Therefore, when the number of selected wavelengths increased, the RMSEP value decreased and then stabilized when it reached a certain value. The overall trend remained the same despite the small fluctuations in the process. The SPA algorithm selected the pear SSC and pH value feature variables. As shown in Figure 7a,b, the RMSEP value stabilized when the number of selected variables exceeded 18 and 11, but the RMSEP reached its best value at 18 and 11 variables (marked as red rectangles). SPA selected 18 and 11 variables as effective variables for predicting SSC and pH of ‘Dangshan’ pears, respectively.

Valid variables were selected using UVE for 2004 wavelengths of the preprocessed full-spectral variables, where the number of random variables was set to 200. The results of selecting the pear SSC and pH feature variables are shown in Figure 8a,b. The blue vertical line in Figure 8 indicates the demarcation line between the input spectral variables and random variables; the red curve to the left of the demarcation line depicts the distribution of the spectral variable’s T-values; and the random variable’s T-values are distributed to the right of the blue demarcation line, as indicated by the purple curve. The threshold used to filter the valid variables was determined by the random variable, the T-value_max, of the maximum value of the random variable T-value, and the threshold was triggered when the T-value of the random variable was equal to 0.99 times the T-value_max. The variables outside the two dashed lines were the valid variables selected, and the remaining variables in between the two lines were excluded. A total of 505 and 557 variables were selected by UVE as valid variables for predicting SSC and pH values of ‘Dangshan’ pears, respectively.

The characteristic variables selected by the three algorithms were used as input variables to construct the PLS prediction models for assessing the SSC and pH of ‘Dangshan’ pears, and the results are shown in

Table 6. Prediction results of different PLS models for the prediction set of SSC and pH of ‘Dangshan’ pears from various origins.

Parameters	Model	Variables	Prediction Set *
			LSW		TZ		YH
			R2p	RMSEP	R2p	RMSEP	R2p	RMSEP
SSC	PLS	2004	0.919	0.180	0.906	0.202	0.921	0.178
	CARS-PLS	70	0.903	0.210	0.904	0.206	0.943	0.142
	SPA-PLS	18	0.875	0.258	0.890	0.221	0.876	0.248
	UVE-PLS	505	0.884	0.235	0.894	0.220	0.913	0.201
pH	PLS	2004	0.935	0.019	0.850	0.032	0.918	0.020
	CARS-PLS	52	0.897	0.029	0.917	0.022	0.874	0.032
	SPA-PLS	11	0.884	0.031	0.824	0.044	0.862	0.033
	UVE-PLS	557	0.903	0.027	0.936	0.018	0.915	0.024

Note: * Lishuangwang (LSW), Tangzhai (TZ), and Yihao (YH).

. For the prediction of SSC, the constructed CARS-PLS model performed the best and achieved better prediction results for the three different pear origins, namely, Lishuwang Orchard, Tangzhai Farm, and Yihao Orchard. Among them, the prediction results of R²_p = 0.943 and RMSEP = 0.142 for the Yihao Orchard were better than the prediction results of R²_p = 0.921 and RMSEP = 0.178 for the full wavelength. The prediction results of the other two locations, Lishuwang Orchard and Tangzhai Farm, were close to the prediction results of the full wavelength. The CARS-PLS model used only 3.5% of the characteristic variables of the full wavelength and achieved prediction results close to or even better than the full-wavelength model. SPA, although it selected the smallest number of variables, performed slightly worse than the other two models, where R²_p was above 0.87. The prediction results of the UVE-PLS model were better than those of the SPA-PLS model, where the R²_p was greater than 0.88. However, the number of input variables was much greater than those of the CARS-PLS and SPA-PLS models, and it was not the best model. Therefore, the UVE-PLS model outperforms the CARS-PLS and SPA-PLS models, and the UVE-PLS model is the best model in terms of prediction accuracy. In addition, the CARS-PLS model is the second-best model, which is better than the SPA-PLS model. However, considering the number of characteristic variables, the UVE-PLS model had 557 input variables, while the CARS-PLS model had only 52 input variables. Thus, the model based on the 52-feature wavelengths by the CARS was selected as the best model for pear pH detection. The results of the comprehensive analysis indicate that the performance of the CARS-PLS model is ideal in the prediction of pear SSC and pH. Accurate predictions of the SSC and pH of pears from different production areas can be achieved, and the influence of pear origin on the model can be reduced.

3.4. Model Validation

To verify the validity of the CARS-PLS model and to determine whether it was affected by variability in pear origin and test year, its validity was verified using 450 pears harvested in 2019 from Lishuwang 1 Orchard (LSW1), Yellow River Gorge Farm (HHGD), and Lishuwang 2 Orchard (LSW2) (Figure 1).

The pear SSC and pH (

Table 7. Statistical results of the measured fruit acidity (pH) values of all ‘Dangshan’ pear samples.

Origin	No. of Samples	Min	Max	Mean	Standard Deviation	F	p
LSW1	207	5.03	5.87	5.63	0.095	75.723	0.000 **
HHGD	109	5.43	5.85	5.66	0.085
LSW2	134	5.25	5.90	5.675	0.100

Note: ** p < 0.01. F is F-ratio and p is probability value.

and

Table 8. Statistical results of the measured fruit soluble solids content (SSC/%) values for all ‘Dangshan’ pear samples.

Origin	No. of Samples	Min	Max	Mean	Standard Deviation	F	p
LSW1	207	9.97	13.77	11.67	0.620	5.7	0.004 **
HHGD	109	10.5	13.37	12.18	0.595
LSW2	134	9.40	13.33	11.27	0.595

Note: ** p < 0.01. F is F-ratio and p is probability value.

) were measured for the 450 Dangshan pear samples using the same method and instrumentation to collect spectral information (Figure 9).

The average spectral curves of the pear samples for both years (Figure 10) were observed and found that although the general trend of the spectral curves was the same, the spectral features were remarkably different at several characteristic peaks. This finding indicates that the internal substances of the pear were essentially the same in both years, but the content of each compound was different. The comparison of Table 2, Table 3, Table 7 and Table 8 further illustrates the remarkable differences between the data from 2019 and 2020. The SSC value for the 2020 pear samples ranged from 6.57 to 11.97, and the SSC value for the 2019 pear samples ranged from 9.40 to 13.77, which was higher than the 20-year range of approximately 15.03–43%; the mean value reached 11.70, which was much higher than the 2020 value of 9.43. The 2020 pear samples had pH values in the range of 4.77–6.34, with a mean value of 5.305, and the 2019 pH ranged from 5.03 to 5.90, with a mean value of 5.65, which was also significantly different than the mean value of the 2020 pear samples.

The factors contributing to these differences mainly include light, precipitation, fertilization, and others. However, light and precipitation are among the most important factors. The query data in the key growth period of pear in the 3-month period indicates that Dangshan County, where the pear samples were collected from, had significantly more cloudy and rainy days in 2020 than in 2019. Rainfall was also much more in 2020 than in 2019; light intensity was significantly less than the average level in 2019 within the same period of time. More cloudy and rainy days and small temperature differences between day and night could significantly affect pear photosynthesis and weaken their photosynthesis, resulting in less sugar accumulation, which was the most important factor leading to the large difference between 2019 and 2020 [46]. In addition, increased precipitation led to poor soil permeability and reduced soil microbial activity, resulting in poorer nutrient uptake by pear trees, which thereby affected the internal quality of pears [16].

The pear SSC and pH values were predicted directly using the CARS-PLS model, constructed based on the pear samples from three different orchards in 2019 to verify the validity of the model in Section 3.3 and to observe whether it was affected by the variability of pear origin and test year. In addition, the spectral information of 450 pear samples was used as the prediction set after preprocessing.

The predicted results are shown in

Table 9. Validation results for the 19-year samples.

Parameters	Model	Variables	Prediction Set
			LSW1		HHGD		LSW2
			R2p	RMSEP	R2p	RMSEP	R2p	RMSEP
SSC	CARS-PLS	70	0.913	0.201	0.930	0.167	0.916	0.185
PH	CARS-PLS	52	0.899	0.028	0.853	0.032	0.906	0.027

. The results show that the predicted R²_p for SSC was above 0.9 in the three different orchards, and the predictions for pH were slightly lower. R²_p was also above 0.85 for all orchards. Although the 19-year data samples were very different from the 20-year data samples, the model achieved valid predictions for the fruit SSC and pH for the 19-year pear samples.

Considerable progress has been achieved in the non-destructive detection of the internal quality of pears in recent years. Yu et al. [47] developed a handheld spectrometer using a linear variable filter (LVF) and a complementary metal oxide semi-conductor (CMOS) linear detector array, which successfully detected the SSC of pears in the 620–1080 spectral interval. Although this method achieved handheld online detection, only the spectral interval at 620–1080 was used for modeling and analysis, and no comparative study of different spectral intervals was conducted. In their study, there was also a lack of an independent validation process that could demonstrate the universal applicability of handheld spectrometers developed based on the 620–1080 spectral interval. Li et al. [48] investigated the quantitative determination of three pear varieties using a multi-species model. A multi-species model and a local origin model were developed and optimized using different variable selection algorithms. The coefficient of determination of the prediction set (R²) and RMSEP of the model were 0.92 and 0.30, respectively, demonstrating the feasibility of accurately determining the SSC of different pear varieties using the multi-species model. Passos et al. [49], based on short-wave NIR spectroscopy in packaging and sorting facilities, successfully detected the SSC of pear samples from different batches, storage times, and maturity levels. They further found that incorporating temperature and fruit size information into the detection model could improve the predictability of fruit SSC. Li et al. [48] and Passos et al. [49] studied multiple pear varieties, batches, and other factors, such as temperature and fruit size. However, only a single detection of the SSC of pear samples was performed, and fruit pH, another important index affecting the internal quality of pears, was not investigated. The effect of pear origin on the non-destructive detection of the internal quality of pears was not evaluated. There was also a lack of an independent validation for the most important detection model in their study. In this study, local and hybrid models for pears of different origins were developed using three-variable screening methods combined with a PLS algorithm to better predict the SSC and pH of pear samples of different origins. Independent prediction sets from different years with large variability were also used for model validation. The biggest difference between this study and previous studies is that our study fully considered the effects of origin differences, meteorology, time (season), and management methods on pear quality. The model constructed in this study is highly accurate and robust, which can better predict pears of unknown origin and different years and has a scalable application prospect.

4. Conclusions

This study selected ‘Dangshan’ pears of different origins to evaluate the effects of fruit origin on the NIR spectral internal quality (SSC and pH) detection models. It was found that compared with the local origin and the pairwise hybrid origins models, the model established by the calibration set of hybrid pears from three producing origins achieved the most ideal prediction results. Combined with the characteristic wavelength variables screened by CARS, the model was further improved. In order to verify the validity of the selected characteristic wavelengths, the above model was directly used to detect the SSC and PH values of pear fruit samples from three different producing areas in 2019, and good detection results were achieved. The predicted R²_p for the pear SSC was above 0.9, and the predicted R²_p for the pear pH was also above 0.85, and the value range of RMSEP was 0.167–0.201 and 0.027–0.032. The results showed that the calibration model can achieve better performance in the prediction of the pear SSC and pH if it involves more origins of pears and uses the effective characteristic wavelengths. Variations due to the difference in the origin of pears on the detection of the fruit SSC and pH by NIR spectroscopy can also be decreased. The results of the current study provide not only the theoretical basis but also practical implementation for the accurate and online detection of the SSC and pH of pears using NIR spectroscopy. The model constructed in this study can be used to develop a more adaptable, stable, and affordable portable instrument for the rapid non-destructive detection of soluble solids and acidity in pears.