A total of 512 snow pears of four different batches of samples were collected from the local fruit market at different time periods in Shuangfu, Chongqing. The surface of these samples did not bear any damage. The average fruit weight was 300–400 g. The shape was round or flat, with the top and base uneven, the longitudinal diameter around 8–9 cm, the transverse diameter around 9–9.5 cm, and the fruit stone diameter of 2–3.5 cm. After each batch of samples was collected and brought back to the laboratory, the snow pears were washed, numbered, and stored in a refrigerator to ensure the accuracy of the experiment. It took eight months to collect the NIR diffuse reflectance spectra of the surface of the samples using a microfiber spectrometer and to measure the standard reference values of the LC according to the Klason method (Bunzel et al., 2011; Cybulska et al., 2012; Assis et al., 2017). Among these samples, the NIR spectra and LC reference value of the 160 samples in batch A were completed in December 2020, and the 120 samples in batch B, 104 samples in batch C, and 128 samples in batch D were completed in March 2021, May 2021, and July 2021, respectively. Different batches of samples in this research referred to the different collection time points of NIR diffuse reflection spectrum of the samples. As shown in Table 1 , the batch A samples were divided into a calibration set (60%) and a validation set (40%) using the Kennard–Stone (KS) algorithm (Tao et al., 2019), and the batch B, C, and D samples were divided into a model update calibration set (40%) and a validation set (60%).

Based on the NIR diffuse reflectance spectrum acquisition system, the NIR spectra of nine measurement positions (three stem-calyx longitude, with an interval of 120°) intersected three latitudes (stem, equator, and calyx) from nine spectral measurement positions (as shown in Figure 1 ) on the surface of four batches of snow pears that were collected using a microfiber spectrometer (NIRQuest256-2.5, Ocean Insight, Orlando, FL, USA). The microfiber optic spectrometer had wavelengths ranging from 900 to 2500 nm, with a resolution of 9.5 nm and 512 data points. We set the integration time of the microfiber optic spectrometer to 70 ms, the scanning number to 5, and the number of smoothing points to 10. We obtained the average NIR spectrum of one sample after three consecutive acquisitions at each measurement point. The noise spectral data at both ends of the spectral curve were removed, and the effective wavelengths ranged from 1033 to 2300 nm, with 387 spectral points.

To make the spectrum and LC correspond more accurately, the fresh snow pear flesh (between 2 cm outside the core and 2 mm under the pericarp of an intact pear) was made into a dry powder immediately after the NIR spectrum acquisition. We used the traditional Klason method to measure the LC reference value of snow pears, and the statistical results are shown in Table 1 . The snow pear dry powder (500 mg) and 72% H₂SO₄ (30 mL) formed the mixed solution; the solution was stirred evenly, sampled in boiling water bath for 2 h, and diluted with deionized water. Then, the solution was poured into a sand core funnel (diameter of 2.5 cm, particle retention of 1.6 μm), filtrated, washed, dried, and weighed to obtained the LC mass ratio (mg/g) of the sample. We conducted three chemical repeated measurements and obtained the value with a relative error within 5% was obtained.

The LC values of snow pear samples of batches A, B, C, and D ranged from 75.05 to 81.04 mg/g, 74.78 to 80.80 mg/g, 75.48 to 81.42 mg/g, and 76.43 to 79.38 mg/g, respectively. Table 1 also shows the lignin distribution of the calibration set and the prediction set, and the LC range in the calibration set was bigger than that in the prediction set for the batch A samples. This result was helpful to build a better calibration model for detecting the LC of snow pears in batch A.

For the multivariate calibration model, it was assumed that a data set of NIR spectrum was X _(mxn), the number of samples was m, the number of variSSables was n, and the data set of the LC reference value was Y _(mx1). The linear relationship between X and y can be established by the PLSR model, as shown in formula (1). The predicted value y ^ could be calculated, as follows:

where b ₀ and b(nx1) were the intercept and regression coefficient of the PLS model, respectively; 1 was the column vector of length n, and its element was 1; and e was the prediction error between ŷ and y.

If only data sets for the NIR spectra and the LC reference value of the new batch of snow pear samples were available, and no data set was available for the NIR spectral of samples of the main batch, it would be impossible to update the calibration model to predict the LC of a new batch of snow pears using the standard strategy. In practical applications, an updated calibration model is often necessary to predict the LC of new samples. Therefore, it was necessary to apply the semi-supervision free parameter model enhancement (SS-FPME) to the updated calibration model. This method reduced the influence of sample variability and external variability of measurement systems to obtain an accurate and robust prediction result. The function formula of SS-FPME was calculated as follows:

where X _s is the data set of the NIR spectra of samples of new batch and the updated data set of the calibration model at the same time; b _0,s is the intercept; b_s is the regression coefficient of calibration model of the new batch sample, and r_th is the constraint of the correlation coefficient; and b _m is the regression coefficient of calibration model of the original main batch sample, which could be analyzed and calculated by PLSR model. We optimized the function formula (2) of SS-FPME using the sequential quadratic programming method of the fmincon optimization routine of MATLAB 2016b software. The method to update the SS-FPME model required the regression coefficient of the primacy model, the spectral data set of a few samples from the new batch, and the data set of the corresponding reference value. We used the root mean square error of the prediction set (RMSEP) to evaluate the performance of the updated calibration model, which was estimated based on the independent test set.

To comprehensively assess the prediction ability of the updated calibration model of different batches of snow pears based on NIR spectroscopy, we used the SS-FPME method to update the calibration model of the old batch of samples based on the updated data set of the new batch of samples to predict the LC of the new batch of samples. We updated the master calibration model according to each new batch of samples independently in the SS-FPME method, referred to as the independent SS-FPME method ( Figure 2A ), and the master calibration model was updated sequentially by multiple batches of the samples, referred to as the sequential SS-FPME method ( Figure 2B ).

For the independent SS-FPME method, Figure 2A ) shows the updating process for the calibration model to predict the LC in the four batches of snow pears. We used the PLSR to establish the master calibration model based on one batch of snow pear samples (batch A), and formed model A to predict the LC of batch A. To improve the accuracy of the calibration model, we had to update the master model (model A) from the calibration set of a new batch of samples (batch B), and formed Ind-model AB to predict the LC of batch B. The calibration set of the new batch of samples contained few samples, and was called the update set. To accurately detect the LC of batch C and batch D, we built the Ind-model AC and Ind-model AD from the calibration set of batch C and batch D independently using the SS-FPME method.

Figure 2B shows the updating process for the calibration model of the sequential SS-FPME method for four batches of snow pears. Similar to the independent SS-FPME method, we built model A (the master model) from the calibration set of batch A using the PLSR algorithm to predict the LC of batch A, and we updated model A to form the Seq-model AB from the calibration set of batch B to predict the LC of batch B. Then, we updated the Seq-model AB to form the Seq-model ABC from the calibration set of batch C sequentially to predict the LC of batch C, and we updated the Seq-model ABC to form the Seq-model ABCD from the calibration set of batch D sequentially to predict the LC of batch D. In this work, the independent SS-FPME method and the sequential SS-FPME method were used and compared to update the calibration model to predict the LC of four batches of snow pears separately to improve the accuracy and robustness of the calibration model to predict the internal qualities of different batches of samples.

Based on NIR spectroscopy, we established the prediction model of the LC of snow pear samples in batch A, which was used as the master model for the detection of LC in four batches of samples in this study. To deduct the influence of instrument background or drift on the signal, eliminate random noise, and improve the signal-to-noise ratio, the first derivative (1-Der, polynomial order = 1, smoothing points = 11), second derivative (2-Der, polynomial order = 2, smoothing points = 11), standard normal variate transformation (SNV), and multiplicative scatter correction (MSC) were used and compared to pretreat the raw average NIR spectra of nine measurement positions at each sample. We carried out the preprocessing methods using the software Unscrambler X 10.4 (CAMO PRECESS AS, Oslo, Norway). The results shown in Table 2 indicated that the prediction model using the SNV preprocessing method achieved better performance. Compared with the no preprocessing method, Figure 3 showed that the Rc and Rp were improved from 0.807 and 0.850 to 0.822 and 0.857, respectively, whereas the RMSECV and RMSEP were reduced from 0.710 and 0.603 to 0.679 and 0.602, respectively. Therefore, we further analyzed the LC detection model based on the NIR data after SNV preprocessing.

Hundreds or thousands of wavelengths in the full spectra of samples may contribute more collinearity and redundancies and contain useless or irrelevant information. This makes the calibration process more time-consuming, is less convenient to meet high-speed spectroscopy features, and reduces the prediction accuracy of the calibration model to measure the LC of snow pears. To eliminate the uninformative wavelengths, predigest the calibration model, and improve the prediction results in terms of accuracy and robustness, we selected and compared 19, 76, 80, 24, and 20 effective wavelengths (as shown in Figure 4 ) to build a model to predict the LC of snow pears using the successive projections algorithm (SPA), synergy interval partial least squares (SiPLS), genetic algorithm (GA), bootstrapping soft shrinkage (BOSS), and competitive adaptive reweighted sampling (CARS) methods, respectively.

In the SiPLS method, we divided the full spectra into 20 subintervals, and selected the 1st, 8th, 15th, and 18th subintervals as the effective regions. During the process of CARS effective wavelengths selection, we set the number of Monte Carlo sampling runs, the maximal principal value, and the number of cross validation to 100, 10, and 10, respectively. The number of iterations and cross-validation of the BOSS algorithm were set to 2000 and 5, and the maximum number of latent variables was set to 20. The statistical data in Table 3 show that the number of latent variables (LVs) of the model (SNV-CARS-PLSR) established based on the effective wavelengths selected by the CARS method was the lowest, which was eight LVs. The Rc of model (SNV-GA-PLSR) obtained by the GA method was the highest, which was 0.846, the Rp of the model (SNV-SPA-PLSR) by the SPA method was the highest (0.863), and the RMSECV and RMSEP values of the model (SNV-GA-PLSR) by the GA method were the lowest (0.637 and 0.624).

According to the results, the SNV-GA-PLSR model (master model A) had higher Rc and Rp values of 0.846 and 0.854 and lower RMSECV and RMSEP values of 0.637 and 0.624 (as shown in Figure 5 ), respectively. Moreover, the difference between the Rc and Rp and the RMSECV and RMSEP also was smaller. Therefore, the SNV-GA-PLSR demonstrated better prediction performance for measuring the LC of snow pears, which we used as the prediction model for the four batches of snow pear samples in this study.

As shown in Figure 6 , the 80 selected effective wavelengths were distributed mainly at 1160 nm, 1198 nm, 1328–1344 nm, 1420–1430 nm, 1552–1575 nm, 1670–1693 nm, 1798 nm, 1821–1831 nm, 1844–1854 nm, 1929–1952 nm, 2063–2086 nm, 2128–2138 nm, 2183–2212 nm, 2264–2277 nm, and 2290–2300 nm. The NIR spectral region primarily contained the frequency doubling and combination bond information for C-H, N-H, and O-H, which was sensitive to the concentrations of organic materials. LC is the organic molecule and the C-H, N-H, and O-H were the most important groups with the main active ingredients. Thus, it is possible to use NIR methods for determination of LC in snow pear. Of these, 1160 nm and 1198 nm were associated with the third overtone of C-H; 1420–1430 nm was associated with the second overtone of the H2O, O-H, N-H, and C-H combination; 1552–1575 nm was associated with the first overtone of N-H; 1670–1693 nm and 1798 nm were associated with the first overtone of C-H; 1821–1831 nm was associated with the second overtone of the C=O stretch; 2063–2086 nm was associated with the H2O and O-H combinations; 2128–2138 nm was associated with the N-H combinations; 2183–2212 nm was associated with the N-H+C-C combinations; and 2264–2277 nm and 2290–2300 nm were associated with the C-H+C-H combinations.

The Table 4 showed that SNV-GA-PLSR model can also simply the calibration model and improve the prediction performance for measuring the lignin content of batch B, C and D snow pears.

For the batch B samples of snow pears, we used master model A to directly measure the LC of the prediction data set of the batch B samples (Bpre), with the Rp of 0.823 and RMSEP of 0.641, as shown in Figure 7A . Based on the independent SS-FPME method, we obtained a new regression coefficient matrix (bs_AB) by using the regression coefficient matrix of master model A (bm_A) to supervise the learning of the calibration data set of the batch B samples (Bcal). Ind-model AB was established to predict the LC of Bpre, and the predictive ability of the updated model (Ind-model AB) was improved to a certain extent. Figure 7B shows that the Rp value increased from 0.823 to 0.837, and the RMSEP value decreased from 0.641 to 0.614.

For the batch C samples of snow pears, Figure 8A shows that the performance of using master model A to directly detect the LC of the prediction data set of the batch C samples (Cpre) was poor, with an Rp of 0.602 and RMSEP of 1.703. Based on the independent SS-FPME method, we obtained the regression coefficient matrix (bs_AC) and the Ind-model AC using the bm_A constraint supervision to learn the calibration data set of the batch C samples (Ccal). The prediction performance was greatly improved, with an Rp of 0.940 and RMSEP of 0.433, as shown in Figure 8B . Based on the sequential SS-FPME method, we used the regression coefficient matrix (bm_A) of master model A in supervised learning Bcal to first construct the bs_AB, and then we used the bs_AB in supervised learning Ccal to construct bs_ABC, and established the Seq-model ABC to measure the LC of the prediction data set of the batch C samples (Cpre). Compared with the Ind-model AC, the prediction performance was further improved: the Rp value increased from 0.940 to 0.952 and the RMSEP value decreased from 0.433 to 0.383, as shown in Figure 8C .

The analysis process for the batch D samples was the same as that for the batch C samples, and the experimental results are shown in Figure 9 . First, master model A was directly used to measure the LC of the batch D samples, and the performance was poor, with the Rp of 0.413 and RMSEP of 0.916 ( Figure 9A ). Then, we built the Ind-model AD based on the calibration data set of the batch D samples (Dcal) and bm_A in the independent SS-FPME method. The Rp and RMSEP of the Ind-model AD to detect the LC of the prediction data set of the batch D samples (Dpre) were 0.806 and 0.322 ( Figure 9B ), respectively. For the sequential SS-FPME method, we built the bs_ABCD and Seq-model ABCD by updating the Seq-model ABC based on the Dcal and bs_ABC. The Rp and RMSEP of Seq-model ABCD were 0.831 and 0.309 ( Figure 9C ), respectively. Therefore, the sequential SS-FPME method updated the master model based on SS-FPME supervised learning of the new batch samples further increased the Rp and reduced the RMSEP of prediction model to measure the LC of the batch C and D samples, and further improved the prediction performance of the updated calibration model. Moreover, the prediction performance of the updated model based on the sequential SS-FPME method was better than that of the independent SS-FPME method. This result indicated that sequential update enhanced the model features in the learning of previous batches.

The constraint condition of regression coefficient had to be adjusted in the process of updating the master model using the independent SS-FPME method and the sequential SS-FPME method, which contained the information variation of the NIR spectra in the current batch and the new batch of snow pear samples. Figures 10A, B show the evolution process of the regression coefficients of master model A in the independent SS-FPME method and the sequential SS-FPME method, respectively. This illustration is helpful to better understand the batch adjustment of the regression coefficients. Compared with the regression coefficient of master model A, the regression coefficient of the updated batch B model was basically the same as that of batch A, whereas the regression coefficients of the updated batch C and D models varied greatly, thus improving the prediction performance of the model. The difference of regression coefficients was unique for each batch of samples. It was difficult, however, to extract information related to chemical composition to analyze the causes of these spectral changes.

Although we used the same microfiber optic spectrometer to collect the NIR spectra and followed the same standard procedures to measure the LC reference for each batch of samples, the performance of detecting the LC of the batch B, C, and D samples using master model A was poor, with lower Rp values and higher RMSEP values. The varieties in the NIR spectra of the samples occurred for several potential reasons, including changes in the detector light source, the acquisition environment temperature, the operation of spectral collection and reference value determination, and the process and equipment of the sample pretreatment. In this study, Table 5 shows that the updated model using the SS-FPME method based on the batch A samples could improve the performance of predicting the LC of the batch B, C, and D samples. Compared with the independent SS-FPME method used to update the master model, the sequential SS-FPME method could enhance the model features from previous supervised learning and obtain better prediction perfosssrmance. Therefore, the updated model based on supervision and learning of a new batch sample using the sequential SS-FPME method could improve the robustness and migration ability of the model to detect the LC of snow pears and provided technical support for the development of a portable detection device.