Hyperspectral Inversion Model of Relative Heavy Metal Content in Pennisetum sinese Roxb via EEMD-db3 Algorithm

Abstract

Detection rapidity and model accuracy are the keys to hyperspectral nondestructive testing technology, especially for Pennisetum sinese Roxb (PsR) due to its extremely high adsorptive heavy metal content. The study of the resolution of PsR is conducive to the analysis of the accumulated heavy metal content in its different parts. In this paper, the contents of Cd, Cu and Zn accumulated in the old leaves, young leaves, upper stem, middle stem and lower stem, as well as the hyperspectral data of the corresponding parts, were measured simultaneously in both fresh and dry states. To begin, the spectral data of PsR were preprocessed by using Ensemble Empirical Mode Decomposition-Daubechies3 (EEMD-db3), Savitzky–Golay (SG), Symlet3 (sym3), Symlet5 (sym5), and multiplicative scatter correction (MSC). The 40 samples were divided into 32 training sets and 8 validation sets. The preprocessed spectral data were transformed by the first derivative (FD) and reciprocal logarithm (log(1/R)) to highlight the singularities using binary wavelet decomposition. After screening the significant bands from the correlation curve, the competitive adaptive reweighted sampling (CARS) and successive projection algorithm (SPA) were applied to extract the spectral characteristic variables, which were used to establish the partial least-squares (PLS) regression and multiple stepwise linear regression (MSLR) inversion models of Cd, Cu, and Zn contents. Based on EEMD-db3 pretreatment, the inversion model of Zn in the dry (fresh) state had R² values of 0.884 (0.880), NRMSE values of 0.179 (0.253) and RPD values of 3.191 (3.221), indicating excellent stability and predictive performance. The findings of this study can not only aid in the rapid nondestructive detection of heavy metal adsorption in various parts of PsR, but can also be applied to guide the development and use of animal feed.

1. Introduction

PsR is a plant with high nutritional value and palatability that is widely used in the preparation of animal feed [1,2]. It can be used to control soil heavy metal pollution due to the characteristic structure of biochar having a good adsorption effect on heavy metal ions such as Cu, Cd and Zn in soil [3,4,5,6,7,8]. When PsR is fed to animals such as fish, cattle and sheep, some of the heavy metal elements are absorbed by the animals, accumulating in their bodies [9]. Long-term ingestion can lead to chronic poisoning in animals. Excessive doses can lead to acute poisoning and even death, and easily endanger food safety throughout the food chain [10]. It is necessary to determine whether the heavy metal content of PsR meets the feed standard. The traditional chemical method for detecting heavy metal content in PsR is time-consuming and costly [11,12,13,14,15]. With the arrival of the fourth industrial revolution, the aging rural population, manpower shortage and other problems are becoming increasingly serious [16,17,18,19]. Agricultural operations are gradually developing towards precision operations, mechanization and intelligent decision-making [20]. Hyperspectral technology has high resolution and can quickly obtain the hyperspectral reflectance information of the target continuous band. It is a simple, rapid and nondestructive detection method [21]. It is widely applied in the quantitative detection of crops, soil composition, food composition detection and floating object detection in water [22,23,24,25,26,27,28,29,30].

Cao et al. [31] applied successive projection algorithms to reduce the dimensions of japonica rice hyperspectral data and extract characteristic bands. The results provided data support for the diagnosis of chlorophyll content in japonica rice. Wu et al. [32] preprocessed the soil reflectance with wavelet transform, then screened the characteristic bands by combining the CARS-SPA. The SVR model had good test accuracy, which provided an effective method for soil salinization diagnosis. However, many scholars have reported the shortcomings of hyperspectral data, such as large amounts of data, complex redundancy and low SNR [33]. To improve the SNR, scholars have mostly applied Savitzky–Golay convolution smoothing, multivariate scattering correction, standard normal variable correction, analysis smoothing processing and wavelet transform to reduce the noise of spectral data [34,35]. Due to the characteristic difference of spectral data for different detection targets, more spectral pretreatment methods should be introduced to improve the correlation between characteristic bands and the content of target components [36].

Empirical Mode Decomposition (EMD) is a signal analysis method proposed by Huang in 1998 [37]. Different from wavelet decomposition, the basis of EMD is directly derived from the data itself, rather than the preset basis function. EMD has an obvious advantage in processing non-stationary and nonlinear data, meanwhile having a high SNR [38]. However, mode aliasing will occur when EMD is applied to the processed signal. Ensemble empirical mode decomposition (EEMD) can effectively solve the mode aliasing problem by introducing white noise into the signal to be analyzed [39].

Zhuo et al. [40] decomposed and reconstructed the initially measured spectral data of spartina alterniflora of wetland using the EMD method. A harmonic analysis–back propagation neural network regression (HA-BP) model for spartina alterniflora chlorophyll content was developed. R² = 0.8528, RMSE = 6.8968, indicating that EMD reconstruction effectively suppresses the original spectral noise and provides a theoretical foundation for vegetation pigment content inversion. Zhao et al. [41] utilized EMD to decompose the original data into several IMFs. The signal component was then obtained by filtering according to the IMF autocorrelation coefficient. The SPA was employed to screen the characteristic variables of the signal components, and a partial least-squares regression model was built to classify the rice blast. The classification accuracy was 94.12%. Li et al. [42] proposed a denoising method based on EEMD and improved universal threshold filtering. The results showed that the denoising performance of the proposed method is better than that of the wavelet-based method. In conclusion, the EEMD can improve the performance of the SNR of a spectral signal with spectral reflectance data, as well as the stability and accuracy of the inversion model. However, the EEMD method is not widely applied in the field of heavy metal content detection in PsR plants. Meanwhile, there are few reports on the estimation of heavy metal content in accumulation using spectral nondestructive detection. The implementation of the EEMD method to preprocess the spectral reflectance data of PsR is beneficial for increasing the SNR of quantitative estimation of PsR heavy metal content and maintaining effective information.

In this paper, the contents of the heavy metals Cd, Cu and Zn accumulated in old, young, upper, middle and lower stems of PsR were studied. The heavy metal content of PsR was compared in fresh and dry moisture content states. Furthermore, the models for estimating heavy metal content with high spectral reflectance were established separately. SG, MSC, sym3, sym5 and EEMD-db3 were applied to denoise the initial spectral data of PsR. FD, log(1/R) and binary wavelet decomposition were then performed to highlight sensitive eigenvariables of the denoised spectral data. Finally, after screening the significant correlation bands using correlation curves, the eigenvariables were extracted using SPA and CARS. PLS regression and MSLR inversion models for the three heavy metals in fresh and dry leaves of PsR were developed. Meanwhile, linear, parabolic, exponential and logarithmic estimation models were constructed by selecting the characteristic bands with the maximum correlation coefficients as independent variables. The results of this study can provide a basis for the rapid detection of heavy metals in PsR and the screening of PsR that meets the fodder standards, as well as provide a reference for forage storage.

The main contributions of this paper are as follows:

(1) The contents of the heavy metals Cd, Cu and Zn in old, young, upper, middle and lower stems were compared and analyzed. The heavy metal content differences between fresh and dry states were investigated.

(2) PsR spectral data were preprocessed with EEMD-db3 for noise reduction to optimize the spectral signal’s SNR. The relationship between spectral data and heavy metal content was improved. The estimation model’s stability and accuracy were enhanced.

2. Materials and Methods

2.1. Method of Obtaining PsR Sample

The experiment was carried out in the ecological experimental farm of South China Agricultural University in August 2020, (Figure 1). In an experimental plot containing different heavy metal concentrations, PsR was planted at a density of 4 plants/m². The test soil was acidic with a pH ranging from 4.5 to 6.0. The concentration of Cd was 0.01–0.07 mg/kg, the concentration of Cu was 70.25–120.65 mg/kg, and the concentration of Zn was 45.40–60.38 mg/kg, respectively. During the planting period, 25 g per plant and 50 g per plant compound fertilizers (N: P: K = 15: 15: 15) were applied in the first and third months of the growing season, respectively. The experimental PsR was planted on 12 August 2020 and harvested on 7 January 2021. Eight PsR were randomly collected. The upper part of each PsR was divided into five parts: old leaf (1), young leaf (2), upper stem (3), middle stem (4) and lower stem (5).

2.2. Hyperspectral Data Acquisition and Heavy Metal Content Determination

Spectral reflectance data of fresh PsR samples were collected using a HyperSIS-VNIR-QE hyperspectral imager (spectral band range 400–1000 nm). The reflectance data of the points at the same position of each sample were corrected by black and white plates through Formula (1), which were used as the original spectral reflectance data of the fresh leaves of PsR.

After collecting hyperspectral data, the plants were dried in an oven at 70 °C for 30 min and at 55 °C for 48 h to obtain dry samples. They were pulverized with a grinder and sifted through 100 mesh, and then placed in sealed plastic bags for the determination of heavy metal content in plants. The heavy metals in plants were boiled using a HNO₃-H₂O₂ microwave, and determined by a graphite furnace atomic absorption spectrophotometer. The results were tested using the national standard materials of plants. Soil pH was measured by a pH meter according to the ratio of water to soil 2.5:1.

$$I_0=lg\left[\frac{\left(I-I_D\right)}{I_W-I_D}\right]$$

(1)

where I₀ is the corrected hyperspectral data; I is the original hyperspectral data; I_W is the whiteboard average hyperspectral data; and I_D is the blackboard average hyperspectral data. Figure 2 shows the mean reflectance curves of the original spectra of five parts of PsR.

2.3. Spectra Pretreatment

Hyperspectral data were characterized by multiple bands, strong correlation, data redundancy and low SNR, then the correlation calculation was complicated [43]. SG, MSC, sym3, sym5 smoothing, and EEMD-DWT were conducted to reduce the noise of the initial spectral data of PsR. After denoising, the spectral data were transformed by the FD and log(1/R), respectively. The db2, db3, db4 and db5 were decomposed into 5 decomposition layers, and then the high- and low-frequency wavelet coefficients of each decomposed spectral data were obtained [44]. Significant correlation bands were screened out by the correlation curve. SPA and CARS were employed to screen feature bands. Meanwhile, the band with the largest correlation coefficient was retained as the characteristic band. SG smoothing is a polynomial smoothing algorithm based on the least-square principle proposed by Savizkg and Golag, also known as convolution smoothing, which is widely used in signal preprocessing. In this study, five-point cubic smoothing was used to remove high-frequency random noise effectively [45]. MSC can effectively eliminate the spectral difference caused by different scattering levels and correct the phenomenon of limit shift and migration of spectral data [46]. The wavelet transform denoising method can effectively reduce the continuous background spectral noise. The selection of wavelet base type and vanishing moment affects the denoising effect [47]. After several trial calculations, sym3 and sym5 with better noise reduction effects were selected.

EMD is a signal preprocessing method based on the local time-scale characteristics of signals, which can adaptively decompose complex signals into intrinsic mode function (IMF) and a residual signal r [48]. Formula (2) needs to satisfy the following two conditions: ① in the entire time range of the function, the number of local extreme points and zero crossing points must be equal, or at most one difference; ② at any point in time, the local maximum envelope (upper envelope) and the local minimum envelope (lower envelope) must be zero on average.

$$x\left(t\right)={\displaystyle \sum }_{i=1}^{n}IM{F}_i\left(t\right)+r\left(t\right)$$

(2)

where $x\left(t\right)$ represents the original signal data; IMF represents the intrinsic modal function; $r\left(t\right)$ represents the residual component and n represents the number of IMF components.

EEMD is an improved signal decomposition method based on EMD. After adding white noise to the original data, EMD decomposition can effectively suppress mode aliasing [49,50]. The specific implementation steps are as follows:

(1) Add gaussian white noise $n\left(t\right)$ to the target signal $y\left(t\right)$ to obtain a new signal $x\left(t\right)$:

$$x\left(t\right)=y\left(t\right)+n\left(t\right)$$

(3)

(2) The signals are decomposed according to the EMD method and a set of IMF components (the first group includes j-IMF, j = 1,2,3...... J) and a residual component are obtained, as shown in Formula (2).

(3) Repeat steps (1) and step (2) i times and add different white noise each time to obtain group m IMF component and a residual component.

(4) By using the zero-mean principle of the Gaussian white noise spectrum, the decomposed overall mean values of IMF components and residual components of group m are taken as the final results to reduce the influence of white noise. The IMF component and residual component corresponding to the target signal are, respectively, expressed in Formulas (4) and (5):

$${\overline{IMF}}_j\left(t\right)=\frac{1}{m}{\displaystyle \sum }_{i=1}^{m}IM{F}_{ij}\left(t\right)$$

(4)

$$\overline{r}\left(t\right)=\frac{1}{m}{\displaystyle \sum }_{i=1}^m{r}_i\left(t\right)$$

(5)

Discrete Wavelet Transform (DWT) conducts binary wavelet as the Wavelet Transform function. After testing, the db3 wavelet function is selected as the generating function in this study. The IMF component was decomposed by EEMD and denoised by db3. Then, the IMF component after denoising is added to the remaining components to reconstruct the original spectral signal data. The specific decomposition steps are shown in Figure 3.

2.4. Inversion Data Selection Method

The FD transformation of the original reflectance can remove the linear and nearly linear components in the original spectral data. It highlights the rate of increase and decrease of spectral reflectance. Then, it can capture the inflection point and extreme point of the original spectral curve. The logarithmic function has good amplification gain in the defined interval (0,1) [51]. The reciprocal logarithmic mathematical transformation of the original spectral reflectance number of vegetation can highlight the characteristics of spectral line waveform changes and enhance the difference of peak and valley characteristics of multiple sets of spectral data. The characteristic bands in spectral data can be highlighted by conducting two kinds of mathematical transformations [52]. The high-frequency signal obtained by binary wavelet decomposition can reflect the details of the signal. The detailed information can reflect the influence of heavy metal content on the reflectance of spectral data. Four kinds of wavelet-generating functions (db2, db3, db4 and db5) were applied to decompose the spectral data of PsR after denoising, and then the high and low-frequency wavelet coefficients were obtained [53].

The correlation curve can reduce the redundant bands after determining the significant bands. As shown in Figure 4, bands with significant correlation coefficients were selected for screening. The CARS algorithm considers each band variable as an individual. Screening highly adaptive individuals as spectral characteristic variables can reduce the high collinearity before the original spectral band [54]. The optimal potential band variables were selected by the Monte Carlo cross-validation method, in which the Monte Carlo sampling times were set as 100.

The sampling times were repeatedly iterated to screen out the characteristic bands. SPA is a forward variable selection algorithm that minimizes the collinearity of vector space. It has achieved good results in obtaining effective information and reducing collinearity [55]. SPA can effectively improve the stability of the model by extracting characteristic bands from spectral data through dimensionality reduction. Figure 5 and Figure 6 are examples of CARS screening and SPA screening, respectively.

2.5. Model Building and Evaluation Methods

The bands with significant correlation were determined by the correlation curve, then the characteristic variables screened by CARS and SPA were adopted as independent variables. The following inversion model of heavy metal content in PsR was constructed after screening independent variables.

PLS regression is a modeling technique used in multiple linear regression analysis, canonical correlation analysis and principal component analysis. This modeling methodology relies on the linear relationship between independent and dependent variables, and can solve the multicollinearity problem while ensuring model stability [23]. MSLR chooses the important variables for the regression analysis in steps based on the importance of the independent variable [27].

According to the correlation curve, the band with the highest correlation coefficient was selected as the independent variable for regression analysis. Regression analysis includes linear regression and nonlinear regression, among which unary linear, exponential, logarithmic and parabolic models are common regression analysis models [32].

To evaluate the accuracy of the objective response, 40 sample data were randomly divided into 32 training sets and 8 prediction sets. R², Relative Percent Deviation (RPD) and Normalized Root Mean Square Error (NRMSE) were adopted to comprehensively evaluate the stability and accuracy of the model. The calculation method is shown in Formulas (6)–(8):

$$RMSE=\sqrt{{\displaystyle \sum }_{i=1}^n{(y_i-{\overline{y}}_i)}^2/n}$$

(6)

$$NRMSE=\frac{RMSE}{\sum _{i=1}^n{y}_i/n}$$

(7)

$$RPD=\frac{\sqrt{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2/\left(n-1\right)}}{RMSE}$$

(8)

where $y_i$ is the measured value of heavy metal content; ${\overline{y}}_i$ is the predicted value calculated by the inversion model; ${\widehat{y}}_i$ is the average predicted value of the model; i is the data number of the bamboo sample; n is the number of validation samples 8. The closer R² is to 1, the better the model fitting degree is. The smaller the NRMSE value is, the higher the inversion model accuracy is. The larger the RPD value is, the better the prediction ability of the model is. When RPD ≤ 1.0 indicates that the prediction ability of the model is very poor and the model is not reliable; 1.0 < RPD ≤ 1.4, indicating that the prediction ability of the model is poor; 1.4 < RPD ≤ 1.8, the model has the ability of quantitative prediction; 1.8 < RPD ≤ 2.0, the prediction ability of the model is good; 2.0 < RPD ≤ 2.5, the model has good predictive ability; RPD > 2.5, the model has the excellent predictive ability [56].

3. Results

3.1. Heavy Metal Accumulation Performance

As shown in Figure 7a, the relative accumulation of the heavy metal Cd in various parts of PsR was significantly different under dry conditions. The highest accumulation was in the upper part of the stem, followed by the lower part of the stem, the middle part of the stem and the old leaf, while the young leaf accumulated the least, with an average of 0.0065 mg/kg per plant. The relative accumulation of Cd in the upper part of the stem was 20.64 times higher than that in the young leaf (p ≤ 0.05). As shown in Figure 7b, the relative accumulation of the heavy metal Cu was greatest in the young leaf, followed by the upper stem, the old leaf and the middle stem, while the relative accumulation in the lower stem was lesser, averaging 4.375 mg/kg per plant. The relative accumulation of Cu in the lower stem was not significantly different from that in the middle stem, but was significantly different from that in the young leaf, the old leaf and the upper stem. The relative accumulation of Cu in the young leaf was 2.25 times higher than that in the lower part of the stem. As shown in Figure 7c, the relative accumulation of the heavy metal Zn in the dry state was highest in the upper part of the stem, followed by the middle of the stem, the young leaf and the old leaf. The relative accumulation of the heavy metal Zn in the lower stem was 19.56 mg/kg. The relative accumulation of Zn in the upper part of the stem was 10.25 times higher than that in the lower part of the stem.

Figure 7 shows that there was no change in the trend of relative accumulation of heavy metals in the young leaf, old leaf, upper stems, middle stems and lower stems by comparing the dry state with the fresh leaf state. A t-test was conducted to analyze the significant difference in the relative accumulation of heavy metals between the dry and fresh leaves of PsR. The results are shown in

Table 1. A significant difference in heavy metal relative accumulation in Pennissimus arundinacea under dry and fresh leaves (p).

Part of PsR	Theory of Testing	Cd Relative Accumulation Content	Cu Relative Accumulation Content	Zn Relative Accumulation Content
Old leaf	F-test	0.005	0.052	0.015
	t-test	0.037	0.000	0.000
Young leaf	F-test	0.061	0.019	0.022
	t-test	0.109	0.006	0.001
Upper stem	F-test	0.009	0.000	0.031
	t-test	0.005	0.001	0.002
Middle stem	F-test	0.169	0.023	0.021
	t-test	0.003	0.009	0.012
Lower stem	F-test	0.012	0.002	0.000
	t-test	0.043	0.000	0.003

.

The significance test showed that the F-test significance of dispersion degree of Cd relative accumulation in young leaf was p ≥ 0.05, while the t-test significance of mean level was p ≥ 0.1. The F-test significance of dispersion degree of relative accumulation of Cd in the middle stem was p ≥ 0.1, while other parameters showed significant differences (p ≤ 0.05). The results showed that the relative accumulation of Cd in the young leaf showed an average level and dispersion degree, while the relative accumulation of Cd in the middle stem showed no significant difference between dry and fresh leaves.

3.2. Construction of Inverse Model for Relative Contents of Heavy Metals

The spectral curves, after denoising via EEMD-db3, SG, sym3, sym5 and MSC, were transformed by the FD, log(1/R), db2, db3, db4 and db5 binary wavelet transform. According to the transform spectral curve and wavelet coefficient correlation curve, the band with the largest absolute value of the correlation coefficient was selected as the independent variable. The linear, parabolic, exponential and logarithmic models of the relative contents of heavy metals were established. The maximum correlation coefficient corresponding to each pretreatment was shown in

Table 2. The maximum correlation coefficient between the prediction index and variable after different pretreatment.

Prediction Index	EEMD-db3	SG	sym3	sym5	MSC
Cd in the dry state	−0.681	0.623	0.613	0.612	0.622
Cu in the dry state	−0.574	0.506	−0.609	−0.522	0.497
Zn in the dry state	0.887	0.812	−0.784	0.758	0.811
Cd in the fresh state	−0.593	0.605	0.547	−0.544	0.643
Cu in the fresh state	−0.631	0.653	0.630	−0.624	0.651
Zn in the fresh state	0.828	0.803	−0.706	0.683	0.615

. As can be seen from Table 2, the absolute correlation coefficients between the relative content of heavy metals and variables in EEMD-db3 treatment were mostly better than the other four pretreatment methods. After EEMD-db3 treatment, the correlation coefficients of Cd and Zn contents in the dry state were −0.681 and 0.887, respectively. The correlation coefficient of Zn in the fresh state was 0.828. The absolute value of the correlation coefficient of Cu relative content in the dry state after EEMD-db3 pretreatment was less than that after sym3 pretreatment. The absolute correlation coefficient of Cd and Cu contents in the fresh state after EEMD-db3 pretreatment was second only to that after MSC and SG pretreatment. The results show that the EEMD-db3 pretreatment method can improve the correlation between the spectral curve and prediction index, and enhance the stability and accuracy of the inversion model.

Significant correlation bands were screened from correlation curves. The characteristic bands of each prediction index were screened by CARS and the SPA algorithm for significantly correlated bands. PLS and MSLR models of the relative content of each heavy metals were constructed by using the selected characteristic bands as independent variables. Comparing the R² of linear, parabolic, index, logarithmic, PLS and MSLR inversion models of each heavy metal, the pretreatment types and corresponding independent variables of the inversion model with the maximum R² of each heavy metal after different pretreatments are listed in

Table 3. The corresponding spectral preprocessing method and the characteristic band of the model.

Prediction Index	The Process of Spectral Pretreatment	Characteristics of the Band
Cd in the dry state	EEMD-db3-db4-D3-SPA	458.11, 572.89, 611.15, 840.71, 867.01
	SG-db2-D3-CARS	491.59, 508.98, 510.72, 522.33, 654.19, 661.37, 666.15, 711.58
	sym3-db4-D3-SPA	548.98, 577.67, 761.8, 766.58, 965.05, 974.61
	sym5-db2-D3-SPA	522.68, 546.59, 632.67, 639.62, 919.61
	MSC-db2-D3-CARS	431.81, 493.98, 520.28, 654.19, 663.76, 675.71, 716.36
Cu in the dry state	EEMD-db3-FD	572.89
	SG-log(1/R)-SPA	534.63, 642.24, 670.93, 802.45, 924.4, 941.14
	sym3-FD-SPA	538.41, 582.46, 603.98, 692.45, 730.71, 800.05
	sym5-FD	529.85
	MSC-db4-D3-SPA	553.76, 560.93, 704.41, 716.36, 718.75
Zn in the dry state	EEMD-db3-db2-D4-SPA	455.72, 505.94, 572.89, 666.15, 850.27, 929.18
	SG-FD-CARS	505.94, 508.33, 603.98, 668.54, 670.93, 721.15, 757.01, 965.05
	sym3-FD-CARS	534.63, 537.02, 541.81, 587.24, 594.41, 601.59, 704.41
	sym5-db4-D4-CARS	534.63, 584.85, 972.22, 974.61, 977
	MSC-log(1/R)-CARS	448.55, 453.33, 479.63, 491.59, 513.11, 630.28, 680.50, 692.45, 900.49
Cd in the fresh state	EEMD-db3-log(1/R)-SPA	374.42, 424.64, 752.22, 761.79, 905.27
	SG-db5-D3-CARS	603.98, 620.72, 694.84, 907.66, 919.62, 948.31
	sym3-db2-D3-CARS	546.59, 560.93, 716.36, 819.18, 831.14, 878.96, 931.57, 974.61
	sym5-db2-D3-CARS	508.33, 639.84, 881.36, 883.75, 886.14, 922.01, 924.4
	MSC-db4-D3-CARS	436.59, 493.98, 658.97, 675.71, 702.02, 704.41, 721.15, 730.71
Cu in the fresh state	EEMD-db3-FD	606.37
	SG-FD-CARS	603.98, 615.93, 694.84, 907.66, 919.62, 931.57, 948.31
	sym3-FD-CARS	685.28, 723.54, 725.93
	sym5-FD	534.63
	MSC-FD-CARS	460.5, 537.02, 553.76, 589.63, 637.45, 642.24, 694.84, 713.97, 809.62, 828.75, 862.23, 883.75
Zn in the fresh state	EEMD-db3-db5-D4-CARS	503.54, 505.94, 513.11, 532.23, 582.46, 587.23
	SG-db5-D4-CARS	367.25, 431.81, 608.76, 737.88, 745.06, 847.88, 881.36, 943.53
	sym3-db2-D4-CARS	412.68, 577.67, 580.06, 922.01, 941.14
	sym5-db3-D3-SPA	386.38, 465.29, 525.07, 556.15, 651.8, 871.79
	MSC-db3-D3-CARS	489.2, 498.76, 515.5, 522.68, 529.85, 919.62

, respectively. The model evaluation indicators are shown in

Table 4. Model types and results of model evaluation indicators.

Prediction Index	Model Type	R2	NRMSE	RPD
Cd in the dry state	MSLR	0.686	0.424	1.670
	MSLR	0.751	0.336	1.560
	MSLR	0.632	0.568	1.375
	MSLR	0.584	0.825	1.271
	MSLR	0.796	0.580	1.382
Cu in the dry state	Index	0.532	0.349	1.405
	MSLR	0.492	0.810	1.193
	MSLR	0.570	0.459	1.358
	Index	0.313	0.500	1.237
	MSLR	0.338	0.594	1.051
Zn in the dry state	MSLR	0.884	0.179	3.191
	MSLR	0.873	0.326	3.333
	MSLR	0.780	0.341	2.159
	MSLR	0.750	0.509	2.113
	MSLR	0.882	0.429	1.912
Cd in the fresh state	PLS	0.592	0.561	1.628
	MSLR	0.734	0.382	2.223
	MSLR	0.561	0.673	1.252
	MSLR	0.564	0.630	1.314
	MSLR	0.764	0.662	1.176
Cu in the fresh state	Index	0.591	0.598	1.147
	MSLR	0.673	0.452	1.226
	MSLR	0.586	0.723	0.968
	Index	0.482	0.508	1.295
	MSLR	0.662	0.570	0.926
Zn in the fresh state	MSLR	0.880	0.253	3.221
	MSLR	0.847	0.337	2.896
	MSLR	0.810	0.303	2.163
	PLS	0.766	0.476	1.681
	MSLR	0.613	0.450	1.682

.

Table 3 and Table 4 show that in the inverse model of the relative Cd content in the dry state, the significant bands were filtered by the correlation curve of the db4 high-frequency coefficient D₃ after EEMD-db3 denoising. The characteristic bands 458.11, 572.89, 611.15, 840.71 and 867.01 of the significant bands were selected by SPA as independent variables. The R², NRMSE and RPD of the constructed MSLR model were 0.686, 0.424 and 1.670, respectively. Its R² was second only to the MSLR model constructed after noise reduction by SG and MSC, and its RPD value was the best among the models. The R², NRMSE and RPD of the PLS model constructed with the characteristic bands 374.42, 424.64, 752.22, 761.79 and 905.27 as independent variables in the inverse model of the Cd content in the fresh state were 0.592, 0.561 and 1.628, respectively. The correlation of the spectral log(1/R) data was denoised by EEMD-db3. The significant correlation bands were obtained from the curves, and later the characteristic bands were filtered by SPA. The model stability and accuracy were slightly lower than those of the MSLR model constructed after pre-processing by SG noise reduction. The synthesis showed that the inversion model constructed by EEMD-db3 pre-treatment was capable of quantifying the relative Cd content. However, its performance was slightly lower than that of the inversion model constructed by SG pretreatment.

The maximum R² of the inverse model for Cu relative content under dry conditions was the MSLR model, which was constructed with the characteristic bands 538.41, 582.46, 603.98, 692.45, 730.71, and 800.05 as independent variables with R² = 0.570. The significant bands were screened by correlation curves of the FD data of the spectra after sym3 noise reduction. The next was the exponential model constructed with band 572.89 as the independent variable, R² = 0.532. Its characteristic band was the band with the largest correlation coefficient among the spectral FD data processed by EEMD-db3. However, the R² of each model was less than 0.6, and the RPD was less than 1.4, indicating that the stability and predictive ability of the models were poor. The maximum R² of the inverse model for the relative Cu content in the fresh state was the MSLR model constructed with the characteristic bands 603.98, 615.93, 694.84, 907.66, 919.62, 931.57, and 948.31 as independent variables with R² = 0.673. The significant bands were screened using log(1/R) correlation curves of SG denoising by CARS. The characteristic bands were screened. However, the RPD of each model was less than 1.4, and the predictive ability of the model was extremely poor. In summary, this shows that the Cu relative content does not apply to the spectral data processing method mentioned in this study.

In the inversion model of the relative Zn content in the dry state, the R², NRMSE and RPD of the MSLR model constructed with the characteristic bands 455.72, 505.94, 572.89, 666.15, 850.27 and 929.18 as independent variables were 0.884, 0.179 and 3.191, respectively. The characteristic bands were filtered by SPA with the significance bands obtained by filtering the correlation curve of db2 high-frequency wavelet coefficients D₄ by EEMD-db3 denoising. Its R² and NRMSE were the best among the models, while the RPD value was second only to the MSLR model constructed by SG preprocessing. In the inversion model for the relative content of Zn in the fresh state, the R², NRMSE and RPD of the MSLR model constructed with the characteristic bands 503.54, 505.94, 513.11, 532.23, 582.46 and 587.23 as independent variables were 0.880, 0.253 and 3.221, respectively. The characteristic bands were obtained by CARS screening and the significance bands were obtained by EEMD-db3 denoised correlation curves of db5 high-frequency wavelet coefficients D₄. Its R², NRMSE and RPD were the best among the models. Collectively, this shows that the model constructed after EEMD treatment can better estimate the relative Zn content quantitatively.

4. Discussion

The bio-carbon structure of the PsR shows good adsorption of heavy metal ions such as Cu ions, Cd ions and Zn ions in the soil [4]. The results of Wang Xina et al. showed that the overall Zn relative content of the PsR was the highest, followed by Cu. The heavy metal concentrations also varied in the rhizomes and leaves of the PsR [57]. Our results showed that although the Zn concentration in the test soil was lower than the Cu concentration, the relative Zn content of the samples was higher, followed by Cu and varied from site to site. This may be due to the higher Zn adsorption capacity of the biochar structure of the grass, or to the higher Zn content of the grass itself. In this study, Zn and Cd accumulated more in the upper stem, while Cu accumulated more in the old leaves. The results of Sun et al. showed that the highest accumulation of heavy metals in forage grasses was in the stems, followed by the roots and leaves [58]. The high levels of Zn and Cd in the stems were consistent with the results of previous studies. The difference is that the higher Cu accumulation in this study was in the older leaves, which may be due to the unique biochar adsorption capacity of the PsR [13].

In the analysis of the correlation between heavy metal content and spectral reflectance, the dry state differs from the fresh state, which may be caused by the water content [59]. The stability and accuracy of the results of the three heavy metal inversion models differ when different pre-processing methods are used to process the hyperspectral data. EEMD can be able to adaptively decompose complex signals into an intrinsic mode function IMF and a residual signal r, while effectively suppressing the modal mixing phenomena [49,50]. It is used as a pre-processing method for spectral signals to reduce the interference of background noise on the characteristic feature signal and to decompose the individual frequency components [59]. Figure 8 shows the validated scatter plots of the better inversion models for each heavy metal. Their validation decision coefficients further indicate that Cd can be quantitatively analyzed for content using the method in this study, while Cu does not apply to the method of this study, and the Zn estimation model can quantify the content more accurately. The EEMD-db3 pre-processing effect in this study is more stable and does not lose out to the traditional noise reduction method. The results were better for the analysis of the heavy metal Zn, with a maximum correlation coefficient greater than 0.8 after pre-treatment. The effective spectral signals of plant heavy metals are reflected at different frequencies, so the results vary when each pre-treatment is analyzed for different components [60]. Therefore, when solving the problem of inversion for quantitative analysis of plant constituents in small samples, we must choose the appropriate pre-processing method according to the characteristics of the data.

There are some limitations in this study: (1) The existing literature for the study of the relative heavy metal content of PsR is scarce, and the subsequent inversion models may be biased. (2) Due to the limitation of the test site, the gradient of heavy metal stress in PsR was not obvious, which affected the analysis of heavy metal uptake and accumulation data in subsequent experimental samples. The next step could be to analyze PsR on the uptake rate of the main heavy metals in the soil and the main sites of uptake, which could further ensure the safety of PsR as fodder. (3) When examining the relationship between spectral reflectance and heavy metal content in different states of royal bamboo grass, we only considered two states. When other royal bamboo grasses contain water, this may appear to be more accurate for heavy metal estimation.

In subsequent research, we can focus on setting different water content gradients for experiments to determine better water content for estimating the heavy metal content of PsR to obtain spectral reflectance data, so as construct a more stable and accurate model. Meanwhile, in the research of estimating the content of target components using hyperspectral nondestructive, besides addressing how to improve the SNR of hyperspectral reflectance data, we should also focus on how to remove the redundant band information and perform dimensionality reduction on hyperspectral data.

5. Conclusions

In this study, our specific conclusions are as follows:

(1) The accumulation of Cd, Cu, and Zn in different parts of the PsR varied. Cd and Zn accumulated the most in the upper part of the stem, whereas Cu accumulated the most in the older leaves. The findings can be used to guide the preparation of PsR forage.

(2) The results of EEMD-db3 denoising and pre-processing of PsR spectral data showed that the MSLR inversion model of Zn content has high stability and predictive performance. R² = 0.884, RPD = 3.191 (in the dry state); R² = 0.880, RPD = 3.221 (in the fresh state), indicating that Zn content can be detected quickly and consistently. This suggests that accelerated and reliable detection of Zn content in PsR is possible. The superior Cd content model showed R² = 0.751, RPD = 1.560 (in the dry state) and R² = 0.734, RPD = 2.223 (in the fresh state), indicating that Cd content could be quantified. However, the greater inversion model for Cu showed R² = 0.507, RPD = 1.358 (in the dry state) and R² = 0.673, RPD = 1.226 (in the fresh state). This implies that the Cu content is inapplicable to the inversion models obtained by pretreatment in this study for estimation.

This study investigated the appropriate humidity ratio to construct the heavy metal content inversion model to boost the reliability and accuracy of the spectral estimation of PsR. Meanwhile, we will continue to research the spectral pretreatment method to strengthen the correlation between the predictive index and the spectral data, thereby improving the inversion model’s accuracy.