Development of a Biomass Component Prediction Model Based on Elemental and Proximate Analyses

Abstract

Emerging global environmental pollution issues have caused a reduction in coal utilization, leading to an increased research focus on biomass use as an alternative. However, due to the low heat values of biomass, studies in this field are still in progress. Biomass primarily comprises cellulose, hemicellulose, and lignin. To determine the composition of these three components, the measurement methods recommended by TAPPI (Technical Association of the Pulp and Paper Industry) and NREL (National Renewable Energy Laboratory) are typically employed involving equipment such as HPLC. However, these methods are time consuming. In this study, we proposed a model for predicting cellulose, hemicellulose, and lignin contents based on elemental and industrial analyses. A dataset comprising 174 samples was used to develop this model. This was validated using 25 additional samples. The R²_P values for cellulose, hemicellulose, and lignin were 0.6104–0.6362, 0.4803–0.5112, and 0.7247–0.7914, respectively; however, the R²_CV values obtained from the validation results were 0.7387–0.7837, 0.3280–0.4004, and 0.7427–0.7757, respectively. The optimal models selected for cellulose, lignin, and hemicellulose were C1, L2, and 100-(C1-L2) or H2, respectively. Our predictions for woody and herbaceous biomass, including torrefied samples, should be applied with caution to other biomass types due to the potential accuracy limitations. To enhance the prediction accuracy, future research should broaden the range of biomass types considered and gather more data specifically related to woody and herbaceous biomass.

1. Introduction

As interest in the environment is on the rise, much research is being conducted on alternative renewable energy sources to replace traditional fossil fuels. In particular, research has been conducted on alternative energy sources, such as hydrogen energy and batteries, which are currently prevalent. Globally, there is a strong reliance on thermal power generation to generate large amounts of electricity. This has caused increasing interest in biomass power plants that use biofuels as an alternative to coal. The use of agricultural and forest-based biomass is particularly advantageous because it is continuously produced by human activities and is relatively evenly distributed worldwide, unlike fossil fuels, which are concentrated in specific regions. However, biomass has been criticized for its high ash content and low calorific value compared with fossil fuels. To address these drawbacks, various thermochemical conversion processes have been conducted. In particular, processes such as torrefaction and carbonization have been developed to use biomass as a solid fuel. During the thermochemical conversion of biomass, the contents of the three components of biomass—cellulose, hemicellulose, and lignin—are important. Cellulose (Figure 1) is a glucose polymer with the structure [C₆H₁₀O₅]_n [1]. Hemicellulose (Figure 2) is a complex of 6-carbon and 5-carbon sugars, primarily composed of arabinose, xylose, mannose, galactose, and glucose [2]. In contrast, lignin comprises three phenylpropanoid units (p-coumaryl, coniferyl, and sinapyl alcohols) derived from cinnamyl alcohol (Figure 3) [3].

However, not all chemical compositions are solely based on these chemical structures. In most cases, other elements such as nitrogen, sulfur, and chlorine are included in addition to C, H, and O. If these elements are considered only from the elemental composition perspective, an elemental analysis will divide only the organic components of the sample into C, H, N, and S, assuming the remaining mass to be oxygen, leading to misunderstandings regarding the composition of sulfur, chlorine, ash, and other elements present in the sample [4]. However, in proximate analysis, the total biomass composition can be determined [5]. Cellulose is primarily composed of volatile matter. Hemicellulose has less volatile matter and more fixed carbon than cellulose and includes some ash. Lignin has relatively less volatile matter and more fixed carbon, with a particularly higher ash content than the other two components [6,7,8,9]. These characteristics cannot be determined using elemental analysis alone.

The ratios of these components vary depending on the biomass sources, such as herbaceous plants, hardwoods, or softwood. The TAPPI (Technical Association of the Pulp and Paper Industry) and the NREL (National Renewable Energy Laboratory) methods were used to determine the amounts of these three chemical components [10,11,12,13,14,15]. However, this method requires extensive time, samples, and equipment, such as HPLC and spectrometers. Consequently, various studies attempted alternative analyses for predicting biomass compositions rather than using conventional methods. Sheng et al. attempted to predict cellulose and lignin contents based on carbon dioxide and hydrogen consumption, and volatile matter [16]. Burhenne et al. predicted the chemical structure using elemental ratios [17]. However, the methods of Sheng et al. had a limited range of O/C and H/C, and that of Burhenne et al. was sensitive to even minor changes in the elemental composition. Díez et al. suggested the low-cost and rapid TGA-PKM method for determining the main lignocellulosic fraction contents of different types of biomasses from agricultural by-products [18]. Xing et al. reported a chemical constituent prediction model from ultimate analysis using a random forest model [19]. However, although an analysis of untreated biomass has been conducted, there is little research on the prediction of torrefied biomass. Therefore, this study proposed a model that predicts the cellulose, hemicellulose, and lignin contents based on the elemental content ratios determined during biofuel evaluation. From untreated biomass to torrefied biomass, this study attempted to make predictions using this method.

2. Methodology

2.1. Collection of Data

The elemental analysis, proximate analysis, and chemical structure results of the biomass were obtained from previous studies. A total of 174 data points were collected and normalized [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]. The collected data are summarized in Figure 4 and Table S1.

2.2. Pearson Correlation Coefficient

The Pearson correlation coefficient (Equation (1)) was used to examine the correlation between the various elements (C, H, N, O, and S), and proximate (VM and FC) and composition (Cell, Hemi, and Lig) analysis results. The Pearson correlation coefficient, as described in Equation (1), was used to analyze the degree of correlation between two populations. It ranges from −1 to 1, where positive and negative values indicate a proportional and inverse relationship, respectively. Values closer to −1 or 1 indicate a stronger linear correlation, whereas those closer to 0 indicate a weaker correlation [57]. Correlation equations with different goodness of fit values were obtained by performing linear and nonlinear regressions on the final analysis data using IBM SPSS version 22.0. The data analyses in this study utilized a combination of the “stepwise” and “enter” methods in SPSS software.

$$R=\frac{\left({\sum }_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)\right)}{\sqrt{{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^2}\sqrt{{\sum }_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}$$

(1)

2.2.1. Linear Regression

Linear regression is a statistical method commonly used to determine the value of a dependent variable based on that of an independent variable [58]. This technique uses a mathematical equation that outputs a simple value based on a combination of input properties. The linear regression equation is as follows [59]:

$$\widehat{y}={\beta }_O+x_1{\beta }_1+x_2{\beta }_2+x_3{\beta }_3+\dots +x_n{\beta }_n$$

(2)

2.2.2. Polynomial Regression

In polynomial regression, the data are approximated using a polynomial function [60]. It involves the use of high-order terms of variables for estimating the polynomial regression and creating a curved response surface [61]. Since there is no universal polynomial equation, the equation should be determined based on the specific problem at hand. The general expression for a polynomial of a function is as follows [59]:

$$f\left(x\right)=c_o+c_{1}x+c_2{x}^2+\dots +c_n{x}^n$$

(3)

2.3. Model Evaluation

Four performance metrics (equations) were used to evaluate the suitability of the models including the coefficient of determination (R²), mean absolute error (MAE), root mean squared error (RMSE), and average absolute error (AAE). The coefficient of determination is a convenient tool for comparing relative performance. The MAE was used because it has the same units as the measured and predicted values and is intuitive. Although the RMSE had the advantage of reducing the distortion of values resulting from the square of the error, errors < 1 were further reduced due to the square, whereas errors > 1 increased. AAE and ABE represent the average error of the correlation equation; if they have positive values, they are evaluated highly, whereas if they have negative values, they are evaluated as somewhat low. The optimal selected prediction models were cross-validated using the data summarized in

Table 1. Data for cross-validation.

	Element Analysis			Proximate Analysis			Composition Analysis			Ref
	C	H	O	VM	FC	Ash	Cell	Hemi	Lig
Mixed waste wood	48.08	5.69	45.8	86.15	10.44	3.41	42.27	27.05	30.68	[62]
Torrefied mixed waste wood (200 °C)	51.76	5.34	42.47	83.03	10.6	6.36	42.78	26.71	30.51
Torrefied mixed waste wood (250 °C)	52.46	5.55	41.46	74.24	18.82	6.94	46.32	18.07	35.61
Oak waste wood	47.26	5.95	46.46	87.3	12.05	0.65	44.64	29.72	25.64
Torrefied Oak waste wood (200 °C)	48.78	5.86	44.94	86.52	12.62	0.86	43.77	28.01	28.22
Logging residue	47.72	6.26	45.6	82.18	16.07	1.75	49.94	21.12	28.94	[63]
pine wood	45.83	6.35	47.51	83.1	16.3	0.6	50	19.67	30.33	[64]
Rice husk	44.91	6.93	47.21	68.55	22.95	8.5	48.32	37.17	14.52	[65]
Corn cob	46.29	6.69	46.69	67.68	22.29	10.03	47.37	36.84	15.79
Groundnut shell	47.51	6.32	45.64	69.69	21.11	9.2	55.06	23.6	21.35
Pine chip	47.31	6.65	45.86	85.97	13.76	0.27	54.01	16.89	29.09	[66]
Torrefied pine chip (225 °C)	49.61	6.09	44.15	84.42	14.89	0.7	44.56	13.91	41.53
Torrefied pine chip (250 °C)	51.73	5.89	42.24	82.51	17.24	0.25	44.32	7.33	48.34
Logging residue chip	47.72	6.26	45.6	82.16	16.07	1.77	48.75	17.24	34.01
Torrefied logging residue chip (225 °C)	50.51	6.14	43.05	80.73	17.9	1.37	46.11	16.59	37.30
Torrefied logging residue chip (250 °C)	53.81	5.75	40.14	78.14	20.37	1.49	44.37	6.75	48.88
Torrefied logging residue chip (275 °C)	53.75	5.44	40.5	71.43	26.69	1.88	37	5.68	57.32
Loblolly pine	50.78	6.29	42.84	84.6	14.8	0.6	42.52	22.03	35.45	[67]
Torrefied loblolly pine (270 °C 2.5 min)	55.36	5.98	38.55	78.6	20.8	0.6	39.29	13.92	46.79
Torrefied loblolly pine (300 °C 2.5 min)	57.74	5.83	36.28	76.4	22.8	0.8	35.85	10.22	53.93
Torrefied loblolly pine (330 °C 2.5 min)	66.77	4.94	28.01	59.96	38.64	1.4	19.33	1.25	79.42
Palm mesocarp fiber	46.29	4.67	47.37	63.29	29.49	7.22	30.43	29.25	40.32	[68]
Palm kernel shell	47.77	4.06	47.55	59.07	34.36	6.57	30.28	28.31	41.41
Sugarcane bagasse sample	46.32	6.28	46.74	83.55	14.28	2.17	43.35	35.33	21.32	[69]
Torrefied sugarcane bagasse (200 °C)	41.88	4.21	53.59	71.26	26.97	1.77	44.19	12.35	43.46
Torrefied sugarcane bagasse (225 °C)	47.1	4.72	47.79	71.95	25.55	2.49	34.03	15.39	50.58
Torrefied sugarcane bagasse (250 °C)	52.63	3.79	43.16	62.27	34.5	3.22	25.82	8.29	65.89

.

$$R^2=1-\frac{{\sum }_{i=1}^{n}Valu{e}_M-Valu{e}_P}{{\sum }_{i=1}^{n}Valu{e}_M-\overline{Valu{e}_P}}$$

(4)

$$MAE=\frac{{\Sigma }_{i=1}^n\left(Valul{e}_M-Valu{e}_P\right) }{n}$$

(5)

$$AAE=\frac{1}{n}\sum _{i=1}^n\left|\frac{Valu{e}_P-Valu{e}_M}{Valu{e}_M}\right|$$

(6)

3. Results & Discussions

3.1. Result of Pearson Correlation Coefficient

The results of Pearson’s correlation coefficient are summarized in Figure 5. Cellulose showed a negative correlation with C, but a positive correlation with H and O. Despite the negative correlation between C and cellulose, both H/C and O/C showed positive correlations. In particular, the H/C ratio exhibited a strong positive correlation (0.658). The VM showed a positive correlation, whereas the FC showed a negative correlation. FC/VM showed a strong negative correlation, which was attributed to the low FC content of cellulose. The correlation between the VM/FC ratios was low. Hemicellulose showed a stronger negative correlation with C than cellulose. H, O, H/C, and O/C showed positive correlations, but there was a slight difference compared to their relationship with cellulose. The correlation between H and hemicellulose showed a weaker positive correlation (0.26) than that between cellulose and H. On the other hand, the correlation between O and hemicellulose was higher (0.42) than that between cellulose and O (0.30). As a result, there was a slight difference between the H/C and O/C ratios. In the case of lignin and each element, there were many cases in which their correlations were opposite to those of cellulose and hemicellulose. Lignin was positively correlated with C and negatively correlated with H, O, H/C, and O/C, which were positively correlated with cellulose and hemicellulose. Lignin levels showed a strong negative correlation with VM and a strong positive correlation with FC. These results were based on the fact that cellulose and hemicellulose are composed of linear carbon structures, whereas lignin has a ring structure that forms stronger bonds, making it less volatile. In addition, there was a strong positive correlation in the case of FC/VM due to its relationship with cellulose, such as FC. However, there was no strong correlation in the case of the VM/FC. Based on these results, the basic prediction model that was suggested is as follows:

$$Cell=f\left(C, H, O, VM, FC\right)$$

(7)

$$Hemi=g\left(C, H, O, VM, FC\right)$$

(8)

$$Lig=h\left(C, H, O, VM, FC\right)$$

(9)

3.2. Prediction Model for Cellulose

The equations with the highest R²_P for predicting cellulose content are summarized in

Table 2. Results of predicted model for cellulose.

No.	Proposed Models	R2P [-]	RMSEP [%]	MAEP [%]	AAEP [%]
C1	$\begin{array}{ll}Cell=-152.237& +0.838C-10.405H+3.3091O-37.061{\left(\frac{H}{C}\right)}^2\\ & + 177.211\left(\frac{H}{C}\right)+20.086{\left(\frac{O}{C}\right)}^2-136.126\left(\frac{O}{C}\right)\\ & + 0.151VM+0.391FC-4.52 \left(\frac{FC}{VM}\right)\end{array}$	0.6104	7.3666	5.6839	49.2202
C2	$$\begin{gathered} Cell=678.363+0.270C^2-0.632H^2-0.166O^2-34.026C \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 24.548H+22.108O-15.474{\left(\frac{H}{C}\right)}^2-10.580\left(\frac{H}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 94.988{\left(\frac{O}{C}\right)}^2-510.643\left(\frac{O}{C}\right)+0.250VM \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.290FC-3.866 {\left(\frac{FC}{VM}\right)}^2+10.266 \left(\frac{FC}{VM}\right) \end{gathered}$$	0.6342	7.3013	5.4302	32.7348
C3	$$\begin{gathered} Cell=810.611+0.311C^2-0.657H^2-0.165O^2-39.014C \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 23.282H+23.513O-14.962{\left(\frac{H}{C}\right)}^2-4.252\left(\frac{H}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 104.943{\left(\frac{O}{C}\right)}^2-595.105\left(\frac{O}{C}\right)-0.001V{M}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.551VM-0.012F{C}^2+0.116FC \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 12.486 {\left(\frac{FC}{VM}\right)}^2+59.697\left(\frac{FC}{VM}\right) \end{gathered}$$	0.6362	7.3263	5.8115	43.1320

. Differences were observed between C1 and C2 when the second-order terms C, H, O, and FC/VM were added to the equation. Due to the increase in the number of factors involved in the equation, C2 showed an increased R²_P of 0.6342, whereas C1 had an R²_P of 0.6104. Additionally, lower RMSE_P, MAE_P, and AAE_P values were observed. When comparing C2 and C3, the impact of the second-order terms on VM, FC, and FC/VM was considered. The R²_P value for C3 increased slightly to 0.6362. However, the RMSE_P, MAE_P, and AAE_P increased for C3, with values of 7.3263, 5.8115, and 43.1320, respectively, compared with C2 values of 7.3013, 5.4302, and 32.7348. This indicates that C3 had larger errors, as shown in Figure 6. The red trend line in Figure 6 was used as a reference for significance at the level of 0.01. As expected, there was little difference in the trends between C2 and C3; however, some data points from C3 deviated further from the trend line compared to those from C2.

3.3. Prediction Model for Hemicellulose

Various factors were added to predict the hemicellulose content. However, the R²_P of the model was lower than that of cellulose and lignin. The equations with the highest prediction accuracies are listed in

Table 3. Results of predicted model for hemicellulose.

No.	Proposed Models	R2P [-]	RMSEP [%]	MAEP [%]	AAEP [%]
H1	$$\begin{gathered} Hemi=398.274-0.118C-36.749H+3.886O-51.759{\left(\frac{H}{C}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 300.624\left(\frac{H}{C}\right)+48.091{\left(\frac{O}{C}\right)}^2-286.902\left(\frac{O}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.055V{M}^2-0.003F{C}^2-9.205VM+3.077FC \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 50.49{\left(\frac{FC}{VM}\right)}^2-275.401\left(\frac{FC}{VM}\right) \end{gathered}$$	0.4901	7.4899	6.1396	53.1694
H2	$$\begin{gathered} Hemi=1465.909+0.212C^2+0.66H^2+0.101O^2-33.374C \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 49.249H+10.983O-66.583{\left(\frac{H}{C}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 363.635\left(\frac{H}{C}\right)+209.649{\left(\frac{O}{C}\right)}^2-1329.208\left(\frac{O}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.376VM-0.673FC \end{gathered}$$	0.4803	7.5634	5.6556	45.8770
H3	$$\begin{gathered} Hemi=1481.552+0.152C^2+1.823H^2+0.093O^2-24.536C \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 75.775H+9.712O-94.539{\left(\frac{H}{C}\right)}^2+494.635\left(\frac{H}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 195.349{\left(\frac{O}{C}\right)}^2-1215.865\left(\frac{O}{C}\right)+0.052V{M}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 8.651VM-0.008F{C}^2+2.644FC \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 42.716 {\left(\frac{FC}{VM}\right)}^2-231.488 \left(\frac{FC}{VM}\right) \end{gathered}$$	0.5112	7.7173	5.7038	48.7658

. When comparing H1 and H2, adding factors related to FC/VM resulted in a higher R²_P value than adding the square terms C, H, and O. This suggested that the relationship between hemicellulose and FC/VM has a stronger correlation than that with C, H, and O, based on the Pearson correlation coefficients. The R²_P values for H1 and H2 were 0.4901 and 0.4803, respectively, showing no significant differences. However, H1 exhibited a slightly higher trend. Additionally, the MAE_P for H2 was lower (5.6556) than that for H1 (6.1396). When comparing H1 and H3, there was a difference when considering the squared terms of C, H, and O. H3 showed a higher R²_P (0.5112) than H1, but the RMSE_P was higher for H3 (7.7173) compared to H1 (7.4899). However, MAE_P and AAE_P were lower for H3 (5.7038 and 48.7658, respectively). The results for each prediction equation are presented in Figure 7. The red line represents the trend line, and the blue line is the confidence interval with a 0.01 significance level. The lowest overshoot was observed for H2. For H1 and H2, relatively significant deviations from the trend line were observed in the prediction results, which contributed to the higher RMSE values.

3.4. Prediction Model for Lignin

The optimal lignin contents are listed in

Table 4. Results of predicted model for lignin.

No.	Proposed Models	R2P [-]	RMSEP [%]	MAEP [%]	AAEP [%]
L1	$$\begin{gathered} Lig=165.252+40.196{\left(\frac{H}{C}\right)}^2-130.961\left(\frac{H}{C}\right)+21.354{\left(\frac{O}{C}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 50.265\left(\frac{O}{C}\right)-0.11VM+0.164FC-4.561\left(\frac{FC}{VM}\right) \end{gathered}$$	0.7247	9.0426	7.0424	28.6080
L2	$$\begin{gathered} Lig=-121.824+39.757{\left(\frac{H}{C}\right)}^2-128.192\left(\frac{H}{C}\right)+23.719{\left(\frac{O}{C}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 56.877\left(\frac{O}{C}\right)-0.042V{M}^2+6.932VM \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.000473F{C}^2-2.954FC-45.172 {\left(\frac{FC}{VM}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 239.132 \left(\frac{FC}{VM}\right) \end{gathered}$$	0.7348	9.1532	7.1781	31.1764
L3	$$\begin{gathered} Lig=-2192.163-0.463C^2-1.165H^2+0.072O^2+63.550C \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 52.493H-33.225O+109.501{\left(\frac{H}{C}\right)}^2 \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 490.382\left(\frac{H}{C}\right)-300.292{\left(\frac{O}{C}\right)}^2+180.969\left(\frac{O}{C}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.050V{M}^2+8.100VM+0.020F{C}^2-2.760FC \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 30.230{\left(\frac{FC}{VM}\right)}^2+171.791\left(\frac{FC}{VM}\right) \end{gathered}$$	0.7914	7.9857	5.9868	26.3036

. Lignin exhibited higher R²_P values than cellulose and hemicellulose. In the case of L1, the least number of factors was considered. However, the R²_P value was 0.7247, which was higher than that observed for cellulose and hemicellulose. L1 and L2 were determined based on whether the second-order VM and FC were considered. L2, which was considered the second-order VM and FC, showed a higher R²_P (0.7348). However, the RMSE_P, MAE_P, and AAE_P were lower for L1. L3 exhibited the highest R²_P value (0.7914). The RMSE_P, MAE_P, and AAE_P were also lower, with values of 7.9857, 5.9868, and 26.3036, respectively. As shown in Figure 8, which graphically represents the results, L1 and L2 exhibited excessive predictions when the observed values were between 90 and 100%. However, for L3, excessive predictions were not observed, although the confidence interval was exceeded.

3.5. Cross-Validation Results for Cellulose

The cross-validation results for the cellulose prediction are presented in

Table 5. Cross-validation results of the predicted model using linear regression and algorithm for cellulose.

	R2CV [-]	RMSECV [%]	MAECV [%]	AAECV [%]
C1	0.7837	3.8149	3.0291	7.5647
C2	0.7458	4.3132	3.2023	7.7781
C3	0.7387	4.8125	4.1379	6.9634

and Figure 9. R²_CV was higher than R²_P. The R²_P values for C1, C2, and C3 were 0.6104, 0.6342, and 0.6362, respectively. The R²_CV values were 0.7837, 0.7428, and 0.7387, respectively. In particular, C1, which had the lowest R²_P value, also had the highest R²_CV value. The RMSE_CV for C1 is 3.8149. Based on the validation results, C1 was identified as the optimal prediction equation.

3.6. Cross-Validation Results for Hemicellulose

The cross-validation results for hemicellulose prediction showed lower performance than that of the prediction model. The results are summarized in

Table 6. Cross-validation results of the predicted model using linear regression and algorithm for hemicellulose.

	R2CV [-]	RMSECV [%]	MAECV [%]	AAECV [%]
H1	0.3292	8.6098	7.2671	61.0694
H2	0.4004	8.2683	7.2084	66.4448
H3	0.3280	9.8534	8.7032	66.0180

. The R²_P values for H1, H2, and H3 were approximately 0.5, with values of 0.4901, 0.4803, and 0.5112, respectively. However, the R²_CV values were lower at 0.3292, 0.4004, and 0.3280 for H1, H2, and H3, respectively. This low performance was also reflected in the RMSE_CV values, which ranged from 8.2683 to 9.8534. The validation results are illustrated in Figure 10, which shows that they fall within the 99% confidence interval. In Figure 10a,b, the results are skewed towards the upper end of the confidence interval. Thus, H2 was selected as the optimal concentration.

3.7. Cross-Validation Results for Lignin

Similar to R²_P, lignin exhibited a higher R²_CV compared to cellulose and hemicellulose. The results are summarized in

Table 7. Cross-validation results of the predicted model using linear regression and algorithm for lignin.

	R2CV [-]	RMSECV [%]	MAECV [%]	AAECV [%]
L1	0.7728	7.7483	6.7726	19.8385
L2	0.7757	7.2735	6.3054	20.2150
L3	0.7427	7.7133	6.6112	19.7636

and Figure 11. The R²_P values for L1, L2, and L3 were 0.7247, 0.7348, and 0.7914, respectively, The corresponding R²_CV values are 0.7728, 0.7757, and 0.7427, respectively. The R²_CV for L3 was lower than its R²_P but increased in L1 and L2. The RMSE_CV values ranged from 7.2735 to 7.7483. Based on the validation results, L2 was considered optimal.

3.8. Prediction and Cross-Validation of Hemicellulose Using Cellulose and Lignin

Based on the relatively stronger correlation between lignin and cellulose than with hemicellulose, the decision was made to predict hemicellulose content based on lignin and cellulose using the selected optimal conditions of C1 and L2. The results are summarized in

Table 8. Prediction and cross-validation results of hemicellulose based on C1 and L1.

R2P [-]	RMSEP [%]	MAEP [%]	AAEP [%]	R2CV [-]	RMSECV [%]	MAECV [%]	AAECV [%]
0.3770	8.5612	6.7581	50.3295	0.4292	7.5979	6.3346	51.9966

and Figure 12. The prediction results showed an R²_P value of 0.3770, which was lower than that of the hemicellulose prediction for H1, H2, and H3. Consequently, the RMSE_P, MAE_P, and AAE_P were higher, with values of 8.5612, 6.7581, and 50.3295, respectively, compared with the results of the previous prediction equations. In Figure 12a, there were cases where the hemicellulose contents were negative, which was attributed to the overprediction of the cellulose and lignin contents. The CV results differed from the predicted results. The R²_CV showed a higher value (0.4292) than the R²_CV of the other prediction equations. Similarly, the RMSE_CV was lower (7.5979) when C1 and L2 were used for prediction compared to H1, H2, and H3, which had values ranging from 8.2683 to 9.8534. Based on these results, it was determined that using H2 or predicting hemicellulose based on cellulose and lignin yielded optimal predictions.

3.9. Application Performance

To thoroughly assess the performance of the developed models, the models are utilized to make predictions on the chemical constituents of the application database. It is important to note that all the samples in this database are different from those present in the training database. Since the mass fraction of volatile matter is provided in the application database, it is possible to directly compare the currently developed model with the previous correlation proposed by Sheng and Azevedo [70]. These correlations can be expressed using the following equations:

$$Cellulose=-1019.07+293.810\left(\frac{O}{C}\right)-187.639{\left(\frac{O}{C}\right)}^2+65.1426\left(\frac{H}{C}\right)-19.3025{\left(\frac{H}{C}\right)}^2+21.7448VM-0.132123V{M}^2$$

(10)

$$lignin=612.099+195.366\left(\frac{O}{C}\right)-156.535{\left(\frac{O}{C}\right)}^2+511.357\left(\frac{H}{C}\right)-177.025{\left(\frac{H}{C}\right)}^2+21.7448VM+0.145306V{M}^2$$

(11)

According to Sheng and Azevedo (2002), the correlation they developed was based on samples with the following ranges of parameters: O/C ratio: 0.56 to 0.83, H/C ratio: 1.26 to 1.69, and volatile matter (VM): 73% to 86%. These ranges were used to establish the correlation between the mass fraction of the volatile matter and other chemical constituents in their model. Figure 13 shows the direct comparison of the chemical composition predicted with the present model and the correlation developed by Sheng and Azevedo. Figure 13 also illustrates the direct comparisons of the chemical composition predicted using the current model, the previous correlation proposed by Sheng and Azevedo, and the experimental data. In the figure, the green lines represent the data distribution, where the relative error is ±20%. This provided a visual representation of the agreement between the predicted values and the experimental data for each model. In the case of Sheng and Azevedo’s model, the prediction performance for torrefied samples was low. Values in the ranges of −422.80–−5.20%, −225.21–144.62%, and −39.32–8731.05% were obtained for cellulose, hemicellulose, and lignin, respectively. The models in this study showed −19.96–21.59%, −24.77–84.08%, and −39.23–355.61%, respectively.

4. Conclusions

This study aimed to predict the cellulose, hemicellulose, and lignin contents based on elemental and industrial analyses, instead of using conventional methods such as HPLC or infrared spectroscopy. Herein, various models were proposed to obtain regression prediction equations using linear regression. The R²_P values for cellulose, hemicellulose, and lignin using linear regression were between 0.6104 and 0.6362, 0.4803 and 0.5112, and 0.7247 and 0.7914, respectively. Prediction for hemicellulose exhibited the lowest performance. Based on this, the optimal equation was used for cross-validating the same. The optimal conditions for cellulose and lignin were selected as C1 and L2 due to their highest R²_CV and lowest RMSE_CV, MAE_CV, and AAE_CV. To address the low accuracy of the hemicellulose prediction model, it was predicted based on the cellulose and lignin prediction models, which were validated as optimal. Despite the lower R² and higher RMSE values compared to those of the hemicellulose prediction equations, the cross-validation results were higher than those of the other prediction equations. Despite the lower performance in terms of R² and higher RMSE compared to those of lignin and cellulose, the prediction and cross-validation results were deemed optimal when both prediction and cross-validation results were considered. Therefore, using both cellulose and lignin for the prediction and the H2 equation was deemed to be the optimal approach.

This study had some limitations. Although we considered data from a wide range of samples, including torrefied samples, predictions were only made using data for woody and herbaceous biomasses. Therefore, the predictions may be inaccurate for food waste or sewage sludge. In the case of hemicellulose, low prediction accuracy was observed due to its low content compared to cellulose and lignin. In addition, it was shown to represent a low prediction due to a decrease in various ranges, depending on the process conditions. Therefore, future research should provide models for a wider range of biomasses and improve prediction equations based on more data pertaining to woody and herbaceous biomass.