Determination of the heat capacity of cellulosic biosamples employing diverse machine learning approaches

Heat capacity is among the most well‐known thermal properties of cellulosic biomass samples. This study assembles a general machine learning model to estimate the heat capacity of the cellulosic biomass samples with different origins. Combining the uncertainty and ranking analyses over 819 artificial intelligence models from seven different categories confirmed that the least‐squares support vector regression (LSSVR) with the Gaussian kernel function is the best estimator. This model is validated using 700 laboratory heat capacities of four cellulosic biomass samples in wide temperature ranges (absolute average relative deviation = 0.32%, mean square errors = 1.88 × 10−3, and R2 = 0.999991). The data validity investigation approved that only one out of 700 experimental data is an outlier. The LSSVR model considers the effect of the cellulosic samples' crystallinity, temperature, and sulfur and ash content on their heat capacity. The overall prediction accuracy of the LSSVR is more than 62% better than the achieved accuracy using the empirical correlation.


| INTRODUCTION
The escalating level of greenhouse gases (GHGs), including carbon dioxide (CO 2 ), methane (CH 4 ), nitrogen (N 2 ), carbon monoxide (CO), and chlorofluorocarbons (CFCs) originated from anthropogenic activities resulted in severe global challenges such as warming. 1-3 On the other hand, the exponential population expansion and a spicy modernization growth intensified fossil fuel consumption in the last decades. [4][5][6] Fossil fuel combustion and related industries [7][8][9] are responsible for 65%-80% of total CO 2 emission in the atmosphere. 10 Tangang et al. declared that the current rising level of GHGs contributes to around 3-5°C temperature increment of this planet at the end of this century, raising the sea level about 95 cm. 11 In this way, according to the BLUE map scenario of the international energy agency, 12 renewable and sustainable energy sources, including biomass, 13 solar irradiation, 14 wind power, 15 can supply a significant percentage of energy consumption worldwide. 16 Currently, biomass is the world's third source of energy. 17 Based on the united nations environment program report, 140 billion tons of biomass are annually produced worldwide. 18 The wooden wastes, agricultural wastes, and residual wastes are the main components of these materials. 19,20 As a main ingredient of biomass, the straw is a low-cost, sustainable and plentiful renewable feedstock, which can be introduced as a valuable source of various chemicals and biofuels to reduce the drawbacks of fossil fuels consumption. 21 Annually, a considerable value of straws, including rice straw (975 million tons), corn stover/cob (1661 million tons), and wheat straw (529 million tons), are produced in the world. 22 From 2007, straw production has increased 1.4% per year, 23 which to obtain sustainable development in 2040, around 20 times of the environmental yield of available agricultural production technologies are required. 21,24 Cellulose, hemicellulose, and lignin are the main ingredients of lignocellulosic biomass. 25 Due to the intricate compositions in the connected diverse straw biomass, the efficient application of plant biomass is faced with numerous obstacles. 21 Generally, most straw biomass is converted to high-value chemicals using biomechanical, biological, or different chemical treatments that cause a significant effect on GHGs reduction and accelerate the sustainable development of the world. 26,27 Preethi et al. investigated the technoeconomic analysis and the environmental concerns of lignocellulosic biomass regarding its application as a valuable energy source. 28 In addition, Rodríguez et al. studied the effects of sintering and slagging parameters in biomass combustion in biofuel production and reducing the adverse environmental effects. 29 Wu et al. investigated hemicellulose's thermal and kinetic behaviors with fast pyrolysis of lignocellulosic biomass. 30 The results showed that gas and tar are the key elements of fast pyrolysis of hemicellulose. 30 Furthermore, recent advances and sustainable development of biofuels production from lignocellulosic biomass have been reviewed. 31 Materials' thermal characteristics are required to monitor the reaction equilibria, estimate the products' energy content, and obtain the adiabatic temperature at the gasification unit. 13,32 The biomass heat capacity is a fundamental thermophysical property required to calculate the standard molar thermodynamic functions and reaction equilibria to design a highly efficient reactor for plant biomass processing. 33 Moreover, precise knowledge of the working capacity and thermodynamic properties of biomass samples are required for effective plant processing, while lack of enough information on the thermodynamic properties of cellulose and lignin is one of the main challenges in developing the biomass industry. 33 The heat capacity of plant biomass with different origins was also experimentally measured using differential scanning calorimetry (DSC) in a temperature range of 5-370 K. 33 Also, in other studies, the heat capacity of cellulose fibers was determined in T = 400 K using a drop calorimeter technique. 34,35 In addition, several studies investigated the heat capacity of different types of cellulose for its application in the pulp industry. 33,36,37 They tried to determine the dependency of paper composition and the specific heat capacity. 36 Uryash et al. measured the cellulose heat capacity and its mixture in water using the adiabatic calorimeter in temperatures ranging from 80 to 330 K. 37 Furthermore, thermal characters of coconut fiber and sugarcane bagasse for textile applications were analyzed by Mothée and De Miranda. 38 However, the literature presents no model for predicting the heat capacity of the cellulosic biomass samples at a wide range of temperatures. The only available empirical model is valid for narrow and almost unusable operating conditions, that is, T < 80 K. 39 This study relies on machine learning models from three different categories to develop a general approach for the considered task. The current study is the first attempt to incorporate the cellulosic biomass samples' crystallinity characteristics and chemical composition on the heat capacity estimation. Furthermore, the available correlation is modified to cover a higher temperature range, but its accuracy is still far lower than the assembled intelligent model. Indeed, the artificial intelligence (AI)-based model improves the obtained accuracy by the modified empirical correlation by more than 62%.

| MATERIALS AND METHODS
This section presents the background and mathematical governed different artificial intelligent models. Furthermore, the laboratory-measured data for the heat capacity of cellulosic biomass samples gathered from the literature are reviewed.

| Machine learning scenarios
Recent progress in the data analysis and computer science areas resulted in implementing statistical 40 and machine learning 41,42 techniques in various fields, mainly in vision-based learning, 43 energy storage 44 and management, 45 and material design 46 and characterization. Moreover, it is possible to develop machine learning methods utilizing extracted/selected features to enhance the prediction accuracy. 47 Routinely, artificial neural networks (ANNs) are more popular than the other AI techniques, including the support vector machine (SVM), or adaptive neuro-fuzzy inference system (ANFIS) for regression tasks. In this way, numerous studies have focused on employing machine learning in the biomass industry. To this end, Tsekos et al. evaluated the lignocellulosic biomass pyrolysis main products yields using the ANN. 48 Hence, they considered the most relevant compositional and reaction parameters over the main products yields of lignocellulosic biomass pyrolysis. 48 Also, the biomass characterization, specifically the moisture content, was determined with different AI techniques by Ahmed et al. 49 Results showed that machine learning approaches have a great potential to be employed in future near-infrared spectroscopy applications. 49 In another attempt, Çepelioğullar et al. tried to model the activation energy of lignocellulosic forest residue and olive oil residue as biomass feedstocks by different neural network topologies. 50 Xing et al. employed ANN and SVM to specify the higher heating values of lignocellulosic samples for biomass-fueled energy processes. 51 Moreover, Karimi et al. introduced the least-squares support vector machine (LSSVM) as the most robust approach to estimate biochar pyrolysis residues' heat capacity. 52 Recently, Obafemi et al. presented a survey on applying different ANNs for estimating the thermal properties of biomass. 53 They reported that the ANN has many advantages compared to other techniques to evaluate the biomass thermal properties. The results were validated based on ultimate, proximate, and thermos-gravimetric analysis. 53

| ANNs
Developing trustworthy, robust, and precise topologies to correlate and model highly nonlinear concepts are an arduous, uphill, and time-consuming task, which sometimes is not possible to achieve. The ANNs as nonlinear learning approaches were developed based on the biological nervous systems of the human brain have a great potential for data analysis, process design, fault detection, and algorithm assessment. 54 In this way, recently, ANNs have attracted significant attention in the areas where precise empirical or semi-empirical correlations are not available as well as measuring experimental valuers in a broad range is an infeasible mission. 55 Generally, creating robust ANN models does not require accurate relations among the input and output values or the parametric nature of considered variables. 56 To develop ANN approaches, a set of independent/influential variables are trained to estimate dependent variables. 57 To this end, interconnected processing units, which are supported from external information sources or previous layers, are employed to treat the data using vast parallel weighted connections, 58 according to the literature. The multilayer perceptron neural network (MLPNN) is among the most popular function approximations. 14 Typically, the MLPNN paradigm with three main layers, that is, input, hidden, and output layer, can model phenomena with any degree of complexity and nonlinearity. 58 On the grounds, the input layer is defined after some data treatment on independent variables of the system. Afterward, these values are transferred to the hidden layer for mathematical processing. Finally, the output layer of the MLPNN is determined after finalizing the receiving data from the hidden layer, which is specified by the following equation 59 : As shown in Equation (1), the neuron's output is measured after employing the weight vector (   W ) on the entry signal (   X ), also applying activation thresholds as biases (b) of the developed system. Then, the transfer function is considered (ζ ) to consummate the net output of each neuron. Radial basis (Equation (2) here ζ (net) specifies the neuron's output, exp indicates the exponential function, and s is the spread factor of the radial basis transfer function.
Designing a robust ANN approach requires the orders of neurons interactions to be specified in different layers. In this way, various ANN models such as MLPNN, cascade feed-forward (CFFNN), general regression (GRNN), and radial basis function (RBFNN) have been introduced in recent years. The RBFNN designed the approach in three main layers, employing a nonlinear activation function for developing the architecture. The GRNN is a one-pass learning topology and a memorybased method that minimizes errors using probability density functions. 61 The radial basis (Equation 2) and linear (Equation 3) transfer functions are utilized in the hidden and output layers of the RBFNN and GRNN models. The MLPNN paradigm developed the network using the independent parameters (bias) for each neuron and training on-line learning approaches by employing a partial fit order. The CFFNN creates the network using direct connections between the input and the successive layers. The hyperbolic tangent sigmoid (Equation 4) and logarithmic sigmoid (Equation 5) transfer functions are utilized in the hidden and output layers of the MLPNN and CFFNN models. 62 It is worth mentioning that this study develops a highly accurate ANN model to estimate the heat capacity of plant biomass samples by evaluating all mentioned topologies.

| Least-squares support vector regression
SVM as a new machine learning topology was firstly developed by Vapnik, 63 based on statistical learning concepts. The SVM is employed in three main areas: pattern recognition, regression analysis, and clustering development. 52 The SVM has several assets than traditional neural networks, such as less risk of overfitting, low tuning variables also a high degree of general optimization. 64 Besides the benefits of SVM, the necessity for a large-scale quadratic for data analysis is the main drawback of this AI approach. 52 This impediment has been obviated in the least-square SVM topology. 65 The LSSVR approach employs linear programming instead of quadratic equations to decrease the complexity of the optimization procedure. 65,66 The LSSVR determines the dependent function by the following equation. 65 Here, ψ x ( ) is the kernel function, also  b , are the weight and bias of the model, respectively. In the next step, the cost function (Equations 7 and 8) must be optimized. 52 After that, the optimized process is justified using the Lagrange function (Equation 9). 52,65 For further proceeding, it is necessary to solve Equation (10) by equating to zero with respect to , b, e k , and α k , that results in 65 It is worth noting that the kernel matrix is measured using the following equation. 65 In addition, it should be considered that the main kernel functions are linear (Equation 12a), polynomial (Equation 12b), and Gaussian (Equation 12c). 52 Here, kernel parameters (σ, d, and t) are determined during optimization. 65,67 2.1.3 | ANFISs ANFIS, as a combination of fuzzy logic and ANN, is a neuro-fuzzy system, which Jang firstly developed in 1993. 68 This AI approach is a multilayer feed-forward network that designs the architecture based on a unique learning algorithm. 52 Accordingly, a combination of lease square and gradient descent is considered to decrease the possibility of getting stuck and enhance the likelihood of the optima minima. 69 To this end, membership functions (MFs) which have already been modified by the ANNs, also the fuzzy IF-THEN rules are employed to develop a fuzzy inference system (FIS). 68 Takagi-Sugeno-Kang (TSK) and Mamdani are among the well-known FIS. 70 The TSK FIS develops a model by knowing the available pattern between the input and output values. Mamdani FIS composes IF-THEN rules according to the specific statements, which causes some vague outcomes. 68,70 Briefly, developing an ANFIS network includes the following steps 52,71 : (1) Initializing MFs: first, the number and type of MFs are specified according to the input parameters. (2) Generation of FIS: second, the numbers of fuzzy rules are determined using some fuzzy subspaces, which are defined for the input space according to the grid partitioning pattern. (3) Determination of learning parameters: in the third step, the learning algorithm, the number of training epochs, also the error tolerance are determined. (4) Training process: the initialized MFs are specified using the training data; the relation among the inputs and outputs is determined considering the fuzzy rules.
Generally, developing the ANFIS approach includes five layers that, because of the complexity of the paradigm, here a mathematical explanation of two inputs (X 1 , X 2 ) is represented. First, the following rules by Equations (13)-(16) are employed for network development 68,70 : Rule I: Rule II: Rule III: Rule IV: In the mentioned rules, m m m m n n n n , , , , , , , , 1 2 3 4 1 2 3 4 r r r r , , , and 1 2 3 4 indicate the parameters and linguistic labels of input data, also A 1 , A 2 , B 1 , and B 2 are the corresponding fuzzy sets of input values. A brief discussion on each layer can be found in the following.
Layer 1: In the first layer, the input data are treated as linguistic criteria. Accordingly, each input variable is connected with two nodes. Moreover, the predefined MFs are applied to specify the linguistic values. Here, the Gaussian model (Equation 17) was employed as one of the most popular functions. 52 Z is the Gaussian MF center, I specifies the variance parameter, and O indicates the layer's output.
Layer 2: In the second layer, as the firing strength layer, the obtained values in the previous layer are evaluated in the way of accuracy and validity by the following equation. 68 Layer 3: Then, the normalization of firing strengths is considered using the following equation (19). 71 Layer 4: Afterward, the developed model's linguistic terms and significant rules are evaluated employing the following equation. 70 It is worth noting ANFIS parameters (m n r , , and i i i ) are specified during the training step.
Layer 5: In the last step, the acceptable numerical values are specified by considering the weighted average aggregation method using the following equation. 68

| EXPERIMENTAL DATA FOR THE HEAT CAPACITY OF THE CELLULOSIC BIOMASS SAMPLES
This section reviews experimental data, monitors the interdependency of the heat capacity to its influential variables, and finally explains the normalization process.
KARIMI ET AL.

| Data gathering
Routinely, the heat capacity of biomass samples is determined using the DSC or adiabatic calorimeter. 33,34 It has been shown that heat capacity is influenced by temperature. 52 Because of the decomposition conditions, there are several limitations on maximum feasible heat capacity, which can be measured using DSC (i.e., 423 K). [35][36][37] The experimental measurement is a challenging and time-consuming task that needs much economic expense and often contains different levels of uncertainty. Accordingly, the current study has developed a straightforward and highly accurate AI topology to estimate the heat capacity of cellulosic biomass samples. Crystallinity index, the chemical composition of biomass samples, and temperature are used for this estimation. As Table 1 shows, four cellulosic biomass samples, including cotton microcrystalline cellulose, wood sulfite cellulose, straw cellulose, and amorphous wood cellulose, are considered. 33 This table also reports the key textural properties of the cellulosic samples, such as crystallinity index, mass fractions of sulfur, and mass fractions of ash.
Furthermore, Table 2 presents the temperature range and corresponding heat capacity of cellulosic biomass samples. 33 Eighty-five percent of the databank (595) were considered in the training algorithm, and 105 data sets were employed for testing the developed AI approaches.
Indeed, the current study aims to extract the relation between heat capacity (Cp pred ) of the cellulosic biomass samples and crystallinity index (CI), their sulfur (ω s ) and ash (ω ash ) contents, and temperature (T) as follows: s pred ash It can be seen from Table 2 that the heat capacity of all cellulosic biomass samples is available at the temperature range of 81-367 K. The average values of the heat capacity of the biomass samples in this temperature range are calculated and shown in Figure 1. This figure shows that the amorphous microcrystalline cellulosic samples have the highest and lowest average values for heat capacity at the temperature range of 81-367 K.

| Data analysis
The dependency of the cellulosic biomass' heat capacity to the crystallinity index, chemical composition, and temperature is quantized using the Pearson method. 72 As Equation (23)  interrelation between dependent-independent (y, x) variables by a factor (r xy ) between −1 and +1. 72 The highest and smallest factors, that is, +1 and −1 are associated with the strongest direct and indirect relevancy between dependent and independent variables, respectively. 73 The zero or close value to zero implies no relationship between a pair of variables. It is possible to calculate the Pearson's coefficient using Equation (23). 74 here, x (Equation 24) and y (Equation 25) are average values of x and y variables, respectively.
The consequence of applying Pearson's method on the collected experimental database is plotted in Figure 2.
This figure states that ash content and temperature have a direct and crystallinity index, and sulfur content indirectly influences the heat capacity of cellulosic biomass samples. Moreover, the relevancy factor of +1 for the Cp-T combination anticipates a strong direct relationship between the Cp of biomass samples and the temperature.

| Normalization
The normalization of the experimental measurements (both feature and response variables) expedites the convergency rate of the training stage, and it improves the generalization ability of the AI-based tool. 75 Furthermore, this preprocessing stage eliminates the potential differences between the magnitude of variables and avoids higher dependency of the prediction to a bigger feature. Therefore, all variables, that is, CI, ω s , ω ash , T, and Cp, are scaled using the following equation.
here, χ represents the original value of a variable. The norm, min, and max subscripts indicate the normalized, minimum, and maximum values, respectively.

| Uncertainty measurement
Seven stable criteria, that is, correlation of determination (R 2 ), average absolute errors (AAE), mean square errors (MSE), root mean square errors (RMSE), relative absolute error (RAE%), root-relative square error (RRSE %), and absolute average relative deviation (AARD%) are utilized to quantize the level of uncertainty in the predictions of the ANNs (MLPNN, CFFNN, RBFNN, and GRNN), LSSVR, and ANFIS (with two different FIS types) paradigms. Equations (27) to (28) present the mathematical forms of these uncertainty matrices. 13 Numbers of data (N), actual (Cp act ) and predicted (Cp pred ) values of biomass heat capacity, and the average value of experimental heat capacities (Cp act ) are needed to calculate these uncertainty matrices.
It is worth noting that the best model selection is made based on numerical values of these indices during the training and test stages. A model is finally selected as the best one that introduces the smallest values for the last six indices (i.e., AARD%, MSE, RMSE, AAE, RAE%, and RRSE%) and R 2 value close to 1. Indeed, the ranking analysis over these seven indices with the same weight is revealed as the most reliable intelligent model for the considered task.

| RESULTS AND DISCUSSION
This section constructs different AI methodologies (819 models) and determines their appropriate structural properties. Then, the most accurate model is chosen using the ranking analysis. Various graphical and statistical inspections then check the prediction accuracy of the selected model. Finally, the assembled model is employed to understand the thermal behavior of cellulosic biomass samples. Table 3 shows that 819 computational models from three different AI classes (i.e., ANN, ANFIS, and SVM) have been constructed. This table also states that the trial-anderror is conducted on the number of hidden neurons for MLPNN and CFFNN, spread factor for the GRNN, the number of hidden neurons and spread factor for RBFNN, the radius of cluster and learning algorithm for the ANFIS2, numbers of cluster and learning algorithm for the ANFIS3, and kernel types for LSSVR. Table 4 presents the structural properties of the best model (with the lowest uncertainty indices) per each category. The performances of the selected models in terms of seven uncertainty matrices (i.e., AARD%, AAE, RAE%, RRSE%, MSE, RMSE, R 2 ) for training and test data sets are also summarized in this table. Table 4 also reports the accuracy of these intelligent models for the whole databank (training + test).

| Intelligent models: Construction and selection
A glimpse at the reported indices in Table 4 approved that the RBFNN has the highest level of uncertainty for predicting the heat capacity of the cellulosic biomass samples.
Since seven statistical matrices are applied to monitor the uncertainty of the selected AI-based models in the training and test stages, it is necessary to utilize the ranking analysis to sort them according to their performances. 72 It should be noted that all the considered indices assume to have the same weight during the ranking analysis. The results of applying the ranking analyses on the performance of the selected AI-based paradigms (Table 4) are plotted in Figure 3. It is clear that the GRNN and LSSVR show the best ability (the first ranking) for predicting the training and test data sets, respectively. On the other hand, since the LSSVR model shows better performance than the GRNN in the test stage, it is selected as the best estimator for the considered task.

| LSSVR model assessment: Graphical inspection
The compatibility between actual heat capacity measurements and predicted results by the LSSVR model for the training and test stages is separately shown in Figure 4. The excellent ability of the assembled LSSVR model for predicting the heat capacity of the cellulosic biomass samples can be approved by the aggregation of the symbols around the diagonal line (Cp Cp = act pred ).
It is a good idea to measure/report the accuracy of the engineered LSSVR model for predicting the heat capacity of the cellulosic biomass samples with different origins. Figure 5 exhibits that the LSSVR uncertainty ranges for AARD = 0.03% (for straw cellulose) to the AARD = 0.47% (for cotton microcrystalline cellulose). Although the AARD of lower than 10% is acceptable for real applications, our developed model uncertainty is far smaller than 10%. The The observed relative deviations between actual Cp data and predicted ones by the LSSVR are illustrated in Figure 6. Although the relative deviations are ranged from −4% to +4%, significant parts of the experimental data are predicted by an infinitesimal uncertainty.
The mathematical formulation of the relative deviation (Equation 34) has an experimental heat capacity in its denominator. Therefore, lower heat capacity in the denominator (actual~0) is expected to provide a more considerable relative deviation even for a slight deviation between experimental and predicted heat capacities in the nominator (Cp Cp − act pred ).
The histogram of the observed residual error (RE) is the last graphical method used for monitoring the F I G U R E 4 Compatibility between actual and predicted values of heat capacity of the cellulosic samples F I G U R E 5 The observed absolute average relative deviation (AARD)% between actual and predicted values of heat capacity of different cellulosic samples F I G U R E 6 The provided relative deviations by the leastsquares support vector regression for estimating the training and test data sets of heat capacity of the cellulosic samples performance of the proposed LSSVR method. As Equation (35) Figure 7 shows the histogram of the RE provided by the LSSVR model for estimating the training and test data sets. This figure approves that the deviation between experimental and predicted heat capacity values is at −0.005 < RE < + 0.005. Furthermore, the significant parts of training and test data sets are estimated with the RE~0.
The average and standard deviation (SD) of the calculated residual errors are 2.4243 × 10 −6 and 0.0018849 J/kg K, respectively. The mathematical formula is shown by the following equations. 76

| LSSVR model assessment: Statistical and analysis of variance
The results of statistical and analysis of variance (ANOVA) for the LSSVR ability to correlate 700 data sets of Cp of biomass samples are reported in Table 5.
This method calculates the reported information in biomass samples' crystallinity characteristics and chemical composition on their heat capacity estimation. There is only one empirical correlation for predicting the heat capacity of straw cellulose and wood amorphous cellulose below T = 80 K. 39 As Equation (38) states, the estimation is done using the heat capacity of the cotton microcrystalline cellulose (i.e., Cp 1 ). 39 Cp T here α and β are adjusting coefficients of the correlation.
The current study extends the range of application of Equation (38) by readjusting its coefficients. The modification is done so that this equation covers the whole temperature range and all biomass samples (i.e., wood sulfite cellulose, straw cellulose, and wood amorphous cellulose). Table 6 reports the values of adjusted coefficients during the modification stage. This table also presents the predictive uncertainty of the modified version of Equation (38) in terms of AARD% and R 2 .
Equation (38) clearly shows that the heat capacity of the second to fourth biomass samples is modeled with respect to the heat capacity of the first sample. Therefore, this equation has no alpha (α) and beta (β) values when i = 1. Indeed, this ratio is equal to one for i = 1.
Comparison study approves that the LSSVR uncertainty is far lower than the modified empirical correlation. Indeed, the LSSVR predictions for the heat capacity of second to fourth biomass samples are 93.4%, 62.5%, and 85.7% better than the obtained results by the modified empirical correlation.

| Experimental data: Validity check
This section inspects the validity of the experimental measurements collected from the literature for the heat capacity of the cellulosic biomass samples using the leverage method. 72 The leverage method divides the standardized residual (SR) versus hat index into the valid and suspect regions. The early domain contains the valid measurements, while the latter includes the suspicious ones. The mathematical form of the SR is expressed by the following equation. 73 As Figure 8 illustrates, only one out of 700 laboratorymeasured heat capacity data is not valid, and the validity of all other ones is approved.
The valid domain is bounded by −3 < SR < + 3 and hat index < critical leverage (CL). Equation (40) needs the numbers of independent variables (IV) and numbers of available data (N) to give the value of critical leverage. Since the biomass heat capacity is a function of four independent variables, and there are 700 experimental data, the CL = 0.02143 (vertical green line in Figure 8). 73 CL IV N = 3 × ( + 1)/ .

| CONCLUSION
Experimentation is the only available technique in the literature for obtaining the heat capacity of the cellulosic biomass samples. The experimental study needs a lot of time/effort and economic cost and is often poisoned by different levels of uncertainty. Moreover, the experimental data cannot be directly incorporated in the process design, optimization, and control. Therefore, this study employed different machine learning scenarios to relate the heat capacity of the cellulosic samples to their crystallinity F I G U R E 8 Distribution of the valid and suspect data in the gathered experimental database index, chemical composition (sulfur and ash content), and temperature. Ranking analysis using seven uncertainty indices over 819 intelligent models from three different classes (i.e., ANN, SVM, and ANFIS) revealed that the least-squares support vector regression equipped with the Gaussian kernel function is the best model for the considered task. This model predicts 700 experimental heat capacities of four cellulosic samples (cotton microcrystalline cellulose, wood sulfite cellulose, straw cellulose, and amorphous wood cellulose) with the AARD = 0.23%, AAE = 0.00044, RAE = 0.115%, RRSE = 0.42%, MSE = 3.55 × 10 −6 , RMSE = 1.88 × 10 −3 , and R 2 = 0.999991. Relevancy analysis confirms that ash content and temperature have a direct and crystallinity index and sulfur content has an indirect influence on the heat capacity of cellulosic biomass samples. The amorphous cellulosic sample has the highest average heat capacity for the temperature range of 81-367 K. Validity check of the experimental data shows that only one out of 700 data sets may be an outlier, and the rest are reliable. Moreover, the range of application of a single available empirical correlation is extended by readjusting its coefficients. Finally, the LSSVR model accuracy is at least 62% better than the obtained results by the modified empirical correlation.