CET-vol 105


 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                DOI: 10.3303/CET23105078 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 25 February 2023; Revised: 27 June 2023; Accepted: 3 May 2023 
Please cite this article as: Moretta F., Del Duca V., Bozzano G., Coppola A., Scala F., 2023, Canonical Correlation Analysis to Biomass CHONS 
Prediction, Chemical Engineering Transactions, 105, 463-468  DOI:10.3303/CET23105078 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL.  105, 2023 

A publication of 

 

The Italian Association 

of Chemical Engineering 

Online at www.cetjournal.it 

Guest Editors: David Bogle, Flavio Manenti, Piero Salatino 

Copyright © 2023, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-04-5; ISSN 2283-9216 

Canonical Correlation Analysis to Biomass CHONS Prediction 

Federico Morettaa, Vincenzo Del Ducab,*, Giulia Bozzanoa, Antonio Coppolac, 

Fabrizio Scalab,c 

aPolitecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan (MI), Italy  
bDICMaPI, Università degli Studi di Napoli Federico II, Piazzale Vincenzo Tecchio 80, 80125 Naples (NA), Italy 
cSTEMS, Consiglio Nazionale delle Ricerche, piazzale Vincenzo Tecchio 80, 80125, Napoli (NA), Italy 

idelducavincenzo@gmail.com 

Fermentation biomasses can be defined as a complex mixture of different natural components and microbes, 

having biodegradable and organic waste as the primary source. Its correct characterization is crucial to have 

proper processing in fermentative units. Firstly, proximate analysis is done to retrieve the content of specific 

compounds in the mixture, such as fat, proteins, and carbohydrates. However, this is often not enough to 

achieve the sufficient precision, since some low-concentration species are not easily found through this 

methodology (i.e., sulfate compounds, ethanol, caproic acid). Consequently, ultimate analysis is performed to 

evaluate the exact amount of every element in the mixture. For biomass-based compounds, atoms content can 

be synthesized in carbon, hydrogen, oxygen, nitrogen, and sulfur. The total content of these elements is also 

known as CHONS. From this, it is possible to derive the exact amount of the relative species in the biomass. 

However, the experimental procedure for its determination is rather time and budget-consuming. On the other 

hand, the amount of data collected in the literature, from both experimental and industrial analysis, can be 

exploited to build a numerical model, based on the multivariate statistical analysis and machine learning 

principles that predict the CHONS content for every type of biomass. In this work, a data-driven model has been 

developed to achieve this aim, having as input a set of relevant variables. Consequently, a dataset has been 

built to gather all these data. The multivariate statistical technique of Canonical Correlation Analysis (CCA) is 

used to find 'hidden' correlations and predict CHON content for 27 different biomass types. In future research, 

machine learning techniques will be applied to compare the results obtained. 

1. Introduction 

Nowadays, the scientific world is facing environmental burdens that can modify consistently the energy 

production and supply. In this scenario, local biomass for the production of green energy vectors (e.g., 

biomethane, biomethanol) can become a significant mitigation resource (World Energy Outlook 2022 – 

Analysis). Biomasses are very heterogeneous, and consequently, it is important to characterize them before 

use. Macromolecules concentration, such as carbohydrates, proteins and lipids, are necessary to predict the 

biodegradability of the system in digestion systems (Triolo et al., 2011). On the other hand, the elemental fraction 

of carbon, nitrogen, hydrogen and oxygen is necessary information to predict the theoretical biomethane 

potential through the Buswell formula (Achinas and Euverink, 2016). These characteristics are related to one 

another. For example, a high protein concentration averagely brings a higher nitrogen fraction due to the 

abundance of the nitrogen-rich functional group of the amino acids. It is of course possible to find an optimum 

between all these properties when mixing more biomasses, to regulate specific properties such as the C/N ratio 

(Guarino et al., 2016). However, the settings of the optimal parameters, for the desired biomass conversion unit, 

need a relative number of experimental analyses to find all the necessary properties. Proximate analysis is done 

to find ash, moisture, fixed carbon and volatile components amount of the biomass. The compositional analysis 

is performed to find the macromolecules, including lignin and cellulose. Elemental analysis instead evaluates 

carbon, hydrogen, oxygen, nitrogen and sulfur percentage (CHONS) in the biomass. All these procedures can 

become much time-consuming and budget-consuming when a lot of feedstocks have to be tested. Nowadays, 

experimental procedures can easily be overridden by data-driven models which, exploiting all the data coming 

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mailto:idelducavincenzo@gmail.com


from past experiments, elaborate reliable predictions in the observed range (Chang et al., 2021). This work 

focused attention on the individuation of specific correlations related to the calculation of the CHONS fraction 

starting from other biomass attributes, representing the first attempt for building up a decision-support system 

seeking the biomass perfect amount and characteristic (Del Duca et al., 2022). For this aim, the dataset from 

Moretta et al. (2022) has been used, which gathers enough data to perform the study. The tool adopted for the 

application of multivariate statistical analysis is the Canonical Correlation Analysis (CCA). Moreover, correlation 

and other statistical indexes were used to find which of these attributes relate better to the evaluation. The 

database has been pre-processed according to the tool input-output system, generating a new ad-hoc dataset, 

which directly undergoes the mathematical procedure. 

2. Methodology 

Canonical Correlation Analysis (CCA) (Wilks, 2019) is widely used to extract the correlated patterns between 

two sets of variables, x and y. x generally represents the input matrix with size (n x m), where n is the number 

of observations and m is the number of specific input variables; conversely, y represents the output matrix with 

size (n x J), where J is the number of specific output variables. 

CCA looks at two sets of variables for modes of maximum correlation between the two sets. Thus, CCA sits at 

the top of a hierarchy of regression models where it can manage multiple predictors (inputs) and multiple 

predictands (outputs). . If x is the set of predictors and y the predictands, then CCA can be used to predict y 

when new observations of x become available (Hsieh, 2000). The method finds linear combinations of the 

original variables by projecting them onto coefficient vectors am and bm, which is chosen such that each pair of 

the new variables vm and wm, called canonical variates, exhibit maximum correlation, while being uncorrelated 

with the projections of the data onto any of the other identified patterns (Eq. 1a-1b). 

𝑣𝑚 = 𝑎𝑚
𝑇 𝑥′ = ∑𝑎𝑚,𝑖𝑥𝑖

′

𝐼

𝑖=1

,     𝑚 = 1,… ,min (𝐼, 𝐽) (1a) 

𝑤𝑚 = 𝑏𝑚
𝑇 𝑦′ = ∑𝑏𝑚,𝑗𝑦𝑗

′

𝐽

𝑗=1

,     𝑚 = 1,… ,min (𝐼, 𝐽) (1b) 

In other words, CCA identifies new variables that maximize the interrelationships between two data sets in this 

sense. The vectors of linear combination weights am and bm, are called the canonical vectors. The number of 

pairs, M, of canonical variates that can be extracted from the two data sets is equal to  the smaller of the 

dimensions of x and y. The canonical vectors am and bm is the choices that result in the canonical variates (Eq. 

2a-2d) having the following properties: 

𝐶𝑜𝑟𝑟(𝑣1, 𝑤1) ≥ 𝐶𝑜𝑟𝑟(𝑣2, 𝑤2) ≥ ⋯ ≥ 𝐶𝑜𝑟𝑟(𝑣𝑀, 𝑤𝑀) ≥ 0 (2a) 

𝐶𝑜𝑟𝑟(𝑣𝑘 , 𝑤𝑚) = {
𝑟𝐶𝑚

,   𝑘 = 𝑚

0,   𝑘 ≠ 𝑚
 (2b) 

𝐶𝑜𝑟𝑟(𝑣𝑘 , 𝑣𝑚) = 𝐶𝑜𝑟𝑟(𝑤𝑘 , 𝑤𝑚) = 0,   𝑘 ≠ 𝑚 (2c) 

𝑉𝑎𝑟(𝑣𝑚) = 𝑉𝑎𝑟(𝑤𝑚) = 1,   𝑚 = 1,… ,𝑀 (2d) 

Equation 2a states that each of the M successive pairs of canonical variates exhibits no greater correlation than 

the previous pair and these correlations between the pairs of canonical variates are called the canonical 

correlations, rC, where [RC] is the diagonal matrix (Eq. 3). 

[𝑅𝐶] =  

[
 
 
 
 
 
𝑟𝐶1

0 0 ⋯ 0

0 𝑟𝐶2
0 ⋯ 0

0 0 𝑟𝐶3
⋯ 0

⋮ ⋮ ⋮ ⋱ ⋮
0 0 0 ⋯ 𝑟𝐶𝑀]

 
 
 
 
 

  (3) 

Equations 2b and 2c state that each canonical variate is uncorrelated with all the other canonical variates except 

its specific counterpart in the mth pair, finally equation 2d states that each of the canonical variates has a variance 

equal to 1. The basic idea behind forecasting with CCA is straightforward: simple linear regressions are 

constructed that relate the predictand canonical variates wm to the predictor canonical variates vm (Eq. 4). 

�̂�𝑚 = �̂�0,𝑚 + �̂�1,𝑚𝑣𝑚,   𝑚 = 1,… ,𝑀 (4) 

464



Where �̂�0,𝑚=0. Because the CCA is calculated from the centred data x’ and y’, and �̂�1,𝑚=𝑟𝐶𝑚
, since the canonical 

variates are scaled to have unit variance, the regression slopes are simply equal to the corresponding canonical 

correlations.  

The database used for the statistical analysis has been built up by the data presented in the scientific literature 

and coming from real plant analysis. A total of 215 observations have been analysed. The input data x has been 

constituted by a combination of ultimate and proximate analysis of the raw biomass, while the output data y 

reports the CHONS percentage of biomass. Table 1 summarizes the input and output variables used for CCA. 

Among a total number of 21 biomass attributes (i.e., total solids, macromolecules, etc.), only a small combination 

of them have been considered as input, looking for the minimum error achievable. 

Table 1: Variables of x and y used for CCA statistical analysis. 

X data Definition y data Definition 

TS 
Total solids in the biomass, as %w/w of the total 

mass 
C Carbon fraction, as %mol. 

VS 
Volatile solids of biomass,  

as %TSw 
H Hydrogen fraction, as %mol. 

SU 
Sugar concentration in biomass,  

as %TSw 
O Oxygen fraction, as %mol. 

PR Protein concentration in biomass, as %TSw N Nitrogen fraction, as %mol. 

LP 
Lipids concentration in biomass,  

as %TSw 
  

LG 
Lignin concentration in biomass,  

as %TSw 
  

HCE 
Hemicellulose concentration in biomass,  

as %TSw 
  

BD Biodegradability index of the biomass   

%TSw = weight percentage of the total solids in the biomass. 

 

The sulfur molar fraction in biomass (S) is evaluated as complementary to the other elements, since its average 

value is relatively lower than the other species and can therefore influence the analysis results increasing its 

stiffness. Sulfur content can be reliably predicted from the average content of cysteine and methionine. 

However, the database used in this study does not have this information. In Table 1, TS is the total solids content 

in the biomass, VS represents the actual amount of elements which can undergo digestion, and C/N is an 

important parameter since gives stability to the evaluation of the carbon and nitrogen output. Similarly, BD 

indicates the biodegradability of the biomass and is directly correlated to its bio-methane potential. Other input 

parameters (SU, PR, LP, LG, HCE) are the macromolecule concentration relative to that substrate under study. 

The CCA analysis has been implemented in MATLAB™ through the command canoncorr(x,y), which computes 

the canonical vectors am and bm, and the canonical variates vm and wm. The performance indicators MAE, MSE, 

SAE and MAPE have been calculated (Table 2) in the evaluation of the correlations between x and y. 

MAE = mean absolute error; MSE = mean square error; SAE = sum absolute error; MAPE = mean absolute percentage error. 

3. Results 

Equations from 5 to 8 report the linear correlations obtained by CCA from x and y data for the CHONS 

evaluation. As said, and as also shown in Table 1, the S fraction is not directly predicted, since it can be 

evaluated as a complementary component of the mixture. Despite the relatively high error obtained from the 

analysis (Table 2), it must be considered that the heterogenicity of the biomass and the goodness of the 

experimental analyses strictly influence the values in the dataset. This can be also seen in Figure 1, where it is 

possible to notice the presence of enough outliers in the CNHO estimation exiting the confidence interval, thus 

increasing the error. This is principally due to the variability of the data-taking process, since the biomasses are 

extremely heterogenous and the fraction of a certain type of it can consistently differ to another one. It is possible 

to say that the CHONS content is strictly related to the relative content of the biomass itself. Consequently, it is 

are obtained for the nitrogen and hydrogen fractions. However, the MAPE index put hydrogen in second place, 

valorising the carbon and nitrogen fraction, showing values lower than 16%. 

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Table 2: Results evaluated in terms of error performance indicators. 

Element MAE MAPE SAE MSE 

C 6.3 15.9 1351.6 85.2 

H 1.5 78.0 315.8 4.7 

N 0.9 15.0 201.6 2.5 

O 7.7 135.1 1663.6 127.6 

The oxygen is the output which has the highest error in the study. This can be caused by the high number of 

outlier values in the database. This depicts the difficulty to find both experimentally, in terms of reliable analysis, 

and numerically the amount of oxygen present in the biomass solids fraction. 

 

Figure 1: boxplot and outliers’ representation of CNHO values from the database, scaled with the z-score 

algorithm. 

Figure 2 shows a comparison between the database and predicted values (Eq. 5-8) for all outputs considered. 

Though this comparison it is easier to look at the goodness of the prediction. CCA predictions well represent 

the trends of the molar fraction of the species.  

𝐶𝑅𝑀 = 0.069 × 𝑇𝑆 + 0.135 × 𝑉𝑆 + 0.001 × 𝐿𝑃 + 0.123 × 𝑃𝑅 − 0.034 × 𝑆𝑈 − 0.069 × 𝐿𝐺 + 0.088 × 𝐻𝐶𝐸

+ 2.715 × 𝐵𝐷 + 25.154 
(5) 

𝑁𝑅𝑀 = 6.76 × 10−5 𝑇𝑆 + 0.012 × 𝑉𝑆 + 0.030 × 𝐿𝑃 + 0.174 × 𝑃𝑅 + 0.032 × 𝑆𝑈 + 0.023 × 𝐿𝐺

− 0.006 × 𝐻𝐶𝐸 − 3.401 × 𝐵𝐷 + 0.701 
(6) 

𝐻𝑅𝑀 = 0.003 × 𝑇𝑆 + 0.025 × 𝑉𝑆 + 0.015 × 𝐿𝑃 + 0.011 × 𝑃𝑅 + 6.06 × 10−4 × 𝑆𝑈 + 0.012 × 𝐿𝐺

+ 0.024 × 𝐻𝐶𝐸 − 0.170 × 𝐵𝐷 + 3.261 
(7) 

𝑂𝑅𝑀 = −0.072 × 𝑇𝑆 − 0.179 × 𝑉𝑆 − 0.051 × 𝐿𝑃 − 0.352 × 𝑃𝑅 − 0.008 × 𝑆𝑈 + 0.029 × 𝐿𝐺 − 0.108 × 𝐻𝐶𝐸

+ 1.491 × 𝐵𝐷 + 71.351 
(8) 

 

RM = Raw Material.  

466



 

Figure 2: Comparison of the predicted value of the CCA model with database values. 

 

Figure 3: Heatmap of the correlation matrix. 

CCA has been used to find hidden linear correlations between the input selected and the output. Figure 3 shows 

the heatmap of the Pearson correlation intensity between all these parameters. From this figure, the higher the 

better the two features are correlated with one another. As it is possible to see, nitrogen and protein fractions 

are strongly correlated, due to the presence of the ammonium functional group in the amino acid. Furthermore, 

carbon and hydrogen fractions are also strongly correlated to each other, since many organic carbon-rich 

species have a high C/H ratio. On the other hand, both carbon and nitrogen have an inverse correlation with 

oxygen. Oxygenated species in the solid phase (i.e., carboxylic acids) are really poor, and the principal source 

of oxygen comes from sugars and ethanol. The oxygen path ends with the decomposition of these species into 

CO2 and H2O. The intensity of the other parameter correlation factor is high enough for the model, but not to 

 

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make any mention in this specific discussion. Whereas Pearson correlations focus on relationships within a 

single dataset, canonical correlations assess the relationships between two distinct datasets, allowing one to 

identify the optimal linear combinations between the variables in the two sets that show the maximum 

correlation. 

4. Conclusions 

This study looked at using statistical analysis to find linear correlations between different variables. Specifically, 

a technique called CCA was used to uncover “hidden” linear correlations between input and output variables, 

and to predict the CHONS content for different types of biomasses. The results of the analysis showed that 

while there were advantages in using CCA, there were also some drawbacks. One advantage was that it was 

easy to implement, although the dataset needed to be carefully constructed.  However, the main limitation of 

CCA was that it could only identify linear correlations between inputs and outputs, which resulted in some errors 

in the predictions made in this study. This limitation could be overcome by using machine learning techniques. 

In future research, machine learning techniques will be applied to the data to find stronger relations between 

the biomass features. Overall, the CCA approach represented an initial attempt to create simple tools for the 

prediction of CHONS content for every type of biomass. 

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	Canonical Correlation Analysis to Biomass CHONS Prediction