Olfactory Profile and Stochastic Analysis: An Innovative Approach for Predicting the Physicochemical Characteristics of Recycled Waste Cooking Oils for Sustainable Biodiesel Production

Abstract

The efficient, economical, and sustainable production of biodiesel from waste cooking oils (WCOs) depends on the availability of simple, rapid, and low-cost methods to test the quality of potential feedstocks. The aim of this study was to establish the applicability of stochastic modeling of e-nose profiles in the evaluation of recycled WCO characteristics. Olfactory profiles of 10 WCOs were determined using a Sensigent Cyranose^® 320 chemical vapor-sensing device with a 32 sensor-array, and a stepwise multiple linear regression (MLR) analysis was performed to select stochastic parameters (explanatory variables) for inclusion in the final predictive models of the physicochemical properties of the WCOs. The most important model parameters for the characterization of WCOs were those relating to the time of inception of the e-nose signal “plateau” and to the concentration of volatile organic compounds (VOCs) in the sensor region. A comparison of acid values, peroxide values, water contents, and kinematic viscosities predicted by the MLR models with those determined by conventional laboratory methods revealed that goodness of fit and predictor accuracy varied from good to excellent, with all metric values >90%. Combining e-nose profiling with stochastic modeling was successful in predicting the physicochemical characteristics of WCOs and could be used to select suitable raw materials for efficient and sustainable biodiesel production.

1. Introduction

The extraction, processing, and consumption of fossil fuels have increased dramatically worldwide since the mid-twentieth century, but this scenario has changed in the last few decades owing to global economic crises and mainly concerns the negative impact of fossil fuels on climate change. The sustained environmental, social, economic, and strategic apprehension about the future of our planet has encouraged the development of novel energy alternatives with particular interest in the production of biofuels, such as biodiesel [1].

One of the main challenges associated with the sustainable production of biodiesel is the procurement of an adequate supply of substrate since the quality of the raw material influences the cost of manufacturing significantly. Currently, vegetable oils serve as the main feedstock in biodiesel production worldwide, and the source material typically accounts for around 80 to 90% of the cost of the final product [2]. However, the use of vegetable oils is associated with a number of disadvantages, including the need for large cultivated areas, the extended growing cycle of the plants (>60 days), and the possibility of disrupting the availability of primary commodities required for food production [3].

In order to reduce the cost of biodiesel production, a low-priced feedstock should be employed, and in this context, waste cooking oils (WCO) generated during food frying have emerged as attractive raw materials. The advantage of WCOs is that they represent inexpensive renewable resources, the recycling of which would prevent inappropriate disposal into the environment whilst offering a profit opportunity for commercial businesses [2,3,4]. In Brazil, however, only 1.7% of WCOs are recycled for biodiesel production, and such a low uptake can be attributed mainly to variability in the quality of the oils, the physical and chemical characteristics of which are influenced significantly by the conditions of the frying process [3]. In particular, vegetable oils suffer varying degrees of degradation during frying and, consequently, exhibit changes in odor, color, viscosity, and acidity, among other properties. Although several reliable physical and chemical methods are available for evaluating the quality of WCOs and their suitability for biodiesel production, such procedures are time-consuming and require large quantities of solvents and chemical reagents [5]. In order to improve the efficiency and economic viability of biodiesel production from WCOs, it is important to develop simple, rapid, and low-cost methods of analysis of the starting materials.

Among the recent innovations in analytical techniques, electronic noses (e-noses) are of special interest because they exhibit outstanding performance in allowing the rapid and facile determination of the properties of unstable materials. These low-cost multi-sensing devices mimic the mammalian olfactory system and provide the aroma profile of samples without identifying individual chemical species present in the mixture [6,7,8]. E-nose techniques have been applied in the evaluation of food, beverages, and pharmaceuticals [9,10,11,12,13]; in the diagnosis of diseases [14,15,16]; and in environmental research [17]. Gancarz et al. [12] demonstrated the potential of the electronic nose equipped with metal oxide sensors to achieve a more precise characterization of the organic compounds generated during the stages of wheat bread production. The detection of organic compounds with the electronic nose has also been applied to assess the quality of fish feed over storage time [13]. Kuchmenko and Shuba [16] further explored the use of the electronic nose in healthcare research, showcasing its ability to rapidly and cost-effectively detect organic compounds released through breath, blood, and urine that are associated with certain diseases. Regarding the analysis of WCOs, Giordani et al. [18] have demonstrated that e-noses are capable of identifying the origin of the residual oil employed in biodiesel production. However, one of the main drawbacks of employing e-nose profiles in WCO analysis has been the difficulty in modeling the results. In view of this, Siqueira et al. [19] proposed a new method of analyzing the signals generated by e-nose sensors using a Stochastic Differential Equation model. This research group also demonstrated that the combination of e-nose profiling and stochastic modeling was successful in predicting whether the physicochemical characteristics of the biodiesel so-produced would comply with Agência Nacional do Petróleo, Gás Natural e Biocombustíveis standards [20]. Moreover, Vidigal et al. [1] showed that the combined methodology was able to predict the oxidative stability of biodiesel.

However, to the best of our knowledge, e-noses have not been used to predict the physicochemical properties of WCOs, even though the characteristics of the feedstock strongly influence the final quality of the biodiesel [5,21]. Hence, as a continuation of our research effort on the development of clean energy technologies, we focused on the elaboration of a simple and low-cost method for the identification of quality WCOs appropriate for use in the production of biodiesel. The objectives of the present study were (i) to propose a methodology using the olfactory profiles obtained by an e-nose and stochastic modeling to predict the physicochemical characteristics of WCOs and (ii) to compare the predicted values with those obtained by conventional laboratory methods.

2. Materials and Methods

2.1. Origin and Laboratory Analysis of WCOs

Samples (n = 10) of WCOs generated from food frying processes were collected from different domestic residences and commercial establishments located in Lorena, SP, Brazil. The samples were filtered through filter paper, homogenized, and analyzed according to conventional laboratory methods. All analyses were performed in triplicate.

Acidity (mg KOH/g) and peroxide (meq O₂/kg) values were measured according to the methods described by the American Oil Chemists’ Society [22,23]. Water content (ppm) was determined according to method D6304-16e1 of the American Society for Testing and Materials [24], a procedure considered both sensitive and accurate for the analysis of diverse types of samples. In this method, samples of WCOs were diluted in methanol and titrated against Karl Fischer reagent until all the water present had been consumed. Analyses were performed using a model AKF5000 Coulometric Karl Fischer Titrator (Koehler Instrument Company, Holtsville, NY, USA) and endpoints detected through an electrode immersed in the sample.

The densities (g/cm³) of 2 mL samples of WCOs were recorded at 20 °C using an Anton Paar (Graz, Austria) model DMA 35N EX digital densitometer. Absolute viscosities (centipoise, cP) of 1 mL samples of WCOs were determined at 40 °C as functions of the shear stress rate using an Ametek Brookfield (Harlow, UK) model LVDVIII viscometer and a CP-42 cone, while kinematic viscosities (mm²/s) were calculated by dividing the absolute viscosities by the respective densities.

The colors of WCOs samples were evaluated according to the CIELAB color space system (L*, a*, and b* color channels) using a HunterLab (Reston, VA, USA) ColorQuest XE bench top spectrophotometer and EasyMatch QC software (version 4.98). The instrument was calibrated in the total transmittance mode for color evaluation of translucent liquids and configured for measurements using a standard D65 light source at a viewing angle of 10° (D65/10° color space). Evaluations were carried out at 25 °C using a cuvette with an optical path length of 50 mm.

2.2. Olfactory Analysis of WCOs by e-Nose

The olfactory profiles of WCO samples were determined using a Sensigent (Baldwin Park, CA, USA) Cyranose^® 320 handheld chemical vapor-sensing device. This instrument incorporates an array of 32 nanocomposite sensors (conductive polymers combined with carbon nanoparticles) that respond to variations in electrical resistance when exposed to vapors [18], and it employs sophisticated algorithms to detect complex volatile organic compounds (VOCs). Individual WCO samples were subdivided into 10 × 4 mL subsamples, each of which was transferred to an appropriate vial and stabilized at 23 °C to achieve liquid-vapor equilibrium. The olfactory profiles of the subsamples were established with the e-nose configured to read samples for 20 s followed by 10 s for baseline formation and 35 s of gas purge and sensor updating.

2.3. Stochastic Modeling

The stochastic model developed by Siqueira et al. [19] was employed to assess the variability of the e-nose signals in the WCO samples according to the stochastic differential equation (Equation (1)) relating the electronic signal strength (X_t) to the time of measurement (t) and the Brownian movement reproducing the signal noise (W_t):

$$d{X}_t=\left[a+{\displaystyle \frac{bk}{e^{kt}}}\right]dt+{\displaystyle \frac{c}{{\left(t+1\right)}^p}}d{W}_t,$$

(1)

The parameters of the model and their respective interpretations are as follows: a is the slope of the linear portion of the signal profile (so-called “plateau” region), b is the signal intensity at the start of the “plateau”, 1/k indicates the approximate time when the “plateau” commences, and c and p are related to the amplitudes of the 95% confidence intervals of the e-nose measurements, whereby the larger the value of c, the greater the signal variability, while the higher the value of p, the lower the signal noise variability. Scilab package version 2023.0.0 (Dassault Systèmes, Vélizy-Villacoublay, France) was used to estimate the model parameters for each of the olfactory profiles obtained by the e-nose. According to this model, the maximum signal value can be estimated by parameter b, while the function m (defined as a + bk) is proportional to the concentration of VOCs present at the sensor. The described model has been applied in previous studies involving the production of biodiesel from WCOs [1,20].

2.4. Statistical Analysis

The physicochemical characteristics of the WCOs, as determined by conventional laboratory methods, were analyzed through descriptive statistics (mean, median, standard deviation, variance, and minimum and maximum values). The five parameters a, b, c, k, and p of the stochastic model relating to each of the 32 sensors (160 parameter values in total) were estimated for all 100 olfactory profiles. Multiple linear regressions (MLRs) were performed for each of the four response variables of interest, namely acid value, peroxide value, water content, and kinematic viscosity. In order to predict the outcomes of these variables, the estimated values for the stochastic parameters were considered as independent (explanatory) variables in each linear regression model, and parameters for inclusion in the final model were selected using the stepwise algorithm. The goodness of fit and the predictive accuracy of the stochastic model were evaluated by calculating R², adjusted R² (R²_adj), predicted R² (R²_pred), and 10-fold R². The Kolmogorov–Smirnov (K-S) test was used to evaluate the assumption of normality of residuals in the final model. Statistical analyses were performed using Minitab Software version 22 (Minitab, State College, PA, USA) with the significance level set at 5%.

3. Results

3.1. Characteristics of WCOs as Determined by Conventional Laboratory Methods

The quality of biodiesel produced from WCOs is determined by the physicochemical properties of the raw material since they directly affect the transesterification reactions [19]. The objectives of the present study were to propose a methodology using e-nose profiling and stochastic modeling to predict the physicochemical characteristics (response variables) of WCOs and to compare the predicted values with those obtained using conventional methods.

Table 1. Physicochemical characteristics of waste cooking oil samples (n = 10) employed in the study.

Variables	Mean	Standard Deviation	Median	Minimum	Maximum	Coefficient of Variation
Acid value (mg KOH/g)	0.355	0.175	0.324	0.158	0.783	0.493
Peroxide value (mEq/kg)	18.351	13.314	15.444	1.941	47.614	0.726
Water content (ppm)	1378.259	1284.149	746.782	344.246	4159.639	0.932
Density (g/cm3)	0.921	0.004	0.920	0.918	0.931	0.004
Absolute viscosity (cP)	36.350	1.588	36.260	34.380	39.500	0.044
Kinematic viscosity (mm2/s)	39.473	1.705	39.237	37.390	42.865	0.043
CIELAB Color axis L*	90.534	8.387	93.913	71.237	98.220	0.093
CIELAB Color axis a*	−0.008	6.437	−1.758	−5.710	15.557	−772.383
CIELAB Color axis b*	39.644	30.255	25.780	4.763	87.230	0.763

presents the physical and chemical properties, as determined by conventional laboratory techniques, of the ten WCOs employed in the study. Acid values of the samples ranged from 0.158 to 0.783 mg KOH/g, with a mean of 0.355 mg KOH/g. The quality of biodiesel is poor when the feedstock has an acid value greater than 1 mg KOH/g because the yield of esters formed during the transesterification reactions is reduced, and a large amount of soap is generated [25]. However, none of the WCO samples employed in the present study exhibited an acid value greater than 1 mg KOH/g.

The peroxide value is a sensitive indicator of the initial phase of lipid oxidation. The WCO samples analyzed in the present study (Table 1) showed peroxide values ranging from 1.941 to 47.614 mEq/kg, with a mean of 18.351 mEq/kg. These values are lower than those reported by Siqueira et al. [20], which varied between 1.98 and 71.82 mEq/kg. Considering that oxidative degradation is associated positively with peroxide value, the WCOs analyzed in our study appeared slightly less degraded than the samples tested by the previous authors. The Brazilian Health Regulatory Agency recommends a peroxide value lower than 10 mEq/kg for frying oils used in the preparation of foods for human consumption [26]. This means that 7 of the 10 WCO samples analyzed in this study could not be used for food preparation and reinforces the need for recycling.

The water content of WCO samples (Table 1) varied between 344.246 and 4159.639 ppm, while the mean and median values were relatively close (1378.259 and 1284.149 ppm, respectively), indicating a symmetrical distribution of this variable. Although the mean water content of WCOs analyzed by Vidigal et al. [1] was much lower (484.33 ppm) than that recorded herein, all waste oils need to be submitted to drying processes because the presence of water, even in small amounts, favors the formation of free fatty acids and parallel reactions during transesterification, thereby reducing the yield of biodiesel [27].

The variation in density of the WCO samples (Table 1) was low (range 0.918 to 0.931 g/cm³), while the mean value (0.921 g/cm³) was close to the means of 0.9217, 0.917 and 0.90 g/cm³ reported, respectively, by Siqueira et al. [19,20] and Vidigal et al. [1]. The absolute viscosities of the WCOs analyzed in the present study varied between 34.38 and 39.50 cP, while the mean value (36.35 cP) was somewhat higher than the means of 33.44 and 33.99 cP recorded by Siqueira et al. [19] for oil samples collected, respectively, from residential and commercial sources. The kinematic viscosities of the WCOs ranged from 37.390 to 42.865 mm²/s, with a mean of 39.473 mm²/s (Table 1), and are comparable with mean values of 36.284 and 36.874 mm²/s reported by Siqueira et al. [19] and 42.69 mm²/s recorded by Siqueira et al. [20]. According to Knothe and Steidley [28], the kinematic viscosity of a biofuel is influenced significantly by the structure of the fatty acids that ultimately give rise to the biodiesel esters. Thus, kinematic viscosity increases with the chain length of fatty acids or the alcohol portion of fatty esters and is greatly affected by the nature and number of double bonds present in unsaturated fatty acids. On this basis, the kinematic viscosity of the WCO is particularly relevant for the production of high-quality biodiesel.

The colors of WCO samples were established from measurements of the L*, a*, and b* channels of the CIELAB color space system. Values of the lightness (L*) channel, which range from 0 for black to 100 for white, varied between 71.237 and 98.2 for the WCO samples (Table 1), with the mean and median values being rather close, indicating a symmetric distribution among the samples. The a* and b* axes represent chromaticity, with negative values of a* corresponding to green and positive values to red, while for b*, negative values correspond to blue and positive values to yellow. For both axes, a value of zero corresponds to grey. The a* values for the WCOs analyzed in the present study ranged from −5.710 to +15.557, with mean and median values of −0.008 and −1.758, respectively, while the b* values ranged from +4.763 to +87.230, with mean and median values of +39.644 and +25.780, respectively. Hence, the studied WCOs typically presented a light appearance with a medium-to-strong yellow component and a very slight greenish tint.

3.2. Characteristics of WCOs as Predicted by Stochastic Modeling

The explanatory variables of the final MLR model for the response variable acid value included the parameters a, c, k, and m (defined as a + bk) of the signals from 25 of the 32 e-nose sensors.

Based on the estimates presented in

Table 2. The analysis of variance and estimates of the coefficients in the final multiple linear regression model for the response variable acid value.

Sources of Variation	Degrees of Freedom	Sum of Squares (Adjusted)	Mean Squares (Adjusted)	F Value	p Value	Regression Coefficients of the Model Parameters (Independent Variables) *
						Estimates	Values
Regression	30	2.91305	0.097102	56.28	0.000	Constant	+0.3924
a(15)	1	0.03573	0.035726	20.71	0.000	a(15)	+0.0257
c(13)	1	0.57792	0.577924	334.96	0.000	c(13)	−0.0937
k(2)	1	0.04312	0.043117	24.99	0.000	k(2)	−0.0294
k(14)	1	0.21635	0.216354	125.40	0.000	k(14)	+0.0648
k(29)	1	0.04727	0.047274	27.40	0.000	k(29)	+0.0289
1/k(26)*1/k(26)	1	0.02984	0.029842	17.30	0.000	1/k(26)*1/k(26)	−0.0070
m(1)*1/k(26)	1	0.11768	0.117679	68.21	0.000	m(1)*1/k(26)	−0.0826
m(5)*1/k(14)	1	0.42206	0.422060	244.63	0.000	m(5)*1/k(14)	+0.2445
m(6)*1/k(27)	1	0.05172	0.051715	29.97	0.000	m(6)*1/k(27)	−0.0488
m(7)*1/k(27)	1	0.01877	0.018768	10.88	0.002	m(7)*1/k(27)	−0.0217
m(8)*m(11)	1	0.05762	0.057617	33.39	0.000	m(8)*m(11)	+0.0243
m(8)*m(17)	1	0.03949	0.039488	22.89	0.000	m(8)*m(17)	−0.0313
m(8)*1/k(2)	1	0.32465	0.324648	188.17	0.000	m(8)*1/k(2)	+0.1654
m(10)*m(25)	1	0.04035	0.040350	23.39	0.000	m(10)*m(25)	−0.0293
m(11)*1/k(27)	1	0.02059	0.020586	11.93	0.001	m(11)*1/k(27)	+0.0255
m(13)*1/k(26)	1	0.06200	0.062000	35.94	0.000	m(13)*1/k(26)	−0.0531
m(14)*m(32)	1	0.21971	0.219709	127.34	0.000	m(14)*m(32)	+0.0735
m(19)*m(22)	1	0.05155	0.051553	29.88	0.000	m(19)*m(22)	−0.0768
m(19)*m(26)	1	0.03354	0.033537	19.44	0.000	m(19)*m(26)	−0.0397
m(22)*m(30)	1	0.06678	0.066776	38.70	0.000	m(22)*m(30)	+0.0454
m(23)*1/k(10)	1	0.23632	0.236317	136.97	0.000	m(23)*1/k(10)	+0.0699
m(23)*1/k(14)	1	0.46235	0.462347	267.98	0.000	m(23)*1/k(14)	−0.3101
m(30)*1/k(25)	1	0.01210	0.012098	7.01	0.010	m(30)*1/k(25)	−0.0200
1/k(1)*1/k(13)	1	0.43020	0.430198	249.34	0.000	1/k(1)*1/k(13)	−0.1480
1/k(1)*1/k(17)	1	0.09894	0.098936	57.34	0.000	1/k(1)*1/k(17)	+0.0836
1/k(3)*1/k(20)	1	0.09576	0.095760	55.50	0.000	1/k(3)*1/k(20)	−0.0724
1/k(6)*1/k(27)	1	0.08880	0.088797	51.47	0.000	1/k(6)*1/k(27)	−0.0371
1/k(18)*1/k(23)	1	0.07293	0.072927	42.27	0.000	1/k(18)*1/k(23)	−0.0679
1/k(19)*1/k(23)	1	0.05444	0.054444	31.56	0.000	1/k(19)*1/k(23)	−0.0352
1/k(25)*1/k(31)	1	0.03191	0.031907	18.49	0.000	1/k(25)*1/k(31)	+0.0322
Error	69	0.11905	0.001725
Total	99	3.03210

* Notation employed for independent variables: x(y), where x is the parameter of the stochastic model and y is the corresponding sensor.

, the regression curve predicting the acid values of the WCO samples was constructed and showed goodness of fit (R² = 96.07% and R²_adj = 94.37%) and predictive accuracy (R²_pred = 91.62% and 10-fold R² = 91.78%) that were considered good since all metrics were greater than 90%. Furthermore, the assumption of normality of the distribution of the residuals was confirmed by the Kolmogorov–Smirnov test (K-S = 0.056; p > 0.15). The scatter plot of the acid values predicted by the final MLR model vs. the observed values for the WCO samples showed that the model furnished an excellent fit with the data (Figure 1a).

The estimates of model parameters a, c, k, and m corresponding to signals from 27 of the 32 e-nose sensors were included in the final MLR model for the response variable peroxide value (

Table 3. The analysis of variance and estimates of the coefficients in the final multiple linear regression model for the response variable peroxide value.

Sources of Variation	Degrees of Freedom	Sum of Squares (Adjusted)	Mean Squares (Adjusted)	F Value	p Value	Regression Coefficients of the Model Parameters (Independent Variables) *
						Estimates	Values
Regression	35	17,427.5	497.93	105.53	0.000	Constant	+20.537
a(14)	1	91.7	91.69	19.43	0.000	a(14)	+1.307
c(7)	1	566.8	566.79	120.12	0.000	c(7)	+3.130
k(8)	1	2572.2	2572.21	545.14	0.000	k(8)	+7.473
k(26)	1	1724.0	1724.02	365.38	0.000	k(26)	+6.464
k(29)	1	72.6	72.65	15.40	0.000	k(29)	+1.096
m(1)*1/k(25)	1	115.8	115.82	24.55	0.000	m(1)*1/k(25)	+3.471
m(4)*1/k(28)	1	107.5	107.51	22.78	0.000	m(4)*1/k(28)	−2.085
m(5)*m(8)	1	551.6	551.58	116.90	0.000	m(5)*m(8)	+3.466
m(6)*1/k(25)	1	1396.3	1396.28	295.92	0.000	m(6)*1/k(25)	−8.668
m(8)*m(9)	1	153.1	153.07	32.44	0.000	m(8)*m(9)	−0.777
m(8)*1/k(24)	1	100.9	100.94	21.39	0.000	m(8)*1/k(24)	−2.488
m(9)*m(23)	1	467.5	467.47	99.07	0.000	m(9)*m(23)	−4.458
m(9)*1/k(6)	1	84.5	84.54	17.92	0.000	m(9)*1/k(6)	+2.133
m(9)*1/k(26)	1	600.9	600.87	127.35	0.000	m(9)*1/k(26)	−4.365
m(10)*1/k(25)	1	2063.8	2063.84	437.40	0.000	m(10)*1/k(25)	−8.678
m(11)*m(32)	1	179.0	178.96	37.93	0.000	m(11)*m(32)	+2.551
m(11)*1/k(6)	1	298.7	298.67	63.30	0.000	m(11)*1/k(6)	+3.929
m(13)*1/k(31)	1	2186.1	2186.13	463.31	0.000	m(13)*1/k(31)	+13.152
m(16)*1/k(2)	1	544.7	544.69	115.44	0.000	m(16)*1/k(2)	−10.259
m(16)*1/k(26)	1	163.8	163.81	34.72	0.000	m(16)*1/k(26)	−1.625
m(18)*1/k(24)	1	553.4	553.41	117.29	0.000	m(18)*1/k(24)	−4.375
m(19)*m(23)	1	84.7	84.71	17.95	0.000	m(19)*m(23)	+2.259
m(19)*1/k(24)	1	1365.4	1365.40	289.37	0.000	m(19)*1/k(24)	−7.174
m(19)*1/k(27)	1	1382.8	1382.84	293.07	0.000	m(19)*1/k(27)	−5.707
m(19)*1/k(31)	1	1623.5	1623.54	344.08	0.000	m(19)*1/k(31)	−13.035
m(21)*1/k(23)	1	40.1	40.06	8.49	0.005	m(21)*1/k(23)	−1.129
m(24)*m(28)	1	1544.7	1544.66	327.36	0.000	m(24)*m(28)	−10.258
m(25)*1/k(2)	1	49.3	49.35	10.46	0.002	m(25)*1/k(2)	+2.355
m(26)*1/k(27)	1	55.9	55.89	11.84	0.001	m(26)*1/k(27)	+1.316
m(28)*m(31)	1	648.4	648.43	137.42	0.000	m(28)*m(31)	−2.895
m(28)*1/k(10)	1	347.5	347.52	73.65	0.000	m(28)*1/k(10)	−4.528
m(31)*1/k(20)	1	71.5	71.49	15.15	0.000	m(31)*1/k(20)	+2.136
1/k(1)*1/k(14)	1	396.8	396.83	84.10	0.000	1/k(1)*1/k(14)	−5.658
1/k(1)*1/k(16)	1	957.1	957.12	202.85	0.000	1/k(1)*1/k(16)	−7.003
1/k(9)*1/k(17)	1	175.3	175.35	37.16	0.000	1/k(9)*1/k(17)	−3.396
Error	64	302.0	4.72
Total	99	17,729.4

* Notation employed for independent variables: x(y), where x is the parameter of the stochastic model and y is the corresponding sensor.

). The regression curve predicting the peroxide values of the WCO samples based on these estimates showed excellent goodness of fit and predictive accuracy of the final stochastic model with metric values R² (98.30%), R²_adj (97.37%), R²_pred (96.71%), and 10-fold R² (96.51%), all of which were greater than 95%. The assumption that the residuals were normally distributed was confirmed by the K-S statistic (0.083; p = 0.091), and the scatter plot of the peroxide values predicted by the final MLR model vs. the observed values of the WCO samples demonstrated that the model afforded an impressive fit with the data (Figure 1b).

Table 4. The analysis of variance and estimates of the coefficients in the final multiple linear regression model for the response variable water content.

Sources of Variation	Degrees of Freedom	Sum of Squares (Adjusted)	Mean Squares (Adjusted)	F Value	p Value	Regression Coefficients of the Model Parameters (Independent Variables) *
						Estimates	Values
Regression	41	164,024,020	4,000,586	264.88	0.000	Constant	+1321.90
a(20)	1	511,873	511,873	33.89	0.000	a(20)	−108.30
c(21)	1	430,418	430,418	28.50	0.000	c(21)	−96.30
k(13)	1	24,303,681	24,303,681	1609.18	0.000	k(13)	+813.20
k(16)	1	5,157,547	5,157,547	341.49	0.000	k(16)	+405.80
m(2)*1/k(5)	1	6,393,239	6,393,239	423.31	0.000	m(2)*1/k(5)	−688.30
m(2)*1/k(27)	1	6,799,692	6,799,692	450.22	0.000	m(2)*1/k(27)	+634.70
m(2)*1/k(32)	1	1,133,538	1,133,538	75.05	0.000	m(2)*1/k(32)	−327.10
m(8)*m(24)	1	558,241	558,241	36.96	0.000	m(8)*m(24)	−142.70
m(9)*1/k(27)	1	516,580	516,580	34.20	0.000	m(9)*1/k(27)	+127.60
m(9)*a(1)	1	988,101	988,101	65.42	0.000	m(9)*a(1)	−186.10
m(10)*m(11)	1	1,996,485	1,996,485	132.19	0.000	m(10)*m(11)	−421.00
m(11)*m(19)	1	228,078	228,078	15.10	0.000	m(11)*m(19)	−87.60
m(11)*1/k(17)	1	1,190,218	1,190,218	78.81	0.000	m(11)*1/k(17)	+418.90
m(12)*1/k(28)	1	238,090	238,090	15.76	0.000	m(12)*1/k(28)	−125.80
m(14)*a(2)	1	647,904	647,904	42.90	0.000	m(14)*a(2)	−181.50
m(15)*1/k(7)	1	603,615	603,615	39.97	0.000	m(15)*1/k(7)	+166.40
m(16)*1/k(15)	1	2,252,536	2,252,536	149.14	0.000	m(16)*1/k(15)	−470.60
m(16)*1/k(17)	1	3,258,639	3,258,639	215.76	0.000	m(16)*1/k(17)	−482.00
m(16)*a(3)	1	798,406	798,406	52.86	0.000	m(16)*a(3)	+225.30
m(17)*m(19)	1	330,620	330,620	21.89	0.000	m(17)*m(19)	−143.40
m(19)*m(26)	1	6,426,334	6,426,334	425.50	0.000	m(19)*m(26)	+676.30
m(19)*m(27)	1	761,778	761,778	50.44	0.000	m(19)*m(27)	+98.60
m(19)*m(30)	1	105,592	105,592	6.99	0.011	m(19)*m(30)	+106.90
m(19)*1/k(27)	1	417,016	417,016	27.61	0.000	m(19)*1/k(27)	−142.30
m(20)*1/k(28)	1	6,138,673	6,138,673	406.45	0.000	m(20)*1/k(28)	+632.50
m(21)*1/k(24)	1	606,524	606,524	40.16	0.000	m(21)*1/k(24)	+145.50
m(22)*m(30)	1	423,005	423,005	28.01	0.000	m(22)*m(30)	−174.60
m(22)*a(2)	1	455,127	455,127	30.13	0.000	m(22)*a(2)	+156.30
m(24)*1/k(2)	1	503,101	503,101	33.31	0.000	m(24)*1/k(2)	+302.50
m(26)*1/k(28)	1	3,151,708	3,151,708	208.68	0.000	m(26)*1/k(28)	−437.90
m(26)*a(1)	1	3,236,057	3,236,057	214.26	0.000	m(26)*a(1)	+400.20
m(28)*1/k(19)	1	2,448,117	2,448,117	162.09	0.000	m(28)*1/k(19)	−292.10
m(30)*1/k(14)	1	6,251,369	6,251,369	413.91	0.000	m(30)*1/k(14)	−583.60
m(31)*1/k(15)	1	99,472	99,472	6.59	0.013	m(31)*1/k(15)	−42.00
m(32)*1/k(16)	1	110,382	110,382	7.31	0.009	m(32)*1/k(16)	+47.40
1/k(6)*1/k(24)	1	3,059,652	3,059,652	202.58	0.000	1/k(6)*1/k(24)	+429.80
1/k(6)*1/k(31)	1	1,072,883	1,072,883	71.04	0.000	1/k(6)*1/k(31)	+110.70
1/k(6)*a(3)	1	868,785	868,785	57.52	0.000	1/k(6)*a(3)	+237.70
1/k(7)*1/k(12)	1	4,512,601	4,512,601	298.79	0.000	1/k(7)*1/k(12)	−600.70
1/k(11)*1/k(26)	1	131,512	131,512	8.71	0.005	1/k(11)*1/k(26)	+153.90
1/k(12)*a(2)	1	3,671,336	3,671,336	243.08	0.000	1/k(12)*a(2)	−578.70
Error	58	875,981	15,103
Total	99	164,900,001

* Notation employed for independent variables: x(y), where x is the parameter of the stochastic model and y is the corresponding sensor.

shows the estimates of model parameters a, c, k, and m corresponding to 27 signals generated by 32 e-nose sensors that were included in the final MLR model for the response variable water content. The regression curve predicting the water content of the WCO samples was based on these estimates and showed excellent goodness of fit and predictive accuracy in the final stochastic model with metric values of R² (99.47%), R²_adj (99.09%), R²_pred (98.43%), and 10-fold R² (97.70%), all of which were greater than 95%. The K-S statistic (0.074; p > 0.15) validated the assumption that the residuals were normally distributed, and the scatter plot of water content values predicted by the final MLR model vs. the observed values of the WCO samples demonstrated that the model afforded an impressive fit with the data (Figure 1c).

The estimates (

Table 5. The analysis of variance and estimates of the coefficients in the final multiple linear regression model for the response variable kinematic viscosity.

Sources of Variation	Degrees of Freedom	Sum of Squares (Adjusted)	Mean Squares (Adjusted)	F Value	P Value	Regression Coefficients of the Model Parameters (Independent Variables) *
						Estimates	Values
Regression	25	274.657	10.9863	50.87	0.000	Constant	+39.469
m(13)	1	22.987	22.9871	106.44	0.000	m(13)	+0.749
b(13)	1	26.203	26.2028	121.33	0.000	b(13)	−0.846
c(22)	1	4.286	4.2856	19.85	0.000	c(22)	−0.268
k(4)	1	1.921	1.9206	8.89	0.004	k(4)	+0.187
m(2)*m(11)	1	3.966	3.9655	18.36	0.000	m(2)*m(11)	+0.446
m(3)*m(16)	1	10.377	10.3773	48.05	0.000	m(3)*m(16)	+0.883
m(3)*1/k(15)	1	2.658	2.6575	12.31	0.001	m(3)*1/k(15)	+0.379
m(4)*m(20)	1	13.114	13.1136	60.72	0.000	m(4)*m(20)	−0.403
m(4)*1/k(27)	1	5.614	5.6137	25.99	0.000	m(4)*1/k(27)	+0.439
m(8)*1/k(27)	1	10.589	10.5893	49.03	0.000	m(8)*1/k(27)	+0.316
m(9)*1/k(3)	1	14.640	14.6404	67.79	0.000	m(9)*1/k(3)	−0.756
m(10)*m(19)	1	30.156	30.1555	139.64	0.000	m(10)*m(19)	−1.524
m(13)*1/k(20)	1	11.072	11.0716	51.27	0.000	m(13)*1/k(20)	−0.369
m(14)*m(32)	1	2.596	2.5957	12.02	0.001	m(14)*m(32)	+0.246
m(16)*m(25)	1	2.888	2.8883	13.37	0.000	m(16)*m(25)	−0.351
m(19)*m(26)	1	10.649	10.6490	49.31	0.000	m(19)*m(26)	+0.539
m(21)*m(23)	1	5.202	5.2021	24.09	0.000	m(21)*m(23)	−0.365
m(22)*1/k(13)	1	6.779	6.7789	31.39	0.000	m(22)*1/k(13)	+0.484
m(23)*1/k(24)	1	1.496	1.4960	6.93	0.010	m(23)*1/k(24)	+0.282
m(23)*1/k(25)	1	4.836	4.8360	22.39	0.000	m(23)*1/k(25)	−0.309
m(26)*1/k(24)	1	4.392	4.3921	20.34	0.000	m(26)*1/k(24)	−0.538
m(27)*m(31)	1	3.658	3.6584	16.94	0.000	m(27)*m(31)	−0.363
m(27)*1/k(4)	1	10.763	10.7627	49.84	0.000	m(27)*1/k(4)	+0.764
1/k(5)*1/k(25)	1	2.616	2.6163	12.12	0.001	1/k(5)*1/k(25)	−0.299
1/k(14)*1/k(31)	1	11.840	11.8404	54.83	0.000	1/k(14)*1/k(31)	+0.624
Error	74	15.981	0.2160
Total	99	290.638

* Notation employed for independent variables: x(y), where x is the parameter of the stochastic model and y is the corresponding sensor.

) of the model parameters b, c, k, and m included in the final MLR model for the response variable kinematic viscosity corresponded to 23 signals generated by 32 e-nose sensors. The regression curve predicting the kinematic viscosity of the WCO samples based on these estimates showed goodness of fit (R² = 94.50% and R²_adj = 92.64%) and predictive accuracy (R²_pred = 90.25% and 10-fold R² = 89.75%) that were considered good since the metric values were close to or greater than 90%. The assumption that the residuals were normally distributed was verified by the K-S statistic (0.088; p = 0.055), and the scatter plot of kinematic viscosity values predicted by the final MLR model vs. the observed values of the WCO samples showed an excellent fit of the model with the data (Figure 1d).

Figure 2 shows the R² adjusted and R² 10-fold values obtained by the regression models for predicting the following physicochemical properties: acid value, peroxide value, water content, and kinematic viscosity. The adjusted R² metric is usually considered to evaluate the quality of fit to the experimental data. On the other hand, the 10-fold value indicates the generalization ability, i.e., the capacity of the model to predict new data. These results of high values of R² adjusted and R² 10-fold demonstrate the high quality of fit of the model to the experimental data as well as the ability to generalize the results to new data.

The olfactory profile depends on the size of the WCO polymer chains, which also influences the physicochemical properties of this material. A better R² adjusted for water content was observed, evidenced by the fact that it presents smaller chains that are more easily detected by the olfactory profile.

3.3. Combined Olfactory/Stochastic Analysis of the WCOs

Table 6. The relation between sensors and model parameters (independent variables) included in the final multiple linear regression model for the response variables acid value (AV), peroxide value (PV), water content (WC), and kinematic viscosity (KV).

E-Nose Sensors	Model Parameters
	a	b	c	k	m
Sensor 01	WC			AV, PV	AV, PV
Sensor 02	WC			AV, PV, WC	KV, WC
Sensor 03	WC			AV, KV	KV
Sensor 04				KV	KV, PV
Sensor 05				KV, WC	AV, PV
Sensor 06				AV, PV, WC	AV, PV
Sensor 07			PV	WC	AV
Sensor 08				PV	AV, KV, PV, WC
Sensor 09				PV	KV, PV, WC
Sensor 10				AV, PV	AV, KV, PV, WC
Sensor 11				WC	AV, KV, PV, WC
Sensor 12				WC	WC
Sensor 13		KV	AV	AV, KV, WC	AV, KV, PV
Sensor 14	PV			AV, KV, PV, WC	AV, KV, WC
Sensor 15	AV			KV, WC	WC
Sensor 16				PV, WC	KV, PV, WC
Sensor 17				AV, PV, WC	AV, WC
Sensor 18				AV	PV
Sensor 19				AV, WC	AV, KV, PV, WC
Sensor 20	WC			AV, KV, PV	KV, WC
Sensor 21			WC		KV, PV, WC
Sensor 22			KV		AV, KV, WC
Sensor 23				AV, PV	AV, KV, PV
Sensor 24				KV, PV, WC	PV, WC
Sensor 25				AV, KV, PV	AV, KV, PV
Sensor 26				AV, PV, WC	AV, KV, PV, WC
Sensor 27				AV, KV, PV, WC	KV, WC
Sensor 28				PV, WC	PV, WC
Sensor 29				AV, PV
Sensor 30					AV, WC
Sensor 31				AV, KV, PV, WC	KV, PV, WC
Sensor 32				WC	AV, KV, PV, WC

shows the relation between the e-nose sensors and the model parameters included in the final MLR model for the four response variables of interest. All 32 sensors were used in at least one of the final prediction models. One sensor (12) was used for a single response variable, five sensors (4, 18, 28, 29, and 30) for two variables, thirteen sensors (1, 3, 6, 7, 9, 15, 16, 17, 21, 22, 23, 24, and 25) for three variables, and the remaining thirteen sensors (2, 5, 8, 10, 11, 13, 14, 19, 20, 26, 27, 31, and 32) were used for four variables of interest.

The parameters most frequently included in the stochastic modeling were 1/k and m, with the former representing the approximate time of inception of the signal “plateau” and m representing the concentration of VOCs in the sensor region. The parameter p was not included as an independent variable in any of the models, while parameter b of sensor 13 was included uniquely in the model for kinematic viscosity. Interestingly, a number of authors [29,30,31,32] have used estimates of parameter b alone to analyze olfactory profiles.

The results presented herein demonstrate that the e-nose array detector affords distinctive responses that vary according to the nature of the sensor and the concentration of VOCs present in the sensor region. Therefore, an assessment of the quality of a WCO requires a more complex and detailed analysis of the olfactory profile, with the most important model parameters being those relating to the inception of the signal “plateau” and the concentration of VOCs. According to information supplied by the e-nose manufacturer, sensors 1 to 4 detect non-polar substances, while sensors 5, 6, 23, and 31 are more capable of detecting polar substances and hydrogen.

4. Conclusions

The efficient production of biodiesel from WCOs relies on the availability of simple, rapid, and economical methods of evaluating the quality of the raw material. Based on the results obtained in the present study, we propose the use of an e-nose device to obtain an olfactory profile of a WCO combined with a stochastic differential model for an interpretation of the profile. Our methodology was successful in predicting the physicochemical characteristics of WCOs and could be used to select suitable samples for biodiesel production. A comparison between the physicochemical values predicted by the MLR model with laboratory values demonstrated that the goodness of fit and predictor accuracy were good (>90%). The time of inception of the signal “plateau” and the concentration of VOCs present in the sensor region were the most important model parameters for predicting the characteristics of WCOs. Our study represents a step forward towards the adoption of clean energy technologies in order to achieve Net Zero Emissions by 2050 and to limit global warming to 1.5 °C, as recommended by the International Energy Agency [33]. It is important to emphasize that the findings of this study are applicable to the physicochemical properties within the specific range (see Table 1). Further research is planned to investigate this methodology across a broader range of these physicochemical characteristics as well as to examine additional variables related to WCO quality.