# Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples

- TL—aged in 250 L new oak wooden barrels;
- TC—aged in 250 L new chestnut wooden barrels;
- AL—aged in 1000 L stainless steel tanks with oak wood staves and micro-oxygenation;
- AC—aged in 1000 L stainless steel tanks with chestnut wood staves and micro-oxygenation.

#### 2.2. Analytical Procedures

#### 2.2.1. Analysis of Chromatic Characteristics

#### 2.2.2. Determination of the Total Phenolic Index

#### 2.2.3. Analysis of Low Molecular Weight Compounds

#### 2.2.4. Spectroscopic Analyses

^{−1}in the range of 4000 to 450 cm

^{−1}.

#### 2.3. Statistical Analysis

#### 2.3.1. Statistical Treatment of Analytical Data

#### 2.3.2. Functional Analysis

#### Functional Data Analysis (FDA)

^{2}was taken into account. The number of bases is the minimum number at which R

^{2}stops improving significantly or surpasses the value of 0.99 (see Martínez et al. [15]). Moreover, the smoothing process involves solving the following problem:

#### Functional Depths

#### Functional ANOVA (FANOVA)

## 3. Results

^{−1}has a very strong influence due to water present in the samples [49]. Nevertheless, for these analyses, the background was measured with water.

^{−1}due to the O–H stretching of alcohols and C–H stretching of CH

_{3}and CH

_{2}, and consequently related to the presence of ethanol and methanol in the alcoholic beverages [49].

^{−1}, it corresponds to C–C and C–O vibrations in volatile compounds [12,14].

^{−1}was assigned to C–OH bending deformation, and the peak at 1275 was assigned to C–O stretching in the acid molecules [11,50].

^{−1}shows other absorption bands assigned to the C=O and C=C groups present in furanic compounds. The highest peaks at 1086 and 1044 cm

^{−1}are ascribed to the C–O stretch absorption bands, which are important regions for ethanol and methanol identification and quantification respectively, and C–C absorption bands, which are related to ethanol and some organic compounds such as sugars, phenols, alcohols, and esters [14,49,51].

^{−1}could be ascribed to out-of-plane C–H bending of aromatic compounds [10], and to CH–OH, C–C, C–O, and C–H bond stretching due to water, sugars, and phenolic compounds [51].

^{−1}(second d column of Figure 6), in which the similarity hypothesis is rejected in the vector analysis. Instead, FDA is able to detect these differences between the curve samples (Table 5). This region is characteristic of the absorption bands assigned to C=O and C=C groups existing in furanic compounds, C–O stretch absorption bands related to ethanol and methanol, and C–C absorption bands also related to ethanol and some organic compounds such as sugars, phenols, alcohols, and esters previously reported, and all of them are important to differentiate the samples in this study. They are mainly identified at the peaks of the 1044 cm

^{−1}and 1086 cm

^{−1}, which are chiefly related to the presence of ethanol and methanol but also related to some organic compounds such as sugars, phenols, alcohols, and esters existing in minor concentration in the beverages. In addition, similarity in the other areas of the entire curve within the sample resulting from alternative technology with chestnut wood is rejected. In the case of the alternative technology, the wine spirits aged with Limousin oak wood are very similar to those aged with chestnut wood but with more distance between the three ageing times (Figure 7), as observed in the chemical analysis. The similarity hypothesis is rejected in all areas and from both points of view (Table 5). Figure 8 shows the differentiation within the samples resulting from chestnut barrels. In this case, the two areas drawn from the whole curve are closer, but the differences between the three ageing times are greater. The hypothesis of similarity between the samples is rejected in all areas and from the vectorial and functional approach (Table 5). Finally, regarding the wine spirits aged in Limousin oak barrels, the 18 and 12-month samples show higher absorbance units than the 6-month sample (Figure 9). The spectrometric curves of the functional graph can be easily distinguished. There are significant reasons to reject the similarity between the three samples in all areas of the full curve from the two analyses (Table 5).

## 4. Discussion

^{−1}of the entire curve. It is attributed to the functional groups present in furanic compounds and also related to ethanol, methanol, and sugars, phenols, and esters existing in the wine spirit [1,4,5,8,14,49,51]. Vector analysis found no evidence to reject the similarity between the samples based on ageing time, but FDA, taking into account all correlated observations measured in the specific area, did.

## 5. Conclusions

^{−1}of the entire curve. Vector analysis found no evidence to reject similarity between the time ageing samples, but FDA, taking into account all correlated observation measured in the specific area, found it.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Fourier transform infrared spectroscopy–Attenuated Total Reflection (FTIR-ATR) absorbance spectra of wine spirit samples.

**Figure 3.**Plots of two of the four significant areas of the curves with an ageing time of 18 months. In the first row, vectorial analysis by means of boxplots. In the second row, functional data analysis (FDA) through curves in the studied interval. The wine spirit sample is divided into four groups (AC, AL, TC, and TL).

**Figure 4.**Plots of two of the four significant areas of the curves with an ageing time of 12 months. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into four groups (AC, AL, TC, and TL).

**Figure 5.**Plots of two of the four significant areas of the curves with an ageing time of 6 months. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into four groups (AC, AL, TC, and TL).

**Figure 6.**Plots of two of the four significant areas of the Alternative Chestnut (AC) curves. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into three groups depending on the ageing time (18, 12, and 6 months of ageing).

**Figure 7.**Plots of two of the four significant areas of the Alternative Oak (AL) curves. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into three groups depending on the ageing time (18, 12, and 6 months of ageing).

**Figure 8.**Plots of two of the four significant areas of the Traditional Chestnut (TC) curves. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into three groups depending on the ageing time (18, 12, and 6 months of ageing).

**Figure 9.**Plots of two of the four significant areas of the Traditional Oak (TL) curves. In the first row, vectorial analysis by means of boxplots. In the second row, FDA through curves in the studied interval. The wine spirit sample is divided into three groups depending on the ageing time (18, 12, and 6 months of ageing).

**Table 1.**Effect of the ageing technology and kind of wood on the chromatic characteristics and total phenolic index acquired by the wine spirits after 6, 12, and 18 months of ageing. AC: Alternative Chestnut, AL: Alternative Oak, TC: Traditional Chestnut, TL: Traditional Oak.

Ageing Months | Code | L *(%) | A * | B * | C * | TPI |
---|---|---|---|---|---|---|

6 | TC | 85.41 ± 1.41 ^{b} | 3.37 ± 1.08 ^{b} | 50.96 ± 2.68 ^{b} | 51.08 ± 2.74 ^{b} | 24.94 ± 1.98 ^{b} |

TL | 93.73 ± 0.42 ^{c} | −1.25 ± 0.17 ^{a} | 26.76 ± 2.21 ^{a} | 26.79 ± 2.20 ^{a} | 11.99 ± 1.18 ^{a} | |

AC | 77.14 ± 1.26 ^{a} | 11.79 ± 1.22 ^{c} | 70.00 ± 1.59 ^{c} | 70.99 ± 1.77 ^{c} | 47.79 ± 3.80 ^{c} | |

AL | 87.55 ± 0.23 ^{b} | 1.75 ± 0.14 ^{b} | 46.24 ± 0.14 ^{b} | 46.27 ± 0.15 ^{b} | 26.88 ± 0.87 ^{b} | |

Variance origin | Technology (S) | 61.9 *** | 52.7 *** | 60.2 *** | 60.2 *** | 42.1 *** |

Wood (W) | 36.7 *** | 31.9 *** | 38.8 *** | 38.8 *** | 52.4 *** | |

SxW | NS | 14.0 ** | NS | NS | 4.2 * | |

Residual | 1.5 | 1.3 | 1.0 | 1.0 | 1.3 | |

12 | TC | 79.11 ± 1.38 ^{b} | 9.89 ± 1.31 ^{b} | 69.41 ± 1.64 ^{b} | 70.11 ± 1.80 ^{b} | 37.90 ± 1.94 ^{b} |

TL | 90.62 ± 1.04 ^{c} | −0.49 ± 0.65 ^{a} | 40.66 ± 3.4 ^{a} | 40.67 ± 3.40 ^{a} | 17.55 ± 1.81 ^{a} | |

AC | 65.58 ± 1.97 ^{a} | 25.63 ± 1.78 ^{c} | 87.25 ± 0.56 ^{c} | 90.95 ± 1.04 ^{c} | 65.72 ± 1.37 ^{c} | |

AL | 79.17 ± 0.60 ^{b} | 10.38 ± 0.53 ^{b} | 70.87 ± 0.61 ^{b} | 71.63 ± 0.68 ^{b} | 37.86 ± 0.23 ^{b} | |

Variance origin | Technology (S) | 49.2 *** | 49.9 *** | 49.4 *** | 50.7 *** | 48.6 *** |

Wood (W) | 49.7 *** | 46.3 *** | 43.5 *** | 44.9 *** | 48.8 *** | |

SxW | NS | 3.1 * | 6.2 *** | 3.6 * | 2.2 * | |

Residual | 1.1 | 0.8 | 0.9 | 0.8 | 0.5 | |

18 | TC | 77.33 ± 1.25 ^{b} | 12.06 ± 1.24 ^{b} | 73.97 ± 1.22 ^{b} | 74.95 ± 1.40 ^{b} | 40.98 ± 2.46 ^{b} |

TL | 89.61 ± 1.17 ^{c} | −0.02 ± 0.84 ^{a} | 44.35 ± 3.74 ^{a} | 44.36 ± 3.74 ^{a} | 18.15 ± 1.63 ^{a} | |

AC | 62.29 ± 1.94 ^{a} | 28.97 ± 1.62 ^{c} | 89.27 ± 0.12 ^{c} | 93.86 ± 0.61 ^{c} | 71.60 ± 2.50 ^{c} | |

AL | 76.59 ± 0.52 ^{b} | 13.19 ± 0.45 ^{b} | 75.87 ± 0.44 ^{b} | 77.01 ± 0.51 ^{b} | 40.55 ± 1.25 ^{b} | |

Variance origin | Technology (S) | 52.2 *** | 52.9*** | 47.7 *** | 50.0 *** | 47.9 *** |

Wood (W) | 46.9 *** | 45.2*** | 40.2 *** | 42.3 *** | 49.5 *** | |

SxW | NS | 1.4* | 11.1 ** | 6.8 *** | 2.1 * | |

Residual | 0.9 | 0.6 | 0.9 | 0.9 | 0.6 |

**Table 2.**Effect of the ageing technology and kind of wood on the contents of low molecular weight compounds (mg/L absolute ethanol) of the wine spirits after 6, 12, and 18 months of ageing.

Ageing Months | Code | Furfural | Ellagic Acid | Vanillin | Coniferaldehyde | sumHPLC |
---|---|---|---|---|---|---|

6 | TC | 38.31 ± 6.90 ^{a} | 8.12 ± 1.41 ^{b} | 2.03 ± 0.01 ^{b} | 6.17 ± 0.63 ^{a} | 163.10 ± 24.08 ^{b} |

TL | 31.73 ± 6.38 ^{a} | 3.43 ± 0.20 ^{a} | 1.49 ± 0.08 ^{a} | 5.21 ± 0.04 ^{a} | 78.99 ± 9.71 ^{a} | |

AC | 127.05 ± 5.07 ^{c} | 15.35 ± 0.38 ^{c} | 4.62 ± 0.20 ^{d} | 10.60 ± 0.65 ^{b} | 296.05 ± 15.91 ^{c} | |

AL | 87.74 ± 4.11 ^{b} | 6.28 ± 0.70 ^{a}^{,}^{b} | 3.26 ± 0.16 ^{c} | 12.20 ± 0.52 ^{b} | 195.23 ± 3.04 ^{b} | |

Variance origin | Technology(S) | 82.7 *** | 30.4 *** | 79.1 *** | 98.5 *** | 63.1 *** |

Wood(W) | 8.1 ** | 56.9 *** | 15.1 *** | NS | 34.6 *** | |

SxW | 8.0 *** | 10.8 *** | 5.3 ** | NS | NS | |

Residual | 1.2 | 2.0 | 0.5 | 1.5 | 2.3 | |

12 | TC | 35.85 ± 6.03 ^{a} | 12.86 ± 1.16 ^{b} | 3.61 ± 0.22 ^{b} | 7.00 ± 0.57 ^{a} | 231.68 ± 26.34 ^{b} |

TL | 31.36 ± 5.80 ^{a} | 5.64 ± 0.34 ^{a} | 2.66 ± 0.23 ^{a} | 6.49 ± 0.58 ^{a} | 95.09 ± 13.67 ^{a} | |

AC | 131.17 ± 4.91 ^{c} | 24.89 ± 1.26 ^{c} | 8.68 ± 0.02 ^{d} | 13.97 ± 0.17 ^{b} | 369.24 ± 8.57 ^{d} | |

AL | 96.08 ± 1.93 ^{b} | 11.94 ± 0.88 ^{b} | 6.77 ± 0.09 ^{c} | 19.61 ± 0.41 ^{c} | 275.32 ± 4.56 ^{c} | |

Variance origin | Technology(S) | 87.9 *** | 41.3 *** | 89.2 *** | 79.7 *** | 64.5 *** |

Wood(W) | 5.2 ** | 50.0 *** | 8.6 *** | 5.1 *** | 33.8 *** | |

SxW | 6.1 *** | 7.8 *** | 1.8 *** | 14.8 *** | NS | |

Residual | 0.8 | 0.9 | 0.3 | 0.4 | 1.7 | |

18 | TC | 36.55 ± 7.28 ^{a} | 15.48 ± 1.41 ^{b} | 4.43 ± 0.34 ^{b} | 6.85 ± 0.75 ^{a} | 271.85 ± 38.84 ^{b} |

TL | 31.63 ± 6.26 ^{a} | 6.81 ± 0.49 ^{a} | 3.13 ± 0.23 ^{a} | 6.41 ± 0.60 ^{a} | 104.10 ± 16.10 ^{a} | |

AC | 113.35 ± 4.27 ^{c} | 28.17 ± 1.15 ^{c} | 8.61 ± 0.07 ^{d} | 11.16 ± 0.15 ^{b} | 347.46 ± 4.33 ^{c} | |

AL | 86.72 ± 0.21 ^{b} | 13.81 ± 0.23 ^{b} | 7.49 ± 0.24 ^{c} | 17.93 ± 0.07 ^{c} | 275.63 ± 4.79 ^{b} | |

Variance origin | Technology(S) | 89.4 *** | 39.1 *** | 92.0 *** | 63.3 *** | 43.6 *** |

Wood(W) | 4.8 *** | 53.7 *** | 7.2 *** | 10.0 *** | 40.9 *** | |

SxW | 4.3 * | 6.2 *** | NS | 26.0 *** | 11.9 * | |

Residual | 1.5 | 0.8 | 0.7 | 0.7 | 3.6 |

TC | TL | AC | AL | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

6 | 12 | 18 | 6 | 12 | 18 | 6 | 12 | 18 | 6 | 12 | 18 | |

L *(%) | b | a | a | b | a | a | b | a | a | c | b | a |

a * | a | b | b | a | a | a | a | b | b | a | b | c |

b * | a | b | c | a | b | b | a | b | b | a | b | c |

C * | a | b | c | a | b | b | a | b | b | a | b | c |

TPI | a | b | b | a | b | b | a | b | b | a | b | b |

Furf | a | a | a | a | a | a | a | ab | b | a | ab | b |

Ellag | a | b | b | a | b | c | a | b | b | a | b | c |

Vanil | a | b | c | a | b | c | a | b | b | a | b | c |

Cofde | a | a | a | a | b | b | a | b | a | a | b | c |

sumHPLC | a | b | b | a | a | a | a | b | b | a | b | b |

**Table 4.**Numerical results of the similarity contrast between the groups AC, AL, TC, and TL, depending on the ageing time of the wine spirit samples. Functional results (FDA) are based on FANOVA using two different tests (FP: permutation test based on a representation of the base function, FB: F test with a reduced bias estimation method). In addition, the results of the ANOVA and Kruskal’s test representing the vectorial results (VA) are shown. All the results are p-values based on a 5% significance level.

TEST\SAMPLE | 3050–2750 cm^{−1} | 1525–120 cm^{−1} | 1150–960 cm^{−1} | 910–750 cm^{−1} | ||
---|---|---|---|---|---|---|

18 months | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | ≈0 | ||

VA | ANOVA | ≈0 | ≈0 | ≈0 | ≈0 | |

Kruskal | ≈0 | ≈0 | ≈0 | ≈0 | ||

12 months | ||||||

FDA | FANOVA | FP | 0.001 | ≈0 | ≈0 | ≈0 |

FB | 0.003 | ≈0 | 1.31 × 10^{−5} | ≈0 | ||

VA | ANOVA | 0.007 | ≈0 | 0.003 | ≈0 | |

Kruskal | 0.008 | 2.23 × 10^{−6} | 0.003 | ≈0 | ||

6 months | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | 1 × 10^{−4} | ||

VA | ANOVA | ≈0 | ≈0 | ≈0 | ≈0 | |

Kruskal | ≈0 | ≈0 | ≈0 | ≈0 |

**Table 5.**Results of the similarity contrast between the three ageing times (18 months, 12 months, and 6 months), depending on the ageing technology. Functional results (FDA) are based on functional ANOVA (FANOVA) using two different tests (FP: permutation test based on a representation of the base function, FB: F test with a reduced bias estimation method). In addition, the results of the ANOVA and Kruskal’s test representing the vectorial results (VA) are shown. All the results are p-values based on a 5% significance level.

TEST\SAMPLE | 3050–2750 cm^{−1} | 1525–120 cm^{−1} | 1150–960 cm^{−1} | 910–750 cm^{−1} | ||
---|---|---|---|---|---|---|

Groups within AC | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | ≈0 | ||

VA | ANOVA | ≈0 | ≈0 | 0.032 | ≈0 | |

Kruskal | ≈0 | 6.72 × 10^{−5} | 0.214 | 1 × 10^{−4} | ||

Groups within AL | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | ≈0 | ||

VA | ANOVA | ≈0 | ≈0 | ≈0 | ≈0 | |

Kruskal | 2.07e-06 | 4.14 × 10^{−6} | 3.34 × 10^{−5} | 3.71 × 10^{−6} | ||

Groups within TC | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | ≈0 | ||

VA | ANOVA | ≈0 | ≈0 | ≈0 | ≈0 | |

Kruskal | ≈0 | 7.32 × 10^{−6} | ≈0 | ≈0 | ||

Groups within TL | ||||||

FDA | FANOVA | FP | ≈0 | ≈0 | ≈0 | ≈0 |

FB | ≈0 | ≈0 | ≈0 | ≈0 | ||

VA | ANOVA | ≈0 | ≈0 | ≈0 | ≈0 | |

Kruskal | 1 × 10^{−4} | 1.95 × 10^{−6} | ≈0 | ≈0 |

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## Share and Cite

**MDPI and ACS Style**

Anjos, O.; Martínez Comesaña, M.; Caldeira, I.; Pedro, S.I.; Eguía Oller, P.; Canas, S.
Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies. *Mathematics* **2020**, *8*, 896.
https://doi.org/10.3390/math8060896

**AMA Style**

Anjos O, Martínez Comesaña M, Caldeira I, Pedro SI, Eguía Oller P, Canas S.
Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies. *Mathematics*. 2020; 8(6):896.
https://doi.org/10.3390/math8060896

**Chicago/Turabian Style**

Anjos, Ofélia, Miguel Martínez Comesaña, Ilda Caldeira, Soraia Inês Pedro, Pablo Eguía Oller, and Sara Canas.
2020. "Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies" *Mathematics* 8, no. 6: 896.
https://doi.org/10.3390/math8060896