# A novel method to correct for wood MOE ultrasonics and NIRS measurements on increment cores in *Liquidambar styraciflua* L

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## Abstract

### **Key message**

**Key message**

**Ultrasounds overestimate the MOE value. This paper analyses the causes of this difference and opens the perspective for a novel method allowing the calculation of the correct MOE from ultrasounds or NIRS measurements on cores.**

### **Context**

**Context**

Standardized methods for determining wood modulus of elasticity (MOE) are destructive and require many replicates. Other methods such as NIRS and ultrasound have been developed to characterize wood properties and overcome these constraints.

### **Aim**

**Aim**

The aim of this study was to compare the two MOE measurement methods (NIRS and ultrasound) applied to cores of wood taken from standing trees (*Liquidambar styraciflua*).

### **Methods**

**Methods**

MOE, measured by an acoustic method in standard samples (360 × 20 × 20 mm), was used as a reference. Then MOE was predicted by an NIRS model and determined using ultrasound in standard samples (360 × 20 × 20 mm), small samples (10 × 20 × 20 mm), and cores (15 mm in diameter).

### **Result**

**Result**

MOE values determined by acoustic method on standard samples and by ultrasonic method on small samples were correlated (*R* ^{2} = 0.72) and were not statistically different. The NIRS PLS regression yielded a model with *R* ^{2} _{cv} = 0.80. The link between NIRS and ultrasound on cores was statistically significant (*R* ^{2} = 0.68).

### **Conclusion**

**Conclusion**

The ultrasonic technique determines an apparent modulus enables comparative data analysis. This apparent modulus can be used for quantitative analysis if a corrective model is used. A correction formula to ultrasonic MOE was proposed in the case of a prismatic geometry.

## Keywords

*Liquidambar styraciflua*Near infrared spectrometry Ultrasonic measurement Modulus of elasticity Cores of wood

## 1 Introduction

The determination of modulus of elasticity (MOE) by standardized methods is time-consuming and requires large quantities of plant material. These methods are generally destructive for the test sample or the tree given that sample extraction requires its felling. Standardized methods therefore cannot be used to monitor changes in MOE during a tree’s growth even though such information is important for the future use of its wood. An alternative technique is to use small samples such as cores. Previous studies (Perrin and Ferrand 1984; Bucur 1981, 1986; Nepveu 1988; Pelletier et al. 2008) have shown that it is possible to determine shrinkage, growth stress, and MOE using cores taken from standing trees. MOE can be determined in cores by ultrasonic or near infrared spectrometry (NIRS) assessment. The studies conducted by Schimleck et al (2003), Baillères et al (2002); Schimleck and Evans (2004), Hein et al (2010), Chaix et al (2010), Leblon et al (2013), and Tsuchikawa and Schwanninger (2013) showed that NIRS is useful for predicting certain physico-mechanical properties of wood. Bucur (1981) conducted ultrasonic measurements on 5-mm-diameter cores. More recent wood science studies (Brancheriau 2013; Ozyhar et al. 2013; Xu and Wang 2014) have improved ultrasonic measurement of MOE but the results obtained were not compared with those of standardized tests or other non-destructive methods. In order to measure MOE on increment cores, the study described herein aimed to (i) compare MOE values determined by the ultrasonic method with values obtained by modal analysis of flexural vibrations, (ii) identify the optimal model for determining MOE by near infrared spectrometry, and (iii) compare MOE values obtained using the ultrasonic method with those determined by NIRS.

## 2 Materials and methods

### 2.1 Study materials

This study is focused on *Liquidambar styraciflua*, a hardwood species of American origin. This species may be of interest for local wood markets in Madagascar because of its technological characteristics and color (American Hardwood Export Council 2008). *L. styraciflua* accounts for 30 % of hardwood stocks in southern USA (Carter and Hughes 1984). The wood of this species is highly popular on American and European wood markets, especially for the production of pallets, paneling, or furniture, because of its suitability for staining and finishing (American Hardwood Export Council 2008 and 2009). The success of this species is attributed not only to its wood, but also to its great plasticity. *L. styraciflua* has a high potential to adapt to different environmental conditions and can be managed by coppicing from the stump (Colonado 1992). In addition, this species is fast growing and has great ability to colonize wasteland (Sabistina 2010). Finally, its abundant seeds multiply easily in the nursery and can be stored in cool dry environments without any decrease in germination potential for about 3 years (Bonner 1970). Based on this potential, *L. styraciflua* is of great interest for Madagascar because it fulfills the requirements of the Malagasy wood market (fast-growing species, multi-purpose wood, high plasticity, and relatively resistant to the passage of fire) (Chaix and Ramamonjisoa 2001).

As part of an international provenance trial on *L. styraciflua*, the Oxford Commonwealth Forestry Institute shipped *Liquidambar* seeds to Madagascar from 13 provenances mainly within the natural area of the species distribution, i.e., southeastern USA, Mexico, and Central America. These 13 *Liquidambar* provenances of were introduced at Mandraka (Madagascar) in 1986. Fifty-four 23- to 24 year-old trees were subsequently felled for thinning purposes. They were derived from the nine best provenances in terms of height and diameter. Two sampling areas were selected (foot of slope and ridge) to maximize the variability of the characters under study. Prismatic bars (*N* = 201, 360 × 20 × 20 mm in L, R, T planes) were then cut from quartersawn boards. In addition, 99 radial cores (15 mm diameter and 378 mm mean length) were taken from the dominant trees (25 years old). All samples were stabilized at 20 °C, 65 % RH.

### 2.2 Experimental procedure

### 2.3 Free flexural vibration tests

The sample was placed on two elastic mountings (vibration deflection on the L-T plane). A steel ball (diameter 13 mm; weight 9 g) was used to create an impact on one end of the bar and a laser vibrometer was placed at the other end. The sound generated was filtered (analogic filtering with frequency cut-off at 10 kHz) and then digitalized with 12-bit resolution. The acquisition parameters were set to ensure a frequency resolution of ±1.35 Hz (first resonance frequency close to 790 Hz). The first three frequencies were used to determine the MOE A based on Bordonné’s solution to Timoshenko’s theory (Brancheriau 2002).

### 2.4 Ultrasound measurements

Emission and acquisition settings were specific to the length of the tested sample: square signal for five periods and time resolution of ±0.2 μs (0.3 % error for the propagation time determined in a 360 mm sample); ± 0.05 μs pulse signal and time resolution (2.5 % error for the propagation time determined in a 10 mm sample). As the MOE US error was greater for small samples, the mean of triplicate measurements/results was used. Theoretically, 70 repetitions would be required to reduce the error to 0.3 %, but only three repetitions were performed given the high number of measurements.

### 2.5 Near infrared spectrometry measurements

Near infrared spectra were taken on the radial tangential plane of the prismatic bars. Chaix et al (2010) showed that regression models yield accurate predictions when measurements are made on this plane. A Bruker Vector 22/N spectrophotometer combined with OPUS version 5.0 software was used in diffuse reflectance mode with a sintered gold standard as reference. This Fourier transform spectrophotometer is designed for reflectance analysis of solids and contains an integrating sphere. The same instrument with the same control software was then used with the same settings to measure absorption spectra of the cores, again in the radial tangential plane. Spectra were acquired over a 12,500 to 3500 cm^{−1} (800 to 2850 nm) range at 8 cm^{−1} resolution. Each spectrum was made up of 2335 absorption values, and 16 scans were averaged for each spectrum to improve the signal-to-noise ratio.

### 2.6 Calibration of the near infrared spectrometry regression model

*Liquidambar*wood) to the information generated by the near infrared absorption spectra (Wold et al 2001; Giordanengo et al 2009). Before constructing the PLS regression, the spectra were converted to first- or second-order spectra using Savitzky and Golay’s (1964) algorithm, then by standard normal variate (SNV) normalization. These data conversions improved the calibration quality by making effective use of and not degrading the spectral information (Naes et al; 2004; Hein et al 2010). The cross-validation technique with five random segments was used to test the preprocessing and build the NIRS calibration model for the MOE of

*Liquidambar*wood. Then we divided the samples into two sets to test the best model, one for calibration (131 samples) and one for external validation (49 samples). The following criteria were used to select the appropriate calibration: (i) values of the coefficient of determination between measured values and values predicted by calibration (

*R*

^{2}c), or cross-validation (

*R*

^{2}cv), or by external validation

*R*

^{2}; (ii) root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP); and (iii) ratio of performance deviation (RPD), which was the ratio between the standard deviation (σ) of the reference measurement of the samples considered and the RMSEP Eq. (2).

*ŷ*

_{i}and

*ŷ*

_{CVi}are obtained by testing the calibration equation directly on data from the calibration and validation samples, respectively. A is the number of latent variables in the model, N is the number of samples, and M is the number of samples for the external validation. For a model to be reliable, RMSEC, RMSECV, and RMSEP must be close in value, and as low as possible,

*R*

^{2}c,

*R*

^{2}cv,

*R*

^{2}, and RPD must be as high as possible (Schimleck and Evans 2004; Fujimoto et al 2008).

### 2.7 Data processing

_{ij}is the MOE measurement

*j*using the method

*i*, μ is the general mean, E

_{i}is the effect of the measurement method numbered

*i*, ε

_{ij}is the residual. Holm’s method was then applied for each MOE value determined by the different methods to detect significant differences (Saporta 2006). A linear regression analysis was performed to identify the link between MOE US and MOE NIRS on cores. All the analyses were conducted using R software version i386 2.15.3 (R Development Core Team 2012).

## 3 Results

### 3.1 Comparison of acoustic and ultrasonic methods used on prismatic bars

*p*< 0.01) between the mean values of MOE US360 and MOE A (difference of 1620 MPa, i.e., approximately 9 %). A difference (2150 MPa, i.e., 12 %) was also noted between MOE US10 and MOE US 360. The pairwise comparison of means showed that MOE US360 was greater than the two other MOE values (Table 1 and Fig. 2). The smallest difference was observed between MOE US10 and MOE A (530 MPa, i.e., 3 %).

Comparison of mean MOE values determined by acoustic and ultrasonic methods (N = 21)

Method | Mean (MPa) | Contrast | Difference (MPa) | |
---|---|---|---|---|

US360 (a) | 18250 | A | 1620 | <10 |

US10 (b) | 16100 | US360 | 2150 | <10 |

A (b) | 16630 | US10 | 530 | 0.20 |

### 3.2 Comparison of the NIRS model and ultrasonic method used on cores

*N*= 180) (Rakotovololonalimanana 2013). The best model in cross-validation was obtained with spectra converted into first-order spectra. The result of the regression yielded an

*R*

^{2}c of 0.82 and an

*R*

^{2}cv of 0.80, with RMSEC at 1077 MPa and RMSECV at 1165 MPa (range 8668 to 23,220 Mpa with 14 outliers). The model prediction error determined by cross-validation was 13 %. For the external validation, the

*R*

^{2}cv and the

*R*

^{2}reached 0.81 and 0.82, respectively, with RMSECV at 1016 MPa and RMSEP at 1234 MPa (range 8668 to 23,200 MPa and 9006 to 20,290 MPa, with 12 and 2 outliers, respectively, Fig. 3). The performance deviation ratio (RPD = SD/RMSEP) was 2.3, which is fully acceptable (Schimleck and Evans 2004).

*N*= 180, since the results were close due to the low group cross-validation number) were used to determine MOE values on core samples (1801 measurements, one measurement each 2 cm). Descriptive statistics for the obtained MOE values are given in Table 2. The statistical distribution of the values was practically identical for the two methods, with a mean of 15,620 MPa for MOE US (standard deviation 2700 MPa) and 15,360 MPa for MOE NIRS (standard deviation 2420 MPa). Figure 4 shows the relation between MOE NIRS and MOE US. The linear relation was significant (F = 3003,

*p*< 0.001) with an

*R*

^{2}value of 0.63 (

*N*= 1801). The standard error of the estimate was 1508 MPa. This error was consistent with the standard errors obtained with MOE US10 and MOE A (950 MPa, Fig. 2c, Rakotovololonalimanana 2013) and the standard error obtained with the NIRS model (RMSEP of 1234 MPa). The linear regression shown in Fig. 4a nevertheless shows bias between the ultrasonic and NIRS models given that the regression coefficients were significantly different from zero (MOE

_{NIRS}= 0.72* MOE

_{US}+ 3972). The pattern in Fig. 4b shows that the points fall in a horizontal band with no apparent systematic features (randomly distributed residuals). The regression was not biased by extreme values because no asymmetry was shown in Fig. 4b. The NIRS model was furthermore built using acoustic method values ranging from 8668 to 23,220 MPa (22 points out of 1801 were outside the calibration interval in Fig. 4a).

Descriptive statistics for MOE values determined by ultrasonic (US) and NIRS methods on cores (*N* = 1801)

Method | Mean (MPa) | SD (MPa) |
---|---|---|

US | 15,620 | 2700 |

NIRS | 15,360 | 2420 |

## 4 Discussion

### 4.1 Acoustic and ultrasonic methods

*7*), where

*m*is mass,

*h*is height,

*w*is width,

*L*is length, and

*τ*is ultrasonic propagation time.

Numerical error values were as follows: Δm = ±0.1 g (m = 95 g for L = 360 mm and m = 2.6 g for L = 10 mm); Δh = Δw = ±0.1 mm (h = w = 20 mm); ΔL = ±1 mm (L = 360 mm) and ΔL = ±0.1 mm (L = 10 mm); Δτ = ±0.2 μs (τ = 74.6 μs for L = 360 mm); and Δτ = ±0.05 μs (τ = 2.07 μs for L = 10 mm). Theoretical uncertainty in this case was 1.9 % for a 360 mm sample and 10.6 % for a 10 mm sample. The measurement errors were acceptable and within the same order of magnitude as those associated with normalized 3- or 4-point static bending tests. Brancheriau et al (2002) reported a measurement error of 9 % for the 3-point bending test and 6 % for the 4-point bend test on 360 × 20 × 20 mm samples.

*V*

_{X}is the propagation speed along the

*X*-axis,

*MOE*

_{X}is the MOE in the

*X*-axis, ρ is the density, S is the surface area of the right section, L is the length,

*I*

_{Gz}and

*I*

_{Gy}are inertias, and ν is the Poisson’s coefficient.

Effect of sample length on MOE values determined by the ultrasonic method

Species | Relative difference (%) | |
---|---|---|

Beech (Bucur 1981) | 32 | MOE (360 × 20 × 20 mm) > MOE core (5 mm) |

Liquidambar | 12 | MOE (360 × 20 × 20 mm) > MOE (10 × 20 × 20 mm) |

Digital simulation | 23 | MOE (360 × 20 × 20 mm) > MOE (20 × 20 × 20 mm) |

In the present case, the directions (X, Y, and Z) in Eq. (8) are collinear to the wood axes (L, T, and R). This equation was used to study the effect of the (L/h) ratio on the determined MOE values (Table 3). Values attributed to the Poisson coefficients were drawn from Guitard (1987) for so-called “standard” hardwood. The true MOE value is assumed to be that obtained by the acoustic method. In the simulation, the MOE of a 360 mm prismatic bar was compared with that of a 20 mm prismatic bar (not a 10 mm bar as in our study) as the model was used within its valid range. The theoretical difference in this case is 23 %, which is consistent with the experimental values. Note that for a (L/h) ratio above 7, the apparent MOE calculated from the conventional Eq. (1) no longer varies and converges toward the true MOE value.

### 4.2 NIRS model

The NIRS model developed is comparable to models described in the literature for *Eucalyptus* species (which have technological properties similar to those of *Liquidambar*) and other species. Schimleck et al (2001) calibrated a model for *Eucalyptus delegatensis* and obtained an *R* ^{2} _{cv} of 0.90 (in cross-validation). Kothiyal and Raturi (2011) obtained an *R* ^{2} of 0.82 for *Eucalyptus tereticornis* (independent validation method with a performance to deviation ratio of 2.3). Most woods of the *Eucalyptus* genus have higher quantities of extractives than *Liquidambar* (Chein et al 2013; Rakotovololonalimanana 2013). Extractives have a major impact on the quality of NIRS models as the absorption spectra obtained are dependent upon the chemical composition of the wood and the covalent bonds therein (Schwanninger et al 2011). The fact that the quality of the model developed here was deemed to be only “fairly good” may be explained by the low levels of extractives in the test wood. Moreover, Narayanamurti et al (1962) reported that extractives have effects on the physico-mechanical properties of wood. The linear relation in Fig. 4 shows bias between the ultrasonic method and the NIRS predictive model. The NIRS model was calibrated with moduli determined by flexural vibration tests (MOE A). The ultrasonic test determined apparent moduli (Eq. 1) using the density and a propagation speed which depended on the frequency of the travelling wave (dispersion phenomenon, Brancheriau 2011). The apparent modulus was thus a function of the MOE, Poisson coefficients, and sample geometry (Eq. 8) but also of the material viscosity (the dispersion was due to the antagonist effects of viscosity and Poisson effect). The difference between moduli determined from vibration frequencies in bending and moduli determined from temporal vibrations in compression could explain the bias observed in Fig. 4. This bias could also be due to the age and quality of the trees from which the samples were taken since the samples intended for the acoustic measurements (reference measurements for the NIRS model) were taken from 23- to 24-year-old thinning trees whereas the cores were taken from dominant or co-dominant 25-year-old trees. Several previous studies (Maeglin 1987; Zobel and Buijtenen 1989; Jeffries 2008) confirmed that the tree age has an impact on the physico-mechanical properties of the wood.

## 5 Conclusion

The MOE values were determined by flexural vibrations (acoustic technique) and ultrasound on bars (360 × 20 × 20 mm) and small samples (10 × 20 × 20 mm). When these values were compared, a significant difference was noted between the acoustic and ultrasound findings on bars but there was no difference between acoustic values on bars and ultrasound values on small samples. The near infrared spectrometry model was obtained on bars based on the acoustic technique. This regression model was characterized by a prediction error of 1234 MPa. The associated performance to deviation ratio of 2.6 allowed us to use the model to predict MOE on cores. The ultrasound and NIRS techniques were compared on cores (linear regression on 1801 measurements). The standard error of the linear regression was in agreement with the determination error of the two techniques. A bias was however revealed by the regression, which highlighted a difference between ultrasound and NIRS (acoustic technique). The acoustic technique determined a MOE theoretically equivalent to that of a 4-point bending test (local modulus). The ultrasonic technique determined an apparent MOE mainly function of the MOE value, geometry, and Poisson coefficients for small samples. The use of ultrasound on cores is, however, possible because this leads to direct determination of the apparent MOE. Another advantage is that ultrasound could be used on small-diameter cores (3 mm). The present analysis proposed a correction formula to MOE obtained by ultrasounds in the case of a prismatic geometry. For complex geometries such as cores, the validity of the ultrasonic MOE correction should be verified using finite element analysis in order to allow for comparison with results from other studies that report on true static MOE.

## Notes

### Acknowledgments

We thank S Lotte (CIRAD Ur BioWooEB) and instrument makers for machining wood samples, P Gallet and S Paradis (CIRAD Ur BioWooEB) for improving Us-Scan software, Honoré Randrianjafy and Hery Rakotondraoelina (DRFP/FOFIFA Madagascar) for providing material, LMGC (Laboratoire de Mécanique et Genie Civil) team, P Langbour, and D Guibal (CIRAD Ur BioWooEB) for providing technical support.

### Funding

Sample collection was funded by *Centre de Coopération Internationale en Recherche Agronomique pour le Développement* (CIRAD) in Montpellier, France and *Département de Recherche Forestière et Piscicole* (DRFP/FOFIFA) in Antananarivo, Madagascar. Laboratory work was funded by CIRAD. The main author received a grant from *Agence Universitaire de la Francophonie* during the 3 years of his PhD from 2011 to 2013. His PhD work was thereafter cofunded by CIRAD.

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