Mobile Edition
Print
Get the Mag
Weekly UpdatesWood stiffness or modulus of elasticity (MOE) is one of the most important wood quality attributes which is closely related to wood strength and utility of solid wood products (Zobel and Talbert 1984, Haygreen and Bowyer 1996). Lumber machine grading (NLGA 1996) takes advantage of the close relationship between lumber stiffness and its strength to grade lumber based on the nondestructive measurement of lumber stiffness. While technologies have been well established for the nondestructive evaluation of lumber MOE over the last several decades, very limited research has been conducted to evaluate wood stiffness in standing trees or green logs nondestructively. It is well-known that MOE of a material can be determined from its density and the velocity of sound waves transmitting through the material (Bodig and Jayne 1993). Based on this principle, some attempts (Nanami et al. 1992a, 1992b, 1993; Nakamura and Arima 1994; Nakamura 1996; Chui and Zhang 1997; Huang 2000; Addis et al. 2000; Wang et al. 2005) have been made to estimate the MOE of standing trees or green logs through nondestructive measurements of the transmission velocity of sound waves. Yet, the challenge to this approach is that it is difficult to measure the density (including wood and moisture) of standing trees or green logs nondestructively.
Computed tomography (CT) scanning is a nondestructive technique which provides cross sectional images in planes through a component. The CT technique has been used in a number of applications such as measuring internal log properties and detecting defects (Taylor et al. 1984, Funt and Bryan 1987, Phillips and Lannutti 1997, Fromm et al. 2001, Macedo et al. 2002, Bhandarkar et al. 2005, Wei et al. 2008), determining moisture flux and diffusion during wood drying (Wiberg and Moren 1999, Wiberg 2001), and optimization of log breakdown (Hodges et al. 1990, Steele et al. 1994, Orbay 2001, Rinnhofer et al. 2003). In addition, some studies (Lindgren 1991, Lindgren et al. 1992, Macedo et al. 2002) have reported that CT scanning technique could be used for estimating wood density of small air-dried wood specimens. Little work, however, has been conducted on the nondestructive evaluation of the density of green logs (or green wood).
The objective of this preliminary study was to investigate the feasibility of estimating the density of green logs and its radial and longitudinal distribution using the CT scanning technique. Development of nondestructive techniques for estimating the density of green logs or standing trees will make it possible to more accurately estimate wood stiffness. Information about the density of standing trees and green logs will also be helpful in log transportation and wood drying.
Materials and methods
Materials
Sample trees of two species were selected from a natural stand near Quebec City, Quebec, for this study. The two species included one softwood, balsam fir (Abies balsamea (L.) Mill.), and one hardwood, eastern beech (Fagus grandifolia Ehrh.). A fresh butt log of about 2 m long was removed from each sample tree. More information on the log samples is given in Table 1.
Measurements
The logs were CT scanned using Siemens's SOMATOM Plus 4 Volume Zoom CT system at room temperature (about 20[degrees]C). Scanning conditions were 140 kV and 178 mA for voltage and current of x-ray tube, respectively. CT images of cross sections of each log were obtained at a regular interval of 10.16 cm (4 in.) along the longitudinal direction from the bottom to the top of the log. In total, 23 and 25 CT images were obtained from eastern beech and balsam fir, respectively. Each CT image was 512 rows by 512 columns in size. A CT image contains 262,144 pixels, and each pixel has a constant area of 0.61 [mm.sup.2] (0.78 by 0.78 mm).
The CT image of a log cross section is composed of pixels which are the smallest elements of the CT images. Each pixel has a CT number value which is proportional to the attenuation coefficients of x-rays (i.e., x-ray absorption coefficients of the log scanned) as the x-rays pass through the corresponding wood zone. CT numbers in CT images are then computed as shown in Equation [1] (Hounsfield 1979):
Measured CT number = 1,000 x ([[mu].sub.x] - [[mu].sub.water])/ [[mu].sub.water] [1]
where:
[[mu].sub.x] and [[mu].sub.water] = the absorption coefficients of the scanned wood and water, respectively.
The absorption coefficient of a log primarily depends on its density and the energy of the x-rays employed. A log with a higher density could absorb more x-rays, and thus would have a higher x-ray absorption coefficient, i.e., a higher CT number value corresponding to a brighter zone in the CT image.
Density of wood is usually lower than that of water. Therefore, wood CT numbers computed using Equation [1] are generally less than zero. In order to avoid negative or zero values for CT numbers of wood, all of the measured CT numbers are modified according to Equation [2]:
CT number = 1,000 x ([[mu].sub.x] - [[mu].sub.water])/[[mu].sub.water] + 1,024 [2]
In this study, all of the CT numbers were determined based on Equation [2]. The two green logs were put in sealed plastic bags once they were scanned to prevent moisture loss. In the laboratory, discs (10.16 cm [4 in.] thick) were then immediately cut successively from the bottom to the top of each log along the longitudinal direction. Each disc corresponded to a cross-sectional CT image of the log. The CT images were acquired during previous CT scanning. As a result, 23 and 25 corresponding discs were obtained from the eastern beech log and balsam fir log, respectively. All of the discs were put into sealed plastic bags after they were cut from the logs.
The mass of each green disc from the two logs were measured to 0.01 g using an electronic balance. Disc volume was determined by the water displacement method as described in the ASTM D2395-83 standard (ASTM 1988). The density of each green disc was then calculated based on its green volume and mass. All of the discs were dried in an oven at 103[degrees]C for 24 hours. The ovendry mass for each disc was determined using the same eletronic balance as used previously. The moisture content (MC) of each disc was determined based on its green and ovendry mass following the standard method (ASTM 1997).
Data analysis
Each CT image has a background which represents the air surrounding the log (dark black color zone as shown in Fig. 1(a, b)). These areas did not contain any of the cross section of the scanned logs and were useless for calculating CT numbers of the logs. Thus, the background should be removed from CT images. A threshold value of 25 was selected using the image processing software Osiris 4.0 to remove the background for all of the CT images. Any pixels in the CT images that have a CT number of less than 25 were labeled as background pixels. For each scanned log, CT numbers of the log cross sections were then detected and recorded according to the threshold. Average value of CT numbers for each log cross section was calculated through a computer program developed using Matlab software.
The linear least squares fitting (Worthing and Geffner 1943) was performed to establish the linear relationship between the measured densities of the green discs and their corresponding average values of the CT numbers. Moreover, the correlation coefficient (r) was calculated using Equation [3] to further quantify the linear relationship between the density of the green discs and the average value of the CT numbers.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [3]
where:
n = the number of the green discs,
x = the average value of the CT numbers, and
y = the value of the measured density.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Results and discussions
Establishment of the linear relationship between green disc density and its CT number
The measured densities of the green discs from each log against their corresponding average values of the CT numbers were plotted for eastern beech (Fig. 2(a)) and balsam fir (Fig. 2(b)). The linear regressions equations (i.e., the relationship between green disc density with its CT number) and the correlation coefficient (r) are listed in Table 2 for the two species. As shown in Table 2, there was a very strong correlation between the measured densities of the green discs and average values of their corresponding CT numbers in eastern beech (r = 0.96). This also holds true for balsam fir which had a relatively lower correlation coefficient (r = 0.79). This suggests that it is feasible to predict the densities of green discs or logs for these two species using linear regression equations (Table 2) along with their CT numbers. Table 2 also shows that the average deviation between the measured and predicted densities of the green discs is smaller in eastern beech (0.47%) than in balsam fir (2.22%).
Prediction of the density distribution along longitudinal direction of the logs
The densities of the green discs along the longitudinal direction of the log were predicted using linear regression equations (Table 2) along with the corresponding CT numbers. The maximum, minimum, and mean of the measured and predicted densities of the discs from the logs are given in Table 3. The means of the measured and predicted densities were the same in balsam fir and almost equal in eastern beech. This suggests that the average density of the green discs in the two species can be predicted accurately using the CT technique. Table 3 also shows that the eastern beech log used in this study had a smaller difference between the maximum and minimum density values compared to the balsam fir log used. This indicates that density in the eastern beech log varies less in the balsam fir log. In other words, density in the eastern beech log was distributed more uniformly along the longitudinal direction than in the balsam fir log. A more uniform density distribution in the green eastern beech log might explain why a closer correlation exists between the measured densities and the CT numbers in eastern beech. Lindgren (1991) reported that MC was also very important to the prediction accuracy of wood density using the CT technique. This study shows a similar trend, i.e., a higher prediction accuracy is associated with a lower MC (Tables 1 and 2). In addition to MC, other factors (e.g., knots, ring width) may affect prediction accuracy (Lindgren 1991). Further study is needed to investigate and better understand the effect of these factors on the prediction of the density in green logs using the CT technique.
FEED