Goodness-of-fit analysis on wood properties data from six Brazilian tropical hardwoods

As part of a larger effort to develop design stresses for six hardwood species indigenous to tropical Brazil, a study was conducted to evaluate the relative goodness-of-fit of four distributions (normal, lognormal, Weibull, and S_B) that are used in wood related applications to the characterization of the modulus of elasticity (MOE) and modulus of rupture (MOR) data obtained from tests on lumber and clear wood specimens. Three criteria [maximum likelihood, Kimball, and Kolmogorov-Smirnov (K-S)] were used to evaluate the distributions over their entire domain. The K-S test was also employed at the lower tail of the distributions to evaluate goodness-of-fit at this crucial location for design stress development. The results showed that with respect to both MOR and MOE, the S_B distribution was as good or better than the other distributions. This was especially noticeable with the MOR data, since this data is often more skewed than MOE and the S_B is particularly well suited to describe positively and negatively skewed data. The lognormal and the Weibull were both found to be useful under certain circumstances; the normal distribution, due to its lack of ability to characterize anything but symmetrical distributions, was found to be of virtually no value in this application. Significant distinctions were found between the structure of MOR and MOE data sets obtained from the tropical and temperate zone species. For reasons believed to be related to gross and anatomical structure, more skewness was found in the two temperate zone species studied than in the six tropical species. As such, the S_B distribution, with its greater ability to quantify skewed data, performed overwhelmingly better than the other distributions. In describing the six tropical species, the advantage of the S_B distribution was less pronounced. Received 16 November 1998     

Modeling diameter distributions of Gmelina arborea plantation in Omo Forest Reserve,Nigeria with Johnson’s SB

Diameter distribution modeling is an essential tool for obtaining reliable information on the structure, growth, and yield of forests. However, this tool has not been duly utilized in many forest plantations, especially in Nigeria. Thus, this article presents the effectiveness of using the Johnson S_B function for modeling diameter distributions of a Gmelina arborea plantation in Omo Forest Reserve, Nigeria. Fifty plots of 0.04 ha were randomly selected across three age series. All trees with DBH ≥ 5.0 cm in the selected plots were measured. Three fitting methods for the S_B distribution were compared: conditional maximum likelihood (CML), moments (MOM), and Knoebel and Burkhart (KB) methods. The parameter recovery model (PRM) was used to recover the parameters of the distribution. The assessment was based on Kolmogorov-Smirnov (K-S), mean square error (MSE), mean absolute error (MAE), and bias. The results showed that the underlying diameter distribution of the Gmelina arborea followed the Johnson’s S_B distribution fitted with MOM. The number of rejections by the K-S test was zero for MOM and CML. The mean K-S value for MOM was statistically different from CML and KB methods. The results obtained after recovering the parameters of the S_B distribution were comparable with the real distributions of the Gmelina arborea stand.     

Species abundance distribution models of Toona ciliata communities in Hubei Province,China

The study of plant species abundance distribution(SAD) in natural communities is of considerable importance to understand the processes and ecological rules of community assembly.With the distribution of tree,shrub and herb layers of eight natural communities of Toona ciliata as research targets,three different ecological niche models were used:broken stick model,overlapping niche model and niche preemption model,as well as three statistical models:log-series distribution model,log-normal distribution model and Weibull distribution model,to fit SAD of the different vegetation layers based on data collected.Goodness-of-fit was compared with Chi square test,Kolmogorov-Smirnov(K-S) test and Akaike Information Criterion(AIC).The results show:(1) based on the criteria of the lowest AIC value,Chi square value and K-S value with no significant difference(p 0.05) between theoretic and observed SADs.The suitability and goodness-of-fit of the broken stick model was the best of three ecological niche models.The log-series distribution model did not accept the fitted results of most vegetation layers and had the lowest goodness-of-fit.The Weibull distribution model had the best goodness-of-fit for SADs.Overall,the statistical SADs performed better than the ecological ones.(2) T.ciliata was the dominant species in all the communities;species richness and diversity of herbs were the highest of the vegetation layers,while the diversities of the tree layers were slightly higher than the shrub layers;there were fewer common species and more rare species in the eight communities.The herb layers had the highest community evenness,followed by the shrub and the tree layers.Due to the complexity and habitat diversity of the different T.ciliata communities,comprehensive analyses of a variety of SADs and tests for optimal models together with management,are practical steps to enhance understanding of ecological processes and mechanisms of T.ciliata communities,to detect disturbances,and to facilitate biodiversity and species conservation.     

Comparing normal,lognormal and Weibull distributions for fitting diameter data from Akashmoni plantations in the north-eastern region of Bangladesh

Statistical probability density functions are widely used to model tree diameter distributions and to describe stand structure. The objective of this study was to compare the performance of normal, logarithmic-normal and three-parameter Weibull distributions for fitting diameter data from Akashmoni (Acacia auriculiformis A. Cunn. ex Benth.) plantations grown in the north-eastern region of Bangladesh. Data from 96 plots, established in 24 plantations in north-eastern Bangladesh and ranging in age from 1 to 6 years, were used for this study. The parameters of the Weibull distribution were calculated using maximum likelihood estimation (MLE) and moment estimation (ME) methods. The goodness of fit of normal, lognormal, Weibull MLE and Weibull ME were tested using one-sample Kolmogorov-Smirnov (KS) tests. The KS test results showed that both lognormal and Weibull distributions were equally effective for describing the diameter distributions of these Akashmoni plantations grown in the north-eastern region of Bangladesh.     

Prediction of bending properties for structural glulam using optimized distributions of knot characteristics and laminar MOE

This study established a prediction model for bending properties of glued-laminated timber (glulam) using optimized knot and modulus of elasticity (MOE) distributions of lumber laminate as the main input variables. For this purpose, knot and MOE data were investigated for all pieces of lumber that were prepared for glulam manufacturing, and statistical distributions of knot size, knot number in one lumber, and MOE of each laminate were optimized as distribution functions. These knot and MOE data were used as input variables in the prediction model for bending properties, and were also used in generating virtual glulam using the inverse transform method. Prediction of bending properties for glulam was carried out using the transformed section method, which is partially provided in ASTM D 3737 (Annex A4). Predicted values were compared with those from full-scale four-point bending tests for 60 six-layered glulams with 10 different laminar combinations. Finally, the allowable bending properties of glulam for each specific laminate combination were determined by calculating the fifth percentile of the modulus of rupture and the average modulus of elasticity from virtual test results of more than 1000 virtual glulams. From the results of this study, predicted bending properties for glulam and their distributions could be used for structural design in both allowable stress design and limit state design.     

An approach to modeling the joint distribution of tree diameter and height data

Advantages of the application of bivariate distribution models to forest management cannot be overemphasized. However, there are quite a number of flexible statistical distributions not yet evaluated in their bivariate domains. Therefore, in this article, we evaluated the bivariate forms of some probability distribution models used in quantitative forestry. Six bivariate distributions were assessed: Burr XII (Burr XII-2), Dagum (Dagum-2), Kumaraswamy (Kum-2), the new Logit-Logistic-Dagum (LLD-2) distribution, Logit-Logistic (LL-2), and the much used Johnson’s S_BB. All models were constructed using the Plackett’s method except for the S_BB distribution. Appropriate constraints were imposed on the boundary parameters of the bivariate distributions using fractions derived from the Gumbel distribution. Models were fitted with maximum likelihood to the joint distribution of diameter and height data of Eucalyptus camaldulensis Dehn from 90 sample plots. Model assessment was based on negative log-likelihood (-ΛΛ), Corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC). The result showed that the Johnson’s S_BB had the overall best performance. Their ranking order was: S_BB > LLD-2 > Burr XII-2 > Dagum-2 > LL-2 > Kum-2. These models can be used to simulate timber harvesting regime.     

Application of the SB distribution to the simulation of correlated lumber properties data

Summary With the emergence of probabilistic design procedures, the need for precise knowledge of the entire probability distributions of load effects and material resistance has never been greater. In order to evaluate these distributions, simulation techniques have provided a reliable and cost and time effective alternative to large scale destructive testing. With the use of the Johnson's S_B probability distribution, a closed-form, analytic procedure has been developed to model the inherent variability in strength, given some nondestructively evaluated parameter. This modeling procedure serves as the basis of a verified simulation process to predict a strength distribution, given a probability distribution of the NDE parameter. The approach presented here, represents a closed-form, analytic solution to a problem which has heretofore been treated in a more subjective fashion. This simulation procedure is complemented by a stratified sampling scheme.The author wishes to recognize Engineering Data Management, Inc. for the use of their computer software, STADMAN, and the Mc Intire-Stennis Research Program for the financial support of this study     

Increased planting density as a means for improving Pinus elliottii lumber stiffness

Faster growth and reduced harvesting ages are causing a reduction in the stiffness of lumber from South African grown pine plantations. The objective of this study was to determine whether increased planting densities of Pinus elliottii would result in improved stiffness of its sawn lumber and whether it would affect other relevant lumber properties. Four planting density treatments (403, 1 097, 1 808, and 2 981 stems ha^?1) of a 12-year-old experimental spacing trial were processed into lumber. The static modulus of elasticity (MOE_stat), modulus of rupture (MOR), warp, knot properties and density of the lumber were measured for 172 boards. Results showed that the planting density had a significant effect on the MOE_stat of the lumber. The higher mean MOE_stat (up to 27% increases) of lumber from densely planted trees seems to be the result of the higher slenderness and the slower diameter growth of these trees. Planting density also had a significant effect on the twist, knot area ratio and the number of knots per board. The magnitude of the effect on each of these properties, however, was relatively low.     

A comparison of diameter distribution models for Khaya ivorensis A.Chev. plantations in Brazil

The purpose of this study was to compare Beta, Gamma, Johnson's S_B and Weibull functions fitted by different methods for describing the horizontal structure of Khaya ivorensis (African mahogany) plantations in Brazil. The database comprised 128 plots from six plantations at varying ages. The function fits were compared using the Kolmogoroff–Smirnoff test, mean bias and mean absolute error for the number of trees and basal area per hectare per diameter class. Johnson's S_B outperformed the other functions, although all functions provided an adequate fit. The best methods were method of moments and maximum likelihood fitted using 25% of the minimum observed diameter as the location parameter for the Johnson's S_B function. The errors were greater in diameter classes with higher frequencies. Location and scale parameters were highly correlated with mean diameter and age for the Weibull and Johnson's S_B functions, respectively, which is convenient for diameter prediction. Gamma's scale parameter had medium correlation with age. Beta's parameters had low correlation with stand attributes assessed.     

Probabilistic evaluation of the final moisture content of kiln-dried lumber using the bootstrap method

This paper presents a probabilistic method of evaluating the final moisture content (MC) of lumber obtained at the end of the kiln-drying process. The final MC data of three different drying tests conducted in past studies were analyzed using the bootstrap method. Target MC was tentatively set below 20 % in the analysis. Two characteristic parameters representing the final MC were estimated with bootstrap confidence intervals. These parameters were the standard deviation (SD) and the percentage of the population that met the MC requirement of less than 20 % (P ₂₀). The histograms of the final MC and the subsequent goodness-of-fit tests revealed that the final MC data of two drying tests did not follow any classical probability distributions, including Normal, Log-Normal, Weibull, and Gamma distributions, thus indicating the need for nonparametric statistics. The uncertainty of the final MC could be evaluated with the estimated SD and P ₂₀. After deriving the relationships between P ₂₀ and the corresponding probability that P ₂₀ is not achieved, we demonstrated how such relationships could provide a kiln operator with information to facilitate better decision-making in optimizing a drying schedule.     

Application of the SB distribution to the prediction of concomitant wood properties

Summary It is frequently the case that multiple strength properties of structural wood members are simultaneously needed in design or research. A method has been developed to predict the probability distribution of concomitant material properties of wood from a knowledge of some correlated, nondestructive material property. The method developed in this study is based on properties of the univariate S_B distribution and the bivariate S_BB distribution. The technique involves a priori knowledge of the correlation relationship between a nondestructive parameter and the strength parameter for the two concomitant properties in question. A relationship is developed between the two nondestructive parameters and a simulation procedure is presented to predict either concomitant property from a single nondestructive measurement. The results showed that when a single parameter was predicted directly from a correlated variable, the simulated and experimental distributions were very similar (average error 3–4%). This result confirms previous findings. For the prediction of the concomitant property from an indirect relationship with another parameter, the absolute value of the average error was about 13%.     

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber I: Effect of length on the strength of lumber

An experimental study was conducted to evaluate the effect of length on the parallel-to-grain tensile strength of Japanese larch (Larix kaempferi, Carriere) lumber. Six hundred pieces of mechanically graded lumber were tested at gauge lengths of 60, 100, and 180 cm. The lumber was sorted into matched groups according to the dynamic Young's modulus measured by the longitudinal vibration method before the lumber was cut to the particular length. The averages of the dynamic Young's modulus of high-grade (H) and low-grade (L) specimens were 12.8 and 7.5 GPa, respectively. Using nonparametric estimates, the estimated length effect parameters of H and L were 0.268 and 0.304 for the 50th percentile and 0.121 and 0.256 for the 5th percentile, respectively. We then concluded that the different length effect factors between H and L could be used when using the lumber for practical purposes. The parameters of L were larger than those for H, and the parameters for 5th percentiles were smaller than the parameters for 50th percentiles. When two-parameter Weibull distribution functions were fitted to the strength data, the estimated shape parameters of the Weibull distribution by the parametric method were almost identifical to the inverse of nonparametric parameters except the 5th percentiles for H. The influence of defects such as knots on the lower tail of the strength distribution in H may be different from that in L.Part of this paper was presented at the 48th annual meeting of the Japan Wood Research Society, Shizuoka, April 1998     

Comparison of selected statistical distributions for modelling the diameter distributions in near-natural <Emphasis Type="Italic">Abies</Emphasis>–<Emphasis Type="Italic">Fagus</Emphasis> forests in the Świętokrzyski National Park (Poland)

The aim of the study is to compare selected theoretical distributions (normal, lognormal, Weibull, gamma, logistic, and exponential) in describing the tree diameter (DBH) distributions of mixed near-natural forests consisting of fir Abies alba Mill. and beech Fagus sylvatica L. growing in various vertical structures. Tree DBH data were collected between 1997 and 2008 from 51 sample plots established in the Świętokrzyski National Park in Poland. The empirical data represent differentiated DBH distributions, ranging from almost symmetric to extremely asymmetric ones. The chi-square test and the modified Kolmogorov–Smirnov test were chosen for the goodness-of-fit testing. In addition to the test statistics, the bias (B), the root mean square error (RMSE) and the graphical method (quantile–quantile plots) were used. In one-storied stands, the most suitable distributions were the normal and logistic distributions; in two-storied and multilayered stands, the Weibull and gamma distribution were the most suitable; and in selection stands, the exponential distribution was the most appropriate to describe the DBH distribution. The order of precision of the tested distributions (from the highest to the lowest) was Weibull, gamma, logistic, normal, exponential, and lognormal. The normal and exponential distribution should be applied only to one-storied and selection forests, respectively. The least suitable distribution for DBH distribution modelling was the lognormal one.     

Feasibility of near-infrared spectroscopy for online multiple trait assessment of sawn lumber

Near-infrared (NIR) spectroscopy coupled with multivariate analysis was applied to estimate multiple traits of sawn lumber. The effects of the lumber conveying speed (LCS) and measurement resolution of spectra (MRS) on the calibrations were examined. NIR spectra ranging from 1300 to 2300 nm were acquired at LCSs of 10, 20, and 30 m/min and at MRSs of 2, 4, and 16 nm. Prediction models of bending strength (F _b), modulus of elasticity in bending tests (E _b), dynamic modulus of elasticity (E _fr), and wood density (DEN) were developed using partial least-squares (PLS) analysis. LCS and MRS did not significantly influence the calibration performance for any wood property. The regression coefficients also showed no clear differences for any of the conditions. This indicates that the important explanatory variables included in the models are not greatly influenced by these measurement conditions. PLS2 analysis results, when presented graphically, allowed easy interpretation of the relationships between wood mechanical properties and chemical components, e.g., bending strength and stiffness were mainly related to polysaccharides cellulose and hemicellulose. NIR spectroscopy has considerable potential for online grading of sawn lumber, despite the harsh measurement conditions.     

Near-infrared spectroscopy prediction of southern pine No. 2 lumber physical and mechanical properties

This study investigated near-infrared spectroscopy (NIRS) to rapidly estimate physical and mechanical properties of No. 2 2 × 4 southern pine lumber. A total of 718 lumber samples were acquired from six mills across the Southeast and destructively tested in bending. From each piece of lumber, a 25-mm-length block was cut and diffuse reflectance NIR spectra were collected from the transverse face using a FOSS 5000 scanning spectrometer. Calibrations were created using partial least squares (PLS) regression and their performance checked with a prediction set. Overall moderate predictive ability was found between NIRS and the properties for the calibration and prediction sets: block specific gravity (SG) (R ² = 0.66 and R _p ²  = 0.63), lumber SG (0.54 and 0.53), modulus of elasticity (MOE) (0.54 and 0.58), and modulus of rupture (MOR) (0.5 and 0.4). Model performance for MOE (R _p ²  = 0.70) and MOR (R _p ²  = 0.50) improved when performing PLS regression on a matrix containing lumber SG and NIR spectra. Overall NIRS predicted MOE better than linear models using lumber SG (R ² = 0.46), whereas lumber SG (R ² = 0.51) predicted MOR better than NIRS. Overall NIRS has reasonably good predictive ability considering the small volume of wood that is scanned with the instrument.     

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber 11: Effect of knots on tensile strength distribution

The tensile strength (TS) test results of Japanese larch (Larix kaempferi, Carriere) lumber of varying length have shown that the length effects on TS were different between high-grade (H) and low-grade (L) lumber. In this paper, we examined the effect of knots on the TS distribution by measuring the number of knots and the knot area ratio of each specimen. There were more knots in L than in H; and the knot area ratio in L distinctly increased as the length increased compared to that in H. The correlation coefficients between physical properties and TS indicated that knots were the most influencial factor for TS among several physical properties: annual ring width, distance from pith, density, dynamic Young's modulus, and knots. We attempted to estimate the length effect parameters by introducing the concept of assumed knot strength. We thought that the length effect parameters for 50th percentiles of TS could be estimated well with fitted 3P-Weibull, and that the parameters for 5th-percentiles could be estimated well with 2P-Weibull fitted to lower-tail 10% data by the likelihood method. The differences of length effect on TS between H and L should be governed by the presence of knots. The independent model based on the concept of assumed knot strength may express the TS of structural lumber of various lengths.     

Modulus of elasticity declines with decreasing planting density for loblolly pine (Pinus taeda) plantations

Context

Loblolly pine is often grown in intensively managed plantations for wood production. In order to fully evaluate the effects of management practices on wood quality and ultimately value, it is necessary to relate mechanical properties to management practices.

Aims

The aim of this study was to evaluate the effect of planting density on mechanical properties of lumber recovered from loblolly pine trees from a 27-year-old spacing trial and develop prediction equations for modulus of elasticity and modulus of rupture from stand, tree, and board characteristics.

Methods

Regression methods were applied to sample trees from three planting densities (2,989, 1,682, and 746 trees ha^?1) and used to relate mechanical properties of lumber extracted from the trees to stand, tree, and board characteristics.

Results

Initial planting density was found to be correlated with modulus of elasticity and, to a lesser extent, with modulus of rupture. Including board characteristics and utilizing the visual grade and board position as regressors produced improved prediction equations.

Conclusions

The mean modulus of elasticity declines with decreasing planting density while the variability increases, suggesting that planting density is a surrogate for frequency and size of knots. Thus, lower planting densities, while producing more lumber, may produce proportionally fewer boards of greater modulus of elasticity than higher planting densities.     

Structure of mixed Picea abies (L) Karst,and Betula pendula Roth and Betula pubescens Ehrh. stands in South and middle Sweden

Observed diameter distributions of forest stands are adapted to the Johnson S _b probability function. The stands investigated are untreated mixed stands of Norway spruce (Picea abies (L.) Karst.) and birch (Betula pendula Roth and Betula pubescens Ehrh.) aged between 20 and 32 years. The adaptation of the Johnson S_b probability function is made both on mixed spruce and birch, and on each species separately. Altogether 156 observations were tested with observed distributions against calculated distributions in the Kolmo‐gorov‐Smirnov test. The fractiles are predicted with multiple regression and two multivari‐ate techniques, simultaneous‐equation models (multivariate regression) and partial least squares with latent variables. The independent variables are characteristics of site and stand. Both multivariate methods predict diameter distribution well when tested.     

Calculation of CFP and verification of effect on CO2 emission reduction for the use of certified wood in Kyoto Prefecture

The representative carbon footprint of product (CFP) value of “certified wood in Kyoto Prefecture” was calculated as 241?kg-CO₂/m³. The CFP value was 158?kg-CO₂/m³ when wood was not kiln dried and final processing was not involved, whereas that of “kiln-dried, finished wood” was 284?kg-CO₂/m³. Comparisons of different types of wood were also conducted to examine CO₂ emission-reducing effects of “certified wood in Kyoto Prefecture”. We compared the CFP of lumber produced (in Japan) from logs supplied from Japan and other countries and that of “certified wood in Kyoto Prefecture”; the lumber products as a target for comparison are shipped to markets throughout the country. The CFP of “certified wood in Kyoto Prefecture” was approximately 50% lower compared to that of North American wood lumbered in Japan and shipped to markets throughout the country, and about 30% lower compared to the mean CFP of lumber produced (in Japan) from logs supplied from Japan and other countries and shipped to markets throughout the country. We then compared the CFP of “products imported from other countries after being cut into lumber” to that of “certified wood in Kyoto Prefecture”. The CFPs of lumber products from North America and Europe were lower than that of “certified wood in Kyoto Prefecture” (kiln-dried, finished wood). However, when only woodchips were used as a heat source in the process of kiln drying, the CFP of “certified wood in Kyoto Prefecture” was lower than any other kiln-dried lumber products. Regarding “certified wood in Kyoto Prefecture”, the use of woodchips as a heat source in the process of kiln drying or a shift to air drying decreases the CFP.     

The potential of young,green finger-jointed Eucalyptus grandis lumber for roof truss manufacturing

South Africa is a timber-scarce country that will most probably experience a shortage of structural softwood lumber in the near future. In this study the concept of using young, green finger-jointed Eucalyptus grandis lumber was evaluated for possible application in roof truss structures while the timber is still in the green, unseasoned state. Drying will occur naturally while the lumber is fixed within the roof truss structure. The objectives of this study were (1) to investigate the strength and stiffness variation of the finger-jointed E. grandis product in both the green and dry state for different age and dimension lumber, (2) to investigate the variation in density, warp and checking in the lumber when dried in a simulated roof-space environment and (3) to evaluate the potential of this finger-jointed product as a component in roof truss structures. Green finger-jointed E. grandis lumber of ages 5, 11 and 18 years and dimensions 48×73?mm and 36×111?mm from Limpopo province were evaluated. The study showed that the young finger-jointed E. grandis timber had very good flexural, tensile parallel to grain, and shear properties in both the green and dry state. The mean and characteristic modulus of elasticity and modulus of rupture values of the finger-jointed E. grandis product were higher and the variation lower in comparison to currently used South African pine sources. The tensile perpendicular to grain and compression perpendicular to grain strength did not conform to SANS requirements for the lowest structural grade (S5). Both tree age and product dimension were sources for variation in the physical and strength properties. Based on the results from this study the concept of producing roof trusses from green, finger-jointed young E. grandis timber has potential.