@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Electrical and Computer Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Saboksayr, Hossein"@en ; dcterms:issued "2009-10-09T19:41:01Z"@en, "2001"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The problem of wood tensile strength estimation of softwood lumber is studied in this thesis. The main contributions brought to this topic here are first, a set of knot geometry features that can be used in board strength estimation, and second a learning algorithm that selects the best set of features for the purpose of strength measurement. The estimation problem is posed as an empirical learning problem that is based on the measured properties of wood. The process of producing the required database consisted of three distinct tasks: selecting and preparing the boards, measuring a set of properties of wood for every board, and estimating the measured strength of each board from the measured profiles. A set of boards, providing a random sample of softwood lumber, already existed at UBC (from previous experiments). These boards were measured and used as the preliminary database. A second set of boards was selected randomly from the regular production of softwood lumber. These boards created the evaluation data set. For the measurement task, all the boards were scanned using the available measurement machines. These machines were SOG and Microwave for grain angle measurement, X-ray for local density measurement, dynamic bending machine for the Modulus of Elasticity measurement, as well as the ultimate tensile strength tester for measuring the tensile strength of a board. The output profiles per board were saved in a data file (one data file per board per machine). The measured data files were stored in a database consisting of a structure of directories. In the strength estimation task all the measured profiles of a board were mapped to specific features (usually statistical moments) and the features were then mapped to the strength of the board. One of the features of a board is the set of its knots. A conic model of a knot was chosen and the related mappings were developed such that the X-ray scanning could be used in order to detect the existence, location, and shape of knots in a board. Then geometrical features were proposed such that the set of knots of a board could be transformed into a set of features suitable for strength estimation methodology of this thesis. Since specimens are costly to measure, means to reduce the number required were developed. To this end statistical learning theory was applied. This theory addresses the suitability of the learning model for the physical problem and the effectiveness of the features for the estimation problem. Based on this theory, the ASEC learning model was developed. The learning problem for wood tensile strength estimation was divided into three problems: defining the most suitable feature set, measuring the suitability of a learning machine, and using the a priori knowledge about the dependence in the learning machine. A method for measuring the suitability of a regression estimator (VC-dimension) was developed in order to select the best model in a class of models. The ASEC learning model was developed in order to find the best set of new features from the given feature set by using the known dependencies. Different learning machines were tested in order to determine what model is most suitable for tensile strength estimation of lumber. The validity of all the methods was demonstrated by analytical proof, by simulation, or by test on the database."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/13832?expand=metadata"@en ; dcterms:extent "18574283 bytes"@en ; dc:format "application/pdf"@en ; skos:note "Tensile Strength Estimation of Lumber By Hossein S. Saboksayr B. A . Sc. (Electrical Engineering) Sharif University of Technology, 1988 M . A . Sc. (Electrical Engineering) Concordia University, 1995 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E STUDIES ( D E P A R T M E N T O F E L E C T R I C A L A N D C O M P U T E R E N G I N E E R I N G ) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A August 2001 © Hossein S. Saboksayr, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. -The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract The problem of wood tensile strength estimation of softwood lumber is studied in this thesis. The main contributions brought to this topic here are first, a set o f knot geometry features that can be used in board strength estimation, and second a learning algorithm that selects the best set of features for the purpose o f strength measurement. The estimation problem is posed as an empirical learning problem that is based on the measured properties of wood. The process o f producing the required database consisted o f three distinct tasks: selecting and preparing the boards, measuring a set of properties of wood for every board, and estimating the measured strength of each board from the measured profiles. A set of boards, providing a random sample o f softwood lumber, already existed at U B C (from previous experiments). These boards were measured and used as the preliminary database. A second set of boards was selected randomly from the regular production of softwood lumber. These boards created the evaluation data set. For the measurement task, all the boards were scanned using the available measurement machines. These machines were S O G and Microwave for grain angle measurement, X -ray for local density measurement, dynamic bending machine for the Modulus of Elasticity measurement, as well as the ultimate tensile strength tester for measuring the tensile strength of a board. The output profiles per board were saved in a data file (one data file per board per machine). The measured data files were stored in a database consisting o f a structure of directories. In the strength estimation task all the measured profiles o f a board were mapped to specific features (usually statistical moments) and the features were then mapped to the strength of the board. One o f the features of a board is the set o f its knots. A conic model of a knot was chosen and the related mappings were developed such that the X-ray scanning could be used in order to detect the existence, location, and shape o f knots in a board. Then geometrical features were proposed such that the set o f knots of a board could be transformed into a set of features suitable for strength estimation methodology o f this thesis. ii Since specimens are costly to measure, means to reduce the number required were developed. To this end statistical learning theory was applied. This theory addresses the suitability of the learning model for the physical problem and the effectiveness o f the features for the estimation problem. Based on this theory, the A S E C learning model was developed. The learning problem for wood tensile strength estimation was divided into three problems: defining the most suitable feature set, measuring the suitability of a learning machine, and using the a priori knowledge about the dependence in the learning machine. A method for measuring the suitability o f a regression estimator (VC-dimension) was developed in order to select the best model in a class o f models. The A S E C learning model was developed in order to find the best set o f new features from the given feature set by using the known dependencies. Different learning machines were tested in order to determine what model is most suitable for tensile strength estimation of lumber. The validity of all the methods was demonstrated by analytical proof, by simulation, or by test on the database. iii Table of Contents ii Abstract „ , , viii List of Tables ix List of Figures Nomenclature X U xvi Acknowledgement Chapter 1. Introduction 1 1.1. Objective and limitations 1 1.2. The paradigm 2 1.3. Specimens 2 1.4. An overview of the experimental work 4 1.5. An overview of the analysis 6 1.6. Review of other attempts to transform measured mechanical properties into strength 7 1.7. Economic importance of this knowledge 10 1.8. Why Geometrical features are important 10 1.9. Outline of this thesis 11 1.10. The Contributions of this thesis 12 Chapter 2. Measurement means; practical constraints 13 2.1. Measurement of the Physical Properties of Wood 14 2.1.1. Modulus of elasticity of wood 14 2.1.2. Moisture content 15 2.1.3. Dielectric Properties 16 2.1.4. Density of wood 17 2.2. Measuring density with an X-ray machine 17 iv 2.3. Measuring Grain Angle with SOG and Microwave Machines 22 2.3.1. Grain angle via an SOG machine 22 2.3.2. Grain angle measurement via microwave 25 2.4. Modulus of Elasticity using the Continuous Lumber Tester 27 2.4.1. Calibration 28 2.5. Ultimate Tensile Strength Tester 36 Chapter 3. Modeling wood failure 37 3.1. Tensile strength of clear wood as a random variable 38 3.2. The effect of grain angle on strength 39 3.3. The effect of density variation on strength 40 3.4. The effect of holes on strength 41 3.5. The effect of knots on strength 41 3.6. Other factors 42 3.7. A 2x4 board as a system 43 3.8. Proposed approach to modeling strength as a continuous function of wood properties 44 Chapter 4. Characterizing a board; features 47 4.1. A general view on defining the features 49 4.2. Properties of clear wood 51 4.3. Characterizing the defects 55 4.4. Geometrical features 57 4.5. Characterizing feature sets are not unique 59 4.6. Board model 60 Chapter 5. Extracting features from measured profiles 62 5.1. The image of a knot in an X-ray image; the shadow image 62 v 5.2. Thresholding; classifying a pixel into knot or clear wood classes 64 5.2.1. Bayesian classification 66 5.2.2. Edge detection 68 5.2.3. Experimental data 70 5.3. Indexing the pixels of a knot 74 5.4. Knot pattern 75 5.4.1. Knot model parameters 78 5.4.2. Measuring and calculating the features of the pattern 78 5.4.3. Matching patterns 82 5.5. Geometrical features of a knot 82 5.6. X-ray image analysis; extraction of board image and defect detection 83 5.6.1. Edges of the board 84 5.6.2. Knot detection 85 5.6.3. Three dimensional knot shape detection (simulation) 90 5.7. Knot detection for real data 96 5.8. X-ray and SOG interrelation 100 5.9. Sufficiency of sampling rate; the problem of resolution 103 5.10. Preparation of specimens and measurement process 105 5.11. Specimen Characterization 112 Chapter 6. Strength Estimation; Empirical Learning for Small Sample Size 120 6.1. Strength estimation as an empirical learning problem 122 6.2. High dimensionality of the feature set 130 6.3. The relationship between estimation accuracy, learning capacity, and sample size 132 6.4. Extending the learning-capacity (VC-dimension) to regression estimators 135 6.4.1. The equivalence of classifiers and regression estimators 135 6.4.1.1. Learning problem statement 135 6.4.1.2. Constructing a classifier by using a regression estimator 137 vi 6.4.1.3. Constructing a regression estimator by using a classifier 138 6.4.2. The VC-dimension of a regression estimator 142 6.4.3. Corollary 143 6.4.4. Measuring the VC-dimension at a point 143 6.5. Strength estimation by using existing methods 149 6.5.1. Linear regression 149 6.5.2. K-Nearest Neighbor and radial basis functions 150 6.5.3. Multi-layer neural networks 151 6.5.4. SPORE 153 6.6. Alternating Space Expansion and Contraction (ASEC) 154 6.7. Estimation accuracy of different learning machines 163 6.8. Discussion of the results 165 Chapter 7. Conclusions and Future Directions 167 7.1. Conclusions 167 7.2. Future Directions 168 Appendix: Board failure; initiation and propagation of a fracture 170 References 174 vii List of Tables Table 1: The average output, average MOE, and transformation coefficients for selected specimens. 31 Table 2: The number of output signals of measurement machines 108 Table 3: Specimen file names 109 Table 4: The measured VC dimension of a linear regression estimator 146 Table 5: The parallel feature sets 157 Table 6: The computed after each iteration of ASEC 162 Table 7: The accuracy of estimation by using different learning machines. 164 Table 8: The accuracy of the estimation for different feature sets. 165 vii i List of Figures Figure 1.1. Wood strength estimation problem paradigm; different stages of the learning problem.2 Figure 1.2. Different Specimen sets that were produced during the course of this research. 4 Figure 2.1. Three-point and four-point bending test. 15 Figure 2.2. The mechanism of a Continuous Lumber Tester 15 Figure 2.3. A simple diagram of the X-ray system and the shadow image 18 Figure 2.4. The profile of one cross-section of the board. 19 Figure 2.5. The shadow of an X-ray image. 20 Figure 2.6. The shadow image of a knot. 20 Figure 2.7. The contour map of an X-ray image. 22 Figure 2.8. The rotating head for grain angle measurement. 23 Figure 2.9. A measured grain angle profile of a board. 24 Figure 2.10. Microwave System for measuring wood grain angle 25 Figure 2.11. The arrangement of the probes (left) and the structure of a probe (right). 27 Figure 2.12. Typical output profiles of a dynamic bending machine. 28 Figure 2.13. The extracted and adjusted dynamic bending machine output profile for specimen #0760 29 Figure 2.14. Measured static MOE of specimen #0760 30 Figure 2.15. Linear relationship between the average measured dynamic bending machine output 32 Figure 2.16. Measured MOE profiles by and static bending methods. 34 Figure 2.17. The repeatability of the measured profiles for machine. 35 Figure 2.18. The repeatability of the measured profiles for machine (continued). 36 Figure 3.1. Strength estimation as a learning problem. 45 Figure 4.1. Steps of strength estimation method. 50 Figure 4.2. The histogram representation of density distribution of a board 53 Figure 4.3. Grain angle profile of a board and its distribution. 54 Figure 4.4. The MOE profile of a board and its distribution. 55 ix Figure 4.5. The local density profile of the board generated by a moving window. 57 Figure 4.6. The density profile of a knot as compared with the density of clear wood of a board. 58 Figure 4.7. Conic model of a knot. 58 Figure 4.8. The model of a board that consists of the clear wood and defects. 60 Figure 5.1. The X-ray image of a knot 63 Figure 5.2. Contour map of an X-ray image. 64 Figure 5.3. Probability distribution of clear wood density and knot wood density. 66 Figure 5.4. Density distribution of X-ray image pixels of a specimen 73 Figure 5.5. Sampling pixels of a knot from an X-ray image. 74 Figure 5.6. A search for neighboring knot pixels. 75 Figure 5.7. A knot pattern (from its image) 76 Figure 5.8. Two orthographic projections of a knot. 77 Figure 5.9. The pattern of a knot. 78 Figure 5.10. The approximate image of the knot. 79 Figure 5.11. The four points of the pattern 80 Figure 5.12. The flow chart for knot pattern analysis. 81 Figure 5.13. The output of the X-ray system with and without the sample board. 84 Figure 5.14. Output of the X-ray imaging machine. 85 Figure 5.15. The edge of all knots of a board detected by fixed Bayesian based thresholding. 86 Figure 5.16. The edge of all knots of a board ... 86 Figure 5.17. Knot detection by using Bayesian thresholding. Specimen 130. 87 Figure 5.18. Knot detection by using Bayesian thresholding. Specimen 70. 87 Figure 5.19. The top view X-ray image and discretized X-ray image of a knot. 88 Figure 5.20. The side view X-ray image and discretized X-ray image of a knot. 89 Figure 5.21. The diagram of a knot cone and its parameters. 92 Figure 5.22. Contour diagrams showing the simulated top X-ray image ... 94 Figure 5.23. Estimation accuracy for the knot diameters. 95 Figure 5.24. The simulated knot pattern that is partially stretching outside the board. 96 x Figure 5.25. The result of applying the knot detection algorithm to the X-ray image. 97 Figure 5.26. The simulated X-ray images. 98 Figure 5.27. The location and size of knots in CCD camera images. 99 Figure 5.28. Most of the knots show a grain variation in the grain angle profile. 101 Figure 5.29. Visual image, X-ray image, SOG profile, and MOE profile. 102 Figure 5.30. The measured signal and its Fourier-transform. 103 Figure 5.31. The measured signal and its Fourier-transform of a typical SOG profile. 104 Figure 5.32. The database structure. I l l Figure 5.33. The coordinate of a knot in a board 113 Figure 5.34. The general flow chart of geometrical feature extraction program 115 Figure 5.35. The flow chart of the knot extraction routine 116 Figure 5.36. The flow chart of knot extraction routine 2 117 Figure 5.37. The flow chart of the statistical feature extraction program 118 Figure 6.1. The learning problem 123 Figure 6.2. Distance of all other boards from a sample board. 131 Figure 6.3. The block diagram for estimating the VC-dimension 147 Figure 6.4. A multi-layer neural network. 152 Figure 6.5. The cascade form of SPORE-1. 153 Figure 6.6. Two iterations of ASEC 155 Figure 6.7. Estimation accuracy from the contracted space (top) and the empirical risk (bottom). 158 Figure 6.8. The curve of the upper bound of the risk functional for the given number of features. 159 Figure 6.9. Replacement of close features in the trajectory table. 161 Figure 6.10. The flow chart of one cycle of the ASEC 163 xi Nomenclature A a a i B CART CCD camera CLT™ cm c D d d i d(.,) E E(.) F feature P F(.) A-) g(-) h h(.) I 0 KAR Minimum of a bounded function Fracture surface Area of either half of a knot pattern Maximum of a bounded function Classification And Regression Tree. A learning method A Charge-Coupled-Devicec digital camera Continuous Lumber Tester, a machine for measuring the dynamic modulus of elasticity of aboard The cost of misclassifying an element of class'/' into class 'f Speed of light Deflection (m) of a board in a bending test Diameter of a knot at the center of the knot Diameter of a knot at either end of it Distance between two points Modulus of elasticity Also, energy of matter Expected value of a random variable A The feature space that represents X A property of a profile, e.g., the average of a profile The physically meaningful set of features. The cumulative distribution function An approximating function /th feature that is selected inyth iteration of subset selection in ASEC A function A measure of the degree of freedom of a data set Also, the learning capacity of a machine An element of the approximating function set, in a dictionary based learning machine Intensity of an electromagnetic wave Also, moment of inertia (m3) of an object Also, size of a subset that is selected in an iteration of ASEC The initial intensity of electromagnetic wave before attenuating in matter Knot Area Ratio, the worst ratio of a knot cross-section to the board cross-section The stress intensity factor for opening mode of failure xn K The critical stress intensity factor for opening mode of failure K The stress intensity factor for sliding mode of failure K The critical stress intensity factor for sliding mode of failure Km The stress intensity factor for tearing mode of failure L The span {rn) of the bending test L(.) A loss function, based on which risk functional is defined A Total number of specimens in a training set A Distance of the center of a knot pattern from either end M(.) The Fourier transform of the MOE profile MEL Machine Evaluated Lumber. A lumber-grading standard MOE Young's Modulus of Elasticity MOR Modulus Of Rupture. The bending stress level that causes board to break MSR Machine Stress Rated; A lumber-grading standard m Mass of matter Also, the mean of a probability distribution function m(.) The measured MOE profile m'(.) The measured MOE profile with zero mean m Mean of the probability distribution function of class'/' N Number of pixels in a class n Number of samples or specimens n. Number of samples or specimens in class'/' o The center of a knot pattern P The load (AO in deflection of a board. profile A measured property in the form of a one dimensional signal or a two dimensional image p. Any point on the knot pattern p A knot pixel in a generated cube p Projection of a knot pixel on the central line of a generated cube p(x) The probability distribution of V if it belongs to class 7 psi Pound per Square Inch Q(.,.) A loss function qt Probability of class V happening R The complete space of physical features R A region in the measured variable X R(.) The risk functional, the mimmization of which is the goal of training a learning machine R (.) Empirical risk functional, by minimizing which a learning machine is trained Rempi) Empirical risk functional of classifiers xiii RempC) Empirical risk functional of regression estimators RZqk) Empirical risk functional of regression estimators that are made up of a group of classifiers r Distance (in a two dimensional polar coordinate) of a material element around the tip of a fracture r2 Coefficient of determination (^(xy) = c o v ^ x ^ ) . An estimation accuracy i A measure a a ' x y r(.) Penalization function S The tensile strength of a board S The set of samples that belong in class; S A set of approximating functions with fixed complexity § Estimated tensile strength S(.) The Fourier transform of the SOG profile SOG Slope Of the Grain. Slope of the grain of wood SPORE A learning method for high dimensional feature space SPF Spruce, Pine, and Fir s standard deviation of a distribution s(.) The measured SOG profile T An iteration of subset selection in ASEC t Thickness of a specimen U Potential energy in a board due to stress U Surface energy of a fracture w The set of parameters of an approximating function w * Optimum set of parameters of an approximating function X The measurable space of physical features Also, the measured density (the value) of a pixel of an X-ray image $ The space of all the measured profiles X A single point in the feature space x The input to a learning machine Y The vector of outputs y The output of a learning machine y A vector z A sample point z The sample space, the set of all sample points Z2^ A set of 2A specimens (.) Penalization functional, which defines the complexity of an approximating function xiv A The difference between two consecutive threshold levels A(.) The difference between practical and ideal risks T* A bootstrap sample from a training set A Population of all the image pixels The upper bound error for empirical risk functional n A real number between zero and one a The angle between two vectors Also, a set of parameters of a learning machine ax Optimum set of parameters resulting from a training set of size A a0 Optimum set of parameters resulting from minimizing the risk functional H The location parameter in an approximating function Also, mass absorption coefficient (1/crri) a The scale factor in an approximating function Also, the stress level in a board Also, the square root of variance of a distribution a The critical stress level c X The shape factor in an approximating function Also, the regularization parameter in an empirical risk functional ys Elastic surface energy per unit thickness 9 Angle (in a two dimensional polar coordinate) of an element around the tip of a fracture p Mass density iglcrrfi) e Total permittivity of matter Also error in strength estimation e(A) Error in empirical risk functional due to the size of the learning set d The permittivity of matter £\" The loss factor in permittivity of matter n Class (clear wood or knot wood) of an image pixel (oj The output of a classifier £ (Z2 )^ Maximum variation in empirical risks of A samples, in a set of size 2 A vx Empirical risk of a set of size A, in VC dimension detection process xv Acknowledgements I would like to acknowledge and express my appreciation for the support, patience, and continuous encouragement o f my supervisor Peter Lawrence, which has contributed a great deal to the completion o f this thesis. I would also like to acknowledge the help and cooperation of Frank Lam (Co-supervisor), David Barrett, Gary Schajer, Greg Grudic, Jacek Biernacki, Carl Flatman, Wilson Lau, Glen Trarup, and Bob Myronuk, A l l the required measurements were done in Wood Products Laboratory (Wood Science Department o f U B C ) as well as our industrial collaborators. The cooperation and help from the laboratory coordinators and researchers is also acknowledged. I also acknowledge my friendly roommates (in CICSR) , M r . Philip K . L i u and M r . Mohamed K . Cherif. The relaxed atmosphere o f my workplace has definitely had a positive effect on my work. xvi To my parents for their unlimited love and support Chapter 1. Introduction 1.1. Objective and limitations The goal o f this research is to find a suitable method for estimating a board's tensile strength by measuring the important-known material properties o f wood. A s wil l be shown, this problem inherently leads to a series of studies of wood structure, wood properties measurement, feature definition, learning systems, and estimation accuracy analysis. This thesis is an attempt to tackle this problem on all levels to produce a coherent analysis o f the problem. From a practical point o f view, the problem of strength estimation can be divided into the following problems: collecting a set of specimens, selecting measurement means, defining and extracting features from the measured signals, and estimating the strength by using the features of a specimen. Strength estimation can be cast as a learning problem. To do so, one needs different parallel measurement profiles of different wood properties and must define a variety of different features, in order to reduce the chance o f having any un-modeled factors. Therefore, a high dimensional feature space is needed for strength estimation. In the end, the problem of wood strength estimation is transformed into a learning problem in a high dimensional (more than 20 dimensions) feature space. The practical restrictions can be considered as conditions of the learning problem. There are potentially three major restrictions to the application o f the resulting strength-estimating model. The first restriction is, that because of measurement difficulty, the number of specimens for the database wil l be limited, which could make the database unsuitable for some learning systems. The second restriction is that properties of each species can vary depending on the region o f harvest, which means that any single model cannot be claimed as a general model of wood strength. Finally, the production lines may have different measurement means that have demonstrated reliability over time. 1 Therefore, many asymptotic learning methods may not be suitable for strength estimation and various learning methods should be explored in order to get the best result. Also, this research does not claim generality for the produced model to many species and wood harvesting regions. However, since the database of this thesis consists o f softwood lumber produced here in British Columbia (from here on B . C . ) the strength estimating model is suitable for B . C . 1.2. T h e p a r a d i g m The problem of wood strength estimation can be summarized as shown in Figure 1.1. The problem can be divided into four major tasks; specimen selection, measurement, feature extraction, and model development. Each part o f the problem is briefly explained in the following. specimen profiles measurement signal conditioning and feature extraction features learning estimated strength a priori knowledge Figure 1.1. Wood strength estimation problem paradigm; different stages o f the learning problem. 1.3. S p e c i m e n s A model is only representative o f the database used to formulate it. For this study, specimens were selected at random from normal production in a regular mill. In particular, four bundles o f regular production from two different mills (two bundles from each) were shipped to the laboratory for measurement and destructive testing. (The boards with obvious fractures were removed.) Each board was assigned a number that was written on the cross-section o f one o f its ends. This number was used to code all the data files that would be related to the same board and was kept constant throughout the project. Also, the same number was used to reference the specimen in the final feature set. During the course o f this research, two independent data sets were produced for the pilot study and the evaluation study, respectively. The pilot study data set consisted of 800 boards and was further divided into two separate sets: set one was used to develop a set o f features and the boards in this set were destructively tested for tensile strength; set two was used as a repetition of the first set as well as for comparing the measurement machines in the laboratory with the measurement machines used in the industry. A description of all the measurement machines and their limitations wil l be presented later in the related sections. In the evaluation study, presented in Sections 6.5 to 6.8, 1100 boards were selected from local mills. Similar to the boards in the pilot study, the boards in the evaluation study were a random sample o f the produced boards. A l l the measurements were done using industrial machines and the tensile strength of the specimens were measured at the University of British Columbia (from here on, U B C ) . The following diagram shows the specimen sets and the related measurement machines. 3 SOG Cook-Bolinder Vision-Smart X-ray UTS Pilot Study Preliminary Set (400 boards) SOG + Cook-Bolinder + Vision-Smart X-ray UTS Microwave CTL™ + Advantage2 Pilot Study Measurement Comparison Set (400 boards) Microwave Dynamic bending machine Advantage2 UTS Evaluation Study (1100 boards) Figure 1.2. Different Specimen sets that were produced during the course of this research. The S O G and Microwave machines measure the local grain angle of wood. Cook-Bolinder and CLT™machines measure the flatwise M O E of the board. Vision-Smart X-ray and Advantage2 measure the local density. U T S is for ultimate tensile strength measurement. 1.4. An overview of the experimental work The measurement means wil l be discussed in detail in Chapter 2. Briefly, they consisted o f the following systems. For X-ray, a Vision Smart X-ray machine (at U B C Wood Products Laboratory) and a Newnes Advantage2 were used. The X-ray machines ([1]) produced two-dimensional 4 density images o f each board. Two images o f the same board, one from the top and one from the side, were produced. The Vision Smart X-ray machine was used for the pilot study and was set in the Wood Products Laboratory o f U B C . The Newnes Advantage2 X -ray machine was used for the evaluation study. The data produced from the two machines were similar, but the Newnes Advantage2 database was used in the evaluation study because o f the higher resolution and because its conveyor had a more consistent speed. For S O G , the capacitance based heads, at U B C Wood Products Laboratory, and the microwave machine were used. These machines measured the local grain angle of wood along the board. The grain angle measurements were very similar between the two machines therefore the microwave measurements were used for strength estimation in evaluation study. For M O E , Cook-Bolinder M O E tester (at U B C Wood Products Laboratory) and Metriguard CLT™([4]) machine (at our industrial collaborator), also called dynamic bending machine here, were used. Cook-Bolinder M O E tester measured the flatwise Modulus o f Elasticity ( M O E ) profile of a board in a three-point test (see Figure 2.1) and measured the M O E profile o f one side o f the board in one scan. A Metriguard CLT™ machine is commonly used for wood grading and produces the two M O E profiles by one pass o f the specimen through the machine (see Section 2.1.1). A s wil l be shown in Section 2.4.1, the CLT™ machine is repeatable and its output is highly correlated to static M O E (see Section 2.1.1). Therefore, in the evaluation data set, only the CLT™ profile was measured and used for strength estimation. The ultimate strength tester (at U B C Wood Products Laboratory) was used to get the tensile strength o f each board in both the pilot study and evaluation study. In the U B C Wood Products Laboratory, all o f the different types of measurements were carried out independently. Once the measurement of one profile o f all the boards was finished, the laboratory was prepared for the next measurement. For each measurement, as each board was fed into the measurement machine its number was registered in a table. The measured profile of each board was saved in a different data file. Once an experiment (e.g. an X-ray measurement) was over, all the data files were renamed so that the file name represented the name o f the measurement (e.g. X-ray) 5 and the board number (e.g. 0114). The calibration files (if any) were kept with the data files in a directory to be used in a feature extraction program. 1.5. A n overv i ew o f the analys is A s was stated above, the selected specimens limited the application of the model. Since the sample boards were from B C , the strength estimation model is suitable only for softwood production in local industry. The limitations of the model not withstanding, the best choice of measured properties for model development is that they produce the minimum amount of uncertainty for board characterization. Measurement selection and feature extraction can be viewed as attempts at specimen characterization, such that boards with different features are mapped to different points in the feature space. Since the strength of a board is a random variable in this space, good feature definition minimizes the variance o f this random variable at a given point. Each specimen is characterized by a set of features, which are the statistical or the geometrical transformations of the measured profiles. The total of 64 features wil l be used to characterize each specimen of the database o f this thesis. Each one-dimensional profile wi l l be transformed into eight statistical features and the combination of the two X-ray images wil l be transformed into 16 features. There wil l be three M O E profiles. O f these three, two profiles are the measured profiles and the third profile is the average profile o f the two measured profiles (at every point along the board). Therefore, there wil l be 24 features from the measured M O E profiles. The measured grain angle profiles wil l be grain angle, grain alignment, longitudinal signal amplitude, transverse signal amplitude, longitudinal signal phase, and transverse signal phase. However, the three signals; grain angle, grain alignment, and longitudinal signal amplitude were used in the strength estimation. Therefore, there wil l also be 24 features from the measured grain angle profiles. Each of these profiles wil l be transformed into: minimum, maximum, average, standard deviation; variance, kurtosis, skewness; and the standard deviation o f the absolute value. The X-ray images o f the board wil l be transformed into the board three-dimensional model. The clear wood features: average, standard deviation, and variance of clear wood 6 density (as a random variable); the board volume; and the board density (sum of clear wood and non-clear wood density). Also, the knots wil l be characterized by: the number of knots; the ratio of knot volume to board volume; average and standard deviation of neighboring knot distances; average and standard deviation o f knot three-dimensional shape form the main axis of the board; average and standard deviation o f the standard-deviation o f all the knot pixels from the main axis of the board; and average and maximum of knot area ratio. The learning model is a regression-like estimator that relates measured features to the strength of the board. The selected features are given in Section 5.11. At this level, the concept o f learning capacity (or V C dimension) of the learning system is important (see Section 6.3). Briefly, the limited number o f measured specimens limits the accuracy of the learning system. In other words, there should be a search among different methods of learning to find the best model for a limited-size training set. Statistical learning theory was used to guide this search. A group of learning systems operating on different concepts was tested to find which method works best. A learning method was suggested whose structure is compatible with the constraints o f this learning problem. Finally, the performance of different learning models was compared. 1.6. R e v i e w o f o ther at tempts to t r a n s f o r m m e a s u r e d m e c h a n i c a l proper t i e s into s trength Since wood is a traditional structural material, there are many heuristic and scientific methods developed for estimating its strength. Among these, the weight o f a piece o f wood, which was used to represent the density o f wood, and the detection o f the presence of knots are the oldest. Scientific methods were later developed for finding the relationship between wood strength and one or more measured properties of wood. Since an estimation method can almost be identically used for tensile or the bending strength of wood, we wil l not distinguish between those. In the following discussion, different approaches to wood strength estimation are summarized. 7 The modulus of elasticity of wood is widely considered as the best single feature for estimating the strength of wood ([5],[6],[7]). In this method, the M O E (modulus of elasticity) profile o f a board is measured and a regression estimator maps the average of M O E profile to the strength o f wood. This method is the basis of an industry standard for machine stress grading. Special measurement machines were developed to measure this profile while the board passes through the machine at high speed. The coefficient of determination (r^xy) = c o v ^ x ^ ) between strength and the measured feature is r 2 « 0.5. i y The existing technology allows only the flatwise M O E profile of a board to be measured, that is, the M O E profile is measured by placing the bending force on the wider face (plank) of the board. Therefore it leaves out the applications where the bending force is applied to the narrower face (edge) of the board. The grain angle of wood has also been used for estimating strength ([8],[9]). In a similar approach, a regression estimator transforms the average grain angle to the strength o f wood. For this purpose, the capacitance based grain angle measurement and microwave based grain angle measurement tools were developed. The capacitance based grain angle measurement machine is most affected by the grain angle at the surface o f the board. The microwave measurement method can produce more than one measurement. It can estimate the average grain angle, and also the moisture content and the local density of wood. The features are usually the statistical moments of the measured profile and a linear regression estimator can be used to map the features to the strength. A finite element model of wood has been developed for estimating the strength of wood by assuming that the grain angle of wood is known at every point ([10]). Other parameters o f wood such as local density, M O E , etc., are typically assumed to be constant. This model is reported to produce accurate results for single knot and double knot pieces o f wood. The highest reported accuracy is r1 = 0.89 ([10]). Because o f the high computation time, this method is useful for laboratory study but is not suitable for industrial speeds. The effect of knots on the strength of wood was studied in ([11],[12],[13]). The use of knots in strength estimation is usually the limiting factor, and is applied in the visual grading of wood. There are category and boundary rules for estimating the impact o f a 8 knot on the strength. Therefore, a board is downgraded if, based on the rules, the knot or knots are considered to be significant strength reducing factors. Although this is obviously a very qualitative assessment o f their effect on strength, this method is an industry standard. This fact shows the high impact o f knots on the quality o f the graded wood. The geometrical features, as wi l l be discussed later, are especially developed to include this factor for characterizing a board. The local density of wood has also been suggested for strength estimation ([14],[15]). For this purpose X-ray machines (called X-ray lumber graders) were developed. It was proposed (arguably) as a non-contact measurement means that can replace the M O E measurement method ([15],[16]). In this case, the statistical features o f an X-ray image of a board are transformed to its strength by using a linear regression model. Visual systems ( C C D cameras, infra-red spectroscopy, and laser scanning) were also used for defect detection and grading of wood ([17],[18]). These methods are based on finding the difference between the color o f defects and that o f clear wood. Also, three-dimensional profiling (using laser scanning) is studied for estimating the defects and shape o f the board. The detected defects are related to the surface o f the board and a regression estimator transforms their features to strength reducing factors of the board. The grade o f wood was estimated in ([19]) by using the slope of the grain, infrared spectroscopy, M O E , and visual scanning. A classification and regression tree ([20]) method was used to learn the best grading thresholds. The goal was to find better rules for strength classes. In the Classification And Regression Tree ( C A R T ) method the feature space is repeatedly divided into smaller sections, as long as the total estimation error is reduced. In learning systems theory, the S P O R E algorithm ([21]) was developed specifically for very high dimensional problems. This method o f learning was originally developed for human-to-robot skill transfer. This method is suitable for very large dimension feature space (about 100 dimensional) and large numbers of specimens (about 10,000) and uses almost no a priori information about the data. A s wil l be shown in Chapter 6, this method is one o f the most successful methods for predicting the strength of wood. In this method, one generates a polynomial in the feature space ([21]) by producing two variable estimator blocks and adding the blocks to the model such that the estimation error is 9 minimized. The restriction of the wood strength estimation problem is that the practical number o f measured specimens is limited to around 1000. This is because the measurement process is costly and time consuming. The S P O R E algorithm has been tested for typical sample sizes of 10000. Therefore, this model may not be stable for a typical sample size used for wood strength estimation problem. 1.7. E c o n o m i c i m p o r t a n c e o f this knowledge The economic importance of this study arises from the limitations of the wood-grading standard. With the M S R lumber grading standard, three criteria must be met for every bundle that is sold. A flat M O E value (E) and an edge M O R (the bending stress that breaks the board) value (F) are provided for a grade. The following three criteria should be met for the assigned grade ([22]): a) The average flat M O E of a grade should be more than E; b) The fifth percentile o f M O E o f the grade should be more than 0.82 x E; c) The fifth percentile of M O R of the grade should be more than 2.1 xF. In practice, a stress-grading machine measures the M O E profile of each board. The average and minimum of this profile is measured and transformed into its grade. Recently, there have been attempts to improve the market value o f the grading system. In a recent study ([23]) it was shown that in M E L grading standards the limiting factor is the ultimate tensile strength of the board. Therefore, an increased estimation accuracy of the tensile strength increases the grade yield by more than 5%. It was shown (by simulation) that an increase in M O E prediction from 0.7 to 0.9 wil l produce more than 17,5 million U$/year in British Columbia ([23]). 1.8. W h y G e o m e t r i c a l features a r e i m p o r t a n t A s wil l be shown in future chapters, the problem o f learning the tensile strength of lumber is an empirical learning problem. In problems with small sample numbers, the a priori knowledge about the input-output dependence directly improves the estimation. 10 The geometrical feature set is a first step in including the classical study of wood failure under stress into this learning problem. Naturally, the features that are introduced are crude and only general information is used as a priori knowledge. It wil l be shown in Chapter 6 that even this set o f features produces relatively good estimation accuracy. The potential advantage of a geometrical feature set approach is that it is based on the three-dimensional model of a board, which wil l be produced by using scanning profiles. Since the model o f knots, the most common defect, is produced here, more refinement of features is possible by more carefully studying the effect of knots on strength. For example, through simulation enough samples can be generated so that a learning machine can find the effect o f common types o f defects on strength. 1.9. O u t l i n e o f this thesis This thesis is presented in seven chapters. Chapter 2 describes the measurement systems used in this project. A look into the wood property that is to be measured is presented. Also, measurement restrictions that are due to the limitations of the measurement machines are presented. Chapter 3 presents the effect of common strength factors and how they are modeled. Chapter 4 presents the chosen approach for feature definition and board characterization. Extraction of features from measured profiles is presented in Chapter 5. Details o f knot detection algorithm that is the basis o f the geometrical feature set is presented in this chapter. The problem of learning systems is discussed in Chapter 6. The learning problem and different learning machine structures are presented. Also, the A S E C learning machine is described in this chapter. The Appendix presents an examination of wood failure. This study motivated the focus of this thesis and provides a basis for comparison between classical study on this subject and the approach of this thesis. A l l the experimental results are given in the related chapters. 11 1.10. T h e C o n t r i b u t i o n s o f this thesis The main contributions of this thesis are as follows: 1. For analyzing an X-ray image, image segmentation (using Bayesian classification) is developed. In this method, the statistical properties of the image is used for segmentation. 2. A geometrical model of knots is developed and the detection algorithm and transformations are presented. 3. For characterization of a board, a geometrical feature set is developed. 4. In order to estimate the accuracy of a learning system, a method for measuring the learning capacity (VC-dimension) of a regression estimator is presented. 5. The A S E C learning method (see Section 6.6) is presented. In this method, the a priori knowledge about the input-output relationship is used to transform the given feature set into a better set of features. This method combines feature transformation and feature selection. 12 Chapter 2. Measurement means; practical constraints In this chapter the measurement systems used in the experiments are introduced and their limitations are discussed. For every wood property there are different technologies of measurement. Each technology and method of measurement is limited by its inherent restrictions that arise from the system's setup or its sensor requirements and limitations. As shown in Section 1.2, the measurement process is the first step in characterizing a specimen. The limitations of the measurement process directly affect the accuracy of the strength estimation because it is the basis o f specimen characterization and there is no other method for later compensation o f the generated error. Measurement restrictions can be examined from three different perspectives. The first limitation is that the measured property is affected by other properties o f wood, that is, one property of wood cannot be singled out. For example, the measured density of wood, i f measured by X-ray methods, increases with the increase of moisture content. The second limitation in the measurement process is influenced by the measurement method and the spatial resolution of the measured profile. Obviously, a property of wood cannot be measured at a single point and is usually the average of that property over an area or volume of wood, either at the surface of the board or through the depth o f the board. Any improvement of the measurement technique can result in a more sensitive machine and, therefore, improve the spatial resolution of the measured profile. The third limitation in the measurement process is dependent on the quality of the measurement machine, the sampling rate, and the noise level o f the output profile. In order to remove the measurement noise, almost all systems use averaging in a short period. For a board-moving system with a set o f fixed sensors, temporal averaging leads to spatial averaging. Higher-speed sensors allow the system to generate the output faster. In the following section the physical basis of the measurement machines is discussed. 13 2.1. M e a s u r e m e n t o f the P h y s i c a l P r o p e r t i e s o f W o o d The physical properties of wood relevant to the measurement systems o f this project are discussed in the following. 2.1.1. Modulus of elasticity of wood The modulus o f elasticity o f a specimen is measured by using bending machines. The board is bent and the force needed to bend the board is measured. Young's modulus or modulus o f elasticity ( M O E ) , is widely recognized by the wood products industry as the best variable estimator o f the bending strength of boards ([5], [6], [7]). It is defined as the ratio of stress over strain. In the three point bending test, as shown in Figure 2.1a, force is applied at the midpoint o f the board. M O E is calculated as follows. MOE = PD 148/D (1) Where P is the load (N), D is the deflection (m), L is the span of the measurement (m), and / is the moment of inertia (m 3 ) . This test is sensitive to the location o f defects in the wood specimen. Therefore, the operator tries to find the weakest point on the board and places it right at the midpoint (and on the tensile stress side), where the force is being applied. To reduce the sensitivity of this, a four-point test is often used (see Figure 2.1b). In this test, the middle part of the board is in constant bending moment, therefore, the whole span between the two forcing points is uniformly tested. 14 F F F — d TK—j ; d Bending force 1 1 Tensile force at the lower half part (a) (b) Figure 2.1 Three-point and four-point bending test. What is shown in Figure 2.1 is the basis of static M O E measurement systems where the board is placed on holders and bending force is applied. In a mill the boards are passed sequentially through a machine that continuously measures the M O E . The CLT™ (Continuous Lumber Tester) is one of these machines. A s shown in Figure 2.2 the dynamic bending machine has four rollers that are slightly displaced from a straight line. The first and last rollers are placed to grip the board and push the board through the system. The middle rollers are slightly displaced (Figure 2.2) so that they bend the board as it passes through. The rollers' locations are fixed, therefore, the bending of the passing board is fixed. The force applied by the board to the bending rollers is measured and sent to the output o f the system. Figure 2.2 The mechanism o f a Continuous Lumber Tester (CLT™, or dynamic bending machine) machine. 2.1.2. Moisture content The conductivity of wood is proportional to its moisture content. Therefore, by placing two conducting nails inside the board and measuring the resistance between them the moisture content of the board can be measured. Although this factor was not used as a feature of specimens, it was regularly checked to make sure that the boards were dry ( moisture content less than 12%). 15 2.1.3. Dielectric Properties Measuring the grain angle o f wood is usually based on its directional electric property. The permittivity of wood depends on the angle between an applied electric field and the longitudinal direction of the tracheid of wood. Also, the permittivity depends on the density, moisture content, and temperature of wood as well as the frequency o f the electric field used to measure it. Although these factors are briefly discussed here, they are not of significant importance because the grain angle measurement is based on the difference of permittivity along the grain and across the grain. The directional and variable permittivity o f wood is based on the polarization of its material and internal water and vapor. There are five polarization types that contribute to the overall polarization of wood. These are electronic polarization, ionic polarization, dipole polarization, interfacial polarization, and electrolytic polarization ([31]). Electronic polarization is due to the polarization o f the atoms o f the dielectric. Ionic polarization is a result o f elastic displacement o f atoms in a molecule. Dipole polarization is due to alignment of the existing dipole molecules in the direction of the electric field. Interfacial polarization is due to the interaction o f water and the cell wall that makes a cavity similar to a dipole. Electrolytic polarization is caused by the electrolysis of the soluble components due to the electric field. The first two polarizations are the major ones while the last three create the loss factor, making the permittivity a complex number as follows: e =s' - ie\" (2) The permittivity is a directional factor with three major directions, longitudinal, radial, and tangential. The longitudinal permittivity is the biggest factor while the radial and tangential permittivity factors are approximately the same. A l l three factors are increased by wood density and moisture content. The permittivity of wood decreases as the frequency o f the applied electric field increases. A n increase in temperature may also cause an increase or decrease in permittivity, depending on the frequency o f the applied electric field ([31]). The loss factor (£\") is usually much smaller than the real part of the permittivity itself, and therefore can be overlooked in the qualitative analysis of the measurement systems. 16 2.1.4. Density of wood It was shown that an X-ray source could be used for wood densitometry ([24]). The X-ray can be generated by an X-ray tube that projects beta rays onto a metal plate. The X-ray absorption phenomenon is a combination o f three absorption factors: the photoelectric absorption, the scattering absorption, and pair production absorption. The electrons of the matter rarely absorb the X-ray photons. This phenomenon is called true absorption or photoelectric absorption. Also, some of the photons are deflected by the atoms of the mass, which results in the scattering factor. In pair production absorption the ray transforms to matter (electron and positron) by the Einstein equation. The attenuation o f the ray as it passes through the board is as follows. where, ju, is the mass absorption coefficient (1/cm), and t is the specimen thickness. This equation can be written as follows. where/? is density (g/cm3) and p/p is the mass-absorption coefficient in square centimeters (area) per gram ([25]). A method of calculating the mass absorption coefficient for different materials is published in [26] and tables of it are published ([25]). A s the attenuated ray comes out of the wood, it is transformed to a measurable signal by an array of sensors. Each sensor is based on ionization of its atoms (gas or crystal) in an applied electric field ([27]), generating photons in the process. Every photon absorbed by the detector generates a pulse o f electric current. The count o f the pulses in a time interval is proportional to the intensity of the X-ray. 2.2. M e a s u r i n g densi ty w i t h a n X - r a y m a c h i n e X-ray scanning is used to measure the local density of wood. A s the X-ray passes through the board its intensity is attenuated. A sensor array measures the ray intensity. I = I0exp(-ttt) (3) I = I0exp(-(ju/p)pt) (4) 17 The board density image is mainly used for knot detection, which leads to the board's structural model. Nevertheless, the system and method o f this densitometry are commonly used and are explained in the following. The system consists of an X-ray source tube, which projects an X-ray fan on the object, and a linear array o f sensors that detects the intensity o f the rays after passing through the board. A metal frame reduces the vibration caused by any moving components. Lead curtains create a shield for the operator from the X-rays. A few rollers lead the board (pushed by the conveyor) through the system. As previously discussed, the attenuated ray coming out of the wood is transformed into a measurable signal by a linear array o f sensors ([27]). < X-ray tube Board cross section Shadow <•—Sensor array Figure 2.3 A simple diagram of the X-ray system and the shadow image results from a non-collimated X-ray. The board is extended and moves perpendicular to this page. The measured variable is the ray density, which is calibrated to wood density. For that purpose a set o f calibration aluminum plates with knot density and different thickness were used. They were placed in the machine and a polynomial was fitted to the output signal so that it transformed the measured intensity to wood density. A n array o f sensors (in a single line) can capture the density profile across the board at the measurement point. Each measurement generates a density profile related to one cross-section o f the board. A conveyor moves the board along, while repeated scanning takes place. In the end, an image o f wood density results for the whole board. The X-ray densitometry method and the structure of the measurement system impose some constraints on the produced image that are discussed here. The X-ray generated from the 18 tube is not collimated; therefore, it creates a shadow of the board corner at the sides o f the density profile. If the angle o f the ray (6) is relatively small (for the vertical distance between the source and the sensor array) there wil l be little horizontal deviation (s) in the projection o f the measured signal and thus no collimation is needed, which was the case for the X-ray system used in this thesis. A s wil l be shown, the angle of the ray can be measured from the X-ray image. The shadow o f the board (s) (as is shown in Figure 2.4) is less than three pixels in the machine used, which is considered negligible in the measured profiles and is ignored in the feature extraction procedure. X-ray profile of the cross section of the board at one point o. o £ e CO >H 0) >> (0 >< 500 — o l I I I , I , U I I I 0 20 40 60 80 100 120 140 sensor number (1 to 128) Figure 2.4 The profile o f one cross-section o f the board. The shadow of the board creates the side ramps. In Figure 2.4 the shadow of the board is 2 pixels at each side and the total number of pixels for the board is 35. Using the standard board size (89mm by 35 mm), one can calculate the maximum ray angle (G) with the center-line as follows (Figure 2.5): 19 e\\ r(35mm) A < — ' V 89 mm \\ . ,„ . , . (2 pixels) w (35 pixels) Figure 2.5 The shadow of an X-ray image. , s „ 5 89 mm , 2 ^ 89 mm v „ „ „ 0 = a t a n ( - ) = a t a n ( - * — ) = a t a n ( ^ * ^ ) = 8.1° (5) There is a more important shadow image that is related to the image o f knots of a board. Figure 2.6 shows an imaginary knot projected on the image plane similar to the result o f X-ray scanning of the board. A similar pattern is generated from the X-ray image o f a knot and wil l be used to detect knots in a board. The density of the image at every point is obviously the summation o f the wood density throughout the thickness of the board at that point. I f two perpendicular images are produced, a sense of density distribution in the body o f the board can be obtained. Figure 2.6 The shadow image of a knot. The sensor array makes a fixed resolution profile across the board. The image resolution along the board depends on the speed o f the board. I f the conveyor can push the board 20 through the system with a constant speed this resolution wil l be constant too. Through the course of this thesis, two X-ray systems were used for X-ray scanning. One o f them (made by Vision Smart) did not have any conveyor attached to it. Therefore a conveyor was placed next to the machine that pushed most of the board through the X-ray scanner and the end of the board (about 90 cm o f the length of the board) would free-run through the system because of its momentum. The deceleration of the board was compensated for as a preprocessing step when the image was being processed. The image was segmented into two parts, the first part related to the part o f the board that was pushed through the X-ray system with constant speed. The second part o f the image was related to the part of the board that was decelerating. A constant speed (that is the average speed during deceleration) was assigned to the second part of the image, as the momentary speed could not be estimated. The strength estimations by using each o f the outputs of the two machines resulted in similar strength estimation accuracy therefore here only a typical system is described. Another consideration regarding the X-ray image is that there should be a zero density region that surrounding the board density image. The content of the surrounding area is noise whose level is much less than the density o f clear wood. A threshold level can separate these parts and extract the density image of the board. Figure 2.7 shows the contour map of the top (for the plank of the board) and side images of the board. The lower right part of the image shows increased density that can be due to natural density variation o f clear wood or related to a defect, such as a resin canal. Vibration of the board is not considered in this case because slight vertical displacement of the board does not affect the measured image. This is because the source is far from the board surface and the slight change in the vertical location o f the board does not create significant change in the sensor readings. The noise level o f the system in the surrounding area is negligible, as can be seen from Figure 2.4. However, filtering by a square filter o f size three was advised (by the manufacturer) for smoothing the wood density. The system stores the measured ray intensity in 16 bits of data, which covers the spectrum of black to white. 21 c o n t o u r m a p of X - r a y s c a n from p l a n k o f t h e b o a r d « 0 75 S 7 0 a | 65 3 • SO JS * 55 50 • N^l: t,ML]» 4 0 0 600 600 1000 1 2 0 0 X - r a y i m a g e p i x e l n u m b e r (in th e o rig in a I p ic tu re ) c o n t o u r m a p of X - r a y s c a n from side o f t h e b o a r d _ 115 m e 0 400 600 BOO 1 0 0 0 1 2 0 0 X - r a y im a g e p i x e l n u m b e r (in the o r i g i n a i p i c t u r e ) Figure 2.7 The contour map o f an X-ray image. The final digital image is displayed by using two diagrams, the contour map and the three dimensional diagram o f the density. The contour map (Figure 2.7) is used for showing the general form of the image and the relative location of the defects in a board. The three dimensional density-diagram (similar to Figure 4.6) is used for showing the density variation due to the existence of a defect. 2.3. M e a s u r i n g G r a i n A n g l e w i t h S O G a n d M i c r o w a v e M a c h i n e s The principle o f grain angle measurement was discussed above. In this section the details of the two grain-angle measurement machines are presented. 2.3.1. Grain angle via an SOG machine The capacitance based measurement system that was used in this research was based on measuring the impedance o f a capacitor whose dielectric was the board at the measurement point and its operation is as follows (based on directional permittivity of wood). If two parallel strips of metal are placed on the top surface o f a board and the 22 impedance o f the created capacitor is measured, the impedance depends on the angle of the electric field o f the capacitor. I f the capacitor (i.e. the two metal plates) is rotated around its center the measured capacitance varies. The maximum capacitance is measured when the electric field is along the direction o f the grain. In a rotating head capacitor a cylindrical head is rotated around its axis. The bottom of the cylinder, where it contacts the board, four pieces of metal and a cross-shaped dielectric compose the circle as is shown in Figure 2.8. This arrangement creates two pairs o f parallel capacitors that are perpendicular to each other (as shown by the dotted lines in Figure 2.8). Therefore i f the electric field of two o f the parallel capacitors is along the grain o f wood then the electric field of the other two capacitors is perpendicular to the grain of wood. The angle o f the head where one of the two impedances is maximized and the other one is minimized is the angle of the grain o f wood. The impedance of each o f the capacitors is most affected by the grain of wood at the surface o f the board. The wood that is beneath the surface is affected less because the magnitude of electric field is less inside the board. Also, the measurement is taken over the area of the head. The diameter of the measurement head was about 5cm. The underlying assumption for accurate measurement is that the grain angle, and other factors that affect the permittivity, are about the same over the area of the measurement head. The measurement head rotates at 60 cycles per second and every half cycle one measurement can be completed. Therefore the sampling rate is limited to 120 samples per second. The grain-angle sampling rate is then controlled by the speed o f the conveyor. The sampling rate o f S O G measurement was about 1500 samples per board, which is about one sample per 3.3mm. The system's resolution is 0.1 degree and its accuracy is (±0.9) degree and the system covers -89 to 89 degrees ([2],[3]). Figure 2.8 The rotating head for grain angle measurement. 23 Figure 2.9 shows a profile that is measured by using this system. The large variations in Figure 2.9 are related to grain angle defects, which are usually related to knots. Small variations are related to the measurement noise. The two constant measurements at the beginning and the end of the profile is produced by the system when the board is not attached to the measurement head. The large variations, at the beginning and the end o f the board's grain angle profile, are produced when the board first reaches the measurement head or leaves it. A measured grain angle profile 1 i 1 1 1 J i MT* | 1*1-J [ J | ] ! i 1 800 1000 1200 1400 1600 1800 2000 sample number Figure 2.9 A measured grain angle profile of a board. The grain angle measuring system consisted of a metal frame and plastic rollers to push the board along the system and before the measurement heads. A stepper motor controls the movement and speed of the board. Two measurement heads were placed on the system so that two profiles could be measured simultaneously, one from the face of the board and one from the edge of the board. The diameters of the two heads were different. One head diameter was almost equal the thickness across the face of the board and the other head diameter was almost equal the thickness across the edge of the board. Four profiles were measured by using this arrangement, two profiles from the two faces and two profiles from the two edges. B y rearranging the system four extra profiles were 24 measured from the two faces of the board, each grain angle profile related to half o f a face. 2.3.2. Grain angle measurement via microwaves The microwave grain angle measurement machine is based on the directional attenuation of an electric field in wood. A simple diagram of such a machine is shown in Figure 2.10 ([28],[29]). In this machine a linearly polarized electromagnetic wave at microwave frequency («10 G H z ) is transmitted through the thickness o f the specimen. The directional conductivity and dielectric property of wood creates a non-symmetric attenuation and delay o f the wave. Therefore, the output wave is an elliptically polarized wave whose major axis is along the grain. The Microwave based grain angle measurement is based on identifying this ellipse. The standard deviation o f the measured grain angle is 2 degrees. M M Linearly polarized transmitting antenna Probe Circularly polarized receiving antenna Figure 2.10 Microwave System for measuring wood grain angle Let's say the electric field is represented by a sine wave as follows: E = E sin(tf*) (6) where the amplitude (E0) and the angular frequency (aj) are constant. Wood as an orthotropic material shows different loss factor and phase factor along and across its 25 grain. This would transform the linearly polarized electromagnetic wave to an elliptically polarized wave as shown in the following ([28],[29]). The incident wave components on longitudinal and transversal axes are as follows: E^E^cosiQ) (7) £ f f = £^s in (e ) (8) where 0 is the angle o f the incident field with the longitudinal axis. A s the transmitted wave propagates through wood, it is attenuated and delayed by the longitudinal and transverse propagation constants. rP = OLp+J% (9) rT = aT+j0r (10) Moisture content is the major factor of the wave attenuation and the wood material is the major factor of the wave delay. If the thickness of the specimen is d, the output wave is as follows: E T O = E I p e V = E 0 cos(9) e V * ^ (11) E ^ = E ^ e V = E 0 sin(0) e- a. op 1 ,1.5 ui o SE 0 5 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 board length (mm) Figure 2.14 Measured static M O E of specimen #0760 by using Metriguard (blue) and Eldelco (green) machines, (a) original measurement, (b) adjusted for sampling position. The extracted and adjusted profile shows the actual measured M O E at the represented points o f the board. The average o f the two profiles in Figure 2.13 (shown as V in Table 1) and the average of the two profiles o f Figure 2.14 (shown as E in Table 1) were used for calibration. The measured average dynamic bending machine and average static M O E are shown in the following Figure 2.15. The coefficient of determination of the two variables is r 2 = 0.92, which shows a linear relationship between the two variables. i | 30 Table 1: The average CLT™ output, average M O E , and transformation coefficients for selected specimens. Specimen # V (CLT™) E ( M O E ) c, c\\ 760 1.3683 1.8833 0.7265 1.3764 83 1.7110 1.8623 0.9188 1.0884 749 1.2610 1.5726 0.8019 1.2471 9 1.1853 1.3637 0.8692 1.1505 570 1.0565 1.2586 0.8394 1.1913 198 1.5896 1.8423 0.8628 1.1590 503 1.5518 1.7860 0.8689 1.1509 616 1.8549 2.0528 0.9036 1.1067 62 1.3717 1.4725 0.9315 1.0735 94 1.0792 1.4200 0.7600 1.3158 642 1.4377 1.7064 0.8425 1.1869 2 1.9447 2.1876 0.8890 1.1249 612 1.6248 1.7914 0.9070 1.1025 623 1.4489 1.7315 0.8368 1.1950 17 1.7727 2.1795 0.8134 1.2295 31 22 2 1 Average of CLT output vs average static MOE 2 -1 . 8 h UJ i i . 8 h -1.7 1.6 1.4r-1.3 12 1.3 1.4 1.5 1.6 1.7 Average of the measured CLT output 1.8 1.9 Figure 2.15 Linear relationship between the average measured dynamic bending machine output and the average static M O E . Therefore for a linear relationship, the calibration equation o f each cell (that produces each dynamic bending machine profile) is as follows: V=CE + C (13) A s was stated before, V is the average of the dynamic bending machine output and E is the average static M O E . C 0 is the output offset of the dynamic bending machine machine and is equal to the output voltage when there is no board inside. Therefore, the part of a profile that is not related to the board (for example, see the side parts o f the two profiles shown in Figure 2.12) is equal to this offset factor. Each measured profile is the output of one force-measuring cell, which measures the required force for bending the board along each o f its faces. For the two cells there wil l be four factors (C 0 1 and C 0 2 for offset factors and C n and C 1 2 for the scale factors), which are shown in the following equations: Cm = 0.0626 (14) C =0.0172 02 32 (15) C M and C 1 2 are calculated by comparing the measured profiles (from dynamic bending machine ) with the static M O E profiles of the selected samples and by using the following equations: Cu =(K-C0l)/Ei (16) Ca =(K-C02)/E2 (17) As shown in Figure 2.13 and Figure 2.16 the two profiles are almost the same therefore the scale factors are about the same (Cn = Cn = C) and are calculated as follows: C, = (El + Ey((Vx - CJ + (V2 - CJ) (18) The 10% of the beginning and the end o f the dynamic bending machine profile are removed in order to avoid the transient part o f the measured profile. The following calibration factors were calculated by using linear regression. Equation (19) is the calibration equation for profile #1 (the output o f cell #1 o f the dynamic bending machine) and Equation (20) is the calibration equation for profile #2 (the output of cell #2) o f the dynamic bending machine: P r o f i l e d : E= 1.1808 (V- 0.0626) (19) Profile #2: E= 1.1808 (V- 0.0172) (20) The final calibrated dynamic bending machine profiles of a few specimens are shown in Figure 2.16. In order to check the consistency o f the measured profiles, five boards were randomly selected and the dynamic bending machine profile of each were measured five times. Figure 2.17 and Figure 2.18 show that the superimposed profiles match well for both cells o f the machine. The measured M O E values are very close but the location of the profiles can be compromised in some cases because of the board slippage under the conveyor rollers of the dynamic bending machine. 33 , ig a LandMark and UBC MOE profiles tor specimen MS95 % IQ° LandMark and U B C MOE profiles for speclmen #0760 , 1 0 - LandMark and UBC MOE profiles for specimen MK21 ! I I i | r-i , A ! I *4 — 1 i i — t / I / I / T N _ 1 / i V > -— -.Z^pA-a ij i / ^ 1 I f \\ ' \" V I ' / ' / 1 1 1 l / / 1 t / / 1 1 III I i , i _ y \\ ~jf i ! a I 1 > C - M . 1 > 1 1 i i itftgiiofd profile Yellow ! 1 — hi \\ i \"I I | ! ! 1 . . I 1 ' -T -andWiark prof LandMark prof UBC Eldelco p UBC Metrlguar el Blue • 2- Red oftle Green 3 profile; Yellow I . . . 1.0 2 2.5 3 3.5 length (m) LandMark and U B C MOE profiles for specimen #0204 I I I I / V \\ f \\ t J i . I i LaMMr LandMi UBC E U B C M L 4 — I irk profile 1: Blu rk profile 2: Rec ielco profile G Itrkjuard praflla — L _ _ ; i V run — 1 I — ! _ _ 2.5 3 3.9 4 4 5 5 k*ngth(m) 0 0.S 1 1.5 2 2.5 3 3.5 4 4.5 5 length (m) , to5 LandMark and UBC MOE profiles br specimen #0098 , if/ LandMark and UBC MOE profles for specimen #0629 A i r | 1 1 1 1 \\ J . . _J 1 \\ V LandMark profile! BIO LandMafk praMa2' RtK 1 I 1 1 1 1 1 \\ JSC EUako preito: Q UBC IflWiguvb paella 1 1 1 ! 1 1 I 1 1 I I i I UJ O ! I I „ _jfcli ™. Ji_Ji~ _____ ! \\ / 1 \\ / 1 n 1 T v ^ f J 1 J 1 1 1 LancMl i 1 Itk prolldl Blue rk prolle2: Red 1 1 1 1 1 1 1 UBC El UBC M laleo profile G Btriguarti profile 1 Yellm i i 1 1 ~ ~ T 1 1 . \" T 1 | I 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 length (m) Figure 2.16 Measured M O E profiles by CLT™ and static bending methods. 34 x iff LandMark repeal led M O E profiles tor spec m e n #0 158. cell #1 X KJ 6 LendMartt repealed MOE proales tor specimen #0158. cell #2 , 1 f / Landmark r e p e a t H d M O E p r o l e s tor specimen#0182. cel l #1 j J'JJx f- second-pass, green third peas: yeJpw fcrffi oass: red 1 l l h pass: magi i t . £ ; . . . . L. . \\ —A— — A . . . . . I » .1 ™ T tecond1 pnf! green hlrd pass yellow M h . W * : M ' K h p * '\"••» « • 0 0.5 1 1.5 2 2A 3 3.5 4 4.5 5 length On) x to6 LandMark repeated MOE profiles tor specimen #0162. cell *2 'J 0.5 1 ' S 2 2.5 3 3.5 4 4.S length i m) / i \\ i j V\" . . . . . . . . MC0fKf|p>9S' gnMfl Mrd pass: yellow brth pe£t j • h t*dt m a g W a . . . . . •-0 0.5 1.5 2 2.5 3 3.5 4 4.5 5 k»ngtri(ra) LandMark repeat eed MOE proOJes tor specimen 40207. ceil an , -o LandMark repeated M O E preflea tor specimen 00207, cad 02 I Mi I ! / 1 \\ ! secondlpass: grain thrt fpass . yeabw M a 0 OS 1 1.5 2 2.5 3 3.5 4 4.5 5 lenglfi imi V v • • • * HI secondposs: green third p a n : yellow brth pass: red • | ] 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 length (m) Figure 2.17 The repeatability of the measured profiles for CLT™ machine. 35 Figure 2.18 The repeatability of the measured profiles for CLT™ machine (continued). 2.5. Ultimate Tensile Strength Tester This machine destructively tests the boards. The board is put under increasing tensile stress until it breaks apart. The tensile stress is recorded at every instant and is kept when the board is broken. The system consists of two grips; one moving and one fixed. A metal frame holds the grips and provides the fencing for security of the operator from wood particles that may fly around due to the release o f tensile stress when the board breaks. The moving grip is driven by a pneumatic system whose measured pressure is transformed to the applied tensile stress. 3 6 Chapter 3. Modeling wood failure I f a board is tested in tension, a three-dimensional stress distribution is generated inside the board. This stress distribution is not usually uniform due to the variation of wood properties inside the board. A crack usually is initiated in one part (or more) where the stress level is high. I f the applied tensile stress (to the board) is increased, the chance o f wood failure under stress is increased. Once the wood fails at a point o f the board, it generates a higher stress zone around it. Since the property of wood usually changes gradually, the excessive stress can also cause the failure at a neighboring point. This phenomenon can generate a chain o f failures that finally ends when the board breaks apart ([33]). In the following sections the factors influencing the strength o f wood are presented. Also, the measurable features o f wood that have important effects on strength are explained. A board is composed of clear wood and various defects, which interact when tensile stress is applied. For example, assuming that wood property is known in a neighborhood, by knowing the geometrical features o f the defects in the board and wood properties, the stress distribution may be estimated. Each of the features (defects and clear wood) and their effect on total strength are discussed in the related sections. The discussions o f each section are mostly limited to qualitative descriptions o f the related physical factors. A feature or a set o f features wil l represent each physical factor. Therefore, the qualitative discussion provides an insight into the problem and helps in defining the features. A n exact relationship between each physical phenomenon and the tensile strength is not needed (and in most cases it is not known). The collective relationship wil l be learned by the estimation (or learning) algorithm, which wil l be discussed in subsequent chapters. Two very important aspects of wood are the complexity of its structure (as a fibrous anisotropic material) and variation in its local features (due to various defects). Therefore, even i f the features of wood were accurately measured at every point o f the board and i f 37 the strength model was fully developed, the computation o f a board's tensile strength doesn't seem feasible for on-line use. Therefore, simplification seems an integral part o f this problem i f a practical strength estimator is desired. 3.1. T e n s i l e s trength o f c l e a r w o o d as a r a n d o m v a r i a b l e In strength-of-material testing in the early twentieth century it was observed that the tensile strength o f similar specimens are dispersed and cannot be modeled by a single value. The tensile strength o f matter, therefore, was modeled by a probability density function. Weibull weakest link theory ([34],[35]) is a theoretical explanation o f the probabilistic behavior of material strength. This theory was based on two major assumptions. The first assumption was that the cause of fracture is the flaw (microscopic cracks) in the material and that these flaws are independent and are randomly scattered in the volume o f the material. The second assumption was that the entire material holds up against the applied stress until one o f the flaws fails. This assumption is actually the weakest link theory, which is applicable to brittle material like glass or china. It was shown that this assumption is valid for wood i f the mode o f fracture is brittle. In non-brittle material the strength of a specimen is not equal to the strength of its weakest element and the failure of the specimen is a random process rather than a sudden event. When the fracture starts, stresses are redistributed and it doesn't necessarily lead to immediate collapse or failure. Also, neighboring points can affect the stress tolerance o f an element of the specimen. For the brittle case, the probability o f fracture at a point, S, is related to the stress level, a, over the volume of the material, V, by the following equation (Weibull distribution, [34],[35]): log(l -S) = -fn(o)dv (21) V where w(.) is a heuristic function and is defined as follows: 38 «(o) = ( ^ % (22) u where