The present invention generally relates to the use of single
and multiple sensor group systems to infer qualitative and/or quantitative estimates
of various properties of wood products, including dimensional stability.

Wood products, such as logs, boards, other lumber products,
or the like, can be graded or classified into qualitative groups by the amount of
warp potential, or dimensional stability, in the product. Crook, bow, twist, and
cup are examples of warp and are illustrated in FIGURE 1. The groups are used to
qualitatively represent the warp state at a specified ambient condition or the degree
of warp instability of a wood product. The qualitative groups are typically ordinal
in nature, though nominal categories may also be used.

Examples of qualitative estimates of warp might be, but
are not limited to, low crook, high crook, crook less than 0.5 inches but greater
than 0.25 inches, medium bow, bow greater than 1 inch, or like estimates. It might
be desirable to classify the warp distortion that a wood product will undergo after
it is remanufactured, its moisture redistributes, or it is placed in a new relative
humidity environment. Examples of these classifications might be, but are not limited
to, low crook at 20% RH, medium crook at 65% RH, high bow at 90% RH, crook greater
than .5 inches at 20% RH. Wood products can also be characterized in a quantitative
manner, such as, an amount of change a wood product will undergo (i.e., crook equal
to .25 inches). Several known methods for determining quantitative estimates are
described below.

The degree of warp depends on several known factors, such
as density, modulus of elasticity (hereinafter referred to as "MOE"), moisture content
variation, pith location, compression wood, grain angle and others. Many of these
factors can be quantitatively or qualitatively evaluated with different types of
sensors. For example, MOE can be estimated from the propagation of sound through
wood, and specific gravity can be estimated from the capacitance of wood. A different
type of sensor group or system may be utilized for detecting each of these properties.

During the three year period from 1995 to 1998, solid sawn
softwood lumber usage in wall framing, floor framing and roof framing dropped by
9.9%, 17.2% and 11 % respectively in the United States (Eastin et al., 2001)^{1}.
In this survey of nearly 300 builders, lumber straightness was rated the most important
factor affecting buying decisions; yet of all the quality attributes surveyed, dissatisfaction
with straightness was highest. It is generally recognized that softwood lumber will
continue to lose market share unless the industry improves the in-service warp stability
of its product.

^{1}
Eastin, I.L., Shook, S.R., Fleishman, S.J., Material substitution in the U.S.
residential construction industry, 1994 versus 1988, Forest Products Journal, Vol.
51, No. 9, 31-37
.

Some wood product applications are intolerant of significant
dimensional change (thickness, width, length) after the product is put in service.
For example, instability of thickness or width dimensions can cause interference
problems for tight-tolerance applications, such as doors and windows. Length instability
of wood used in truss chords can result in a problem known as truss uplift; where
the truss can raise above interior wall plates forming a gap between the ceiling
and interior wall.

In the United States, most softwood dimension lumber is
visually graded for a variety of attributes that affect its appearance and structural
properties. These attributes include knots, wane, dimension (thickness, width, and
length), decay, splits and checks, slope-of-grain, and straightness (warp). Strict
quality control practices overseen by third party grading agencies are in place
to ensure that all lumber is "on-grade" at the point the grade is assigned. Unfortunately,
the straightness and dimension of a piece are not static and can change after the
piece is graded. Additional warp and size change can develop after the piece is
in the distribution channel or after it is put into service. Typical moisture content
of fresh kiln dried lumber averages 15% but ranges from 6% to 19%. This lumber will
eventually equilibrate to a moisture ranging from 3% to 19% depending on time of
year, geography and whether the application is interior or exterior (Wood Handbook)^{2}.
This moisture change results in changes in both dimension and warp properties. Any
piece of lumber is prone to develop additional "in-service" warp if a) its shrinkage
properties are not uniform and it changes moisture or b) its moisture content is
not uniform at the point the original grade was assigned. Neither of these conditions
is detectable with traditional visual grading methods. Customers of wood products
seek stability in both dimension and warp properties.

^{2}
Wood Handbook, General Technical Report 113 (1999) Department of Agriculture,
Forest Service, Forest Products Laboratory
.

The wood handbook^{2} provides guidelines for assessing
the width and thickness stability of solid sawn lumber. Average thickness and width
shrinkage is governed by grain orientation as well as radial and tangential shrinkage
properties. These average radial and tangential shrinkage values vary by species
and are reduced if heartwood is present. Although these methods can be used to estimate
the average thickness and width shrinkage behaviour of a species, methods for precise
quantification do not exist. There are even fewer design tools for estimating length
shrinkage.

^{2}
Wood Handbook, General Technical Report 113 (1999) Department of Agriculture,
Forest Service, Forest Products Laboratory
.

A number of studies (e.g. Johansson, 2002^{3} and
Beard et al., 1993^{4} have attempted to define visual indicators that correlate
with warp stability. Candidate indicators have included features such as percent
juvenilewood, grain orientation, compressionwood, pith location, wane, knot properties
and growth rate. Although these studies demonstrate that spiral grain can be a useful
predictor of twist stability, they generally agree that there are no reliable visual
indicators of crook and bow stability.

^{3}
Johansson, M., and Kliger, R., Influence of material characteristics on warp
in Norway Spruce studs, Wood and Fiber Science, 34(2). 2002, pp 325-336, 2002 by
the Society of Wood Science and Technology

^{4}
Beard, J.S., Wagner, F.G., Taylor, F.W., Seale, R.D., The influence of growth
characteristics on warp in two structural grades of southern pine lumber, Forest
Products Journal, Vol. 43, No. 6, pp 51-56
.

Several theoretical models have also been developed to
help explain how moisture and various wood properties interact to cause distortion.
Nearly fifty years ago, a mathematical model was developed to explain lumber twist
as a function of spiral grain angle, distance from pith, and rate of tangential
shrinkage during moisture loss (Stevens et al., 1960^{5}). Other recent
work has sought to develop finite element models to predict crook and bow distortion
(Ormarsson et al., 1998^{6}) as a function of three-dimensional patterns
of density, growth rings, moisture, modulus of elasticity, etc. Another finite element
model is described in a series of
U.S. Patents (Nos. 6,308,571
;
6,305,224
; and
6,293,152) to Stanish et al.
All of these models teach that the fundamental cause of lumber warp is
related to the fact that it shrinks significantly when it dries and this shrinkage
is both anisotropic and highly non-uniform. Prediction of warp stability of a wood
product is made even more difficult by the fact that its moisture content changes
with the vapour pressure of the surrounding environment and this "equilibrium moisture"
can be highly variable between two locations within a piece depending on the chemistry
and fibre differences between those two locations.

^{5}
Stevens, W.C., and Johnston, D.D., Distortion caused by spiralled grain, Timber
Technology, June 1960, pp 217-218
.

^{6}
Ormarsson, S., Dahlblom, O., Petersson, H., A numerical study of the shape
stability of sawn timber subjected to moisture variation, Wood Science and Technology
32 (1988) 325-334, Springer-Verlag 1998
.

Today the patterns of equilibrium moisture and shrinkage
coefficients within a full size lumber product can be accurately measured only in
a laboratory environment. The laboratory technique involves cutting the piece of
lumber into small "coupons" and measuring the moisture content and shrinkage coefficients
using ASTM standards D-4492 and D-143, respectively. Although much is known about
equilibrium moisture and shrinkage behaviour of wood, there are as yet no comprehensive
theoretical models and no methods of monitoring these properties in a real time
production environment.

Much of the fundamental research to develop shrinkage models
for wood was done several decades ago. Shrinkage is known to be related to microfibril
angle (Meylan, 1968^{7}). This relationship is best where microfibril angle
is in the range of 30° to 40° and outside this range, the relationship
is rather poor. Wooten (Wooten, 1967^{8}) observed that longitudinal shrinkage
of high microfibril angle wood (>40 degrees) in seedlings seemed to correlate
with the thickness of the S_{1} layer - although no data was presented.
Cave (Cave, 1972^{9}) proposed a shrinkage theory which includes effects
of the S_{1} layer. More recently, Floyd (Floyd, 2005^{10}) demonstrated
that certain hemicellulose components, particularly galactan, interact with microfibrils
to affect longitudinal shrinkage rates. This combined work suggests that measurements
relating to microfibril angle and wood hemicellulose chemistry should be useful
in predicting shrinkage patterns in wood.

^{7}
Meylan, B.A., Cause of high longitudinal shrinkage in wood, Forest Products
Journal, Vol. 18, No. 4, April 1968, pp 75-78
.

^{8}
Wooten, T.E., Barefoot, A.C., and Nicholas, D.D., The longitudinal shrinkage
of compression wood, Holzforschung, Bd. 21 (1967), Heft 6, pp 168-171
.

^{9}
Cave, I.D., A theory of the shrinkage of wood. Wood Sci. Tech (1972), 6:284-292
.

^{10}
Floyd, S. "Effect of Hemicellulose on Longitudinal Shrinkage in Wood." In
The Hemicellulloses Workshop 2005: WQI Limited - New Knowledge in Wood Quality.
Conference held in The Wood Technology Research Centre. University of Canterbury,
New Zealand, 10-12 January 2005, edited by Kenneth M. Entwistle and John C. F. Walker,
115 - . Christchurch, New Zealand, 2005
.

Several researchers have recently reported some success
using these approaches to estimate shrinkage properties. The above referenced patents
issued to Stanish et al. teach a method of inferring shrinkage behaviour by interpreting
patterns of acoustic or ultrasound propagation velocity (related to microfibril
angle). Several recent patents and publications have begun to disclose methods of
estimating shrinkage coefficients which are more compatible with a high speed lumber
manufacturing process. For example, Nystom (Nystrom et al.^{11}) demonstrated
the relationship between longitudinal shrinkage and an optical property of wood
("tracheid-effect") that is also related to microfibril angle. The "tracheid effect"
is taught in
U.S. Patent No. 3,976,384
issued to Matthews et al. A large number of recent publications and patents
(e.g. Kelley et al.^{12}) teach a method^{11}
Nystrom, J.; Hagman, O.; Methods for detecting compression wood in green and
dry conditions., Proceedings of the SPIE - The International Society for Optical
Engineering (1999) vol.3826, p.287-94
.

^{12}
Kelley, S.; Rials, T.; Snell, R.; Groom, L.; Sluiter, A; Wood Science and
Technology (2004), 38(4), 257-276
of inferring shrinkage properties by using chemometric methods of near infrared
spectroscopy (NIRS). NIRS is of particular interest because the method is sensitive
to both physical attributes of the fibres (e.g. microfibrils) and chemical attributes
(e.g. hemicellulose).

Unfortunately, none of the individual methods described
above are accurate enough to give adequate estimates of the dimensional stability
of a single piece of lumber. Thus, a need exists for the use of single or multiple
sensor systems to provide a qualitative and/or quantitative estimate of the current
or future warp distortion of the wood product or of warp-related properties of the
wood product.

Embodiments of the present invention are described in detail
below with reference to the following drawings:

- FIGURE 1 provides examples of crook, bow, twist, and cup in a wood product;
- FIGURE 2 is a plot of misclassified boards in an embodiment of the present invention;
- FIGURE 3 is a plot of misclassified boards in an embodiment of the present invention;
- FIGURE 4 is a calibration plot for a differential shrinkage-coefficient model
in an embodiment of the present invention;
- FIGURE 5 is a plot of predicted change in crook against the measured change
in an embodiment of the present invention;
- FIGURE 6 is a chart of different initial moisture content profiles;
- FIGURE 7 is a chart of predicted crook changes for each profile in FIGURE 6;
- FIGURE 8 is a plot of moisture content profiles at different depths;
- FIGURE 9 is a plot of predicted moisture content for a wood product in an embodiment
of the present invention;
- FIGURE 10 is a plot comparing the second derivative values calculated using
a method of the present invention with the corresponding second derivative values
calculated from the crook profiles predicted by the finite-element model;
- FIGURE 11 is a plot of crook values calculated using a method of the present
invention compared to corresponding crook values predicted using a finite-element
model;
- FIGURE 12 is a plot comparing second derivative values calculated using a method
of the present invention with corresponding second derivative values calculated
from bow profiles predicted by a finite-element model;
- FIGURE 13 is a plot of bow values calculated using a method of the present invention
compared to corresponding crook values predicted using a finite-element model;
- FIGURE 14 is an example of a grayscale image from a line-light-source projected
onto a wood product;
- FIGURE 15 provides several examples of a bi-exponential model fit to tracheid-effect
line images;
- FIGURE 16 is a calibration plot for a differential shrinkage-coefficient model;
- FIGURE 17 is a calibration plot for absolute-crook at 20% RH;
- FIGURE 18 is a plot of a comparison between shrinkage-coefficient estimates;
- FIGURE 19 is a plot of spectra for wood products based on whether the wood products
contain pitch;
- FIGURE 20 is a plot of measured and predicted shrinkage values plotted against
fitted values; and
- FIGURE 21 is a plot of measured strain difference versus predicted strain difference.

The present invention generally relates to a variety of
methods for obtaining and validating improved estimates of shrinkage patterns, moisture
patterns and warp stability for a wood product. The term "wood product" may be interpreted
to mean a board, log, other type of lumber, or the like. The methods involve the
use of single and/or multiple sensor group systems to provide qualitative and/or
quantitative estimates. It has been discovered that estimates of dimensional stability
can be much improved when an assortment of measurements are used together, where
each measurement contributes information relating to one or more variables. The
measurements may be taken at one or more sections of the wood product, which may
differ in size given a particular embodiment. The properties observed at the one
or more sections may allow a qualitative and/or quantitative estimate of dimensional
stability of a region of interest. In a first embodiment, the region of interest
may be a coupon or other portion of the wood product. In another embodiment, the
region of interest may overlap with one or more sections of the wood product. In
another embodiment, the region of interest may be the entire wood product. In yet
another embodiment, the region of interest may be the same as the one or more sections
detected by the sensor group(s). In another embodiment, the region of interest does
not have an overlap with the one or more sections. The dimensional stability assessed
may be cup, crook, bow, twist, length stability, thickness stability, width stability,
or any combination of these. Provided below are various embodiments of the present
invention:

A. Methods of using multiple sensors (sensor fusion) to provide
qualitative and/or quantitative assessments via analysis of regions of interest
in a wood product where nonuniformity of composition (e.g. moisture), shrinkage
rate or grain angle may result in warp instability of the wood product
In an embodiment of the present invention, a classification
algorithm may be created to classify a wood product into one of a plurality of groups
or categories. The groups may be based on qualitative or quantitative characteristics.
For example, in an embodiment, the categories may be different grades. Warp classification
of wood products, such as boards may require inputs from one or more sensor groups
detecting properties of the boards. The sensor groups may be a part of those systems
previously mentioned for analyzing a wood product. The technologies for these systems
are known by those skilled in the art. For example, the sensor groups may obtain
moisture content measurement, electrical property measurement, structural property
measurement, acousto-ultrasonic property measurement, light scatter (tracheid-effect)
measurement, grain angle measurement, shape measurement, color measurement, spectral
measurement and/or defect maps. Structural property measurement may measure modulus
of elasticity, density, specific gravity, strength, or a combination of these. Acousto-ultrasonic
property measurement measures may measure velocity and/or damping. The spectral
measurement may be characterized by absorption or reflectance values over a wavelength
spectrum ranging from ultraviolet through near infrared.

Using this approach, the prediction model or algorithm
of the present invention may use inputs of many different resolution scales. Some
examples are board average MOE, moisture content measured across the width of the
board in one foot increments along the length of the board, spectroscopy data collected
every inch, or laser data collected every R inch.

The inputs are functions of the sensor signals and may
be either quantitative or qualitative. For example, an input could be the estimated
moisture content for each 12 inch lineal section of a piece of lumber, as estimated
by a moisture meter. Another example is an indicator for the presence or absence
of a knot in a 12 inch by 1 inch section of wood, based on a color image. Inputs
may be direct sensor measurements, pre-processed signals, combined signals from
several sensors or predicted measures from other sensors. Signal pre-processing
may include, but is not limited to, such steps as filtering, smoothing, derivative
calculations, power spectrum calculations, Fourier transforms, etc., as is well
known in the art. Predicted measurements from other sensors may include, but are
not limited to, shrinkage-coefficients predicted from sensors which measure the
light scattering and light absorption properties of wood and used as inputs to a
partial least squares, or "PLS", prediction model.

The prediction algorithm(s) or model(s) based on the set
of inputs can be derived using many techniques which include, but are not limited
to, regression trees, classification trees, linear discriminant analysis, quadratic
discriminant analysis, logistic regression, Partial Least Squares or other supervised
learning techniques such as neural networks. There are many forms of equations or
algorithms that could be used, and a general reference is Hastie, et al^{13}.

^{13}
Hastie, T., Tibshirani, R., and Friedman, J., (2001) The Elements of Statistical
Learning, Springer, New York
.

These algorithms can be developed to classify boards into
2 or more groups. For example, boards might be classified into four grades (#1 grade,
#2 grade, #3 grade, #4 grade) or into two classifications (warp and no warp), or
into three categories (crook less than 0.25 inches, crook between 0.25 and 0.5 inches,
crook greater than 0.5 inches). Typically, the parameters in the models or algorithms
are derived from a training-set of data and the performance is tested on a testing-set
of data before being used in production, although other approaches exist.

Various embodiments are contemplated involving the use
of sensor groups and algorithms. In a first embodiment, a single sensor group may
provide inputs to a classification algorithm which classifies wood products into
one of a plurality of groups or categories, such as grades, for example.

In a second embodiment, a single sensor group may provide
inputs to a classification algorithm as in the previous example. However, in this
embodiment, a second algorithm may be selected after classifying the wood product.
This second algorithm may be selected from a plurality of algorithms which are used
to assess the dimensional stability in a quantitative manner.

In a third embodiment, two or more sensor groups may provide
two or more inputs to a classification algorithm to classify wood products into
one of a plurality of categories.

In a fourth embodiment, two or more sensor groups may provide
two or more inputs to an algorithm for providing a quantitative assessment of dimensional
stability of wood products.

In a fifth embodiment, two or more sensor groups may provide
two or more inputs to a classification algorithm to classify wood products into
one of a plurality of categories. Next, a second algorithm may be selected after
classifying the wood product. This second algorithm may be selected from a plurality
of algorithms which are used to assess the dimensional stability in a quantitative
manner.

The following example illustrates how information from
multiple sensors was used to predict a warp classification for lumber.

__Example 1__
Three groups of lumber, each containing approximately 200
8-foot long 2 inch by 4 inch boards, were obtained from a mill. Via the use of multiple
sensors, each piece of lumber was measured for crook, bow, average moisture content,
ultrasonic velocity and a density profile was obtained. Each piece of wood was then
placed in a 20% relative humidity, or "RH" environment for 5 weeks and then measured
again for crook and bow. In this example, the objective was to classify the boards
into two final warp classes (at 20% RH) using the initial data from multiple sensors.
The final warp classes were defined as follows: a board was classified as a "rogue"
if the absolute crook at 20% RH was greater than 0.5 inches or the absolute bow
at 20% RH was greater than 1.0 inches. Otherwise the board was classified as a "non-rogue".

The initial data from lumber groups 1 and 3 were used to
develop and train the classification algorithm and the initial data from boards
in group 2 were used to test it. Five inputs were used to develop the classification
algorithm: initial absolute crook, initial absolute bow, ultrasonic velocity, initial
moisture content and a measure of the variability in board density. The boards from
groups 1 and 3 were assigned into the two groups, rogue and non-rogue, based on
their final absolute crook and final absolute bow. Using this definition, there
were 92 rogues and 309 non-rogues in the training set, groups 1 and 3.

Linear discriminant analysis was used to develop a discriminant
function to classify the boards. The table below shows the percentage of boards
that were correctly classified as rogue or non-rogue and those that were incorrectly
classified in the training set.
<u>Table 1</u>
True Group

Put into Group
Non-Rogue
Rogue

Non-Rogue
280
16

Rogue
29
76

Total
309
92

Eighty-three percent, or 76 out of 92 rogues, were correctly
classified as rogues. Ninety-one percent, or 280 out of 309 non-rogues, were correctly
classified as non-rogues. FIGURE 2 provides a plot of the misclassified boards.

The linear discriminant function developed on the training
set was then applied to the test set of boards, group 2. This group had 62 boards
assigned as rogues and 143 assigned as non-rogues. The results of the classification
using the discriminant function are shown in the table below.
<u>Table 2</u>
True Group

Put into Group
Non-Rogue
Rogue

Non-Rogue
135
12

Rogue
8
50

Total
143
62

In this case, 50 of the 62 rogues were correctly classified
with the initial data as rogues, which translates to 81% accuracy. Also, 135 non-rogues
were correctly classified using the initial data as non-rogues, which translates
to 94% accuracy. A graph of the misclassified boards is shown in FIGURE 3.

A special case of the methods described above may occur,
for example, when the classes that are predicted are existing industry grade classes
and an objective is to sort wood products into those grade classes. Another special
case occurs when existing grades are not used, but the wood product is to be sorted
into new classes developed based on a particular use of the wood product. An example
is classifying lumber into categories including those that will warp significantly
in dry climates versus those that will not.

Estimates of the cost of misclassification can be used
in the creation of the classification models or algorithms. For example, there may
be a higher cost associated with a rogue board being classified as a non-rogue,
than there is for a non-rogue being classified as a rogue. In these cases, the models
and/or algorithms can be developed using these costs in such a way as to minimize
the occurrence of the costlier mistake^{14}.

^{14}
Ripley, B.D. (1996) Pattern Recognition and Neural Networks, Cambridge: Cambridge
University Press
.

Shrinkage Rate Coefficient as an Indicator of Dimensional Stability
Wood is a hygroscopic material that undergoes dimensional
changes when it experiences a change in moisture content. This phenomenon occurs
on a local (fiber) scale. The dimensional change that occurs with changes in moisture
content is due to drying or swelling forces in the wood. Dimensional changes in
wood occur whenever there is a change in the distribution of internal (or external)
stresses. The degree of moisture-induced-shrinkage (and consequently, shrinkage-related
stress) depends on several known factors, such as galactan content, micro-fibril
angle, specific gravity, MOE, and others. Many of these factors can be quantitatively
or qualitatively evaluated with different types of sensors. For example, MOE can
be estimated from the propagation of sound through wood, and specific gravity can
be estimated from the capacitance of wood. The combined use of multiple sensors
can then be used to estimate the moisture-induced shrinkage patterns in wood. The
spatial resolution of the patterns depends on the spatial resolution of the measurements.

The extent of moisture-induced dimensional change for a
given piece of wood depends on physical and chemical properties of the wood, as
well as both the magnitude of the moisture change and the values of the initial
and final moisture contents. The shrinkage behavior of wood is commonly expressed
as a shrinkage-coefficient (alternatively called LSRC=Longitudinal Shrinkage Rate
Coefficient); this is defined as
$$\mathit{LSRC}\mathit{=}\frac{\mathit{\&Dgr;}\begin{array}{}\end{array}\mathit{l}\mathit{/}\mathit{l}}{\mathit{\&Dgr;}\begin{array}{}\end{array}\mathit{MC}}$$

where *l* is the length of the wood segment, MC is the moisture content of
the wood, and the Greek letter &Dgr; is the familiar mathematical difference operator.
This shrinkage-coefficient is a function of the moisture content.

Estimation of shrinkage-coefficient patterns from multiple
sensors may be achieved via a shrinkage-coefficient prediction equation and/or algorithm,
as well as inputs from the sensors to the equation or algorithm. More than one shrinkage-coefficient
prediction equation and/or algorithm may be utilized for each section of a wood
product. The estimation of shrinkage patterns in a piece of wood can be determined
from the appropriate shrinkage-coefficients and starting and ending moisture states.

The inputs to a shrinkage model are functions of the sensor
signals and may be either quantitative or qualitative. For example, an input could
be the estimated moisture content for each 12 inch lineal section of a piece of
lumber, as estimated by a moisture meter. Another example is an indicator for the
presence or absence of a knot in a 12 inch by 1 inch section of wood, based on an
RGB image. Inputs to the models may be direct sensor measurements, pre-processed
signals, or combined signals from several sensors. Signal pre-processing may include,
but is not limited to, such steps as filtering, smoothing, derivative calculations,
power spectrum calculations, Fourier transforms, etc., as is well known in the art.

The shrinkage-coefficient prediction equation(s) and/or
algorithm(s) are used to map the set of inputs to a real-valued number. There are
many forms of equations or algorithms that could be used, and a general reference
is Hastie, et al^{15}. A common example is a linear model of the form
${\mathit{y}}_{\mathit{i}}\mathit{=}{\mathit{\&bgr;}}_{\mathrm{0}}\mathit{+}{\displaystyle \mathit{\sum}_{\mathit{i}}}{\mathit{\&bgr;}}_{\mathit{ij}}{\mathit{x}}_{\mathit{ij}},$
where y_{j} is the response variable (e.g., LSRC) and the set of inputs
x_{ij} may be the inputs described above, or basis expansions of those inputs.
Typically, the coefficients for such a model will not be known a-priori, and may
be determined from a training-set of data. Other examples of supervised learning
procedures include regression trees, additive models, neural networks, penalty methods,
and boosting methods.

^{15}
Hastie, T., Tibshirani, R., and Friedman, J., (2001) The Elements of Statistical
Learning, Springer, New York
.

The spatial resolution of the inputs will determine the
spatial resolution of the shrinkage estimates. If the resolution of the shrinkage
estimates is high enough, it is possible to estimate shrinkage patterns throughout
a piece of wood such as a board. In an embodiment, resolution required for a 2x4
piece of lumber may be 12 inches (long) x x inch (wide) x x inch (thick),
although any practical level of resolution is possible. The section of board over
which a prediction is made is a coupon. The pattern of coupon shrinkage estimates
can be used to represent the shrinkage patterns in a wood product.

Two general types of shrinkage estimates may be used: 'absolute'
shrinkage estimates which predict, for example, a shrinkage value for each coupon-level
piece of a board; and 'differential' shrinkage estimates which predict a shrinkage
difference between a coupon and a reference coupon.

Localized moisture content changes in wood may occur, for
example, when there is a change in the ambient RH conditions, or when moisture-content
non-uniformities in the wood are allowed to equilibrate. The estimated shrinkage
patterns - either absolute or differential - can then be used to estimate the moisture-induced
dimensional changes in the wood product. This could be accomplished, for example,
by using the patterns of shrinkage estimates as inputs to a finite element model,
although other options exist.

The following example illustrates how information from
multiple sensors was used to estimate the dimensional change in wood due to a change
in ambient relative humidity.

__Example 2__
The sensor data used were "Tracheid-effect" line images
and absorbance spectra obtained from near infrared (NIR) spectroscopy. (Additional
information describing these two sensor technologies can be found in (Nystrom and
Hagman)^{16} and (Williams and Norris)^{17} respectively). A training
data set consisting of approximately 350 12"x1"x3/4" pieces of wood was used to
build a shrinkage-coefficient calibration model. Each piece of wood was scanned
for both Tracheid-effect images and NIR spectra. Several parameters were calculated
from each Tracheid-effect image. In addition, each piece of wood was equilibrated
at two different times in two different relative humidity environments - 20% RH
and 90% RH. Length measurements were made at each humidity condition and the moisture-induced
dimensional change was recorded.

^{16}
Nystrom, J.; Hagman, O.; Methods for detecting compression wood in green and
dry conditions., Proceedings of the SPIE - The International Society for Optical
Engineering (1999) vol.3826, p.287-94
.

^{17}
Williams, P., Norris, K. (editor), (2001) Near-Infrared Technology in the
Agricultural and Food Industries, Second Edition, American Association of Cereal
Chemists , St. Paul, Minn.), 312 pp
.

A prediction model for dimensional change was developed
based on first-principle considerations using Tracheid-effect parameters and NIR
spectra as inputs. The prediction equation used is *LSRC = &bgr;*
_{0} *+ &bgr;*
_{1} · *D +* &bgr;_{2} · *R + &bgr;*
_{3} · *R · D ,* where LSRC is the moisture-induced length-wise
dimensional change of each piece of wood, the &bgr;'s are regression coefficients
estimated from the training dataset, D is the 'exponential decay' (rate of decay
of the intensity as a function of distance from the projected light-source) of the
tracheid-effect line intensity, and R is the ratio of two NIR absorbance values,
A1700/A1650. The calibration plot for a differential shrinkage-coefficient model
is shown in FIGURE 4.

Following the calibration of the shrinkage-coefficient
model, 23 8-foot 2"x4" boards were scanned for both tracheid-effect images and NIR
spectra. These pieces of wood had already been cycled through two relative humidity
environments, and the change in crook and bow were recorded on each piece. The parameters
calculated from the tracheid-effect and NIR data were used as inputs to the differential
shrinkage-coefficient model to produce a map of differential shrinkage-coefficient
values for each piece of lumber. A shrinkage map was calculated from the shrinkage-coefficient
estimates and the target moisture contents. The shrinkage map was then input to
a finite element model (DIMENS) to predict the change in warp-profile of each piece
of lumber. The predicted change in crook is plotted against the measured change
in FIGURE 5.

The previous example illustrates the prediction of moisture-induced
crook-change from estimated shrinkage maps using a finite element model. Similar
methods can be used for cup and bow. Analogous methods can be used to predict moisture-induced
twist from estimated grain-angle, pith location and possibly other variables.

Residual stress arises only in the presence of shrinkage
differences, noting that uniform shrinkage is an indication of no residual stress
present in a sample. Thus, it is proposed that there should be a strong relationship
between residual longitudinal stress and longitudinal shrinkage differences, rather
than between residual longitudinal stress and longitudinal shrinkage itself. This
requires a scan for residual stress when the nearby shrinkage is different, not
just when the local shrinkage is relatively high.

During the manufacture of lumber, it is sometimes desired
to rip a piece in order to generate 2 or more narrow pieces whose combined value
is greater than the wider parent. If there are residual stresses in the parent board,
those stresses might be relieved during this ripping operation causing the ripped
pieces to spring outward and undergo added undesirable warp distortion. Thus, there
is a need to understand whether or not this potential exists in a parent piece of
lumber before a rip decision is made. Estimates of longitudinal shrinkage patterns
can be used for this purpose as illustrated by the following example.

__Example 3__
Eighteen 2x4 cross sections were equilibrated to 20% RH
and ripped into four equal coupons. The instantaneous strain of each coupon was
determined from the difference in length before and after ripping. A longitudinal
shrinkage rate coefficient (LSRC) was also determined for each coupon. Two pairs
of coupons on either side of centerline were reviewed. Data from these pairs was
analyzed to determine whether predicted LSRC differences (based on methods described
earlier) could be used to identify pairs having high instantaneous strain difference
(i.e. sections likely to distort during a ripping operation.)

Results are shown in FIGURE 21. The test demonstrated that
LSRC estimates can indeed be used to identify pieces of lumber that likely contain
significant internal stresses and are, therefore, not candidates for a ripping operation.

The method can be applied to a board that has residual
moisture gradients resulting from kiln-drying and that will subsequently change
shape as the internal moisture equilibrates both within the piece (moisture leveling)
and to its external environment. If the subsequent shape change is large enough,
such a board may no longer meet the warp limits for its designated grade.

Shape change may be predicted according to the above method
using the predicted shrinkage-coefficients for each coupon within the board, together
with the anticipated moisture content change of each coupon. If the final state
is one of uniform, equilibrated moisture content, then the moisture content changes
of the coupons will not all be the same if there initially are moisture gradients
within the board. In the method, the moisture content change for each coupon may
be determined from the initial moisture content distribution and the final target
moisture content. The moisture content change is then multiplied by the corresponding
longitudinal shrinkage rate coefficient determined for the coupon. The resulting
coupon shrinkage values are processed using, for example, a finite-element and/or
an algebraic warp prediction model to determine the anticipated warp changes due
to leveling and equilibration of the initial moisture gradients. The predicted warp
changes are finally added to the initial warp values of the board to determine whether
or not the final shape of the piece will exceed any of the warp limits for its designated
grade.

An example of the above-described method is provided below:

__Example 4__
The anticipated crook changes of three 8-ft. 2 inch x 4
inch boards (B4-179, D4-175, and B4-59) were determined for several different hypothetical
moisture content leveling and equilibration scenarios. Three different initial moisture
content profiles, as previously measured in kiln-dried lumber, were used and the
final equilibrium moisture content was assumed to be 12%. The longitudinal shrinkage
rate coefficients of the coupons within the three boards were determined using the
above-described methods. FIGURE 6 illustrates different initial moisture content
profiles and FIGURE 7 illustrates predicted crook changes for each profile. The
predicted crook change for each board is added to its actual crook at its initial
moisture content condition in order to determine whether or not the crook at the
final moisture content condition would exceed the crook limit for the designated
grade of the board.

B. Methods of combining measurements of surface moisture patterns
with a measurement of bulk (average) moisture to estimate moisture gradients and
patterns within a wood product
At the end of kiln drying, the moisture content in each
piece of lumber is typically distributed in a non-uniform manner, with relatively
higher moisture contents near the core of the piece and lower moistures at and near
the surfaces. This activity is illustrated in FIGURE 8. Such patterns may not be
symmetric in cross-section, with edge-to-edge and face-to-face differentials. The
patterns may vary along the length of the board, typically with relatively lower
moisture contents near each end. Prior testing has shown that such moisture patterns
persist in the lumber for weeks after drying, and thus will often remain at the
time of planing.

Because of such moisture variability, board warp profile
predictions of the kind described above may require an estimate of the moisture
content of each shrinkage coupon. These estimated moisture content values may be
used together with the specified final target moisture content to determine the
moisture content changes for which the warp change of the board must be predicted.

At any location along the length of a board, the surface
moisture content profile and the corresponding average moisture content may be combined
to obtain an estimate of the moisture content for each shrinkage coupon in that
length section. An estimated moisture content is determined for each shrinkage coupon
position using a linear model that employs the average moisture content of the corresponding
board section (for example, from an NMI meter) and the surface moisture content
for that coupon position (for example, from an electrical-resistance pin-type moisture
meter). The moisture content estimate model is of the general form:
$${\mathrm{MC}}_{\mathrm{ij}}\mathrm{=}\mathrm{k}{\mathrm{0}}_{\mathrm{i}}\mathrm{+}\mathrm{k}{\mathrm{1}}_{\mathrm{i}}\mathrm{*}{\mathrm{A}}_{\mathrm{j}}\mathrm{+}\mathrm{k}{\mathrm{2}}_{\mathrm{i}}\mathrm{*}{\mathrm{S}}_{\mathrm{ij}}$$
where

MC_{ij} is the estimated moisture content of the "i"th shrinkage coupon
in the "j"th board section (generally there would be 8 coupons per section)

k values are constants but may have different values for each shrinkage coupon position
"i"

A_{j} is the average moisture content of the "j "th section

S_{ij} is the surface moisture content of the "i"th shrinkage coupon in
the "j "th board section.

In general, there would be a different set of k values
associated with each board width.

Figure 9 illustrates results from a test of the claimed
method. In that test, it was shown that when combining both the average moisture
content and the surface moisture content pattern, the error of the prediction of
coupon (element) moisture content was reduced from 1.7% to 1.3% mc (RMSE), as compared
to predictions based on the average moisture content alone.

Near Infrared (NIR) absorbance spectroscopy techniques
can be used to measure the moisture content of materials. There are many examples
known to those skilled in the art demonstrating the basic method for many biological
materials, including wood. In most examples, the material is ground and thus relatively
homogeneous with the surface and interior having similar moisture contents.

In wood this may not be the case. Water has several absorption
bands in the NIR region. Due to the strength of these absorption bands and the optical
density of wood, the NIR reflectance spectrum at the water absorption bands is a
measure of the surface moisture (within a few millimeters of the surface). If full
NIR spectrum methods are used, a single NIR reflectance spectrum can be used in
both surface moisture and shrinkage prediction models. If discrete wavebands, or
ratios of discrete wavebands, are used, then it is likely that the NIR wavebands
selected for surface moisture prediction models will be different from those used
to model shrinkage.

The most common NIR models for moisture are multiple linear
regression models of second derivative spectra at a few (typically three or less)
wavebands. However, full spectrum models, or models using ratios of absorbance values
or ratios of derivative values can also be used. Using these methods, NIR spectral
data are analyzed to determine and assign a surface moisture content for each shrinkage
coupon.

The amount of light absorbed by water varies from water
absorbance band to band. In general, the longer the wavelength the more light that
is absorbed for the same water content. Thus, by selecting the wavelength for water
measurement, one can control to some degree the depth of penetration of the light
into the material. Thus, there would be more penetration into the wood at the 960
nm water band than at the 1910 nm water band. If one was interested in the surface
moisture content, then longer wavebands like 1910 nm should give a measure closer
to the surface, while 960 nm should give an average moisture content to a greater
depth. Such measurements may be taken by, for example, devices or systems such as
a Kett High Moisture NIR meter (model number KJT100H) manufactured by Kett Corporation.

A number of the bulk properties of wood are affected by
its moisture content. For example, below the fiber saturation point, both the modulus
of elasticity (MOE) and the electrical resistance increase with decreasing moisture
content. Such relationships form the basis for a variety of moisture measurement
methods including, for example, dielectric, electrical resistance, and nuclear magnetic
resonance. These methods are employed in various commercial lumber moisture measurement
systems, such as those made by Wagner and NMI (dielectric), and by Delmhorst (electrical
resistance). In both the Wagner and NMI planer moisture meters, the lumber passes
over a capacitance-measuring plate and the average, or bulk, moisture content of
the wood in the measurement zone is determined by its dielectric properties. Such
state-of-the-art planer moisture meters are not yet able to resolve the cross-sectional
variability in moisture content with a resolution on the order of the shrinkage
coupon dimensions. They provide a cross-sectional average moisture content that
is characteristic of a short length section of the board. That average moisture
content can be used with an NIR-based estimate of moisture content variation over
the surface of the board to estimate the moisture gradients and patterns within
the board, following the above-described method.

C. Methods of estimating the dimensional stability of a wood
product from simple algebraic differences in moisture, shrinkage rates and grain
angles observed on outer surfaces.
Finite-element modeling of lumber warp behavior has shown
that crook and bow stability are governed almost entirely by the pattern of variation
in the lengthwise shrinkage within the piece. Specifically, differentials in lengthwise
shrinkage across the width largely determine crook, while differentials across the
thickness are responsible for bow. Furthermore, it has been discovered that the
quantitative relationship between crook or bow stability and lengthwise shrinkage
can be established using relatively simple mathematical operations, rather than
more sophisticated and complicated finite-element modeling methods. In particular,
the curvature of any board length-segment or section, expressed as the second derivative
of the crook or bow profile, can be determined from a linear combination of the
shrinkage values of the coupons comprising that segment or section. The overall
crook or bow profile of the board can be determined from a section-by-section double-integration
of those second derivative values.

To determine crook, each board segment must be divided
into at least 2 shrinkage coupons across the width. In general, better results may
be obtained when each board segment is divided into at least 4 coupons across the
width. If a board segment is divided into four shrinkage coupons, having shrinkage
values T1, T2, T3, and T4, then the crook resulting from that shrinkage will exhibit
a curvature over that segment (expressed as the second derivative of the board's
edge profile) that can be determined by a linear combination of the general form:
$$\mathrm{C\u02ba}\mathrm{=}\mathrm{k}\mathrm{1}\left(\mathrm{T},,\mathrm{1},\mathrm{-},\mathrm{T},,\mathrm{4}\right)\mathrm{+}\mathrm{k}\mathrm{2}\left(\mathrm{T},,\mathrm{2},\mathrm{-},\mathrm{T},,\mathrm{3}\right)\mathrm{+}\mathrm{k}\mathrm{3}$$

where

C" is the second derivative of the crook profile along the edge of the board

k values are constants but may have different values for each board width

T values are coupon shrinkage values that are determined by the product of the corresponding
longitudinal shrinkage rate coefficient (LSRC) and moisture content change (MC):
$$\mathrm{Ti}=\mathrm{LSRCi}\times \mathrm{MCi}$$

This method was tested in the following example:

__Example 5__
Finite-element model predictions were made for crook in
138 different examples of 8-ft. 2x4 boards. Each of these example boards was divided
into 6 length segments and each length segment was divided into 8 shrinkage coupons,
using a 4x2 configuration, namely, with four coupons across the width by two coupons
through the thickness. The shrinkage values for each pair of coupons at each width
location were averaged to give four shrinkage values across the width, per the above
equation. The second derivative of the predicted crook profile was calculated for
each board segment, and a least-squares regression was used to determine the coefficients
(k) in the equation above. FIGURE 10 illustrates a plot comparing the second derivative
values calculated using that equation (C") with the corresponding second derivative
values calculated from the crook profiles predicted by the finite-element model,
and shows excellent agreement.

To predict the crook of a board, the second derivative
values calculated using the above equation (C") are integrated twice to yield the
actual edge profile of each board segment. This method was tested using coupon longitudinal
shrinkage rate coefficients determined for 23 8-ft. 2x4 boards. First, the second
derivative values for each length segment were calculated using the above equation,
then those derivative values were integrated twice to determine the crook profile
of each of the 23 boards. The resulting crook values are compared to the corresponding
crook values predicted using the finite-element model, and show excellent agreement
in FIGURE 11.

To determine bow, each board segment must be divided into
at least 2 shrinkage coupons through the thickness. If a board segment is divided
into two shrinkage coupons, having shrinkage values T1 and T2, then the bow resulting
from that shrinkage will exhibit a curvature over that segment (expressed as the
second derivative of the board's face profile) that can be determined by a linear
combination of the general form:
$$\mathrm{B\u02ba}\mathrm{=}\mathrm{k}\mathrm{1}\left(\mathrm{T},,\mathrm{1},\mathrm{-},\mathrm{T},,\mathrm{2}\right)\mathrm{+}\mathrm{k}\mathrm{2}$$

where

B" is the second derivative of the bow profile along the face of the board

k values are constants but may have different values for each board width

T values are coupon shrinkage values that are determined by the product of the corresponding
longitudinal shrinkage rate coefficient (LSRC) and moisture content change (MC):
$$\mathrm{Ti}=\mathrm{LSRCi}\times \mathrm{MCi}$$

This method was tested in the following example:

__Example 6__
Finite-element model predictions were made for bow in 138
different examples of 8-ft. 2x4 boards. Each of these example boards was divided
into 6 length segments and each length segment was divided into 8 shrinkage coupons,
using a 4x2 configuration, namely, with 4 coupons across the width by two coupons
through the thickness. The shrinkage values for each set of 4 coupons at each face
were averaged to give two shrinkage values through the thickness, per the above
equation. The second derivative of the predicted bow profile was calculated for
each board segment, and a least-squares regression was used to determine the coefficients
(k) in the equation above. The plot in FIGURE 12 compares the second derivative
values calculated using that equation (B") with the corresponding second derivative
values calculated from the bow profiles predicted by the finite-element model, and
shows excellent agreement.

To predict the bow of a board, the second derivative values
calculated using the above equation (B") are integrated twice to yield the actual
face profile of each board segment. This method was tested using coupon longitudinal
shrinkage rate coefficients determined for 23 8-ft. 2x4 boards. First, the second
derivative values for each length segment were calculated using the above equation.
Then, those derivative values were integrated twice to determine the bow profile
of each of the 23 boards. The resulting bow values are compared to the corresponding
bow values predicted using the finite-element model, showing excellent agreement
in FIGURE 13.

D. Methods of estimating the shrinkage and grain angle properties
of wood by interpreting the intensity pattern that is diffusely reflected from a
surface illuminated by a light source (laser or non-laser).
The tracheid-effect in wood is known (see, for example
Nystrom, 2003). When a wood surface is illuminated by a point or line light source,
the patterns of diffuse reflectance are influenced by the physical and chemical
properties of the wood. Metrics or parameters calculated from these patterns may
be used to estimate physical properties of the wood, such as, for example, shrinkage
and grain-angle properties.

Many types of parameters may be calculated from the diffuse
reflectance patterns. When the diffuse-reflectance is focused to an area array camera,
the grayscale pattern of the resulting image may be analyzed with standard or non-standard
image analysis techniques, as is well known in the art. An example of a grayscale
image from a line-light-source is shown in FIGURE 14. Examples of some standard
image analysis metrics include size of area formed between two grayscale thresholds,
and convex hull area of an image.

Statistical and mathematical parameters may also be calculated
from patterns of diffuse reflectance. For example, the rate of decay of the intensity
as a function of distance from the projected light-source may relate to the dimensional
stability of wood. There are many different models for estimating the rate of decay.
A common model is log(intensity) = A + kx, where x is the distance from the projected
light source, and A and k are model parameters. Examples of other models are described
in Bates and Watts, 1988. It has been empirically noted that the rate of decay of
diffusely reflected light intensity may be represented by a combination of exponential-decay
processes. The bi-exponential process can be represented by the equation:
*E*(*y*_{i}
)*=&phgr;*
_{1} exp(-&phgr;_{2}
*x*_{i}
) + &phgr;_{3} exp(-&phgr;_{4}
*x*_{i}
), &phgr;_{2} > &phgr;_{4} > 0. The estimated parameters
from the exponential decay processes may reflect different wood properties and could
each be used as inputs to a shrinkage model. FIGURE 15 shows several examples of
the bi-exponential model fit to tracheid-effect line images.

Parameters, such as those related to the rate of decay
of light intensity, may be estimated on either 'side' of the light image or by combining
information from each side. Empirical evidence also suggests that a comparison of
decay rates on the 'left' and 'right' side of a light source may provide useful
predictive information.

When the light source is a spot, other parameters may be
computed from the diffuse reflectance patterns. A spot light source typically makes
an ellipse pattern on the surface of wood. Parameters such as the ellipse ratio,
ellipse orientation, and ellipse angle may be calculated, as discussed in (Zhou
and Shen, 2002). The surface grain angle may be estimated from the ellipse angle.

The physical properties of wood that influence the tracheid-effect
may be local in nature. The spatial resolution of estimates based on the calculated
parameters will then depend on the frequency of sampling the light intensity patterns.
The various attributes computed from the intensity patterns can be used as inputs
to a shrinkage prediction equation or algorithm. Such an equation maps the set of
inputs to a real-valued number. There are many forms of equations or algorithms
that could be used, and a general reference is Hastie, et al. The following example
illustrates how information from a laser line image was used to estimate longitudinal
shrinkage rate coefficients of wood:

__Example 7__
A training dataset consisting of approximately 350 12"x
1"x 3/4" pieces of wood was used to build a shrinkage-coefficient calibration model.
Each piece of wood was scanned with a Tracheid-effect line image and a side-spot
image. Several parameters were calculated from each Tracheid-effect image. In addition,
each piece of wood was equilibrated at two different times in two different relative
humidity environments - 20% RH and 90% RH. Length measurements were made at each
humidity level and the moisture-induced length change was recorded.

A prediction model for dimensional change was developed
using tracheid-effect parameters as inputs. The prediction equation was constructed
using multivariate-adaptive-polynomial-spline-regression. Five main terms were included
in the model: 'Right' decay parameter, mean Ellipse ratio, convex-hull-area-height,
mean-angle, and the within-piece standard deviation of the ratio of the 'right'
and 'left' decay parameters. In addition, 3 spline-knots and the interaction between
'right' decay and mean-angle were included in the model. The calibration plot for
a differential shrinkage-coefficient model is shown in FIGURE 16.

The previous example illustrated the prediction of wood
shrinkage-coefficients from parameters calculated from both line-intensity and spot-intensity
images. Analogous methods can be used to predict grain-angle from both line and
spot images.

E. Methods of using multiple sensors (sensor fusion) to infer
crook and bow directly
Crook and bow result from dimensional instability in a
piece of wood. Many factors are known to be associated with the dimensional stability
of wood. For example, wood with high MOE is generally dimensionally stable, while
wood with large amounts of compression-wood is typically unstable and prone to crook
or bow. Moisture-induced dimensional instability is a result .of moisture-induced
shrinkage patterns in a wood product, such as a piece of lumber. One approach to
estimating dimensional change, discussed above and illustrated in Example 2, first
estimates the shrinkage-coefficient patterns in a piece of wood, then uses these
shrinkage-coefficient patterns to predict crook or bow resulting from a change in
moisture content using, for example, a finite element model. This can be thought
of as a two-step approach to warp prediction wherein a first step is to predict
shrinkage, and a following step is to predict warp.

Another approach is to directly predict the crook or bow
of a piece of wood using data from multiple sensors and a single prediction model
or algorithm. Using this approach, the prediction model or algorithm may use inputs
of many different resolution scales. The model inputs are functions of the sensor
signals and may be either quantitative or qualitative. For example, an input could
be the estimated average moisture content for the entire piece of wood, as estimated
by a moisture meter. Another example is an indicator for the presence or absence
of a knot in a 12" by 1" section of wood, based on an RGB image. Inputs to the models
may be direct sensor measurements, pre-processed signals, or combined signals from
several sensors. Signal pre-processing may include, but is not limited to, such
steps as filtering, smoothing, derivative calculations, power spectrum calculations,
Fourier transforms, etc., as is well known in the art.

The crook or bow prediction equation(s) and/or algorithm(s)
are used to map the set of inputs to a real-valued number. There are many forms
of equations or algorithms that could be used, and a general reference is Hastie,
et al. Typically, the model or algorithm parameters will not be known a-priori,
and must be determined from a *training-set* of data. The following example
illustrates how information from multiple sensors was used to directly estimate
the dimensional change in wood due to a change in ambient relative humidity.

__Example 8__
Three units of lumber, each containing approximately 200
8-foot 2x4 boards were obtained from a mill. Each piece of lumber was measured at
the mill for crook, bow, average moisture content, acoustic velocity and specific
gravity. Each piece of wood was then placed in a 20% RH environment for 5 weeks
and then measured again for crook and bow. In this example, the objective was to
estimate the final crook or bow (at 20% RH) using the initial data from multiple
sensor groups. Three inputs were used to develop an absolute-crook prediction model:
initial absolute crook, acoustic velocity, and initial moisture content. A simple
linear regression model with these inputs was trained on two units of lumber. The
calibration plot for absolute-crook at 20% RH is shown in FIGURE 17.

F. Methods of rapidly simulating "in-service" warp distortion
of a wood product and/or rapidly estimating shrinkage properties of a wood product
by using electromagnetic energy to dry and redistribute absorbed water.
Hygroscopic materials, such as wood, absorb or release
an amount of moisture needed to reach equilibrium with the surrounding environment.
Consequently, most wooden materials will undergo significant moisture change between
the time they are manufactured and when they reach final equilibrium after put into
service. Typical interior equilibrium moisture levels in the United States vary
by geography and season with average values ranging from 6% in the desert Southwest
to 11% along the Gulf Coast. (__Wood__ Handbook^{2}). Once wood is placed
in a new environment it takes approximately 6 weeks to reach a new equilibrium moisture
condition. Until that equilibrium state is reached, moisture gradients exist from
the inside to the outside of a piece of wood.

An objective of the present invention is to predict how
straight an individual piece of lumber will be after it reaches a final equilibrium
state, i.e., where no moisture gradients exist. This prediction relies on estimating
lengthwise shrinkage patterns within the piece of lumber and then interpreting how
those shrinkage patterns interact to cause warp. In order for this technology to
be applied, quality control procedures may be required to ensure that the "in service"
warp prediction is accurate. Such procedures must be capable of providing rapid
feedback on the accuracy of estimates of both shrinkage-coefficients and resulting
distortion. The long time required for a wooden piece to reach moisture equilibrium
presents a problem to the development of operationally feasible quality control
methods. To resolve this problem, it is proposed to utilize electromagnetic energy
to accelerate the rate at which a wood product reaches a new equilibrium moisture.

Electromagnetic energy is efficiently absorbed by polar
molecules such as water. When wood is placed in a microwave or radio frequency field,
the energy is preferentially absorbed by regions having higher moisture. As a result,
water in these high absorbing regions rapidly migrates to lower moisture regions,
thereby leveling the moisture gradients. This process can, therefore, be used on
wood to quickly achieve a new moisture state that emulates in-service equilibrium
in which moisture gradients are minimized.

This method can be used to validate both shrinkage-coefficient
predictions and warp of full size pieces. The method can be used to emulate shrinkage
or in-service distortion resulting from moisture leveling or moisture loss. To emulate
distortion resulting from moisture leveling, the piece must be wrapped in a moisture
barrier before it is placed in an electromagnetic field. Electromagnetic energy
in the frequency range of, for example, 13.6MHz (RF) to 2.45GHz (microwave) can
be used in this method. This full range can be used to accelerate the process of
determining shrinkage-coefficients of small samples (less than 50 cubic inches);
whereas the RF portion of the spectrum is preferred for inducing warp in full size
lumber samples. In an embodiment, the wood product is dried to a moisture content
which is less than 20%.

In an embodiment, a method is provided for confirming a
warp distortion prediction (i.e., quality control) for a wood product. The method
comprises the steps of:

- obtaining an initial moisture pattern for the wood product; predicting warp
distortion of the wood product based on the initial moisture pattern; placing the
wood product in an environment wherein the wood product is subject to electromagnetic
energy; applying sufficient electromagnetic energy to the wood product to change
its moisture content to a second level wherein the moisture content has a second
value equivalent to an expected long term in-service equilibrium value; measuring
warp distortion of the wood product at the second moisture level; and comparing
the predicted warp distortion to the warp distortion at the second moisture level.

The following example describes an experiment conducted
to compare longitudinal shrinkage rate coefficients determined by RF drying compared
to conventional conditioning in a controlled environment:

__Example 9__
A set of candidate wood specimens was equilibrated (size
approximately S" thick x 1" wide x 12" long) in 65% relative humidity for at
least 3 weeks. 30 representative samples were selected from the equilibrated group.
The weight and length of each specimen were measured. Each specimen was dried to
approximately 5% moisture using RF dryer (drying done on approximately 5 minute
cycle using a 20KW 40MHz dryer at Radio Frequency Company, Millis Massachusetts).
The weight and length of each specimen was re-measured. The acquired data is used
to estimate longitudinal shrinkage rate coefficients (LSRC_{1}) using the
formula:
$${\mathrm{LSRC}}_{1}=\mathrm{length\; change}\xf7\mathrm{initial\; length}\xf7\mathrm{moisture\; content\; change}$$

Next, the RF dried coupons were re-conditioned in 20% RH.
The weight and length of each specimen were re-measured. This data was used to re-estimate
longitudinal shrinkage rate coefficients (LSRC_{2}). A comparison was made
between shrinkage-coefficient estimates LSRC_{1} and LSRC_{2}. The
results are plotted in FIGURE 18 and show excellent agreement between the conventional
and accelerated methods of estimating shrinkage-coefficients.

G. Methods of using multi-sensor data to estimate the shrinkage
properties of wood by first using the multi-sensor data to identify the type or
class of wood that is being evaluated, and then using the multi sensor data to estimate
shrinkage using a class-specific equation and/or algorithm.
Parameters calculated from multiple sensors, such as tracheid-effect
line images and spectroscopy data, have shown to be useful in predicting the shrinkage
properties of wood. Many of the parameters found to be associated with shrinkage
are also influenced by chemical or physical features of the wood that may or may
not be associated with shrinkage. For example, wood that contains pitch may be more
prone to moisture-induced dimensional instability than typical clear-wood. However,
both tracheid-effect images and certain spectral bands are greatly influenced by
pitch in ways very different from non-pitch-containing wood with similar shrinkage
properties. FIGURE 19 shows two spectra. The "top" spectra is from a sample containing
pitch, the other from a sample that does not contain pitch. Both wood samples have
similar shrinkage behavior; however there are several important differences between
these spectra, including a sharper peak at 1200nm and a steeper rise between 1650
and 1700 nm in the pitch-containing spectrum. These spectra are typical of other
pitch and non-pitch containing southern-pine samples.

This suggests that improved shrinkage estimates could be
obtained by having different models or algorithms for different types of wood. Such
a strategy can be accomplished with a two-step approach to shrinkage prediction.
First, the wood-type of a region of interest is identified using inputs from one
or more sensors (Classification Step). The type of qualitative assessment may be
done with respect to a dimensional stability property, or other property. For example,
the dimensional stability property which enables classification may be crook. In
another embodiment, the property allowing classification may be "pith containing".
Second, a class-specific shrinkage prediction model or algorithm is applied based
on the results of the first step (this second step can be referred to as a Prediction
Step). Examples of wood types include, but are not limited to, knots, compression-wood,
pitch, pith-containing, early-wood, late-wood, species and blue-stain. The models
or algorithms to classify regions of interest or to predict shrinkage behavior will
typically be learned from a training set of data. Methods for classification and
prediction have previously been discussed.

The classification-step will predict membership into any
of K+2 categories, where K is the number of named classes (e.g., knots). The other
two categories are for "outliers", namely, cases which do not look like others that
have been observed, and "doubt", namely, cases in which class membership is too
uncertain to make a decision. Example 10 describes a two-step approach to estimating
shrinkage properties using multi-sensor data.

__Example 10__
In this example, the data used were Tracheid-effect line
images and NIR absorbance spectra. A training dataset consisting of approximately
350 12"x1"x3/4" pieces of wood was used to build a shrinkage-coefficient calibration
model. Each piece of wood was scanned for both tracheid-effect and NIR absorbance
data. Several parameters were calculated from each Tracheid-effect image. In addition,
each piece of wood was equilibrated at two different times in two different relative
humidity environments: 20% RH and 90% RH. Length measurements were made at each
humidity level and the moisture-induced dimensional change was recorded.

A partial least squares model was trained on all cases
using only the NIR absorbance data. FIGURE 20 illustrates two plots of results.
The left-hand plot shows the measured shrinkage values plotted against the fitted
values of all cases. The ratio of NIR absorbance values at 1200 nm and 1270 nm has
been found to be a useful indicator for the presence of pitch. If the ratio A1200/A1270
is greater than 1.18, the sample likely contains pitch. Samples with this ratio
greater than 1.18 are highlighted in the left-hand plot. The fit of these samples
is rather poor. A second set of models was then developed; one only on samples with
A1200/A1270 greater than 1.18, and one only on samples with this ratio less than
1.18. The right-hand plot in FIGURE 20 shows the predicted results using class-specific
models. That is, samples with A1200/A1270 greater than 1.18 were predicted with
the model trained on the "pitch-containing" samples, while the samples with A1200/A1270
less than 1.18 were predicted with the model trained on the "non-pitch-containing"
samples. The results show that the fit of the 'pitch-containing' samples is improved.
The fit of the samples with the ratio less than 1.18 is also improved, although
to a smaller extent than for the samples with the ratio greater than 1.18.

In other examples of the two-step prediction approach,
particularly for the "outlier" or "doubt" categories, an option for the prediction-step
would be to simply estimate the shrinkage value of a coupon from the average value
of its neighbors. Alternatively, data from sub-regions within a coupon that have
been labeled as an outlier or with doubt could be excluded from data aggregation
(i.e., 'masked').

In an embodiment, a first algorithm may be provided for
classifying the region of interest into a category within a plurality of categories
directed to qualitative assessments of dimensional stability. A second algorithm
may be provided for obtaining a quantitative estimate of dimensional stability.
This second algorithm may have a set of factors, such as for example A, B, C, and
D which represent different equations, respectively. A calculation performed by
the second algorithm may be contingent on the classification performed via the first
algorithm. For example, if via the first algorithm, the wood product is classified
into a "pitch" category, factor "B" may default to zero, or some other value and/or
formula. In another example, if via the first algorithm, the wood product is classified
as "pith-containing", factor "D" and/or factor "C" may default to zero or other
value, or be changed to another formula. Other variations based on classifications
are also contemplated and may be understood by those skilled in the art.

While the embodiments of the invention have been illustrated
and described, as noted above, many changes can be made without departing from the
spirit and scope of the invention. Accordingly, the scope of the invention is not
limited by the disclosure of the embodiments. Instead, the invention should be determined
entirely by reference to the claims that follow.