2007:119 CIV
M A S T E R ' S T H E S I S
Log Diameter Measurements Using Ultrasound
Reza Tavakolizadeh
Luleå University of Technology MSc Programmes in Engineering Computer Science and Engineering
Department of Computer Science and Electrical Engineering Division of EISLAB
2007:119 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--07/119--SE
Log Diameter Measurements Using Ultrasound
Reza Tavakolizadeh
Lule˚ a University of Technology
Dept. of Computer Science and Electrical Engineering EISLAB
January 28, 2007
A BSTRACT
The log diameter measurement error in today’s harvesters results in a poor possibility for adaptation of logs to the requirements of sawmills. To increase the accuracy of these measurements, different methods for non-contact diameter sensing have been tried for over 10 years. Unfortunately none of these tried methods have resulted in serial production of a system for non-contact sensing.
The overall goal of this project is to develop a method for non-contact measurements of log diameter using ultrasound.
As a first step in this project, this thesis will investigate the possibility of using ul- trasound for log diameter measurements. The thesis will also suggest ideas for further developments.
iii
P REFACE
I would like to thank, first and foremost, my supervisor Johan Carlson for his guidance and encouragement.
I would also like to thank Johan Oja at the Division of Wood Science and Technology, Bj¨ orn Hannrup at Skogforsk and the financiers ProcessIT Innovations and Komatsu Forest AB.
Last but not least, final thanks goes to my family and to Sheila for their love and support.
Reza Tavakolizadeh
v
C ONTENTS
Chapter 1: Introduction 1
1.1 Background . . . . 1
1.2 Current and Previously Tried Methods . . . . 1
1.3 Objectives . . . . 2
1.4 Performance requirements . . . . 2
Chapter 2: Theory 3 2.1 General Idea . . . . 3
2.2 Ultrasound . . . . 3
2.3 Distance Measurement . . . . 4
2.4 Ellipse Fitting . . . . 7
Chapter 3: Experimental Setup and Measurements 9 3.1 Data Acquisition Equipment . . . . 9
3.2 Measurement Rig . . . . 11
3.3 Software . . . . 11
3.4 Measurements . . . . 12
Chapter 4: Results and Analysis 15 4.1 Spruce Log . . . . 15
4.2 Pine Log . . . . 16
4.3 Tomography . . . . 16
Chapter 5: Discussion and Further Developments 23
Chapter 6: Conclusions 27
C HAPTER 1 Introduction
1.1 Background
Measurements of log diameter in today’s harvesters are relatively unreliable. This results in poorer possibilities for adaptation of logs to the requirements of the sawmills. The main requirement is to have logs in lengths appropriate to the diameter class. This requirement can only be met more frequent if diameter sensing is made more accurate in harvesters.
The organization behind this project is Skogforsk (the Forestry Research Institute of Sweden) in cooperation with ProcessIT Innovations (a collaboration center at LTU) and Komatsu Forest AB as the financiers.
The project has mainly been carried out in the Ultrasonic Lab at EISLAB but also in the labs of Division of Wood Science and Technology, two divisions at Lule˚ a University of Technology.
1.2 Current and Previously Tried Methods
In today’s harvesters the log diameter is measured by sensors installed in the limbing- knifes which generally run over bark. But occasionally, specially during the the warmer periods of the year, the limbing-knifes run under bark which results in poorer measure- ments. Other sources of error include failure of the limbing-knifes to maintain contact with the log, logs being oval or out of round, etc. All this scenarios result in measuring errors having a standard deviation of 5-8 mm [1].
During 1996 a non-contact measuring device was installed on a harvester. The device consisted of batteries of lamps, two line-scanner cameras and a computer with specially developed software [2]. The results from field trials in 1997 were encouraging and more
1
2 Introduction accurate than conventional measuring using the limbing-knifes but the system has so far not been serial produced due to uncertainty about the operation safety [1].
1.3 Objectives
The main objective in this project is to investigate the possibility of using ultrasound for non-contact log diameter measurement. A measurement rig will be built and diameter of different log sorts will be estimated and compared with the true diameter. The investi- gation will include test of accuracy, repeatability and performance for the different logs, if there is enough time.
1.4 Performance requirements
There is a request for diameter estimations on each centimeter along the log. The log
moves through the harvester with a speed of 5 m/s which mean a necessary measurement
frequency of at least 500 Hz. The other requirement is a lower standard deviation of the
measuring error compared to today’s 5-8 mm. There is also a requirement about the
robustness and the operation safety of the designed system.
C HAPTER 2 Theory
This chapter starts by explaining the general idea for problem approachment. After this an introduction to ultrasound is given followed by the mathematical theories behind the used methods.
2.1 General Idea
The general idea is to first estimate the coordinates of some reflection points on the log by sending out ultrasound pulses and recording the reflection. The reflection coordinates are estimated based on the direction and the coordinates of ultrasound transducers but also on the time it takes for the pulses to bounce back. In other words the distance from each transducer to the log is estimated. The theory for this is given in section 2.3.
The next step is to fit an ellipse to the estimated reflection points. This ellipse will represent the cross section of the log at that measurement point. The theory of ellipse fitting is given in section 2.4.
2.2 Ultrasound
Ultrasound is defined as sound with a frequency greater than the upper limit of human hearing which is approximately 20 kHz. This upper limit tends to decrease with age and most adults are not able to hear above 16 kHz.
The most common areas of use of ultrasound in industries are flaw detection in materials and flow measurements. Frequencies of use are usually from 2 to 10 MHz but other frequencies are used for special purposes.
How sound propagates in a medium varies considerably. In air the speed of sound, at all frequencies, is highly dependent on the temperature, humidity, pressure and CO 2
concentration [3]. This has to be taken into consideration if the properties of the medium
3
4 Introduction change while using ultrasound.
In this project ultrasound waves with a frequency of approximately 40 kHz are used for distance estimations.
2.3 Distance Measurement
The used method for distance measurements in this project is based on the cross corre- lation function of the envelopes of received and reference signal. The function output is interpolated for a more accurate distance estimation.
Other common methods for distance estimation are based on zero crossing and level thresholding which do not require any reference signal.
2.3.1 Cross correlation function
A frequently used method for distance measurements is to estimate the time delay, Θ, between two pulses, s[k] and r[k], by maximizing the cross correlation function R sr [k], according to
Θ = arg max
k R sr [k] = arg max
k
∞ n=−∞
s[n]r[n − k]. (2.1)
However this approach will only yield time delay estimates in whole samples. An alternative method for estimation of subsample time delay is proposed in [4].
In this project the envelope of the pulses s[k] and r[k] are first detected and then the cross correlation function of the detected envelopes is interpolated to find a more accurate time delay down to the subsample level.
2.3.2 Envelope detection
The envelope of a signal is the outline of the signal and an envelope detector can be seen as a system detecting the envelope by connecting all of the peaks in the signal (see Fig.
2.1).
A common and very efficient technique for envelope detection is based on the Hilbert transform. Assume that the signal can be modeled as
s(t) = e(t) × m(t), (2.2)
where e(t) is the low frequency part and m(t) is the high frequency part of the signal. If e(t) and m(t) have non overlapping spectra, the Hilbert transform of s(t) can be written as (see [5], theorem 2.6.5 for proof)
s(t) = e(t) × ˜ ˜ m(t), (2.3)
2.3. Distance Measurement 5 where ˜ m(t) denotes the Hilbert transform of m(t).
Define
z(t) = s(t) + j × ˜ s(t) =
= e(t) × m(t) + j × e(t) × ˜ m(t) (2.4) and let
m(t) = cos(wt), (2.5)
which has the Hilbert transform [6]
m(t) = −sin(wt). ˜ (2.6)
By using this and taking the absolute value of z(t), abs(z(t)) = |e(t)| ×
cos 2 (wt) + sin 2 (wt) = |e(t)|, (2.7) the requested envelope, |e(t)|, is detected if e(t) ≥ 0. In this approach abs(z(t)) will work well as an envelope detector as long as the modulating signal, m(t), is narrow banded [7].
In Fig. 2.1 an example of applying this envelope detector on an arbitrary signal is shown.
2.3.3 Interpolation
Interpolation is a specific case of curve fitting, where a function which goes through a set of data points is estimated. The simplest form of interpolation is linear interpolation while a polynomial interpolation is more accurate. Lagrange’s classical formula of polynomial interpolation is given below [8].
Given a set of data
(x 1 , y 1 ), (x 2 , y 2 ), ..., (x n , y n ), (2.8) where
x 1 = x 2 = ...x n , (2.9)
y ≈ (x − x 2 )(x − x 3 )...(x − x n )
(x 1 − x 2 )(x 1 − x 3 )...(x 1 − x n ) y 1 + (x − x 1 )(x − x 3 )...(x − x n ) (x 2 − x 1 )(x 2 − x 3 )...(x 2 − x n ) y 2 + +... + (x − x 1 )(x − x 2 )...(x − x n−1 )
(x n − x 1 )(x n − x 2 )...(x n − x n−1 ) y n =
6 Introduction
0 0.5 1 1.5 2 2.5 3
−1
−0.5 0 0.5 1
Amplitude
Sample
Arbitrary Signal
The Detected Envelope
x10 3 Figure 2.1: Result of applying the envelope detector on an arbitrary signal.
=
n k=1
n j=1
j=k(x − x j )
(x k − x j ) y k . (2.10)
The most commonly used method to calculate the coefficients of the interpolating poly- nomial is the method of least squares.
2.3.4 Least Squares
With this method the best-fit curve of a given type is the curve that has the minimum sum of the deviations squared from a given set of data.
Assume that the given data points are
(x 1 , y 1 ), (x 2 , y 2 ), ..., (x n , y n ), (2.11) where x is the independent variable and y is the dependent variable. If the fitting curve f (x) has the deviation d from each data point
d 1 = y 1 − f(x 1 ),
d 2 = y 2 − f(x 2 ), (2.12)
.. .
2.4. Ellipse Fitting 7 d n = y n − f(x n ),
then according to the method of least squares [9], the best fitting curve has the property such that
= d 2 1 + d 2 1 + ... + d 2 n =
n i=1
d 2 i =
n i=1
(y i − f(x i )) 2 (2.13) is a minimum.
2.4 Ellipse Fitting
There are two broad ellipse fitting techniques: clustring (such as Hough-based methods [10]) and least squares fitting (see subsection 2.3.4). The technique used in this project is based on least squares fitting. In this technique a set of parameters, representing an ellipse, are found which will minimize the distance from the data points to the ellipse.
The equation of an ellipse, centered at (x 0 , y 0 ) can be written in parametric form as
x − x 0 = αcosθ
y − y 0 = βsinθ (2.14)
where α and β represent the semi axis. This parametric equation can be written in implicit form as
x − x 0
α
2 +
y − y 0
β
2
= 1. (2.15)
A more general form for the implicit equation of an ellipse is that of a conic section ax 2 + bxy + cy 2 + dx + ey = 1, (2.16) which may be written in vector form as
[x 2 xy y 2 x y][a b c d e] T = 1 (2.17) or in matrix form as
Da = l (2.18)
where l is an n × 1 column vector.
To fit an ellipse to n data points, n ≥ 5, the n × 5 design matrix D can be formed with
rows
8 Introduction
d(i) = [x(i) 2 , x(i)y(i), y(i) 2 , x(i), y(i)], (2.19) and the parameter vector a can be estimated by means of the least squares solutions of the equation
Dˆ a = l + . (2.20)
Thus
a = (D ˆ T D) −1 D T l (2.21)
and the minimum square error is
2 = (l − D T a)(l − Dˆa) ˆ
= n − l T D(D T D) −1 D T l (2.22)
= l T (I − D(D T D) −1 D T )l.
C HAPTER 3 Experimental Setup and
Measurements
This chapter describes the equipment used in the experiment. The first section de- scribes the equipment used for data acquisition, the second section describes the mea- surement rig and the third one describes the software used for visualization och data saving. The last section describes the different logs used in this project.
3.1 Data Acquisition Equipment
The equipment used for the ultrasound signal generation is a pulse generator and seven ultrasound transmitters. The data collection equipment consists of a computer with a data acquisition card and seven ultrasound receivers. A schematic view of the experi- mental setup is given in Fig. 3.1.
3.1.1 Pulse Generator
The pulse generator used in this project is a Parametric pulse receiver, model 5052PR, with adjustable pulse energy and repetition rate. The pulse energy was set to the highest level and the repetition rate to the lowest level. This corresponded to a voltage level of 230 V and a repetition rate of approximately 200 Hz.
3.1.2 Ultrasound Transducers
The ultrasound transducers used have a very narrow spectrum, with a center frequency of 40 kHz. The transmitter och receiver units are separated and the manufacturer is Sencera Co. Ltd, Taiwan.
9
10 Introduction
Figure 3.1: Schematic view of the experimental setup. The measurement rig is described in detail in 3.2.
Figure 3.2: A pair of transducers mounted on the measurement rig.
The corresponding transducers can be seen in Fig. 3.2. A signal example for these can be observed in Fig. 3.3.
3.1.3 Data Acquisition Card
The Data Acquisition Card used is the National Instruments PCI-6143 board [11] with
8 differential 16-bit analog inputs channels, each sampling at a rate up to 250 kS/s.
3.2. Measurement Rig 11
0 1 2 3 4 5
0 2 4 6 8 10 12 14
Amplitude, (mV)
Time, (ms)
Figure 3.3: The envelope of received signal, transmitted between a pair of ultrasound transducers facing each other 20cm apart.
3.2 Measurement Rig
The measurement rig consists of seven pair of ultrasound transducers. Six pairs of these transducers are mounted on a half circle with a diameter of 80 cm as seen in Fig. 3.4.
Each pair of these transducers are used for distance estimation to the log from their mount point in a certain direction. The last pair of transducers form a reference channel (not shown in Fig. 3.4) which has two purposes. Firstly the signal from this channel is used for estimation of the ultrasound speed before each distance measurement. This will compensate for environmental changes instantaneously even if they occur very suddenly (see section 2.2). Secondly the same signal is used as reference signal when calculating the cross correlation function (see section 2.3) as a first step for distance estimation to the log from each transducer.
3.3 Software
The used software for calculations, data collection and visualization has been MATLAB,
version 7.2.0.232 (R2006a) with Data Acquisition Toolbox version 2.9. For simplifica-
tion of data collection and visualization an graphical user interface (GUI), which can be
observed in Fig. 3.5, was created in MATLAB. The received signal to the six transduc-
ers can be observed in real time in the plots titled “Channel.1” to “Channel.6”. The
estimated distance from each transducer is also displayed on the top right corner of the
12 Introduction
Figure 3.4: A schematic view of the measurement rig. Each arrow represents a pair of trans- ducers pointing to the same direction as the arrow. The circles represent the cross sections of logs with different diameter.
associated plot. The main plot in the middle of the GUI illustrates the the measurement rig in black line with location of each pair of transducer on it with a black circle. The estimated reflection point of ultrasound on the log is shown with white circles together with the estimated ellipse based on the reflection points. Information about the estimated ellipse is given in the box above the main plot.
3.4 Measurements
Two different types of logs has been used in this project for diameter estimation. The first set of measurements were done at the Ultrasonic Lab on one spruce and one pine log, both with the bark still on. The spruce log had a length of around 1.25 m and an average diameter of approximately 27 cm at one end and 29 cm at the other end. The pine log had a similar length but an average diameter of approximately 30 cm at one end and 32 cm at the other end. For each log 41 points with an interval of 2.5 cm between them were subject to measurements. An ellipse was estimated at each point representing the log cross section at that point.
The second set of measurements were done on a thinner pine log at the Division of
Wood Science and Technology in Skellefte˚ a. Here 10 measurements were done with an
interval of 3 cm between each measurement. Also the x-ray tomography at this division
was used to produce a tomogram for each measurement point. The results and analysis
of all of these measurements is presented in next chapter.
3.4. Measurements 13
Figure 3.5: The created graphical user interference in MATLAB for visualization and data
collection.
C HAPTER 4 Results and Analysis
The results during the initial measurements were not satisfactory. It turned out that the transducers disturbed each other too much which resulted in wrong distance estimation between the log and the transducers. The first tried approach for a solution was to somehow screen of the signal from each transducer from the others but this approach was soon given up. The second and final approach was to measure the distance to the log by two transducer, each on one side of the log, at a time. By doing so a satisfactory distance estimation for each transducer was achieved since there was no distortion between them.
The reason for chosen this approach was the simplicity but also the possibility to achieving the same result by running all the transducer at the same time if the center frequency of each transducer, on each side of the log, differ from the other two. Due to the very narrow spectrum of the transducers, a center frequency difference of a couple of kHz should be enough for limitation of the disturbance from the other transducers.
4.1 Spruce Log
The result of estimation of 41 ellipses on the spruce log can be observed in Fig. 4.1. The gap between each estimated ellipse is linearly interpolated for a better visualization. As it can be observed in Fig. 4.1 the variation of the width axis and lower part of the height axis (representing the bottom of the log) is considerably lower than the variation of the top part of the height axis (representing the top part of the log). This will result in a more accurate estimation of the width diameter than the height diameter. The explanation for this can be found in the placement of the transducers (see Fig. 3.4) which are more placed “on the sides” and “below” the log than “above” it.
The calculated ellipse circumference for each measurement point is shown in top of Fig.
4.3 together with the measured log circumference for the whole log. This circumference was measured with a meter-band at the first and last ellipse estimation point. The
15
16 Introduction circumference between these two points are assumed to increase linearly and is hence presented with a line. The result of a fitting a line, with the least squares method, to the estimated ellipse circumferences is also shown in this figure. As it can be observed the estimated circumference for one point can differ by up to 5 cm from the measured circumference but the fitted circumference values never differ by more than 2 cm. This corresponds to a top diameter error of around 6 mm if it is assumed that estimated and measured circumferences are those of a circle.
4.2 Pine Log
The result of the exact same measurement procedure as in section 4.1 can here be observed for the pine log in Fig. 4.2 and bottom of Fig. 4.3. As it can be observed in Fig. 4.2 the same variation phenomena is present on the plots representing the pine log as the ones representing the spruce log (see section 4.1).
As seen in bottom of Fig. 4.4 the difference between the fitted and measured circum- ference is at most 1 cm. This corresponds to a top diameter error of around 3 mm if it is assumed that estimated and measured circumferences are those of an circle. This error can probably be minimized by calibration since it’s almost constant along the log.
4.3 Tomography
In Fig. 4.7, Fig. 4.6 and Fig. 4.7 the tomogram and estimated ellipses for 9 measure-
ment points are shown. These are the result from the measurements on the pine log in
Skellefte˚ a. As seen on the estimated ellipses in the plots the ultrasound pulses tend to
bounce on the bark rather then on the wood under it.
4.3. Tomography 17
Figure 4.1: Estimated 3D-plot of the spruce log (top), seen from the top (middle) and seen from
the side (bottom).
18 Introduction
Figure 4.2: Estimated 3D-plot of the pine log (top), seen from the top (middle) and seen from
the side (bottom).
4.3. Tomography 19
0 20 40 60 80 100
82 84 86 88 90 92 94 96
Circumference, (cm)
Length, (cm)
Figure 4.3: Calculated circumferences of the estimated ellipses (crosses) and the measured cir- cumference (solid line) for the spruce log. The dashed line is the best fitted line to the crosses, obtained using the least squares method.
0 20 40 60 80 100
90 92 94 96 98 100 102 104 106 108
Circumference, (cm)
Length, (cm)
Figure 4.4: Calculated circumferences of the estimated ellipses (crosses) and the measured cir-
cumference (solid line) for the pine log. The dashed line is the best fitted line to the crosses,
obtained using the least squares method.
20 Introduction
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Figure 4.5: Tomograms for the first 3 measurement points on a pine log. The estimated ellipse
for each measurement point is shown in white.
4.3. Tomography 21
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Figure 4.6: Tomograms for measurement points 4 to 6 on a pine log. The estimated ellipse for
each measurement point is shown in white.
22 Introduction
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
Width, (cm)
Height, (cm)
6 12 18 24 30
6 12 18 24 30
