Evaluation of Flatness Gauge for Hot Rolling Mills

Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Evaluation of flatness gauge for hot rolling mills

Examensarbete utfört i Bildbehandling vid Tekniska högskolan vid Linköpings universitet

av Oliver Larsson LiTH-ISY-EX--15/4894--SE

Linköping 2015

Department of Electrical Engineering Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

Evaluation of flatness gauge for hot rolling mills

Examensarbete utfört i Bildbehandling

vid Tekniska högskolan vid Linköpings universitet

av

Handledare: Kristoffer Öfjäll

isy, Linköpings universitet

Lars-Åke Classon

Shapeline

Examinator: Maria Magnusson

isy, Linköpings universitet

Avdelning, Institution Division, Department

Avdelningen för Bildbehandling Department of Electrical Engineering SE-581 83 Linköping Datum Date 2015-09-29 Språk Language Svenska/Swedish Engelska/English   Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport  

URL för elektronisk version

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-121643 ISBN

— ISRN

LiTH-ISY-EX--15/4894--SE

Serietitel och serienummer Title of series, numbering

ISSN —

Titel Title

Utvärdering utav planhetsmätningar vid varmvalsverk Evaluation of flatness gauge for hot rolling mills

Författare Author

Oliver Larsson

Sammanfattning Abstract

In the steel industry, laser triangulation based measurement systems can be utilized for evaluating the flatness of the steel products. Shapeline is a company in Linköping that manufactures such measurement systems. This thesis work will present a series of experiments on a Shapeline measurement system in a relatively untested environment, the hot rolling mill at SSAB in Borlänge.

The purpose of this work is to evaluate how the conditions at a hot rolling mill affects the measurement performance. It has been anticipated that measuring in high temperature environment would introduce difficulties that do not exist when measuring in cold environ-ments.

A number of different experiments were conducted, where equipment such as laser and camera bandpass filter were alternated. Via the experiments, information about noise due to the environment in the hot rolling mill was gained. The most significant noise was caused by heat shimmering. Using the presented methods, the magnitude and frequency spectrum of the heat shimmering noise could be determined. The results also indicates that heat shimmering cause large errors and is quite troublesome to counter. In addition to this, the quality of the line detections under the hot rolling mill circumstances was examined. It could be observed that the line detections did not introduce any significant errors despite the harmful conditions.

Nyckelord

Abstract

In the steel industry, laser triangulation based measurement systems can be uti-lized for evaluating the flatness of the steel products. Shapeline is a company in Linköping that manufactures such measurement systems. This thesis work will present a series of experiments on a Shapeline measurement system in a rel-atively untested environment, the hot rolling mill at SSAB in Borlänge.

The purpose of this work is to evaluate how the conditions at a hot rolling mill affects the measurement performance. It has been anticipated that measuring in high temperature environment would introduce difficulties that do not exist when measuring in cold environments.

A number of different experiments were conducted, where equipment such as laser and camera bandpass filter were alternated. Via the experiments, informa-tion about noise due to the environment in the hot rolling mill was gained. The most significant noise was caused by heat shimmering. Using the presented meth-ods, the magnitude and frequency spectrum of the heat shimmering noise could be determined. The results also indicates that heat shimmering cause large errors and is quite troublesome to counter. In addition to this, the quality of the line detections under the hot rolling mill circumstances was examined. It could be observed that the line detections did not introduce any significant errors despite the harmful conditions.

Acknowledgments

I would like to thank my examiner Maria Magnusson and supervisor Kristoffer Öfjäll. Both of them have been really supportive. Thanks also goes to Shapeline who hosted this master thesis work. Special thanks goes to Emil Ekblad who worked long and hard days together with me during the experiments in Borlänge. Finally I would like to thank my mother for bringing me good coffee, when I was writing the report.

Linköping, September 2015 Oliver Larsson

Contents

2.1.3 Two Laser Lines for Detecting Vibrations . . . 11

2.2 Noise . . . 13 3 System 17 3.1 Overview . . . 17 3.2 Camera . . . 17 3.3 Laser . . . 18 3.4 Calibration equipment . . . 18 3.5 Surroundings . . . 18 4 Method 21 4.1 Heat Shimmering . . . 21 4.1.1 Frequency spectrum . . . 22 4.1.2 Covariance Matrix . . . 22 4.2 Comparative Measurements . . . 23 4.3 Line Detection . . . 23 5 Experiments 29 5.1 Overview . . . 29 5.2 Reference Object . . . 29 5.3 Equipment . . . 30

6 Results and Discussion 33 6.1 Cylinder Measurements . . . 33

6.2 Comparative Measurements on Cylinder and Strip . . . 36

viii Contents

6.3 Using different laser devices and camera band pass filter . . . 40 6.4 Noise and Vibration Compensation with Two Laser Lines . . . 44 6.5 Line Detection Errors . . . 48

7 Discussion 49

8 Conclusion 51

1

Introduction

1.1

Overview

Shapeline develop gauge systems based on a laser sheet triangulation technique. Their systems are widely used in the steel industry for measuring flatness on ap-plications such as steel plates or steel strips. The achieved degree of flatness is important for many steel products. For example buckles in steel strips directly affects strength properties of the material[1]. To assure quality and strength it is necessary to collect and evaluate requisite information about flatness. Even small deformations of the material can reduce desirable properties of the prod-uct. Another important aspect is the confidence of the measured flatness. The measurements have to be trustable and robust against different kinds of noise. Flatness measurements also supplies valuable information for controlling rolls in a hot rolling mill production line. Information about the flatness can be used to adjust preceding rolls to compensate for irregularities in the surface of a strip. This can significantly reduce the number of strips that will be sent to the roll feed (an extra process stage where a strip is straightened out) or the number of discarded strips, which eventually will increase the production rate. This de-mands both precise and high resolution flatness measurements.

Shapeline has developed successful applications when measuring on cold mate-rials. However, steel manufacturers have shown interest in measuring flatness in their hot rolling mills production lines. At these lines the steel material can reach the temperature of 1100 degrees. The step from measuring on cold to warm ma-terials introduces new harmful conditions. The speed of the production line is high, up to 25m/s. In addition to this the camera images can easily get distorted by atmospheric disturbances such as steam or heat shimmering. These possible

2 1 Introduction

error sources will be discussed further in Section 2.2.

The hot rolling mill consist of several stages which are illustrated in Fig. 1.1.

Figure 1.1:Hot Rolling Mill Layout (Source: SSAB[5]).

1. In the first stage steel slabs (thick blocks of steel) are reheated by furnaces. 2. The slabs are subsequently passed to the roughing mill where the thickness

are reduced from 220 mm to 30 mm.

3. The steel surface has a layer of oxide nuclei. This layer is removed by high pressure water beams.

4. At the finishing rolls, the steel are rolled into the desired width and thick-ness.

5. In the measure house the equipment for the flatness and temperature mea-surements are located.

6. In the end, the strip is cooled and coiled onto a coil.

1.2

Purpose

The purpose of this master thesis work is to evaluate the performance of the Shapeline system in a hot rolling mill environment.

A major challenge is to evaluate the confidence and accuracy of the measure-ments. For cold material applications it is possible to measure a strip by hand. By-hand measurements can in this case be regarded as the ground truth. Mea-surements from an optical gauge system can be directly compared the physical measurements, in order to get a proper evaluation of measurement accuracy. For the hot rolling mill case, this evaluation method is not possible to accomplish in practice. The problem is to physically obtain reference data for a 800-1200 de-grees steel strip. To obtain the reference data when the temperature has dropped may introduce uncertainties. During the change of temperature the steel mate-rial will contract. The temperature distribution can not be assumed to be ho-mogenous over the whole volume. Consequentially the magnitude of contraction will not be equal over the whole volume. This may create buckles that was not present at high temperatures. Consequently, one can not be sure that the shape

1.2 Purpose 3

of a cold reference strip correspond to the shape in the heated state.

One way to estimate the performance of the Shapeline gauge system is to iden-tify present sources of error. A second approach is to establish the magnitude of the distortions and how much harm they inflict on the actual performance. This thesis will present an investigation focusing on identification of error sources. To acquire such information several experiments will be conducted at a hot rolling mill of SSAB in Borlänge. By these experiments, it will be possible to estimate and model the disturbing error sources.

The list below summarizes the objectives of the conducted experiments. • Identify error sources for the hot rolling mill environment. • Determine the magnitude and duration of the errors.

2

Theory

2.1

Laser Triangulation

Shapeline’s system for measuring flatness is based on a laser sheet triangulation technique. This technique uses a laser projecting a line onto a surface, in this case the surface of a strip. If the surface is completely flat the projected line will be straight, as shown in Fig. 2.1(a). However, if the strip is not flat the projected line will not remain straight. Fig. 2.1(b) shows how the projected line changes its shape according to the shape of a surface. By using information about the shape of the projected laser line it is possible to reconstruct the actual shape of a strip. A camera is used to collect images of the projected laser line. During a measure-ment session the object is gradually moved through a laser plane until the whole object is scanned.

In some image ranging application there can occur issues due to either camera or laser occlusion. This causes blind spots in the captured images and can occur when something is blocking the view between camera and the illuminated part of the object. Occlusion never occur in the measurement at the hot rolling mill. Height curvatures of the strip are not large enough to occlude neither the camera view nor the laser light.

6 2 Theory

Figure 2.1: (a) A laser line projected onto a flat surface. (b) A laser line projected onto a curvaceous surface.

2.1 Laser Triangulation 7

Figure 2.2:Laser triangulation layout.

The layout of the system with its components is illustrated in Fig. 2.2. There are different coordinate systems. The laser coordinate system is placed so that the y-axis is aligned along the laser plane. The camera coordinate system is placed so that the negative z-axis is aligned with the camera view direction. The origin of the camera coordinate system coincide with the position of the optical centrum of the camera. The world coordinate system is located near the object which is to be measured.

2.1.1

Geometry

The objective is to find the relation between real world 3D points and correspond-ing depicted 2D points in image space. This problem can be approached in many different ways. The following approach is utilized by the current measure sys-tem. For this case the intersection between the laser plane and a view ray needs to be determined. A view ray is emanating from the sensor plane, which is illus-trated in Fig. 2.3. Considering the perspective distortion, the view ray direction depends on focal length f of the sensor optics. The direction of a view ray can furthermore be expressed as the vector

d_c= (u, v, −f ), (2.1)

where u and v is the position in the sensor plane in millimeter and f is the fo-cal length in millimeter. The direction vector can be transformed from camera coordinates to world coordinates by multiplying by a rotation matrix C

d_w= dcC, (2.2)

where C describes the rotation of the camera in the world coordinate system. The line equation of a view ray is defined as

8 2 Theory

Figure 2.3:Laser triangulation layout.

where c0is an arbitrary point on the line and t is a variable parameter.

The laser sheet can be defined by the plane equation

(p − l0) · nw= 0 (2.4)

were l0is an arbitrary point on the laser plane and p is another point on the laser

plane which is also located on the view ray defined in (2.3). The vector nwis the

normal of the laser plane in world coordinates. The line equation parameter t can be found by inserting (2.3) into (2.4). Solving for t gives

t = (l0−c0) · nw

dw· nw . (2.5)

An arbitrary coordinate a component i of p be expressed as:

pi = l0i+ (uC1i+ vC2i+ f C3i)t (2.6)

By rearranging and substitute constant expressions, C, f, nw, in (2.5) and (2.6)

leads to

pi =

ki0+ (uki1+ vki2+ ki3)

k4u + k5v + 1

(2.7) which is the relation between image coordinates u and v and intersecting posi-tion p at the laser plane.

2.1 Laser Triangulation 9

There are four unknown parameters per component of p in addition to the un-known parameters k4 and k5 in the denominator. There are 14 in total, that

need to be determined to be able to perform a complete triangulation. These unknowns can be estimated by a calibration procedure.

To perform a calibration an object with known geometry is used. Several record-ing of the object for different poses are collected. The parameters in (2.7) are determined to minimize the least square error, between the known true geome-try and the reconstructed geomegeome-try, using for example the Levenberg–Marquardt algorithm[3].

2.1.2

Line detection

An important part of the laser triangulation scheme is the line detection. A line detection method extracts the position of the captured laser line in the camera image. For our system laser lines are detected column-wise.

Figure 2.4:Camera frame with a laser line.

Fig. 2.4 shows one camera frame of a laser line. To determine the vertical pixel position v for each column u there are several methods that can be utilized. Some of the most common line detection methods is discussed in [4].

Laser devices for triangulation produces a laser line where the intensity across the line is approximately Gaussian distributed, which can be anticipated in Fig. 2.5. This is an important property in order to get an exact position of the laser line.

Line Detection - Center of Gravity

A common and fairly straight forward method is to calculate the center of gravity for each column. Using this method the laser line for an arbitrary column u is

10 2 Theory

Figure 2.5:Laser line cross sections from a hot steel strip.

located at row v which is extracted through

v = Nrows P i=0 iIu(i) Nrows P i=0 Iu(i) , (2.8)

where Nrowsis the number of image rows and Iu(i) is the intensity value for the

pixel [u, i].

Line Detection - Gaussian Approximation

Another method which is discussed in [2] is called Gaussian approximation. This method uses pixels close to the peak. The peak is assumed to fit a Gaussian curve. Through this assumption the estimated position can be calculated. Similar to the previous method this one detects the line position column wise. First of all the row vI max, the row where the maximum intensity can be found, is determined.

Whereafter the offset, σ, from vI maxis determined by

σ = 1 2

ln(I(vmax−1)) − ln(I(vmax+ 1))

ln(I(vmax−1)) − ln(I(vmax)) − ln(I(vmax+ 1))

, (2.9)

where I(v) is the intensity value for row v.

2.1 Laser Triangulation 11

2.1.3

Two Laser Lines for Detecting Vibrations

A strip usually oscillates up and down on its way along the production line. These vertical movement can arise to for example irregularities in the underlay. With-out taking this into consideration vertical movements, from here on called vibra-tion, of a strip would be interpreted as the actual shape of the vibrations. Fig. 2.6 shows an example how a vertical movement is superimposed on the true shape.

12 2 Theory

To detect and compensate for vibrations, two laser devices producing two sep-arate lines, can be utilized. In [6] a method for such compensation is proposed. Fig. 2.7 shows a system with two lasers from the side. Two measure points are here simultaneously acquired, one corresponding to each laser. Measure point P0(t) is located before the other point,P1(t), on the y-axis.

The method in [6] assumes that for each time step, the object has moved a dis-tance which is equal to the disdis-tance between P0 and P1 along the y-axis.

Conse-quently, the measured point P1(t0) is located at the same y-position as P0(t1). The

height difference between these points correspond to the displacement due to vi-bration at time t1. The vibration,V (t) is considered to be equal for both P0(t1) and

P1(t1) since they are captured simultaneously. Consequently,

Figure 2.7: Illustration of a 2D case where a vibration offset between two samples are determined.

V (t1) = P1(t0) − P0(t1). (2.10)

To compensate for vibration V (t1) is added to P1(t1). For next time instance t2

both V (t1) and V (t2) is used to adjust as

P1adjusted(t2) = P1(t2) + V (t1) + V (t2). (2.11)

For a arbitrary measure point P1(tn) the compensation can be expressed as

P1adjusted(tn) = P1(tn) + n

X

i=1

2.2 Noise 13

where the summation term can be interpreted as an integration of the movement due to vibration.

The method proposed in [6] is restricted to the fact that P1(t0) and P0(t1)

mea-sures on the same y-position on the strip. In reality it is hard to achieve that kind of timing. This also assumes that the laser angle is 90◦. For other angles than 90◦, the y position of a measure point also depends on the height, z, which in [6] have not been taken into consideration.

Another important aspect is the summation term in (2.12). In real world situa-tions each measurement would contain some amount of noise. In (2.12) the noise contribution would be summed as well, leading to drift error.

A similar technique for utilizing two lasers is used by the Shapeline gauge system. The algorithm in the Shapline system is somewhat more flexible. It is invariant for the laser angle. It also implements methods in order to counter the influence of noise when previous vibration detections is summed up, which would corre-spond to the summation term in (2.12).

2.2

Noise

The rough environment in a hot rolling mill introduces many possible error sources that affects the performance and accuracy of flatness measurements. This section will concern the most challenging noise sources for this investigation. To be able to state an actual accuracy for the measurements it is important to identify the influence of the present noise.

Material Properties

As previously mentioned line detection algorithms usually presumes the laser in-tensity to be Gaussian distributed across the line. A steel strip surface may hold properties that affects distribution of the laser intensity. There may exist some areas on the surface which are dark, areas that absorbs more light. Fig. 2.8 shows a case where the laser line partly illuminates a dark area and partly a bright area. It can be observed that the original intensity distribution has changed. When per-forming line detection an error will arise due to this change.

Heat Shimmering

Heat shimmering is another source of error when conducting optical measure-ments in hot environmeasure-ments. There have been attempts to physically model and simulate heat shimmering. One recent paper is [7], which also describe the under-lying physics carefully. In the hot rolling mill the high temperature strip creates a rising air convection above the strip. Hot air close to the surface rise and meet cold denser air. In between the cold and hot air it emerges a gradient in the

14 2 Theory

Figure 2.8: A case where the intensity is reduced for a certain part of the laser line cross section, leading to a erroneous line detection using the CoG-scheme.

refractive index. When laser light passes through air volumes with different re-fractive index it will change its original direction. Consequently refracted laser light will intersect another part of the strip compared to if no heat shimmering was present. This will result in a false estimations of the shape of the strip. A pos-sible scenario is shown in Fig. 2.9. Heat shimmering is an unwanted effect which is highly present in the hot rolling mill environment. The steel strip is about 800 degrees Celsius and moves at a relatively high speed. In combination with a pow-erful fan nearby, a lot of air turbulence is expected creating high frequent density gradients in the air volume between cameras and lasers.

2.2 Noise 15

Figure 2.9:Illustration - impact of heat shimmering. PLis the point the strip

3

System

3.1

Overview

Figure 3.1:System layout overview.

For the current system two camera devices along with two pairs of laser de-vices was used. The laser dede-vices comes in pairs of two in order to be able to detect vibrations. A system layout is illustrated in Fig. 3.1.

3.2

Camera

Shapeline has developed a camera platform called ShapeCat. ShapeCat supports very high frame rates which is necessary when measuring an object that moves fast. The camera performs line detection with an FPGA mounted inside the

18 3 System

era. The position and intensity of the detected lines are sent through an ethernet interface. The ethernet interface of the camera supplies some user functionally where eg. the shutter speed or frame rate can be adjusted.

It is possible to change camera optics depending on desired measure range and width.

A camera layout is shown in Fig 3.2. A bandpass filter can be placed between the sensor surface and the optics. This filter should have its center wavelength close to the wavelength of the laser light and suppress light from light sources with different wavelengths.

Figure 3.2:Camera Layout.

3.3

Laser

The laser component produces a laser light sheet. Using an optical lens the light is spread at a specified fan angle. There are lasers with different fan angles. The wider fan angle the more the laser output effect is spread out. To maintain good line detections, a laser with more power or a increased shutter speed may be required.

3.4

Calibration equipment

For the experiments different hardware configurations will be applied. When-ever a component is changed, eg. a laser or a lens, a new calibration has to be performed. To make the calibration procedure more convenient and to be able to calibrate while the production line is running, the cameras and lasers were mounted onto a rotatable aluminium frame. While calibrating, the frame is tilted upwards, so that cameras and lasers are directed to the calibration object. When a successful calibration is completed the frame is pulled back to be directed to the strip, ready for measuring.

3.5

Surroundings

Both movements and shape of a strip varies during different stages of the process due to influence of nearby machineries. For every strip there are three significant phases which will influence the measurements. Fig. 3.3 shows the three phases.

3.5 Surroundings 19

The first phase starts when a strip front end passes the last roll stand. The front end of a strip is at this point not attached and moves freely, oscillating up and down.

The second phase start when the loose front end reaches the coil which is lo-cated after the cooling section. The strip is winded up onto the coil with a large force. On the other end the strip is still fixed at the last roll of the finishing stand. Due to the coiling force a stretch is applied onto the strip. When a strip is under stretch the oscillations up and down are reduced. The stretch is also straighten-ing out buckles or edge waves in the strip material.

The last phase proceeds when the back end of a strip passes the last roll and moves freely towards the coil. Yet again oscillation and curvature can be distin-guished, comparable to the first phase but considerably shorter.

When analyzing measurement data, in a raw format, the following trends can be expected:

• The first part would look wavy, due to vibrations in the material. One would also expect to roughly distinguish shape of buckles in the material. • When the stretch is applied the strip would be substantially flat. Most of

deviations would be derived from noise.

20 3 System

Figure 3.3: Three phases of a strip. (1) Loose front end of a strip. (2) Strip under stretch. (3) Loose back end of a strip.

4

Method

The following chapter will present methods used for evaluating the flatness mea-surements conducted at the hot rolling mill at SSAB. A method for identification of heat shimmering will be presented. This method will establish the impact of the heat shimmering on the measurement performance.

Then another method for analyzing how hot rolling mill conditions affects the line detections is presented.

4.1

Heat Shimmering

The following method was used to analyze and determine the influence of heat shimmering. The objective here is to obtain data where distortions of heat shim-mering is isolated. Since strip vibration and shape is unknown we need to ex-clude these parameters. This can be achieved by measuring on a non-moving object with a known geometry, yet still under identical circumstances, that is, the same air turbulence and temperatures as when measuring on a strip. Chapter 5 will clarify how this setup is realized in practice.

The known geometry can be subtracted from the obtained measurements leaving only distortions left. From here the magnitude of the distortion(s) can be easily observed. Additionally, characteristics such as frequency spectrum and spatial covariance will be determined. Furthermore these characteristics can be com-pared to characteristics found in a strip measurements. Similar spectrums and covariances would indicate that same type of heat shimmering is affecting the strip measurements.

22 4 Method

4.1.1

Frequency spectrum

The frequency spectrum is of interest here. The data used for computing the spectrum by Fourier transform samples over time. Analyzing the spectrum will give an estimate how fast the heat shimmering changes in time. If the heat shim-mering spectrum is similar to white noise an averaging filter could be applied in order to suppress the influence of heat shimmering.

4.1.2

Covariance Matrix

For the heat shimmering case, the height of a point Pi on the laser line can be

considered to be a random variable, see Fig. 4.1.

For a data set with a sufficient number of samples a covariance matrix

Figure 4.1:Sample points.

Σ_cov=              

Cov(P0, P0) Cov(P0, P1) . . . Cov(P0, Pn)

Cov(P1, P0) Cov(P1, P1) . . . Cov(P1, Pn)

..

. ... . .. ...

Cov(Pn, P0) Cov(Pn, P1) . . . Cov(Pn, Pn)

             

can be computed. Analyzing the covariance matrix supplies useful information about the correlation between measured points. This will tell how the impact of heat shimmering varies along the laser line. Eg. if the impact in uniform across the whole line or more local or even independent between each measure point. Another way to represent the relation between different measure point is the correlation matrix. The correlation matrix can be determined from the covariance matrix

Σ_corr= diag(Σcov)

−1

2_{Σcovdiag(Σcov)}−12_,

where diag sets all non-diagonal elements to zero. Positive values in the corre-lation matrix indicate correcorre-lation. Values close to zero indicate no correcorre-lation,

4.2 Comparative Measurements 23

whereas negative values indicates inverted correlation. A compact measure for correlation for noise due to heat shimmering can be determined from the correla-tion matrix by computing a vector holding average correlacorrela-tion between measure points. The vector is computed by adding the elements in Σcorrrow wise. Before

a row r is added, the data is first shifted r steps to the left. When all rows have been shifted and added, all elements in the vector is divided by total number of rows of Σcorr.

4.2

Comparative Measurements

The fix object spectrum can be compared with spectrum from part of a strip. It would be beneficial to select data from were the strip is under stretch, described in Section 3.5, where vibration and buckles in the material is less significant. For this part of the strip the spectrum should be very similar to that have been ob-served on the fix object.

In conformity with the spectrum, the covariance for the fix object should also be similar to the covariance for the stretched part of the strip.

If these relations can be shown, it will be possible to state that the heat shimmer-ing for the fix object measurements is also present for the strip measurements.

4.3

Line Detection

Another approach is to evaluate how the conditions in the hot rolling mill affects the line detection. As described in Section 2.2 the quality of the line detection can decrease due to the steel material properties.

The laser device produces a laser line where the intensity distribution of the cross section is considered to be Gaussian distributed. By analyzing how the intensity distribution deviates from the Gaussian distribution, a rate of the impact of mea-surement noise can be achieved. In order to determine how the intensity distri-bution varies, raw frames from the cameras were collected. For each column in each frame the following analysis were made, see also Fig. 4.2.

• Find the intensity level of the background Ibackground. This is done be

com-puting an average of some pixels Ii far away from the laser line,

Ibackground= n P i=m Ii n − m. (4.1)

• Thereafter the background intensity is subtracted from all pixel at the cur-rent row. Then a Gaussian curve is fitted to the adjusted column of pixels.

24 4 Method

• The sum of the absolute difference for the measured values and the fitted Gaussian curve represent the noise rate and is expressed as the misfit

mf it= N P i=0 |_(Ii−_{Ibackground) − Iif itted}| N P i=0 Ii . (4.2)

Figure 4.2:Gaussian Curve fitted to a column of pixels. Background inten-sity is estimated from pixels between the column n and m.

The next step is to relate the degree of misfit mf it to the actual degradation of

performance in pixels or millimeters. In order to do this, simulations were made according to the flow chart in Fig. 4.3. During a simulation, a Gaussian curve is generated. The curve is distorted by simulated pink noise, introducing a specified misfit. Pink noise have been observed in later experiments, therefore pink noise is used in this simulation. Fig. 4.4 shows an example of how the curves were distorted.

Results from performed simulations is presented in Table 4.1. Table 4.1 also presents the mean absolute deviation pixel in pixels. Via the calibration of the

4.3 Line Detection 25

equipment a ratio k of the pixel distance in vertical direction to distance in z (in mm) is produced. The mean absolute deviation pixel can be translated into

millimeters using

mm= kpixel.

The results in Table 4.1 can be compared to the mf it acquired from real

mea-surement data. By interpolating between simulated mf itand corresponding mm

in Table 4.1 it is possible to determine a rough estimate of height errors that is caused by line detection errors.

mf it pixel mm 2% 0.0226 0.0229 4% 0.0442 0.0449 6% 0.0671 0.0682 8% 0.0878 0.0893 10% 0.1080 0.1098 15% 0.1614 0.1640

26 4 Method

Figure 4.3: Flowchart for simulating impact of noise on a resulting line de-tection.

4.3 Line Detection 27

Figure 4.4:Simulation of distorted laser intensity distribution. C is the orig-inal distorted curve. Cdist is C distorted by generated noise, causing an 8%

5

Experiments

5.1

Overview

This chapter concern the experiments at the hot rolling mill. The hardware dif-ferent setups will be presented. This chapter will also present how the data, re-quired by the method in Section 4.1, were acre-quired.

5.2

Reference Object

The strip is transported on conveyor rollers, where each roller is a metal cylinder with a radius of 0.40m. Section 4.1 proposes a method that requires a known fix object. To realize this experiment the gauge system will be setup to measure partly on the strip and partly on of the cylinders. Fig. 5.1 illustrates the layout of the system when the lasers are adjusted to be directed onto one of the cylinders.

However, the surface of the metal cylinder is glossy. Consequentially most of the incident laser light will be reflected around the normal of the cylinder. To assure that sufficient light reaches the camera from both lasers they are further tuned according to the geometry shown in Fig. 5.2. It is important that the cam-era receives sufficient light from both lasers. At the same time it is also important that the camera does not receives too much light from either of the lasers, which can saturate the captured laser lines. The cylinder is not moving, only rotating,

30 5 Experiments

Figure 5.1:Laser lines projected both onto the strip and the cylinder beneath the strip.

and has a smooth surface. This means that the laser line will illuminate a flat surface, containing only height deviations small enough to not be considered. If heat shimmering is present laser light gets refracted, causing erroneous height de-viations which has been explained in Section 2.2. Throughout the measurement conducted on the cylinder it is possible to isolate the impact of heat shimmering.

5.3

Equipment

Data sets used by proposed method were collected for several hardware configu-rations. Configurations with different bandpass filters, laser wavelengths, camera shutter speed were tested in order to find the most robust configuration that is capable of suppress the most troublesome noise.

The center wavelength of the selected bandpass filter have to correspond to the wavelength of the laser light. Table 5.3 presents the combinations of bandpass filter and laser types that were used.

Laser Wavelength Filter Center Frequency Filter Band Width

447nm (Blue) 447nm 12nm

447nm (Blue) 447nm 20nm

660nm (Red) 660nm 10nm

660nm (Red) 660nm 20nm

532nm (Green) 532nm 10nm

5.3 Equipment 31

Figure 5.2:Laser angles are tuned in order to make sufficient light to reach the camera.

6

Results and Discussion

This chapter will present and discuss the results of the conducted experiments. First the identification of errors due to measurement will be presented. The occur-rence and magnitude of these errors have been estimated using proposed meth-ods. Compensation for vibration is not used when analyzing data in Sections 6.1-6.3.

6.1

Cylinder Measurements

By the experiment discussed in Section 5.2 flatness measurements of a cylinder next to the strip were acquired. Despite the flat surface of the cylinder, height de-viations could be observed, which implies that significant noise affects the mea-surements. Fig. 6.1a shows a topography of the measured cylinder, where the max absolute height deviations at some points reaches over 1.5 mm and standard deviation of 0.3559 mm. For this context that is considered to be large deviations.

For every measure point in x-direction the Fourier transform is applied over a number of samples in y-direction (time). A frequency spectrum for every mea-sure point along the x-axis is obtained. From these spectra an average spectrum is computed, which is shown in Fig. 6.2. As seen in the figure the low frequen-cies dominates the spectrum. This means that only low pass filtering will not be enough to suppress the noise. Fig. 6.1b shows the low pass filtered topography of the cylinder containing the low frequent noise. In this case the height deviations reach 0.5 mm.

Throughout this experiment substantial noise have been observed in the cylin-der measurements. The magnitude of the noise is too large to cylin-derive from line

34 6 Results and Discussion

Figure 6.1: Topographies of cylinder measurement. Height values are in mm. (a)Topography (b)Topography - low pass filtered.

detection errors. The only imaginable source of error is heat shimmering. From this, the assumption is made that this noise is caused by heat shimmering.

6.1 Cylinder Measurements 35

Figure 6.2: Average frequency spectrum for height measurements on the cylinder.

36 6 Results and Discussion

6.2

Comparative Measurements on Cylinder and

Strip

As mentioned in the previous section, distortions were observed in the cylinder measurements. This section will make a comparison between the measurements on the strip and on the cylinder. The question is if the same heat shimmering distortions can be observed in the strip measurements.

Fig. 6.3.a present a part of both strip and cylinder which have been measured. The height difference between strip and cylinder can be distinguished. Distor-tions are visible on both of them.

The lower plot in Fig. 6.3.b present a topography for the same data as in Fig. 6.3.a. The only difference is that a mean has been computed and subtracted for each col-umn. This was applied in order to remove the static height difference between strip and cylinder. The strip and cylinder part has been separated with a dark vertical line, at around x=560 mm. By visual inspection, the distortions on cylin-der and strip look similar. In addition, the height deviations close to the borcylin-der between cylinder and strip, look reasonably continuous. The standard height de-viation, σz, for strip and cylinder is very close. The results as well as the camera

and laser equipment are presented in Table 6.2 below.

Area λlaser _{Center Freq.}Filter _BandwidthFilter σz |maxz|

Strip 660 nm (red) 660 nm 10 nm 0.3463 mm 1.9848 mm

Cylinder 660 nm (red) 660 nm 10 nm 0.3559 mm 1.5722 mm Table 6.1:Cylinder measurement results.

In Fig. 6.4 the frequency spectra in the time(y) direction for the cylinder and the strip is shown. The distribution among frequencies seems to be very similar for the spectra.

Analyzing covariance and correlation between adjacent measure points on the laser line, discussed in Section 4.1.2, show that the noise is somewhat correlated. Fig. 6.5 shows the average cross correlation for both the strip and the cylinder. It can be observed that the correlation is very significant within 10 mm and de-crease further away. As seen in the figure almost identical correlation between measure points can be observed on both the strip and cylinder.

The observed similarities in both spectrum and covariance implies that heat shim-mering with same variation and magnitude also occur on the strip.

6.2 Comparative Measurements on Cylinder and Strip 37

Figure 6.3:(a) Reconstruction of strip (left) and cylinder (right). (b) Topography of strip (left) and cylinder (right).

38 6 Results and Discussion

6.2 Comparative Measurements on Cylinder and Strip 39

40 6 Results and Discussion

6.3

Using different laser devices and camera band

pass filter

Several tests have been performed using different hardware configurations. Dif-ferent type of laser devices with difDif-ferent wavelengths, λlaser, were tested.

Band-pass filters inside the cameras was also altered. The different filters had different widths, wf ilter, letting through various spans of wavelengths. Each filter has

also a center wavelength, λcenter, which is the wavelength which is least

atten-uated by the filter. The shutter speed was adjusted in order to avoid saturated laser lines. Additional experiments were also performed with increased shutter speeds, which did not affect the results.

The aim of these experiments is to determine if there are any hardware config-uration that is more robust than another to the troublesome conditions at the hot rolling mill. For the following tests, data from the stretched part of the strip were used, making the assumption that the strip is flat, and the height deviations are solely caused by distortions.

Table 6.3 present the height standard deviation σz and max absolute height

de-viation |maxz|for each hardware test. Throughout the conducted tests it can be

observed that changing laser wavelength or bandpass does not result in any im-provements. The standard deviations and maximum values listed in Table 6.3 are larger than the result from the experiments presented in Section 6.2. There are no clear explanation to this, though it should be mentioned that measurements presented in Section 6.2 and measurements presented in Table 6.3, were captured at two different occasions. Topographies of the measurements for each hardware configuration is shown in Fig. 6.6-6.10. By visual inspection, it can be observed that the distortions appear very similar to the distortions observed in previous experiments, see Fig. 6.1 , apart from the magnitude. It should also be noticed that the scale differs in Fig. 6.1 compared to Fig. 6.6-6.10, where the later figures cover smaller areas.

Config λlaser λf ilter widthf ilter σz |maxz|

1 447 nm (blue) 447 nm 12 nm 0.6755 mm 3.15 mm

2 447 nm (blue) 447 nm 20 nm 0.6997 mm 2.98 mm

3 660 nm (red) 660 nm 10 nm 0.78 mm 3.68 mm

4 660 nm (red) 660 nm 20 nm 0.6997 mm 3.36 mm

5 532 nm (green) 532 nm 10 nm 0.7393 mm 3.40 mm

6.3 Using different laser devices and camera band pass filter 41

Figure 6.6:Topography configuration 1.

42 6 Results and Discussion

Figure 6.8:Topography configuration 3.

6.3 Using different laser devices and camera band pass filter 43

44 6 Results and Discussion

6.4

Noise and Vibration Compensation with Two

Laser Lines

For the current system two laser line are utilized in order to detect and compen-sate for vibration in the strip, which was described in the topic of Section 2.1.3. In the final output of the system, where a devibration algorithm has been ap-plied, the estimated flatness seemed to be erroneous. For some cases vibrations are partially detected but not properly compensated. For some other cases false detections occur.

For the case where false detections occur data from the stretch part of the strip were selected. Previous observations indicated that during this phase the strip is flat and still yet under influence of significant noise. Our gauge system has now occasionally detected vibrations, as seen Fig. 6.11. Two contradictions arises here. Vibrations of this magnitude is certainly not expected when the strip is un-der stretch. In addition to this, the vibration seen in Fig. 6.11 has not a uniform distribution across the strip, which is a distinction for data containing vibrations. Consequently, in this case we are probably distinguishing false detected vibra-tions. In order to gain further understanding about these discrepancies we will

Figure 6.11:Detected vibration for the stretched part of the strip.

examine the height data derived from both laser lines before any vibration com-pensation have been applied. Fig. 6.12 presents a set of height measurements, for each laser line, from the same part of the strip. The data have been slightly low pass filtered to suppress the most disturbing high frequent measurement noise. Comparing the two laser lines, an offset of up 0.8 mm can be observed, which propagates over distances up to 100 mm. This may seem contradictory because the both laser lines illuminates the same part of the strip. However, by consider-ing the fact that the laser light from each laser takes different paths through the air between laser to strip and finally to the camera, the behavior becomes under-standable. The laser light is refracted in different ways by the heat shimmering. Through the previous analysis of covariance of the heat shimmering, we were able to observe that the correlation decreases over larger distances. The distance between the laser lines is 25 mm and that leads to the fact that the noise due to

6.4 Noise and Vibration Compensation with Two Laser Lines 45

Figure 6.12: (a) Topography from height measurements from laser 1. (b) Topography from height measurements from laser 2. (c) Absolute difference between topographies in (a) and (b).

heat shimmering for each laser can be expected to be uncorrelated. Heat shim-mering errors between 2 and 3.6 mm, respectively, are presented in Table 6.3 and Table 6.2, are affecting each line individually, which is causing these systematic offsets between the measurement from the both laser lines.

The next step is to determine the heat shimmering impact on algorithms for com-pensating vibrations by demonstrating an example with two laser lines on a flat, non-vibrating, surface under heat shimmering noise. Fig. 6.13 illustrates this case where two uncorrelated noise sources s0 and s1are affecting measurement

p0and p1. p0is captured from laser line one laser line and p1from the other.

Us-ing height measurements from both laser lines, the algorithm for compensatUs-ing for vibration reviewed in Section 2.1.3, can be applied. The detected vibration for time t1, V (t1) = P1(t0) − P0(t1), is consequentially not zero. The algorithm have

detected a false vibration.

The deviations between laser lines expands over large areas, which can be ob-served in Fig. 6.12. This false vibration detection will sum up and increase in

46 6 Results and Discussion

Figure 6.13:Vibration Noise.

magnitude and lead to the erroneous compensations which have been observed in Fig. 6.11.

Fig. 6.14 shows a case where a successful compensation have been performed. The measurements are selected from phase three where distinct vibrations occur. The upper plot shows a part of a strip before any compensation have been ap-plied. Distinct patterns of vibration can be seen within the dotted boxes. In the lower plot compensation has been applied. The pattern of vibration seen in the upper plot is removed in the lower plot.

6.4 Noise and Vibration Compensation with Two Laser Lines 47

Figure 6.14: Successful compensation for vibration. (a) Strip before com-pensation have been applied. Patterns from vibration can be observed. (b) Strip after compensation have been applied. Patterns from vibration have been removed.

48 6 Results and Discussion

6.5

Line Detection Errors

As mentioned in the previous sections, it has been found that conditions in a hot rolling mill affects flatness measurements. Heat shimmering refracts light caus-ing troublesome biases in the measurement.

Still the light distribution across the line remains to be examined. It has pre-viously been shown that to perform a good line detection the laser line should have a Gaussian intensity distribution. However, the present measurement noise might affect the intensity distribution and make it less Gaussian. Consequently, it will degrade the quality of the performed line detections.

The method described in Section 4.3 compares measured intensity of a line seg-ment to the closest Gaussian curve available. The misfit will be presented in proportion to the total intensity of the fitted Gaussian curved.

Table 6.3 shows the estimated misfit, mf it, from the Gaussian curve. Then mf it

is compared to values in Table 4.1. By this comparison it is possible to determine a rough estimate of average height error, σmm, due to environment impact on the

laser line intensity distribution.

Data conducted using different laser wavelength and camera bandpass filter was used for this experiment, for which the result are also shown in Table 6.3.

Centerλ W idth Laserλ mf it σmm

447 nm 14nm 447 nm 0.0650 0.0702 mm 640 nm 10nm 640 nm 0.0714 0.0771 mm 447 nm 20nm 480 nm 0.0554 0.0598 mm 640 nm 20nm 640 nm 0.0555 0.0598 mm

Table 6.3:Estimated line detection errors. Centerλ and W idth is the center frequency and the width of the bandpass filter in the camera, respectively. Laserλ is the wavelength of laser light. mf itis calculated and σmmis taken

from Table 4.1.

The estimated errors are much smaller than the errors that have been observed previously in this chapter. It is also important to consider that in cold environ-ments line detection error normally is caused by properties of the strip material, such as reflectivity or absorption capacity. Now for this hot environment, heat shimmering or emitted light from the glowing strip might as well affect laser line intensities. It might be hard to separate this error contribution from each of these possible factors.

7

Discussion

During this master thesis some additional experiments have been performed, which is presented in the list below. The results of these experiments have not been presented in this report since they either overlap with other results or lack significance.

• An experiment, similar to the experiment presented in Section 5.2, were also performed. Instead of using the cylinder, an aluminium baulk was placed near the hot strip. In the baulk experiment, distortions from heat shimmering could be distinguished. But the baulk was not completely still during the measurements. The movements of the baulk were manifested in the measurements. Consequently, the cylinder experiment was used in-stead of the baulk experiment.

• Attempts to improve the data using different filters have been made, with-out any satisfying results. As previously mentioned, a low pass filter can reduce some of the noise. The troublesome low frequency components of the heat shimmering is harder to deal with.

• A basic simulation of movements of the camera and the laser modules was implemented in C++. At a certain point during this work, there was a sus-picion that the cameras or lasers were not still. Through the simulation in-formation about how such movements would affect the measurements was gained. The suspicion of movements of the equipment was later excluded. • In the early stage of this work, an experiment using two lasers with

dif-ferent wavelengths was conducted. The lasers were illuminating the same part of the strip. Since the light from each laser is taking different paths through the air they will refract in different ways. A difference in measure-ments from each laser could be observed, which indicates that heat

50 7 Discussion

mering affects the measurements. Similar symptoms has been observed in Section 6.1

8

Conclusion

The purpose of this investigation was to evaluate the performance of a flatness gauge system from Shapeline for hot rolling mill environment. An important part of the investigation was to acquire a better understanding of the environ-ment and how it affects the resulting measureenviron-ments. Via the conducted exper-iments, some insights about hot rolling mill conditions have been gained. As previously mentioned in this report, there is a lack of information about the true shape of the strip in the state where it is about to be measured. Facing this fact some assumptions about the strip had to be made, e.g. that the stretched part of the strip is considerably flat and that no vertical movement occur.

Throughout the experiments performed at the hot rolling mill in Borlänge several observations have been made. The most important observation was the impact of heat shimmering, causing height deviations up to about 1.5-3.5 mm for the used system configurations. Without any adaptations to software algorithms and mea-surements these deviations will have an significant effect on the measurement results. In addition, it have been observed that noise due to heat shimmering contains a lot of significant low frequent components which easily could be mis-interpreted as the actual shape of the strip. After low pass filtering of the data, it contained isolated noise due to heat shimmering, which might have similar ap-pearance as center buckles on the strip.

It has also been observed that this noise is only correlated for measure points that reside close to each other. As explained through the analysis in the previous chapter this has an bad impact on the standard methods that are used for com-pensating vertical vibrations in the strip. There exist cases where the method, if used as is, introduces artifacts in the resulting measurement when exposed to this heavy noise.

52 8 Conclusion

The precision is severely degraded due to the present noise. Nonetheless, it is important to recognize these are initial results. There is still room for a lot of improvements, on a software based as well as a mechanical level.

For less noisy and cooler environments, the same equipment and software have shown to give very good result, supplying both precise and confident flatness measurements. However, to make a reliable application for a hot rolling mill en-vironment counter measures must be implemented. Different kind of hardware were tested during the experiment. The results presented in Section 6.3 indicate that changing neither laser wavelength nor camera bandpass filter will improve the measurement performance.

A mechanical solution might be a strong fan close to the strip where the mea-surements takes place. Trying to blow away hot air rising from the strip might reducing density gradients in the air and accordingly reducing refractions of the laser light, i.e heat shimmering.

Bibliography

[1] Michael Degner. Modern Hot Strip Production. Stahleisen , Communications. Cited on page 1.

[2] T Meueller and E Reithmeier. Image sementation for laser triangulation based on chan-vese. Measurement, 63(14):100–109„ 2015. Cited on page 10.

[3] JorgeJ. Moré. Numerical analysis. 630:105–116, 1978. URL http://dx. doi.org/10.1007/BFb0067700. Cited on page 9.

[4] R.B.Fisher and D.K.Naidu. A comparison of algorithms for subpixel peak detetion. in Image Technology, Advances in Image Processing, Multimedia and Machine Vision, pages 385–404, 1996. Cited on page 9.

[5] SSAB. Hot rolling mill. URL http://www.ssab.com/Global/SSAB/ Brochures/en/Images_steelbok/Rolling_mills_1.jpg. Cited on page 2.

[6] Rubén Usamentiaga, Julio Molleda, Daniel F Garcia, and Francisco G Bulnes. Removing vibrations in 3d reconstruction using multiple laser stripes. Optics and Lasers in Engineering, 53:51–59, 2014. Cited on pages 12 and 13. [7] Ye Zhao, Yiping Han, Zhe Fan, Feng Qiu, Yu-Chuan Kuo, Arie E Kaufman,

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