MICROMAGNETIC AND MULTIPARAMETER MEASUREMENT FOR
MICROSTRUCTURAL MATERIAL PROPERTIES CHARACTERIZATION

By

Shuo Zhang

A THESIS

Michigan State University

in partial fulﬁllment of the requirements

Submitted to

for the degree of

Electrical Engineering – Master of Science

2018

ABSTRACT

MICROMAGNETIC AND MULTIPARAMETER MEASUREMENT FOR
MICROSTRUCTURAL MATERIAL PROPERTIES CHARACTERIZATION

By

Shuo Zhang

Magnetic Barkhausen noise (MBN) is measured in low carbon steels, and the relationship between
microstructural properties and parameters extracted from MBN signal has been characterized. In
the present study, the relationship between the number of turns of pick-up coils and MBN signals in
both time-domain and frequency-domain is studied for the sensor coil optimization. With optimized
pick-up coil, the characteristics of MBN are investigated for various mild steels with diﬀerent grain
sizes, carbon contents and hardness. To investigate the relationship between proﬁles of MBN
signals and carbon contents of samples, the parameter has been extracted experimentally by ﬁtting
the original proﬁles with two Gaussian curves. The gap between two peaks (∆G) of ﬁtted Gaussian
curves shows a better linear relationship with carbon contents of samples in the experiment. The
peak positions of MBN signal’s frequency response proﬁles have been observed decreasing with
the increase of grain sizes. The fact is related to the length of two pinning sets reduces with the
increase in the grain size. As a result, the frequency increases for the decrease of the time interval
between two impulses. Due to the mechanical properties, such as hardness, are closely related to the
grain size of the mild steels, the relationship can be described by Hall-Petch relation. The hardness
can be predicted with the parameter MBN frequency peak position. To ensure the sensitivity
of measurement, advanced multi-objective optimization algorithm Non-dominant sorting generic
algorithm III (NSGA III) has been used to fulﬁll the optimization of the magnetic core of sensor [1].
The relationship between the properties of samples and Magneto-Acoustic Emission (MAE) signals
has also been investigated. Multi-features have been extracted and selected to ﬁt a linear regression
model to predict the hardness and grain size of the samples.

ACKNOWLEDGEMENTS

I want to express my appreciation for Professor Yiming Deng, my adviser, who give me patient
instruction for the research and my academic work. And I would like to thanks for the tremendous
support of my family and friends throughout my time at school.

This work is partially supported by the U.S. Department of Transportation CAAP Research
Grant: DTPH5615HCAP03L. I wish to thank project manager Dr. J. Merritt, J. Arnold and J.
Prothro for their support.

The sample heat-treatment was processed by Hansen Balk steel treatment company. I would

like to show my thanks for the manager Martin Balk for the support.

iii

TABLE OF CONTENTS

LIST OF TABLES .
LIST OF FIGURES .
CHAPTER 1

1.1 Motivation .
.
1.2 Background .

vi

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INTRODUCTION .
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1
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1
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2
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1.2.1 Review of micro-magnetic and magnetic method . . . . . . . . . . . . . .
2
2
1.2.1.1 Hysteresis loop . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.2.1.2 Magneto-Acoustic Emission . . . . . . . . . . . . . . . . . . . .
1.2.1.3 Magnetic Barkhausen Noise . . . . . . . . . . . . . . . . . . . .
7
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1.3 Contributions .
1.4 Summary .
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CHAPTER 2 METHODOLOGY .
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2.1 Sample preparation .

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2.1.1

Sample heat treatment

2.2 Properties measurement .
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2.2.1 Microstructure
2.2.2 Vickers hardness test

2.3 Optimization algorithm .
2.4 Summary .
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3.1 Schematic .

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3.1.1 Hall sensor
3.1.2

CHAPTER 3 EXPERIMENT SET-UP FOR MBN . . . . . . . . . . . . . . . . . . . . . . 21
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Sensor Holder design and sensor coil connection . . . . . . . . . . . . . . 23
3.2 Data acquiring and storing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Data processing and parameter extraction . . . . . . . . . . . . . . . . . . . . . . 25
3.3.1 Root mean square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.2 MBN proﬁle . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Frequency spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3
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3.4 Optimization program .
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3.5 Summary .

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4.1 Schematic and sensor of MAE experiment
4.2 Data processing .

CHAPTER 4 EXPERIMENT SET-UP FOR MAE . . . . . . . . . . . . . . . . . . . . . . 33
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4.2.1
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4.2.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.3 Data preparation .
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Package tsfresh .

4.3 Summary .

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iv

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CHAPTER 5 RESULTS .
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5.1 Optimization results .

Sensor optimization with NSGA III

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5.1.1 MBN signals for diﬀerent of pick-up coils . . . . . . . . . . . . . . . . . . 38
5.1.2
. . . . . . . . . . . . . . . . . . . . . 40
5.2 Carbon content eﬀect on the MBN signal . . . . . . . . . . . . . . . . . . . . . . . 41
. 43
5.3 Grain size eﬀect on MBN frequency spectrum . . . . . . . . . . . . . . . . . . .
5.3.1 Grain size eﬀect on MBN frequency spectrum . . . . . . . . . . . . . . . . 43
5.3.2 Excitation signal eﬀect on MBN frequency spectrum . . . . . . . . . . . . 47
Predict hardness with parameter frequency peak position . . . . . . . . . . 49
5.3.3
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. 52

5.4 Predict grain size and hardness with MAE signal
5.5 Summary .

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CHAPTER 6 CONCLUSION AND FUTURE WORK . . . . . . . . . . . . . . . . . . . 54
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6.1 Conclusion .
6.2 Future work .

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BIBLIOGRAPHY .

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v

LIST OF TABLES

Table 21: Carbon content, grain size, Vickers hardness and heat treatment of steel samples

18

Table 51: Decision making with L2 norm with diﬀerent weight

. . . . . . . . . . . . . . . 40

Table 52: Predicted hardness and corresponding error of steel samples . . . . . . . . . . . 51

vi

LIST OF FIGURES

Figure 11: B-H Curve and parameters

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Figure 12: Diagrams illustrating measurements of MAE signal

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.

Figure 13: Principle of Magnetic Barkhausen Noise . . . . . . . . . . . . . . . . . . . . .

3

6

8

Figure 21:

Iron carbon phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 13

Figure 22: Annealing process

.

.

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Figure 23: Normalizing process

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. 14

Figure 24: Microstructure of steel samples with magneﬁcation of 1000X . . . . . . . . . . 16

Figure 25: The diagram for Vickers hardness test

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Figure 26: Vickers hardness tester

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 27: Pareto-front for cost and comfort of the car

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. 19

Figure 28: NSGA II algorithm .

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Figure 31: The schematic and physical prototype for the experimental setup . . . . . . . . 21

Figure 32: Printed circuit board to hold the hall senor

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Figure 33: Transfer characteristics of Hall sensor

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. 22

Figure 34: Transfer characteristics of Hall sensor

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. 23

Figure 35: Transfer characteristics of Hall sensor

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. 24

Figure 36: Transfer characteristics of Hall sensor

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. 24

Figure 37: The schematic of the Labview program . . . . . . . . . . . . . . . . . . . . . 25

Figure 38: The front panel of the Labview program . . . . . . . . . . . . . . . . . . . . . 26

Figure 39: Magnetic Barkhausen Noise periodic signal

. . . . . . . . . . . . . . . . . . . 27

Figure 310: Magnetic Barkhausen Noise signal for one period . . . . . . . . . . . . . . . . 28

vii

Figure 311: Magnetic Barkhausen Noise signal for one period . . . . . . . . . . . . . . . . 28

Figure 312: Magnetic Barkhausen Noise proﬁle

. . . . . . . . . . . . . . . . . . . . . .

. 29

Figure 313: Frequency spectrum, frequency proﬁle and ﬁtted curve of sample 1008 . . . . . 30

Figure 314: Flowchart of optimization and ANSYSEM models . . . . . . . . . . . . . . . . 31

Figure 315: Variables and objectives for optimization . . . . . . . . . . . . . . . . . . . .

. 31

Figure 41: Schematic for the MAE experiment set-up . . . . . . . . . . . . . . . . . . .

. 34

Figure 42: physical prototype for the sensor

. . . . . . . . . . . . . . . . . . . . . . . .

. 34

Figure 43: Wide-band AE sensor and frequency response . . . . . . . . . . . . . . . . .

. 34

Figure 44:

schematic of tsfresh .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 51: Normalized MBN proﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 39

Figure 52: Normalized MBN frequency response

. . . . . . . . . . . . . . . . . . . . . . 39

Figure 53: Pareto front in objective ﬁeld . . . . . . . . . . . . . . . . . . . . . . . . . .

. 41

Figure 54: Measured MBN proﬁles ﬁtted with two Gaussian curves . . . . . . . . . . . . . 42

Figure 55: The gaps between two peaks for both simulated and experimental results as a

function of carbon contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 56: Fitted MBN frequency proﬁles of diﬀerent samples

. . . . . . . . . . . . . .

. 45

Figure 57: MBN frequency response peak position as a function of grain size

. . . . . .

. 45

Figure 58: MBN frequency response peak position as a function of grain size (grain size

larger than 15 µm) .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 59: MBN frequency response peak position and grain size for each samples (high

amplitude excitation signal) . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 46

Figure 510: Fitted MBN frequency response peak proﬁle for samples with diﬀerent exci-

tation signal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

. .

. .

Figure 511: MBN frequency response peak position as a function of grain size (high

amplitude excitation signal) . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 49

viii

Figure 512: Hardness as a function of grain size . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 513: Predicted hardness and hardness measured by Vickers hardness tester . . . . . . 50

Figure 514: Predicted grain size with diﬀerent datasets . . . . . . . . . . . . . . . . . . .

. 51

Figure 515: Predicted grain size with MAE signal and actual grain size

. . . . . . . . . . . 52

Figure 516: Predicted hardness with MAE signal and hardness measured by Vickers hard-

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. .

ness tester

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

ix

CHAPTER 1

INTRODUCTION

1.1 Motivation

Over the next decade, the demand for energy is projected to reach record levels. The United
States has a golden opportunity to become a powerhouse in global energy markets, to truly achieve
full energy independence and to use natural gas to power our economy. The pipeline infrastructure
forms a critical aspect of US economy. The United States system for natural gas pipelines consists
of 210 systems overall running through the diﬀerent states. This makes the accurate pipe property
determination crucial, especially in the ﬁeld of oil and natural gas transportation. At the present
date, 63 percent these pipelines contain too many twists and turns that do not allow the conventional
methods of inspection such as pipeline inspection gauge (PIG), or automatic robots to be used in
such situations. And those pipelines, which have been laid down for decades of years, usually
lack reliable information for the property and microstructure changing and then issues in the
concern for the safety and integrity of the whole system. Therefore, accurate and eﬃcient pipeline
properties determination and evaluation is crucial for maintaining the healthy and long-lasting
system. However, to characterize the piping materials for better understanding the microstructure
properties, state-of-the-art techniques relying on microscopes often involve destructive procedures
(polish and etch) for microstructure observation and identiﬁcation of chemical constituents to
estimate material properties accurately which is impossible for in-situ inspection.

Due to various gaps that exist in pipe properties measurement, the desire for novel techniques
provides the impetus for the development of Micromagnetic method, such as Magnetic Barkhausen
Noise (MBN) and Magneto-Acoustic Emission (MAE), which are sensitive to the multi-properties
of ferromagnetic materials. This M.S. Thesis work is to involve estimation of the basic material
properties, microstructure, composition, etc. with the use of electromagnetic and acoustic sensors
and Several major tasks are proposed to address the above-mentioned M.S. Thesis work objectives.

1

New parameters have been extracted and new methods have been developed for properties charac-
terization. Experimental testing, advanced data analysis, and probabilistic methods are integrated
into the proposed tasks.

1.2 Background

1.2.1 Review of micro-magnetic and magnetic method

For the ferromagnetic materials, they consist of small, ﬁnite and magnetic regions called domains
which are randomly oriented in the virgin state. In the peacetime its direction desultorily, magnetic
mutual oﬀset, the whole object does not show magnetism. When the magnetic ﬁeld H applied,
the magnetization vectors inside the domain would rotate into the direction of the applied ﬁeld
and convert the multi-domain state into a single domain. This process is performed by moving
the domain walls, the so-called Bloch wall, stepwise [2] [3]. Those discontinuous pulses due to
movement of domain wall can be measured in the form of both magnetic signal and acoustic signal.

1.2.1.1 Hysteresis loop

Among diﬀerent kinds of magnetic inspection, the measurement of the hysteresis loop of steel is the
most common way to get information about the microstructural changes and material properties.
Fig. 11 shows the graph of typical hysteresis loop and the deﬁnition of various parameters derived
from hysteresis loops such as coercive force and remanence. For ferromagnetic material, the
coercivity is the intensity of the applied magnetic ﬁeld required to reduce the magnetization of
that material to zero after the magnetization of the sample has been driven to saturation. And the
remanence or remanent magnetization or residual magnetism is the magnetization left behind in
a ferromagnetic material after an external magnetic ﬁeld is removed. Those paramters have been
investigated to measure the hardness, residual stress, and plastic deformation.

The eﬀect of stress on the magnetic hysteresis properties of diﬀerent kinds of steels have been
investigated by various of authors. K.J. Stevens measures the uni-axial stress by the magnetic
properties such as maximum magnetization, remanence, and coercive ﬁeld get from hysteresis

2

Figure 11: B-H Curve and parameters

loops [4].An experimental investigation was carried out to study the eﬀect of stresses that approach
and exceed the yield point, on the magnetic properties of ground samples of medium carbon steel
upon surface grinding by M. Vashista et al.. It shows that maximum magnetization and permeability
derived from hysteresis loop increase with residual stress but starts to decrease when tensile residual
stress exceeds yield strength of material [5]. H. Kwun et al. shows the hysteresis loops in specimens
of AISI 410 stainless and SAE 4340 steels were sensitive to both hardness and stress. Qualitatively,
for all the specimens investigated, tensile stress increased the magnetic induction (B) and the slope
of the sides of the hysteresis loops; compressive stress did the opposite [6].

The magnetic hysteresis loop is also sensitive to the plastic deformation of the steels. Few
investigators have demonstrated their results in the papers. Plastic deformation aﬀects the hysteretic
magnetic properties of steels because it changes the dislocation density, which aﬀects domain-wall
movement and pinning. J.M. Makar et al. report measurements of the bulk magnetic properties
of pearlitic steels recorded in-situ during plastic deformation. Remnant magnetization was found
to increase at lower tension levels, but higher stress levels produced a decrease in value that was
attributed to stress induced changes in magnetic anisotropy. The high ﬁeld magnetization decreased

3

monotonically with stress in both the pre-yield and plastically deformed regions [7]. Martin J. Sablik
et al. modify the model to study the eﬀect of plastic tensile deformation on hysteresis loops with
the same Bmax .With increasing residual tensile strain Hc increase, the slope of the hysteresis loop
decreases, whereas with increasing elastic tensile strain, the slope increases [8].

The inﬂuence of microstructure transformation of the steel after room temperature rolling is also
an essential part of the magnetic hysteresis loop. The detection of α martensite phase in austenitic
stainless steel after 15 to 55% reduction in thickness was investigated by K. Mumatz et al. Saturation
magnetization was increased with the increasing percent reduction in thickness for the increasing
volume percent of α martensite. Whereas coercive force and remanence ratio decreased with the
increasing percent reduction in thickness. These results were attributed to the shape magnetic
anisotropy due to formation of a diﬀerent shape of martensite [9]. Low carbon steel specimens cold
rolled at ratios of 0–40% have been examined comprehensively by H. Kikuchi et al.. the coercive
force and the magnetizing current at peak in rms voltage increase monotonically due to the increase
in dislocation density below 10% and the formation of cell structure; these microstructural changes
enhance the intensity of interaction between pinning site and domain wall [10].

Other microstructural or mechanical properties, such as grain size, hardness and even aging of
steels also have an impact on the magnetic hysteresis loop. JW Wilson et al. have established the
correlations between electromagnetic properties and hardness of power generation steel (P9 and
T22) with the diﬀerent microstructural state through major and minor B-H loop measurement [11].
F.J.G. Landgraf et al. show how the hysteresis curve is changed with variables such as the second
phase, grain size, texture and deformation. The growth of a second phase (as in aging) or the
decrease in grain size show changes in the domain wall movement region (coercive force) and the
domain annihilation region with little change in the domain nucleation region. In the case of the
eﬀect of texture and deformation, a larger amount of domain rotation can explain the decrease in
remanence and high-induction permeability [12]. J.N. Mohapatra et al. recorded and analyzed for
5Cr–0.5Mo steel after aging at 600 ℃ for various lengths of time. A decrease in coercivity at
the initial stage of aging, extending up to 200 h of aging, was found due to the interstitial carbon

4

diﬀuses towards the grain boundary making the matrix magnetically softer. Beyond 200 h of aging
the precipitation of alloy carbides attains subsequent growth, making the material magnetically
harder [13].

However, there are some drewbacks for the hystersis loop. The hystersis loop of the steel is
inﬂuenced by multiproperties of the steel and can hardly ﬁnd a linear relationship for properties
characterization.

1.2.1.2 Magneto-Acoustic Emission

Magneto-Acoustic Emission (MAE) is acoustic emission pulses driven by local sources of mag-
netostriction strain due to the irreversible displacement of domain walls which is similar to the
Magnetic Barkhausen Noise (MBN). Whereas, MAE only responses to the non-180 degree domain
wall, for the reason that 180-degree domain wall will not inﬂuence the magneto-elastic energy.
The MAE signals with low amplitude and high frequency (50KHz-1MHz) can be detected by high
sensitivity acoustic emission sensor with wide operating frequency band. Therefore the MAE
eﬀect is determined by both magnetic and elastic properties of ferromagnets. Fig. 12 illustrates
the shape of MAE signal when the triangular magnetic ﬁeld applied. The peak of the MAE signal
is happened near the coercivity points of the hysteresis loop. Due to the mechanism of MAE, it is
sensitive to multi-properties of the ferromagnetic materials and carries information of changes in
microstructure and mechanical properties.

Based on analysis of some typical features of MAE signal [14] [15] [16] in time domain such
as the root-mean-square (RMS) value, the peak value, position and number of the pulse during a
period, the relationship between MAE signal and crystallographic texture, plastic and elastic stress
has been investigated.

D. O’Sullivan et al.

found that MAE absolute energy is linearly inversely proportional to
hardness for both the plastically strained and heat treated samples. With high measurement
depth than MBN, MAE can be used as an eﬃcient tool to evaluate the information along depth
direction [17]. John W. Wilson et al. used MAE and MBN for case depth measurement in En36

5

Figure 12: Diagrams illustrating measurements of MAE signal

gear steel. The overall amplitudes for both MBE and MAE exhibit a good correlation with case
depth [18]. K. Praveena et al.
investigated the MAE signal for sample nanocrystalline Mn-Zn
ferrites and found that the MAE activity along hysteresis loop is proportional to the hysteresis
losses during the same loop and the domain wall creation or annihilation processes are the origins
of the MAE [19]. R. Ranjan et al. had dealt with the eﬀects of grain size and carbon content on
the magnetic properties of steel. And the MAE had shown an increase in the number of pulses and
average pulse height with the grain size [20]. Miriam Rocío Neyra Astudillo et al. had studied
the MBN and MAE for A508 Class II forged steel used for pressure vessels in nuclear power
stations and showed that the MBN and MAE signal is sensitive to the crystallographic texture and
microstructure [21]. D.H.L Ng et al. reported that MAE is capable of detecting the direction of
the stress axis for mild steel and nickel bars [22].

Whereas, there are some drawbacks for MAE measurement. At ﬁrst, the technique is sensitive

6

to disturbing noise in the environment. As a result, it has a low signal to noise ratio. Secondly, the
MAE signal only response to non-180 degree domain walls. So investigations with this technique
are of interest for comprehensive interpretation studies and their interaction with the microstructure
is observed.

1.2.1.3 Magnetic Barkhausen Noise

MBN is a promising nondestructive electromagnetic method for detecting properties of the ferro-
magnetic materials. The simple principle of the Magnetic Barkhausen Noise shows as following:

a) Magnetic domains show random orientation without the external magnetic ﬁeld.
b) Those domains with moments aligned most closely with the applied ﬁeld will increase in

volume at the expense of the other domains.

c) The move of the domain wall is discontinuous. The irreversible jump of domain wall energy

for encountering pinning sites will lead to uneven and discontinuous change in magnetization.

d) This uneven change will lead to the tiny impulse in the hysteresis curve like (d) show in ﬁgure

13.

With the principle showing above, the MBN signal shows excellent performance in evaluating
mechanical characterizations and electromagnetic properties of steel, and this is due to the sen-
sitivity of MBN signals to microstructural changes. The relationship between MBN signal and
microstructure (grain boundary [23], grain size [23], composition [24]), hardness [25], applied and
residual stress [26], fatigue and damage [27], and the plastic and elastic deformation [28] have been
investigated based on the analysis of typical features of MBN signal in time domain (such as the
root-mean-square (RMS) value, the peak value, position and half-width value of proﬁle curve).

The eﬀect of microstructure on the MBN signal has been widely investigated for diﬀerent
aspects and diﬀerent samples in details. Ktena et al. compared interlaboratory results about the
relationship of MBN and grain size and the strain showed that MBN decreases with increasing
grain size and increases with strain, consistently [29]. H. Sakamoto et al. described the theoretical
relationships between RMS values of MBN and the microstructures of carbon steels. It showed

7

1/2
g

in ferrite grains and RMS =Cp*d2

that RMS = Cg*d
p in cementite-dispersed ferrite grains,
where dg and dp are ferrite grain size and cementite particle diameter, respectively. Cg and Cp are
constant [30]. S. Yamaura et al. also got the same relationship between MBN RMS value and the
grain size for pure iron samples with diﬀerent heat treatment [23]. MBN signal is also sensitive to
the grain phase and composition fraction. L. Clapham et al. presented that the pearlite content of
plain carbon steels has a signiﬁcant eﬀect on MBN signal. The MBN pulse height distribution for
fully pearlitic steels is highly asymmetrical, exhibiting a tail. Conversely, samples containing no
pearlite generated a comparatively narrow and symmetrical pulse height [31]. The characteristics
of the Barkhausen noise phenomenon were investigated for various crystalline microstructures of
plain steels by O. Saquet et al., including ferrite, pearlite, and martensite, which enabled us to get
a better understanding of the dependency of MBN signal on complex microstructure [24].

(a)

(b)

(c)

(d)

Figure 13: Principle of Magnetic Barkhausen Noise

Another application for MBN signal is to measure the hardness of the steel and the depth of
case hardened or decarburized steel. Franco et al. showed linear correlations between diﬀerent
MBN parameters and hardness measurements in the steel SAE 4140 and SAE 6150 with diﬀerent
excitation signal frequency [32]. M. Blaow et al. concluded in the paper that the shape and position
of the MBN proﬁle are signiﬁcantly aﬀected when a gradient in microstructure is induced by a
gradient in carbon content [33]. V. Moorthy et al. analyzed the MBN signal with a number of
narrow ranges of low frequencies to give useful insights into the microstructural gradient through
the depth of the case. This type of analysis might also be used to evaluate steels with diﬀerent case
depths, as it would indicate the approximate depth at which the transition from the hard to the softer

8

region takes place [25]. O. Stupakov et al. investigated the applicability of the BN technique for
evaluation of the decarburization depth of the industrial spring steel. The classical number of BN
counts and especially the alternative second-peak-based parameter U2, were shown to be perfect
indicators of the sand blasting treatment having perfect sensitivity with the decarburization depth
of up to 150-200 µm [34].

MBN is also a very promising method for non-destructive, fast and accurate prediction of
residual stresses. Stewart et al. analyzed the diﬀerent parameters of MBN with applied stress,
including tension and compression, and determined residual stress near the edge of the weld with
the conclusion [35]. J. Anglada-Rivera showed that the peak amplitude of the Barkhausen voltage
increases with the applied stress, reaching a maximum value and then beginning to decrease at
higher tensile stress for 1005 commercial steel [26]. H.Ilker Yelbay developed an MBN stress
calibration set-up and a residual stress measurement system with scanning ability to determine the
residual stresses in the welded steel plates by MBN technique [36].

MBN is also an eﬃcient tool to detect the damage of plastic deformation and fatigue load. A.
Dhar et al. measured the MBN signal on hot-rolled mild steel samples uniaxially deformed to
diﬀering magnitudes of plastic strain to study the dependence of MBN activity on the plastic strain.
Angular MBN had been implied to monitor the deformation induced magnetic anisotropy [37]. C.-
G. STEFANITA et al. performed a study to diﬀerentiate the eﬀects of elastic and plastic deformation
on MBN signal. Elastic strain eﬀects on the MBNenergy were determined to be far more signiﬁcant
than plastic strain eﬀects [28]. The various stages of fatigue damage in low carbon structural steel
had been characterized using MBE signal analysis technique during high cycle fatiguing by S. Palit
Sagar et al. The observed trends in the variation in MBE peak voltage showed an initial increase
followed by a decrease. After that, a sharp increase was found during online monitoring of fatigue
till failure [27].

9

1.3 Contributions

It is known that the frequency response of the pick-up coils would change with the number of
turns winded. The peaks of frequency response move to the lower frequency with the increase of
the number of turns of pick-up coil [38]. In this paper, the relationship between the MBN proﬁle
and frequency response and pick-up coils with turns number 80, 200, 400 have been investigated
as guidance for the choice of pick-up coils for the experiment.

Other than those conventional parameters mentioned in previous work, new parameters have
been introduced and related to signiﬁcant microstructural properties. Pérez-Benitez et al. presented
a numerical model to ﬁt the original experimental results and showed that the carbon content was
linear to deﬁne a parameter “overlapping factor” which is the gap between two peaks of theoretical
ﬁtting curves [39]. Vashista et al. used two Gaussian curves to ﬁt the two peaks of 18NiCrMo5 steel
with diﬀerent treatments and extracted parameters of two peaks include peak height, peak position
and the full width of half maximum [40].
In present work, two methods have been combined.
Parameter gap between two peaks (∆G) extracted from the ﬁtting curve ﬁtted by two Gaussian
curves shows a linear relationship with the carbon content of samples.

Other than those parameters extracted in the time domain, it is also important to study the
results from the frequency response of the MBN signal, which provides a wealth of information.
S. Yamaura et al. derived a new parameter, P60/P3, to study the eﬀect of grain size of pure iron
specimens on the Barkhausen noise, where P60 and P3 are the spectrum intensities at 60 kHz and
3 kHz respectively [23]. M. Vashista et al. showed that the frequency response of the pick-up
coils would change with the number of turns of the coil. The peaks of frequency response move
to the lower frequency with the increase of the number of turns of pick-up coil [38]. In this study,
the relationship between the MBN frequency response and grain size and hardness of samples in
the experiment. For frequency response for diﬀerent samples, in contrast to the description in the
previous paper [38] that the frequency response of a pick-up coil does not change signiﬁcantly
with the diﬀerent microstructure of test material, as grain size decreases, the position of peaks of
frequency proﬁles increases. For mild steels, the grain size of the steels and the their hardness exist

10

the hall-petch relationship. Therefore, we can predict the hardness with the parameter Fpp.

Similar to MBN, MAE is due to the displacement of domain wall during magnetization.
Whereas, MAE is acoustic emission signal detected by the acoustic sensor. Even though, the
sensor we are using is a highly sensitive wide-band acoustic sensor, tremendous acoustic noise in
the environment will have an inﬂuence on the signal measured. Therefore, the signal to noise ratio
of MAE signal is relatively smaller than MBN signal’s, making it diﬃcult for parameter extraction.
As a result, for signal processing of MAE signal, we introduce the machine learning method for
feature extraction and linear regression. The hardness and grain size have been predicted in the
network and the results show good accuracy.

Considering the sensitive, weak and noise-like properties of the MBN signal, a suitably eﬃ-
cient sensor is indispensable to achieve accurate measurement of the microstructure of materials.
Previous work has investigated the relationship between the magnetic ﬁeld with diﬀerent single
objectives like material of the core, the shape of core tips and distance between two poles [41].
These kinds of studies are important as the guidance for designing the experiment but are still
not enough when there is a trade-oﬀ between two objectives. To ensure the sensitivity of the
measurement, a detailed parametric study of sensor core design is conducted with multi-objective
optimization algorithm NSGA III [42] and ANSYSEM simulation. An optimized sensor which is
suitable for various diameter pipes is developed.

1.4 Summary

The principle and application of traditional magnetic and micro-magnetic method has been
reviewed in the behind section. The Magnetic Barkhausen Noise method with wide application
and sensitivity has been chosen as the main method for investigation. Contributions for this paper
has been summarized and described.

11

CHAPTER 2

METHODOLOGY

2.1 Sample preparation

2.1.1 Sample heat treatment

Parallelepiped samples were prepared from various types of mild steels obtained commercially,
which include 1008, A36 and 1018 with diﬀerent carbon contents of 0.04 wt%, 0.12 wt% and
0.19 wt% respectively. As Fig. 21 showing, those steels using in the experiment whose carbon
contents less than 0.83% mainly consist of ferrite and pearlite. To change the microstructure of
steels obtained oﬀ-the-shelf and investigate the inﬂuence of heat treatment to the Barkhausen noise
signals, each kind of steels were normalized and annealed by heating the samples above the Ac3
around 50 ◦F to 150 ◦F to austenitize the original grains. The carbon contents of the samples are
from 0.04 wt% to 0.19 wt %, according to the Fig. 21, the corresponding austenitizing temperature
are from 1600 ◦F to 1650 ◦F. Considering all the samples, we set the temperature with 1706 ◦F as
shown in the Fig. 22 and Fig. 23. The heat rate for the heat treatment also has an inﬂuence on the
austenitize temperature, the samples have been heated with a related slow ramp rate of 300 ◦F/ h to
make sure a low austenitize temperature. To make the sample heated suﬃciently, according to the
thickness of the sample, the samples have been held at the temperature for one hour. The cooling
rate, which is the only diﬀerence between annealing process and normalizing process, is the most
import procedure to control the grain size and grain phase of the steel. For annealing, the steels are
cooled in the furnace with a relatively slow rate of 225 ◦F / h to around 800 ◦F. This process will
lead to a coarse-grain structure of the steel. The grain size will become smaller with the increase
of the cooling rate. For normalizing, the samples are cooling in the air which has a relative higher
cooling rate and leads to a ﬁne-grain structure. The grain phase of the steel after annealing and
normalizing are still ferrite and pearlite. Whereas, martensite will present when the cooling rate

12

increase further, such as cooling in water or oil, which is known as quenching. Each kind of steels
was normalized to get samples 1008 N, A36 N and 1018 N and annealed to get the samples 1008
A, A36 A and 1008 A with the vacuum furnace. To make the samples fully saturated, all steels
were cut into small pieces with dimensions of 100mm × 30mm × 4.76mm.

Specially, steel 1026 pipeline with outside diameter of 152.4 mm and a wall thickness of 4.57
mm is introduced to be examed the relationship between carbon content and the MBN signal and
to be used in optimization of the sensor geometry.

Figure 21: Iron carbon phase diagram

2.2 Properties measurement

2.2.1 Microstructure

To observe the microstructure on the surface of each sample, small pieces of the samples were cut
and polished with diamond paste (6 µm and 0.2 µm).The metallographic structure was revealed
by etching with the 4% Nital solution. Fig. 24 shows the microstructure observed under an optical
microscope with the magniﬁcation of 1000X. Bright regions in the majority of the picture represent

13

Figure 22: Annealing process

Figure 23: Normalizing process

14

the ferrite grains and the dark ones spread in between are pearlite grains, which can be taken as
the second phase particles. With the graph obtained from the microscope and the scale bar marked
on the bottom right corner of the picture, we can predict the area for the whole picture. The
grain number can be counted from the picture and the average grain size for ferrite grain can be
calculated. The grain size, grain shape, Vickers hardness and second phase percentage drastically
changed after heat treatment. From the Fig. 24, we can ﬁnd that the grain size for annealed sample
is larger than normalized one, which is consisted with the conclusion before. And the second phase
(pearlite, dark particles) proportion will change a lot during heat treatment. The samples 1018,
1018 annealed, 1018 normalized, A36 and A36 normalized all have a large propertion of pearlite
grains.

2.2.2 Vickers hardness test

The Vickers hardness test method is very useful for testing on a wide type of materials, but test
samples must be perfectly polished to enable measuring the size of the impressions. It consists of
indenting the test material with a diamond indenter, in the form of a right pyramid with a square
base and an angle of 136 degrees between opposite faces subjected to a load of 1 to 100 kgf. The
full load is normally applied for 10 to 15 seconds. After loading, when we move the indenter away,
there is a small impression with the shape of rectangular pyramid under the microscope. The Fig.
25 shows the diagram for the Vickers hardness test and the top view of the impression. By using
screw micrometer, the diagonal lengths, which are the d1 and d2 in Fig. 25, can be measured
accordingly.

The HV number is determined by the ratio F/A, where F is the force applied to the diamond in
grams-force (gf) or kilograms-force (kgf) and A is the surface area of the resulting indentation in
square micrometers mm2 or square millimeters µm2. A can be determined by the formula 2.2 :

d =

d1 + d2

2

15

(2.1)

(a) 1008

(b) 1008 annealed

(c) 1008 normalized

(d) 1018

(e) 1018 annealed

(f) 1018 normalized

(g) A36
Figure 24: Microstructure of steel samples with magneﬁcation of 1000X

(h) A36 annealed

(i) A36 normalized

d2

d2

≈

HV =

F
A

≈ 1.8544 • F

d2

A =

1.8544

2 • sin(136◦
2 )
mm2] ≈ 1854.4 • F
[ kg f

d2

(2.2)

(2.3)

[ g f
µm2]

The F in equation 2.3 stands for the load force, which is set by yourself. The d represents the
average of two the diagonal line of the indent. Vickers hardness values are generally independent
of the test force. And Fig. 26 shows the tester we are using. On the top of the machine, there are
screw micrometers to measure the diagonal lengths through the microscopes. On the middle of the

16

picture, it is the main part of the machine, which includes the diamend indenter, microscope and
the platform to ﬁx and control the position of samples. On the bottom of the device, there is a green
button on the panel to start loading of the force.

Figure 25: The diagram for Vickers hardness test

The micro-hardness of the samples are obtained with Vickers hardness tester with load 200g f .
According to equation 2.1 and 2.3, we can calculate the Vickers hardness for diﬀerent samples.
The tests have been conducted on every sample for ﬁve times, and the ﬁnal hardness is obtained by
taking the average of results of ﬁve times.The details of the chemical composition, heat treatment
process and microstructure are summarized in Table 21. From the table we can see, the Vickers
hardness of the samples increase with the increase of the carbon content and decrease with the
increase of the grain size.

2.3 Optimization algorithm

To optimize the magnetic core of the sensor, algorithm NSGA III has been adopted and
implemented. NSGA III is an advanced optimization algorithm to search the Pareto-front (optimal
solution set) for multi-objective problems. For each point on the Pareto-front, we cannot ﬁnd any

17

Figure 26: Vickers hardness tester

Table 21: Carbon content, grain size, Vickers hardness and heat treatment of steel samples

Without heat treatment

Vickers hardness Heat treatment
110.21
172.19
185.33
256.84
95.06
116.33
118.81
99.71
120.7
133.43

Annealing: 1706◦F, 1hr, 4hrs cool to 800◦F

Normalizing: 1700◦F to 1750◦F, 1hr, cool in air

Samples
1008
A36
1018
1026
1008 A
A36 A
1018 A
1008 N
A36 N
1018 N

Carbon Content (CC wt%) Grain Size(GS) (d/µm)
0.04
0.12
0.19
0.25

32
11
10
15
40
22.5
25
34
16.5
22

18

point which is better than it in the objective space. The Fig. 27 shows a typical Pareto-front for
cost and comfort of the car. The comfort of the car will be limited by the cost of the car. The red
line from point 1 to point 2 describes the set of the optimal points in the objective ﬁeld when we
try to minimize the cost and maximize the comfort coeﬃcient of the car. The points in Pareto-front
mean that the most comfortable car we can get with the same price.

Figure 27: Pareto-front for cost and comfort of the car

The procedure for NSGA II is shown bellow:
1. Pt/Qt : the parents/oﬀspring of generation t Pt+1 : the parents of generation t+1
2. All elements in Pt and Qt compete with each other for non-domination.
3. The elements in the optimal-front F1 (if ||F1|| ≤ ||Pt+1||) are selected into the next generation.
4. This procedure repeats until ||F1|| + ||F2|| + . . . + ||Fk|| ≥ ||Pt+1||.
5. If ||F1|| + ||F2|| + . . . + ||Fk|| > ||Pt+1||, extra elements are rejected based on the crowding

distance sorting.

NSGA III is more eﬀecient than the previous version NSGA II for the reson that it introduces

reference direction to get a good distribution.

19

Figure 28: NSGA II algorithm

2.4 Summary

In this chapter, we focus on the information obtaining and analysis about the basic steel prop-
erties. At ﬁrst, the process for heat-treatment of the samples has been introduced and detailed
described. Samples with diﬀerent grades has been annealed and normalized with vacuum furnace
to change the grain size of samples. Following this, the steel microstructure analysis have been
performed to obtain the grain structure images using optical microscopy. Imaging analysis will
be performed to obtain the statistical information and metrics about the pipe steel microstructure,
such as grain size distribution. Next, surface hardness measurements have been performed using
Vickers hardness testers. And the optimization algorithm has been introduced.

20

CHAPTER 3

EXPERIMENT SET-UP FOR MBN

3.1 Schematic

Fig. 31 shows the schematic and physical prototype for the experiment setting. The MBN
signal is generated by discontinuous movements of domain walls when low-frequency sinusoidal or
triangular signal magnetic ﬁeld (5Hz) is applied. Pick-up coils attached near the surface of samples
with the diﬀerent number of turns (80 turns, 200 turns, 400 turns) are ﬂexibly connected with
other parts of the experimental apparatus and are used to detect Barkhausen signals. Filtering and
amplifying circuit with passband 0.5 to 200 kHz is used to ﬁlter out the low-frequency excitation
signal, harmonic and high-frequency background noise and to amplify the MBN signal to millivolt
level. Barkhausen noise signals detected by the coil and applied signal measured from resistance
in series with excitation coils were captured by the data acquiring card with the sampling rate of
200 kHz/s.

Figure 31: The schematic and physical prototype for the experimental setup

21

(a)

(b)

Figure 32: Printed circuit board to hold the hall senor

3.1.1 Hall sensor

To get the corresponding relationship between the realistic magnetic ﬁeld the sample experienced
and the timing when Magnetic Barkhausen Noise generated, we introduce one hall sensor which
can measure the magnetic ﬂux directly. To hold the small sensor, we design a simple PCB and
connect the components to the circuit (Fig. 32). The chip with three pins is our linear hall-eﬀective
sensor SS39ET from Honeywell. With supplied voltage amplitude 5 V, the relationship of the
output voltage and magnetic ﬂux with the units gauss has been shown in Fig. 33. The sensor can
measure a wide range of magnetic ﬂux density that between -1000 gauss to 1000 gauss and with a
high sensitivity 1.4 mv/gauss. With the hall sensor, we can know the magnetic ﬁeld between two
poles directly.

Figure 33: Transfer characteristics of Hall sensor

22

3.1.2 Sensor Holder design and sensor coil connection

Based on the original experiment setup, to keep the relative position of excitation core and pick-up
coil consistently, we design a holder to integrate the excitation part and pick up part. The model
of the holder is designed with software Auto CAD. Fig. 34 shows the schematic and physical
prototype for the holder. The hollow quadrangular prism on the left-hand side is used to fasten the
holder to the pole of the magnetic core. The size of the hollow prism is designed to ﬁt the magnetic
core. On the right-hand side, there is a sensor holder to hold the cylinder like pick up coil. On the
top of the sensor holder, one hole is designed to allow the wire to reach out.

Figure 34: Transfer characteristics of Hall sensor

To investigate the inﬂuence of pickup sensor, pickup coils with the diﬀerent number of turns
(Fig. 36) has been introduced in the experiment. From the Fig. 35, the sensor and other parts of
the experiment are ﬂexibly connected for easy replacement.

3.2 Data acquiring and storing

The processed analog signal can be acquired by NI PCI device combining with LABVIEW
sampling program to convert the analog signal into the digital signal for further processing in the

23

Figure 35: Transfer characteristics of Hall sensor

Figure 36: Transfer characteristics of Hall sensor

computer. The maximal sampling rate for the NI card is 500 kHz/s. The LABVIEW program
diagram is shown in Fig. 37. The sampling program consists of the establishment of the physical
channel, setting of the sample clock, reading the sample data and writing the data to ﬁle. At ﬁrst,
we should set the pysical channel of the input signal. For the NI card we are using, it can support
multi-channel input and output simultaneously. And then, due to the signal type we are measuring
is voltage, we set the acquisition mode as continuous voltage input. For the part of the setting of
the sample clock, considering the maximum frequency of the signal and the speed of reading and
writing of the data acquisition equipment, we choose the frequency of 200 kHz as the sampling
rate. For sample mode, we choose the continue sampling mode to get continue image on the front
panel until we turn oﬀ the button. The data acquisition is done in a while loop and the recarded
data is saved in a lvm ﬁle for postprocessing in MATLAB. To get the frequency spectrum of the
signal directly from the front panel, we can carry on the FFT transformation on the original signal.

24

Fig. 38 shows the front panel when the input is a 100Hz sin signal. In the front panel, there are
some buttons to control the maximum and minimum value for input voltage. We set the limitation
for input voltage to 10 V and -10 V separately. And we can choose the acquisition channel with
the button the DAQmx Pythsical channel. The maximal number of channels for the device is
two considering the maximal sampling rate of the NI card and the sampling rate we choose for
acquisition. One is for our excitation signal, and another is for the Magnetic Barkhausen Noise.
Both of the two channels wavelets would show at the same time on the time waveform window, and
their corresponding frequency spectrums would show on the spectrum window. The front panel
can show the waveform simultaneously as the data acquired.

Figure 37: The schematic of the Labview program

3.3 Data processing and parameter extraction

3.3.1 Root mean square

The value of root-mean-square as the most popular methods to show the intensity of the Barkhausen
noise is intimately linked with the properties of metals. The expression for calculating the RMS of
the noise is shown in below.

RMS =

X2
i

(3.1)

(cid:118)(cid:117)(cid:116) 1

n

N

i=1

25

Figure 38: The front panel of the Labview program

For some experiment, they are using RMS voltage meter to get the parameter directly. We can
also get the value by MATLAB function rms for the Magnetic Barkhausen Noise signal acquired.

3.3.2 MBN proﬁle

MBN signals repeat every half period and usually occur around the zero cross point of the excitation
signal, as shown in the Fig. 39. The blue triangular waveform is the excitational signal measured
by hall sensor and the orange signal is the MBN signal. To remove the noise in the signal, an
average of ten half-periods of MBN signals have been taken for subsequent data processing and
analysis. To determine the start points for one period, we introduce the minimal point of excitation
magnetic ﬁeld measured by hall sensor as the indicator for start of the period. It is easy to ﬁnd
the zero cross point of the excitation signal with MATLAB program and the minimum point of the
periodic signal can be obtained by adding 1/4 period after zero cross point. From Fig. 310, we can
ﬁnd that the original signal measured from hall sensor is not smooth enough to check the zero cross
point. It is better to ﬁlter the original signal with moving average with window size 50 points. The

26

signal processed (red line) overlaps with the original one and is smoother than before. Fig. 311
shows the averaged Magnetic Barkhausen Noise and corresponding excitation signal plot against
time. In consideration of the randomness of MBN, to get relative robust and reliable parameters,
parameters are obtained from averaged MBN signals.

Figure 39: Magnetic Barkhausen Noise periodic signal

The proﬁle of the MBN signal is extracted as a plot of RMS calculated with the adjustable
window size of 1/40 of the points per period as a function of the magnetic ﬁeld measured by hall
sensor. The output signal for the hall sensor is voltage signal. With the transfer characteristics of
the Hall sensor, we can get the B, magnetic ﬂux density, describes the ﬁeld felt by objects. With the
formula H=B/µ0, we can calculate the magnetic strength which is the same when the hall sensor is
close to the surface of the sample. Fig. 312 shows the Magnetic Barkhausen Noise proﬁle and the
peak position and value detected. The peak value and the position are detected by MATLAB code
to feed back the maximum point of the proﬁle and corresponding position for the point.

27

Figure 310: Magnetic Barkhausen Noise signal for one period

Figure 311: Magnetic Barkhausen Noise signal for one period

28

Figure 312: Magnetic Barkhausen Noise proﬁle

3.3.3 Frequency spectrum

The frequency spectrum of the MBN signal has been determined from the Fast Fourier Transfor-
mation (FFT) of the time-domain signals. Fig.313 shows the frequency spectrum of the sample
1008, the frequency proﬁle and ﬁtted proﬁle correspondingly. The proﬁle of the intensity of the
frequency response has been extracted by moving average with the window size of 1000 data points.
To extract the parameter peak of frequency intensity, a smooth proﬁle has been obtained by ﬁtting
the original one with a 15-degree polynomial.

3.4 Optimization program

To optimize the magnetic core of the sensor, advanced optimization algorithm NSGA III has
been adopted and implemented. Fig. 314 shows the procedure of the optimization. To calculate
the magnetic ﬁeld at the center of two poles, a 3D model has been built in the ANSYSEM software.
To reduce the simulation time it takes, half model with one symmetric boundary has been used
to gain the same result. The python code as an interface between MATLAB code and simulation

29

Figure 313: Frequency spectrum, frequency proﬁle and ﬁtted curve of sample 1008

software ANSYSEM, can call ANSYSEM project and feed the population points into the variables
to change the shape of the core in the model. And then the magnetic ﬁeld value can be obtained
from one text ﬁle saved after simulation procedure.

Three objectives which are important for the design of the sensor for a special sample. One is
to maximize the magnetic ﬁeld at the center of two poles for the pick-up coil to gain a relatively
strong signal. The second one is to minimize the overall eﬀective area of the magnetic core to
obtain a good spatial resolution. Also, the sample shape should be taken into consideration. The
large gap between poles of the magnetic core and the pipeline sample can aﬀect magnetic coupling
and result in the lower magnetic ﬁeld inside the sample. To design a sensor which is good for both
the worse situation, the pipeline sample with outside diameter 6 inches and the best situation, the
ﬂat sample, two models have been built. A, b, c deﬁned in Fig. 315 are important variables which
can control the shape of the core directly. a and b as the length and width of poles have an inﬂuence
on the contact area between core and samples. c determines the distance between two poles and
is related to the number of turns of excitation coils winded around. As a result, in the model, the
excitation signal is set linear to the parameter c. The height of the magnetic core is not taken into

30

012345678910Frequency /Hz10400.511.522.5Intensity10-3Frequency specturmFrequency profileFitted lineconsideration in the optimization and keeps it as a constant.

Figure 314: Flowchart of optimization and ANSYSEM models

Figure 315: Variables and objectives for optimization

3.5 Summary

In this chapter, the detail of experiment set-up has been introduced, including the physical
prototype for the excitation part as well as the software design for the data acquisation and storage.
And then the basic parameters for MBN signal have been introduced and explained, like root mean
square, MBN proﬁle, and MBN frequency spectrum. All of those parameters are extracted by
MATLAB code. Next, the process for optimization of the magnetic core with NSGA III has been

31

described. We introduce ANSYSEM software to calculate the magnetic ﬁeld with ﬁnite element
method. And the objects and variables have been presented.

32

CHAPTER 4

EXPERIMENT SET-UP FOR MAE

4.1 Schematic and sensor of MAE experiment

The schematic of the MAE experiment is quite the same with the experiment set-up of MBN
including signal generator, power ampliﬁer, sensor, signal ﬁlter and ampliﬁer and data acquisition
card as shown in the Fig. 41. What is special for the MAE experiment is that, instead of magnetic
coil, the MAE signal is obtained by a wide-band acoustic emission sensor made by piezoelectric
materials. The structure of the acoustic emission sensor is shown in the Fig. 43 (a). Piezoelectric
material is a kind of smart material which exsists the linear electromechanical interaction between
the mechanical and the electrical state in crystalline materials. The acoustic emission sensor
employs the reverse piezoelectric eﬀect which is the internal generation of electrical charge resulting
from an applied mechanical force. The movement of the domain wall during magnetization would
generate acoustic waves with low amplitude and high-frequency (50 kHz-1 MHz). Those acoustic
waves can be detected by piezoelectric crystal inside the acoustic emission sensor which give rise
to structure deformation of the crystal lattice and occurrence of electric dipole moments in solids.
And this can generate electrical current changing with the magnitude of mechanical stress. The
Fig. 43 (b) shows a ﬂat sensitivity from 100 kHz to 1 MHz, which is a wide-band acoustic emission
sensor.

An essential requirement in mounting a sensor is suﬃcient acoustic coupling between the sensor
surface and the structure surface. The ﬁrst thing is to make sure that the sensor’s surface is smooth
and clean, allowing for maximum couplant adhesion. What is more, application of a thin layer
couplant can ﬁll gaps caused by surface roughness and eliminate airgaps to ensure good acoustic
transmission.

33

Figure 41: Schematic for the MAE experiment set-up

Figure 42: physical prototype for the sensor

(a)

(b)

Figure 43: Wide-band AE sensor and frequency response

34

4.2 Data processing

4.2.1 Package tsfresh

Tsfresh is a python package. It automatically calculates a large number of characteristics of time
series signals, the so called features, including simple statistical features such as min, max and
mean and frequency spectrum features. Further the package contains methods to evaluate the
explaining power and importance of such characteristics for regression or classiﬁcation tasks.
In the process of feature extaction, there are three dictionaries predeﬁned to selection. The
ComprehensiveFCParameters includes all 788 features without parameters and with parameters.
The MinimalFCParameters can be used for quick tests including around 8 features which have
the "minimal" attribute. The E f f icientFCParameters contains almost the same features as
in ComprehensiveFCParameters except those features are marked with the "high_comp_cost"
attribute. This can save the runtime and memory of the process and is selected in our experiment.
The all-relevant problem of feature selection is the identiﬁcation of all strongly and weakly
relevant attributes. This problem is especially hard to solve for time series classiﬁcation and
regression in industrial applications. To limit the number of irrelevant features, tsfresh deploys
the algorithem for feature selection. It is an eﬃcient, scalable feature extraction algorithm, which
ﬁlters the available features in an early stage of the machine learning pipeline with respect to their
signiﬁcance for the classiﬁcation or regression task, while controlling the expected percentage
of selected but irrelevant features. The procedures for feature selection follow three steps and
are skeched with Fig. 44. At ﬁrst, a comprehensive and well-established feature cluster has
been extracted to discribe the raw time series signals. In the second step, each feature vector is
individually and independently evaluated with respect to its signiﬁcance for predicting the target
under investigation. The results of the tests is the vector of p-values, quantifying the signiﬁcance
of each feature for predicting the target. And then the vector of p-values is evaluated on basis of
Benjamini-Yekutieli procedure [43] to determine which features to keep.

35

Figure 44: schematic of tsfresh

4.2.2 Linear regression

In statistics, Linear regression is a regression analysis of the relationship between a scalar dependent
variable and one or more explanatory variables using a least-squares function. The case of one
explanatory variable is called simple linear regression. For more than one explanatory variable,
like the situation in our experiment, the process is called multiple linear regression.

In our experiment, the goal is to predict the hardness and grain size with features extracted from
MAE signals. In this case, linear regression can be trained to ﬁt a predictive model to an observed
data set of hardness and grain size values of the sample and corresponding features.

4.2.3 Data preparation

Data preparation is done by MATLAB code to segment the periodic MAE signal into one period
signal. For each periods of signal contains 20,000 points. And for each samples, we are using
100 signals as the datasets. So there is 900 signals and around 18,000,000 points. It is a large

36

dataset, to improve the eﬃciency and save the run time, the E f f icientFCParameters dictionary
has been used for feature extraction. The data is integrated and rearranged into the format of data
input required for the package.

4.3 Summary

The experiment set-up, priciple of the sensor and data processing procedure for MAE signal
has been introduced in this section. Instead of magnetic coils, the MAE signal is measured by
acoustic emission sensor made by piezoelectric materials which has ﬂat frequency response over
a wide-band. Data processing of the MAE signals is done by using the python package tsfresh. It
is a package special for extracting and selecting features of time series signals. And then a linear
regression model is followed to predict the hardness and grain size of the samples.

37

CHAPTER 5

RESULTS

5.1 Optimization results

5.1.1 MBN signals for diﬀerent of pick-up coils

To investigate the inﬂuence of the diﬀerent number of turns of pick-up coils to the MBN signal,
three diﬀerent coils (80 turns, 200 turns, 400 turns) have been prepared in NDE Lab to measure
the MBN emission with the same excitation signal. Fig. 51 shows the normalized MBN proﬁles,
which have been divided by the peak values of each original proﬁle. There is no obvious shift in
the peak positions of proﬁles for signals detected with diﬀerent pick-up coils. All peaks overlap
with each other, whereas with the increase of the number of turns, the signal-to-noise ratio (SNR)
has improved dramatically. The noise can be deﬁned as the area below the minimal value of the
MBN proﬁle.

Fig. 52 shows the normalized MBN frequency spectrum proﬁle over bandwidth 0 to 100 kHz
obtained from the time-domain signals above. The frequency spectrum proﬁle is used to show the
intensity changes along the bandwidth. Considering that the intensity changes with the number
of turns of pick-up coils, normalized proﬁles can put them on the same scale and make them
comparable. For the same MBN signal, it is obvious that the sensor with the larger number of turns
is more sensitive to the low frequency. The coil of 400 turns has a higher intensity in bandwidth
from 20 kHz to 60 kHz. The high-intensity frequency response of the coil with 200 turns shifts
to bandwidth from 60 kHz to 100 kHz. For the 80-turn coil, the frequency response is almost ﬂat
over the whole bandwidth, except for some impulses related to noise.

38

Figure 51: Normalized MBN proﬁle

Figure 52: Normalized MBN frequency response

39

-3000-2500-2000-1500-1000-5000500100015002000Magnetic field H/(A/m)00.10.20.30.40.50.60.70.80.91Normalized intensity80 turns200 turns400 turnsNoise012345678910Frequency/Hz1040.750.80.850.90.951Normalized intensity80 turns200 turns400 turns5.1.2 Sensor optimization with NSGA III

(cid:118)(cid:117)(cid:116) m

3

i=1

The following Fig. 53 shows the Pareto fronts gotten from the NSGA III algorithm. The points
on the surface is a set of optimal points in the objective ﬁeld. For decision-making, the L2 norm
method with idea point as the reference point is used to ﬁnd one adequate point in the Pareto front.
The deﬁnation of L2 norm method can be destribed as the formula:

fi − zi
− f min
m is the number of objectes and z is the idea point. wi, f max

d = min(

f max
i

wi(

i=1

i

)2)

i

− f min

and f min

are the weight, maximal
value and minimal value for the ith object. The values for each of the objects are normalized by
deviding f max
. By slightly changing the weight, diﬀerent combinations of objectives have
been gotten and shown in Table 52. Compared with the original design, the eﬀective areas of point
1, 2, 3 decrease a lot at small sacriﬁces for the magnetic ﬁeld. Performance improvement ratios
deﬁned as:

i

i

i

(5.1)

m =

optimizedi − originali

originali

(5.2)

It is calculated by summing up the improvement ratio for each objectives. From the result, it

suggests that the optimized points are better than the original design.

Table 51: Decision making with L2 norm with diﬀerent weight

Point 3 Original design
Point 1 Point 2
(1,3,3)
(1,2,2)
(1,1,1)
Wight
Eﬀective area (mm2)
2377.17
876.60
1634.14
465.59
461.04
383.61
Magnetic ﬁeld of pipeline H (A/m)
831.19
691.05
Magnetic ﬁeld of ﬂat sample H (A/m) 537.21
22.65
14.10
21.89
a (mm)
23.48
20.04
17.6
b (mm)
21.49
55.91
37.74
c (mm)
11.97% 17.23% 6.36%
Performance improvement ratio

2500
490.7
780
25
25
50

40

Figure 53: Pareto front in objective ﬁeld

5.2 Carbon content eﬀect on the MBN signal

Proﬁles of MBN signals are plotted against the real-time ﬁeld measured by integrated Hall
sensor. Due to the nonlinearity during the magnetization and diﬀerent magnetic permeability of
various samples, there are diﬀerences of positive and negative Hmax for the same and diﬀerent
samples. Proﬁles of MBN signal of samples 1008, A36 and 1018 in Fig. 24 show obvious slope
changes in the high magnetic ﬁeld strength which can be taken as second peaks. For steel 1026,
even though there is no sharp slope change from the proﬁle, it can be explained by the reason
that the second peak merged with the ﬁrst one depending on the distribution of pinning strength of
microstructural obstacles in response to a given range of magnetization which has been described in
previous studies [44]. For the property observed in the ﬁgure, two Gaussian curves have been used
to ﬁt two peaks in MBN proﬁles separately. The ﬁrst peak in low magnetic ﬁeld strength is related

41

(a) 1008

(b) A36

(c) 1018

(d) 1026

Figure 54: Measured MBN proﬁles ﬁtted with two Gaussian curves

to the nucleation and annihilation of domain walls in grain boundaries of ferrite and the second
peak at higher amplitude position indicates the displacement of domain walls due to the second
phase particles which are harder pearlites in samples [40]. It is obvious that the shapes of proﬁles
for diﬀerent samples change slightly with the change of the relative position of two peaks. From
(a) to (d) in Fig. 54, the gaps between two peaks (∆G) deﬁned as the diﬀerence of mean values of
two Gaussian distributions become smaller with the increase of the carbon content. A plot of the
parameter (∆G) and carbon content for four samples is given in Fig. 58. Most of the experimental
results collected by multiple measurements lie around the ﬁtted line suggests the reliability of the
data.

42

-2000-1500-1000-500050010001500H/(A/m)00.010.020.030.040.050.060.07Voltage/V1008 MBN profilefitted curveGaussian 1Gaussian 2262.259-2500-2000-1500-1000-500050010001500H/(A/m)00.010.020.030.040.050.060.070.080.090.1Voltage/VASTM-36 MBN profilefitted curveGaussian 1Gaussian 2189.81-2500-2000-1500-1000-5000500100015002000H/(A/m)00.010.020.030.040.050.060.070.080.09Voltage/V1018 MBN profilefitted curveGaussian 1Gaussian 276.69-2500-2000-1500-1000-500050010001500H/(A/m)00.010.020.030.040.050.060.07Voltage/V1026 MBN profilefitted curveGaussian 1Gaussian 2-10.6Figure 55: The gaps between two peaks for both simulated and experimental results as a function
of carbon contents

5.3 Grain size eﬀect on MBN frequency spectrum

5.3.1 Grain size eﬀect on MBN frequency spectrum

Grain size as a signiﬁcant microstructural property has an important inﬂuence on the MBN signals.
A Hall-Petch type relationship between the grain-size and the MBN power observed for polycrys-
talline iron was found. The relationship can be described by the formula MBN =Cg • d−1/2
[23].
Grain size also has an inﬂuence on the frequency spectrum of the MBN signal. The relationship
between the length of the wall displacement between pinning obstacles and the local magnetic
moment is described as the following formula:

g

δ (cid:174)m = (cid:174)β((cid:174)S · δ(cid:174)l)

(5.3)
(cid:174)β is a coeﬃcient related to the type of domain wall and atomic magnetic moment. (cid:174)S is the face of
moving Bloch wall. δ(cid:174)l is the length between two pinning obstacles associated with microstructure
morphology closely, which can be further expressed as δ(cid:174)l = (cid:174)v· δt. (cid:174)v is the average wall velocity and

43

δt is the time interval between two pinned states. Frequency content can roughly be characterized
by f=1/δt [24].

With the decrease of the grain size, there are more pinning sets around grain boundaries, and this
fact results in the short displacement length δ(cid:174)l, which further leads to the increase of the frequency
content. Fig. 56 shows the ﬁtted frequency spectrum proﬁle of samples with the excitation voltage
of 700 mv generated by the signal generator. The lines in the same color stand for the same samples
with diﬀerent heat treatment processes. Steel 1008 groups with large grain sizes from 32 µm to 40
µm have obvious sharp peaks in the low-frequency regions. Whereas, the peak positions of steel
A36 and 1018 with ﬁne grains are moving to the high-frequency ranges. From Table 21 and Fig.24,
the grain size for each kind of samples with diﬀerent heat treatment processes is following the same
trend where samples after normalizing are larger than samples without heat treatment and smaller
than samples after annealing. When we take a look at lines with the same color, the peak positions
are increasing with the decrease of the grain size from annealed samples to samples without heat
treatment.

The relationship between grain size and main frequency content has been plotted in the Fig.
57. Each point in Fig. 57 is obtained by taking the average of results from multiple measurements
to get reliable parameters. The relationship between grain size and frequency peak position are
perfectly ﬁtted by the power function.

Fpp = 1.0022E + 06 ∗ Gs−1.349

(5.4)

(Fpp stands for frequency peak position of MBN signal and Gs is grain size of the sample). The
sensitivity of the parameter, frequency peak position, increases when the grain size of samples
decreases. For those samples with ﬁne grain, small changes in grain size will result in a large
shift of the frequency peak, whereas those samples with the coarse grain (larger than 15 µm), the
frequency peak position has good linearity with grain size. Fig. 58 shows the linear relationship
between frequency peak position and samples with the grain size larger than 15 µm.

44

Figure 56: Fitted MBN frequency proﬁles of diﬀerent samples

Figure 57: MBN frequency response peak position as a function of grain size

45

012345678910Freq/Hz1044.555.566.577.588.59Intensity10-41008A10081008N1018A10181018NA36AA36A36NFigure 58: MBN frequency response peak position as a function of grain size (grain size larger
than 15 µm)

Figure 59: MBN frequency response peak position and grain size for each samples (high amplitude
excitation signal)

46

5.3.2 Excitation signal eﬀect on MBN frequency spectrum

It has been showed that the MBN time-domain proﬁle would show two peaks for steels with two-
phase of particles when the applied magnetic ﬁeld is high enough. The ﬁrst peak in low magnetic
ﬁeld strength is related to the nucleation and annihilation of domain walls in grain boundaries of
ferrite and the second peak at higher amplitude position indicates the displacement of domain walls
due to the second phase particles [40]. The intensity of the second peak will increase as the applied
magnetic ﬁeld increases [45]. The excitation signal also inﬂuences the frequency spectrum.

Previous works show the results with the excitation signal of 700 mV. When increasing the
excitation signal from signal generator to 1.2 V, the frequency peak of samples normalized A36,
annealed 1018 and normalized 1018 have been shifted to a higher frequency from the original
position (Fig.59). Frequency proﬁles in Fig.510 are from the same sample with diﬀerent excitation
signal amplitudes. They show two peaks for both proﬁles and the second peak intensity increases a
lot with the increase of excitation signal. It is because that when the excitation voltage increases, the
MBN signal that comes from the second phase particles, which are harder pearlites for low carbon
samples, has been increased. Pearlite is a two-phase, lamellar structure composed of alternating
layers of ferrite (88 wt%) and cementite (12 wt%). It usually has more pins and is diﬃcult for
magnetization. As a result, the frequency response for pearlite is in high-frequency regions, and
this is consistent with previous works [24]. This fact results in the increase of the second peak of
the frequency proﬁle for samples with large proportions of second phase particles. It can be further
conﬁrmed by the fact that samples normalized A36, annealed 1018 and normalized 1018 all have
large proportions of second phase particles. The second peaks of the frequency spectrum are in the
region from 40 kHz to 50 kHz, and this overlaps with the frequency region of samples 1018 and
A36. This explains why samples 1018 and A36 do not show a small frequency peak shift when
excitation signal increases.

47

(a) 1018 annealed

(b) 1018 normalied

Figure 510: Fitted MBN frequency response peak proﬁle for samples with diﬀerent excitation

signal

(c) A36 normalized

48

012345678910Freq/Hz1045.45.65.866.26.46.6Intensity10-41018A 700mv1018A 1.2vFirst peakSecond peak012345678910Freq/Hz1046.66.877.27.47.67.888.2Intensity10-41018N 700mv1018N 1.2vFirst peakSecond peak012345678910Freq/Hz1045.85.966.16.26.36.46.56.66.76.8Intensity10-4A36N 700mvA36N 1.2vSecond peakFirst peakFigure 511: MBN frequency response peak position as a function of grain size (high amplitude
excitation signal)

5.3.3 Predict hardness with parameter frequency peak position

The grain size has a strong eﬀect on the mechanical behavior of the materials. For mild steel,
the grain reﬁnement can enhance the hardness. This grain-size dependence is described by the
Hall-Petch relation.

H = H0 + K • Gs−1/2

(5.5)

Where H0 is the hardness of an indeﬁnitely large, error-prone grain, and K is the Hall-Petch
constant, which describes the grain boundary structure. Gs is the average grain size, and H is
the hardness of a diﬀerent kind of steel. The relationship between hardness measured by Vickers
hardness tester and grain size has been plotted in Fig. 512. The parameter H0 and K can be
predicted from Fig. 512, which are 10.237 and 531.32 respectively for mild steel.

With combination equation 5.4 and equation 5.5 mentioned before, it is easy to obtain a
relationship between hardness H and parameter frequency peak position Fpp. The relationship
can be described by the following equation:

49

Figure 512: Hardness as a function of grain size

H = H0 + K • (Fpp/1E + 06)0.371

(5.6)

Therefore, with the equation 5.6, the hardness of the mild steel can be predicted, and Fig. 513
shows values for predicted hardness and hardness measured by Vickers hardness tester. The results
show good accuracy for prediction and the errors are less than 10%.

Figure 513: Predicted hardness and hardness measured by Vickers hardness tester

50

Table 52: Predicted hardness and corresponding error of steel samples

Samples Vickers hardness Predicted hardness
1008
A36
1018
1008 A
A36 A
1018 A
1008 N
A36 N
1018 N

105.99
179.92
181.98
97.08
116.27
117.68
102.72
130.82
121.05

110.21
172.19
185.33
95.06
116.33
118.81
99.71
120.7
133.43

error
-3.8%
4.5%
-1.8%
2.1%
-0.05%
-0.9%
3.0%
8.3%
-9.3%

5.4 Predict grain size and hardness with MAE signal

Fig. 514 shows the result for predited grain size with diﬀerent datasets. The coeﬃcient of
determination (R2) for those three samples are 0.49, 0.91 and 0.94 respectly, which means that the
accuracy for prediction increases with the increase of the number of datasets. With the increase of
the dataset, the training of the network would be better for ﬁnding the relationship between features
and the properties of steels. To make sure the data train well and considering the computitional
time for training, we are using 900 samples in our dataset.

(a) 99 samples

(b) 270 samples

(c) 900 samples

Figure 514: Predicted grain size with diﬀerent datasets

Fig. 515 and Fig. 516 show the results for predicted grain size and hardness with MAE signals.
Compared with (a) and (b) in both ﬁgures, they show that the accuracy for prediction would increase
a lot when the irrelevant features are eliminated. Because those irrelevant features like noise which
can disturb the prediction. After feature selection, the total number of features is droped to 229

51

10152025303540Actual grain size/um1020304050Predicted grain size/um(a) Predicted grain size without feature selection

(b) Predicted grain size with feature selection

Figure 515: Predicted grain size with MAE signal and actual grain size

(a) Predicted hardness without feature selection

(b) Predicted hardness with feature selection

Figure 516: Predicted hardness with MAE signal and hardness measured by Vickers hardness

tester

from 788, which could slim the network, save the computional cost and accelerate the speed. It is
very important when the number of samples increase dramatically. And the ﬁnal predicted results
with coeﬃcient of determination (R2) 0.94 are well trained to predict the properties of sample
steels.

5.5 Summary

In this chapter, the results for research have been described detailedly. At ﬁrst, the optimizations
of the pick-up coil and magnetic core have been introduced. Secondly, some new parameters of
MBN siganl have been extracted and the relationship between those parameters and properties of

52

10152025303540Actual grain size/um1020304050Predicted grain size/um100120140160180Actual hardness80100120140160180200Predicted hardnesssteel has been investigated. Thirdly, the machine learning method has been introduced for MAE
signal feature extraction and steel sample properties’ prediction.

53

CHAPTER 6

CONCLUSION AND FUTURE WORK

6.1 Conclusion

In this thesis, Magnetic Barkhausen Noise (MBN) measurements were conducted on various
mild steels with diﬀerent heat-treatments. New parameters were introduced to quantiﬁcationally
characterize the inﬂuence of microstructural and mechanical properties, including carbon content,
grain size, and hardness, of sample steels and following conclusions were obtained:

1. Sensor optimization has been introduced in the present study. Three coils with the diﬀerent
number of turns have been compared for sensitivity. The result shows that pick-up coils with a
larger number of turns have higher SNR and are sensitive to lower frequency response.

2. For the optimization for the magnetic core, NSGA III has been introduced and applied to
design a magnetic core with small size, high magnetic ﬁeld, and suit for diﬀerent diameter pipelines.
3. In the experiment, the shape of proﬁles of MBN signals is changed with carbon content.
By extracting parameter with two ﬁtted Gaussian curves, a linear relationship has been revealed
between gaps and carbon content of samples.

4. The experimental work shows that the peaks of frequency responses of the MBN signals
move to higher frequency with the decrease of grain size, which results from the decrease of the
length between two obstacles with the decrease of grain size. The relationship can be perfectly
ﬁtted by the function Fpp = 1E + 06 ∗ Gs−1.349. As a result, with the information of MBN
frequency spectrum, the grain size of the sample can be inferred.

5. The grain size has a strong eﬀect on the mechanical properties of the steels. The grain size
dependence of hardness of steels can be described by Hall-Petch relationship. Therefore, the Fpp
can also be an eﬃcient parameter to predict the hardness of the steels.

6. The inﬂuence of the excitation signal also has been investigated. With the increase of the
excitation signal, the part of MBN signal that comes from the second phase particles has been

54

increased and this results in the increase of the second peak of the MBN frequency spectrum for
samples with a large portion of pearlite. The frequency peak position of those samples moves to a
higher frequency. As a result, the parameter Fpp is good to predict the grain size of ferrite with a
smaller applied magnetic ﬁeld.

7. By using the package tsfresh, multi-features of MAE signal have been calculated and relevent
features have selected to predict the hardness and grain size of the samples. The result shows a
good accuracy.

6.2 Future work

According to previous works, MBN and MAE is a powerful tool to study and characterize
microstructural properties of low carbon steels. As for practical application, estimation of the basic
material properties, such as microstructure, composition as well as various surface mechanical
properties with the usage of acoustic and electromagnetic sensors can be fused and correlated to
a multimodal system to integrate these and obtain a probabilistic strength and toughness with a
high degree of accuracy. Therefore, it is important to link the parameters of MBN and MAE signal
to more microstructural properties of aging steel and tailor the MBN and MAE system for multi-
parameter microstructural properties study through sensor optimization, advanced data processing,
and statistical modeling.

What is more, existing techniques focus on the single modality deterministic estimation of pipe
strength and ignores inhomogeneousity and uncertainties. In view of this, a novel information fusion
framework using multimodality diagnosis for pipe materials is proposed for accurate probabilistic
strength and toughness estimation under uncertainties. Advanced data analysis using Gaussian
Processing model will be performed for surrogate modeling and uncertainty quantiﬁcation. A
generalized Bayesian network methodology is proposed to fuse multiple sources of information
from the multimodality diagnosis results. Probabilistic pipe strength and toughness estimation is
inferred based on the posterior distribution after information fusion. If successful, this study can
help to accurately and eﬀectively assess the reliability of pipeline systems, and eventually help the

55

decision making process to balance the pipeline safety and economical operations.

56

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57

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