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Impact of Geospatial Classification
Method on Interpretation
of Intelligent Compaction Data
Mehran Mazari, Cesar Tirado, Soheil Nazarian, and Raed Aldouri
Administration in 1974. In 1975, Geodynamik was founded to continue the development of roller-mounted compaction meters (3).
Later, Geodynamik and Dynapac introduced the compaction meter
value to monitor the roller-integrated compaction process. For the
following five years, a number of roller manufacturers began offering
systems that used compaction meter values. In 1982, Bomag introduced the omega value (which was a measure of compaction energy
and time) and Terrameter. With the introduction of mechanistic and
performance-related soil properties, Bomag launched the vibration
modulus as a measure of dynamic soil stiffness. In 1999, Ammann
introduced the soil stiffness parameter, followed by the compaction
control value of SAKAI in 2004. The IC systems have been under
continuous development since then.
The IC data, in the generic form of intelligent compaction measurement values (ICMV), are best described and interpreted as colorcoded maps. These maps, which are also known as choropleth or
thematic maps, display the geo-referenced or spatial data on a map in
which each class is separated by color. An understanding of the spatial
pattern of the ICMV data depends on the optimal selection of both
the number of classes and the values of the breaks between classes.
The use of more than three colors is common in many geospatial and
cartographic analyses. In the case of IC data, assigning the three colors
to be gray, light gray, and dark gray was considered practical. The
ultimate goal of using the ICMV color-coded maps is to identify lessstiff areas (often marked as red spots but appearing as dark gray in this
paper) and to improve the uniformity of compaction throughout the
construction area. Supplemental spot tests could then be suggested
within the identified less-stiff areas to investigate the mechanistic and
the moisture and density properties of the compacted geomaterials as
part of the quality control process.
A number of studies have been dedicated to investigating different
geospatial classification techniques. Brewer and Pickle evaluated the
impact of a few classification methods on the interpretation of the
geo-referenced data (4). They recommended the quantile method,
followed by the natural breaks method and a modified version of
the equal intervals method, to describe the spatial data effectively.
Osaragi evaluated the performance of several classification methods
on different sets of population data using the principles of information theory and data entropy (5). He concluded that the distribution of
the geospatial data affected the selection of the optimal classification
approach.
Xiao et al. highlighted the effects of geospatial data uncertainty
on the classification method (6). They defined a minimum classification uncertainty level and an overall classification robustness
factor. The latter term was defined as the proportion of data that
met a minimum uncertainty threshold. Xiao et al. concluded that a
Intelligent compaction is an emerging technology in the management
of pavement layers, more specifically, of unbound geomaterial layers.
Different types of intelligent compaction measurement values (ICMVs)
are available on the basis of the configuration of the roller, vibration
mechanism, and data collection and reduction algorithms. The spatial
distribution of the estimated ICMVs is usually displayed as a color-coded
map, with the ICMVs categorized into a number of classes with specific
color codes. The number of classes, as well as the values of the breaks
between classes, significantly affect the perception of compaction quality
during the quality management process. In this study, three sets of
ICMV data collected as a part of a field investigation were subjected to
geostatistical analyses to evaluate different classification scenarios and
their impact on the interpretation of the data. The classification techniques were evaluated on the basis of the information theory concept of
minimizing the information loss ratio. The effect of the ICMV distribution on the selection of the classification method was also studied. An
optimization technique was developed to find the optimal class breaks
that minimize the information loss ratio. The optimization algorithm
returned the best results, followed by the natural breaks and quantile
methods, which are suited to the skewness of the ICMV distribution.
The identification of less-stiff areas by using the methods presented will
assist highway agencies to improve process control approaches and
further evaluate construction quality criteria. Although the concepts
discussed can apply to any compacted geomaterial layer, the conclusions
apply to the type of compacted soil in this particular test section.
Intelligent compaction (IC) is an emerging technology for monitoring
the compaction of base and soil layers and for managing compaction
data to improve the quality of compacted layers. The advantages of
IC are reported as improved quality and uniformity, reduced overcompaction and undercompaction, better identification of less-stiff
spots, and increased lifetime of the roller (1, 2).
IC is a specific terminology for a wider concept belonging to
continuous compaction control, initiated by the Swedish Highway
M. Mazari, Civil Engineering Department, California State University, Los Angeles,
5151 State University Drive, Los Angeles, CA 90032. C. Tirado, Metallurgy
Building, Room M-105D; S. Nazarian, Engineering Building, Room A-207, Center
for Transportation Infrastructure Systems; and R. Aldouri, Center for Regional
Geospatial Service, Engineering Building, Room A-219, University of Texas at
El Paso, 500 West University Avenue, El Paso, TX 79968. Corresponding author:
M. Mazari, mmazari2@calstatela.edu.
Transportation Research Record: Journal of the Transportation Research Board,
No. 2657, 2017, pp. 37–46.
http://dx.doi.org/10.3141/2657-05
37
38
Transportation Research Record 2657
smaller number of classes would yield a more robust classification.
Sun and Wong introduced a modified natural breaks method that
ensured the statistical differences among the values that defined the
class breaks (7). Jiang proposed a new classification method for
geospatial data with heavy-tailed or positively skewed distributions,
called the head/tail breaks method (8). In that method, the number
of classes and class breaks was determined on the basis of the hierarchical levels among data. Jiang concluded that the head/tail method
was superior to the natural breaks algorithm for geo-referenced data
with heavy-tailed distributions.
The main objective of this research was to evaluate different
classification methods and their impact on the interpretation of
geospatial IC data. Three sets of ICMV data, collected along a test
section, were evaluated after being subjected to different classification
algorithms. The impact of the ICMV data distribution on the selection
of the class breaks was also studied. The following sections of the
paper first describe the principles of ICMV, followed by a description
of the process of data collection, the analysis, and the evaluation of
classification methods.
Intelligent Compaction Measurement Values
The concept of correlating the stiffness of the compacted layer to the
excitation frequency initiated the use of accelerometers to monitor
the compaction process (3). This idea was further improved and
became the basis of measurement for some of the IC roller vendors.
The acceleration-based ICMV is generically defined as given in
Equation 1:
A 
ICMV = C ×  4 
 A2 
(1)
vibration harmonics could also be identified during the compaction
process (3).
Field Investigation
Field investigation was carried out along US-67 near Cleburne, Texas.
The premapping of the existing embankment layer was followed by
the placement, compaction, and mapping of a 12-in. clayey layer.
A 500-ft-long and 25-ft-wide test section was selected to perform the
IC data collection. Three IC systems were employed to collect the
data during the premapping of the existing embankment layer. Two of
these IC systems were installed on the first roller; one was an original
equipment manufacturer system and the other one was a retrofit kit.
The third system was an original equipment manufacturer IC system
on the second roller. Once the process of field data collection was
completed, the ICMV data were exported in comma-separated values
format for further geospatial and geostatistical analyses.
Figure 1a illustrates the cumulative distributions of the ICMV
data collected by the three IC systems. IC Systems 1 and 2 provided
similar cumulative distributions of ICMVs, whereas IC System 3
yielded a slightly different pattern. The ICMV data are further demonstrated in the box plot format in Figure 1b. IC System 1 shows a
lower median and range of collected data; IC System 2 shows the
lowest interquartile range (IQR) among the three systems. (The IQR
is defined as the difference between the third and first quartiles.)
On the basis of the outlier analysis of IC System 2, ICMVs that
are greater than 56.9 and less than 8.1 (defined as 1.5 × IQR above
the third quartile or below the first quartile) can be categorized as
suspected outliers, illustrated in Figure 1b as bold dashes. The only
applicable outliers (defined as 3 × IQR above the third quartile or
below the first quartile) are shown as bold triangles in Figure 1b.
where
Statistical Analysis of ICMV Data
A2=acceleration of the forcing component of the vibration,
A4=acceleration of the first harmonic of the vibration, and
C=a constant value.
This type of ICMV takes only the forcing frequency and first harmonic
into account. However, if the compacted layer becomes stiffer, other
The descriptive statistics of the ICMVs from different IC systems are
summarized in Table 1. The mean ICMVs from the three systems are
close to one another. However, the standard deviation, and, as a result,
the coefficient of variation, of the third set is significantly greater
100
80%
80
ICMV
60%
ICMV
0
0
20
10
80
70
60
50
40
30
20
10
0
0%
40
IC System 1
IC System 2
IC System 3
M
20%
60
or
e
40%
90
Cumulative Frequency
100%
IC System 1
IC System 2
(b)
(a)
FIGURE 1 Illustration of (a) cumulative distribution of ICMVs and (b) box plots of ICMVs from IC systems.
IC System 3
Mazari, Tirado, Nazarian, and Aldouri
39
TABLE 1 Descriptive Statistics of ICMV Data
System
IC System 1
IC System 2
IC System 3
Mean
Median
Mode
SD
CV (%)
Skewness
Kurtosis
29.6
27.6
26.8
28.6
28.1
22.0
25.8
28.7
16.0
12.0
10.6
18.3
40.5
38.4
68.3
0.48
0.26
1.95
0.15
0.83
3.86
Note: CV = coefficient of variation.
collected ICMVs can affect the selection of the class breaks during
the classification of the data and also affect the interpretation of the
results. Furthermore, the Kurtosis statistic, which is similar to the
skewness and measures the heavy tails, shows that the ICMV data
from System 3 have the heaviest-tailed distribution (9).
Figure 2 compares the distributions of the three sets of ICMV
data. The mean (µ) and standard deviation (σ) values are also illustrated in that figure, appearing as vertical dashed and dash-dot lines,
than that of the other two. This could be because of the different
algorithm and mechanism of obtaining the ICMVs in that IC system.
The coefficient of variation of IC System 2 is the lowest of the three
systems.
The skewness of the third data set is significantly greater than that
of the first and second data sets. This means that the third set of ICMV
data contains a longer tail in the distribution curve and is positively
skewed compared with the other two sets of data. The skewness of the
800
1,000
700
900
800
700
+1σ
−1σ
500
400
Frequency
µ
300
+1σ
−1σ
600
500
µ
400
300
200
ICMV
ICMV
(a)
(b)
160
140
Frequency
120
100
+1σ
−1σ
80
µ
60
40
20
96
88
80
72
64
56
48
40
32
24
16
8
0
0
ICMV
(c)
FIGURE 2 Distribution of ICMV data from IC systems: (a) IC System 1, (b) IC System 2, and (c) IC System 3.
90
84
78
72
66
60
54
48
42
36
30
24
18
0
78
72
66
60
54
48
42
36
30
24
18
6
0
12
0
0
100
6
200
100
12
Frequency
600
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Transportation Research Record 2657
respectively. As in Table 1, the distribution of the ICMV data from
IC System 3 shows a long tail compared with the other two systems.
This fact is well illustrated in Figure 2c as the distribution shows a
positive skewness (right-hand tail). The following sections highlight
the impact of the distribution characteristics on the selection of the
classification method.
data. For the xi geospatial data (i.e., the ICMV data in this study),
the AIC statistic can be estimated from the following equation (5):
m
AIC = −2∑ ∑ xi log qˆ k + 2 ( m − 1)
(2)
k =1 i ∈Gk
where
xi=geospatial data,
m=number of classes,
q̂ k= Si∈Gk xi /Xnk
Evaluating the Classification Methods
Information and data classification are terms that apply to a wide
range of attributes. In the case of geospatial and geo-referenced data
(e.g., IC data), the choice of the classification method could significantly affect the interpretation of the collected information. In almost
every classification problem, two main issues should be addressed:
(a) the optimal number of classes to represent the geospatial data
and (b) the break values that define the boundaries among different
classes of data (5). The most common classification methods used in
the analysis of geospatial data will be applied to the IC data collected
by System 1, to compare the results and seek insight in selecting
the most optimized classification method.
Figure 3 illustrates implications of the ICMV classification. The
class breaks and the domain of each class are demonstrated on the
rank-size distribution, where the ICMV data are first sorted from
the greatest value to the least one; then the rank of each ICMV among
the total number of data is estimated (Figure 3a), and the cumulative
distribution graph is drawn (Figure 3b). The selection of the class
breaks significantly affects the number of data points within each
class and consequently impacts the interpretation of the produced
color-coded map.
One approach to finding the most suitable classification method
is to minimize the Akaike’s information criterion (AIC) among different classification techniques (10). The use of the AIC is popular in
the field of information theory. It involves minimizing the KullbackLeibler (KL) distance between the proposed model and the expected
targets. The KL distance has been used in information theory to measure the difference between two probability distributions; it shows
the amount of information loss or gain when migrating from one
probability distribution to another (11). Although the AIC statistic is
mainly applied to the selection of the best model in a set of information models, it could also be applied to the classification of geospatial
and
Gk=kth class of the data,
nk=number of data in class Gk,
X=global sum of xi data, and
n=total number of features.
The AIC statistic was calculated for four popular classification
methods in this study. Figure 4 illustrates the results of these classification methods as color-coded maps along with the frequency
distributions of the ICMV data from IC System 1. These methods
include the quantile, natural breaks, geometrical intervals, and equal
intervals methods. In the quantile method, each class contains an equal
number of data points. The natural breaks classification method (also
called the Jenks natural breaks classification method) breaks the data
into a specified number of classes on the basis of the maximization of
the difference, or variance-minimization, between the groups of data
(12). This method is also known as the goodness of variance fit (GVF)
to optimize the classification accuracy. The GVF criterion is defined as
GVF = 100 − ( xi∈Gk − Gk ) ( xi − X ) × 100
2
2
(3)
where
xi=a geo-referenced feature,
xi∈Gk=representation of features in class Gk,
–
Gk=average of features in class Gk, and
–
X =average of all features.
The geometrical intervals method identifies the class breaks on
the basis of the intervals that represent a geometric series. In other
100
100%
80
80%
Class 1
Class 3
Class 2
Frequency
60
40
Class 2
40%
20%
20
Class 1
ICMV Rank
ICMV
(a)
(b)
FIGURE 3 Distribution of ICMV data and sample class breaks in (a) rank-size distribution and (b) cumulative distribution.
78
72
66
60
54
48
42
10,000
36
8,000
30
6,000
24
4,000
18
2,000
12
0%
0
6
0
60%
0
ICMV
Class 3
77.2
700
33.9
23.8
800
Frequency
600
+1σ
−1σ
500
400
µ
300
200
100
66
72
72
78
60
66
54
60
48
42
36
30
24
18
6
12
0
0
ICMV
(a)
77.2
700
38.5
24.1
800
Frequency
600
+1σ
−1σ
500
400
µ
300
200
100
78
54
48
42
36
30
24
18
12
6
0
0
ICMV
700
77.2
11.8
800
30.7
(b)
Frequency
600
500
+1σ
−1σ
400
µ
300
200
100
66
72
66
72
78
60
60
54
48
42
36
30
24
18
12
6
0
0
ICMV
700
77.2
28.4
800
52.8
(c)
Frequency
600
500
+1σ
−1σ
400
µ
300
200
100
ICMV
(d)
FIGURE 4 Different classification methods: (a) quantile, (b) natural breaks, (c) geometrical intervals, and (d ) equal
intervals for geospatial analysis of IC data from System 1.
78
54
48
42
36
30
24
18
12
6
0
0
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Transportation Research Record 2657
words, this method generates geometric intervals by optimizing the
sum of squares of the number of features in each group. Inversely,
the equal intervals method classifies the features in different groups
in a way that the width of each class is the same. The width of
interval is defined as the range of data divided by the number of
features in each data group (13). The graphs on the right-hand side
of Figure 4 show the class break values with respect to the mean (µ)
and standard deviation (σ) of the collected ICMV data. The shaded
areas in these graphs represent the three colors used in the maps to
differentiate the areas with various ranges of ICMVs. Observing the
differences among the four color-coded maps in Figure 4, one can
interpret less-stiff areas differently. For example, Figure 4c indicates
that most of the areas within the test section are either well compacted
(gray) or acceptable (light gray). On the other hand, Figure 4d represents a totally different intuition, that the majority of the test section is either less stiff (dark gray) or barely acceptable. However, the
acceptable compaction criteria in this study were drawn on the basis
of the existing compaction data during the construction process to
improve the compaction uniformity; they are not mechanistic-based
target values. A comprehensive and yet complicated process needs to
be conducted to establish the target ICMVs.
The results of the AIC estimations are summarized in Table 2.
The natural breaks method provides the lowest AIC. Although the
AIC could be employed as an indicator of a classification method’s
performance, it might not be the only criterion to evaluate the effectiveness of the classification method. Another approach to find the
best breaks between classes is to estimate the ratio of the information
loss in each classification method. This concept is also correlated to
the KL divergence criterion (11). Assuming that P is the true distribution of data and Q is the target distribution, the KL divergence
is the natural distance function between P and Q. This measure is
mainly referred to as information gain ratio, which could be translated
to the loss of information during the interpretation of the geospatial
data for a given classification method. The information loss in terms
of a KL divergence criterion is estimated from Equation 4a, where
L is the rate of information loss:
n
n
i =1
i =1
L = ∑ pi log ( pi ) − ∑ pi log ( qˆ k )
(4 a)
where
n
pi =
∑x
i =1
X
i
; qˆ k =
∑x
i ∈Gk
Xnk
i
n
with X = ∑ xi
(4 b)
i =1
The results of such an analysis are also included in Table 2 for
different data classification methods applied to the collected ICMV
data. Based on AIC and L, the natural breaks method, followed by
the quantile method, are the most efficient techniques for classifying
the geo-referenced IC data. Both AIC and L are lowest for these two
classification methods. On the other hand, the geometrical intervals
and equal intervals methods returned higher AIC and L values, meaning that those methods may not be optimal for the representation and
interpretation of these IC data. The advantage of the natural breaks
method is that it can identify the trend between different classes of data
and determine the class breaks on the basis of the numerical values.
Table 2 also summarizes the percentage of area within the test
section identified by each classifying color, as illustrated earlier in
Figure 4. As an example, the natural breaks method shows 30% of
the test section as relatively less stiff (dark gray), while the geometrical intervals indicates the same condition for only 15% of the
section. This difference can significantly affect the interpretation of
the collected IC data. The following section provides an algorithm
that can optimize the classification of the ICMV data on the basis
of the concept of information loss.
Optimization of Class Break Values
An optimization algorithm was developed to estimate the class breaks
on the basis of the minimization of the information loss ratio, L. This
method simulates the process of biological evolution through a series
of computation stages and within a specific population of solutions.
The offspring solutions are then introduced to the population of parent
solutions, along with some mutations to provide new solutions. The
convergence of the general model is defined as the minimization of
a fitness function. This procedure is stopped during the evolution as
soon as the fitness function cannot be improved any further. In this
optimization study, the convergence factor was selected as 0.0001,
the mutation rate as 0.075, and the population size as 100. The calculated AIC for the optimized class breaks is 2.2532 × 106, which
is the least, compared with the AIC values reported in Table 2. The
ratio of the information loss, L, is 0.6866%, which is the smallest,
compared with the other methods in Table 2. The optimized set of
class breaks minimizes both the AIC and L criteria when classifying
the collected geo-referenced ICMV data.
Figure 5 illustrates the color-coded map and distribution of ICMV
data for IC System 1 on the basis of the optimized class breaks. The
results of this optimized classification are close to the ones from the
natural breaks and quantile methods in Figure 4, a and b. In other
words, the natural breaks method, followed by the quantile method,
are reasonable estimates of the optimized classification approach for
this set of ICMV data.
Although the classification techniques discussed in this section
are well suited to the collected IC data, the selection of the best class
TABLE 2 Comparison of Performance of Geospatial Data Classification Methods for ICMV Data
from System 1
Classification Method
AIC (× 106)
L (%)
Marked as
Gray (%)
Marked as
Light Gray (%)
Marked as
Dark Gray (%)
Quantile
Natural breaks
Geometrical intervals
Equal intervals
2.2535
2.2533
2.2695
2.2552
0.7424
0.7169
0.9591
1.0457
56
50
60
32
13
20
25
31
31
30
15
37
Note: L = rate of information loss.
Mazari, Tirado, Nazarian, and Aldouri
43
77.2
700
35.1
20.8
800
Frequency
600
ICMV
500
+1σ
–1σ
400
µ
300
200
100
0
6
12
18
24
30
36
42
48
54
60
66
72
78
0
ICMV
FIGURE 5 Optimized values of class breaks for ICMV data (System 1).
breaks depends on the distribution of ICMVs. As an example, the
skewness of the data and the ratio of the head to the tail in the best-fit
distribution may affect the selection of the classification technique.
Furthermore, not all IC data fit into a normal distribution, as has been
observed in a number of field studies (2, 14). The following section
discusses the impact of ICMV distribution on the selection of the
classification method.
Impact of ICMV Distribution on Selection
of Data Classification Algorithm
To understand the impact of ICMV distribution on the selection
of the classification technique, the two well-behaved classification
methods were applied to the data obtained from IC Systems 2 and 3.
Figure 6 illustrates the result of such analyses for the natural breaks
and quantile methods. The class breaks for the ICMVs from System 2
are shown in Figure 6, a and b, which are relatively close. However,
the selection of a properly optimized classification method is more
critical for the data collected by System 3, because the ICMVs represent a heavy-tailed distribution (Figure 2c). Comparing Figure 6,
c and d, the range of class breaks for System 3 can be seen to be significantly different between the quantile and natural breaks classification algorithms. The reason for such a noticeable difference is that
the quantile method classifies the data on the basis of the number of
features in each class while the natural breaks method finds the actual
break points between the values.
As shown in Figure 6, the natural breaks method performs more
efficiently than the quantile method on the basis of the information
loss ratio, L. In the case of the heavy-tailed data, the interpretation
of the ICMV trends and identification of less-stiff areas are very
sensitive to the selection of the classification method. Furthermore,
the minimum value of L for the ICMVs from System 3 is still greater
than those values for IC System 2. The anomalies in the collected
ICMVs could be traced to the properties of the IC system components,
such as the vibration sensor, the GPS unit, and the data acquisition
process. As a result, there is a need for a uniform calibration system
for the IC rollers’ components.
Not only can the classification approach for geo-referenced IC
data affect the understanding of the results but also the statistical
significance of spatially distributed IC data can be of major concern
for the compaction quality management process. The following
section analyzes the spatial significance of the IC data in this study.
Spatial Significance Analysis of IC Data
Because of the variable range of ICMVs and uncertainties associated with the process of establishing the breaks between classes and
selecting a classification method, it would be beneficial to understand
the statistical significance of the geo-referenced IC data. The spatial
analysis techniques are used to identify the spatial pattern and the “hot
spots” in the geo-referenced data. These methods estimate the local
correlation of a geospatial data point with respect to its neighbors
within a specific distance. Of these methods, the Getis-Ord process is
more popular because it compares the local averages with the global
average; the other methods compare each observation only with its
neighbors (15). The results of Getis-Ord hot spot analysis reveal
the locations that have unusual patterns as well as the significance
of the differences between local and global averages within the area
of interest. This method basically tests the null hypothesis, which
assumes that there is no significant correlation between each data
point and its neighbors up to a specified distance. Thereafter, a statistical significance test is carried out to accept or reject the null hypothesis using the z-score and p-value. The z-score defines whether to
accept or reject the null hypothesis. The p-value shows the probability of falsely rejecting the null hypothesis during the statistical
significance testing. Both of these statistics require the assumption
of normal distribution of data. The range of acceptable z-scores and
p-values are dependent on the confidence level. For example, at a
95% confidence level, the range of z-scores is 1.96 to −1.96 and the
corresponding p-value is .05.
In practical terms, if a large ICMV is not surrounded by other
large ICMVs, it is not considered to be statistically significant. On
the other hand, if a large ICMV is surrounded by other large ICMVs,
it will be marked as statistically significant and can be a hot spot. At
different confidence levels, the z-score and p-value could be used
to identify the spatial significance of collected ICMVs as compared
with the global average of all neighbors.
Figure 7 illustrates the results of spatial significance analysis in
terms of the estimated p-values. For example, at the 99% confidence
level, if the p-value is less than .01 (i.e., the z-score is either less
44
Transportation Research Record 2657
800
700
+1σ
–1σ
600
500
Frequency
700
µ
400
+1σ
–1σ
600
500
µ
400
300
200
200
100
100
0
0
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
300
ICMV
ICMV
(a)
(b)
120
80
ICMV
ICMV
(d)
FIGURE 6 Impact of ICMV distribution on data classification: (a) System 2—quantile (L = 1.1344%), (b) System 2—natural breaks
(L = 0.9606%), (c) System 3—quantile (L = 2.2823%), and (d ) System 4—natural breaks (L = 1.9287%).
96
88
80
72
64
56
48
40
32
96
88
80
72
64
56
48
40
0
32
0
24
20
16
20
8
40
0
40
(c)
µ
60
24
60
+1σ
–1σ
16
µ
100
8
80
Frequency
+1σ
–1σ
0
120
Frequency
99.5
140
62.7
99.5
28.0
19.0
140
30.7
160
160
100
90.5
34.1
900
800
Frequency
20.7
31.8
900
90.5
1,000
23.7
1,000
Mazari, Tirado, Nazarian, and Aldouri
45
(b)
(a)
(c)
FIGURE 7 Spatial significance of ICMV data at different confidence levels: (a) 99% confidence level, (b) 95% confidence level,
and (c) 90% confidence level (● = spatially significant and ● = not spatially significant).
than −2.58 or more than 2.58), the collected ICMV data are significantly different from the rest of the test section. Figure 7a illustrates
the distribution of p-values at this confidence level. The dark gray
areas have a spatially significant difference with respect to the rest of
the test section; the gray areas tend not to show a significant difference. At lower confidence levels of 95% and 90% (Figure 7, b and c),
the area covered by spatially significant ICMVs increases. Furthermore, the dark gray zones in Figure 7, b and c, are similar to those
observed in Figures 4a and 5b. The advantage of this type of analysis
is that it is independent of the range and distribution of ICMV data.
However, the confidence level significantly affects the interpretation
of the collected IC data.
Summary and Conclusions
To understand compaction quality and uniformity, one may classify
the IC data and represent the results as a color-coded map. Although
the process of classification is straightforward, it has a significant
impact on the color-coded maps and consequently adds bias to the
quality management process. To understand this phenomenon, four
basic classification techniques were evaluated using three sets of
IC data.
The following conclusions can be drawn from the analyses
performed in this study:
• The natural breaks algorithm and the quantile method seem to
perform more efficiently than the geometrical intervals and equal
intervals techniques. Because the quantile algorithm divides the data
on the basis of the number of features in each class, its performance
might not be optimal for different types of ICMV distributions. On the
other hand, the natural breaks method identifies the variance of each
class with respect to the mean and determines the location of class
breaks on the basis of numerical values of features.
• To improve the objectivity of the representation of data, an
algorithm was introduced to optimize the values of the class breaks
systematically. The performance of the optimization algorithm in
terms of information loss ratio was superior compared with the other
classification techniques.
• The distribution of the IC data significantly impacts the selection
of the classification algorithm and the subsequent interpretation of
the color-coded maps. The heavy-tailed ICMV distribution is very
sensitive to the selection of class breaks.
• The statistical significance of the ICMVs within a test section
can be represented as the results of statistical hypothesis testing in
terms of z-score and p-value at different confidence levels.
• Overall, the interpretation of IC data depends significantly on the
classification technique to generate the color-coded maps. A solution
could fit different sets of ICMVs. A comprehensive statistical analysis
of the collected IC data is crucial in the identification of less-stiff areas
and improving the uniformity of compaction.
• Compared with conventional quality control and quality assurance processes, the use of ICMV color maps simplifies the process
for identification of less-stiff areas. However, either the modulus- or
density-based quality management approaches could still be employed
to evaluate the compaction quality of less-stiff zones. The processes
discussed in this paper emphasize the importance of systematic and
objective ICMV classification methods in the quality control work,
considering the type of geomaterials.
• It is understood that as compaction proceeds, the dispersion of
the ICMV data decreases. However, the IC data in this study were
collected only after the completion of the compaction process, known
as mapping. Even though the mapping data show less uncertainty
compared with the pass-by-pass data, the identification of less-stiff
areas is still dependent on the classification criteria. The methods and
analyses reviewed in this study allow quality management agencies
to understand the uncertainty and nonuniformity of compaction data
better.
46
Acknowledgments
This study was carried out as part of the FHWA EDC-2 project in
cooperation with the Texas Department of Transportation. The authors
thank Jimmy Si, Richard Izzo, Antonio Nieves, Mike Arasteh, and the
study panel for help and advice throughout this study.
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The contents of this paper reflect the authors’ opinions and do not necessarily
reflect the policies and findings of FHWA.
The Standing Committee on Geotechnical Instrumentation and Modeling
peer-reviewed this paper.
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