A Sensing-Information-Statistics Integrated Model to ... - IEEE Xplore

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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015

A Sensing-Information-Statistics Integrated Model to Predict Asphalt Material Density With Intelligent Compaction System Qinwu Xu, George K. Chang, and Victor (Lee) Gallivan

Abstract—Intelligent compaction (IC) is an innovative technology that has been used in road and earthwork construction. However, the current IC technology is unable to measure material density directly as the acceptance criteria by owner agencies. To tackle this issue, the authors have developed a sensing-informationstatistics integrated model to predict asphalt material density for 100% coverage of construction area. Instrumented with the satellite navigation system, accelerometer, and infrared sensors, IC rollers measure mechanical responses of roller drums and material temperature in real time. With these measurements, panel data models—including both the multivariate linear and nonlinear models—were developed to predict asphalt material density. A reasoning model was proposed to estimate idiosyncratic errors due to uncertainty of measurements. An information management software was developed to analyze IC measurements with univariate statistics and geo-statistical models. Statistical models were implemented and validated with data collected from four paving projects in the US. Results indicate that the multivariate nonlinear panel data model can predict asphalt material density at the project level for 100% coverage of the construction zone within reasonable accuracy. Therefore, this model may serve as an enhanced quality control and acceptance tool for asphalt pavement construction to improve consistency and uniformity and long-term performances. Index Terms—Intelligent system, material density, multivariate, nonlinear model, panel data, prediction.

I. INTRODUCTION NTELLIGENT construction systems have been developed for civil infrastructures to improve the efficiency and safety. These systems include the intelligent navigation system [1], the instrumented roller compactor system to monitor vibration behavior [2], the autonomous robotic system to inspect bridge deck defeats [3], and the intelligent vibration system to extend bridge life [4]. Intelligent compaction (IC) system refers to the vibratory roller system instrumented with accelerometers, realtime kinematic (RTK) global positioning system (GPS), infrared sensors, and on-board computers that can display various roller operating settings on color-coded maps in real time [5]–[8]. The IC system utilizes sensor and information technologies as shown in Fig. 1. The accelerometer is a hardware mounted on the roller

I

Manuscript received January 24, 2014; revised October 18, 2014 and February 23, 2015; accepted April 17, 2015. Date of publication April 24, 2015; date of current version October 21, 2015. Recommended by Technical Editor Y. Li This work was supported by the U.S. Federal Highway Administration under DTFH61-07-C-00032. Q. Xu and G. Chang are with the Transtec Group, Inc., Austin, TX 78731 USA (e-mail: [email protected]; [email protected]). V. L. Gallivan is with Gallivan Consulting, Inc., Carmel, IN 46033 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2015.2426145

Fig. 1.

Framework for intelligent construction (modified from Bomag).

drums to measure the vibration frequency and amplitude. GPS signal is transmitted from satellites to the roller GPS receiver, GPS base station (fixed), and hand-held GPS rover. The GPS base station provides correctional signals to GPS receivers and hand-held rover to achieve accuracy within 2 cm. With accurate GPS information, roller positions and roller passes can be tracked and documented. With accelerometer measurements, the IC measurement value (ICMV)—an index related to material stiffness under compaction, could be calculated using either mechanical models or the vibration frequency models. Generally, infrared sensors are attached to the front and/or rear drum to measure material temperatures. By monitoring IC measurements in real time, compaction efforts can be controlled and/or adjusted with manually or automatically to optimize the desired rolling patterns, resulting in more uniform compaction and performance. Under this research, IC measurements were recorded by vendor-specific on-board computer system. The data were then processed and analyzed using the developed Veda software, a geospatial data management software. Asphalt in-place density measurement is the most commonly used method for compaction acceptance as in-place density is known to relate to asphalt durability and long-term performance of asphalt concrete pavements. Previous research led by the Federal Highway Administration (FHWA) and the National Cooperative Highway Research Program had shown that there are

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XU et al.: SENSING-INFORMATION-STATISTICS INTEGRATED MODEL TO PREDICT ASPHALT MATERIAL DENSITY

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TABLE I DESCRIPTION OF IC FIELD SITES Highway & state US 89, Utch I-95, Florida I-71, Ohio I-95, ME

Date

Asphalt layer

IC Rollers

August 6–9, 2012 October 15–18, 2012 June 24–27, 2013 August 18–22, 2013

63.50-mm base course 38.10-mm base course 44.45-mm base course 50.80-mm base course

Sakai Sakai Hamm/Sakai Hamm

inconsistent relationships between ICMV and material densities [8], [9]. There were attempts to incorporate density gauges on Ammann IC rollers without success, which could be due to factors including the movement and vibration of the roller. Instead of direct density measurement, there were limited research on using numerical models to predict material density from the roller measurement data. Minchin [10] and Commuri and Mai [11] developed the on-board density-measuring systems using techniques such as artificial intelligence. However, these rollers with density developments have not been validated to satisfy the FHWA [8], [11]. For example, these systems are unable to measure IC data in real time with precise GPS coordinates for 100% coverage. The objective of this research is to develop a sensinginformation-statistics integrated model to predict asphalt material density with 100% coverage. This model is intended to be used to improve existing methods to serve as an enhanced quality assurance. IC produces massive amount of information from instrumented rollers. Generally, raw IC data were collected at center of the front drum at 10 Hz, resulting in a sampling spatial frequency of 0.3 m. The raw data are then gridded to produce data at 0.3 m by 0.3 grids. The gridded data were subsequently analyzed using univariate statistic and geostatistical techniques with the Veda software. The gridded data can also be extracted from Veda to feed into multivariate, linear, and nonlinear panel data models to predict densities. The linear and nonlinear models refer to that the predicted density statistically follows a linear or nonlinear function of dependent variables, respectively. These density models were then validated with IC data from four asphalt paving projects. However, the comparison between the density models and existing technique in literature due to their inaccessibility [10]. Section II describes the development of the density models; Section III describes the model validation; and Section IV is the conclusion of this study. II. DEVELOPMENT OF IC DENSITY MODEL A. Experimental Design Field constructions were performed in four highways and states in the USA. Table I summarizes the project information. Under each field project, a ground-based GPS base station was set up to provide RTK correctional signals, and a hand-held GPS rover was used to measure coordinates at spot test locations. Behind paver and before compaction, asphalt density was measured with a nuclear density gauge (NDG), with values ranging from 60% to 80% of the theoretical maximum specific gravity (Gmm) due to lack of use of screed vibration in the US. Subsequent compaction was performed by two IC rollers at the breakdown and intermediate positions in vibration mode.

Fig. 2. Field operation of intelligent compaction system for adaptive control (courtesy of Hamm).

Finish compaction was conducted with a conventional roller in static mode. Fig. 2 illustrates such field operation. At randomly selected one to three locations, NDG measurements were performed after each pass of all rollers. After the finish compaction, in situ spot tests are performed at 60 locations within 457 m in a pattern of a pair of test locations every 15 m. The spot tests included: 1) NDG measurements, 2) lightweight deflectometer for asphalt (LWD-a) tests, 3) falling weight deflectometer (FWD) tests, and 4) coring in cylindrical specimens with a 10-cm diameter, for subsequent bulk density tests in laboratory. B. ICMV ICMV relates to the stiffness of the materials under compaction. ICMV includes two types: 1) mechanical model-based values, including roller-integrated stiffness, Kb (in kN/m), and vibration modulus, Evib (MN/m2 ); and 2) vibration frequency analysis-based, including compaction meter value (CMV) [12] [13], Hamm measurement value (HMV), and compaction control value (CCV) [14]. The roller-integrated soil stiffness, Kb , was developed by Case/Ammann in kN/m. It is computed from a 1-D nonlinear mechanical model based on the theory of chaotic vibration. The simplified Kb equation is md + me re cos φ kb = 4π 2 f 2 (1) a where f is the excitation frequency, md is the drum mass, me re is the eccentric moment of the unbalanced mass, φ is the phase angle, and a is vibration amplitude. Evib was developed by Geodynamics and adopted by Bomag based on the one-degree-of-freedom lumped parameter model [15]. Evib is calculated as a “slope” of the stress to displacement as a modulus value in MPa [see Fig. 3(c)] [15]. The Evib value is determined from the following equations: 1 − v2 F 2 L Evib = 1.8864 + ln (2) Zd L π W 16 R (1 − η 2 ) F (3) W = π Evib L

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Fig. 3.


ICMV types and algorithms. Fig. 4.

where v is Poisson’s ratio of the material; L is length of the drum; F is roller–soil interaction force; zd is measured deformation of material under compaction; R is radius of the drum; and W is contact width of the drum, calculated using Lundeberg’s theoretical solution for a rigid cylinder sitting on an elastic halfspaced earth [16]. The CMV is a dimensionless value developed by Geodynamik [12] based on the ratio of frequency amplitude at subharmonic and fundamental frequency from the drum rebounds signals (see Fig. 3). The CMV is calculated using the following equation: CMV = C1 A2Ω /AΩ

(4)

where C1 is a constant of 300, A2Ω is amplitude at the subharmonic frequency spectrum, and AΩ is amplitude at the fundamental frequency spectrum. The CMV was found to relate the soils stiffness from plate load tests. The HMV is similar to the CMV. The RMV, a similar index to the CMV, was developed by the Geodynamik system. The CCV is developed by Sakai based on a similar concept that as the ground stiffness increases the roller drum starts to enter into a “jumping” motion, which results in vibration accelerations at various frequency components as displayed in Fig. 3. The CCV is calculated as 100 (A0.5Ω + A1.5Ω + A2Ω + A2.5Ω + A3Ω ) CCV = (5) A0.5Ω + AΩ where A1.5Ω and A2.5Ω are amplitudes at subharmonic frequency spectrums; A3Ω is amplitude at the third-order harmonic frequency spectrum. In addition to the aforementioned ICMV models, other methodologies including compaction value (CV) for earth rock [17], the neural network method [11], [18], and statistical method [19] have also been used for determining ICMV. The accelerometer-based ICMV has an influence depth deeper than the compacted pavement layer. Mooney and Facas [20] applied a finite-element model and an inverse computation method to extract mechanical properties of subbase layer and underlying subgrade materials. Herein, a simplified model is proposed to decouple the ICMV to extract asphalt layer properties by removing the influences of the underlying layers. This model is computationally efficient in order to produce results with 0.1 s (i.e., 10 Hz) in order for real-time onboard IC display. This model is based on a two-layer single-degree freedom lumped system as shown in Fig. 4. To meet the force equilibrium of the lumped system for a two-layer structure, the condition should satisfy the following equation: F = k(d1 + d2 )

(6)

F = k1 d1

(7)

F = k2 d2

(8)

Two-layer single-degree lumped system.

where F is force exerted by the roller; k is composite stiffness of the entire layer system, which corresponds to the measured ICMV on top asphalt layer; k1 is stiffness of the support layers corresponding to the measured ICMV on the support layers before paving the top asphalt layer; k2 is stiffness of the single asphalt layer as unknown, corresponding to the ICMV of the single asphalt layer; d1 is deflection of the support layer; and d2 is deflection of the asphalt layer. Substitute (7) and (8) into (6) and dismiss F on both sides, the stiffness of the asphalt layer (k2 ) can be derived as k2 =

k × k1 . k1 − k

(9)

The model can be extended to a multilayer system, in which the force equilibrium is formed as F = k1 d1 = k2 d2 = · · · kn dn = k(d1 + d2 + · · · + dn ) (10) where kn is stiffness of the top asphalt layer of a multilayer system; ki (i = 1, 2 . . . n − 1) is stiffness of the ith support layer of a multilayer system starting from the very bottom layer (i = 1). The stiffness of the top asphalt layer can be solved as kn =

−1 ki kΠni=1 n −1 i= j n −1 Πi=1 ki − k j =1 Πi=1,2...n −1 ki

(11)

where Πki is the factorial function of ki in terms of i. This model can be applied to different types of ICMV to extract layer properties. C. Information Management Method Fig. 5 illustrates the frame work for the sensing-informationmodel and information management. During roller compaction, it produces real-time information with 100% coverage of the construction zone including: 1) received GPS information from satellites and base station, and accounted roller speed and pass number; 2) accelerometer recorded dynamic responses including vibration frequency and amplitude, from which the material stiffness index ICMV is calculated; and 3) infrared-sensor recorded material temperatures. The in situ spot tests include measurements at random spots: 1) the NDG measuring material density; 2) FWD measuring deflection and back-calculating material moduli; and 3) coring for measuring bulk density. As shown in Fig. 5, recorded data from both roller compaction and spot tests “flow” into the module of information management for data store and management. The roller data are stored in time and space series, which then “flow” into the statistical modeling module. Here, the density is expressed in %G mm. The spot test data (spot coordinates, coring densities, etc.) also


Fig. 5.

Fig. 6.

Fig. 8.

Developed Veda software for IC data analysis and visualization.

Fig. 9.

Density growth with roller pass.

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Network of information flow.

(a) All-passes and (b) final coverage IC data.

illustrates the data catalogue and storage mechanism. Data fusion and cache are applied but only for the processed data and IC measurements in the information management software instead of raw data of sensors in real time to improve computation speed. The size of cache is limited by the storage capacity of hard drives. Both univariate statistics (mean and standard deviation) and geostatistics (semivariogram) were used to analyze the extracted data. Fig. 8 presents a screenshot of the developed software, Veda that displays colored-cased IC data maps and core data. At each core location, IC data falling within a circle of 1-m radius (half of the drum width) were extracted. The mean values of the extracted IC data were used for correlation analysis between core densities and IC measurements (such as: ICMV, temperatures, speeds, and etc.). The extracted data were also used to calibrate the density model (see Fig. 5).

Fig. 7. Data catalog and storage (arrows show how recorded data are used to determine the other parameter). 1 Vibration frequency. 2 Vibration amplitude.

D. Statistical Models

“flow” into the statistical modeling module for statistical correlation with roller measurement data. Applying the linear and nonlinear panel data model with the Kriging technique, densities at all grid points are predicted. The gridded IC data were classified into gridded all-passes data and final coverage data (see Fig. 6). All-passes data include all IC measurements from every single roller pass at a given data mesh. The final coverage data include the last roller pass data. All gridded data were stored so that any data layers can be easily drilled down and filtered for analysis and display. Fig. 7

1) Density Growth Trend: Experimental results show that densification is mainly achieved during vibratory compaction at elevated temperatures while the increase of density due to static compaction (finishing rolling) is minimal, as displayed in Fig. 9. However, different densification curves were also observed in the field where the same equipment and materials were used (e.g., curve 1 and curve 2 in Fig. 9). Therefore, the densification characteristic is very complex in nature, and the IC-density model development is based on the IC data during breakdown and/or intermediate compaction in order to capture the most dominating factors.

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3) Multivariate Linear Panel Density Model: A multivariate, linear panel data model with fixed effect at the geospatial local level (“local” is the compaction area of one roller based on GPS recording, i.e., a 2 m-diameter area) was used to predict density, in which model parameters of constant and slope coefficients vary across individual location. Fig. 10.

ρ (i, j) = ρ0 (i) +

Geostatistical semivariogram and statistics.

N

βk (i)Xk (i, j) + ε (i, j)

(16)

k =1

2) Geostatistical Semivariogram: Geostatistical semivariogram is used in the developed information management module (see Fig. 5) to characterize compaction uniformity. Semivariogram is measure for uniformity that considers spatial factor. For a given geospace with a defined direction (e.g., east-bound of paving direction), the experimental semivariogram sˆ(l) is defined as the average squared difference of values X(u), as separated approximately by lag distance of l for all possible locations of u as in the following equation [21]: 1 sˆ (l) = E (X (u) − X (u + l))2 (12) 2 where E is the mean value; u is location vector; l is lag distance vector (a constant for the same lag areas); and X is the variable value such as IC measurements. To compute the semivariogram numerically, the lag length (i.e., 10 m), search direction, and bandwidth are defined by users, and then, semivariogram is numerically calculated as follows after discretization: 1

[X (ui ) − X (ui + l)]2 2n n

ˆs (l) =

(13)

i

where n is the number of pairs for a lag distance l of a specific lag area and ui is a location. For a specific construction zone, multiple semivariogram values, called experimental data, are computed based on the lag distance from the starting to the end of the zone. Semivariogram parameters including the sill value C and the range lR (see Fig. 10). Sill is defined as the plateau that the semivariogram reaches, which represents the value of variance by considering the geospatial dependence. A lower sill and/or greater range values indicate a better uniformity, while the opposite indicate a less uniform condition [22]. In order to determine C and lR , theoretical semivariogram models can be fitted to the experimental semivariograms [21]. The exponential model was found to be adequate to fit the experimental data points 3l s (l) = C 1 − e− α . (14) The range value is determined at a lag distance where the tangent angle of the semivariogram curve is (π/3∂s (l) ∂l = tan(π/3)). From (14), the range can be determined as follows: π α a lR = − ln tan (15) 3 3C 3 where C and α are model parameters. Results of the ICMV (Sakai CCV) semivariogram are shown in Fig. 10 for the data from base mapping, first lift asphalt compaction, and second lift of asphalt compaction. The uniformity improves from the ground up as indicated for increased sill values and decreased range values.

where i is the location index with GPS coordinates; j is the time index, represented by the roller pass number; ρ0 (i) is the initial material density after paving but before roller vibration at the ith location as an individual heterogeneity, treated as a fixed but unobserved effect since it is a parameter to be estimated; X(i, j) is the observed independent variable at the ith location and jth time, such including the ICMV, vibration frequency and amplitude, material temperature, and roller speed; βk (i) is the slope of the kth independent variable at the ith location; and ε(i, j) is the idiosyncratic errors or disturbances across the ith location and jth time due to uncertainty, which is assumed to follow the normal distribution with the mean of μ(ε) variance of σ 2 (ε). The cause of ε(i, j), the uncertainty refers to random small factors that are unable to be precisely quantified in the model prediction such including: 1) the variable environmental conditions at different locations such as moisture and temperature and 2) variable material conditions such as the variable initial density ρ0 at different locations. The environmental factors are not directly incorporated into the model as dependent variables as they are uncertain and unable to be precisely quantified. A Kriging model was to estimate idiosyncratic errors, ε. For the project-level (at least a few kilometers of construction zone), one universal model is used to predict material densities of all locations bounded within the project zone. Therefore, the location effect is dismissed, and a homogeneous or pooled panel model with fixed effect is yielded as follows: ρ (i, j) = ρ0 +

N

βk Xk (i, j) + ε(i)

(17)

k =1

where ρ0 is the fixed effect at the initial conditions; ε is the fixed-effect error across location but independent of time; and βˆk is the slope that can be determined according to the ordinary least-square (OLS) method. 4) Multivariate, Nonlinear Panel Density Model: A heterogeneous multivariate, nonlinear panel-data model was developed from multiple trials using different mathematical formulas to predict material density using IC measurements. Two panel data model forms for the local level are proposed as follows: ρ (i, j) = ρ0 (i) + (ρm (i)

−

k

α k (i)X k (i,j )

β (i )

j

− ρ0 (i)) e

+ ε (i, j)

ρ (i, j) = ρ (i, j − 1) + (ρm (i)

−

− ρ(i, j − 1)) e

k

α k (i)X k (i,j ) j

(18)

β (i )

+ ε (i, j) (19)


where (i, j) is material density at the location iand time or pass count j and ρm is maximum density of materials that could be up to 100%. The physical meaning of this model includes: 1) density increment of each roller pass cannot exceed the difference between max value and the previous or initial density value; 2) the exponential term is to predict the percentage of density variation as dependent on IC information, which is constrained between zero and one; and 3) the β parameter is used to describe how fast the density changes (a higher β value indicates a greater increment across the time, j). For the project-level, the homogeneous panel data–data multivariate, nonlinear models with fixed effect can be expressed as follows for the two panel data model formats: β

−

ρ(i, j) = ρ0 + (ρm − ρ0 ) e

k

j

+ ε(i)

−

(20)

α X (i,j ) k k k j

+ ε(i).

β

(21)

To determine the model parameters for density prediction, a few random samples at coring location (i.e., 5) are used to determine model parameters. For the linear model, model parameters are estimated following the OLS method. For the nonlinear model, the Frank–Wolfe algorithm [23] is used for the nonlinear programming of a constrained optimization to determine the model parameters by minimizing the density difference. n

m

[ρ (i, j) − ρˆ (i, j)]2 /mn

(22)

i=1 j =1

where ρˆ(i, j) is the measured density at location i and time j; ρ(i, j) is the predicted density; β ∈ (0, 2] and ρ ∈ (0, 100] as the constrained conditions. To validate the model, the fitted model parameters from small samples (i.e., 5) are used to predict the large samples measured at all those coring locations (i.e., 60), and the root mean squared (R2 ) value is used for evaluation. 5) Reasoning Model: In this research, a reasoning model was proposed to estimate idiosyncratic errors of density prediction ερ (i) caused by uncertainty to improve prediction accuracy. Other models including the multivariate linear model were also tested for error estimation, but did not improve the prediction accuracy and were not detailed here. Kriging is a geospatial estimation method to estimate the missed points. The basic form of the Kriging model as a linear regression estimator [21] can be expressed as follows:

n (u )

Z ∗ (u) = m (u) +

NDG density versus ICMV. TABLE II MULTINONLINEAR MODEL PARAMETERS

Parameter

Coefficients Standard Error

α k X k (i,j )

ρ(i, j) = ρ(i, j − 1) + (ρm − ρ(i, j − 1)) e

min L =

Fig. 11.

λα [Z (uα ) − m(uα )]

(23)

a=1

where u is location vector for estimation; u(a) is location vector of the neighboring data points and a is number of a data point; n(u) is number of data points in the neighbor; m(u) and m(ua ) are means of z(u) and z(ua ); and λa is Kriging weight assigned to the datum z(ua ). Using those observed errors in validation spots (i.e., five spots) to consider both the geospatial effects and the linear effects of the IC information, a reasoning model was proposed

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Intercept (Gmm%) HMV Frequency (Hz) Roller Speed (kmph) Temperature (°C) Pass count

t sta

P-value

Lower 95%

Upper 95%

–58.57

177.38

–0.33

0.76

–623.08

505.94

0.27 0.36

0.33 0.6

0.79 0.6

0.49 0.59

–0.8 –1.55

1.33 2.28

–6.18

12.15

–0.51

0.65

–44.84

32.48

1.07

1.143

0.75

0.51

–3.47

5.61

3.56

3.4

1.05

0.37

–7.26

14.39

as follows to predict idiosyncratic errors: n (u ) n (u )

λα m (ερ ) + λα ερ (uα ) ερ (u) = 1 − a=1 a=1

+ γk Xk (u)

(24)

k

where ερ and m (ερ ) are idiosyncratic error of density prediction and its mean value; Xk (u) is the observed variable (IC information) at the location vector u for k = 1, 2 . . . N ; γk is the fitted model parameters. The weight parameter λα is determined by minimizing the variance of the error estimation as follows: minL = σ 2 [ˆ ερ (u) − ερ (u)]

(25)

where εˆρ (u) is the observed error of density at location u from the experimental data. III. VALIDATION OF IC DENSITY MODELS A. Linear Model Results Fig. 11 indicates the range of coefficients of determination (R2 ) for the correlation between densities and ICMV. It can be deduced that ICMV measurements do reflect in-place asphalt density during breakdown compaction. The multivariate, linear panel data model with fixed effect at the local level produce reasonable correlation of R2 of 0.95 and adjusted R2 of 0.87, as shown in Table II for the IC field project in Maine. However, the density prediction at the project-level (a few kilometers) using this model yields a relatively poor correlation, as shown in Fig. 12. A significant portion of predictions are beyond the confidence level of (ρ − σ, ρ + σ), where ρ is measured density and σ is its standard deviation. This indicates

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TABLE III MULTINONLINEAR MODEL PARAMETERS Parameter

Maine

Florida

Ohio

Utah

ρ0 ρm a1

80.1 97.8 1.27 × 10 −6 1.28 × 10 −5 2.37 × 10 −8 1.29 × 10 −2 0.0685

79.5 91.1 1.45 × 10 −4 0.00

78.0 99.0 2.15 × 10 −2 1.50 × 10 −3 0.00

84.7 100.0 2.37 × 10 −5 1.46 × 10 −5 0.00

1.50 × 10 −3 0.5020

1.23 × 10 −3 0.1070

a2 a3

Fig. 12.

Multivariate, linear panel-data model density prediction.

a4 β

Fig. 13.

8.42 × 10 −4 1.24 × 10 −2 0.0685

Fig. 14.

Density model idiosyncratic error.

Fig. 15.

Predicted densities of a construction zone.

Multivariate, nonlinear model density prediction.

the linear model is not suitable to predict the density growth at the project level. B. Nonlinear Model Results The multivariate, nonlinear model validation was conducted to explore the possibility of using such a model to overcome the limitation of the final coverage ICMV to correlate to in-place asphalt density at the project level. The pass-by-pass NDG measurements were used along with the selected core data to make up at five random locations for the IC-density model fitting. Then, the fitted model was used to correlate its density prediction with remaining actual core density data measured at 55 locations. The IC-density model fitting and validation for these four demonstration projects are presented in Fig. 13 with model parameter values listed in Table III. Results indicate that the nonlinear model has made significant improvements over the linear model. The model Form I produced slightly higher R2 than Form II for these four projects. The R2 values of 0.34, 0.47, 0.70, and 0.90 for the projects in Ohio, Florida, Maine, and Utah, respectively, for the nonlinear model prediction. The vast majority of predictions fall within the confidence level of (ρ − σ, ρ + σ), and all values are fallen within the bound limits [ρ0 , ρm ax ]. However, the correlation results from nonlinear model prediction were not always consistent for all field projects. As observed from the above pass-by-pass IC data analysis (see Fig. 9), the compaction curves can vary from one location to another even with the same equipment, materials, and paving

method. Therefore, a single IC-density model, no matter how well calibrated, would face the challenge to match a variety of compaction curves. Meanwhile, idiosyncratic errors due to the uncertainty of materials, locations, supporting conditions, paving, and compaction operations, etc., exist and affect the final density. Fig. 14 shows the idiosyncratic errors (difference between predictions and actual density measurements without using the Kriging model), which indicates that the errors follow normal distribution as proposed in the panel date models. The Kriging model was used to capture the prediction errors caused by influences of geospace and linear factors of IC information. The use of Kriging model results in improved correlation where R2 value has improved 0.03, 0.14, 0.06, and 0.05 for the Maine, Florida, Ohio, and Utah projects, respectively. The narrow range of core density values after the finishing roller would also pose challenges to the correlation between the IC-density model prediction and actual density measurements. Therefore, a technique to look beyond the R2 values is warranted. As seen in Fig. 15, the vast majority of density prediction is within the confidence level (ρ − σ, ρ + σ). Fig. 15 presents results of nonlinear density model prediction for the Maine project. The associated semivariogram model and statistics parameters are shown in Fig. 16. The sill value of the semivariogram is 4.51%Gmm2 , while the variance or


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and for technical support and equipment supplies from roller vendors (Hamm, and Sakai), local DOTs and contractors of the field projects. REFERENCES

Fig. 16.

Statistics of density: a) semivariogram; b) histogram.

standard deviation is 9.49%Gmm2 . The mean value of the density prediction is 92.65%Gmm with COV of 3.32%. Therefore, the nonlinear density model can be used to predict density with 100% coverage of the compacted area as an enhanced QC tool (see Fig. 15). With this information, the construction quality and compaction uniformity can be properly measured and assessed. This model can also be used to advance the current practice for more comprehensive compaction acceptance.

IV. CONCLUSION A sensing-information-statistics integrated model was developed for predicting asphalt material density using IC data and limited in-place density measurements. GPS information and real-time measurements of instrumenting sensors including the mechanical responses and temperatures were collected with IC systems. Information management methods and statistical models were developed and implemented in the Veda software. Both linear and nonlinear panel data models with fixed effects were developed to predict material density using IC data. A reasoning model was proposed to estimate idiosyncratic errors due to uncertainty. Four IC projects were then conducted to validate the IC-based density models. The main findings from this study are as follows. 1) The multivariate, linear panel-data model with fixed effect predicts density well at the local level, but not at the project level. 2) The multivariate, nonlinear panel-data model with fixed effect improved the density predictions at the project level over the linear model with the majority of predictions fall within the confidence level of (ρ − σ, ρ + σ). 3) The use of reasoning model also improved the prediction by capturing the idiosyncratic error due to measurement uncertainty. 4) The sensing-information-statistics integrated model developed under this study can serve as an enhanced quality control tool for compaction. This model can also be used to advance the current practice for more comprehensive compaction acceptance.

ACKNOWLEDGMENT The authors would like to thank Accelerated Implementation of Intelligent Compaction Technology for Embankment Subgrade Soils, Aggregate Base, and Asphalt Pavement Materials

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