paper 4

1. Hyperspectral Imaging Features for Mortar Classification and Compressive Strength
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Assessment
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Liang Fan 1, Ming Fan 2, Abdullah Alhaj 1, Genda Chen 1,* and Hongyan Ma 1
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1
Department of Civil, Architectural and Environmental Engineering, Missouri University
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of Science and Technology, Rolla, MO 65401, United States; lf7h2@mst.edu;
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ahanbc@mst.edu; mahon@mst.edu
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2
Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and
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State University, Blacksburg, VA 24060; mingfan@vt.edu
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* Correspondence: gchen@mst.edu; Tel.: +01-573-341-4462
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Abstract: In this study, hyperspectral imagery with two computational algorithms are
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proposed to classify the type of mortar and assess the in-situ strength of fresh mortar in near
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real time. Each scanning on a mortar surface includes 30 spatial pixels selected for analysis,
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each assigned with a light reflectance spectrum over 400 - 2500 nm. Three groups of mortar
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samples with a water-to-cement (W/C) ratio of 0.6, 0.5 and 0.4, respectively, were cast and
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scanned from Day 1 to 14 of curing. Reflectance data at a wavelength range of 1920 nm to
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1980 nm, associated with the O-H chemical bond, were extracted and averaged to classify
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the different mortar types with K-Nearest Neighbors (KNN) and Support Vector Machine
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(SVM) algorithms and to predict their compressive strength from a regression equation. The
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results showed that the average reflectance increased with time due to water molecules
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reaction during curing process. The KNN classification model with K=5 had a prediction
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accuracy of 70% to 75%, and the SVM classification model with C=1000 and σ=10 showed
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a prediction accuracy of approximately 90%. Therefore, the SVM classification algorithm
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is recommended for use in mortar classification. The compressive strength is well correlated
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with the average reflectance with a coefficient of over 0.98.
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Keywords: Hyperspectral imaging; W/C ratio; reflectance; KNN; SVM; compressive
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strength
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1. Introduction
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Concrete is a mixture of aggregate, sand, cement and water in a certain proportion. The
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cement and water together, referred to as cement paste, hardens through hydration reactions
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and binds the aggregate and sand to achieve the strength of concrete in a curing process over
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time [1]. Concrete hydration process starts immediately after concrete casting. Cement reacts
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2. with water to generate hydration products like C-S-H gel and calcium hydroxide. The
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hydration products grow, interconnect, and bond aggregate and sand. Concrete is formless
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and shaped to various forms of interest, when newly mixed, and durable, when cured and
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hardened. In the construction of highway pavements, ACI Code 301-72 requires a minimum
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of curing period for concrete pavement to ensure that the constructed roadway is safe to
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traffic without damage [2]. In the repair and resurface of existing roadways and their
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transportation network in an urban environment, it is imperative to determine the early-age
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strength of concrete pavements so that the impact of roadway construction on traffic is
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minimized.
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Coring and pullout test are two of the conventional approaches that have been used for
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on-site evaluation of the compressive strength of concrete. With the coring method, concrete
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cores are acquired by drilling a concrete structure at selected locations, and tested for their
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compressive strength [3]. During the pullout test, a metal disk is attached to the concrete
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surface with super glue. After a short curing period, the metal disk is pulled perpendicularly
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off the surface and the pullout force can be used to calculate the compressive strength of the
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concrete structure [4]. The pullout force can be related to the compressive strength of
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concrete based on a pre-determined calibration curve. Both the coring and pullout test are
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destructive, potentially compromising the integrity of concrete structures.
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Nondestructive approaches such as the maturity method and the ultrasonic pulse velocity
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(UPV) have also been used to determine the compressive strength of concrete. The maturity
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method allows the estimate of early-age compressive strength of in-place concrete in real
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time. A maturity index as a function of curing time and temperature is determined according
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to the ASTM C1074 Standards [5]. In applications, a reference strength-maturity curve must
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be developed for each project-specific material in advance. With the UPV method, the
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velocity of an ultrasonic pulse that travels through concrete is measured and converted to the
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strength of concrete based on their pre-determined calibration curve [6]. The field application
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of this method is limited due to the effects of voids, cracks and steel bars.
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Hyperspectral imagery has been used to assess various conditions of concrete by imaging
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a concrete surface and analyzing the light reflectance as a function of wavelength for each
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pixel in an image. Such a reflectance-wavelength spectrum can be divided into many narrow
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and continuous wavelength bands for their correlation to specific materials on the concrete
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surface [7]. By analyzing the change of reflectance values at these prominent bands, different
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materials can be discriminated and classified. For instance, dark gray, light gray and
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dolomitic limestone were distinguished in the selection of Portland cement clinkers based on
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3. the reflectance variations of carbonate (CO3) and Al-OH in wavelength ranges of 2125–2400
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nm and 2170–2250 nm, respectively [8]. The carbonation degradation depth of concrete was
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estimated from reflectance values at a wavelength of 440 nm, 1500 nm, and 2340 nm [9].
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The total chloride content in mortar specimens was linearly related to the reflectance at a
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wavelength of approximately 2260 nm [10]. The status of concrete (hydration, curing and
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hardening) was determined by constructing a logistic regression model with reflectance
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spectra [11].
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In the past decade, hyperspectral imaging has also been used to estimate the compressive
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strength of concrete. For example, a partial least square regression model was developed to
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establish the relation between concrete strength (7, 14 and 28 days) and its corresponding
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reflectance over the entire wavelength range [12]. The reflectance spectrum of eight concrete
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samples with various W/C ratios and curing ages moved upward with an increase of
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compression strength [13]. In both studies, the mix designs of concrete were not introduced
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and the relation between the compression strength and the reflectance at a characteristic
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wavelength range was not clearly interpreted. Three groups of 28-day cured concrete
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specimens with a W/C ratio of 0.5, 0.65 and 0.8 were differentiable by comparing absorbance
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values (complimentary to reflectance) in a wavelength range of 1940-1970 nm [14]. In that
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study, the relation between absorbance and compression strength was not discussed.
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The ultimate goal of this study is to rapidly classify the type of concrete with various
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W/C ratios in pavement construction of highways through hyperspectral imaging from an
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unmanned aerial vehicle, and determine the early-age compressive strength of concrete
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pavements from light reflectance spectra. The focus of this paper is to develop a dataset with
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light reflectance and its corresponding compressive strength of mortar of various types, a
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classification model for mortar type, and a regression curve of reflectance versus compressive
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strength corresponding to a specific mortar type. Specifically, three groups of mortar cuboid
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samples with a W/C ratio of 0.4, 0.5 and 0.6 were cast. For each group, five mortar samples
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were tested for compressive strength after 1, 3, 5 7, 9, 11, 13, or 14 days of curing. Another
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nine samples were scanned using a hyperspectral camera from Day 1 to 14. A large set of
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reflectance data were extracted from the scanned images and used to train Nearest Neighbors
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(KNN) and Support Vector Machine (SVM) classifiers for discrimination of three mortar
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types. The compressive strength of each type of mortar samples was measured corresponding
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to the hyperspectral imaging schedule and related to the light reflectance by an exponential
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regression model developed.
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4. 2. Experiment Setup
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2.1. Sample preparation
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Three types of mortar samples were prepared and designated as C1, C2, and C3 in Table
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1. They are a mixture of water, ordinary Portland cement and Missouri river sand with a
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W/C/Sand weight ratio of 0.194/0.324/1.0, 0.182/0.364/1.0, and 0.165/0.415/1.0, or a W/C
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ratio of 0.6, 0.5, and 0.4, respectively. Type I Portland cement was used as detailed in Table
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2 for its chemical composition. The Missouri river sand used had the maximum particle size
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of 4.75 mm, a specific gravity of 2.64, and a fineness modulus of 2.71. Freshly mixed mortar
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was poured into standard cubic steel molds that are 50 mm × 50 mm × 50 mm in size. After
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casting, the specimens were covered with wet burlaps and plastic sheets to prevent surface
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cracking due to shrinkage. After 24 hours of curing, they were demolded for compressive
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tests and hyperspectral scanning. For each type of mortar mixture, compressive tests of 40
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samples were conducted according to the ASTM Standard C39 [15], 5 samples tested after
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1, 3, 5, 7, 9, 11, 13, and 14 days of curing and hardening. All the samples were cured in air
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with a temperature of 23 ± 1.7 °C and a relative humidity (RH) of 50 ± 5%. Hyperspectral
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scanning on 9 samples with each mortar mixture was conducted continuously for 13 days
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from the end of 1st day to 14th day of curing and hardening. For each cuboid sample, only
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the four vertical side surfaces were scanned since the horizontal top surface was relatively
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uneven. In addition, the top surface had a thin layer of cement paste due to water bleeding
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during mortar settlement, which made its composition different from the side surfaces [16].
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Table 1. Mix proportions of three types of mortar samples by weight (kg/m3
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Types of mortar samples C1 C2 C3
Water 288 270 245
Ordinary Portland cement 480 540 615
Missouri river sand 1482 1482 1482
Table 2. Mass percentage (%) of oxides in cement
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SiO2 CaO Al2O3 Fe2O3 MgO SO3 Loss of ignition
19.8 64.2 4.5 3.2 2.7 3.4 2.6
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5. 2.2. Hyperspectral scanning
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A wideband hyperspectral camera (Headwall Hyperspec VNIR-SWIR dual sensor) was
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used to scan the mortar samples. The co-aligned VNIR-SWIR sensor has a broad wavelength
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range of 400 - 2500 nm. The VNIR sensor has a spectral range of 400-1000 nm with 2.2 nm
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in spectral resolution and the SWIR sensor has a spectral range of 900-2500 nm with 6 nm
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in spectral resolution. Figure 1 shows the experimental setup of a cuboid mortar sample. A
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light source (LED illumination) was set at 0.5 m away from the mortar sample and lit the
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sample from one side (left in the photo). The hyperspectral camera was set right in front of
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the mortar sample at 1.2 m standoff distance from the front vertical side of the mortar sample
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for better resolution of near-distance imaging. The camera was installed on a tripod, both
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connected to a laptop installed with Hyperspec III software to control the camera’s rotation
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(±5°) in the horizontal plane and collect images continuously. A grey tarp was set right behind
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the mortar sample as a reference.
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Figure 1. Test setup of a cuboid mortar sample with illumination light, a hyperspectral
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camera, a laptop computer, and a grey tarp.
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Prior to each sample scanning, the hyperspectral camera was calibrated through the
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collection and processing of dark and white reference data. Measuring electric current in the
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camera system, the dark reference was collected with the camera lens covered, and deducted
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from any scanned image to cleanse noise. The white reference was used to get a white balance
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to enhance imaging quality. It was collected by aiming the camera lens at the grey tarp with
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a reflectance of 32%. The grey tarp was chosen in this study since its color was close to that
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of the mortar samples. Frame period and exposure time were adjusted to ensure that 60% of
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the saturated light intensity was detected by using the grey tarp since a lack of light intensity
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6. can generate too many bad pixels to correct mathematically. The rotation angle was adjusted
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so that the camera can scan the mortar surface area of interest at a fixed standoff distance of
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1.2 m. The rotation speed of the camera was also adjusted until no distorted shapes or forms
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were seen in the captured image.
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At the completion of each sample scanning, the scanned data files were transferred from
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the camera (480 GB solid-state drive) to the laptop computer. SpectralView software was
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then used to extract the reflectance spectrum for each pixel in the image by:
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Calibrated Reflectance = 𝑅𝑎𝑤−𝐷𝑎𝑟𝑘
𝑊ℎ𝑖𝑡𝑒−𝐷𝑎𝑟𝑘
× 𝑊ℎ𝑖𝑡𝑒 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑎𝑛𝑐𝑒 C𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 (1)
where Raw is the raw reflectance spectrum without processing, Dark means the dark
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reference spectrum, White means the white reference spectrum, and White Reference
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Reflectance Calibration denotes the maximum reflectance of white reference spectrum to
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ensure no saturation in measurement. The software SpectralView automatically calculates
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the normalized reflectance using the dark/white reference spectra.
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2.3 Data classification techniques
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Two classification models with KNN and SVM algorithms were established to
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distinguish various types (W/C ratios) of mortar samples from the reflectance dataset as
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shown in Figure 2. The reflectance dataset is a group of data with each datum showing a
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reflectance value and its corresponding class label (W/C ratio). In this study, 80% of the
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reflectance data were used for training and the remaining 20% were used for testing of the
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classification models. Both KNN and SVM algorithms were trained in Python to construct
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the classification models. The established classification models were then used to predict the
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label (Class A, Class B or Class C) for a W/C ratio of 0.6, 0.5, or 0.4 given a test example of
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known reflectance value.
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Figure 2. Reflectance data classification using classification algorithms.
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2.3.1 KNN
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The KNN algorithm computes the proximity of a test example z to K data points in the
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7. training set, which are closest to z. The test example is classified based on the majority class
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label of its K nearest neighbors [17]. Weights are assigned to the contributions of the
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neighbors so that the impact of data depends on their distances to the test example. Choosing
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the right parameter K is important to ensure a better accuracy in classification. A small K can
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result in overfitting due to noise in the training data, whereas a large K can lead to
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misclassification because the nearest neighbors may include data that are located far away
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from its neighborhood [17].
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2.3.2 SVM
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The SVM algorithm creates a line in two-dimensional planes, a plane in three-
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dimensional spaces, or more generally a hyperplane to divide the data into several classes
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[18]. Support vectors are the data points nearest to the hyperplane. The distance between the
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hyperplane and the nearest data is called margin [18]. The goal of SVM is to choose a
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hyperplane with the maximum margin. To briefly describe the SVM technique, a linear
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classifier is introduced first and then extended to the nonlinear classifier. Next, the maximum
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margin of a hyperplane is described.
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Linear classifier is used to find a line or a plane (hyperplane) to separate dataset
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{𝐱𝑖, 𝑦𝑖}𝑖=1
𝑛
into two classes. Here, 𝐱𝑖 is the 𝑖𝑡ℎ
vector in the given dataset, 𝑦𝑖 is the label
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associated with 𝐱𝑖. The hyperplane is defined as [18]:
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𝑓(𝐱) = 𝐰𝐱 + 𝑏 = 0, 𝐰𝐱 = ∑ 𝑤𝑖𝑥𝑖
𝑖
(2)
where w is a weight vector, and b is a bias. As illustrated in Figure 3 for the case of two-
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dimensional plane x1x2, f(x) =0 is a line that divides the entire dataset into two classes: f(x)
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>0 and f(x) <0.
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Figure 3. A linear classifier with maximum margins that divides the data into two sets.
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8. When the data cannot be separated by a linear classifier, they can be mapped to a higher
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dimension and converted to linearly separable data through a projection function 𝜑 [18, 19].
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The classifier then becomes:
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𝑓(𝐱) = 𝐰𝜑(𝐱) + 𝑏 (3)
As the high-dimensional projection function is complicated to compute, this classifier is
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projected back to the original dimension through a transformation known as the kernel
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function. In this case, the weight vector can be expressed into a linear combination of the
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training data [18]:
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𝐰 = ∑ 𝛼𝑖
𝑛
𝑖=1
𝜑(𝐱𝑖) (4)
where 𝛼𝑖 is the coefficient related to a decision boundary. The kernel function is defined as
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[18]:
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𝑘(𝐱𝑖, 𝐱) = 𝜑(𝐱𝑖)𝜑(𝐱) (5)
The classifier then transforms to:
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𝑓(𝐱) = ∑ 𝛼𝑖
𝑛
𝑖=1 𝜑(𝐱𝑖)𝜑(𝐱) + 𝑏 = ∑ 𝛼𝑖
𝑛
𝑖=1 𝑘(𝐱𝑖, 𝐱) + 𝑏 (6)
Two kernels are widely used in the literature for various applications: polynomial kernel and
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Gaussian kernel. A polynomial kernel is defined as [18]:
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𝑘(𝐱𝑖, 𝐱) = (𝐱𝐱𝑖 + 1)𝑑 (7)
A Gaussian kernel is defined as [18, 19]:
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𝑘(𝐱𝑖, 𝐱) = exp (−
‖𝐱−𝐱𝑖‖𝟐
2𝜎2
)
(8)
where d is the degree of polynomial kernel and σ is a parameter that controls the width of
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Gaussian kernel. Both parameters control the flexibility of the classifier. When σ is increased,
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a greater curvature is introduced to the decision boundary but overfitting will occur if σ is
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too large.
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SVM looks for a higher margin to get a better classification result for the testing data.
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The margin of a hyperplane f (x) is defined as:
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9. 𝑚(𝑓) =
1
‖𝐰‖
(9)
As indicated in Equation (9), to maximize the margin of the classifier is equivalent to
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minimize‖𝐰‖2
. The maximum margins are the margins that push up against the support
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vectors. To ensure that the linearly-separable data are classified correctly, the maximum
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margin and its constraint are defined as [18, 19]:
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Minimize
1
2
‖𝐰‖2 (10)
Subject to: 𝑦𝑖(𝐰𝐱 + 𝑏) ≥ 1 𝑖 = 1, … , 𝑛. (11)
When the data are not completely separable, the constraint is relaxed and a greater margin
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can be achieved by [18, 19]:
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Minimize
1
2
‖𝐰‖2
+ 𝐶 ∑ 𝜉𝑖
𝑛
𝑖=1
(12)
Subject to: 𝑦𝑖(𝐰𝑥 + 𝑏) ≥ 1 − 𝜉𝑖 (13)
where 𝜉𝑖 (0≤ 𝜉𝑖 ≤ 1) is the margin error that allows an example to be in the margin and C
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is the penalty that lowers the misclassification rate. When C is increased, a smaller margin
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error is achieved. C needs to be adjusted to ensure the maximum margin with a minimum
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margin error [18, 19].
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3. Results and Discussion
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3.1. Hyperspectral information
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Figure 4 shows the raw hyperspectral image of one mortar specimen, the image after
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subtraction of dark reference, and the image after dark and white reference deductions. The
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sensor current measured from the dark reference can induce perturbation and generate a noisy
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and drifted spectrum. The white reference can rectify illumination non-uniformity and non-
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flatness of a spectrum. Removal of the dark reference and the white reference can correct
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the image and produce right reflectance spectra. For each type of mortar, 9 cuboid samples
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were prepared, 4 side faces of each sample were scanned, and 30 spectra were extracted over
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a 50 mm × 50 mm side surface area, totaling 1080 spectra for each scanning day. The spectra
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10. were collected from the flat surface area only to avoid any non-uniform illumination from
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uneven spots.
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(a) (b) (c)
Figure 4. Hyperspectral image of a mortar specimen: (a) raw, (b) after subtraction of dark
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reference, and (c) after dark and white reference deduction.
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Figure 5 shows the average reflectance spectra of samples with three different W/C ratios
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over a period of 14 days. Each line represents the average reflectance spectrum of 1080
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spectra in the wavelength range of 1200 nm to 2400 nm. The average spectra can reduce
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potential biases and are more representative of the scanning surface. As seen in Figure 5, the
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reflectance value on the average spectra rapidly ascends from Day 1 to Day 3 and then
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gradually increased till Day 14 of test. After 1 day of testing, the samples were scanned after
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they were demolded and put in air at the room temperature for 1 hour. The higher moisture
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content on the sample surface resulted in the lower reflectance value due to water absorption.
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The rapid increase of reflectance from Day 1 to Day 3 is because the hydration process during
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this period rapidly consumes more water compared with that at a later stage.
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252
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
1200 1400 1600 1800 2000 2200 2400
Reflectance
(R)
Wavelength (nm)
Day 1 Day 3 Day 5 Day 7
Day 9 Day 11 Day 13 Day 14
(a)

11. 253
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Figure 5. The average reflectance spectra over a wavelength of 1200 nm to 2400 nm for
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samples with a W/C ratio of: (a) 0.6, (b) 0.5, and (c) 0.4.
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When shot on the surface of materials, some of the incident light leads to vibration of
257
molecules and is absorbed by the chemical bond between atoms in the molecules. In the Near
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Infrared Region (NIR) (from 780 nm to 2500 nm), higher vibrational energy is acquired to
259
absorb the light, which stimulates the overtones and combinations of fundamental vibrations
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[20, 21]. Basically, overtones and combinations of the vibrations of C-H, O-H, N-H, and S-
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H chemical bonds dominate NIR spectroscopy with each chemical bond corresponding to a
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wavelength region for light absorbance [21]. The combination of OH and H2O corresponds
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to the region of 1900 nm to 2000 nm [21-24], which is of particular interest in this study. The
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reflectance change in this wavelength range can be used to track the change of H2O molecules
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due to hydration consumption in the process of mortar curing. The reflectance values over
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0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
1200 1400 1600 1800 2000 2200 2400
Reflectance
(R)
Wavelength (nm)
Day 1 Day 3 Day 5 Day 7
Day 9 Day 11 Day 13 Day 14
0.06
0.07
0.08
0.09
0.1
0.11
0.12
1200 1400 1600 1800 2000 2200 2400
Reflectance
(R)
Wavelength (nm)
Day 1 Day 3 Day 5 Day 7
Day 9 Day 11 Day 13 Day 14
(b)
(c)

12. the wavelength range of 1920 nm to 1980 nm as shown in the marked red circles in Figure 5
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are averaged and defined as dR (1920-1980). The average reflectance dR (1920-1980) with
268
an error bar of ± one standard deviation for three types of mortar over the curing period of
269
14 days are plotted in Figure 6. Logarithmic regression was conducted to fit into the
270
experimental data for the three types of mortar. R2
value for each type of mortar is higher
271
than 90%, indicating good fitting of the regression curve. The overall reflectance during the
272
14 days shows an increasing trend when the W/C ratio is reduced from 0.6 to 0.4 since the
273
mortar with lower W/C ratio has less water content. For each type of mortar, the average
274
reflectance increases because water is reacted and reduced during the hydration process. As
275
less water is left on the sample surface, less light is absorbed by water molecules and
276
reflectance of the light is increased. Therefore, the regression curve can be used to predict
277
the curing process for mortar samples.
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Figure 6. The average reflectance dR (1920-1980) over a curing period of 14 days for
279
samples with W/C ratios of: (a) 0.6, (b) 0.5, and (c) 0.4.
280
3.2 Classification results with KNN and SVM
281
Both KNN and SVM algorithms were used to first establish classification models with
282
the training data, and then predict classification labels for the test data. In the KNN algorithm,
283
the parameter K varied from 1 to 40 in model training. Its corresponding prediction
284
y = 0.007ln(x) + 0.07
R² = 0.92
W/C=0.6
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14
Average
reflectance
dA
(1920-1980)
Curing Time (Day)
y = 0.011ln(x) + 0.07
R² = 0.93
W/C=0.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14
Average
reflectance
dA
(1920-1980)
Curing Time (Day)
y = 0.007ln(x) + 0.09
R² = 0.91
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14
Average
reflectance
dA
(1920-1980)
Curing Time (Day)
(b)
(a)
(c)

13. accuracies after 1, 4, 7, and 13 days of testing are presented in Figure 7. In this study, accuracy
285
is defined by the relative difference in percentage between the number of correct predictions
286
and the number of actual test data. It is observed that K = 5 yields the highest prediction
287
accuracy for Day 1, Day 7, and Day 13, and K = 6 provides the highest accuracy for Day 4.
288
Overall, K = 5 is chosen for the KNN classification model. Figure 8 shows the predicted
289
classifications after 1, 7, and 13 day of testing with K = 5 and after 4 day of testing with K =
290
6. In Figure 8, ‘True’ represents the test data and ‘Pred’ symbolizes the prediction data with
291
the trained KNN classification model. The predicted classification (yellow triangles) and the
292
actual classification (blue squares) are in general agreement.
293
294
Figure 7. Prediction accuracies as a function of K after 1, 4, 7, and 13 day of testing.
295
296
45
50
55
60
65
70
75
80
0 5 10 15 20 25 30 35 40
Accuracy
(%)
K value
Day 1
Day 4
Day 7
Day 13
(b)
(a)

14. Figure 8. Classification predictions after (a) 1, (b) 4, (c) 7, and (d) 13 day of testing.
297
To test the applicability of parameter K, K=5 is applied to predict the classifications of
298
the test data after 2, 5, 8, and 14 day of testing, and the predicted classifications are compared
299
in Figure 9 with their actual classifications. It can be seen from Figure 9 that the predictions
300
are in good agreement with the actual classifications. Specifically, the prediction accuracies
301
during the 4 days of testing range from 70% to 75% as shown in Figure 10, which falls into
302
the same range of accuracies achieved after 1, 4, 7, and 13 day of testing. This comparison
303
indicates that K = 5 is the best fit for the KNN model. Due to low prediction accuracies (<
304
75%) for the KNN model, the SVM algorithm is attempted to improve the prediction
305
accuracy for mortar classification.
306
(d)
(c)
(a) (b)

15. Figure 9. Classification predictions with K = 5 after (a) 2, (b) 5, (c) 8, and (d) 14 day of
307
testing.
308
309
Figure 10. Prediction accuracies with K = 5 after 2, 5, 8, and 14 day of testing.
310
In this study, the average reflectance dR(1920-1980 nm) and its corresponding Min-Max
311
normalized reflectance calculated from Equation (14) forms two features in x1-x2 plane. The
312
representative training data in the feature plane after 13 day of testing are presented in Figure
313
11. It can be seen that the three classes of training data are mainly distributed along three
314
straight lines due to the correlation of two features selected. The relatively low reflectance
315
for a w/c ratio of 0.6 can be easily separated from the other classes using a linear separator.
316
However, the two straight lines representing the feature data in other two classes are crossed
317
each other, making it impossible to separate them directly with a linear classifier. Therefore,
318
a nonlinear classifier with the Gaussian kernel and a relaxed constraint were used to obtain a
319
high prediction accuracy of the classification model.
320
0
20
40
60
80
100
Accuracy
(%)
Day 2 Day 5 Day 8 Day 14
(c) (d)

16. Min-Max normalized reflectance=
dR (1920−1980) −Min.
Max.−Min.
× 100% (14)
321
where Min. and Max. represent the minimum reflectance and the maximum reflectance of
322
the whole data set during each test day, respectively. dR (1920 − 1980) represents the
323
average reflectance over a wavelength range of 1920 nm to 1980 nm, corresponding to each
324
datum used in the dataset.
325
326
Figure 11. Training data in the feature plane after 13 day of testing.
327
To improve the accuracy of classification predication, the hyperparameters C and σ in
328
the SVM model were first tuned. Figure 12 shows the prediction accuracies after 1, 4, 7, and
329
13 day of testing when C is examined from 10-2
to 103
and σ is tested from 10-3
to 10. It can
330
be observed from Figure 12 that C=103
and σ=10 yield the highest prediction accuracies of
331
94.5%, 89.9%, 95%, and 87.4% after 1, 4, 7, and 13 day of testing, respectively. The
332
predicted classifications from the SVM model are compared in Figure 13 with the actual
333
classifications displayed when C = 103
and σ = 10. Compared with the classification results
334
in Figures 8 and 9 predicted from the KNN model, the overlapped range between the
335
predicted data and test data in Figure 12 is enlarged with a higher accuracy. Therefore, C =
336
103
and σ = 10 are chosen for the SVM classification model.
337

17. Figure 12. Prediction accuracies as a function of C and σ in the logarithmic format after (a)
338
1, (b) 4, (c) 7, and (d) 13 day of testing.
339
340
(a) (b)
(c) (d)
(a) (b)

18. Figure 13. Classification predictions of the test data after (a) 1 , (b) 4 , (c) 7 , and (d) 13 day
341
of testing with C = 103
and σ = 10.
342
343
To evaluate their applicability, the two hyperparameters C = 103
and σ = 10 are applied
344
to the test data collected after 2, 5, 8, and 14 day of testing. The predicted results are compared
345
in Figure 14 with their actual classifications. Figure 15 shows 93.4%, 92.9%, 93.0%, and
346
92.5% prediction accuracies after 2, 5, 8, and 14 day of testing, respectively. Therefore, C =
347
103
and σ = 10 in the SVM model are appropriate for the classification of mortar.
348
(c)
(d)
(a) (b)

19. Figure 14. Classification predictions with C = 103
and σ = 10 after (a) 2, (b) 5, (c) 8, and (d)
349
14 day of testing.
350
351
Figure 15. Prediction accuracies with C = 103
and σ = 10 after 2, 5, 8, and 14 day of testing.
352
3.3 Relation between average reflectance and compressive strength of mortar samples
353
For each W/C ratio, five mortar samples were tested in compression after 1, 3, 5, 7, 9,
354
11, 13, and 14 day of curing, following the ASTM C39 Guideline. The average and standard
355
deviation of the five compressive strengths of mortar for each testing day were determined.
356
The average strength with an error bar of ± one standard deviation is displayed in Figure 16
357
as a function of the curing day. Overall, the compressive strength of mortar decreases with
358
the increase of W/C ratio. For each W/C ratio, the compressive strength increases
359
logarithmically with the curing time. The short error bars in Figure 16 indicate consistent
360
data obtained from the compressive tests.
361
0
20
40
60
80
100
Accuracy
(%)
Day 2 Day 5 Day 8 Day 14
(c) (d)

20. 362
Figure 16. Compressive strengths of mortar samples with W/C ratios of 0.6, 0.5, and 0.4.
363
After 1, 3, 5, 7, 9, 11, 13, and 14 day of curing, both the compressive strength and the
364
average reflectance dA (1920-1980) were obtained. Their correlations for W/C ratios of 0.6,
365
0.5, and 0.4 are drawn in Figure 17. Exponential regression of the test data was conducted
366
for each W/C ratio with R2
larger than 90%. These relations indicate that the average
367
reflectance can be used to predict the compressive strength of mortar. Such relationships can
368
potentially be applied to predict the strength of early-age concrete pavement in practice.
369
y = 10.1ln(x) + 4.7
R² = 0.98
y = 11.2ln(x) + 6.6
R² = 0.99
y = 13.4ln(x) + 10.1
R² = 0.99
0
10
20
30
40
50
0 2 4 6 8 10 12 14
Compression
strength
(MPa)
Curing time (Day)
0.6
0.5
0.4
y = 0.041e79x
R² = 0.99
W/C=0.6
0
10
20
30
40
0.04 0.08 0.12
Compression
Stregnth
(MPa)
Average Reflenctance
dA (1920-1980)
y = 0.214e51x
R² = 0.98
W/C=0.5
0
10
20
30
40
0.04 0.08 0.12
Compression
Stregnth
(MPa)
Average Reflenctance
dA (1920-1980)
(a) (b)

21. Figure 17. Average reflectance dA (1920-1980) versus the compressive strength of mortar
370
with a W/C ratio of: (a) 0.6, (b) 0.5, and (c) 0.4 over 14 days.
371
3.4 Further work
372
Concrete samples with a wide range of mixture designs will be scanned with
373
hyperspectral camera. The SVM classification model will be kept updated and improved with
374
the reflectance data extracted from newly scanned concrete samples. The reflectance dataset
375
needs to be enlarged to include as many types of concrete as possible. Field test will be
376
conducted with hyperspectral camera installed on UAV to establish a similar correlation
377
between reflectance and compressive strength under actual in-situ conditions.
378
4. Conclusions
379
This study utilized a hyperspectral camera to scan the surface of mortar samples and
380
extract the reflectance data for the classification of different types of mortar and the
381
prediction of their compressive strength. Based on experimental data, regression analysis,
382
and classification results, the following conclusions can be drawn:
383
• The reflectance spectra over a wavelength range of 1200 nm to 2400 nm are
384
consistently shifted upward as mortar samples are cured and hardened over time. In
385
particular, the average reflectance in 1920-1980 nm wavelength increases
386
logarithmically with time because water molecules on each sample surface are
387
gradually reacted during the hydration process. As the water content of mortar is
388
reduced, less light is absorbed and more light is reflected. The average reflectance
389
can be accurately predicted from the curing time with their correlation coefficient
390
of over 0.9.
391
• The KNN classification model with K=5 represents the best fit to the test data taken
392
from mortar samples with a W/C ratio of 0.4 to 0.6. The classification (W/C ratio)
393
y = 0.045e66x
R² = 0.99
W/C=0.4
0
10
20
30
40
50
0.04 0.08 0.12
Compression
Stregnth
(MPa)
Average Reflenctance
dA (1920-1980)
(c)

22. prediction accuracies are in the range of 70% to 75%. The SVM classification model
394
with C=103
and σ=10 are the best fit to the test data with a prediction accuracy of
395
approximately 90%. Thus, the SVM classification model is recommended to
396
classify various types of mortar.
397
• The compressive strength of mortar can be exponentially related to the average
398
reflectance in 1920-1980 nm wavelength with a correlation coefficient of over 0.95.
399
With this strong exponential relation, hyperspectral imaging can be used as a rapid
400
and nondestructive evaluation tool to predict the compressive strength of mortar.
401
With further studies on concrete specimens, hyperspectral imaging is promising for
402
the prediction of early-age strength of concrete pavement in practical applications.
403
Author Contributions: Conceptualization, L.F., G. C. and H. M.; methodology, L.F. and
404
M.F.; validation, L.F. M.F. and G. C.; formal analysis, L.F. and M.F.; investigation, L.F.,
405
M.F. and A.A.; resources, G. C.; data curation, L.F. and M.F.; writing—original draft
406
preparation, L.F. and M.F.; writing—review and editing, L.F., M.F. and G.C.; visualization,
407
L.F., M.F. and G.C.; supervision, G.C.; project administration, G.C.; funding acquisition,
408
G.C. In general, the first two authors contributed equally to the preparation of this paper.
409
Funding: Financial support to complete this study was provided by the U.S. Department of
410
Transportation, Office of the Assistant Secretary for Research and Technology (OST-R)
411
under the Auspices of the INSPIRE University Transportation Center under Grant No.
412
69A3551747126 at Missouri University of Science and Technology. The findings and
413
opinions expressed in this paper are solely those of the authors and do not represent the
414
official policy or position of the USDOT/OST-R, or any State or other entity.
415
Conflicts of Interest: The authors declare no conflict of interest.
416
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