A data-driven method for real-time compaction quality evaluation of a cement-stabilized base layer

Abstract

Adequate and uniform compaction is essential for the safety and durability of a pavement structure. The current compaction quality control, which relies on limited spot tests data, cannot provide timely feedback about compaction quality. The main objective of this paper is to develop a novel data-driven method for compaction quality assessment of cement-stabilized base in a real-time manner. The basic idea is to consider the drum of the vibratory roller together with the underlying cement-stabilized base layer as a spring-mass-dashpot system. The compaction level of the base is connected to the stiffness of the system and to the corresponding natural frequencies. In this study, the vibration of the drum was monitored during operation. The fundamental mode natural frequency of the system at different compaction levels of the base was identified by the fast Bayesian fast Fourier transform method. The results indicate that the natural frequency of the vibratory system has a positive correlation with the degree of compaction (DOC) of the underlying cement-stabilized base layer. Therefore, a novel and practical method for on-site compaction quality assessment utilizing measured natural frequency is proposed in this paper. A data-driven classification method based on support vector machine (SVM) was developed to realize the compaction quality evaluation. The classification results show that the proposed method can recognize signal patterns corresponding to different DOCs. The proposed method combines vibration theory and machine learning to provide a technical reference for the research of continuous compaction control with vibratory rollers.

Keywords

Compaction quality cement-stabilized base layer natural frequency support vector machine data-driven

Introduction

The service life of a roadway is related to the compaction quality of its pavement and subgrade. Conventional compaction quality control relies on spot tests, such as the sand replacement method, nuclear gauge test, falling weight deflectometer, and plate bearing test, measured at several spots along a roadway. These manual measurements have several drawbacks: (1) the processes are usually time-consuming and may interrupt the compaction operation; (2) the testing results cannot reflect the overall pavement quality due to the limited sample points; (3) the measurements are conducted periodically during the compaction operation after a certain number of passes of the vibratory roller, and therefore, it is impossible to provide real-time compaction quality information to vibratory rollers operators, which may lead to improper compaction. In order to address these problems, the intelligent compaction (IC) technique, also termed the continuous compaction control, has been developed to provide information on compaction quality to the operator of vibratory rollers in real-time (Wang et al., 2022).

The core of the IC technique includes the representation of intelligent compaction measure value (ICMV), the relationships between ICMV and density (or degree of compaction (DOC)) of compacted materials, and the control of compaction quality in real-time. References (Adam and Pistrol, 2016; Liu et al., 2020) summarized the state-of-the-art research on ICMV. The proposed ICMVs in these studies can be classified into two categories:

Frequency-based ICMVs, which include compaction meter value (CMV), resonance meter value (RMV), compaction control value (CCV), and machine drive power. CMV, which is widely used for quality assurance, is calculated from the vibration amplitudes at the operating frequency and the first harmonic. On top of the first harmonic, CCV and RMV also consider the first sub-harmonic and other higher-order harmonics.

Mechanics-based ICMVs (e.g., the vibration modulus $E_{vib}$ and the soil stiffness $K_{s}$ ) use the force–displacement curve measured on the drum to determine the modulus of the compacted layer.

Considering the periodical loss of contact between soil and drum, Anderegg and colleagues (Anderegg and Kaufmann, 2004; Anderegg et al., 2006) developed a feedback control system to automatically adjust the roller’s parameters (including frequency, amplitude, and roller speed) during compaction. A few years ago, researchers began to apply artificial intelligence to assess compaction quality in real-time. Barman and colleagues (Barman et al., 2016, 2018; Imran et al., 2018) presented an intelligent compaction analyzer (ICA) to identify compaction quality. Some field tests showed that the results correlate well with the modulus of subgrade. Cao et al. (2021) employed an artificial neural network (ANN) model to predict the CMV value during compaction, and the results were in good coherence with measured data. Besides, An and colleagues (An et al., 2020; Zhang et al., 2019a) adopted sound compaction value as an index to evaluate the compaction quality of rockfill materials and proposed an optimization procedure to optimize the overall compaction process based on genetic algorithm. Nevertheless, the above methods are still immature and need further study before they can be applied in the industry. First, as a harmonic-based indicator, CMV is easily influenced by many factors (Hu et al., 2020). Zhu et al. (2018) conducted a test on the multi-layer structure and concluded that CMV is sensitive to the characteristics of underlying layers, such as the stiffness and moisture content. Mooney and Rinehart (Mooney and Rinehart, 2007, 2009) demonstrated that $K_{s}$ decreased with increasing excitation force on a soft layer while the converse was obtained with a stiffer layer. Further analysis by (White et al., 2011) showed that many factors, including the type of roller, variation of the operating setting of the machine, and instability of practicing condition, imposed an adverse effect on the accuracy of these ICMVs. Besides, a full-scale test was carried out at subgrade compaction and further revealed that there was a poor correlation between compaction efficiency and excitation force (Wersäll et al., 2017, 2018). It implies that the applicability of some mechanics-based ICMVs (e.g., soil stiffness, vibration modulus, etc.) should be further verified.

Although there are some problems in existing compaction indexes, vibration acceleration response is still an efficient tool to monitor compaction status. The authors had been successful in identifying the packing/compaction level (health status) of ballast underneath a railway sleeper using acceleration responses (Adeagbo et al., 2021a; Lam et al., 2020). It is well known that the vibratory drum and underlying compacted layer form a spring-mass-dashpot system. The response measured on the roller drum changes as the layer becomes stiffer (Foroutan et al., 2020; Mazari et al., 2017; Susante and Mooney, 2008). Therefore, to evaluate the compaction quality using output-only vibration signals, it is important to extract characteristics related to the stiffness of the vibratory drum-compacted layer system from the signal. Recently, vibration-based analysis has had many successful applications on structural health monitoring of civil engineering structures, e.g., railway tracks, long-span bridges, and high-rise buildings (Adeagbo et al., 2021b; Lam and Adeagbo, 2022; Reynders, 2012). As operational modal analysis (OMA) uses output-only responses to identify modal parameters (such as natural frequencies, mode shapes, and damping ratios) without using the system input information, the measurement of external excitation can then be avoided. Several OMA methods (for example, the classical peak picking method, which directly identifies the modal frequencies according to the peaks of the power spectra) have been successfully implemented in civil engineering structures, such as buildings and bridges. The identified modal parameters can then be used for structural model updating and health monitoring (Devriendt et al., 2009; Lam et al., 2019; Li and Kiureghian, 2017). Stochastic Subspace Identification (SSI) is another popular method for OMA since it has a complete mathematical theory and needs less input information. Though having advantages like as mentioned, SSI has shortcomings such as the selection of system order needs to be conducted before extracting modal parameters. Besides, SSI cannot provide uncertainties information for the selection (He et al., 2021). To identify the modal parameters and to quantify the associated posterior uncertainties, the fast Bayesian FFT method was developed (Au, 2011), which is computationally efficient, thus making real-time OMA possible. The fast Bayesian FFT method has been successfully adopted for model updating of existing civil engineering structures (Lam et al., 2017, 2019). It must be pointed out that the OMA has not been applied to analyze the vibration characteristics of a drum-compacted layer system, nor for evaluating the compaction quality of pavement layers.

This paper employs the fast Bayesian FFT method for OMA so as to evaluate the compaction quality of the base layer and propose a data-driven model to realize the quality evaluation in real-time. An in situ test was carried out on cement-stabilized material, and the vertical vibrations of the roller drum were measured at different DOCs of the base layer. The DOCs were measured by the sand replacement method. By using the fast Bayesian FFT method, modal parameter identification is achieved through the output-only responses. The changes in the identified natural frequency of the drum-compacted layer system, which is caused by the changes in DOC due to the increasing number of passes of a vibratory roller, were discussed. A method based on modal parameter identification was proposed to evaluate the compaction quality and establish a relationship between measured vibration signal and DOC. A data-driven model based on the support vector machine (SVM) was proposed to classify the measured signal into different DOCs. Thus, in the quest to ensure that the required compaction quality is achieved, the vibration compaction quality can be evaluated and monitored continuously and in real-time without being interrupted by DOC tests.

In situ test program

Test beds

A field test was carried out at the extension project of G2 Expressway in Shandong Province, China. The typical pavement structure is shown in Figure 1, which includes a semi-rigid base layer (2 × 18 cm cement-stabilized aggregate), a sub-base layer (18 cm cement-stabilized weathered sands), and a subgrade layer (natural soil). Before the field test, the compaction of the lower 18 cm thick layer of cement-stabilized aggregate had been completed. Thus, the layer to be compacted in the field test is the top 18 cm thick layer of cement-stabilized aggregate. The pavement materials were carefully mixed, paved, and compacted under the optimum water content (see Table 1).

Figure 1.

The pavement structure in the field test.

Table 1.

Details of the compacted layer.

Layer	Materials	Depth (cm)	Cement mass percent (%)	Maximum dry density (g/cm³)	Optimum water content (%)
Semi-rigid base	Cement-stabilized gravel	18	4.9	2.348	4.9

Instrumented roller

A roller with a single vibratory drum was used in this study. The details of the roller are summarized in Table 2. A uniaxial accelerometer was used to measure the vertical vibration of the system at a sampling frequency of 2000 Hz. As shown in Figure 2, the sensor was well-fastened to the back of the drum with a magnetic suction seat. A UT8508M data acquisition system placed in the roller cab was used to record the vibration data. The roller was operated at a relatively steady speed and excitation frequency to minimize the noisy signal caused by the roller.

Table 2.

Details of instrumented roller.

Parameters	Unit	Value
Operating mass	kg	26,000
Mass of drum	kg	13,000
Drum width	mm	2170
Operating speed	km/h	5.85
Excitation frequencies	Hz	32/28/34
Amplitude	mm	1.9
Excitation force	kN	290
Sampling frequency	Hz	2000

Figure 2.

The single-drum vibratory roller adopted in the test and the sensor installation.

Degree of compaction test

The in situ test was carried out on the first to sixth lanes (each with 150 m length and 2.17 m width). Note that the width of the vibratory drum is designed to be the same as that of the lane. As shown in Figure 3, the roller followed the middle dashed line in each lane to perform the compaction. The compaction of the top semi-rigid layer on each lane consists of eight passes (denoted as Pass 1 to Pass 8). After every two roller passes, the DOC test was carried out on a pair of sampling locations (indicated with the same label in Figure 3). Based on the specification, these two sampling locations are designed on opposite sides of the lane with at least 80m spacing. Hence, there were four pairs of test locations in total for eight roller passes. Thus, there are four different pairs of sampling locations in Figure 3 labeled as ①,②,③, and ④, corresponding to the test done after the second, fourth, sixth, and eighth roller passes, respectively. For each test, the average value of the DOC from each pair of sampling locations is considered as the DOC value. As an industrial practice, the drum was vibrated with an excitation frequency of 32Hz, 28Hz, and 34Hz in Pass 1, Passes 2 to 4, and Passes 5 to 8, respectively. Furthermore, two static passes (without vibration excitation) were performed before Pass 1 (for building up certain stiffness on the layer).

Figure 3.

Locations of DOC test (indicated as crosses) for a lane.

The DOC of the compacted layer at a given sampling point is calculated by the sand replacement method (F20-2015, 2015)

ρ_{d} = \frac{m_{d}}{m_{b}} \times ρ_{s}

(1)

K = \frac{ρ_{d}}{ρ_{b}} \times 100 %

(2)

where $K$ is DOC of the compacted layer at a given sampling location; $ρ_{d}$ is the dry density of the sampled material; $m_{d}$ is the dry mass of the sampled material taken out from the sample pit; $m_{b}$ is the mass of standard sand used to fill the sample pit; $ρ_{c}$ is the maximum dry density obtained by moisture-density test (see Table 1); and $ρ_{s}$ is the dry density of the standard sand (= 1.529 g/cm³).

After vibration compaction started, the $K$ values for the two sampling locations which are labeled as ①, as shown in Figure 3, were calculated by the sand replacement method. For the sake of reliability, the mean $K$ value obtained at the two sampling locations is considered as the DOC of the lane after 2 passes. After 4 passes, the $K$ values for the two sampling locations ② were calculated, and the corresponding average is the DOC of the lane after 4 passes. Similarly, the DOC of the lane after 6 and 8 passes were calculated. After the in situ test, four DOC values (corresponding to 2, 4, 6, and 8 passes) were obtained for each lane.

The minimum DOC requirement of the cement-stabilized aggregate base is 98%. Based on field practice, at least 6 passes are required to meet this requirement (8 passes were considered in this test program).

In situ test results and discussions

Modal analysis of vibratory drum-compacted layer system

Fast Bayesian FFT Method

Instead of other modal parameters identification methods like manual peak picking, frequency domain decomposition, etc., that only helps to estimate the modal parameters (especially natural frequencies) without any information on the accuracy or certainty, the fast Bayesian FFT method, which builds on the Bayesian theory to quantify the uncertainty in identified modal parameters are employed in this paper. The fast Bayesian FFT method was developed by Au (2012a) based on the original Bayesian FFT method (Au, 2012b) to reduce the computational demand. For the completeness of this paper, a brief overview of the theory is presented, and readers are referred to the references for more details.

For the $j$ th time step in a measured time-domain data set with $N$ time steps and $n$ measured degrees-of-freedom (DOFs), the fast Fourier transform (FFT) of the data vector ${\overset{\cdot\cdot}{y}}_{j}$ is defined as

\begin{matrix} F_{k} = \sqrt{\frac{2 Δ t}{N}} \sum_{j = 1}^{N} {\overset{..}{y}}_{j} \exp [- 2 Π i \frac{(k - 1) (j - 1)}{N}] \\ f o r j, k = 1, \dots, N \end{matrix}

(3)

where $i^{2} = - 1$ , $Δ t$ is the time step. Let $Z_{k} = [Re F_{k}; Im F_{k}] \in ℝ^{2 n}$ be an augmented vector of the real and imaginary parts of $F_{k}$ . Usually, only the FFT data within a selected frequency band and denoted as ${Z_{k}}$ are used for statistical inference.

In this study, the ultimate modal parameter of interest is the natural frequency ${f_{i} : i = 1, \dots, m}$ , where $m$ is the number of target modes. Since the natural frequencies are only obtainable via the FFT data, the set of uncertain parameters $θ$ to be identified for each $i$ th mode is then consisted of the natural frequency $f_{i}$ , the Hermitian power spectral density (PSD) matrix of modal forces, and the PSD of the prediction error. Assuming a constant PSD in the resonance band of the considered mode, and assuming the prediction error as i. i.d Gaussian white noise, the conditional probability of the uncertain $θ$ based on the FFT data ${Z_{k}}$ , termed the posterior probability distribution function (PDF), can be obtained following Bayes’ theorem as

p (θ | {Z_{k}}) \infty ({Z_{k}} | θ) p (θ)

(4)

where $p ({Z_{k}} θ)$ is the likelihood PDF, and $p (θ)$ is the prior PDF through which the modeler’s experience and judgment about $θ$ can be incorporated. Assuming a non-informative prior, then $p (θ | {Z_{k}}) \propto p ({Z_{k}} | θ)$ . To obtain the most probable value of the set of uncertain parameter $θ$ , the likelihood function $p ({Z_{k}} | θ)$ therefore need to be maximized, which is equivalent to minimizing the negative of the likelihood or its logarithm (to prevent the problem of numerical overflow). Assuming a large number of FFT ordinates and zero-mean Gaussian multi-dimensional distribution, the negative log-likelihood is given as

N L L F (θ) = - \ln ({Z_{k}} | θ) = \frac{1}{2} \sum_{k} (\ln | C_{k} (θ) | + Z_{k}^{T} C_{k}^{- 1} (θ) Z_{k})

(5)

where $| C_{k} (θ) |$ is the determinant of the covariance matrix $C_{k} (θ)$ . Minimizing the $NLLF (θ)$ function is still computationally intensive, especially with long measured data, and so the fast Bayesian FFT algorithm was developed to further speed the process by eliminating some modal parameters and allowing the MPVs of the modal parameters to be obtained almost instantaneously. More details on the quantification of the uncertainties involved with each modal parameter identified in $θ$ are provided in (Au, 2012b).

Analysis of the output response

For the vibratory drum-compacted layer coupled system, the output responses of the system contain information about the system properties and the input excitation. As shown in Figure 4, the output responses can be classified into three types, including harmonic response, ambient vibration, and stochastic response. Each of them is respectively excited by different types of input excitation. First, the stochastic response is induced by random disturbance. It has features of low amplitude and wideband. This type of response is regarded as undesired noise and should be eliminated out of the spectrum. Second, the harmonic responses are mainly comprised of excitation frequency and its harmonic bifurcations. The relationship between harmonic frequencies and roller passes is shown in Figure 5. In practical compaction work, the roller switches successively between the excitation frequency in the order of medium-frequency (32 Hz), low-frequency (28 Hz), and high-frequency (34 Hz). The first-order and second-order super-harmonic frequencies (around 60 Hz and 90 Hz, respectively) have a similar trend with the excitation frequencies. Besides, during every vibratory period, the drum periodically impacts the base layer, exerting a moving impact force on the compacted layer. This action is equivalent to the application of a series of impact forces with a relatively long contact time to the drum-compacted layer system (i.e., the spring-mass-dashpot system). The longer the contact time of an impulse, the smaller the frequency range in the resultant spectrum at the lower frequency region will be. In this study, this frequency range is approximately from 0 to 15 Hz. This effect is termed “ambient vibration” in the response spectrum in Figure 4. By using the Fast Bayesian FFT method, the modal parameters can then be identified (see the section In situ test results and discussions).

Figure 4.

Analysis on the output response of vibratory drum-compacted layer system.

Figure 5.

Relationships between harmonic frequency and roller passes.

Natural frequency identification using the fast Bayesian FFT method

For the sake of identifying lower-order resonant peaks, only the response around 0–20 Hz is considered. As an example, Figure 6 shows the singular value spectrum of the responses after different passes from lane 1. By using the Fast Bayesian FFT method, the distinct peaks marked on the plots are regarded as first-order resonant peaks, and the frequency corresponding to each peak is considered as the low-order natural frequency of the system for each of the considered passes, respectively. It can be clearly observed in the spectrum that the resonant peaks are around 10 Hz and change as the number of roller pass increases. The results of the Fast Bayesian FFT method are summarized in Figure 7. It should be noted that the compacted layer is a nonlinear structure with infinite degrees-of-freedom. Hence, in theory, it has an infinite number of resonant peaks. However, low-order natural frequencies are relatively easily excited and observed in the spectrum. The relationship between natural frequencies and stiffness exists in any resonant frequency. Therefore, it is more efficient to identify the system parameters by using low-order natural frequency rather than higher-order natural frequency.

Figure 6.

The singular value spectrum of responses after different passes from lane 1.

Figure 7.

The most probable values for natural frequency based on fast Bayesian FFT method.

Analysis of natural frequency and DOC

Relationship between natural frequency and number of passes

As shown in Figure 7, the natural frequency shows an upward trend from the first to the eighth pass for the considered lanes (i.e., Lanes 1–6). During the eight consecutive passes, the mean values of natural frequencies have a fast increase in the first six passes, then a decrease between the sixth and seventh pass, and finally a slight increase between the last two passes. It reveals that the stiffness of the compacted layer is low at the beginning of compaction and then has a swift increase as the number of passes increases. At the initial stage, the compacted layer is in a loose state, and with plastic deformations during the several passes, the density of the compacted layer increases fast under the compacting force. There is a decrease in the natural frequency at the seventh pass, implying that the stiffness of the compacted layer decreases; and afterward, an increase in the natural frequency can be seen in the eighth pass. The natural frequency undergoes a fluctuation between the sixth pass and the eighth pass because at the sixth pass, the compacted layer has reached a high density, and its ability to resist plastic deformation is strong. However, at the seventh pass, the layer achieved over-compaction with the additional compacting force, leading to a decrease in the natural frequency. After the eighth pass, the stiffness of the layer picks an upward trend again, even going slightly higher than that obtained after the sixth pass, as the layer can now regain additional resistance to deformation after the over-compaction state. It is evident that compactions after sixth pass may be needless in field compaction operations, owing to the over-compaction phenomenon and an almost stable value of the stiffness (and natural frequencies) after overcoming the phenomenon.

Correlations between natural frequency and degree of compaction

Figure 8 illustrates the results of DOC measured in the first to sixth lanes for the four tests done after the second, fourth, sixth, and eighth compaction roller passes. The DOC values in the lanes show a steadily upward trend with an increase in the number of passes. Between the second and fourth passes, the average DOC values increased significantly from 94.3% to 96.6%, while the average has only a slight increase from 98.2% to 98.8% between the sixth and eighth passes. After 6 passes, the DOC values in all testing lanes rise to over 98% (except in the second lane, 97.6%), and the values of DOC eventually reach 98% for all lanes after 8 passes, meeting the requirement of the standards (F20-2015, 2015). Though with significant variability across the number of passes, the DOC values have a similar rising trend as that of the natural frequency (see Figures 7 and 8). The DOC values gradually become less sensitive to the number of passes as it increases. This reveals that the compacted layer has achieved a relatively uniform DOC at the latter stage compared to that of the early stage. To investigate the correlation between the DOC value and the natural frequency obtained at the same number of passes, linear regression analysis was carried out, and the result is presented in Figure 9. It can be observed that the natural frequencies have a positive correlation with the DOC values. The R² value of 0.7308 in the graph is relatively high, indicating that the correlation between DOC and natural frequency is consistent and stable.

Figure 8.

Testing results of DOC.

Figure 9.

Correlation between natural frequencies and DOCs.

Evaluation method for compaction quality during construction

Based on the above analysis, there is a significant correlation between the natural frequency of the system and the DOC of the compacted layer. Also, the changes in the natural frequency can well reflect the changes in the DOC of the compacted layer. Therefore, a method based on the variation of the system’s natural frequency can be adopted to evaluate the compaction quality during construction. The main procedure of this method is shown in Figure 10, which includes the following steps:

Acquisition of vibration signal: After material for the compacted layer is paved on the roadbed, compaction work is carried out according to the pre-designed rolling pattern. During this period, vibrational sensors are used to acquire continuous vibration signals of the vibrational system.

Signal processing: The signal processing technique is used to analyze the time-frequency characteristic of the ambient response. The system’s resonant peak can be determined by either observing the periodical change of amplitude of the resonant peak or following the increment in the resonant peak’s frequency as the number of passes increases. A band-pass filter is implemented to eliminate the signal components which are irrelevant to the ambient response. These components include the excitation frequency of the drum and its sub-harmonic or super-harmonic frequencies, as well as other stochastic signals that are discontinuous in the time domain.

Operational modal analysis: The processed time-domain signal is analyzed in the frequency domain by obtaining its Fourier transformation and power spectral densities (PSD). With the utilization of PSD transformation, the signal can be further denoised. Then, the Fast Bayesian FFT method is applied to directly identify the natural frequencies corresponding to the system resonant peak in the PSD diagram.

Compaction quality assessment: The obtained natural frequencies are used to assess the overall compaction quality of the compact lane. When the natural frequency changes significantly as the number of passes increases, the DOC does not meet the requirement yet. The compaction quality requirement will be achieved when the natural frequency maintains a relatively stable value with an increasing number of passes.

Figure 10.

The procedure for assessment of compaction quality based on the natural frequency.

A Data-driven classification model

The analyses carried out in the previous sections revealed the theoretical correlation between the natural frequency and the DOC of compacted materials is high. It was also demonstrated that the measured time-domain signal could be used to extract features related to the DOC. In view of the limited natural frequency and the number of roller passes obtained during the compaction process, real-time compaction quality estimation is a typical small-samples classification problem. Support vector machine (SVM) is widely used in small-samples classifications and has a lot of successful applications in engineering (Lei et al., 2022; Yücel et al., 2021). Thus, a method based on SVM is presented to achieve an automated and rapid evaluation of the compaction quality in this paper.

Signal Pre-processing

Considering the demand of real-time evaluation, the long measured signal at each roller pass needs to be divided into lots of short signals. In this study, the long signals are cut into many 1 s short signals, with each short signal having 2000 data points, such that an overlap of 1000 data points from the previous signal is ensured. The random vibration caused by the roller and other factors leads to the fluctuation of the signal amplitude. To eliminate the influence of amplitude fluctuation, each short signal was normalized as

x = \frac{x_{i} - x_{\min}}{x_{\max} - x_{\min}}

(6)

where $x_{i}$ is the $i^{th}$ value in a short signal array. $x_{\max}$ and $x_{\min}$ is the maximum and minimum value in the array, respectively. The measured signal from first to fifth lane is set as the training set, while the measurement from the sixth lane is set as the testing set. The DOC results, as shown in Figure 8, are divided into three categories of <94%, 94%–98%, and >98%, with a corresponding marking of −1, 0, and 1, respectively.

Model parameters determination

The SVM uses a kernel function to map a low-dimensional inseparable features space into a high-dimensional space and seeks an optimal hyperplane to classify the space. Therefore, the type of kernel function selected has a significant influence on the learning effect (Chaiyasarn et al., 2021; Lu et al., 2021). The radial basis kernel function (RBF) was employed in this paper since it is widely used in SVM and commonly has good results (Zhang et al., 2019b). The RBF is expressed as

k (x, y) = \exp (- \frac{x - y^{2}}{2 σ^{2}})

(7)

where x is the instance, and y is the center of the RBF. The correction of error during training directly affects the learning performance of the model. In the RBF, the error penalty parameter $C$ which determines the trade-off between the training error and the generalization performance, and the kernel parameter $σ$ play the key role in classification ability (Yang et al., 2021). In order to seek for the optimal parameter $C$ and $σ$ which make the training model has the highest accuracy. This paper employs the grid search method to search various pairs of parameters $C$ and $σ$ from 2⁻² to 2¹⁰. Then the cross-validation method is applied to optimize the $C and σ$ values which have the best accuracy. In this paper, using the data from the previous natural frequency and DOC analyses, the optimal values for the parameters $C$ and $σ$ are selected as 1 and 0.0039, respectively.

Results of SVM-based classification

The training set with 1076 samples and the testing set with 307 samples were used to train and test the classification SVM, respectively. Table 3 shows the classification results of the SVM. From a total of 307 samples in the testing set (obtained from the sixth lane), 269 samples were correctly classified, culminating in an overall recognition accuracy of 87.6%. The SVM has better classification performance in DOC intervals of 94%–98% and >98%, with a recognition accuracy of 86.1% and 91.2%, respectively. Considering that the number of training samples with DOC <94% is relatively small (only 118 out of 1076 samples), the model has a relatively low recognition accurate rate in DOC <94% category (i.e., 79.3%). In conclusion, the established model based on SVM is able to carry out compaction quality evaluation to a satisfactory level and shows better performance in recognizing the patterns with DOC value near the required standard.

Table 3.

Classification results by SVM.

DOC (%)	Number of training samples	Number of testing samples	Number of correct estimation	Accurate rate (%)
<94	118	58	46	79.3
94–98	228	79	68	86.1
>98	730	170	155	91.2
Summary	1076	307	269	87.6

Summary and conclusions

Compaction quality evaluation during construction is very important for ensuring the uniformity of compaction and efficiency of operations. Based on the variations of the natural frequency of the system formed by the roller drum and the base beneath the drum, a method for compaction quality assessment for cement-stabilized base is presented. A field compaction test on cement-stabilized aggregate was conducted, and the vibration responses of the vibratory drum-compacted layer system were acquired. After signal processing and analysis, the fast Bayesian FFT method is implemented to identify the main modal parameters (natural frequencies) in the power spectrums. The relationships between the natural frequency and the number of passes are obtained. Finally, SVM-based classification was presented to estimate the DOC of the compacted layer. The main conclusions can be drawn as follow:

The low-order natural frequency of the vibratory system does not follow the same trend as the excitation frequency in terms of the variation in the number of roller passes. However, with an increase in the number of roller passes, the change in the natural frequency is similar to that of the DOC. Hence the low-order natural frequency of the system can reflect the DOC of the compacted material.

With an increase in the number of passes, the natural frequency of the system rises swiftly at first and then becomes almost flat. When the natural frequencies no longer have a significant increase with the increase in the number of roller passes, the DOC meets the requirement. Based on this observation of the natural frequency trend, a new method is proposed to assess the compaction quality of cement-stabilized base during construction.

An SVM-based classification method is developed for DOC evaluation. The results show that the established SVM has satisfactory performance in recognizing signal patterns corresponding to different DOCs. This data-driven method presents a promising way to evaluate compaction quality in real-time and may be applicable with varying conditions on-site.

It should be noted that the natural frequency of the vibratory drum-compacted layer system is affected by many factors (e.g., the type of materials for the compacted layer, variability in boundary conditions of the underlying layer, type of roller, etc.). Hence, the variation trend of the natural frequency with the number of roller passes and DOC values needs further experimental verification in varied conditions. Furthermore, artificial intelligence is believed to be a useful tool to identify system parameters and compaction conditions in real-time during construction, which deserves further research in the future.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. R5020-18 [RIF 8799008]).

ORCID iDs

Heung-Fai Lam

Mujib Olamide Adeagbo

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