Prediction of Service Life of Thermoplastic Road Markings on Expressways

Abstract

Currently, historical data and on-site surveys—particularly in the context of China—are heavily relied upon to determine the best time to maintain expressway road markings. This study aims to determine what influences the service life of thermoplastic road markings on expressways in Shandong Province, China, while considering both those motorways’ unique characteristics and the local environment. Additionally, a scientific evaluation of the road markings’ retroreflective coefficient’s decay pattern will be undertaken. We collected the retroreflective data for twelve consecutive months regarding the thermoplastic road markings on five expressways and potential influencing factors such as age of marking and annual average daily traffic. The service life of the markings was forecast using a multiple linear regression. Dominance analysis was used to quantitatively analyze each explanatory factor’s impact on the service life of the markings, and statistically significant variables were also found. Using LightGBM, a machine learning technique, a nonparametric prediction model was also created based on examining the relevance of influencing elements. The modeling results show that LightGBM generates an R² of 0.942, implying that it offers better interpretability and higher accuracy than the regression-based approach. Additionally, LightGBM outperforms MLR according to final validation accuracies, with a score of 95.02% or more than 8% that of MLR. The results are useful for expressway marking upkeep and for driving safety.

1. Introduction

Road markings are one of the most important components of expressways. They convey traffic information such as guidance, restrictions, and warnings to traffic participants. Due to their exceptional abrasion and weather resistance, high construction efficiency, cost-effectiveness, and prolonged service life, thermoplastic road markings have emerged as one of the most extensively utilized road marking solutions on expressways at present [1].

Road markings with higher visibility improve drivers’ attention to the road, while drivers tend to take their gaze off the road and look for other references when road markings are less visible [2]. Road marking visibility is even more important at night, as drivers can only rely on the area illuminated by their vehicle’s headlights to keep their vehicle moving safely. The visibility of road markings at night is determined by the core index of the retroreflectivity coefficient. Where this coefficient is larger, the higher is the visibility [3] and the more drivers are able to see the road and lane contours clearly, thus reducing the probability of traffic accidents [3].

Under the influence of various factors, the retroreflectivity of road markings may diminish, affecting a driver’s visual recognition of road markings and creating traffic safety hazards [4]. Traffic accidents and congestion are often related to drivers’ difficulty in the visual recognition of road markings, especially at night, in bad weather or in low light conditions. Therefore, by scientifically studying the law of reflectivity attenuation, we can develop more accurate and efficient maintenance plans, ensure good visibility of road marking, and reduce the risk of accidents. In addition, scientific marking maintenance can also reduce the waste of resources. At present, the maintenance time of expressway marking mostly relies on historical experience and field surveys, which leads to maintenance that is either early or too late, thus wasting human, material, and financial resources. By understanding the attenuation law of the reverse reflection coefficient and making accurate life cycle prediction, the maintenance work can be rationally arranged to extend the service life of road markings to their maximum extent and improve maintenance efficiency.

Life prediction is of great significance in the promotion of the sustainable development of various industries. Nagoor Basha Shaik et al. (2020) have evaluated the life of crude oil pipelines and natural gas pipelines and have proposed a feedforward inverse propagation network (FFBPN) method by which to build a model for the prediction of the remaining service life of crude oil pipelines. The accuracy and robustness of the model showed very satisfactory results. Nagoor Basha Shaik et al. (2022) proposed a recurrent neural network (RNN)-based method for predicting the life of equipment with corrosion dimension classes exposed to critical condition monitoring has been proposed, and the life prediction of dry gas pipeline has been realized. The above studies help to assess the life condition of existing pipelines, can reduce annual maintenance costs, and help to take necessary measures to better protect pipelines and safety [5,6]. Liu Mingjun et al. (2023) have established a new nonlinear Wiener degradation model to characterize the degradation process of slewing supports. The developed model can be effectively applied to the degradation process of fan slewing supports and contribute to the sustainable development of wind power generation [7]. Similarly, it is of great significance to scientifically predict the service life of expressway marking for the sustainable development of expressways and driving safety.

The service life of a marking is the time required to reduce the value of the retroreflectivity of a newly laid marking to a minimum standard. The minimum reverse reflection coefficient standard of China’s thermoplastic road marking is 80 mcd·m⁻²·lx⁻¹. If the coefficient of a segment of markings is lower than the level mentioned above, they must be re-laid [8,9]. The service life of markings is mainly based on their retroreflectivity [9]. Numerous scholars have primarily focused on retroreflectivity and have conducted corresponding research on road markings [10,11,12]. In terms of predicting the service life of markings, the main research approach is to establish parameterized predictive models [13,14,15,16,17,18,19].

Previous studies have shown the importance of reflectance in studying the life cycle of road markings. Zhang et al. (2006) have stated that road markings must exhibit adequate visibility throughout their life cycle. When analyzing the performance and cost-effectiveness of road marking materials, a critical factor is the retroreflectivity [10]. Dario Babić et al. (2017) compared dynamic and static methods for measuring the retroreflectivity of markings. They found that the inverse reflectance coefficients obtained would vary with different measurement methods and suggested using dynamic or dynamic–static combination measurement methods [11]. Bahar et al. (2006) have described the National Transportation Product Evaluation Program (NTPEP) dataset that is used to study road markings in the U.S. The NTPEP dataset contains the following influencing factors: age of marking, marking color, marking material, traffic volume, roadway surface material, climate, and frequency of snow removal. They have noted that the presence and visibility of markings significantly impacts driving safety [12].

For the studies regarding predictive models of service life, Sitzabee et al. (2009) developed a linear attenuation model for the retroreflectivity of thermoplastic road markings in North Carolina. The influencing factors of the model were the age of marking, initial retroreflective value, annual average daily traffic (AADT), marking color, and marking location. The model has an R² value of 0.6 [13]. Luana Ozelim et al. (2014) established a linear prediction model for white and yellow road markings based on regional conditions in Alabama. The factors considered were the age of marking and AADT and the model R² was 0.448 and 0.488 [14]. Chieh Wang et al. (2016) investigated the service life prediction method of markings under different weather conditions in winter. Segmented multivariate linear modeling was proposed to explain the impact of winter weather events explicitly [15]. Dario Babić, Andelko Scukanec et al. (2019) developed linear models for predicting the service life of three road markings based on the age of the markings, initial retroreflectivity, marking location and AADT for ambient solvent-based coatings, thermoplastic coatings, and cold-plasticized coatings [16].

In addition to developed linear models, Adam M. Pike et al. (2015) proposed a markings service life index model that considers factors such as age of marking, marking material, and pavement type [17]. Deo Chimba et al. (2018) compared the Markov Chain (MC) model with a linear model and found that the attenuation of road marking retroreflectivity showed an exponential curvilinear trend, with decreased rates of attenuation as time increased [18]. Maged Mohamed et al. (2020) used a three-wheel polishing device (TWPD) and a weather monitor to study the performance indicators (retroreflectivity, color change and durability) of waterborne and thermoplastic road marking. Their results show that the durability of thermoplastic road markings obeyed a linear degradation function, and the rest of the performance indicators were logarithmically degraded under different loads [19]. Momen R. Mousa et al. (2021) used the NTPEP dataset to develop prediction models for high dimensionality and high multicollinearity between the variables and used the CatBoost algorithm for transverse and longitudinal markings separately, with the model accuracy being higher than that of previous studies [20].

Dong Kai (2009) took the reflective brightness of different functional markings on roads in Beijing as an example from which to analyze the remaining effective life of the markings. It is proposed that the loss of marking luminance has a very important relationship with the function and location of the marking [21]. Hao Xiaoyan et al. (2019) analyzed the visibility decay law of expressway markings in Shanxi Province and established an exponential model for the decay of road markings’ retroreflectivity over time, and the model R² values in the range of 0.177–0.475 [22]. Huang Kai and Wang Wenhui (2020) explored the correspondence between road marking life and traffic volume and preliminarily explored the estimation curves and corresponding equations of marking life under Class 1–3 service levels [23]. Yang Furong and Gao Ziqiang (2022) compared the performance decay characteristics of two-component, thermoplastic and water-based pavement markings under actual working conditions. They established the respective life prediction models, but the consideration factor was only the age of marking, and was combined with the use of the cost and the service life of the markings to give a proposal for the paving of markings in different situations [24].

Table 1. Summary of retroreflectivity prediction models in the literature.

Year	Authors	Influencing Factors (Variables Included in the Model)	Model
1997	Andrady	Age (age of marking), initial retroreflectivity	Logarithmic
1999	Lee, Maleck and Taylor	Age	Simple linear regression
2002	Abboud and Bowman	Annual average daily traffic (AADT)	Logarithmic
2004	Kopf	Age, marking color, AADT	Simple linear regression
2007	Fitch	Age, AADT	Logarithmic
2009	Sitzabee et al. [13]	Age, AADT, initial retroreflectivity, marking color, marking location	Multiple linear regression
2011	Hummer et al.	Age, initial retroreflectivity	Linear mixed-effects model
2012	Mull and Sitzabee	Age, AADT, initial retroreflectivity, plow events	Multiple linear regression
2012	Robertson et al.	Age, initial retroreflectivity, lane width, AADT	Multiple linear regression
2019	Dario Babic [16]	Age, initial retroreflectivity, marking location, winter maintenance	Multiple linear regression
2015	Pike and Songchitruksa [17]	Age, initial retroreflectivity	Exponential models
2018	Deo Chimba et al. [18]	Age, marking color, marking location	Markov chain model
2019	Hao Xiaoyan et al. [19]	Age	Exponential models
2020	Huang Kai and Wang Wenhui [23]	Age, traffic volume	Simple linear regression
2020	Chia-Pei Chou et al.	Retroreflectivity, marking image	Visual recognition methods
2022	Laura, Nascimento, Mazzoni et al.	Age, initial retroreflectivity, traffic volume, weather condition, marking materials	Generalized linear mixed models
2022	Yang Furong et al.	Age	Simple linear regression

summarizes relevant studies found in the literature and presents the influencing factors included in the model.

To summarize, the research on the prediction of road marking service life mainly focuses on modeling road marking retroreflectivity attenuation under the consideration of different influencing factors. However, there are no fixed criteria for determining influencing factors, and more studies have used the establishment of linear, exponential, and logarithmic models. There has been little research on this aspect in China [21,22,23,24]. Current research fails to consider other, more complex, factors, such as climatic conditions, partly due to limited data availability. An inability to grasp important influencing factors and the use of relatively simple prediction methods result in a smaller-than-expected R², poor interpretation, and low prediction accuracy. This paper attempts to fill these gaps by analyzing the important factors affecting the service life of the markings, establishing a prediction model, and striving to improve the prediction accuracy.

2. Methodology

In assessing the magnitude of influence exerted by diverse factors on the service life of road markings, conventional single-factor models, such as simple linear regression and exponential models, are deemed inadequate because of the large number of influencing factors. The logarithmic model limits the types of independent variables and can only analyze the relationship between categorical variables. Consequently, the above similar methods are not applicable in this study. Multiple linear regression serves as a valuable tool for scrutinizing the causal connection between dependent variables and multiple independent variables, unhampered by any constraint on the nature of the independent variables under consideration. Notably, this approach facilitates the preliminary assessment of whether independent variables exert a significant influence on dependent variables, an observation that finds validation in prior research endeavors [13,14,16]. However, it is not rigorous enough to analyze the relative importance of each influencing factor by relying only on multiple linear regression because the relative importance of the influencing factors may change with the change of the sub-models derived from the full model. The method of dominance analysis effectively addresses this issue. One of this method’s most notable merits is its comprehensive examination of all conceivable sub-model scenarios, allowing for the assessment of the relative significance of each influencing factor.

Because most previous studies used only multiple linear regression parameterized models for their predictions, the predictive accuracy and efficacy of the models have been suboptimal. A possible reason for this is that the high dimensional problem between variables is not solved, and the analysis of the nonlinear effects of the independent variables is also missing. This conundrum can be deftly resolved through the implementation of non-parametric methodologies. The LightGBM (a machine learning method) algorithm uses an efficient feature-splitting strategy and parallel computation, which greatly improves the training speed of the model, especially for large-scale data sets and high-dimensional feature spaces. It can also continuously improve the model’s predictive ability during training, and optimize the model through gradient lifting techniques, thus obtaining high accuracy in classification and regression tasks. The non-parametric method based on LightGBM can solve the high-dimensional problem between variables and can reflect the nonlinear influence of independent variables more accurately. It has been applied to passenger flow and navigation speed predictions in transportation [25,26]. The model achieves not only a high prediction accuracy, but also ensures strong generalization ability and fast calculation speed.

Therefore, to determine the important influencing factors affecting the service life of the markings and further improve the prediction accuracy, this study used multiple linear regression to preliminarily analyze the influence of various factors on the service life of markings and established a parameter prediction model. Based on the derived parameterized prediction model, the important influencing factors determining the service life of the markings were identified through the method of dominance analysis. Based on the important influencing factors, LightGBM was used to train the non-parametric prediction model.

2.1. Multiple Linear Regression

The multiple linear regression method is an analytical method by which to study the influence of multiple independent variables on dependent variables. Through the significance test (p-value), we can determine whether independent variables have a significant influence on dependent variables. The Statistical Package for the Social Sciences (SPSS R26.0.0.0) software is used to process and analyze the collected data, analyze the relationship between the influencing factors and the attenuation of the retroreflective coefficient of the markings, and establish a parametric markings service life prediction model. The model solely encompasses variables that exhibit statistical significance exceeding the 95% threshold.

2.2. Dominance Analysis

The primary approach of the dominance analysis is to establish a regression model, known as the full model, based on empirical research. All derived sub-models are generated from the full model, amounting to 2^p−1 (where p denotes the number of independent variables in the full model). After conducting a comprehensive comparative analysis of all of the sub-models, the relative importance of each influencing factor is determined. The criterion for assessing the magnitude of influence is the percentage of each independent variable’s overall average contribution to the model variance among all sub-models. By employing this criterion, no exaggerated or overlooked importance of any independent variable in relation to the dependent variable occurs. Consequently, this method resolves the issues associated with traditional approaches that rely on slope-based indicators and variance-reduction indicators for determination [27].

This study focuses on the retroreflectivity of the markings as the dependent variable. It calculates the change in R-squared when each influencing factor is incorporated into the sub-model equations that do not include that specific factor. The cumulative average of these changes in R-squared represents the value-added contribution of the influencing factor. The calculation formula is as follows:

$$C_{x_i}^{(k)}=({\displaystyle \sum R_{y{x}_h{x}_i}^2})/(k^P-1)x_i{x}_{h}k$$

(1)

where $x_i$ is one of the influences in the full model; $C_{x_i}^{(k)}$ is the average contribution of the explained influence factors when $x_i$ is added to the sub-model containing each influence factor of $k$ but excluding $x$ itself; and $x_h$ is the other $k$ influences included in the sub-model in addition to the influences $x_i$.

Therefore, the total average contribution of the influencing factors to the dependent variable is calculated as follows:

$$C_{x_i}=\frac{1}{P}{\displaystyle \sum _{k=0}^{p-1}{c}_{x_i}^{(k)}}$$

(2)

The overall average contribution of each influencing factor reflects its degree of importance.

2.3. LightGBM Algorithm

2.3.1. The Basic Principle of Gradient Boosting Decision Trees (GBDT)

The main idea of GBDT as an algorithm is that it should iteratively train weak classifiers with the objective function of reducing residuals, and ultimately should linearly combine the weak classifiers through an additive model to classify or regress data. When GBDT performs regression analysis, the residuals of the predecessor prediction are fitted to the predecessor prediction residuals by continuously adding new learners, which makes the residuals of the subsequent learners decrease continuously, thus obtaining a model with higher accuracy.

2.3.2. LightGBM Algorithm

The LightGBM algorithm is a framework that implements the idea of GBDT algorithm and belongs to one of the boosting integration algorithms. Boosting is a branch of machine learning that integrates learning algorithms and is the classical machine learning algorithm currently used for prediction [26]. The LightGBM algorithm, on the other hand, uses gradient-based one-side sampling (GOSS), exclusive feature bundling (EFB) and a histogram-based algorithm to further improve on XGBoost [28]. Figure 1 depicts the predictive analytics process based on the LightGBM algorithm.

3. Data Sources and Description

3.1. Selection of Influencing Factors

This study referred to the previous relevant literature to select influencing factors [16,17,18]. We examined whether widely validated influencing factors, such as the age of the markings, the road marking pattern and the volume of traffic, were suitable for the characteristic conditions of the expressways under study.

Furthermore, we hold great esteem for the insights provided by industry practitioners, be they the dedicated personnel engaged in expressway marking maintenance or the adept technicians tasked with measuring and formulating marking maintenance strategies.

The influencing factors selected in this study refer to previous research and the feedback of industry practitioners, and thus have a certain reliability. Compared with previous studies, this study proposes two factors that influence the maximum road speed limit and the glass bead content. The average monthly temperature and average monthly precipitation are used to represent the influence of climate conditions. The discussion of the selection of influencing factors is given below.

• Maximum road speed limit

There are differences in the maximum speed limits of different expressways and the driving conditions of vehicles under different speed limits are different, as are the degrees of wear and tear on the road markings.

• Annual average daily traffic

The higher the traffic volume, the more the wheels run over the road markings, increasing the wear and tear on the markings and affecting their service life [29].

• Initial retroreflectivity

Under the same conditions, the higher the initial reverse reflection coefficient of the road markings, the longer the attenuation time to the minimum required reverse reflection coefficient.

• Age of marking

The age of marking is the time between the completion of laying and each measurement. The longer the same marking is applied, the shorter the remaining service life.

• Glass bead content

The thermoplastic road marking relies mostly on the glass beads contained within the reflective light source. Within a certain range, the higher the content of glass beads, the higher the retroreflectivity of the markings.

• Road marking pattern

The most common types of markings on expressways are dashed lines and solid lines, and different types of lines have different functions and different levels of wear and tear.

• Average monthly temperature and average monthly precipitation

The long-term exposure of road markings to the outdoors—to wind, sun, rain and snow corrosion—will have a certain impact on the marking, affecting its service life.

Through the above discussion, eight influencing factors that affected the service life of expressway thermoplastic road markings were determined, including the maximum speed limit of the road, the average daily traffic volume, the road marking pattern, the initial retroreflectivity, the age of marking, the glass bead content, the average monthly temperature, the average monthly precipitation and the average monthly precipitation. As shown in

Table 2. Selection of influencing factors.

Classification of Influencing Factors	Name of Influencing Factors	Literatures
Road factors	Maximum road speed limit	Novel proposition
	Annual average daily traffic	[13,14,16]
Marking factors	Road marking pattern	[17]
	Initial retroreflectivity	[13,16,17]
	Age of marking	[13,14,16,17,18,20]
	Glass bead content	Novel proposition
Environmental factors	Average monthly temperature	[20]
	Average monthly precipitation	[20]

.

3.2. Data Collection

3.2.1. Data Sources

Five expressways in Shandong Province were selected to collect data on the retroreflectivity of thermoplastic road markings, road marking pattern, initial retroreflectivity, age of marking, glass bead content and AADT flow for 12 consecutive months in the field. Maximum road speed limits are derived from publicly available data on government expressway speed limits [30]. Average monthly temperature and average monthly precipitation were obtained from the 1 km-resolution monthly mean air temperature and monthly mean precipitation datasets of China from 1901 to 2022 from the National Earth System Science Data Center (NESDC) [31].

3.2.2. Equipment for Collecting Retroreflectivity Data

To improve the accuracy of the data, a combination of dynamic and static measurements was used to collect the relevant retroreflective data. The applied equipment included a Zehntner vehicle-mounted retroreflectometer and a Jingqu RP-R12, RP-R18 marking retro-reflectometer respectively. All of the equipment had an angle of incidence of 88.76° and an observation angle of 1.05°. Dynamic and static methods were used to measure the left and right solid lines and dashed lanes of the selected road section, and the average value of the two measurements was the inverse reflection coefficient of the real and dashed lines of the road section. The dynamic vehicle-mounted device is shown in Figure 2 and the static handheld devices are shown in Figure 3.

3.2.3. Road Sections for Data Collection

The expressways names and section information are shown in

Table 3. Road sections for data collection.

Expressway Name	Sections
G20 Qingdao–Yinchuan Expressway	Ji’nan section
G3 Beijing–Taipei Expressway	Ji’nan section
G3 Beijing–Taipei Expressway	Tai’an section
S38 Lanshan–Heze Expressway	Linzao section
G2001 Ring Expressway of Ji’nan	Northern surround section

. Thirty miles of each segment of the expressway were randomly selected and data on eight variables were collected using the method described above. The collected data correspond to each variable and were used to obtain a preliminary statistical database. Some of the collected data are shown in

Table 4. Marking retroreflectivity data for G20, Qingdao–Yinchuan Expressway, Ji’nan section (mcd·m⁻²·lx⁻¹).

Age of Marking	Months
	1	2	3	4	5	6	7	8	9	10	11	12
Dotted line 1	451	436	381	297	232	232	315	221	155	252	184	140
Solid line 1	379	381	291	259	359	359	321	284	315	291	285	287
Dotted line 2	356	321	170	215	135	135	120	120	94	130	130	78
Solid line 2	381	351	305	346	324	324	308	308	220	265	265	221

and

Table 5. Data for each influencing factor of G20, Qingdao–Yinchuan Expressway, Ji’nan section.

Influencing Factors	Data
Age of Marking (M)	1	2	3	4	5	6	7	8	9	10	11	12
AADT (cars)	Converted to 115,000 by vehicle conversion factor
Road marking pattern	Dotted line						Solid line
Initial retroreflectivity (mcd·m−2·lx−1)	Dotted line 1: 488 Dotted line 2: 418						Solid line 1: 425 Solid line 2: 430
Average monthly temperature (°C)	15.5	19	21.6	23.3	24.3	23.9	23.7	9.4	10.8	13.4	13.9	15.1
Average monthly precipitation (mm)	268	323	1025	1085	927	809	748	234	250	468	540	520
Maximum road speed limit (km/h)	120
Glass bead content (%)	35%

.

3.2.4. Data Pre-Processing

The collected data necessitates preprocessing prior to direct application. Data preprocessing includes data cleaning and data normalization. Noisy samples in the raw data can be identified and processed through data cleansing. Data cleansing through Python mainly uses the isnull and fillna functions to detect and fill lost values, respectively, deleting outliers that are larger than a specific standard deviation value, and using the duplicated and drop_duplicates functions to detect and delete duplicate data, respectively. Normalization of the data by Equation (3) removes the effect of magnitude.

$$X_j=\frac{X-X_{\min }}{X_{\max }-X_{\min }}$$

(3)

where $X_j$ is the result of normalizing the parameter $X$ and $X_{\min }$ and $X_{\max }$ are the minimum and maximum values of $X$, respectively.

4. Results and Discussion

4.1. Predictive Modeling of Markings Service Life Based on Multiple Linear Regression

4.1.1. Diagnosis of Independent Variable Multicollinearity

The multicollinearity diagnosis results are shown in

Table 6. Diagnostic table for multicollinearity of independent variables.

Variables	Significance (Sig)	Tolerance	VIF
Age of marking	0.000	0.554	1.838
AADT	0.000	0.187	5.336
Road marking pattern	0.000	0.855	1.169
Initial retroreflectivity	0.000	0.853	1.172
Average monthly temperature	0.035	0.216	4.631
Average monthly precipitation	0.001	0.274	4.650
Maximum road speed limit	0.261	0.159	6.289
Glass bead content	0.000	0.361	2.767

. A general VIF value of more than 5 indicates a possible multicollinearity problem.

Because the model only includes variables with more than 95% statistical significance, the test of significance shows that the maximum speed limit is not statistically significant at p = 0.261 > 0.05, so this variable is removed. After removing this variable, the VIF values for each independent variable remained below 5, indicating that multicollinearity is not a concern and is within an acceptable range.

4.1.2. Model Summary and Analysis of Variance (ANOVA)

The results of the goodness-of-fit test and residual independence test are shown in

Table 7. Model summary.

Model	R	R2	Adjusted R2	Std. Error of the Estimate	Durbin–Watson
1	0.773	0.599	0.593	50.467	1.035

, the model’s goodness-of-fit R² is 0.599, and the model table is relatively good; the Durbin–Watson value is 1.035, and the result is greater than 1 and between 0 and 4, which is consistent with independence.

The results of the ANOVA are shown in

Table 8. ANOVA.

Model	Sum of Squares	Degree of Freedom (df)	Mean Square	F	Sig.
Regression	2,255,778.126	7	322,254.018	126.527	0.000
Residual	1,517,968.740	596	2546.927
Total	3,773,746.866	603

, F = 126.527 in this model with a significance of p < 0.001, which leads to a reduction in the residual variance and indicates that the modeling is successful.

4.1.3. Modeling

The regression analysis results are shown in

Table 9. Results of multiple linear regression analysis.

Model	Unstandardized Coefficients		Standardized Coefficients Beta	t	Sig.
	B	Std. Error
(Constant)	148.261	44.578		4.402	0.001
Age of marking	−11.241	0.681	−0.577	−16.516	0.000
AADT	−10.771	1.326	−0.242	−8.126	0.000
Road marking pattern	59.848	4.415	0.378	14.557	0.000
Initial retroreflectivity	0.743	0.085	0.244	8.699	0.000
Average monthly temperature	1.880	0.926	0.113	2.031	0.043
Average monthly precipitation	−0.059	0.012	−0.241	−4.856	0.001
Glass bead content	−28.392	4.186	−0.180	−6.782	0.000

, and the resulting prediction model for markings service life is as follows.

$$\begin{array}{c}{{\displaystyle R}}_L=148.261-11.241\times t-10.771\times {{\displaystyle T}}_{Aad}+59.848\times {{\displaystyle S}}_L+0.743\times {{\displaystyle R}}_{L,initial}\\ \hspace{1em} +1.88\times {{\displaystyle T}}_{mavg}-0.059\times {{\displaystyle Rf}}_{mavg}-28.392\times {{\displaystyle C}}_{GlassB}\end{array}$$

(4)

where ${{\displaystyle R}}_L$ is the retroreflectivity of existing road markings, mcd·m⁻²·lx⁻¹; $t$ is the age of marking, in months; ${{\displaystyle T}}_{Aad}$ is the annual average daily traffic, in cars; ${{\displaystyle S}}_L$ is the road marking pattern, with categorical variables that are represented by a dashed line (noted as 0) and a solid line (noted as 1); ${{\displaystyle R}}_{L,initial}$ is the initial retroreflectivity, mcd·m⁻²·lx⁻¹; ${{\displaystyle T}}_{mavg}$ is the average monthly temperature, in °C; ${{\displaystyle Rf}}_{mavg}$ is the average monthly precipitation, in mm; and ${{\displaystyle C}}_{GlassB}$ is the percentage of glass bead content.

The histograms of regression normalized residuals and the P–P plots are shown in Figure 4. Figure 4a,b shows the distribution of residual errors of the model. The dispersion of residual errors or their deviation from the normal distribution can be ignored, thus showing a normal distribution and indicating that the requirements of linear regression are met.

Figure 5 shows the relationship between the model regression residuals and the regression standardized values. The expectation with a scatter plot is that the results should be a set of uniformly distributed data points with a mean of zero. In this study, the data points have a good distribution around the mean value, indicating a symmetrical distribution up and down. The distribution characteristics do not change with the increase in value, and the conditions of homogeneity and independence of data variance are thus met.

4.2. Judgment of Important Influencing Factors of Service Life of Markings Based on Dominance Analysis

As can be seen from Table 9, “Age of marking”, “AADT”, “Road marking pattern”, “Initial retroreflectivity”, “Glass bead content” and “Average monthly precipitation” have a significant effect on the service life of the markings (p < 0.01), “Average monthly temperature” has an effect on the service life of the markings (0.01 < p < 0.05). The above influencing factors are expressed as $X_1$, $X_2$, $X_3$, $X_4$, $X_5$, $X_6$, $X_7$ in that order, and their respective value-added contributions and total average contributions are calculated.

The value-added contribution and total average contribution of the above seven influencing factors are calculated from Equations (1) and (2), and the results are shown in

Table 10. Value-added contribution and total average contribution of each influencing factor.

Number of Influencing Factors in the Model (k)	$\mathbf{Value}\mathbf{Added}\mathbf{Contribution}(\mathit{C}$)
	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{X}}_6$	${\mathit{X}}_7$
k = 0	0.307	0.038	0.116	0.012	0.049	0.017	0.001
k = 1	0.312	0.044	0.123	0.019	0.075	0.054	0.003
k = 2	0.304	0.047	0.126	0.026	0.088	0.076	0.008
k = 3	0.285	0.050	0.127	0.031	0.088	0.084	0.013
k = 4	0.255	0.049	0.128	0.037	0.081	0.077	0.020
k = 5	0.217	0.047	0.129	0.043	0.043	0.056	0.028
k = 6	0.175	0.044	0.135	0.053	0.005	0.022	0.035
Total average contribution	0.258	0.047	0.128	0.035	0.063	0.062	0.018
Percentage/%	42.3	7.7	21.0	5.7	10.4	10.1	2.9

.

From the previous section, we can see that as many as 127 (2⁷−1) sub-models are derived from the seven influences. Due to space constraints, it is not possible to list all of them, only the value-added contribution of each influencing factor after consolidation. Table 10 shows that when $k$ = 0, the value-added contribution of each influencing factor is ranked as follows: $X_1$ > $X_3$ > $X_5$ > $X_2$ > $X_6$ > $X_4$ > $X_7$; when $k$ = 1–4, the rankings are: $X_1$ > $X_3$ > $X_5$ > $X_6$ > $X_2$ > $X_4$ > $X_7$; when $k$ = 5, the order is: $X_1$ > $X_3$ > $X_6$ > $X_2$ > $X_4$ > $X_5$ > $X_7$; when $k$ = 6, the order is: $X_1$ > $X_3$ > $X_4$ > $X_2$ > $X_7$ > $X_6$ > $X_5$. Thus, $X_1$ is completely dominant over $X_3$ and $X_3$ is completely dominant over $X_2$, $X_4$, $X_5$, $X_6$, $X_7$ [23]. The remaining variables are compared with the total average contribution because the value-added contribution varies with the inclusion of different influencing factors. Finally, the influence degrees of each influencing factor on the service life of the thermoplastic road markings are obtained in descending order: $X_1$ age of marking (0.258), $X_3$ road marking pattern (0.128), $X_5$ glass bead content (0.063), $X_6$ average monthly precipitation (0.062), $X_2$ annual average daily traffic (0.047), $X_4$ initial retroreflectivity (0.035), and $X_7$ average monthly temperature (0.018). The total average contribution of each variable explaining or influencing the dependent variable as a percentage of the known variance is, in order, $X_1$ (42.3%), $X_3$ (21%), $X_5$ (10.4%), $X_6$ (10.1%), $X_2$ (7.7%), $X_4$ (5.7%), $X_7$ (2.9%). The results show that the most important factors affecting the service life of expressway thermoplastic road markings are the age of marking and the road marking pattern, followed by the glass bead content, the average monthly precipitation and the AADT, and finally the initial retroreflectivity and the average monthly temperature.

4.3. Judgment of Important Influencing Factors on the Service Life of Markings Based on Dominance Analysis

The machine learning prediction model is trained using the LightGBM algorithm, encompassing the following steps in the training process.

4.3.1. Identification of Variables and Data Collection

Based on the results of multiple linear regression and dominance analysis, the significant influences on the service life of markings are used as variables for model training. The data are collected in the same manner as above.

4.3.2. Data Pre-Processing

By means of data cleansing, it is possible to identify and address noisy samples present in the raw data. Furthermore, the normalization process, as denoted by Equation (3), facilitates the elimination of dimensional influence on the data.

Table 11. Data after pre-processing.

Age of Marking	AADT	Road Marking Pattern	Initial Retroreflectivity	Average Monthly Temperature	Average Monthly Precipitation	Glass Bead Content	Retroreflectivity of Road Marking
1	11.5 × 104	0	418	15.5	268	30	356
2	11.5 × 104	0	418	19	322.5	30	321
3	11.5 × 104	0	418	21.6	1024.7	30	170
4	11.5 × 104	0	418	24.3	1085	30	215
5	11.5 × 104	0	418	24.3	926.8	30	135
6	11.5 × 104	0	418	24.9	808.8	30	135
7	11.5 × 104	0	418	22.7	747.4	30	120
……	……	……	……	……	……	……	……

shows the pre-processed data.

4.3.3. The Partitioning of the Dataset

The dataset is partitioned into a training set and a testing set, with the training set used to train the model and the testing set used to validate and evaluate the model’s accuracy. The data set is split using a random partitioning approach, where 70% of the samples are randomly selected from the preprocessed dataset to compose the training set, while the remaining 30% of the samples form the testing set.

4.3.4. Model Training

The computer configuration for model training and validation is a 64-bit Windows 11 operating system with 16 GB of operating memory and an AMD Ryzen5 5600 4.50 GHz processor. The LightGBM algorithm is invoked on the training set data using the sklearn interface of the Python 4.10 programming language. The main packages and machine learning libraries used for the modeling process are Pandas, Numpy, Scikit-learn, etc. The model inputs are age of marking, AADT, road marking pattern, initial retroreflectivity, average monthly temperature, average monthly precipitation, and glass bead content. The model output is set to the scalar retroreflectivity.

When the LightGBM algorithm is used to build the prediction model, the parameters have a great influence on the model prediction. Therefore, random search parameters are used to optimize LightGBM parameters including n_estimators, learning_rate, bagging_fraction, feature_fraction, max_depth, and min_child_samples. The MAE values are used as the scoring function and the values of each parameter are shown in

Table 12. Setting of each parameter value.

Parameter Names and Optimization Boundaries	Parameter Value
1 ≤ n_estimators ≤ 300	200
0.1 ≤ learning_rate ≤ 1	0.1
0.1 < bagging_fraction ≤ 1	1
0.1 < feature_fraction ≤ 1	0.8
5 ≤ max_depth ≤ 10	10
5 ≤ min_child_samples ≤ 20	10

.

4.3.5. Model Validation

Validation of a model is one of the most critical steps in assessing the quality of a developed AI-based model. It is common practice to assess a model’s performance through various statistical metrics. However, researchers have argued that the accuracy of a model cannot be assessed or judged solely on statistical criteria [32]. A third criterion for evaluating the strength of a developed data-driven model is its ability to predict responses when presented with a completely independent test data set [33]. Therefore, these criteria were used in this study to evaluate the prediction accuracy of the developed LightGBM-based model.

• Model performance evaluation

In this study, the following statistical parameters were used to evaluate the performance of the established model: the coefficient of determination, R²; the mean square error, MSE; the mean absolute error, MAE; and the mean absolute percentage error, MAPE. R² reflects the goodness of fit between the predicted value and the actual value. The closer R² is to 1, the better the model fits. MSE is determined by calculating the average of the square of the difference between the predicted value and the actual observed value, and the closer the MSE is to 0, the better the model fits. MAE is a commonly used index to measure the difference between the predicted value of a model and the actual observed value. It is used to evaluate the fitting degree of a model on given data. The closer MAE is to 0, the higher the accuracy of the model. MAPE reflects the degree of deviation between the predicted value and the real value. Generally, we believe that the MAPE value of the model is less than 10%, indicating that the prediction model has high accuracy [24].

$$MSE=\frac{1}{n}{{\displaystyle \sum _{i=1}^n(y_{a,i}-y_{m,i})}}^2$$

(5)

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_{a,i}-y_{m,i}\right|}$$

(6)

$$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|\frac{y_{a,i}-y_{m,i}}{y_{a,i}}\right|}\times 100\%$$

(7)

where $n$ is the number of samples; $y_{a,i}$ is the actual value of the $i$ observation sample; and $y_{m,i}$ is the predicted value of the $i$ sample. The results of the model evaluation are shown in

Table 13. Results of model evaluation.

	MSE	RMSE	MAE	MAPE (%)	R²
Training set	49.7909	7.0562	11.944	4.167	0.916
Testing set	41.5114	6.4429	16.793	5.949	0.942

.

The evaluation of the model reveals that the training and testing sets’ R² values for the service life prediction model of markings, based on LightGBM, are 0.916 and 0.942, respectively, indicating a high level of model interpretability. Additionally, although there are many types of variables in this study (continuous variables, categorical variables, fixed values), which may affect the accuracy of the model, the results obtained through model evaluation show a relatively ideal result. The MSE values of the model training set and the test set were 49.7909 and 41.5114, MAE values were 11.944 and 16.793, and MAPE values were 4.167% and 5.949%, respectively, showing reasonable model accuracy and precision.

2.

Variable importance analysis

The LightGBM model uses a gradient lifting algorithm based on decision trees, which evaluates the importance of variables in the training process. The importance of variables is calculated based on two factors: split gain and feature frequency. LightGBM modeling can use a built-in model function—plot importance—to extract the importance of features to the model. Figure 6 shows the percentage of each variable’s importance to the model.

As can be seen from Figure 6, the age of marking is the most important variable, followed by the road marking pattern, and the average monthly precipitation is the input variable with the least contribution to the model performance.

4.3.6. The Prediction Results of the Testing Set

The predicted outcomes of the testing set are presented in

Table 14. The prediction results of the testing set.

Testing Set Prediction Results	Retroreflectivity	Age of Marking	AADT	Road Marking Pattern	Initial Retroreflectivity	Average Monthly Temperature	Average Monthly Precipitation	Glass Bead Content
135.375	135	5	11.5 × 104	0	418	24.3	926.8	30
120.157	126	7	11.5 × 104	0	418	22.7	747.4	30
117.894	120	8	11.5 × 104	0	418	9.4	234.6	30
96.075	99	9	11.5 × 104	0	418	10.8	249.6	30
324.329	326	3	12 × 104	1	406	21.5	1150.3	30
232.811	234	11	12 × 104	1	406	14.2	662.8	30
355.325	359	6	10.5 × 104	1	439	24.9	808.8	30
372.208	389	2	8.5 × 104	0	471	19.7	174	35
250.599	247	3	14 × 104	0	437	21.8	1120.7	35
359.599	359	6	11.5 × 104	1	425	24.9	808.8	35
……	……	……	……	……	……	……	……	……

, and the corresponding prediction graph is depicted in Figure 7. The method employed in this study yields predicted values for the retroreflective coefficient of road markings. The service life of road markings is determined by reaching the minimum retroreflective coefficient value.

Figure 7 illustrates the comparison between predicted values and actual values. The minimum difference between the actual value and the predicted value is 0.36102 mcd·m⁻²·lx⁻¹, the maximum difference is 49.4863 mcd·m⁻²·lx⁻¹, and the average difference is 15.2486 mcd·m⁻²·lx⁻¹. The difference of less than 20 mcd·m⁻²·lx⁻¹ accounts for 86.9% of the test set, and the difference of less than 10 mcd·m⁻²·lx⁻¹ accounts for 50.3% of the test set. The prediction results of the test set show that the model has good prediction performance, but there are still some predicted values that are significantly different from the actual values. A possible reason for this is that the life decays of the inner solid line and the outer solid line (emergency lane line) are different, as the inner solid line is run over by vehicles less frequently, and the outer solid line is often run over by vehicles.

5. Example Analysis

5.1. Example Data

The prediction model obtained in the previous section is applied to the example and the prediction results are evaluated. Example data are derived from the five previous expressways, and the data are not applied to model training. The data are processed and imported into the model, and the prediction results are evaluated by the prediction validity equation [34].

$$P=(1-\mid \frac{Y_1-Y_{}}{Y_{}}\mid )\times 100\%$$

(8)

where $P$ is the predictive validity, $Y_1$ is the predicted value, and $Y$ is the actual value. Some of the data are shown in

Table 15. Selected example data.

Age of Marking	AADT	Road Marking Pattern	Initial Retroreflectivity	Average Monthly Temperature	Average Monthly Precipitation	Glass Bead Content	Retroreflectivity
1	10.5 × 104	0	467	15.5	268	35	404
2	10.5 × 104	0	467	19	322.5	35	436
3	10.5 × 104	0	467	21.6	1024.7	35	276
4	10.5 × 104	0	467	23.3	1085	35	256
5	10.5 × 104	0	467	25.3	926.8	35	235
6	10.5 × 104	0	467	23.9	808.8	35	232
1	8.5 × 104	1	410	16.2	133	30	374
2	8.5 × 104	1	410	19.7	174	30	348
3	12 × 104	1	406	21.5	1150.3	30	326
4	12 × 104	1	406	23.2	1300.5	30	298
……	……	……	……	……	……	……	……

.

5.2. Evaluation of Prediction Results

Table 16. Prediction validity of multiple linear regression prediction model.

Real Values	Projected Values	Validity	Average Validity
404	395.84	97.98%	87.36%
436	407.97	93.35%
276	300.18	91.24%
256	288.58	87.27%
235	288.55	77.21%
232	283.52	77.79%
315	273.65	86.87%
221	267.72	78.86%
298	302.44	98.51%
……	……	……

and

Table 17. Prediction validity of LightGBM-based prediction model.

Real Values	Projected Values	Validity	Average Validity
404	404.99	99.76%	95.02%
436	435.01	99.77%
276	275.91	99.97%
256	255.96	99.98%
235	235.46	99.77%
232	232.25	99.89%
315	315.29	99.78%
221	222.93	99.13%
298	270.08	90.63%
……	……	……

show the prediction validity of the two models.

The average prediction validity of the multiple linear regression parameterized prediction model is 87.36%, the model has good prediction effect. The combination of the dominance analyses provides a better response to the magnitude of the variable impact relationship.

The LightGBM-based prediction model has an average prediction validity of 95.02% and a high prediction accuracy. Because the model explains some of the nonlinearity and high dimensionality of the independent variables, the predictive validity is improved. It can also better predict the attenuation of the retroreflectivity of expressways thermoplastic road markings and determine the service life of the markings.

6. Discussion on Results

• By synthesizing relevant research and conducting on-site investigations of expressways, we have identified the factors that influence the service life of road markings. This determination was made by considering the characteristics of regional expressways and the environmental features surrounding them.
• Multivariate linear regression and dominance analysis were used to establish a parametric prediction model. A parametric prediction model was established using multiple linear regression and dominance analysis, and the ranking of important factors affecting the service life of the thermoplastic road marking was obtained. The degree of influence in descending order was: “Age of marking” (0.258), “Road marking pattern” (0.128), “Glass bead content” (0.063), “Average monthly precipitation” (0.062), “AADT” (0.047), “Initial retroreflectivity” (0.035), and “Average monthly temperature” (0.018).
• Based on linear regression and dominance analysis, the LightGBM machine learning method was used to build a non-parametric prediction model. The R² of the model training set and testing set were 0.916 and 0.942, and the MAPE were 4.167% and 5.949%, with high model accuracy and strong generalization ability.
• In order to judge the prediction effect of the model, the average prediction effectiveness of the multiple linear regression prediction model was 87.36%, and the average prediction effectiveness of the prediction model based on LightGBM algorithm was 95.02%, as obtained by example analysis. Both models showed better predictions. The former better reflected the relationship between the influencing factors and the dependent variable. The latter could achieve the prediction of the service life of expressway thermoplastic road marking under the premise of ensuring higher prediction accuracy and stronger generalization ability.

7. Conclusions

This study employs multiple linear regression, dominance analysis, and the LightGBM machine learning method, in conjunction with the characteristics of regional expressways, to conduct a comprehensive analysis of the significant influencing factors of thermoplastic road markings. Consequently, parametric and non-parametric prediction models are established. Through rigorous validation, the models demonstrate a notable degree of accuracy, providing robust theoretical support for the prediction of the service life of thermoplastic road markings on expressways. Moreover, these predictive models offer valuable guidance for the maintenance of road markings, which can effectively avoid the replacement of markings at inappropriate times. Every time thermoplastic marking is replaced, it can cause irreversible damage to the expressway, so avoiding premature road marking replacement can reduce the overall cost associated with maintenance and promote sustainable development. By avoiding the late replacement of road markings, better visibility of the road at night is ensured, improving the safety associated with driving on the expressway.

In the future, data on the relevant variables of more sections of expressways should be collected to train the model further and to render the model more reliable and accurate. In addition, the universality of the study in this paper needs further discussion, especially for thermoplastic marking in other countries and regions of the world.