Evaluation of Air Pollutants in Extra-Long Road Tunnel with the Combination of Pollutants Nonlinear Evolution and Machine Learning Method

Abstract

The extra-long expressway tunnel has a high socio-economic effect on inter-regional development, with high traffic and strong traffic winds. Nevertheless, the impacts of the tunnel traffic volume on pollutant evolution are rarely considered. This study conducted a field measurement in a real-world extra-long highway tunnel for 578 days. For the first time, the nonlinear dynamics of traffic pollutants (CO, VOCs, NO₂, PM_2.5, PM₁₀) were analyzed using the Multifractal Detrended Fluctuation Analysis approach. Using the Random Forest model, the impacts of traffic and environmental parameters on air quality were quantified. The findings indicated that COVID-19 had a considerable impact on tunnel traffic, although the variance in pollutant concentration was not very noteworthy. The bidirectional effect of traffic was the main reason for this phenomenon. The Canonical Correlation Analysis was unable to quantify the correlation between pollutants and environmental parameters. The pollutant concentration evolution has a steady power-law distribution structure. Further, an inverse Random Forest model was proposed to predict air pollutants. Compared with other prediction models (baseline and machine learning), the proposed model provided higher goodness of fit and lower prediction error, and the prediction accuracy was higher under the semi-enclosed structure of the tunnel. The relative deviations between the predictions and measured data are less than 5%. These findings ascertain the nonlinear evolutionary mechanisms of pollutants inside the expressway tunnel, thus eventually improving tunnel environmental sustainability. The data in this paper can be used to clarify the changes in the traffic environment under the COVID-19 lockdown.

1. Introduction

In order to strengthen inter-regional economic and social links and shorten travel time, extra-long highway tunnels have gained high importance in Chinese transportation planning [1,2]. By the end of 2020, there were 1394 very long road tunnels (L > 3000 m) with a total length of 6235.5 km, an increase of 19.5% compared to the same period last year (Ministry of Transport of the People’s Republic of China, 2021). Extra-long tunnels have a semi-enclosed structure, which can cause severe air pollution if pollutants are not discharged in time [3,4]. Combined with the intensive traffic volume, the air pollution inside can induce traffic accidents and endanger the health of drivers and passengers [5,6,7]. Traffic pollutants, including metal ions and aerosols, can cause harm to human health [8,9,10,11]. Yang et al. noted through field tests that NH₃ levels in road tunnels are several times higher than those in ordinary roads [12]. At the same time, the traffic of heavy trucks in mountainous areas and their proportion of the total traffic in road tunnels increased significantly, exacerbating the levels of CO, NO₂, SO₂, and particulate matter in the air of such buildings [13,14,15,16]. Song et al. conducted a two-week field test and found a linear relationship between the proportion of heavy vehicle traffic and pollutant levels, with the PM_2.5, NO, NO₂, NO_x, and CO being 75, 81, 24, 65, and 33 times more intense than those from light-duty vehicles, respectively [17]. In addition, such buildings hurt the local environment, especially in residential and environmental areas [18,19]. These findings highlight the importance of understanding the dynamics of pollutants in extra-long road tunnels to help derive an appropriate response to control traffic pollution.

The spatial distribution of tunnel pollutants is well studied, and the pollutant concentration is linearly related to the length of the ventilation interval [20,21]. There are two main approaches to studying the temporal evolution patterns of tunnel pollutants: computational fluid dynamics (CFD) models and field measurement methods. CFD models, mainly numerical simulations, simulate air pollutants’ diffusion and decay processes based on hydrodynamics under pre-defined conditions [22,23,24,25]. Previous studies have focused on identifying the key influencing factors of air pollutants inside tunnels and their mechanisms of action, including tunnel slope [26], building section size [27], natural wind [28], traffic wind [29], ventilation system [30], meteorological variables [31], nearby vegetation [32,33], particulate properties [34], etc. Song et al. investigated utilizing mutual validation between field tests and model experiments. The dynamic changes of pollutants inside the tunnel were investigated, and the effect of vehicle travel speed on the diffusion of pollutants was evaluated [35]. They suggested that the accumulation of pollutants along the traffic direction is significant for road tunnels and concluded that the level of pollutants after stabilization over time is higher than that in megacities. The core advantages of CFD models are high computational efficiency and good operability. However, the simulation conditions are ideal, leading to unanticipated differences in the temporal distribution of pollutants in the simulation results, such as neglecting non-tailpipe emissions.

Field measurements in real road tunnels are rare because of coordination with tunnel managers, cooperation with traffic management, and high experimental costs. Thus, tunnel field measurements are ideal for directly estimating pollutant levels (both tailpipe and non-tailpipe emissions) and erasing the external environment’s effect [17]. Li et al. conducted field measurements on four typical bifurcated tunnels and proposed that tunnel pollutant dispersion varies with tunnel structure [36]. Monitoring Taiwan’s traffic emissions from the Hsuehshan tunnel showed that the pollutant emission factor was twice as high uphill as downhill [37,38,39]. Xu et al. obtained a more complex pattern of organic emission evolution inside the tunnel considering new energy vehicles through field tests [40]. Zhang et al. conducted field measurements of tunnels in four Chinese cities using tracers. They put forward that non-tailpipe emissions account for 60–74% of PM₁₀ components of tunnels, and road slope and road roughness are the fundamental factors determining non-tail gas emissions of roads [15]. Hou et al. performed in situ sampling of aerosol particles in a tunnel in a coastal city in southern China and analyzed the particles using transmission electron microscopy and energy dispersive X-ray spectrometry. They suggested that the aging of particles is weaker than the atmospheric environment due to the absence of photochemical reactions inside the tunnel [41]. Based on the monitoring results for the Caldecott Tunnel in San Francisco, Dallmann et al. quantified the emission factors of motor vehicles, including medium- and heavy-duty trucks [42]. Tong et al. performed continuous and single-point measurements in five urban road tunnels and showed that the wind speed inside the tunnel depends strongly on the vehicle speed [43]. Xu et al. used a multiple fractal detrended fluctuation analysis (MF-DFA) model to analyze the collected aerosol data. The data were decomposed and analyzed. The aerosol level was found to have multifractal properties and long-term persistence [44]. On-site monitoring allows for quick and direct access to first-hand data. However, the single field monitoring scenario and short monitoring period limit the field measurement results.

In summary, although these two methods reveal the evolutionary patterns of air pollutants inside extra-long road tunnels from different perspectives, the bidirectional effects of traffic on air pollutants have not been fully understood. Moreover, most studies tend to be descriptive in their analysis and rarely predict air pollutants inside tunnels, in particular, prediction models that consider the long-term persistence characteristics of pollutants. In addition, the international spread of COVID-19 in 2020 has severely limited human activity. China is one of the earliest countries to enter the post-COVID-19 era. China has adopted resilient policies to control the epidemic spread. As a result, industrial activities such as energy production have largely resumed, but traffic emissions have been significantly affected ([45]).

To fill these research gaps, we selected the YEL Tunnel, a vital traffic link in the Beijing-Tianjin-Hebei region of China, as the subject of our study, aiming to (1) analyze the variation in traffic flow and pollutant concentrations under different control levels, based on the field measurements; (2) determine the traffic pollutant temporal evolution mechanism in an extra-long expressway tunnel; (3) confirm the contribution of each factor to traffic emissions, and to forecast pollutant emissions and concentrations. The findings will inform environmental policymakers and researchers and contribute to understanding the bidirectional role of traffic winds on pollutant concentrations in a tunnel environment.

2. Tunnel Description

The Yingerling Tunnel is the longest tunnel on an expressway (G18) around Xushui District in Hebei Province, with an overall length of 5656 m in the southbound tunnel and 5677.3 m in the northbound tunnel. The design speed is 80 km/h, and its cross-sectional area is 99.47 m². The G18 Expressway, which opened to traffic at the end of 2019, is a crucial link to the Beijing-Tianjin-Hebei area. The tunnel is an essential conduit for carrying coal from Shanxi Province to the Beijing-Tianjin-Hebei area. The tunnel adopts the longitudinal mechanical ventilation system (as shown in Figure 1) and is a double-hole single-way tunnel. The northbound tunnel was chosen as the sample tunnel, as it is an uphill tunnel with a gradient of +2.15%, in which more pollutants are generated by vehicles running in it. Furthermore, the distance between the southbound and northbound tunnels is higher than 50 m, and pollutant channeling may be ignored. The operating power of the jet fan is 37 kW with the 1450 r/min for operating speed and 99,000 m³/h of airflow. The surrounding rock is Granite (density: 2650 kg/m³); C25 shotcrete (thickness 15 cm) was used in the initial lining. The secondary lining is made of C35 mold concrete (45 cm thick). The pavement structure is divided into two layers; the lower is 6 cm thick SBS composite modified asphalt (ARHM-20), and the upper is 4 cm thick flame retardant asphalt (SMA-13).

3. Experimental Method

3.1. Traffic Data

We installed video monitors on the tunnel sidewalls at the appropriate elevation to capture the daily traffic data in the tunnel. Following each sample session, the videotapes were replayed, and the daily traffic and vehicle types were manually categorized and calculated. The vehicle types were classified as LDV (light-duty vehicle, Seaters ≤ 15, Length < 6 m), HDV (hard-duty vehicle, Seaters > 15, Length ≥ 6 m), LDT (light-duty truck, Mass ≤ 3.5 t), MDT (medium-duty track, 3.5 t < Mass ≤ 15 t), and HDT (heavy-duty truck, Mass > 15 t), according to the Chinese specification “Technical specifications for safety of power-driven vehicles operating on roads” (GB 7258-2017). We found that most vehicles traveled at speeds above 100 km/h, except for the HDT, during the sampling period.

3.2. Environmental Parameters

We collected wind speed, temperature, relative humidity, air pressure by Kestrel 5500 handheld weather gauge with the parameters shown in

Table 1. Technical parameters of sampling instruments.

Project	Instrument	Producers	Range	Resolution	Accuracy
Temperature	Kestrel 5500	Kestrel	−29~70 °C	0.1 °C	0.5 °C
Relative humidity			10~90%	0.1	2%
Air pressure			700~1100 hPa	0.1 hPa/mb	1.5 hPa/mb
Wind speed			0.6~40 m/s	0.1 m/s	3%
	AR866A	SMART SENSOR	0~30 m/s	0.01 m/s	1%
CO	HFP-1201	Huafan (Xi’an)	0~1000 pPM	1 pPM	3%
VOCs	HYPERSENSE 1000	Peking ZhongHA	0~1000 mg/m3	0.1 μg/m3	3%
NO2	PAC7000-NO2	Draeger Company	0~50 pPM	0.1 pPM	3%
PM2.5	HW-N1	Hanvon	0~999.9 μg/m3	0.1 μg/m3	5%
PM10	HW-M1	Hanvon	0~999.9 μg/m3	0.1 μg/m3	5%

.

The local precipitation data were obtained from the China National Environmental Science Center. The distribution of data collection points and sections is shown in Figure 2. There are 6 monitoring sections, each with 6 measurement sites and two extra wind speed measurement stations for high-level wind speed collecting utilizing the AR866A anemometer attached to the telescopic pole. The test is carried out in the order of the measurement points, with the tester standing downwind of the station and the observer not being in the same cross-section as the test instrument during the test, as shown in Figure 3. Five-time periods were chosen: 5:00–6:00, 9:00–10:00, 13:00–14:00, 17:00–18:00, and 23:00–24:00, which were moved forward to ensure the pollutant characteristics correspond to meteorological parameters. Each point is read five times in a row, with the average value as the new record value for the collection point. The average collection point value is taken as the value for this section. The daily value of the tunnel is taken as the average value of the six monitoring sections across the five time periods.

3.3. Pollutant Concentration

We found that the peak traffic periods are 10:00–12:00 and 17:00–19:00 after analyzing traffic characteristics. Thus we picked five time periods for this test: 7:00–9:00, 10:00–12:00, 14:00–16:00, 17:00–19:00, 20:30–22:30. Each test was repeated every 30 min, for a total of 5 tests each period. The instrument was scanned three times throughout each test to eliminate unintentional mistakes, and the average value was used as the test value. During the collecting time, the tunnel fans were not turned on. A fixed CO concentration data collector was arranged in the tunnel and the CO concentration data was recorded and corrected at this location by HFP-1201 before each daily measurement. The pollutant concentration data is obtained but not recorded at high wind speeds (over 10 m/s). All instruments are adjusted using the same timing to guarantee that the recorded data is synchronized for subsequent analysis.

4. Methodology

4.1. Multifractal Detrended Fluctuation Analysis Method (MFDFA)

Kantelhard proposed the MFDFA method based on the DFA (Detrended Fluctuation Analysis) method ([46]). The analysis step is as follows:

(1)

For the pollutant concentration time series x_t, t = 1, 2, 3, …, N, construct the cumulative deviation series Y_i. The time series Y_i is divided equidistantly into N_s intervals.

$$Y_i={\displaystyle \sum _{t=1}^i\left(x_t-{\overline{x}}_t\right)}$$

(1)

(2)

To obtain the mean square error F²(v, s), the local trend of the 2N_s subintervals is calculated by fitting each subinterval v (v = 1, 2, …, 2N_s) with the least-squares method. The y_v(i) is the fitted polynomial for the v segment of data in Equation (2).

$$\{\begin{array}{c}{F}^2\left(v,s\right)=\frac{1}{s}{\displaystyle \sum _{i=1}^s{\left\{Y\left[\left(v-1\right)s+i\right]-y_v\left(i\right)\right\}}^2}\begin{array}{cc}& v=1,2,\cdots ,N\end{array}\\ F^2\left(v,s\right)=\frac{1}{s}{\displaystyle \sum _{i=1}^s{\left\{Y\left[N-\left(v-N_s\right)s+i\right]-y_v\left(i\right)\right\}}^2}\begin{array}{cc}& v=N+1,\cdots ,2N\end{array}\end{array}$$

(2)

(3)

The fluctuation function F_q(s) of order q is calculated, as shown in Equation (3).>

$$\{\begin{array}{c}{F}_q\left(s\right)={\left\{\frac{1}{2N_s}{\displaystyle \sum _{v=1}^{2N_s}{\left[F^2\left(s,v\right)\right]}^{q/2}}\right\}}^{1/q}\begin{array}{cc}& q\ne 0\end{array}\\ F_0\left(s\right)=\exp \left\{\frac{1}{4N_s}{\displaystyle \sum _{v=1}^{2N_s}\ln \left[F^2\left(s,v\right)\right]}\right\}\begin{array}{cc}& q=0\end{array}\end{array}$$

(3)

(4)

The power-law relationship between the volatility function F_q(s) of order q and the time scale s holds when the time series x_t has self-similarity, as shown in Equations (4) and (5).

$$\begin{array}{c}{F}_q(s)\propto s^{h(q)}\\ \ln F_q(s)=a\ln s+b\end{array}$$

(4)

$$h(q)=\frac{\log F_q(s)}{\log s}$$

(5)

where: h(q) is the generalized Hurst exponent and defines. The mass index τ(q) and the fractal dimension D(q) in multifractal theory satisfy the Equation (6).

$$\begin{array}{l}\tau (q)=qh(q)-1\\ D(q)=\frac{\tau (q)}{q-1}=\frac{qh(q)-1}{q-1}\end{array}$$

(6)

Legendre Transformation obtains the singular exponent α and multifractal spectrum f(α).

$$\begin{array}{l}\alpha =\tau (q{)}^{\prime }=h(q)+qh(q{)}^{\prime }\\ f(\alpha )=q\alpha -\tau (q)=q\left[\alpha -h(q)\right]+1\end{array}$$

(7)

The multifractal strength can describe the degree of inhomogeneity in pollutant concentrations. The width of singular exponent ∆α (∆α = ∆α_max − ∆α_min) and ∆h (∆h = h_max − h_min), according to the multifractal theory, can be used to characterize the multifractal strength.

4.2. Random Forest Model (RF)

The Random forest model integrates bagging and random feature selection methods, is insensitive to multicollinearity, and results in robustness to missing and unbalanced data ([47,48]).

The Regression Random Forest models are modeled in this paper, as it has great application potential. However, it cannot directly predict pollutant concentrations as the control levels for COVID-19. Since the epidemic control levels indirectly affect traffic pollution emissions by affecting daily traffic of different vehicle types, the study constructs a dynamic emission model for traffic pollutants to estimate the combined emissions of different pollutants per kilometer.

The RF model in the paper is developed and validated on a dataset from 1 January 2020 to 31 January 2021 and predicts pollutant emissions in the remaining observed period. The combined CO, VOCs, NO₂, PM_2.5, PM₁₀ are the dependent variables. The environmental parameters and the daily traffic are independent variables (as shown in

Table 2. Variables for the traffic emissions random forest models in this study.

Abbreviation	Variables	Units
Environmental parameters
Temp	Air temperature	°C
RH	Relative humidity	%
Pressure	Atmospheric pressure	hPa
Precipitation	Precipitation in Baoding area	mm
Vehicle parameters
N-1	Count of LDV vehicle per day	n.a.
N-2	Count of HDV vehicle per day	n.a.
N-3	Count of LDT vehicle per day	n.a.
N-4	Count of MDT vehicle per day	n.a.
N-5	Count of HDT vehicle per day	n.a.
Prediction variables
CO_e	Vehicle emissions for CO	g/km
VOCs_e	Vehicle emissions for VOCs	g/km
NO2_e	Vehicle emissions for NO2	g/km
PM2.5_e	Vehicle emissions for PM2.5	g/km
PM10_e	Vehicle emissions for PM10	g/km

). Wind speed has little effect on vehicle emissions despite its evident impact on pollutant concentration. Similarly, the wind direction is parallel to the tunnel axis ([20]), so the wind speed and direction are not included in the independent variables. The training set was randomly selected with 70% of the data, and the remaining 30% was used as the validation set. The number of trees was 200, the split variables per node were four, and the model used the MSE split criterion.

5. Results and Discussion

5.1. Traffic Characteristic

On 23 January 2021, to stop the spread of COVID-19, Hebei Province, China, activated a Level-I control for a major public health emergency. The government adopted a series of strict control measures, and unprecedented traffic activity reduction. According to the difference in control levels, 1 January 2020–31 July 2021 is divided into 10 periods, as shown in

Table 3. The different control periods for COVID-19 in Hebei Province.

No.	Level	Period	No.	Level	Period
1	N (1)	1 January 2020–23 January 2020	6	Ⅲ (6)	6 August 2020–1 January 2021
2	Ⅰ (2)	24 January 2020–29 April 2020	7	Ⅱ (7)	2 January 2021–23 January 2021
3	Ⅱ (3)	30 April 2020–5 June 2020	8	Ⅰ (8)	24 January 2021–7 February 2021
4	Ⅲ (4)	6 June 2020–15 June 2020	9	Ⅱ (9)	8 February 2021–20 February 2021
5	Ⅱ (5)	16 June 2020–5 August 2020	10	Ⅲ (10)	21 February 2021–31 July 2021

.

The daily traffic volume of different vehicle types at the YEL Tunnel showed significant differences under different epidemic control levels, as shown in Figure 4. The average daily traffic flow at the YEL Tunnel was 11,708 veh/d when no epidemic control measures were in place (1–23 January 2020). The traffic flow of LDV decreased by approximately 66%, HDV decreased by 32%, LDT decreased by 31%, MDT decreased by 28%, HDT decreased by 34% on the day when level-I control was in place for COVID-19 (24 January 2020). The decrease in LDV daily traffic is the most obvious. The epidemic control policy affected the traffic flow significantly, except for HDT. The HDT only shows a solid response to the level-I control. The HDV traffic flow was low throughout the observation period, which means that public transport was significantly restricted. The LDV traffic flow rose rapidly after the initial level-I control. However, after the second level-II control, it still remained low.

5.2. Monitoring Results

5.2.1. Pollutant Concentrations

The pollutant (CO, VOCs, NO₂, PM_2.5, PM₁₀) concentration difference between entrance and exit are shown in Figure 5. The concentration data were processed to the interval [0, 1] using the normalization method to compare the pollutant concentration data characterized by different magnitudes. Non-aerosol pollutants (CO, VOCs, NO₂) correspond to the level of epidemic control. The control level is stricter, the pollutant concentration is lower. Interestingly, CO concentration peaks at the end of the relatively stringent level-II control (29 April 2020). Traffic flow, particularly LDVs, increased significantly in the short term, resulting in higher CO concentration. The CO concentration then levels off as the desire to travel decreases. Aerosol pollutants show the opposite characteristics, where the more stringent the epidemic control, the higher the concentrations instead, except for level-I control. It should be noted that the pollutant concentration differences were not significant, and the mechanical ventilation system was inactive during the observed period. The maximum difference ratio between the average pollutant concentration in different periods ($({\overline{c}}_{\max }-{\overline{c}}_{\min })/{\overline{c}}_{\min }$) is 35% for CO, 28% for VOCs,25% for NO₂, 52% for PM_2.5, 52% for PM₁₀.

5.2.2. Tunnel Environment Parameters

The data collection results of temperature, air pressure, and relative humidity are shown in Figure 6. The temperature and air pressure inside the tunnel have seasonal characteristics and opposite patterns. The temperature range was −12.2~32.2 °C, and the air pressure was 993.2~1038.8 hPa. The characteristic of relative humidity variation was not noticeable.

Traffic winds significantly influenced the wind speed inside the tunnel because the mechanical ventilation system was mothballed for energy saving. The semi-enclosed structure of the tunnel determines the intensity of the traffic wind is positively correlated with the traffic flow. The multivariate nonlinear function was used to fit the collected wind speed data and traffic flow, as shown in Equation (8), showing the HDT type has the most stimulating effect on the tunnel wind speed.

$$v={10}^{-4}•(2.60N_{LDV}+6.50N_{HDV}+2.86N_{LDT}+3.90N_{MDT}+7.63N_{HDT})+1.0103$$

(8)

where v (m/s) is the wind speed. N_LDV, N_HDV, N_LDT, N_MDT, N_HDT, are daily traffic of LDV, HDV, LDT, MDT, HDT, respectively.

5.3. Relationship between Pollutant Concentrations and Environmental Parameters

The various pollutant concentrations were grouped into a troop. The environmental parameters were another troop. Considering that there is a certain amount of error in the data collection process, the Spearman method was used to conduct the Canonical Correlation Analysis between the pollutant troop and the environmental parameter troop in the Spss software. The result is shown in Figure 7. As the wind speed increased, the concentrations of CO, COVs, NO₂ increased, while PM_2.5 and PM₁₀ decreased. The correlation between relative humidity and pollutant concentrations is low, with a positive correlation with CO, and a negative correlation with other pollutants. Due to the linear relationship between temperature and air pressure, the correlation between temperature and pollutant concentrations is not analyzed here to avoid multicollinearity and air pressure.

The wind speed has a weighty effect on pollutant concentrations for expressway tunnels where the mechanical ventilation system is mothballed. On the one hand, traffic wind decreases pollutant concentrations through dilution, but greater traffic wind means higher daily traffic and larger pollutant emissions. The variation feature in CO, VOCs, NO₂ concentrations evidenced the perspective. Therefore, despite considerable fluctuations in daily traffic, the variation of pollutant concentrations is slight. Remarkably, aerosol pollutants decrease with increasing daily traffic. Compared to the pollutant concentrations on the day when the maximal average daily wind speed was 8.49 m/s, the CO concentration decreased by 30.9%, 28.5% for VOCs, 21.4% for NO₂, 4.2% for PM_2.5, 4.1% for PM₁₀ on the day with the lowest average daily wind speed of 2.27 m/s. In addition, to avoid multicollinearity, it is necessary to further analyze pollutant emission factors using RF models based on the analysis of pollutant concentration evolution mechanisms.

5.4. Pollutants’ Nonlinear Evolution

The MFDFA was used to explore and analyze various pollutant concentrations. Figure 8 depicts the relationship between F_q(s) and s for each pollutant. They all have significant power-law scaling relationships within the monitoring period. The DFA scaling exponent a was estimated linearly using the Least Squares Method. All DFA scaling exponents are greater than 1.4 (as shown in Figure 8f).

The scaling exponent a for all pollutants is higher than 0.5, indicating that pollutants have solid long-term persistence. Long-term persistence reflects the variation pattern of correlation between pollutant concentration and time in the YEL Tunnel. In other words, the correlation between pollutant concentration and time does not strictly follow the Markov process but follows the power-law decay. The larger the scaling exponent a, the stronger the long-term persistence. The long-term persistence of CO concentration is the most significant, while that of PM_2.5 is relatively weak.

The MFDFA was used to explore the multifractal characteristics caused by the long-term persistence of pollutant concentration. The scaling exponent function τ(q), the generalized Hurst exponent h(q), the multifractal spectrum f(α), and ∆α were calculated.

Figure 9a shows the relationships between the Generalized Hurst exponent h(q) and the parameter q show multifractal solid characteristics. All Generalized Hurst exponent h(q) > 0.5, leading to the same conclusion as Figure 8. There is a slight difference between the h(2) and a, which is caused by the Finite Size Effect (FSE) ([49]). The h(q) shows a pattern of decreasing with increasing q values, which demonstrates that the long-term persistence of all pollutants has the structure of multifractal scale-invariance.

The scaling exponent function τ(q) is a nonlinear function of the parameter q, as shown in Figure 9b. The τ(q) has a similar evolutionary trend, and τ(q) of each pollutant intersects at q = 0. This reveals that all pollutant concentration groups have self-similarity in structure and dynamics. They have similar nonlinear dynamical evolutionary mechanisms.

Figure 9c shows the variation curves of the multifractal spectrum f(α) corresponding to pollutant groups. The multifractal strength can be characterized by the width of singular exponent ∆α (∆α = ∆α_max − ∆α_min). The larger the value of ∆α, the stronger the multifractal, which implies the strength of the long-term persistence in actual pollutant concentration changes. The ∆f reflects the frequency change of the maximum and minimum fluctuations in the long-term persistence of pollutants.

Figure 9d presents the degree of multifractality: VOCs > CO > NO₂ > PM₁₀ > PM_2.5. This is partly because the YEL Tunnel is located in a mountainous area with high forest cover and the long-term nature of VOCs released by vegetation. Another reason is the photochemical reaction of VOCs. CO is slightly higher than VOCs in data dispersion. The long-term fluctuation of CO is the most significant. The distribution homogeneity of dynamic change in PM_2.5 and PM₁₀ is the most uneven. α₀ is the abscissa of the extreme point in the multifractal spectrum.

The results of MFDFA for pollutant evolution in different periods are shown in Figure 10. Compared to the non-epidemic period, the ∆α of pollutant evolution was slower during the epidemic period. The trend of multifractal strength (∆α) is consistent across pollutants. This suggests that the reduction in daily traffic resulted in a weaker long-term persistence of pollutants during COVID-19. The combination of seasonality and control level results in a fluctuating alteration of ∆α. Overall, the tighter epidemic control level leads to long-term persistence and weaker fluctuating intensity of pollutants. In particular, the long-term persistence of pollutants in the relaxed control time of 2021 has still not returned to the status of pre-epidemic time.

From the above studies, the response mechanism of pollutant concentration to traffic pollution emission reduction is governed by the dynamics of nonlinear interactions. Firstly, the tunnel ventilation was mainly dependent on traffic winds during the measurement period. Secondly, the pollutant concentration evolution has a steady power-law distribution structure. Therefore, the temporal evolution of each pollutant concentration may have a Self-organizing Critical (SOC) state [50]. It is challenging to predict pollutant concentrations directly, as they have long-term persistence.

5.5. Prediction of Air Pollutants in YEL Tunnel

The pollutant concentration needs to be converted into pollutant emission for further analysis to clarify the traffic emission characteristics. Equation (9) calculates the pollutant emission mass for the vehicle fleet through the tunnel ([51]).

$$E{F}_{total}=\frac{\Delta C\times A\times v\times T}{L}$$

(9)

where: EF_total (mg/km) is the traffic emissions. ∆C (mg/m³) is the difference in pollutant concentration between the outlet and inlet. A (m²) is the cross-sectional area of the tunnel (99.47 m²). v (m/s) is the air velocity parallel to the tunnel alignment. T is for one day. L is the tunnel length (5.6773 km).

Using MSE, RMSE, MAE, MAPE error functions and the coefficient of determination R² calculated for each RF model clarified the model’s fit quality. The established RF models were validated using the partitioned validation dataset (1 January 2020 to 31 January 2021). The RF model generalization ability was certified by the 10-Fold Cross-validation (as shown in Figure 11).

The RF model has an excellent fitting effect, as shown in

Table 4. The validation for the RF model.

Code	MSE	RMSE	MAE	R2	MAPE	MSE *	RMSE *	MAE *	R2 *	MAPE *
CO	9,359,226.8	3059.3	2126.8	0.9983	1.0388	9,988,660.5	3160.5	2219.4	0.9971	1.5187
VOCs	1346.4	36.7	22.8	0.9882	1.8102	1194.7	34.6	21.3	0.9893	1.6982
NO2	3,066,479.4	1751.1	1065.1	0.9805	2.3059	2,820,593.7	1679.5	993.4	0.9826	2.1507
PM2.5	5611.1	74.9	39.7	0.9632	3.5809	6286.6	79.3	45.1	0.9503	3.8625
PM10	5709.1	75.6	46.2	0.9698	3.4651	6212.3	78.8	48.2	0.9636	3.6166

Note: * is the 10-Fold CV, where the final result is the mean of the 10 cross-validation results.

. The 10-Fold cross-validation results show a slight variability in MAE and MSE values. The PM_2.5 has the most significant difference with a 12.04% increase in MSE and a 13.58% increase in MAE, while the MSE value for VOCs decreased by 11.26% and the MAE value decreased by 6.19%. Overall, the 10-Fold Cross-validation results show very little difference from the original test results, indicating the RF model generalizes well. The model can explain most of the fluctuations in pollutant emissions.

The importance of various independent variables in the RF model is shown in Figure 12, which indicates the main impact of the traffic flow. The total traffic flow contributes 84.55%, 96.24%, 93.66%, 76.47%, 77.60% to the output results of CO, VOCs, NO₂, PM_2.5, PM_10, respectively. The YEL Tunnel is the main transportation corridor for heavy-industrial raw materials in North China. PM sources include coal dust, secondary dust, clutch, and tire wear. However, all these factors are closely related to traffic flow. From the perspective of traffic flow of different vehicle types, the HDT has the largest influence on the generation of various pollutants, contributing 61.54%, 58.76%, 82.38%, 39.26%, 40.61% to the output results of CO, VOCs, NO₂, PM_2.5, PM_10, respectively. Analyzing the reason, firstly, the traffic flow of HDT in the ERL Tunnel is least affected by the control policy; secondly, the emission coefficient of HDT is high. Its influence weight on NO₂ is the largest, so HDT is the main source of NO₂ emissions. The contributions of all environmental parameters to the output results of CO, VOCs, NO₂, PM_2.5, PM₁₀ are 15.45%, 3.76%, 6.34%, 23.53%, 22.40%, respectively. Among these, the effects of air pressure and precipitation are negligible. However, CO and aerosol pollutant emissions are sensitive to temperature and humidity, as vehicle engines have different working efficiency under different temperatures and relative humidity. CO and aerosol pollutant emissions will increase as the low-temperature condition causes poor fuel atomization. The high-temperature condition causes premature combustion, which leads to larger CO and aerosol pollutants emissions. Similarly, an increase in relative humidity favors the production of particulate matter. Temperature contributes 10.35% to CO generation, 19.98% to PM_2.5 and 16.90% to PM₁₀. Relative humidity is 5.04% for CO, 3.13% for PM_2.5 and 5.43% for PM₁₀. To sum up, the HDT flow is the controlling factor for emissions of each pollutant.

To reflect the prediction accuracy of the RF model, the Multiple Linear Regression model (MLR), Polynomial Regression model (PR), and Classification And Regression Tree model (CART), eXtreme Gradient Boosting model (XGB) were established based on the divided training data set. The prediction accuracy in pollutant emissions, calculated by different models, is obtained as shown in

Table 5. The validation for different models.

Model	The Goodness of Fit (R2)
	CO	VOCs	NO2	PM2.5	PM10
MLR	0.4021	0.5259	0.3805	0.3462	0.3025
PR	0.5005	0.5188	0.3966	0.2218	0.2564
RF	0.9983	0.9882	0.9805	0.9632	0.9698
CART	0.9860	0.9021	0.9410	0.8905	0.8582
XGB	0.9905	0.9941	0.9606	0.9153	0.9055

.

The machine learning algorithms have higher prediction accuracy than traditional regression models for analyzing traffic emissions. The RF model is 88–221% better than the MLR model and 90–334% better than the PR model in prediction accuracy. The prediction capability of the CART and XGB model for non-aerosol pollutants is similar to that of the RF model. However, the RF model is better at predicting aerosol pollutants emissions, with an 8–13% improvement over the CART model and 5–7% over the XGB model. The RF model still has a considerable advantage over similar machine learning algorithms in this study.

The prediction results for traffic emissions from 1 February–31 July 2021 are shown in Figure 13. As can be seen from the values of R² and MAPE, the established RF model shows good accuracy. The maximum R² is 0.9948, and the minimum is 0.9514, as shown in

Table 6. The validation for prediction results.

Code	MSE	RMSE	MAE	R2	MAPE
CO	10,761,006.4	3280.4	2490.1	0.9948	1.6591
VOCs	2102.6	45.99	30.3	0.9852	2.4129
NO2	3,247,377.2	1802.0	1089.2	0.9803	2.3583
PM2.5	6964.5	83.5	46.3	0.9514	3.8052
PM10	5308.7	72.9	45.6	0.9734	3.3862

. Combined with the calculation results on the validation data set, the RF model has better prediction accuracy for CO, COVs, NO₂. In particular, the calculation accuracy for aerosol pollutants slightly improves the prediction period, which proves that the RF model has a good generalization ability (compared to 10 cross-validation results).

The predicted concentrations at different control levels are shown in Figure 13. The coefficient of determination (R²) for CO is 0.9825, R² = 0.9825 for VOCs, R² = 0.9903 for NO₂, R² = 0.9758 for PM_2.5, and R² = 0.9845 for PM₁₀. Therefore, the method of back-calculating pollutant concentrations by predicting traffic emissions is implementable, and the results are highly accurate. Compared to the results for pollutant emissions, the concentrations of aerosol pollutants have a little improvement in the prediction accuracy. In combination with the MFDFA results, the long-term persistence of aerosol pollutant concentrations is minimized. Therefore the prediction accuracy is improved by converting emissions to concentrations due to the effect of traffic wind. Collectively, the prediction results for level-3 control are better than the others, mainly due to the relatively stable traffic flow in the situation. Overall, the RF model’s good performance indicates the prediction results’ reliability.

6. Conclusions

We collected and analyzed daily traffic, environmental parameters, and pollutant concentrations for the YEL Tunnel in North China from 1 January 2020 to 31 July 2021. The mechanism of pollutant concentration variation in the tunnel was analyzed and discussed by the MFDFA method. The RF models were established for predicting the different pollutant emissions. The main findings from this study are as follows.

(1)

Different epidemic control levels had different degrees of impact on daily traffic for different types of vehicles, with the HDT only showing a stronger response to level-I control. The same control level also had different effects on traffic flow in different periods.

(2)

The pollutant concentrations did not fluctuate significantly during the observation period. Typical correlation analysis results show wind speed largely influences pollutants concentration, ranging from −0.523 to 0.673. The correlations between aerosol pollutant concentrations and wind speed are negative, and the aerosol pollutants are more likely to be discharged from the tunnel. The traffic wind dilutes the pollutant concentrations, and the higher the traffic wind, the higher the pollutant emissions.

(3)

The MFDFA results indicate that the pollutant concentrations inside the tunnel exhibit long-term persistence, with CO concentrations being the most significant (h_co(2) = 1.791), and relatively weak for PM_2.5 concentrations (h_PM2.5(2) = 1.602). The evolution of each pollutant has a stable power-law distribution structure, and the pollutant evolution may have the Self-Organized Critical (SOC) state.

(4)

Through the validation results for the 10-Fold CV and different mathematical models, the created RF models demonstrated high prediction accuracy and generalization ability. The HDT traffic flow was the controlling factor for each pollutant (39.26 to 82.38%). The concentration inversion findings revealed that the prediction accuracy (R²) is 0.9942 for CO, 0.9825 for VOCs, 0.9903 for NO₂, 0.9758 for PM_2.5, and 0.9845 for PM₁₀.