In this research, road maintenance vehicles were fitted with a road surface temperature sensor (depicted in Fig. 1), which utilizes an infrared thermometer to gauge the temperature of three bridges, as illustrated in Fig. (2). While the vehicle is in motion, the sensor is capable of measuring the temperature every 0.2 seconds. Pavement temperature data were obtained from three bridges, each approximately 300 meters in length, from December 2022 to February 2023. Data collection took place on a total of 397 days, with measurements recorded once per day during nighttime. Its precision is greatly enhanced by a narrow half-angle of 5°, resulting in accurate surface temperature measurements [15-17]. At 0°C, the sensor exhibits an accuracy of ±0.3°C. Furthermore, concurrent atmospheric data (air temperature and relative humidity) were acquired from the closest weather station during the same time period from an open API operated by the weather agency.

Fig. (1). Pavement temperature sensor.

In order to efficiently utilize the gathered data for de-icing operations, it was crucial to consolidate the information according to specific roadway sections. To achieve this, the Korean government implemented a standardized node-link system (depicted in Fig. 3). This system divides the entire public highway network into nodes and links, taking into account various roadway characteristics, such as bridges, tunnels, overpasses, underpasses, intersections, and the number of lanes. Since the temperature of the pavement differs depending on the type of roadway, the aggregation of data using the node-link system is regarded as a logical and effective approach.

Fig. (2). Data collection sites.

Fig. (3). Standard node-link system of Korea.

Fig. (4). Air temperature vs. pavement temperature.

For the analysis of pavement temperature, the standard node-link system was employed to aggregate the data into a single median value on a daily basis, which served as a representative measure of central tendency. Nevertheless, as the measurements of pavement temperature obtained from moving vehicles may include outliers due to factors like debris on the road, driving on the shoulder lane, intermittent stops during patrolling, and so on, it was crucial to adopt a careful aggregation method to address any unforeseen consequences caused by these outliers. Among the three commonly used measures of central tendency (mean, median, and mode), the median was chosen because it is less influenced by extreme observations [18, 19].

Fig. (4) depicts a graph illustrating the pavement temperature and air temperature recorded at one of the aforementioned three bridges. Similar patterns were observed at the other two bridges. Overall, the bridge temperature was consistently lower than the air temperature, with the air temperature exhibiting greater variability. table 1 and 2 display that, on average, the bridge temperature was approximately 2 times lower than the air temperature, while the maximum temperature reached about 4 °C higher. In contrast, the air temperature had a minimum temperature of approximately 2 °C lower than the pavement temperature. Unlike the air temperature, which fluctuates considerably due to air flow, the pavement temperature is presumed to exhibit relatively low variability due to the geothermal and latent heat properties of the structure, as shown in Fig. (5).

A predictive model for nighttime black ice using atmospheric data was established. The input data for a k-NN model included temperature, humidity, dew point temperature, temperature differences between consecutive days, and humidity differences between consecutive days (see Fig. 6). These data were collected over a span of two years at the three bridges mentioned earlier. To create the baseline data, we combined the input data with pavement temperature data obtained from patrol vehicles. Detailed information regarding the baseline data will be presented in the subsequent chapter. The configuration of the k-NN model is illustrated in Fig. (6). Since the scales of the input data varied, we applied standard scaling to normalize the data prior to training the models. The training and test sets were divided into a 7:3 ratio, and the raw data were classified based on the ratio of dry/icing conditions to ensure a balanced distribution in both sets. The analysis encompassed a total of 397 days, with 193 days classified as icy conditions and 204 days as dry conditions.

Fig. (5). Boxplot of air and pavement temperature.

To implement the k-NN algorithm in Python, the following steps were followed:

1. Load the labeled training dataset, which contains input feature vectors and their corresponding class labels or target values.

2. Choose a value for k, which represents the number of nearest neighbors to consider during predictions.

3. Compute the distances between a new input sample and all the training samples using a distance metric. This metric quantifies the similarity or dissimilarity between two data points.

4. Identify the k-training samples with the smallest distances to the input sample. These samples will be the nearest neighbors.

5. For classification tasks, assign the class label that appears most frequently among the k-nearest neighbors to the input sample.

Finding the best value for k is crucial in the k-nearest neighbors (k-NN) algorithm. A small k can lead to overfitting, making the model overly sensitive to noisy data. Conversely, a large k can result in over-smoothing, causing the model to overlook local patterns in the data. The optimal value for k is typically determined through techniques like cross-validation or grid search. These methods involve evaluating different k values and selecting the one that performs best based on evaluation metrics. Fig. (7) illustrates the process of selecting the optimal k value, with a value of one being identified as the optimal choice.

Fig. (6). Building block of k-NN model.

Fig. (7). Model performance by k values.

Fig. (8). Model performance by distance measures.

The choice of distance metric in the k-nearest neighbors (k-NN) algorithm depends on the characteristics of the data and the specific problem being addressed. Euclidean and Manhattan distances (Eqs. 1 and 2) are commonly used options. Therefore, the selection of the optimal metric was performed for these two metrics, as shown in Fig. (8). The analysis revealed that for a value of k equal to one, the optimal metric was found to be the Euclidean distance. Typically, k-NN algorithms can be computationally expensive when dealing with large datasets, as they involve calculating distances for each new sample against all the training samples. However, in this study, the data size was relatively small (only a few bytes), which did not pose a hindrance to the extensive computations.

(1)

(2)

where d_(x,y) = distance between points x and y.

To assess the precision of the predicted black ice data, it is crucial to establish a baseline. While employing a reference device to directly measure the road surface conditions would be the most reliable and straightforward approach, it was not feasible within the scope of this study due to labor-intensive requirements, costs, and the need for device acquisition. Instead, we relied on a physical principle described in Eq. (3), which indicates that frost develops on the pavement when the pavement temperature is not only below freezing but also lower than the dew point temperature.

(3)

where T_p = pavement temperature and T_d = dew point temperature.

The concept of dew point temperature pertains to the specific temperature at which moisture in the air reaches saturation, resulting in the formation of fog or frost and causing the relative humidity to reach 100%. To determine the dew point temperature, the commonly employed approach is to utilize the Magnus formula, which is a widely accepted method for this purpose [15]. This formula calculates the saturation vapor pressure over liquid water at a given temperature (T) using Eq. (4).

(4)

The Eq. (4) incorporates the parameters α (6.112 hPa), β (17.62), and λ (243.12°C). By rearranging the terms in Eq. (4), we can derive Eq. (5), which provides an expression for the dew point (T_d) based on the vapor pressure.

(5)

By substituting the definition of relative humidity (E=RH*EW/100) into Eq. (5), we can derive Eq. (6), which enables us to calculate the dew point (T_d) using both the atmospheric temperature (T) and relative humidity (RH).

(6)

Eqs. (4-6) employ the well-established Magnus formula, which is widely recognized as a reliable method for estimating the dew point temperature using the atmospheric temperature and relative humidity. This formula exhibits an error rate of approximately 0.35°C [16].

To validate the precision of the Magnus formula, a winter road segment was surveyed, specifically focusing on frost-induced black ice occurrences. It was observed that black ice formed (on the left) when the criteria for frost formation were satisfied, whereas no black ice was observed (on the right) when those criteria were not met, as depicted in Fig. (9).

Fig. (9). Pavement with frost (left) and without frost (right).

The developed model was evaluated using a test dataset consisting of 119 samples, which accounted for 30% of the entire data, and the performance is presented in Table 1. The evaluation metrics used, including accuracy, precision, recall, and F1 score, are commonly employed to assess the effectiveness of machine learning models. These metrics, as defined in Eqs. (7-10), indicate that the model yielded satisfactory outcomes with accuracy, precision, recall, and F1 score values of 0.95, 0.97, 0.93, and 0.95, respectively. Additionally, Table 3 showcases the confusion matrix, which further demonstrates the model's strong performance across all cases. Particularly noteworthy is its capability to accurately identify “icy” conditions, which is crucial for winter road maintenance.

(7)

(8)

(9)

(10)