3.2.3. Trajectory Clustering

Before performing cluster analysis, outliers are removed from the vehicle trajectory dataset to filter out unusual driving cases that have not passed through the entire link or have stopped for a long time. Cluster analysis is performed to assemble the data into several similar vehicle trajectory groups. The k-means method is used to find the optimal number clusters and the center of each cluster. As a variable for each cluster analysis, the ratio by OpMode, which can describe the characteristics of the vehicle trajectory, is used. As in previous studies, aggregated characteristics, such as average speed and maximum acceleration, could be used as variables for clustering, while the ratio for each OpMode was selected as a cluster analysis variable. The main purpose is to utilize the value of the center of each group, which is the OpMode distribution, for micro-level emission calculation. Another purpose is to use the same scaled cluster variables. Using the values of the cluster center, the emissions of the cluster center can be calculated. The weighted average of emissions of all vehicles is obtained by applying the cluster size as a weight, which means the emissions per vehicle on the corresponding road section. It can be used as a micro-level link emission factor.

### 3.2.4. Calculate Link Emission Factor

After cluster analysis, the OpMode distribution and cluster size of each cluster center are extracted, which are used to calculate the emissions of all clusters by Equation (2):

$$\text{Emission}\_{\text{pol}} = \sum\_{1}^{k} (\sum^{\text{opumale}} R\_{\text{opumale}} \, \ast \, EF\_{\text{opumale},\text{pol}})\_{k} \, \ast \, \text{size}\_{k} \, \ast \, \text{meanTT})\_{i} \tag{2}$$

where ( *opmode Ropmode* ∗ *EFopmode*, *po<sup>l</sup>*) *k* : represents the emissions of cluster *k*, *Ropmode* is the ratio of each OpMode, *EFopmode*, *pol* the OpMode emission factors by pollutants (pol, in g/sec), *k* is the cluster number, *sizek* is the cluster size and *meanTT* is the average driving time of vehicle trajectories

Finally, as shown in Equation (3), by dividing the total emissions by the total number of vehicles used in the cluster analysis, the micro-level link emission factor of the vehicle type is calculated by the following:

$$micLEF\_{pol} = \text{ emissions}\_{pol} / \text{number of vehicles} \tag{3}$$

where *micLEFpol* : micro-level emission factor (g/veh).

According to the collected vehicle trajectory data, the data will be spatio-temporally expanded and applied to the regional and national levels. A database of micro-level link emission factors for a nationwide tra ffic network can be established. The procedure for estimating the micro-level link emission factors should be performed by vehicle type and analysis time interval on each road section. When a vehicle type-specific tra ffic volume database is provided, the emissions from all the vehicles on the tra ffic network will be easily calculated by applying the database of micro-level link emission factors for a nationwide tra ffic network.
