## 3 Theory and Methods
### Convolutional LSTM Networks
\[i_{t}=\sigma(W_{i}\times[h_{t-1},x_{t}]+b_{i}) \tag{7}\]6  
In this paper, we introduce the RMSDC technique based on a deep learning configuration. We comprehensively explain the RMSDC structure, including its mathematical formulations and concepts. The detailed descriptions and processes of the RMSDC are presented in the subsequent sections, as depicted in \[i_{t}=\sigma(W_{i}\times[h_{t-1},x_{t}]+b_{i}) \tag{7}\]7 The alignment between the output \(y_{j}\) and input \(x_{t}\) is determined by the probability \(\alpha_{j}^{t}\). An alignment model, which is a feed-forward neural network function of \(h_{t}\) and the previous decoder hidden state \(h_{t}\), calculates the corresponding energy for \(\alpha_{j}^{t}\). The temporal context vector \(s_{j}\) serves as the input to the decoder at output time-step \(j\). This method, commonly used in temporal interpretability studies, enables the computation of temporal attention weights [60]. Dataset  
The dataset contains data for months, including weather conditions and measurements from numerous sensors relating to road conditions; environmental variables are also included in the data, such as in [61]. Each row of data represents a single measurement performed at a particular time and location for the Smart Road. The following are the data columns:  
\[i_{t}=\sigma(W_{i}\times[h_{t-1},x_{t}]+b_{i}) \tag{7}\]8 Flow chart for RMSDC based on multivariate. Day: The measurement was taken on this day. Time (+01:00): The measurement time is adjusted for the local time zone (+01:00). S1-S3: Road surface condition measurements from three distinct sensors (S1, S2, and S3)  
Friction: A measurement of the friction coefficient of the road surface, which indicates how slippery the road is, with 0.1-0.81 as the measured friction value. Ta: The air temperature at the time and place of measurement. S7: A sensor measurement of the road surface's moisture content. Tsurf: The road's surface temperature at the time and location of measurement. S9-S11: Road surface condition measurements from three distinct sensors (S9, S10, and S11)  
Water: The amount of water on the road's surface at the time and location of meas urement. Speed: The vehicle's speed at the time and location of the measurement. The direction in which the vehicle was traveling at the time the measurement was taken. The latitude of the site where the measurement was taken. The longitude of the site where the measurement was made. Height: The elevation above sea level where the measurement was taken. Accuracy: The GPS measurement's precision. Tdew: The temperature at the dew point at the time and location of measurement. Friction 2: A second measure of the friction coefficient of the road surface that may be measured with a different method or sensor. Distance: The distance the vehicle has traveled since the previous measurement. Serial (RCM411): The serial number or identifier of the data collection device (data logger). State: is a categorical variable that indicates the overall condition of the road surface--Dry, Moist, Wet, Icy, Snowy, and Slushy--with values from 1-6. To examine more information from the dataset, we extract the days from Timestamp (changing this string to a DateTime object) and visualize the distribution of values each day. As illustrated in Figure 5, there were some variances in using values on different days. We analyzed each data group by separating it using these spatial and temporal characteristics, allowing us to obtain insights on the spatial distribution of road surface conditions at different locations and the temporal patterns of road surface conditions across time. This divide will allow for more targeted and detailed investigations, which will help understand how road surface conditions vary across geographical regions and how they evolve over time. RMSDC is an effort to apply the LSTM model to a time-series in both the spatial and temporal directions--based on geographical and sensor data, to be particular. We use an LSTM model throughout the spatial domain.