# Pavement Distress Initiation Prediction by Time-Lag Analysis and Logistic Regression
## 5 Conclusions  
Previous research has focused on establishing relevant prediction models and exploring the impact of multiple factors on the initiation and deterioration of pavement distresses through long-term data. This paper used road image data with a short collection period to predict the initiation of pavement distresses and explore the relationship between the changes in various weather factors and the initiation of distresses. The conclusions obtained are as follows:  
(1) The time-lag cross-correlation analysis was processed between initiation of pavement distresses and maximum temperature, minimum temperature, daily average temperature, daily total precipitation, and relative humidity. It can be found that the correlation of the number of distress initiations between the maximum temperature of the day and relative humidity at the same time is \(-0.10\) and \(0.23\), respectively. Moreover, the correlation of distress initiation between minimum temperature nine days ago, daily average temperature nine days ago, and daily total precipitation two days ago is \(0.14\), \(-0.12\), and \(0.24\), respectively. This indicates that the impact of temperature and precipitation on road distress initiation has a time-lag effect;  
(2) Through the analysis of the correlation between the number of pavement distress initiations and the related factors of road alignment, it can be known that the coefficient of initiation of road distress and the distance from the pavement to the intersection center is \(-0.17\), which means there is a negative correlation. Moreover, the coefficient is \(0.26\), which means there is a positive correlation with the number of historically accumulated distresses on the pavement. However, since the coefficients are both below \(0.01\), the initiation of pavement distress has a weak correlation with the road grade of the neighboring road;  
(3) Binary logistic regression models with or without time-lag variables were utilized to establish a distress initiation prediction model and explore the degree of influence of each variable on distress initiation. The weather factor variables of one model consider the influence of the time-lag effect, while the weather factor variable of the other model does not consider the impact of the time-lag effect. The AIC and BIC of the model containing time-lag variables are \(1335.703\) and \(1375.964\), both lower than the other, revealing that the first model is more precise than the second model. The modeling results show that the AUC of the training and testing sets in the model considering time lag is \(0.759\) and \(0.761\), respectively, indicating that the weather factor variables considering the time-lag effect could help improve the prediction of pavement distress initiation accuracy. Based on the research of this paper, the following research can be carried out in the future. Firstly, in the temporal aspect, the time range of image acquisition for pavement distress can be extended to improve the robustness of the results. By extending the acquisition time range of the dataset to more than one year, the differences in predicted data under the same monthly and quarterly data from different years can be explored by experiencing weather changes in a complete year, and the estimation bias of model parameters can be reduced. Secondly, in the spatial aspect, the regional span of pavement distress image acquisition can be expanded to improve the adaptability of the conclusions. Studying the pavement distress initiation under different traffic volumes under the same type of area can help explore the anomalies of distress generation due to traffic characteristics (e.g., road sections with more heavy vehicles) or explore the differences of various road classes on distress generation. Due to the generality of the method in this paper, the trending conclusions on weather and geometric factors on distress generation can be applied to more areas.