# Pavement Distress Initiation Prediction by Time-Lag Analysis and Logistic Regression
## 1 Introduction  
Pavement distress initiation is closely related to the service life of the pavement and is usually accompanied by the deterioration of asphalt material and subgrade structural damage [1, 2, 3, 4]. The presence of pavement distress not only accelerates pavement deterioration and reduces pavement life, but also affects driving safety and comfort to a large extent [5, 6, 7, 8]. Pavement maintenance can effectively reduce pavement distress, and the common means of maintenance are mainly daily routine maintenance, major annual repair, and pre-maintenance. Since major annual repair and pre-maintenance require large investment in road refurbishment in a short period of time, the development of a corresponding maintenance plan is fully studied. The development of a maintenance plan requires observation and prediction for the initiation and deterioration of pavement distress. Pavement distress initiation and deterioration prediction based on long-term inspection records has proven to be an effective support for the development of major annual maintenance plans and pre-maintenance plans [9]. In this paper, we distinguish between long term and short term and high frequency and low frequency, depending on the granularity of time. High frequency implies that data are collected at the daily or weekly level, and low frequencyrefers to data collected at the yearly level. Due to the lack of relevant datasets, the long term here is only restricted to refer to yearly data collected for many years. However, unlike major annual maintenance supported by a long-term pavement condition prediction model trained on large granularity data, daily maintenance needs the support of a short-time pavement distress occurrence prediction model. Higher frequency data collection can reveal more detailed correlations among variables, e.g., weather data in annual data are involved in modeling as static variables, while weather data at the daily or weekly level can be valued for their time-series properties in modeling. Therefore, in order to improve the efficiency of daily pavement maintenance, it is important to develop a short-time pavement condition generation prediction model. Previous studies on predicting the occurrence of pavement distress have typically been based on long-term testing records, such as the Long Term Pavement Performance (LTPP) program [10] and the AASHO road testing program [11]. [PERSON] [12] concluded that the long-term deterioration trends of pavement condition index (PCI) and riding quality index (RQI) can be classified into four types, namely, concave, convex, inverse S, and pre-fast decay curves, based on the long-term observation data of five Chinese provinces, and the deterioration processes are represented by functional expressions. [PERSON] et al. [13] studied the effects of construction, traffic, and climatic factors on pavement performance based on long-term pavement performance test data from 15 European countries and concluded that the log-normal function predicted the generation of pavement cracks most accurately. [PERSON] et al. [14] evaluated the generation time of road cracks based on data from the Long Term Pavement Performance (LTPP) project, and found that service life, traffic volume, and pavement structure are important in the crack occurrence process, while a survival model containing a Weibull hazard function is most relevant to describe various crack occurrences. The above studies explored the factors influencing crack occurrence based on long-term pavement condition data, which led to the construction of prediction models for pavement distress occurrence and deterioration, and these studies were useful for annual pavement condition prediction. However, daily routine maintenance requires a high-frequency prediction model for pavement distress initiation and deterioration, which means that prediction models must be trained using pavement distress data with small time intervals.