Temporal clustering of retroreflective marking

The quality and reliability of road infrastructure and its equipment play a major role in road safety. This is especially true if we are interested by autonomous cars traffic able to read road marking. This kind of vehicles needs an accurate maintenance strategy to guarantee a road with marking perceptible for a human eye or an autonomous car. To simplify the study of a road and because a maintenance campaign is generally applied for a part of the road, a solution based on an Agglomerative Hierarchical Clustering to cluster all markings is chosen. In the case of no follow-up of the maintenance for markings, a maintenance detector will be introduced and described. Finally, with this classification, it is possible to extract all maintenance cycles and identify the different maintenance actions. This approach is a first step to analyze the useful life of marking with a Weibull analysis. Skip center line of the French National Road 4 is considered to illustrate the proposed approach. Keyword : Agglomerative Hierarchical Clustering, retroreflection, marking, maintenance cycle Figure 1. Sectional view of a white water-based paint retroreflective marking. Figure 2. Representation of a white marking according to it retroreflexion level (mcd/m2/lx) A first valve paints the road, a second puts glass beans on the marking and a last adds the anti-skid products. The quantity of each component depends to the constructor. The retroreflexion level of a marking is evaluated by a retroreflectometer. In this paper, an Ecodyn from Vectra is considered. This retroreflectometer is fitted to a car side and reliable to a laptop inside the car (Fig. 4a). This instrument measuring gives off a white light to markings and measuring the quantity of light retroreflected (Fig. 4b). Ecodyn measuring also thanks to some sensors the daytime and the nighttime contrast. The laptop creates automatically a data base and associate each measure to a point of reference thanks to an associated software (Fig. 4c). The current configuration could analyze the retroreflection level each 40 cm but gives only an average on 100 m. In fact, each measure represents an average of three or four markings. To simplify, a measure is analyzed like one marking. To evaluate the economic impact of replacing a marking, a performance-based approach of the maintenance is chosen. Specifically in markings case, a preliminary work is: how each marking was installed? What kind of marking was chosen? What is the current maintenance strategy? Are there some strategic area? The major part of the literature supposes some conditions. For example: a test desk is considered (Bahar, et al., 2006) (Zhang & Wu, 2006), the study starts 6 months after the lay date (Karwa & Donnell, 2011), the kind of marking is known (Sarasua, et al., 2003) or the road is monthly inspected (Sathyanarayanan, et al., 2008). In addition, followup of the maintenance campaigns for markings and regular inspection campaigns are complete. In the reality, the follow-up may incomplete and markings could be inspected only once a year. As a result, incomplete data on the monitoring of marking retroflectivity exists and installment dates of markings must be estimated. Our approach is similar to (Migletz, et al., 2001) : the study is based on a specific road regularly inspected. To simplify the road and because a maintenance campaign is generally applied for a part of its, a solution based on an Agglomerative Hierarchical Clustering (Tufféry, 2011) to cluster all marking according to the geographic position and the retroreflection evolution is chosen. The study of the road is reduced to some cluster represented by an average profile. To estimate lay date of marking, a maintenance detector based on the previous clustering and accorded to AFNOR rules (AFNOR, 2009 ) is proposed. Our hypothesis is that each cluster represents a specific part of the road. This part admits its own retroreflection evolution and past maintenance actions can be deduce. Skip center line of the French National Road 4 (NR4) is considered to illustrate the proposed approach. This road joins Paris and Strasbourg. Since 2007, the part between Courgivaux and Perthes (~104 km) is managed by the DIR Est with two management teams (Direction Interdépartementale des Routes de l’Est, 2008). In order to evaluate the state of markings, one inspection a year is organized in collaboration with the CEREMA with an Ecodyn where each measure is located by a reference point. Unfortunately, it doesn’t exist any follow-up of the maintenance campaigns for markings. The following sections present the Agglomerative Hierarchical Clustering and the maintenance detector both applied on skip center line of the NR4. Figure 3. (a) A truck able to lay marking, (b) The "sandwich" lay technique. Figure 4. Presentation of an Ecodyn: (a) An Ecodyn fitting to a car, (b) The measuring process, (c) Example of a data base (Vectra France, 2017). 2 THE AGGLOMERATIVE HIERARCHICAL CLUSTERING 2.1 Definition and properties of the AHC The Agglomerative Hierarchical Clustering (Tufféry, 2011) (AHC) consists to produce sequences of partitions of increasing heterogeneity between partition into n clusters where each object is isolated and partition into one cluster which includes all the objects. A marking is defined by its geographic Point of Reference (PR), inspections measures and retroreflexion evolution between two inspections. The general form of the AHC is the following: 1. Each marking is a cluster. 2. The distance between clusters are calculated. 3. The two closer clusters are merged into one. 4. Start again at step 2 until there is only one cluster, which contains all marking. The second step introduces a distance between two clusters. In the case of two markings, the Euclidian distance d is considered. Else, the Ward distance (1) is chosen where X, Y are both clusters; x, y their average profiles; , their numbers: Y X n n y x d Y X dw 1 1 ) , ( ) , (