SIGNAL + DRAHT (103) 10/2012 42 n ETCS The analysis of the human factor has enabled us to determine for each elementary cause of driver error the factor by which ETCS level 1 has reduced the frequency of overpassing end of authority compared with the lineside signalling/ warning systems reference. Cumulating the frequency obtained for each elementary cause results in a frequency of overpassing end of authority incidents Freq { EV(C)} in the presence of ETCS level 1 of the order of 5·10–3/ h. 5.3 Quantification of the probability of EV(B) A fundamental element influencing the conditional probability Prob{EV(B)} is the statistical distribution of the distance D between the signal and the danger point. As a first approximation, the distribution function of this distance F(D) can be modelled by an exponential behaviour: F(D) 1 – e– D/do Moreover, this probability is closely linked to the train’s movement in rear of the signal and the emergency braking distance EBD, which is itself correlated with the speed of the train when it passes the signal: Prob {EV(B)} = · F(EBD(V local )) The coefficient is a proportionality factor of the order of 1/2. It is assumed that a probable worst case corresponds to a value of the speed V local of the train when passing the SBG which is below the Release Speed ( RS) or the speed limit in shunting/staff responsible mode (ceiling speed) with a value ∆v equal to 5 m/h. The emergency stopping distance depends fundamentally on the type of rolling stock operating on the infrastructure. It is calculated using the standard braking model recommended by ERA adapted to low speeds (≤ 40 km/h) to improve the precision of the simulations. The effective stopping distance of the train, EBD (Emergency Braking DisBy introducing SH&SR , the proportion of trains that reach the danger point in shunting or staff responsible mode (typically of the order of 0.2 to 0.25 by analogy with lineside signalling), the safety constraint HR ≤ THR(ER1) can be formulated on the basis of the parameters Release Speed (RS) and speed limit in shunting/staff responsible mode (ceiling speed) as follows ( i , i and C are constants): V 0 RS(km/h) $ a i i / $ F(EBD i (RS–Dv)) +c SH&SR $ b i $ F(EBD i (CS–Dv)) #C i / Figure 3: Safety constraint ceiling speed (shunting or staff responsible mode) as a function of release speed tance), is obtained by increasing the emergency braking distance by the distance travelled during the ETCS system reaction time, by the offset relative to the position of the Eurobalise antenna compared with the front of the train and the location of the SBG balise group, and by the correction due to the track gradient. 5.4 Model The tolerable hazard rate (ER1) is decomposed according to the technical modes (or operational circumstances) of the train when it overpasses the end of authority. It is based on the effective braking distance EBD and the distribution function F(D). The probability of the event EV(B) established with lineside signalling/warning systems is used to compute the term relative to the movement N. The distribution function F(EBD) is then broken down according to the respective traffic proportions of passenger trains as well as freight trains with braking position G and braking position P. where i = passenger train, freight train with braking position G or freight train with braking position P, v 0 = 40 km/h. 6 Sample result The calculations involved the safety constraint by using a braking model and the exponential distribution for the distance signal-danger point. The numerical results obtained for the Ceiling Speed in shunting/staff responsible mode as a function of the Release Speed for the two train families Type (A) (unfavourable braking performance) and Type (B) ( favourable braking performance) are shown in graphical form in Figure 3 for the two SH&SR values considered. The curve obtained for a given population of trains is a boundary separating the domain (ceiling speed, release speed) into two regions: the lower region, for which the tolerable hazard rate safety target is met, and the upper region, for which the target is not met. When braking performance improves, the boundary representing the safety constraint moves to-
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