Pedestrian Risk Index (PRI)

Description

The PRI estimates the conflict probability and severity for pedestrian crossing scenarios by combining the TTZ with the impact speed [Cafiso2011]. It is defined for a scenario with a vehicle \(A_1\) and a VRU \(P\) both approaching a conflict area \(\mathit{CA}\). The scenario shall include a unique and coherent conflict period \([t_{c_\mathit{start}}, t_{c_\mathit{stop}}]\) where \(\forall\,t \in [t_{c_\mathit{start}}, t_{c_\mathit{stop}}]:\,\mathit{TTZ}(P, \mathit{CA}, t) < \mathit{TTZ}(A_1, \mathit{CA}, t) < t_s(A_1, t)\). Here, \(t_s(A_1, t)\) is the time \(A_1\) needs to come to a full stop at time \(t\), including its reaction time, leading to

\[\mathit{PRI}(A_1, \mathit{CA}) = \int_{t_\mathit{c_\mathit{start}}}^{t_{c_\mathit{stop}}}(s_{imp}(A_1, \mathit{CA}, t)^2 \cdot (t_s(A_1, t) - \mathit{TTZ}(A_1, \mathit{CA}, t))) \mathrm{dt},\]

where \(s_\mathit{imp}\) is the predicted speed at the time of contact with the pedestrian crossing. The PRI thus quantifies over two aspects of a whole scenario: the temporal difference is claimed to be a surrogate for the accident probability, whereas the impact speed is approximate for its severity. One possibility of estimating \(s_\mathit{imp}\) is defined by the authors as

\[s_\mathit{imp}(A_1, \mathit{CA}, t) = \sqrt{\|v_1(t)\|_2^2+2a_{1,\mathit{long,min}}(t) (d(p_1(t),p_\mathit{CA}(t)) - \|v_1(t)\|_2 t^r_1)} \text{,}\]

where \(t_i^r\) is the reaction time of actor \(A_i\). Note that depending on the DMM, other formulae for \(s_\mathit{imp}\) may be employed.

Properties

Run-time capability

Theoretically possible, but primary design goal is a-posteriori analysis

Target values

Faded markings: 1992, visible markings: 1623, visible markings, speed bump: 407, raised visible markings, speed bump: 161 [Cafiso2011]

Subject type

Pedestrian

Scenario type

Scenarios with a unique and coherent conflict period, where one vehicle and pedestrian both approach a pedestrian crossing

Inputs

\(a_\mathit{1,long,min}\), \(t_i^r\), for each \(t \in [t_{c_\mathit{start}}, t_{c_\mathit{stop}}]\): \(v_i(t)\), \(v_p(t)\), \(t_s(A_i,t)\), \(d(A_i, Z)\), \(d(P, Z)\)

Output scale

\((0,\infty)\), risk number (m²/s³), interval scale

Reliability

Depends on reliability of TTZ, but with the advantage of being robust against ‘jumps’ in TTZ due to integration over time

Validity

High if all assumptions hold, due to consideration of severity and probability, but dependent on validity of TTZ and \(v_\mathit{imp}\); no empirical analysis available

Sensitivity

High, as constant velocity model can be considered an adverse estimation of future development at pedestrian crossings

Specificity

Medium, as prediction model does not consider reactive behavior of participants on each other

Prediction model

Same as TTA