A review of ssm and their applications in connectedand automated vehicles safety modeling

标签：based review vehicles CAV al SSM applications safety TTC

ABSTRACT

Surrogate Safety Measures (SSM) are important for safety performance evaluation,since crashes are rare events and historical crash data does not capture near crashes that are also critical for improving safety. This paper focuses on SSM and their applications, particularly in Connected and Automated Vehicles (CAV) safety modeling. It aims to provide a comprehensive and systematic review of significant SSM studies, identify limitations and opportunities for future SSM and CAV research, and assist researchers and practitioners with choosing the most appropriate SSM for safety studies. The behaviors of CAV can be very different from those of Human-Driven Vehicles (HDV). Even among CAV with different automation/connectivity levels, their behaviors are likely to differ. Also, the behaviors of HDV can change in response to the existence of CAV in mixed autonomy traffic.Simulation by far is the most viable solution to model CAV safety. However, it is questionable whether con-ventional SSM can be applied to modeling CAV safety based on simulation results due to the lack of sophisticated simulation tools that can accurately model CAV behaviors and SSM that can take CAV’s powerful sensing and path prediction and planning capabilities into crash risk modeling, although some researchers suggested that proper simulation model calibration can be helpful to address these issues. A number of critical questions related to SSM for CAV safety research are also identified and discussed, including SSM for CAV trajectory optimization, SSM for individual vehicles and vehicle platoon, and CAV as a new data source for developing SSM.

替代安全措施（SSM）对于安全性能评估非常重要，因为碰撞是罕见事件，历史碰撞数据没有捕捉到对提高安全性同样关键的接近碰撞事件。本文关注SSM及智能网联汽车（CAV）安全建模中的应用。本文旨在提供对重要SSM研究的全面和系统性回顾，识别SSM和CAV研究的未来局限性和机会，并帮助研究人员和从业者选择最适合安全研究的SSM。CAV的行为可能与人类驾驶车辆（HDV）的行为非常不同。即使在具有不同自动化/连接水平的CAV之间，它们的行为也可能不同。因此，HDV的行为也可能因混合自动驾驶交通中CAV的存在而改变。到目前为止，仿真是模拟CAV安全最可行的解决方案。然而，由于缺乏能够准确模拟CAV行为的复杂仿真工具，以及能够将CAV强大的感知能力和路径预测和规划能力纳入碰撞风险建模的SSM，因此是否可以将传统的SSM应用于基于仿真结果的CAV安全建模存在疑问。尽管一些研究人员建议适当的仿真模型校准可能有助于解决这些问题。本文还确定并讨论了与CAV安全研究相关的一些关键问题，包括CAV轨迹优化的SSM、针对单个车辆和车队的SSM，以及将CAV作为开发SSM的新数据来源。

1.Introduction

Surrogate Safety Measures (SSM) are important for traffic safety evaluation, largely due to the lack of reliable statistical safety models in many cases. This is particularly true for transportation facilities with complex site characteristics and/or nontraditional traffic safety treat- ments, where limited or no historical crash data is available for devel- oping safety predictive models (Tarko et al., 2009). The research on SSM can date back to early 1970s (Hayward, 1971), and onsiderable achievements have been made in this field since then. Nowadays, SSM are increasingly being employed by researchers and practitioners to understand the safety implications of new traffic designs and various safety treatments using recorded videos and/or traffic simulation results.

代理安全措施（SSM）在交通安全评估中非常重要，这主要是因为在许多情况下缺乏可靠的统计安全模型。这对于具有复杂现场特征和/或非传统交通安全处理的交通设施尤其如此，这些地方有限或没有历史事故数据可用于开发安全预测模型（Tarko等人，2009年）。SSM的研究可以追溯到1970年代初（Hayward，1971年），自那时以来在这一领域取得了相当大的成就。如今，研究人员和从业者越来越多地采用SSM来通过记录的视频和/或交通模拟结果，理解新交通设计和各种安全处理的安全影响

An important application of SSM is modeling the safety impacts of Connected and Automated Vehicles (CAV) and their interactions with Human-Driven Vehicles (HDV). Research on CAV has attracted tremendous attention recently owing to their great potential to improve safety and traffic operations. However, the technology is not yet mature enough for large-scale CAV deployment in the real world. Therefore, CAV studies are mostly based on microscopic traffic simulations, and
SSM have been widely adopted for quantifying the safety benefits of CAV based on simulation results. Many SSM have been proposed. This provides plenty of options to researchers and practitioners, but also presents challenges in terms of how to choose from them. Given the
challenges and the abundant existing studies on SSM, now it is both an appropriate and important time to conduct a comprehensive and critical review of SSM, answering questions such as (1) what conventional SSM have been used in CAV safety studies; and (2) the pros and cons of these SSM. The answers will help researchers and practitioners choose the most appropriate SSM for various studies. Additionally, even though SSM have been popular for modeling new traffic safety designs and treatments and CAV, criticisms have been raised regarding their ability
to accurately and objectively characterize a transportation facility’s (e.g., intersection, road segment) safety performance. It is critical to review existing SSM, identify opportunities for improvements, and provide guidance for future research in this area.

代理安全指标（SSM）在智能网联汽车（CAV）的安全影响方面具有重要的应用价值，特别是在评估CAV与人类驾驶车辆（HDV）的互动方面。由于CAV在提高安全性和交通运营方面的潜力，它们最近吸引了巨大的研究兴趣。然而，这项技术尚未成熟到可以在现实世界中大规模部署的程度。因此，CAV研究大多基于微观交通模拟，SSM已被广泛采用，用于量化基于模拟结果的CAV的安全效益。已经提出了许多SSM，为研究人员和从业者提供了多种选择，但也带来了如何选择合适SSM的挑战。鉴于SSM的挑战和现有研究的丰富性，现在是进行全面和关键性SSM评估的合适时机。评估SSM时需要回答的关键问题包括：(1) 在CAV安全研究中使用了哪些传统的SSM；(2) 这些SSM的优缺点是什么。通过回答这些问题，研究人员和从业者可以选择最适合其研究的SSM。尽管SSM在模拟新的交通安全设计和CAV方面很受欢迎，但也有批评声音指出它们在准确和客观地描述交通设施（如交叉口、路段）的安全性能方面存在局限性。需要审查现有的SSM，识别改进的机会，并为未来的研究提供指导。

1.1. Scope and aim

SSM has attracted substantial attention recently and some of the previous studies focusing on vulnerable road user safety have been nicely summarized by Johnsson et al. (2018). This article provides a comprehensive and critical review of SSM and discusses their various applications, especially in CAV related safety studies. The objectives of this study are three folds:
1 Understand the state-of-the-art of SSM and their applications in CAV safety studies;
2 Discuss the current issues of SSM used in CAV safety studies; and
3 Identify promising future research directions of SSM and their applications in CAV safety.

1.1 范围与目标

SSM最近受到了大量关注，一些先前专注于易受伤害道路使用者安全的研究已经被Johnsson等人（2018年）很好地总结。本文提供了对SSM及其在CAV相关安全研究中各种应用的全面和批判性回顾。本研究的目标有三个方面：

理解SSM及其在CAV安全研究中的应用的最新进展；
讨论在CAV安全研究中使用的SSM的当前问题；
确定SSM及其在CAV安全应用中有前景的未来研究方向

1.2. Structure

This paper is structured as follows: Section 2 provides a comprehensive review of the literature related to SSM. Section 3 discusses the pros and cons of SSM-based safety studies and reviews how SSM have been used in CAV safety evaluation. In Section 4, research questions and issues related to SSM for CAV safety studies are discussed. Finally, Section 5 concludes this study, discusses the main issues and gaps in SSM research particularly in the context of CAV, and identifies opportunities for further research.

1.2 结构

本文的结构如下：第2节提供了与SSM相关的文献综述。第3节讨论了基于SSM的安全研究的优点和缺点，并回顾了SSM在CAV安全评估中的应用。第4节讨论了与CAV安全研究相关的研究问题和SSM问题。最后，第5节总结了本研究，讨论了SSM研究中的主要问题和空白，特别是在CAV的背景下，并确定了进一步研究的机会。

2. Surrogate safety measures (SSM)

Over the past few decades, substantial efforts have been made in developing Surrogate Safety Measures (SSM). In this section, we start with providing an overview of SSM and CAV. Then, we summarize and discuss various SSM proposed in previous research.

再过去的几十年里，人们在开发SSM付出了巨大的努力。在本章节中，我们先概述SSM和CAV。然后我们总结和讨论了解以往的研究中提出的各种SSM。

2.1. Overview of SSM and CAV

2.1.1. SSM

Crash frequency and severity are considered two important indicators that directly measure the safety performance of a design,countermeasure, or system. However, crashes are rare events. For new safety strategies (e.g., a new traffic sign), it will take time for their safety impacts to be revealed by real-world crash frequency and severity data. Therefore, relying on historical crash data to evaluate a safety strategy’s performance is not the best choice and to some extent is unethical. To address this issue, SSM derived from traffic conflicts have become an increasingly popular solution. Traffic conflicts are observable non-crash events, in which the interactions among multiple road users in space and time create a risk of collision if these users do not change their courses of movements (Amundsen and Hyden, 1977). A Conflict is considered to be etiologically connected to a crash, when a failure (e.g., human operator failure, road failure, and vehicle failure) that leads to the conflict cannot be properly corrected (Davis et al., 2011; Tarko, 2020). Due to the un- derlying causal relationship, measures used to identify traffic conflicts and quantify their severities could be considered as SSM. Compared to crashes, traffic conflicts are much more frequent.

事故频率和严重程度被视为直接衡量设计、对策或系统安全性能的两个重要指标。然而，事故是罕见事件。对于新的安全策略（例如新的交通标志），需要时间才能通过实际的事故频率和严重程度数据揭示其安全影响。因此，依赖历史事故数据来评估安全策略的表现并不是最佳选择，并且在某种程度上是不道德的。为解决这一问题，基于交通冲突导出的安全性能指标（SSM）成为越来越受欢迎的解决方案。交通冲突是可观察到的非事故事件，指多个道路使用者在空间和时间上的互动，如果这些使用者不改变其行动方向，则可能导致碰撞风险（Amundsen和Hyden，1977年）。当导致冲突的失效（例如人为操作失误、道路问题和车辆问题）无法得到适当纠正时，冲突被认为与事故有因果关系（Davis等人，2011年；Tarko，2020年）。由于这种潜在的因果关系，用于识别交通冲突并量化其严重程度的措施可以被视为SSM。与事故相比，交通冲突要频繁得多。

It is worth noting that many safety related measures have been developed over time. However, not all of them can be considered as SSM. According to Tarko et al. (2009), two qualifying criteria for SSM are: (1) it should be derived from traffic conflicts which are directly linked to crashes, and (2) the relationship between traffic conflicts and the related potential crash frequency and/or severity can be quantified by some practical methods. From this perspective, traffic exposure/flow measurements, such as Annual Average Daily Traffic (AADT), speed variation, and average operating speed are not SSM, although these measurements have been proven to be associated with crash risk and are sometimes adopted as crash “surrogates”. In this paper, only safety measures satisfying the above two qualifying criteria are reviewed and discussed.

值得注意的是，随着时间的推移，已经开发出许多与安全相关的措施。然而，并非所有措施都可以被视为安全性能指标（SSM）。根据Tarko等人（2009年）的说法，SSM的两个资格标准是：（1）它应当源自直接与事故相关联的交通冲突，以及（2）交通冲突与相关潜在事故频率和/或严重程度之间的关系可以通过某些实用方法来量化。从这个角度来看，交通曝露/流量测量，如年平均日交通量（AADT）、速度变化和平均运行速度并不属于SSM，尽管这些测量已被证明与事故风险相关，并有时被采纳作为事故的“替代指标”。在本文中，只有满足上述两个资格标准的安全措施才被审查和讨论。

2.1.2. CAV

Connected and Automated Vehicles (CAV) are interconnected and can perform driving functions with limited or completely without the assistance of human drivers. The level of automation ranges from Level 1 to Level 5, as shown in Table 1 (National Highway Traffic Safety Administration (NHTSA, 2016). At Levels 1 and 2, individual and combined assistant driving functions are automated, respectively. Level 3 allows a fully automated control under certain conditions. A full automation can be achieved at Levels 4 (only in certain circumstances) and 5. Currently, Level 2 automation technologies have been deployed in some automobiles and Level 3+ automation technologies are still under research and development. It can be expected that higher levels of automation will be achieved in the future.

联网和自动驾驶汽车（CAV）是互联的，并且可以在有限或完全不需要人类驾驶员协助的情况下执行驾驶功能。自动化水平从一级到五级，如表1所示（国家公路交通安全管理局（NHTSA），2016）。在一级和二级，分别实现了单个和组合的辅助驾驶功能自动化。三级在特定条件下允许完全自动化控制。完全自动化可以在四级（仅在特定情况下）和五级实现。目前，二级自动化技术已经在一些汽车中部署，而三级以上的自动化技术仍在研究和开发中。可以预期，未来将实现更高水平的自动化。

CAV can communicate with drivers, other vehicles on the road (vehicle-to-vehicle [V2V]), roadside infrastructure (vehicle-to-infra-structure [V2I]), and the “Cloud” [V2C]. Through information sharing, early motion planning and automated control, CAV are expected to significantly improve traffic safety and mobility.

The behaviors of CAV can be very dissimilar from those of Human-Driven Vehicles (HDV) and their impacts are not well understood so far, since there are not many CAVs on the road yet and the technologies are evolving each day. Additionally, CAV at various automation and communication levels can behave differently. Both factors bring much complexity and uncertainty to CAV safety studies.

Table 1
Levels of Vehicle Automation (National Highway Traffic Safety Administration
(NHTSA, 2016).

Levels of Automation	Who does what, when?
Level 0	The human driver does all the driving
Level 1	An advanced driver assistance system(ADAS) on the vehicle can sometimes assist the human driver with either steering or braking/accelerating, but not both simultaneously
Level 2	An advanced driver assistance system(ADAS) on the vehicle can sometimes assist the human driver with either steering or braking/accelerating, but not both simultaneously
Level3	An Automated Driving System (ADS) on the vehicle can itself perform all aspects of the driving task under some circumstances. In those circumstances, the human driver must be ready to take back control at any time when the ADS requires the human driver to do so. In all other circumstances, the human driver performs the driving task.
Level 4	An Automated Driving System (ADS) on the vehicle can itself perform all driving tasks and monitor the driving environment – essentially, do all the driving – in certain circumstances. The human need not pay attention in those circumstances.
Level 5	An Automated Driving System (ADS) on the vehicle can do all the driving in all circumstances. The human occupants are just passengers and need never be involved in driving.

2.2. SSM and SSM-based models

In this section, we focus on reviewing important SSM and SSM-based models without going into details regarding their applications, which are discussed in Section 3. SSM are measures to identify traffic conflicts, which are statistically connected to crashes. The calculation of SSM in general is sensitive to the pre-determined thresholds used for defining traffic conflicts. After traffic conflicts are identified, SSM-based models are utilized to quantify the severity of a conflict. Some SSM-based models estimate the probability for a crash to occur, instead of generating a binary outcome (i.e., crash vs. non-crash).

在这一部分，我们重点回顾重要的安全代理度量（SSM）及基于SSM的模型，而不详细讨论其应用，这将在第3节中讨论。SSM是用于识别交通冲突的度量，与交通事故有统计上的关联。一般来说，SSM的计算对定义交通冲突的预设阈值很敏感。在识别出交通冲突后，基于SSM的模型用于量化冲突的严重性。一些基于SSM的模型会估计发生碰撞的概率，而不是生成二元结果（即，碰撞或不碰撞）。

2.2.1. SSM

As shown in Fig. 1, there are three main sub-categories under SSM, which are time-based SSM, deceleration-based SSM, and energy-based SSM. These three sub-categories of SSM are described in detail below. As explained later in this section, some distance-based SSM have also been proposed. Since these distance-based SSM rely on deceleration assumptions as well, they are covered in the deceleration-based SSM (Section 2.2.1.2) and are not discussed separately.

如图1所示，SSM下有三个主要的子类别，分别是基于时间的SSM、基于减速的SSM和基于能量的SSM。这三个SSM的子类别将在下文详细描述。正如本节后文所解释的那样，也提出了一些基于距离的SSM。由于这些基于距离的SSM同样依赖于减速假设，它们被归类为基于减速的SSM（2.2.1.2节），因此不单独讨论。

2.2.1.1. Time-based SSM.

Time-based SSM measure the risk of an interaction in terms of its time proximity to a collision. The most common time-based SSM is Time-to-Collision (TTC), which was initially proposed by Hayward (Hayward, 1972) and defined as “the time that remains until a crash between two vehicles would have occurred if the crash course and speed difference are maintained.” An important assumption behind TTC is that both the speeds and directions of the involved vehicles are maintained. It is described mathematically as:

2.2.1.1. 基于时间的SSM。基于时间的SSM以与碰撞的时间接近程度来衡量交互的风险。最常见的基于时间的SSM是时间到碰撞（Time-to-Collision, TTC），最初由Hayward提出（Hayward, 1972），定义为“在保持碰撞方向和速度差的情况下，两辆车之间发生碰撞前剩余的时间”。TTC背后的一个重要假设是涉及车辆的速度和方向都保持不变。其数学描述如下：

$TTC_{i}=\frac{(X_{i-1}-X_{i}-L_{i})}{V_{i}t-V_{i-1}(t))}$ 公式（1）

Where,
X: vehicle position (i = following vehicle; i -1 = leading vehicle);
l: vehicle length; and
v: vehicle velocity.
Another popular time-based SSM is Time-to-Accident (TA) initially proposed by Perkins and Harris (1967). TA is calculated with estimated distance and speed when the evasive action is initially identified by a field observer. The major difference betweenTTC and TA is that TTC is measured at the beginning of the conflict occurrence, while TA is calculated based on the observed evasive action. Both indicators use certain thresholds to determine whether a conflict is at high risk or not.

另一个流行的基于时间的SSM是时间至事故（Time-to-Accident, TA），最初由Perkins和Harris（1967年）提出。TA根据现场观察员最初识别出的回避动作时的估计距离和速度来计算。TTC和TA之间的主要区别在于，TTC是在冲突发生之初进行测量，而TA是基于观察到的回避动作进行计算。这两个指标都使用特定的阈值来确定冲突是否存在高风险。

Based on TTC, a few more complicated SSM were developed.Minderhoud and Bovy (2001) proposed Time-Exposed TTC (TET) and Time-Integrated TTC (TIT). TET is the time during a conflict when the TTC is below a certain threshold value, and TIT is the area between the threshold level and the TTC curve when the curve drops below the threshold. Compared to TTC and TA, TET and TIT focus on measuring the risk associated with the duration of dangerous driving conditions.Both TET and TIT require a continuous calculation of TTC.

基于时间碰撞（Time-to-Collision, TTC）的概念，开发了一些更复杂的代理安全指标（Surrogate Safety Measures, SSM）。Minderhoud 和 Bovy 在2001年提出了时间暴露TTC（Time-Exposed TTC, TET）和时间积分TTC（Time-Integrated TTC, TIT）。TET 是指在冲突期间，TTC低于某个特定阈值的时间。而TIT 是指当TTC曲线降到阈值以下时，阈值水平与TTC曲线之间的面积。与TTC和TA（Time-to-Accident）相比，TET和TIT专注于测量与危险驾驶条件持续时间相关的风险。TET 和 TIT 都需要持续不断地计算TTC。

Where,
Δt: time step length;
TTC∗: TTC threshold value;
$TTC_{(it))}$ : the TTC for the $i_{th}$ vehicle at time t; n: the vehicle ID;
N: the total number of vehicles; and
δ: switching variable.

Fig. 1. SSM knowledge map.

Other SSM developed based on TTC include time headway (Vogel,2003), time to zebra (TTZ; Varhelyi,´ 1998), time-to-lane crossing (TTL),reciprocal of TTC (i.e., 1/TTC by Chin et al., 1992), ModifiedTime-to-collision (MTTC) (Ozbay et al., 2008), and T2. Time headway is the elapsed time between the front of the lead vehicle passing a point on the roadway and the front of the following vehicle passing the same point. TTZ indicates the TTC between a crossing pedestrian and a vehicle that is approaching the crosswalk. TTL is defined as the time duration available for a driver before any lane boundary crossing. MTTC predicts TTC of a car-following conflict by considering the accelerations of both the lead and following vehicles, instead of assuming constant velocity. T2 is the predicted arrival time of the second road user (e.g., vehicle,bicyclist), calculated while the first road user has not left the conflict point yet (Laureshyn et al., 2010). When both road users are on a collision course, T2 is equal to TTC.

除了基于TTC（Time-to-Collision）的其他代理安全指标（SSM）包括以下几类：

时间车头时距（Time Headway）：Vogel（2003）提出，指前车通过道路上某点到后车通过同一地点所经过的时间。
人行横道时间（Time to Zebra, TTZ）：Varhelyi（1998）定义，指行人穿越人行横道时与接近车辆的TTC。
车道变换时间（Time-to-Lane Crossing, TTL）：指驾驶员在进行车道变换前可利用的时间长度。
TTC的倒数（Reciprocal of TTC）：Chin等人（1992）提出，即1/TTC，用于评估安全风险。
改进的时间至碰撞（Modified Time-to-Collision, MTTC）：Ozbay等人（2008）提出，通过考虑前车和后车的加速度来预测跟车冲突的TTC，而不是假设恒定速度。
T2：Laureshyn等人（2010）提出，指第二个道路使用者（如车辆、自行车手）预计到达冲突点的时间，在第一个道路使用者尚未离开冲突点时计算。如果两个道路使用者都在碰撞路线上，T2等于TTC。

这些SSM都旨在提供对交通冲突中潜在碰撞风险的更深入理解，它们考虑了不同的交通场景和车辆动态，以评估和预测交通安全状况

Post-Encroachment Time (PET) is another important time-based SSM, which refers to the time lapse from the moment that the first vehicle departs a conflict point to the moment that the second vehicle approaches that point. PET was first proposed by Allen et al. (1978),which has no speed and direction assumptions and requires no assumption of the collision course like TTC.

后侵时间（Post-Encroachment Time, PET）是另一种重要的基于时间的代理安全指标（SSM），它指的是从第一辆车离开冲突点到第二辆车接近该点所经过的时间间隔。PET最初由Allen等人在1978年提出，这个指标的特点是它不依赖于速度和方向的假设，也不需要像时间至碰撞（TTC）那样假设可能发生碰撞的轨迹。

Where,
t2: arriving time at a conflict point of the 2nd vehicle; and
t1: time of the 1st vehicle departing the conflict point.

Based on the PET definition, additional safety indicators have been proposed. For example, gap time (GT) was proposed to measure the time difference between the entries into the conflict point of two vehicles. The time advantage (TAdv) can be considered as an extension of the PET concept as well (Laureshyn et al., 2010), which is the predicted PET value assuming that the two road users continue with their initial paths and speeds.

The above-mentioned time-based SSM are summarized in Table 2. In general, time-based SSM measure the time proximity to a crash occurrence. Certain thresholds are required for them to identify “crash”conditions or high-risk interactions.

基于后侵时间（Post-Encroachment Time, PET）的定义，已经提出了其他一些安全指标。例如，间隔时间（Gap Time, GT）被提出来衡量两辆车进入冲突点的时间差。时间优势（Time Advantage, TAdv）也可以视为PET概念的扩展（Laureshyn等人，2010年），这是在假设两个道路使用者继续按初始路径和速度行驶的情况下预测的PET值。

上述基于时间的代理安全指标（SSM）在表2中进行了总结。通常，基于时间的SSM测量接近发生碰撞的时间。它们需要特定的阈值来识别“碰撞”条件或高风险互动。

Table 2
Summary of major time-based SSM.

指标	定义	缺点	优点
Time to collision (TTC)	如果车辆继续以当前速度和方向行驶，将会发生碰撞的时间	1.恒速假设（不考虑规避动作） 2.需要一个阈值来确定交互严重性（阈值敏感）	1.经常使用 2.易于测量
Time to Accident (TA)	当其中一名道路使用者通过保持当前速度和方向开始规避动作时，碰撞的剩余时间。	1.依懒对躲避动作的观察； 2.阈值敏感；	1.易于测量
Time Exposed Time-to-Collision (TET)	驾驶员在接近前方车辆所有TTC小于阈值时刻的总和	1.不同风险间有不同值； 2.阈值敏感； 3.需要连续计算。	1.适用于微观模拟； 2.提供一段时间内的总风险。
Time Integrated Time-to-Collision (TIT)	在低于某个TTC阈值的时间内，TTC曲线的积分	1.难以解释其含义； 2.阈值敏感；	1.适用于微观模拟； 2.提供一段时间内的累计风险； 3.提供不同价值的风险变化；
Post-Encroachment Time (PET)	从第一辆车离开潜在冲突区域的时刻起到第二辆车进入同一区域的时刻止的时间间隔	1.适用于交叉/角度交互的情境； 2.不能反应交互动态的变化； 3.阈值敏感；	1.反应驾驶员的行为; 2.易于测量。
Headway (H)	领头车辆前方通过道路上的一个点与后车前方通过同一点之间的经过时间	1.与以下案例相关； 2.不考虑超车和变道引起的横向移动	易于测量
Gap time (GP)	两辆车进入冲突点的时间	适用于交叉/角度交互的情境；	易于测量
TAdv	道路使用者继续使用路径和速度则预测PET值	1.适用于交叉/角度交互的情境； 2.取决于恒定速度和方向的假设； 3.阈值敏感	可以作为风险指标进行持续测量。
Modified Time -to-collision (MTTC)	修改后的模型考虑了由于加速而导致的所有潜在纵向冲突情况	1.难以连续收集车辆瞬时加速度数据； 2.不适合变道或者减速差异	1.比驾驶员更先进； 2.考虑驾驶差异。

2.2.1.2. Deceleration-based SSM.

Instead of measuring time proximity,deceleration-based SSM focus on how vehicles’ deceleration can prevent crash occurrence. As early as in 1976, Cooper and Ferguson (1976) proposed DRAC (Deceleration Rate to Avoid the Crash) to determine the severity of an interaction. DRAC is the minimum braking rate required for a vehicle to avoid collision with another vehicle. The calculation of DRAC (see Eq. (7) below) is based on the assumption that one vehicle takes evasive actions while the other retains its speed and direction. To determine the risk of collision, some thresholds are also needed for DRAC.

2.2.1.2. 基于减速的代理安全指标（Deceleration-based SSM）。与测量时间接近性不同，基于减速的SSM专注于车辆的减速如何能够防止碰撞发生。早在1976年，Cooper和Ferguson提出了避免碰撞的减速度（Deceleration Rate to Avoid the Crash, DRAC）来确定交互的严重程度。DRAC是避免与另一辆车相撞所需的最小制动率。DRAC的计算（见下文的公式（7））基于这样一个假设：一辆车采取避让行动，而另一辆车保持其速度和方向。为了确定碰撞风险，DRAC也需要一些阈值。

Where,
t: time interval;
P: position of a vehicle (i = the following vehicle, i ? 1 = the lead
vehicle);
L: vehicle length; and
V: velocity.

Cunto (2008) further extended DRAC and developed a Crash Potential Index (CPI) by considering a vehicle’s braking capability or maximum deceleration rate (MADR). CPI represents the probability that DRAC exceeds the maximum deceleration rate (MADR) at a moment. MADR depends on vehicle type and environment conditions such as pavement skid resistance. CPI can be calculated as:

Cunto 在2008年进一步扩展了 DRAC（Deceleration Rate to Avoid Crash，避免碰撞的减速度），并通过考虑车辆的制动能力或最大减速度（MADR）开发了一个碰撞潜力指数（Crash Potential Index, CPI）。CPI 表示在某一时刻 DRAC 超过最大减速度（MADR）的概率。MADR 取决于车辆类型和环境条件，如路面的摩擦系数。CPI 的计算公式如下：

Where,
MADR is the maximum braking rate;
Δt is time step length;
Ti is the total travel time; and
ti and tfi are the initial and final time steps, respectively.

Some studies differentiated distance-based SSM from deceleration based SSM. In essence, distance-based SSM can also be considered as deceleration-based SSM, since they are both based on assumptions of MADR. The rear-end collision risk index (RCRI) was proposed to identify dangerous conditions by comparing the stopping distance of the lead and following vehicles (Oh et al., 2006), assuming the lead vehicle takes an emergency stopping maneuver with the maximum deceleration rate (i.e., MADR). RCRI can be written as:

一些研究将基于距离的代理安全指标（SSM）与基于减速度的SSM区分开来。本质上，基于距离的SSM也可以被视为基于减速度的SSM，因为它们都基于最大减速度（MADR）的假设。尾部碰撞风险指数（Rear-end Collision Risk Index, RCRI）被提出用于通过比较领头车辆和跟随车辆的停车距离来识别危险情况（Oh等人，2006年），假设领头车辆以最大减速度（即MADR）进行紧急停车操作。RCRI可以写成以下形式：

Where SSDL and SSDF are the stopping distances of the lead and following vehicles, respectively, vF and vl are the speeds of the flowing and lead vehicles, respectively; td is the time delay; S is the clearance distance; and dm is the maximum deceleration rate.

SSDL和SSDF是前后车制动距离，VF和 Vl是前车和自车的车速；Td时间延迟；S值安全距离；dm是最大减速度。
Based on RCRI, the time exposed rear-end crash risk index (TERCRI) was proposed to measure the aggregated risk over time (Rahman and Aty, 2018):

基于尾部碰撞风险指数（Rear-end Collision Risk Index, RCRI），时间暴露的尾部碰撞风险指数（Time Exposed Rear-end Crash Risk Index, TERCRI）被提出来衡量随时间累积的风险（Rahman 和 Aty，2018年）:

Where Δt is the time step length. Other distance-based SSM include:Potential Index for Collision with Urgent Deceleration (PICUD) (Unoet al., 2002), Proportion of Stopping Distance (PSD) (Astarita et al.,2012), Difference of Space distance and Stopping distance (DSS) (Okamura et al., 2011), Unsafe density (UD) (Barcelo et al., 2003). They all rely on the assumption of emergency deceleration rates. Among them,PIUCD is calculated as:

其中，Δt 是时间步长，N 是在特定时间间隔内考虑的车辆总数，RCRIn(t) 是在时间 t的第 n 辆车的 RCRI 值。TERCRI 通过累加在每个时间步长内所有车辆的 RCRI 值得到，从而提供了一段时间内尾部碰撞风险的总和。这个指标有助于评估在特定交通场景或交通流中，尾部碰撞风险随时间的累积效应。

Where,
vl and vf: velocity of lead and following vehicles, respectively
S0: distance between the lead and following vehicles;
Δt: the following drivers’ reaction time;
a: emergency deceleration rate to stop.
PSD measures the ratio between the remaining distance to the potential point of collision and the minimum acceptable stopping distance.
It is formulated as:

Where Di,t is the available distance between vehicles.
DSS was defined by the difference of the space and stopping distance,
which can be derived by:

Where μ is the friction coefficient; g is the gravity acceleration; and d2 is the distance between the two vehicles.
UD was developed to consider the severity of a potential rear-endcrash if the leading vehicle decelerates with maximum braking capacity.

Where b is the deceleration rate of the lead vehicle, bmax is the maximum possible deceleration rate of the lead vehicle, and vl and vf are the speeds of the lead and following vehicles, respectively. Other notable deceleration-based SSM include Deceleration Rate (Malkhamah et al., 2005) and Deceleration-to-Safety Time (Topp, 1998) (Table 3).

Table 3
Summary of Major deceleration-based SSM.

Indicator	Definition	Limitations	Advantages
Deceleration Rate to void the Crash (DRAC)	后车与前车车速差除以碰撞的时间	1.只应用在纵向跟车情况 2.需要特定的阈值来确定碰撞的严重性	容易测量
Rear-end collision risk index RCRI)	追尾风险指数	1.只应用在纵向跟车情况 2.依赖某个边界来确定碰撞的严重程度（即MADR阈值）	风险可以持续测量
Time exposed rear-end crash risk index (TERCRI)	追尾风险指数	1.只应用在纵向跟车情况	衡量一段时间内的总风险
Crash Potential Index (CPI)	在给定的时间间隔内，给定车辆DRAC超过其最大可用减速率（MADR）的概率	1.只应用在纵向跟车情况 2.需要持续观察 3.依懒某个边界来确定碰撞的严重程度（即MADR阈值）	1.适用于模拟； 2.提供随时间推移的风险； 3.提供不同CPI值的风险变化
Potential Index for Collision with Urgent Deceleration (PICUD)	当两车紧急制动完全停止时，两车之间的距离	1.主要适用于变道情况 2.阈值尚未满足 3.不考虑横向交互	适用于评估连续车辆的碰撞风险。
Proportion of Stopping Distance (PSD)	与潜在碰撞点的剩余距离与最小可接受停车距离之间的比率。	基于规避行为	1.能够评估单一冲突； 2.易于测量
Difference of Space distance and Stopping distance (DSS)	DSS由空间和停车距离的差异来定义。	提供不安全车辆数量的信息，但不能考虑危险程度和持续时间。	1.能够评估单一冲突； 2.易于测量
Unsafe Density (UD)	在确定的模拟步骤中，道路上连续两辆车之间的“不安全”等级	1.难以解读意思，主要是为了比较 2.仅用于纵车互动	建议微观模拟

2.2.1.3. Energy-based SSM.

Unlike time- and deceleration-based SSM which measure the crash proximity of a conflict, energy-based SSM instead were proposed to measure the severity of an interaction. Among them, DeltaV needs to be paid special attention to. It measures the change in velocity forced on road users because of a collision. It depends on the speed and the mass of each road user involved and the angle at which the road users approach each other (Shelby, 2011). Based on momentum conversation assumption (i.e., an inelastic crash), DeltaV can be calculated as:

2.2.1.3. 基于能量的代理安全指标（Energy-based SSM）

与基于时间和减速度的代理安全指标不同，后者衡量冲突的接近程度，而基于能量的SSM被提出来衡量交互的严重程度。其中，DeltaV特别值得关注。它衡量了由于碰撞而强加给道路使用者的速度变化。它取决于每个道路使用者的速度、质量以及他们相互接近的角度（Shelby, 2011）。基于动量守恒假设（即非弹性碰撞），DeltaV可以按以下方式计算：

Where v1 and v2are the pre-crash velocities for the two involved vehicles with potential collision course; and m1 and m2 are the masses of the two vehicles.

Based on DeltaV, some other energy-based SSM have been developed. Bagdadi (2013) proposed conflict severity (CS), which is an integrated indicator combining DeltaV, TA and an assumed maximum average deceleration. The TA and the maximum average deceleration are used to estimate the effectiveness of the evasive actions taken by the involved road users. Another indicator based on DeltaV is the extended DeltaV indicator proposed by Laureshyn et al. (2017a,b). It combines DeltaV with a time indicator and a deceleration constant to estimate the collision probability as well as the potential severity.

基于DeltaV，已经开发出了一些其他的基于能量的代理安全指标（SSM）。Bagdadi在2013年提出了冲突严重性（Conflict Severity, CS），这是一个综合指标，结合了DeltaV、时间至事故（Time to Accident, TA）和假设的最大平均减速度。TA和最大平均减速度被用来评估涉及道路使用者采取的避让行动的有效性。基于DeltaV的另一个指标是由Laureshyn等人在2017年提出的扩展DeltaV指标。它将DeltaV与时间指标和减速度常数结合起来，用以估计碰撞概率以及潜在的严重程度。

Two other notable energy-based SSM are crash index (CAI) (Ozbayet al., 2008) and conflict index (CFI) Alhajyaseen (2015). Instead of calculating DeltaV, they incorporate some other kinetic energy terms. More specifically, CAI estimates the kinetic energy involved in a car-following interaction based on acceleration, speed and MTTC:

另外两个值得注意的基于能量的代理安全指标（SSM）是碰撞指数（Crash Index, CAI）和冲突指数（Conflict Index, CFI），他们没有计算Deltav，而是加入了其他的动能项。更具体的说cai，CAI根据加速度、速度和MTTC来评估碰撞潜在的动能:

Where VL, Vf, aL, and af are the speeds and accelerations of the lead and following vehicles, respectively.

CFI combines PET with the speeds, masses and angles of the involved road users to estimate the released kinetic energy in a collision. It is designed to consider both crash robability and consequence (i.e.,severity).

CFI将PET与相关道路使用者的速度、质量和角度相结合，以估算碰撞中释放的动能。它的设计考虑了碰撞的可能性和后果（即严重程度）。

Where α represents the percentage of the released energy that will affect vehicle occupant(s), ΔKe is the change in total kinetic energy before and after the crash, and eβPET is used to weight conflicts depending on the probability of a crash to occur.

α（α）代表在碰撞中释放的能量中，将影响车辆乘员的百分比。这个系数用于估计碰撞能量中有多少比例可能对车内人员造成伤害。

ΔKe（ΔKe）表示碰撞前后车辆的总动能变化。动能的变化通常与碰撞的严重程度有关，可以用来评估碰撞的潜在破坏力。

eβPET）是一个用于权衡冲突的指数，它根据碰撞发生的概率来调整权重。这里的PET可能指的是“Post-Encroachment Time”（后侵时间），这是一种衡量在特定交通冲突发生后，车辆需要多长时间来避免碰撞的指标。

2.2.2. SSM-based models

SSM discussed in Section 2.2.1 use pre-determined thresholds to identify traffic conflicts (which are statistically connected to crashes) from interactions among road users. This approach is known to be subjective and threshold-sensitive. On the other hand, SSM-based models attempt to directly link each traffic conflict to either crash or non-crash, by estimating its crash risk/probability. To our best knowledge, there are two kinds of SSM-based models: uncertainty models and extreme value models.

The idea of uncertainty models was initially introduced by Davis et al. (2011). They showed that in addition to motion estimation, the variance in drivers and vehicles are also important factors that should be considered in predicting crashes. For the same interaction, different
combinations of people/vehicles could lead to distinct results. By considering this uncertainty in drivers and vehicles and measuring the general trend (e.g., average), the safety implication of an interaction can be more accurately modeled.

The general uncertainty modeling framework can be described as:

第2.2.1节中讨论的代理安全指标（SSM）使用预先确定的阈值来从道路使用者之间的交互中识别出与碰撞在统计上相关的交通冲突。这种方法被认为是主观的，并且对阈值敏感。另一方面，基于SSM的模型试图通过估计每次交通冲突的碰撞风险/概率，直接将其与碰撞或非碰撞联系起来。据我们所知，有两种基于SSM的模型：不确定性模型和极值模型。

不确定性模型的概念最初由Davis等人在2011年提出。他们表明，除了运动估计之外，驾驶员和车辆的变异性也是在预测碰撞时应该考虑的重要因素。对于相同的交互，不同的人/车辆组合可能导致不同的结果。通过考虑驾驶员和车辆的这种不确定性，并测量一般趋势（例如平均值），可以更准确地模拟交互的安全性含义。

一般的不确定性建模框架可以描述为：

Where Ai represents the ith necessary condition for crash avoidance (e.g.,braking rate, reaction time, steering rate). During an interaction, if all necessary conditions are satisfied, crash will be avoided. Otherwise,crash may occur with probability P(crash). When the probabilities of those necessary conditions are independent, the framework can be rewritten as:

Ai代表第 ith 个避免碰撞的必要条件（例如，制动率、反应时间、转向速率）。在一次交互过程中，如果所有这些必要条件都得到满足，碰撞将被避免。否则，如果这些条件中的任何一个或多个没有得到满足，碰撞可能会以概率 P(crash)P(crash) 发生。当这些必要条件的概率相互独立时，该框架可以被重写为：

这个公式表示，碰撞发生的概率是所有独立的必要条件满足的概率的补数的乘积。换句话说，如果每个条件 Ai 发生的概率是 P(Ai)，那么所有条件都满足的概率是∏i=1NP(Ai)∏i=1NP(Ai)。因此，至少有一个条件不满足（即发生碰撞）的概率就是 1 减去所有条件都满足的概率。这种框架有助于在考虑多个独立因素的情况下，评估碰撞发生的总体风险。

To calculate the probability of a necessary condition being satisfied,the distribution of the population needs to be identified. The probability can then be either calculated by integration (i.e., analytical way) or approximated through stochastic models (e.g., random sampling).

为了计算满足必要条件的概率，需要确定人群的分布。然后，可以通过积分（即分析方法）计算概率，或者通过随机模型（例如，随机抽样）进行近似。

Based on this general framework, several SSM-based models have been developed. Saunier and Sayed (2008) proposed a crash probability model based on motion prediction methods. Wang and Stamatiadis (2014a) introduced a Monte-Carlo stochastic process to quantify the crash probabilities of simulated conflicts, considering the variances in drivers’ reaction abilities and vehicles’ braking capabilities. The Monte-Carlo process can be applied to three main conflict types (crossing, rear-end and lane-changing), covering most real-world conflict cases (Wang and Stamatiadis, 2014b). Wang and Stamatiadis (2016) further conducted sensitivity analyses to explore how drivers’ reaction time distribution may affect SSM and whether there is room for improvement in crash predictions. Kuang et al. (2015) also proposed a tree-structured model for estimating rear-end crash probability based on the general uncertainty modeling framework.

基于这个通用框架，已经开发了几种基于SSM的模型。Saunier和Sayed（2008）基于运动预测方法提出了一个碰撞概率模型。Wang和Stamatiadis（2014a）引入了一个蒙特卡洛随机过程来量化模拟冲突的碰撞概率，考虑到了驾驶员反应能力和车辆制动能力的变化。蒙特卡洛过程可以应用于三种主要的冲突类型（交叉、追尾和变道），涵盖了大多数现实世界的冲突案例（Wang和Stamatiadis，2014b）。Wang和Stamatiadis（2016）进一步进行了敏感性分析，探讨驾驶员反应时间分布如何影响SSM以及碰撞预测是否有改进的空间。Kuang等人（2015）也基于一般不确定性建模框架提出了一个用于估计追尾碰撞概率的树状模型。

Recently, Extreme Value Theory (EVT) based models have also been used to estimate the crash probability of vehicle interactions, which relies on the assumption of extreme value distributions. There are two approaches for applying EVT: block maxima and peak over (Songchitruksa and Tarko, 2006). For the block maxima approach, observations are aggregated into fixed blocks over time and the maximum of each block is considered as an extreme. Those extremes follow the generalized extreme value distribution shown below:

最近，基于极值理论（Extreme Value Theory, EVT）的模型也已被用于估计车辆交互的碰撞概率，该模型依赖于极值分布的假设。应用EVT有两种方法：块最大值和峰值超过（Songchitruksa和Tarko，2006）。对于块最大值方法，观察结果被聚合成时间上的固定块，每个块的最大值被视为一个极端值。这些极端值遵循以下所示的广义极值分布：

Where μ is the location parameter, σ is the scale parameter, and ε is the shape parameter.
For the peak over approach, a threshold u is determined and the threshold exceedance is calculated as y = x - u. y follows the generalized Pareto distribution as:

Songchitruska and Tarko (2006) applied the block maxima approach EVT to evaluate signalized intersection safety, by assuming that the observed PET (i.e., variable x) follows the generalized extreme value distribution in Eq. (25). The crash probability (CR in Eq. (27) below) for each observation can be estimated when PET is equal to or less than 0 s(i.e., a crash):

Songchitruska 和 Tarko（2006）应用了块最大值法（EVT）来评估信号交叉口的安全性，他们假设观察到的后车车头时距（PET，即变量x）遵循方程（25）中的广义极值分布。当PET等于或小于0秒时（即发生碰撞），可以估计每个观测值的碰撞概率（即方程（27）中的CR）：

Where CR is the risk of crash, Z is the negated PET, F is the generalized extreme value distribution or the generalized Pareto distribution depending on which EVT approach is used. By assuming that the traffic conflict observation period t is representative for a long period T, the estimated crashes Nt can be calculated as:

在这里，CR 表示碰撞风险，Z 是指代后侵时间（Post-Encroachment Time, PET）的否定值，FF 是广义极值分布或广义帕累托分布，具体使用哪种分布取决于采用的极值理论（Extreme Value Theory, EVT）方法。通过假设交通冲突的观察期 tt 对于一个较长时期 TT 是有代表性的，可以计算估计的碰撞次数 NtNt，公式如下：

Songchitruska and Tarko (2006) reported a high level of consistency between estimated and actual crashes. Since then, a number of univariate EVT safety studies has been conducted considering SSM such as PET (Zheng et al., 2014a,b; Wang et al., 2018) and TTC (Åsljung et al., 2017;Farah and Azevedo, 2017; Tarko, 2018; Orsini et al., 2019, 2020). In particular, Åsljung et al. (2017) analyzed 250,000 km driving data using the EVT framework, and concluded that EVT was a promising tool for CAV safety evaluation. Zheng et al. (2018) and Wang et al. (2019a,b) further extended the univariate EVT framework to bivariate and used it to evaluate the safety of freeway entrances and signalized intersections, respectively. Zheng et al. (2018) modeled the combination of PET and the length proportion of merging, and reported promising results. Wang et al. (2019a,b) modeled the combinations of four SSM: TTC, TA, PET and maximum eceleration. According to their results, the combination of TA and PET appeared to be the best. Since then, bivariate EVT models have been applied in several other safety studies, in which various SSM combinations were examined, including TTC and PET (Zheng and Sayed,2019), TTC/PET and DRAC (Zheng et al., 2019a), and TTC and distance headway (Cavadas et al., 2020). The uncertainty and extreme value SSM models are summarized in the table below (Table 4).

Songchitruska 和 Tarko（2006）报告了估计碰撞和实际碰撞之间高度的一致性。从那时起，已经进行了一系列考虑SSM（如PET（郑等人，2014a，b；王等人，2018）和TTC（Åsljung等人，2017；Farah和Azevedo，2017；Tarko，2018；Orsini等人，2019，2020））的单变量EVT（极值理论）安全研究。特别是，Åsljung 等人（2017）使用EVT框架分析了25万公里的驾驶数据，并得出结论，EVT是评估CAV（连接和自动化车辆）安全性的有希望的工具。郑等人（2018）和王等人（2019a，b）进一步将单变量EVT框架扩展到双变量，并分别用于评估高速公路入口和信号交叉口的安全性。郑等人（2018）模拟了PET与合并长度比例的组合，并报告了有希望的结果。王等人（2019a，b）模拟了四种SSM的组合：TTC、TA、PET和最大加速度。根据他们的结果，TA和PET的组合似乎是最佳选择。从那时起，双变量EVT模型已经被应用于其他几个安全研究中，在这些研究中检查了各种SSM组合，包括TTC和PET（郑和Sayed，2019）、TTC/PET和DRAC（郑等人，2019a）以及TTC和距离车头时距（Cavadas等人，2020）。不确定性和极值SSM模型在下表（表4）中进行了总结。

Table 4
Summary of energy-based SSM.

3.SSM for CAV safety studies

This section focuses on reviewing safety studies using SSM and simulation, and how SSM have been utilized for CAV safety evaluation. We start with analyzing the limitations of field bservation-based SSM,followed by discussion on the widely adopted approach of using simulation-based SSM for safety studies. We then summarize how simulation-based SSM have been utilized in evaluating CAV safety (Table 5).

这一节集中回顾了使用代理安全指标（SSM）和仿真进行的安全研究，以及SSM如何被用于自动驾驶车辆（CAV）的安全评估。我们首先分析了基于现场观察的SSM的局限性，随后讨论了广泛采用的基于模拟的SSM进行安全研究的方法。然后我们总结了模拟基础的SSM是如何在评估CAV安全中被利用的（见表5）。

3.1. Field observation-based SSM

SSM were initially developed based on field safety studies (i.e., conflict studies). Field observations are often time-consuming and labor intensive. Moreover, human observation errors could be introduced and affect the reliability of field-based safety studies. To address these issues,computer vision and various sensor techniques (Ismail et al., 2010;Autey et al., 2012; Laureshyn et al., 2017a,b; Wu et al., 2018; Fu et al.,2016; Machiani and Abbs, 2016; Chen et al., 2017) have been introduced to continuously detect and track vehicle motions, without much human intervention. Ismail et al. (2010) conducted a conflict-basedbefore-after (BA) studies on the safety impact of a scramble phase treatment, by an automated video technique. Four SSM were used: TTC,PET, DST, and GT. Based on the similar approach, Autey et al. (2012) evaluated the safety implication of right-turn smart channels. Laureshynet al. (2017a,b) applied three approaches to derive pedestrian SSM using intersection videos. The three approaches were the Swedish traffic conflict technique (Swedish TCT), the Dutch conflict technique (DOC-TOR) and the Canadian probabilistic surrogate measures of safety (PSMS) technique. TCT and DOCTOR manually count critical traffic conflicts based on time-based SSM (e.g., TTC, PET), while PSMS considers probabilities of vehicle trajectories to estimate potential crashes. PSMS relies on video processing techniques to automatically track road users. Overall, the three methods generate similar results. However, the PSMS method needs to be further improved in deriving cyclists related SSM due to inaccurate trajectories extracted. To improve SSM extraction in low light and adverse weather conditions, Wu et al. (2018) developed a LiDAR-based approach to obtain trajectories of all road users at intersections. They focused on vehicle-pedestrian near-crash identification and proposed two SSM: Time Difference to the Point of Intersection (TDPI) and Distance between Stop Position and Pedestrian (DSPP). Fuet al. (2016) used videos from a thermal camera to derive SSM for pedestrians at unsignalized crosswalks and found it to work well under low visibility conditions. SSM and safety indicators considered include vehicle approaching speed, post-encroachment time (PET), yielding compliances, conflict rates, and pedestrian exposure. Machiani and Abbas (2016) developed a TTC-based histogram to evaluate the safety of dilemma zone based on radar data. Chen et al. (2017) utilized drone collected videos at an intersection and derived Post-encroachment Time (PET) and Relative Time to Collision (RTTC) to analyze vehicle-pedestrian collision risk.

SSM最初是基于现场安全研究（即冲突研究）开发的。现场观察通常耗时且劳动密集。此外，人为观察错误可能会被引入，影响基于现场的安全研究的可靠性。为了解决这些问题，引入了计算机视觉和各种传感器技术（例如Ismail等人，2010年；Autey等人，2012年；Laureshyn等人，2017a,b；Wu等人，2018年；Fu等人，2016年；Machiani和Abbs，2016年；Chen等人，2017年），以连续检测和追踪车辆运动，而无需太多人工干预。Ismail等人（2010年）通过自动化视频技术进行了基于冲突的前后（BA）研究，以评估混乱阶段治疗的安全性影响。使用了四种SSM：TTC、PET、DST和GT。基于类似的方法，Autey等人（2012年）评估了智能右转通道的安全含义。Laureshyn等人（2017a,b）应用了三种方法使用交叉口视频导出行人SSM。这三种方法分别是瑞典交通冲突技术（Swedish TCT）、荷兰冲突技术（DOC-TOR）和加拿大概率代理安全度量（PSMS）技术。TCT和DOC-TOR手动基于基于时间的SSM（例如TTC、PET）计数关键交通冲突，而PSMS考虑车辆轨迹的概率来估计潜在的碰撞。PSMS依赖于视频处理技术来自动跟踪道路使用者。总的来说，这三种方法产生了类似的结果。然而，由于提取的轨迹不准确，PSMS方法在导出与自行车相关的SSM方面需要进一步改进。为了在低光照和恶劣天气条件下改善SSM的提取，Wu等人（2018年）开发了一种基于LiDAR的方法来获取交叉口所有道路使用者的轨迹。他们专注于车辆-行人接近碰撞的识别，并提出了两个SSM：到达交叉口的时间差（TDPI）和停车位置与行人之间的距离（DSPP）。Fu等人（2016年）使用热成像摄像机视频导出未信号化人行横道上行人的SSM，并发现其在低能见度条件下表现良好。考虑的SSM和安全指标包括车辆接近速度、后侵入时间（PET）、让路合规性、冲突率和行人暴露。Machiani和Abbas（2016年）开发了一个基于TTC的直方图，根据雷达数据评估困境区的安全。Chen等人（2017年）利用无人机收集的交叉口视频导出后侵入时间（PET）和相对碰撞时间（RTTC），以分析车辆-行人碰撞风险。

Leveraging the computer vision and sensor technologies, human labor requirements can be significantly reduced and data accuracy can be improved for field-based safety studies. However, those techniques are relatively complicated and require well-trained safety analysts to apply. Moreover, observation errors can still happen under certain conditions, such as occlusion by large vehicles, adverse weather and poor visibility, and poor lighting conditions. Recent advancements in deep learning have substantially improved the accuracy of computer vision-based object detection and tracking. Some commercial software products have already been developed for video-based safety evaluation. Although a detailed analysis and comparison of these deep learning-based computer vision algorithms/products is out of the scope of this paper, such algorithms/products demonstrate great potential to address the aforementioned concerns about computer vision and sensor technologies, making field observation-based safety evaluation much more viable and SSM more important than before. Compared to SSM generated based on traffic simulations (see Section 3.2 below), SSM from field observations are more realistic. As the penetration rate of CAV increases, field observation can be an important approach to derive SSM for evaluating CAV safety.

利用计算机视觉和传感器技术，可以显著减少现场安全研究中的人力需求，并提高数据的准确性。然而，这些技术相对复杂，需要受过良好训练的安全分析师来应用。此外，在某些条件下，如大型车辆遮挡、恶劣天气和能见度差以及照明条件不佳时，观察错误仍然可能发生。深度学习的最新进展已经大幅提高了基于计算机视觉的对象检测和追踪的准确性。一些商业软件产品已经被开发用于基于视频的安全评估。尽管对这些基于深度学习的计算机视觉算法/产品的详细分析和比较不在本文讨论范围内，但这些算法/产品显示出巨大的潜力，可以解决前述关于计算机视觉和传感器技术的担忧，使得基于现场观察的安全评估更加可行，代理安全指标（SSM）也比以往更加重要。与基于交通模拟生成的SSM（见下文3.2节）相比，来自现场观察的SSM更加现实。随着CAV（连接和自动化车辆）的普及率提高，现场观察可以成为推导评估CAV安全的重要方法。

3.2. Simulation-based safety studies using SSM

Simulation tools have been extensively utilized in traffic analysis.Initially, traffic simulation was mainly for operational evaluations.Compared to field-based studies, simulation tools are able to build traffic scenarios quicker and easier and allow for comparison of different strategies under the same traffic input. Due to the advantages offered by simulation, many researchers also attempted to conduct safety evaluations using SSM based on traffic simulations.

模拟工具已广泛应用于交通分析中。最初，交通模拟主要用于运行评估。与基于现场的研究相比，模拟工具能够更快更容易地构建交通场景，并允许在相同的交通输入下比较不同策略。由于模拟所提供的优势，许多研究人员也尝试使用基于交通模拟的代理安全指标（SSM）进行安全评估。

Despite the advantages, there are doubts about simulation-based safety evaluations. Some researchers (Tarko, 2018) criticized that simulation tools are unable to replicate extreme and dangerous vehicle interactions/traffic conditions, since driver behavior models in simulation tools are developed to represent normal driving habits instead of distracted and aberrant behaviors. In this sense, they claimed that simulation-based SSM only reflect traffic exposure instead of true safety impacts. Another issue with simulation-based SSM is that simulated vehicles follow certain preprogrammed paths. For example, vehicles in VISSIM follow links and connectors. If the connectors for two opposing left-turns at an intersection are coded without any overlap, the chance for those left-turn vehicles to have head-on crashes does not exist. In reality, left-turn vehicles may not always follow lane marking and can make wide/narrow turns. Such uncertainty in vehicle turning radius is not adequately considered in existing simulation tools and can generate biased SSM results.

尽管模拟工具具有诸多优势，但关于基于模拟的安全评估也存在一些疑问。一些研究者（例如Tarko, 2018）批评说，模拟工具无法复制极端和危险的车辆互动或交通条件，因为模拟工具中的驾驶员行为模型是为了代表正常的驾驶习惯，而不是分心或异常行为。从这个意义上说，他们声称基于模拟的SSM只反映了交通暴露情况，而非真正的安全影响。另一个与基于模拟的SSM有关的问题在于，模拟车辆遵循某些预设的路径。例如，在VISSIM中，车辆遵循链接和连接器。如果一个交叉口处两个相对左转的连接器在编码时没有重叠，那么这些左转车辆发生正面碰撞的可能性就不存在。然而在现实中，左转车辆可能不会总是遵循车道标记，可能会进行宽转弯或窄转弯。这种车辆转弯半径的不确定性在现有的模拟工具中没有得到充分的考虑，可能会产生有偏见的SSM结果。

On the other hand, others believed that the theoretical foundation for simulation-based safety studies is valid. Although some extreme cases may not be captured by simulations, a large number of vehicle interactions can still be observed by a well-calibrated simulation model. Studies have shown that by properly calibrating simulation models, the distribution of simulated SSM can be highly consistent with that of field observed SSM (Gettman and Head, 2003; Huang et al., 2013; Ozbay et al., 2008; Zheng et al., 2019b), supporting that SSM based on traffic simulation results are reliable and valid. For instance, Zheng et al. (2019b) applied EVT models on simulated conflicts and reported promising results. Another interesting way of evaluating safety based on simulation is to directly simulate driver errors and identify the resulting crash consequence (Astarita and Giofr´e, 2019). Such a method also requires proper model alibrations.

另一方面，其他研究者认为基于模拟的安全研究的理论基础是有效的。尽管一些极端情况可能无法通过模拟捕捉到，但通过一个校准良好的模拟模型，仍然可以观察到大量的车辆互动。研究表明，通过适当校准模拟模型，模拟得到的SSM的分布可以与现场观察到的SSM高度一致（Gettman和Head, 2003; Huang等人, 2013; Ozbay等人, 2008; Zheng等人, 2019b），这支持了基于交通模拟结果的SSM是可靠和有效的。例如，Zheng等人(2019b)在模拟冲突上应用了极值理论(EVT)模型，并报告了有希望的结果。另一种基于模拟的评估安全的方法是直接模拟驾驶员错误，并确定由此产生的碰撞后果（Astarita和Giofré, 2019）。这种方法同样需要适当的模型校准。

3.3. Simulation and SSM for evaluating CAV safety

Since CAV have not been deployed at large scales in the real world, it is difficult to collect field data to explore CAV’s safety implications. Currently, microscopic traffic simulation has been the main tool for CAV safety studies. CAV can eliminate driver errors (e.g., distracted driving) but are still affected by potential mechanical and communication errors,software bugs, and sensor malfunctions. Such errors, compared to mistakes made by human drivers, are relatively easier to model by traffic simulations. In this sense, simulating 100 % CAV could produce more reliable outputs than Human-Driven Vehicles (HDV). However, when dealing with a mixed environment with both CAV and HDV, careful simulation model calibration is important for generating reliable safety results.

由于连接和自动化车辆（CAV）尚未在现实世界中大规模部署，因此很难收集现场数据来探索CAV的安全影响。目前，微观交通模拟已成为CAV安全研究的主要工具。CAV可以消除驾驶员错误（例如分心驾驶），但仍然可能受到潜在的机械和通信错误、软件故障和传感器故障的影响。与人类驾驶员所犯的错误相比，这些错误相对容易被交通模拟所建模。从这个意义上说，模拟100%的CAV可能比模拟人类驾驶的车辆（HDV）产生更可靠的输出。然而，在处理包含CAV和HDV的混合环境时，仔细校准模拟模型对于生成可靠的安全结果至关重要。这是因为CAV和HDV的交互作用可能会引入新的复杂性，需要通过模拟模型准确地反映这些交互作用及其对交通安全的潜在影响。因此，研究人员需要确保模拟模型能够合理地表示CAV的技术特性和行为模式，以及它们与人类驾驶车辆在同一交通流中的互动。

When applying microscopic traffic simulation tools for CAV safety modeling, specialized software packages such as VISSIM, Paramics,SUMO are often utilized to generate detailed vehicle trajectories. Either the Surrogate Safety Assessment Model (SSAM) or other custom developed tools are then used to analyze trajectories and compute SSM (FHWA, 2003, 2008). Other than specialized traffic simulation packages, general-purpose simulation tools (e.g., Matlab) have also been adopted for safety analysis, in which the traffic environment and scenarios are much simplified compared to those in specialized microscopic simulation packages. The current literatures on simulation-based safety modeling and SSM applications can be categorized into two groups, (1) safety effects evaluation; and (2) trajectory optimization, as summarized in Tables 6 and 7 respectively.

在应用微观交通模拟工具进行CAV（连接和自动化车辆）安全建模时，通常会使用VISSIM、Paramics、SUMO等专业软件包来生成详细的车辆轨迹。然后，会使用代理安全评估模型（SSAM）或其他定制开发的工具来分析这些轨迹并计算代理安全指标（SSM），这一方法在FHWA（美国联邦公路管理局）2003年和2008年的报告中有详细描述。除了这些专业的交通模拟软件包，通用的模拟工具（例如Matlab）也被用于安全分析。与专业的微观模拟软件包相比，这些通用工具在模拟交通环境和场景时通常会采用更简化的模型。目前，基于模拟的安全建模和SSM应用的文献可以归纳为两大类：(1) 安全效应评估；(2) 轨迹优化，如表6和表7分别总结的那样。在安全效应评估中，研究者们利用SSM来评估不同交通设计或操作策略对交通安全的影响。而在轨迹优化中，SSM被用作评估和指导车辆轨迹优化的依据，以提高交通流的安全性和效率。这些研究有助于理解CAV在不同交通环境中的表现，并为CA

V的集成和交通管理系统的设计提供支持。

As for safety effects evaluation, mainly time-based and deceleration based SSM have been used, and the most popular SSM is TTC (Rahman et al., 2018, 2019a,b; Tibljaˇs et al., 2018; Li et al., 2018; Virdi et al.,2019; Morando et al., 2018; Papadoulis et al., 2019). For instance,Morando et al. (2018) found that increasing automated vehicles penetration rate could significantly improve traffic safety at both signalized intersections and roundabouts. Other than TTC, TIT and TET have also been frequently used (Li et al., 2017a,b,c, ; Rahman and Aty, 2018; Rahman et al., 2019a,b). Additionally, TA has been adopted (Wu et al., 2019). Applications of deceleration-based SSM include the distributions of hard braking (Zhong et al., 2019), RCRI (Li et al., 2018; Rahman and Aty, 2018; Rahman et al., 2019a,b), sideswipe crash risk (i.e., the number of lane-changing conflicts) (Rahman and Aty, 2018), and TER-CRI (Rahman and Aty, 2018). Other safety indicators have also been applied for CAV safety effects evaluation, such as standard deviation of speed (Rahman and Aty, 2018; Fu et al., 2019) and Maximum speed (MaxS) (Tibljaˇs et al., 018). Note that in most literature, CAV and HDV were evaluated based on the same SSM (e.g., TTC = 1.5 s or 2 s), and no separate SSM for CAV were found in those studies.

在安全效应评估方面，主要使用了基于时间的和基于减速度的代理安全指标（SSM），其中最受欢迎的SSM是时间至碰撞（TTC）。例如，Morando等人（2018年）发现，提高自动化车辆的渗透率可以在信号交叉口和环形交叉口中显著提高交通安全性。除了TTC之外，时间积分时间至碰撞（TIT）和时间暴露时间至碰撞（TET）也经常被使用（Li等人，2017a,b,c；Rahman和Aty，2018；Rahman等人，2019a,b）。此外，还采用了时间至事故（TA）（Wu等人，2019）。基于减速度的SSM的应用包括紧急制动的分布（Zhong等人，2019）、后端碰撞风险指数（RCRI）（Li等人，2018；Rahman和Aty，2018；Rahman等人，2019a,b）、侧面碰撞风险（即车道变换冲突的数量）（Rahman和Aty，2018）以及时间暴露后端碰撞风险指数（TER-CRI）（Rahman和Aty，2018）。其他安全指标，如速度的标准差（Rahman和Aty，2018；Fu等人，2019）和最大速度（MaxS）（Tibljaš等人，2018）也被应用于CAV的安全效应评估。需要注意的是，在大多数文献中，CAV和HDV都是基于相同的SSM进行评估的，例如，将TTC设定为1.5秒或2秒，而在这些研究中并没有为CAV找到单独的SSM。这表明在进行安全评估时，研究者通常采用统一的标准来衡量CAV和HDV的安全风险，而不是为CAV设计特定的指标。随着CAV技术的发展，未来可能会开发出专门针对CAV的SSM，以更准确地评估它们的安全性能。

In trajectory optimization studies, CAV maneuver decisions (e.g.,merging, crossing) and/or trajectories are planned ahead of time and are optimized considering safety constraints onsisting of SSM. For maneuver decisions, distance and time gap constraints are often adopted to optimize merging and crossing maneuver safety and to ensure enough safety space between vehicles (Lee and Park, 2012; Xu et al., 2018, 2019, 2020; Dong et al., 2020; Jing et al., 2019; Ren et al., 2020). For trajectory planning, minimum safety headway/gap and TTC constraints have been used to ensure longitudinal safety (Zhao et al., 2017; Duan and Zhao, 2017; Huang et al., 2018; Yao and Friedrich, 2019; Ren et al., 2020). In some studies, SSM have also been used in the CAV longitudinal trajectory optimization objectives (not just as constraints). The adopted SSM and safety indicators include minimum safety time gap/headway (Alonso and P´erez-Oria, 2010; Fernandes and Nunes, 2015; Milanes and Shladover, 2016; Xu et al., 2018; Zhou et al., 2020; Qu et al., 2020),minimum deceleration (Cherian and Sathiyan, 2012), platoon string stability (Roncoli et al., 2015; Flores and Milan´es, 2018; Wang, 2018,Wang, 2019; Huang et al., 2019), TET and TIT (Jeong et al., 2017;Rahman and Aty, 2018; Liu et al., 2020), and inverse TTC (Jeong et al.,2017; Qu et al., 2020). Among these studies, string stability was often used as the control objective for CAV platoons with ACC/CACC functions. Although string stability strictly speaking is not considered as SSM, previous literature has proved that better string stability could bring important safety benefits.

在轨迹优化研究中，针对CAV（连接和自动化车辆）的操作策略（例如并道、横穿）和/或轨迹是提前规划并优化的，同时考虑了包含SSM（代理安全指标）的安全约束。对于操作策略，通常采用距离和时间间隔约束来优化并道和横穿操作的安全性，并确保车辆之间有足够的安全空间（Lee和Park，2012年；Xu等人，2018年、2019年、2020年；Dong等人，2020年；Jing等人，2019年；Ren等人，2020年）。在轨迹规划中，使用最小安全车头时距/间隙和TTC（时间至碰撞）约束来确保纵向安全（Zhao等人，2017年；Duan和Zhao，2017年；Huang等人，2018年；Yao和Friedrich，2019年；Ren等人，2020年）。在一些研究中，SSM也被用作CAV纵向轨迹优化目标的一部分（不仅仅是作为约束）。采用的SSM和安全指标包括最小安全时间间隙/车头时距（Alonso和Perez-Oria，2010年；Fernandes和Nunes，2015年；Milanes和Shladover，2016年；Xu等人，2018年；Zhou等人，2020年；Qu等人，2020年），最小减速度（Cherian和Sathiyan，2012年），车队串联稳定性（Roncoli等人，2015年；Flores和Milanes，2018年；Wang，2018年、2019年；Huang等人，2019年），TET（时间暴露时间至碰撞）（Jeong等人，2017年；Rahman和Aty，2018年；Liu等人，2020年）和TIT（积分时间至碰撞），以及逆TTC（Jeong等人，2017年；Qu等人，2020年）。在这些研究中，串联稳定性经常用作具有ACC（自适应巡航控制）/CACC（协同自适应巡航控制）功能的CAV车队的控制目标。尽管严格来说串联稳定性并不被视为SSM，但以前的文献已经证明，更好的串联稳定性可以带来重要的安全益处。

4. Discussion

4.1. Developing simulation models for CAV

Microscopic traffic simulation models were introduced initially for modeling vehicle movements following normal traffic rules. The traffic flow models behind various simulation tools are designed to generate typical traffic interactions that frequently occur. However, the essence of SSM lies in a model’s ability to also produce infrequent and risky interactions. Some researchers (Gettman and Head, 2003; Huang et al.,2013; Ozbay et al., 2008) argued that simulation tools are able to generate valid data for computing SSM through proper model calibration. The calibration process will make simulated road users more (or less) aggressive, and generate simulated interactions that are overall consistent with field observations. Thus, a proper simulation calibration procedure is vital for simulation-based safety studies. Additionally,some human factors (e.g., distraction, non-compliance of traffic rules) are not well defined in many simulation tools. With better knowledge of driver behaviors that contribute to crashes and near crashes, these human factors could be properly modeled and incorporated into simulation tools, which will make simulation-based safety outputs more realistic and reliable after careful calibration.

微观交通模拟模型最初是为了模拟遵循正常交通规则的车辆运动而引入的。各种模拟工具背后的交通流模型旨在生成频繁发生的典型交通互动。然而，SSM（代理安全指标）的本质在于模型也能够产生不常见且具有风险性的互动。一些研究者（Gettman和Head, 2003; Huang等人, 2013; Ozbay等人, 2008）认为，通过适当的模型校准，模拟工具能够生成用于计算SSM的有效数据。校准过程将使模拟的道路使用者变得更具（或不那么）攻击性，并生成总体上与现场观察一致的模拟互动。因此，适当的模拟校准程序对于基于模拟的安全研究至关重要。此外，许多人为因素（例如，分心、不遵守交通规则）在许多模拟工具中并没有很好地定义。随着对导致碰撞和接近碰撞的驾驶员行为更好的了解，这些人文因素可以被适当地建模并纳入模拟工具中，这将使基于模拟的安全输出在经过仔细校准后更加真实和可靠。这意味着，随着对驾驶员行为和交通环境的深入理解，我们可以不断提升模拟工具的能力，使其更好地反映实际交通情况，从而为交通安全研究和评估提供更加准确的数据和分析。

Regarding CAV related safety research, simulation by far is the most viable choice for many researchers without access to CAV. For fully automated vehicles without human in the loop, theoretically the behaviors and mechanism of CAV can be well captured by simulation,since there is no need to consider human factors such as reaction time and distracted driving. However, research is still needed to calibrate simulation models for modeling mixed autonomy traffic to accurately reflect CAV behaviors and human driver reactions to CAV. In this case,traditional and virtual reality (Xie et al., 2018) driving simulators could play an important role by bringing human drivers into the loop and model how CAV and human drivers interact with each other in a simulated environment. Another option is to use data from pilot connected vehicles deployment projects and automated vehicles field tests,which is detailed later in Section 4.7.

在涉及CAV（连接和自动化车辆）的安全研究方面，对于那些无法直接接触到CAV的研究人员来说，模拟迄今为止是最可行的选择。对于完全自动化的车辆，理论上讲，由于不需要考虑如反应时间和分心驾驶等人为因素，CAV的行为和机制可以很好地通过模拟来捕捉。然而，为了准确地反映CAV的行为以及人类驾驶员对CAV的反应，仍然需要对模拟模型进行校准，以模拟混合自主性的交通。在这种情况下，传统和虚拟现实（例如Xie等人，2018年）驾驶模拟器可以通过将人类驾驶员纳入循环，并在模拟环境中模拟CAV与人类驾驶员之间的互动，从而发挥重要作用。另一个选择是使用来自试点连接车辆部署项目和自动化车辆现场测试的数据，这在第4.7节中有更详细的说明。这种方法不仅可以帮助研究人员更好地理解CAV在各种交通场景中的表现，还可以评估不同交通管理和控制策略对CAV集成交通流的影响。通过这些模拟和校准过程，研究人员可以为CAV的安全部署和操作提供有力的支持，并为未来交通系统的规划和发展做出贡献。

As for simulation tools, general-purpose simulation software (e.g., Matlab) has been often used for safety optimization while specialized traffic simulation software packages (e.g., VISSIM) have been mainly used for safety impacts evaluation. Safety studies based on specialized traffic simulation tools require considerable efforts for model development and calibration, while they could generate more detailed and accurate results than general-purpose simulation tools, and are more suitable for safety impacts evaluation. On the other hand, general purpose simulation tools are computationally less demanding and can be well integrated with complex optimization algorithms to identify promising safety strategies for further detailed analyses using specialized simulation models. However, simulations using general-purpose tools often make simplified assumptions and may ignore important aspects of vehicle/traffic characteristics and vehicle interactions. There fore, the choice of simulation tools is essentially a trade-off between accuracy and efficiency. It is also an interesting research topic that deserves further investigation so that guidelines can be developed for selecting the most appropriate modeling tools and/or for developing new tools for simulation-based CAV safety studies. For example, a hybrid simulation tool might be developed that considers simplified traffic models for roadway segments (focusing on rear-end and side-swipe crash risk) while more detailed models for intersections, ramps,and driveways.

在模拟工具方面，通用模拟软件（例如Matlab）通常用于安全优化，而专门的交通模拟软件包（例如VISSIM）主要用于安全影响评估。基于专业交通模拟工具的安全研究需要在模型开发和校准上投入大量精力，但它们能够生成比通用模拟工具更详细和准确的结果，更适合进行安全影响评估。另一方面，通用模拟工具在计算上要求较低，可以很好地与复杂的优化算法集成，以识别有前景的安全策略，以便使用专业模拟模型进行更详细的分析。然而，使用通用工具进行的模拟通常做出简化的假设，可能忽略车辆/交通特性和车辆交互的重要方面。因此，选择模拟工具本质上是在准确性和效率之间的权衡。这也是一个值得进一步研究的有趣研究课题，以便为选择最合适的建模工具和/或为基于模拟的CAV安全研究开发新工具制定指导方针。例如，可以开发一种混合模拟工具，该工具考虑了路段的简化交通模型（专注于追尾和侧面碰撞风险），同时为交叉口、匝道和车道等提供了更详细的模型。这种混合工具的开发可能需要结合不同工具的优势，以实现在特定应用中的最优性能。例如，在交通流相对简单、车辆交互较少的路段，可以使用简化模型快速评估策略；而在交通复杂性高、安全风险大的区域，如交叉口，可以使用更详细的模型来捕捉交通行为的细微差别。通过这种方式，可以在保证模拟结果准确性的同时，提高模拟的效率和实用性。

4.2. The validity/transferability of SSM

A critical issue regarding SSM is its validity. In previous literature, substantial efforts have been devoted to validating SSM. However, those studies were performed considering traditional traffic environments with only Human Driven Vehicles (HDV). When modeling safety in mixed autonomy traffic or fully automated traffic, it is unclear whether the SSM validated in traditional traffic environments can still be applicable. On one hand, the behaviors of CAV can be very different from those of HDV. Even among CAV with different automation/connectivity levels, their behaviors are likely to differ. On the other hand, the behaviors of HDV can change in response to the existence of CAV. Given the new situation, conventional SSM or SSM-based models, may need to revise accordingly. For instance, the thresholds used in SSM may need to be adjusted. Specifically, can TTC = 1.5 s still be a good choice for both HDV and CAV? Another valid question is that for SSM-based models, are those underlying models transferable to the new traffic environment? For example, does extreme value distribution calibrated in traditional traffic environment still hold for a 100 % CAV environment or mixed autonomy traffic?

关于代理安全指标（SSM）的一个关键问题是其有效性。在以往的文献中，大量工作都致力于验证SSM的有效性。然而，这些研究是在只考虑人类驾驶车辆（HDV）的传统交通环境中进行的。在模拟混合自主性交通或完全自动化交通的安全性时，尚不清楚在传统交通环境中验证的SSM是否仍然适用。一方面，CAV（连接和自动化车辆）的行为可能与HDV有很大不同。即使在不同自动化/连接级别的CAV之间，它们的行为也可能不同。另一方面，HDV的行为可能会因CAV的存在而改变。鉴于这种新情况，传统的SSM或基于SSM的模型可能需要相应地进行修订。例如，SSM中使用的阈值可能需要调整。具体来说，TTC（时间至碰撞）= 1.5秒是否仍然是HDV和CAV的好选择？另一个有效的问题是基于SSM的模型，那些在传统交通环境中校准的基础模型是否适用于新的交通环境？例如，在传统交通环境中校准的极值分布是否仍然适用于100% CAV环境或混合自主性交通？这些问题指向了随着交通环境的变化，特别是随着CAV的引入和集成，可能需要对现有的SSM进行重新评估和调整。这可能包括重新考虑用于评估安全风险的阈值，以及确保用于模拟和预测碰撞风险的统计模型和分布能够反映CAV特有的行为模式和交互方式。因此，未来的研究需要关注SSM在新的交通环境下的适用性和有效性，以及可能需要的新模型或现有模型的调整。

Based on our review, few research (e.g., Weng et al., 2020) so far has attempted to address this issue. Most existing CAV safety studies assume that conventional SSM are still valid and transferable to CAV environment. For future simulation-based CAV safety studies, the validity of SSM needs to be carefully examined and compared with field data when available. In addition, the transferability of SSM deserves attention. It is important to understand whether an SSM can provide reliable results across various traffic environments (e.g., all human vs. mixed autonomy traffic), infrastructure types, traffic compositions, weather conditions,etc.

根据我们的回顾，很少有研究（例如，Weng等人，2020年）尝试解决这个问题。大多数现有的CAV（连接和自动化车辆）安全研究假设传统的SSM（代理安全指标）仍然有效，并且可以转移到CAV环境中。对于未来的基于模拟的CAV安全研究，需要仔细检查SSM的有效性，并在可能的情况下与现场数据进行比较。此外，SSM的可转移性也值得关注。了解一个SSM是否能够在各种交通环境（例如，全人类驾驶与混合自主性交通）、基础设施类型、交通组成、天气条件等中提供可靠的结果是很重要的。

4.3. SSM and SSM-based models

Traditionally, SSM depend on certain thresholds to identify risky interactions linked to crashes. Generally, they are easier to calculate compared to SSM-based models, but have obvious shortcomings. For example, safety studies typically set TTC threshold to 1.5 s to identify risky interactions. This implies that all interactions with TTC values greater (or less) than 1.5 s are considered equally dangerous (i.e.,resulting in the same crash severity level), if TTC is the only SSM considered. TTC does not account for any potential evasive actions that are likely being taken during the course of an interaction. Also, in reality, drivers have varied reaction times and vehicles have different braking performance. Consequently, interactions with the same TTC can be associated with quite different levels of crash risk and severity out comes depending on driver and vehicle characteristics, type of interaction, evasive actions, etc. Even for the same interaction type, different vehicle speeds with the same TTC can pose various levels of difficulty for drivers to avoid the crash as well as lead to diverse levels of crash severity. Although some TTC variations (e.g., TIT) could estimate the severity of an interaction, a TTC threshold is still required as a precondition. Similarly, the downside of DRAC (or its variations) is that traffic interactions are divided into groups based on a set of threshold values (Cunto, 2008). Those thresholds are important but often require additional evaluations to find their optimal values. For future studies,the thresholds for SSM need to be examined very carefully.

传统上，SSM依赖于某些阈值来识别与碰撞相关的风险互动。与基于SSM的模型相比，它们通常更容易计算，但也存在明显的缺点。例如，安全研究通常将TTC（时间至碰撞）阈值设定为1.5秒来识别风险互动。这意味着所有TTC值大于（或小于）1.5秒的互动都被认为具有同等的危险性（即，导致相同的碰撞严重程度），如果只考虑TTC这一个SSM的话。TTC没有考虑到在互动过程中可能采取的任何潜在避让行动。此外，在现实中，驾驶员有不同的反应时间，车辆的制动性能也各不相同。因此，即使TTC相同，根据不同的驾驶员和车辆特性、互动类型、避让行动等，互动可能与不同程度的碰撞风险和严重程度相关联。即使是相同类型的互动，不同车速但TTC相同的情况也可能给驾驶员避免碰撞带来不同程度的困难，也可能导致不同程度的碰撞严重性。尽管一些TTC的变化（例如TIT，时间积分时间至碰撞）可以估计互动的严重程度，但仍然需要TTC阈值作为前提条件。同样，DRAC（减速率以避免碰撞，或其变化形式）的缺点在于，交通互动是基于一系列阈值将互动分组的（Cunto, 2008）。这些阈值很重要，但通常需要额外的评估来找到它们的最佳值。对于未来的研究，SSM的阈值需要非常仔细地检查。

SSM-based models can directly estimate an interaction’s crash risk or probability without explicitly setting thresholds, which is an important advantage over conventional SSM. However, bias could still be introduced by SSM-based models. The reviewed SSM-based models may not be able to capture all potential crash risk impacts of an interaction due to either their inherent statistical nature or external factors that are not included. For example, a univariate EVT only captures certain crash risk aspects of an interaction since it measures just one indicator. More specifically, an EVT SSM based on TTC may only be able to measure the risk in terms of time proximity, while other risk aspects (e.g., speed, mass, deceleration, etc.) are not reflected. Therefore, it is worthwhile to explore more advanced solutions such as bivariate EVT models (Wanget al., 2019a,b). Even if this EVT SSM is very comprehensive and can cover all risk aspects, its EVT distribution is still an approximation of the underlying true pattern. The parameters of the fitted EVT distribution could be biased due to partial/inaccurate observations and limited sample size. All these factors may lead to biases in EVT model estimation and inaccurate SSM-based models, thus should be handled with care.

SSM-based可以直接估计交互的碰撞风险或概率，而无需明确设定阈值，这是传统SSM的重要优势之一。然而，SSM-based模型仍然可能存在偏差。由于它们的统计本质或未包含的外部因素，评审的SSM-based模型可能无法捕捉交互的所有潜在碰撞风险影响。例如，单变量的极值理论（EVT）只能捕捉交互的某些碰撞风险方面，因为它只测量一个指标。具体来说，基于TTC的EVT SSM可能只能以时间接近度量风险，而其他风险方面（如速度、质量、减速等）则没有反映出来。因此，值得探索更先进的解决方案，如双变量的EVT模型（Wanget al.，2019a，b）。即使这种EVT SSM非常全面并且能够涵盖所有风险方面，其EVT分布仍然是对潜在真实模式的一种近似。由于部分/不准确的观察和有限的样本大小，拟合的EVT分布的参数可能存在偏差。所有这些因素可能导致EVT模型估计的偏差和不准确的SSM-based模型，因此应该谨慎处理。

4.4. Specific SSM for CAV

It can be expected that the mixed autonomy traffic environment will emerge sooner than a 100 % CAV environment. The behaviors of Human-Driven Vehicles (HDV) are different from those of CAV, and can also be affected by CAV. Compared to HDV, CAV have much shorter reaction time (approaching zero depending on CAV system design) and are able to share precise and complex information (e.g., vehicle maneuvers) in real time with each other and with infrastructure. Thus, even if conventional SSM are still applicable for evaluating CAV safety, it is questionable whether they are accurate enough. Therefore, dedicated SSM need to be developed for CAV at different automation/connectivity levels, based on field data or driving simulator results.

可以预期，混合自动驾驶交通环境将比100%的自动驾驶车辆（CAV）环境更早出现。人驾驶车辆（HDV）的行为与CAV的行为不同，而且CAV的行为也会影响HDV。与HDV相比，CAV具有更短的反应时间（根据CAV系统设计逼近零）并且能够实时与其他车辆和基础设施共享精确和复杂的信息（例如车辆操作）。因此，即使传统的状态空间模型（SSM）在评估CAV安全性方面仍然适用，它们是否足够准确仍然是个问题。因此，需要针对不同自动化/连接水平的CAV开发专门的SSM，这些SSM可以基于现场数据或驾驶模拟器的结果。

For example, vehicle platooning is a promising and viable solution for improving mobility and safety. A well-known vehicle platooning technique is Cooperative Adaptive Cruise Control (CACC), which is enabled by vehicle connectivity and Level 1 automation. In mixed autonomy traffic, a vehicle platoon could include both HDV and CAV at different connectivity and automation levels. As such, the longitudinal safety of each vehicle could differ, depending on its ability of sensing the surrounding and reacting to potential risk. Many CACC studies are focused on examining string stability, which can also be considered as a safety performance indicator for the whole platoon. However, the underlying relationship between string stability and individual vehicle’s safety is not explicitly understood and needs to be further explored.

例如，车辆编队是改善移动性和安全性的一种有前景且可行的解决方案。一个众所周知的车辆编队技术是协同自适应巡航控制（CACC），它依赖于车辆之间的连接和一级自动化。在混合自动驾驶交通中，一个车辆编队可以包括不同连接和自动化水平的HDV和CAV。因此，每辆车的纵向安全性可能不同，这取决于它感知周围环境和对潜在风险做出反应的能力。许多CACC研究集中于检验串联稳定性，这也可以被视为整个编队的安全性能指标。然而，串联稳定性与个体车辆安全之间的潜在关系并没有被明确理解，需要进一步探讨。

In addition, SSM for specific traffic scenarios may also need to be investigated, such as lateral safety related to lane-changing and merging maneuvers. Measuring lateral safety is important for both HDV and CAV, especially in mixed autonomy traffic. For example, when modeling cooperative lane changing/merging scenarios with CAV (Ren et al.,2020, 2021), a small headway may not necessarily lead to collision if all vehicles involved are fully connected and aware of each other’s next move. Based on the literature review, research on SSM for lateral risk caused by lane changing and merging maneuvers is very limited (Vogel, 2003; Wang and Stamatiadis, 2013; Kanagaraj et al., 2015).

此外，还需要研究特定交通场景的（SSM），例如与变道和合流操作相关的横向安全性。测量横向安全对于HDV和CAV都很重要，特别是在混合自动驾驶交通中。例如，在建模带有CAV的合作变道/合流场景时（Ren等，2020，2021），如果所有涉及的车辆都完全连接并且知晓彼此的下一步动作，即使车距很小，也不一定会导致碰撞。根据文献综述，对于由变道和合流操作引起的横向风险的状态空间模型研究非常有限（Vogel，2003；Wang和Stamatiadis，2013；Kanagaraj等，2015）。

4.5. Universal SSM

Since CAV and HDV may coexist for an extended period and given the above issues, it is interesting to research whether a universal set of SSM can satisfy the needs of simulation-based CAV safety studies under mixed traffic environment. In this environment, CAV differ from HDV in terms of behaviors and capabilities. Moreover, CAV can have various automation levels. Even at the same automation level, CAV manufactured by different companies are likely to demonstrate quite different behaviors. Additionally, users may be able to set the driving behavior of a CAV to aggressive mode, cooperative mode, etc. If different SSM are adopted for different road users (e.g., CAV, HDV), it could be difficult for decision making due to two main reasons: (1) How to combine different SSM into an aggregate value for plan/design comparison; and (2) How to weight different SSM. In this case, a universal set of SSM would be helpful to assist decision makers with identifying plans of maximum safety benefits during transportation planning, infrastructure design,traffic control and management, etc.

由于CAV和HDV可能在相当长的时间内共存，并考虑到上述问题，研究一个通用的状态空间模型（SSM）集是否能满足混合交通环境下基于仿真的CAV安全研究的需求是很有趣的。在这种环境下，CAV在行为和能力上与HDV有所不同。此外，CAV可以具有不同的自动化水平。即使在相同的自动化水平下，不同公司制造的CAV可能展示出截然不同的行为。此外，用户可能能够将CAV的驾驶行为设置为攻击性模式、合作模式等。如果为不同的道路使用者（例如CAV、HDV）采用不同的SSM，决策可能会面临两个主要问题：（1）如何将不同的SSM组合成一个整体值以进行计划/设计比较；（2）如何对不同的SSM进行加权。在这种情况下，一个通用的SSM集将有助于帮助决策者在交通规划、基础设施设计、交通控制和管理等方面确定最大安全效益的计划。

4.6. SSM for safety-oriented CAV trajectory optimization

CAV can plan their trajectories (e.g., lane changing and car following) ahead of time. When planning such trajectories, safety is always an important consideration. SSM-based models are suitable for such a purpose, since they can be modified to continuously monitor and predict a CAV’s crash risk status by considering uncertain aspects such as sensor malfunctions, cyber-attack, communication latencies, signal transmission range limitations, data packet loss, vehicle dynamics, and traffic flow disturbance and other dangerous events (e.g., pedestrian jaywalk).

自动驾驶车辆（CAV）可以提前规划它们的轨迹（例如变道和跟车）。在规划这些轨迹时，安全性始终是一个重要考虑因素。SSM-based models的模型非常适合这样的目的，因为它们可以通过考虑不确定因素（如传感器故障、网络攻击、通信延迟、信号传输范围限制、数据包丢失、车辆动态和交通流干扰等）来连续监测和预测CAV的碰撞风险状态，以及其他危险事件（例如行人横穿马路）。

For the constraints used in trajectory optimization, most literature adopted a simple static safety distance boundary (Zhao et al., 2017;Duan and Zhao, 2017; Yao and Friedrich, 2019; Ren et al., 2020). In other words, a minimum distance has to be maintained at each time step to ensure safety. To improve the safety and robustness of CAV trajectory control, the static safety distance boundary may be made time- and environment-dependent, taking factors such as vehicle speed into consideration. In addition, lateral positions planning can be incorporated into longitudinal trajectory optimization, which is particularly important for lane-changing and merging maneuvers. For instance, SSM related to lateral crash risk can be included in either the objective function or some constraints.

对于轨迹优化中使用的约束条件，大多数文献采用了简单的静态安全距离边界（Zhao等，2017；Duan和Zhao，2017；Yao和Friedrich，2019；Ren等，2020）。换句话说，必须在每个时间步保持最小距离以确保安全。为了提高CAV轨迹控制的安全性和鲁棒性，可以使静态安全距离边界变为时间和环境相关，并考虑车辆速度等因素。此外，横向位置规划可以整合到纵向轨迹优化中，这对于变道和合流操作尤其重要。例如，与横向碰撞风险相关的SSM可以包含在目标函数或某些约束中。

4.7. New data sources for developing SSM

Besides field observation using various sensors (see Section 3.1), it is anticipated that some new data sources such as connected vehicles and even automated vehicles will play an important role in developing SSM.For instance, He et al. (2018) used the data from the Safety Pilot Model Deployment (SPMD) (Gay and Kniss, 2015) to develop SSM. The SPMD study was conducted in Ann Arbor and included about 3000 participating vehicles and 30 roadside equipment (RSE) installed mostly at signalized intersections. Those vehicles broadcast Basic Safety Messages (BSMs) containing vehicle speed, location, etc. at 10 Hz. Based on the SPMD data, they calculated MTTC, TTC, and DRAC and correlated them with historical crash records. Also based on the SPMD data, Xie et al.(2019) proposed a new SSM called Time to Collision with Disturbance (TTCD). Compared to conventional TTC, TTCD can better consider the risk in cases when the following vehicle is slower than but very close to the leading vehicle. Under such circumstances, a small speed disturbance may lead to a crash. Guo et al. (2010) considered near-crash events derived from the SHRP2 Naturalistic Driving Study (NDS) data (Blatt et al., 2015) as a crash surrogate, which is defined as “Any circumstance that requires a rapid, evasive maneuver by the participant vehicle, or any other vehicle, pedestrian, cyclist, or animal, to avoid a crash.” (Guo et al., 2010). Ishak et al. (2017) also looked at the NDS data and tried to relate a driver’s odd of being involved in distracted driving behaviors to five measures: GPS speed, lateral and longitudinal acceleration, throttle position, and yaw rate. Although they were unable to find statistically significant relationships, the results from a neural network model suggest that the five measures are useful in identifying distracted driving.

除了使用各种传感器进行现场观察（见第3.1节），预计一些新的数据来源，如连接车辆甚至自动化车辆，将在SSM的开发中发挥重要作用。例如，He等人（2018年）利用了安娜堡的安全试点模型部署（SPMD）（Gay和Kniss，2015年）的数据来开发SSM。SPMD研究在安娜堡进行，包括约3000辆参与车辆和30个道路边设备（RSE），主要安装在信号控制的交叉口。这些车辆以10赫兹的频率广播基本安全消息（BSMs），包含车速、位置等信息。基于SPMD数据，他们计算了MTTC、TTC和DRAC，并将它们与历史碰撞记录进行了相关性分析。另外，基于SPMD数据，Xie等人（2019年）提出了一种称为带扰动时间至碰撞（TTCD）的新型SSM。与传统的TTC相比，TTCD在以下情况下可以更好地考虑风险：后继车辆速度低于但非常接近前车时。在这种情况下，小的速度扰动可能导致碰撞。Guo等人（2010年）考虑了从SHRP2自然驾驶研究（NDS）数据（Blatt等，2015年）中衍生出的近碰事件作为碰撞替代物，其定义为“参与车辆或任何其他车辆、行人、骑车者或动物需要快速规避动作以避免碰撞的任何情况”（Guo等，2010年）。Ishak等人（2017年）也查看了NDS数据，并尝试将驾驶员分心驾驶行为与五个指标相关联：GPS速度、横向和纵向加速度、油门位置和横摆率。尽管他们未能找到统计上显著的关系，神经网络模型的结果表明这五个指标在识别分心驾驶中是有用的。

Stipancic et al. (2018) used driver smartphone GPS data to derive SSM. Since GPS data only contains information for the subject vehicle, hard braking and accelerating events are used to define SSM and are compared to historical crash data. Similarly, Strauss et al. (2017a,b) used cyclist hard braking events extracted from GPS data to analyze bicycle safety. Boonsiripant (2009) used vehicle speed profile derived from GPS data and developed over ten safety indicators, including speed variation, mean of speed band, acceleration noise, stop frequency per trip per mile, etc. For SSM and safety indicators derived based on GPS or speed profile data, properly specifying the thresholds for hard braking and accelerating events is important, and may benefit from taking the corresponding traffic environment (e.g., freeways vs. local roads) into consideration. Following this direction, SSM may also be derived from Waze, INRIX, and smartphone accelerometer data.

Stipancic等人（2018年）使用驾驶员智能手机GPS数据推导出SSM。由于GPS数据仅包含主体车辆的信息，他们利用急刹车和加速事件定义了SSM，并将其与历史碰撞数据进行了比较。类似地，Strauss等人（2017a，b）利用从GPS数据中提取的骑行者急刹车事件分析了自行车安全性。Boonsiripant（2009年）利用从GPS数据中导出的车辆速度轨迹，并开发了十多个安全指标，包括速度变化、速度段均值、加速噪声、每英里每次行程停止频率等。对基于GPS或速度轨迹数据推导出的SSM和安全指标，恰当地指定急刹车和加速事件的阈值非常重要，并可能受到相应交通环境（例如高速公路与市区道路）的影响。在这个方向上，SSM也可以从Waze、INRIX和智能手机加速计数据中推导出来。

As can be seen, recently there has been a considerable amount of interest in using observed data for deriving SSM. Compared to simulated data, observed data better capture the randomness in traveler behaviors and generate more realistic risk measures. These datasets can be broadly classified into three categories:

正如您所看到的，最近对使用观察数据推导SSM表现出了相当大的兴趣。与模拟数据相比，观察数据更能捕捉旅行者行为的随机性，并生成更现实的风险评估。这些数据集可以广泛分类为三类：

Video/Lidar/radar data: These datasets are typically collected from roadside sensors or drones at fixed locations, and analyzed automatically by computer programs. They can capture vehicles, pedestrians, and cyclists and the interactions among them. Depending on where a sensor is mounted, its view might be blocked by obstacles (e.g., trees or trucks). The SSM derived using such datasets and the safety analysis results are often specific to the location where the data is collected, and may not be directly generalized to other sites.Such data provide useful information in studying how built environment (e.g., intersection geometry and control) affects the behaviors of a wide range of travelers under different traffic volume,weather, and lighting conditions.

视频/Lidar/雷达数据：这些数据集通常由道路边的传感器或固定位置的无人机收集，并通过计算机程序自动分析。它们可以捕捉车辆、行人和骑行者以及它们之间的互动。根据传感器安装的位置，其视野可能会被障碍物（例如树木或卡车）阻挡。使用这类数据推导出的SSM和安全分析结果通常特定于数据收集的位置，并不直接推广到其他场所。这些数据在研究建成环境如何影响各种交通量、天气和照明条件下的广泛旅行者行为方面提供了有用的信息。

GPS and speed profile data: Such datasets may come from the smartphones of drivers and cyclists, electronic logging devices in commercial vehicles, ridesharing companies, insurance companies, companies selling traffic data, etc. They usually cover a large area and provide good opportunities to investigate how traveler behaviors vary as a result of changing environments, and to identify hot spots. Some datasets may also include the information about the data contributors (e.g., age, gender). A challenge in deriving SSM from such datasets is that limited information (other than roadway geometry and traffic control) regarding the surrounding environment (e.g., distance to front vehicle) is available. Also, the sample sizes across locations could be significantly different, which may lead to biased SSM results. Additionally, SSM developed based on GPS and speed profile data can only account for the risk of rear-end crashes (not other types such as side-swipe) due to the limitation of the data.

GPS和速度轨迹数据：这类数据集可能来自驾驶员和骑行者的智能手机、商用车辆的电子记录设备、顺风车公司、保险公司、销售交通数据的公司等。它们通常覆盖广泛的区域，并提供了研究旅行者行为如何随环境变化而变化以及识别热点的良好机会。部分数据集可能还包括数据贡献者的信息（例如年龄、性别）。从这类数据集中推导SSM的挑战在于，除了道路几何和交通控制之外，有关周围环境（例如与前方车辆的距离）的信息有限。此外，不同位置的样本量可能会显著不同，这可能导致SSM结果存在偏差。此外，基于GPS和速度轨迹数据开发的SSM只能考虑追尾碰撞的风险（而非其他类型，如侧撞），这是由数据限制所致。

Connected vehicles testing data and Naturalistic Driving Study (NDS) data: Notable connected vehicles datasets include the SPMD data (Gay and Kniss, 2015) and the USDOT Connected Vehicles Pilot Study data (USDOT, 2021). The connected vehicles and NDS data are included in the same category due to their similarities. Both types of datasets provide detailed information about the subject vehicle,including distance to obstacle, speed, longitudinal and lateral accelerations, vehicle steering and braking, etc. These detailed information (e.g., steering, lateral acceleration, and distance to obstacle) sets them apart from the above GPS and speed profile data, and make it possible to calculate SSM such as TTC. In addition, the NDS dataset includes videos capturing roadway and driver’s face, which are important for detecting distracted driving and dangerous traffic scenarios (e.g., road debris) and associating them with vehicle kinematics. Such relationships may be generalized and used to analyze the more widely available GPS and speed profile data.

连接车辆测试数据和自然驾驶研究（NDS）数据：值得注意的连接车辆数据集包括SPMD数据（Gay和Kniss，2015年）和USDOT连接车辆试点研究数据（USDOT，2021年）。由于它们的相似性，连接车辆和NDS数据被归入同一类别。这两类数据集提供了关于主体车辆的详细信息，包括距障碍物的距离、速度、纵向和横向加速度、车辆转向和制动等。这些详细信息（例如转向、横向加速度和距障碍物的距离）使它们与上述GPS和速度轨迹数据有所不同，并使得可以计算出诸如TTC等SSM。此外，NDS数据集包括捕捉道路和驾驶员面部的视频，这对于检测分心驾驶和危险交通场景（例如道路碎片）并将其与车辆运动学关联起来是非常重要的。这些关系可能被推广并用于分析更广泛可用的GPS和速度轨迹数据。

Some automated driving technology development companies such as Baidu, Lyft and Waymo have also made their data available. Such datasets are the most comprehensive and capture all traffic surrounding the automated vehicle and the automated vehicle’s movement. Different from the NDS data, automated vehicles datasets also include camera and/or Lidar data for the left, right and rear views, allowing us to analyze the risk of side-swipe and rear-end (the automated vehicle being rear-ended by another vehicle) crashes. They may potentially be used to analyze the collision risk among the surrounding traffic (e.g., a nearby car with a pedestrian). Note that automated vehicles supposedly can predict the movements of the surrounding traffic and take proactive actions to avoid collision. Therefore, the estimated SSM associated with the automated vehicle could be biased, since they reflect the behaviors of an extremely safe “driver”. In this case, SSM associated with the surrounding traffic may better reflect the typical traffic safety risk. Although this review has not identified any studies using real-world automated driving data for deriving SSM, this certainly is an interesting area for future research.

一些自动驾驶技术开发公司如百度、Lyft和Waymo等也已经公开了它们的数据。这类数据集是最全面的，可以捕捉自动驾驶车辆周围的所有交通情况以及自动驾驶车辆的运动。与NDS数据不同，自动驾驶车辆数据集还包括左侧、右侧和后方视角的摄像头和/或激光雷达数据，使我们能够分析侧撞和追尾（即自动驾驶车辆被后方车辆追尾）碰撞的风险。它们还可能用于分析周围交通中的碰撞风险（例如附近的车辆与行人之间的碰撞）。需要注意的是，自动驾驶车辆据称能够预测周围交通的动向并采取积极措施避免碰撞。因此，与自动驾驶车辆相关的估计SSM可能存在偏差，因为它们反映了极为安全的“驾驶员”的行为。在这种情况下，与周围交通相关的SSM可能更能反映典型的交通安全风险。尽管此次综述尚未发现有研究使用真实世界的自动驾驶数据来推导SSM，但这无疑是未来研究的一个有趣领域。

4.8. New concepts for evaluating future CAV safety

Since CAV are controlled by algorithms, CAV safety performance depends much on how conservative (i.e., safe) the control algorithms are designed to be. Incorporating proper safety principles into CAV control algorithms and thoroughly evaluating their safety performance become very important. Shalev-Shwartz et al. with Mobileye (2018) proposed a Responsibility-Sensitive Safety (RSS) concept, which is a technology-neutral framework consisting of five safety principles that can be adopted by any CAV manufacturers to design CAV control algorithms to ensure consistency in safety. Under this framework, various SSM can be utilized to evaluate CAV safety. Weng et al. (2020) proposed a Model Predictive Instantaneous Safety Metric (MPrISM) for modeling automated vehicles safety. MPrISM is a high-dimensional model predictive TTC metric that estimates the TTC when other road users behave very aggressively while the automated vehicle tries its best longitudinal and lateral maneuvers (compared to only longitudinal in most previous studies) to avoid crash. Nister et al., 2019 developed a Safety Force Field (SFF) model as the basis of CAV control system. Similar to MPrISM, SFF also considers a high-dimensional (e.g., both longitudinal and lateral) model predictive approach to estimate crash risk, and this approach can be used to develop new SSM. If a CAV’s perception system works properly, the SFF can guarantee safety. Winner et al. (2019) discussed the PEGASUS project (Project for the Establishment of Generally Accepted quality criteria, tools and methods as well as Scenarios and Situations). As its names suggest, this project focuses on the standards, procedures, testing scenarios, etc. needed for evaluating CAV safety. Additionally, Fraade-Blanar et al. from RAND (2018) recently released a report on the framework and measures for evaluating CAV safety. Some of these studies are not directly related to developing new SSM (e.g., RSS, RAND report, PEGASUS). However, they can help us understand the challenges facing CAV safety, and how to adopt existing SSM and/or develop new ones to evaluate CAV safety. In particular, the high-dimensional MPrISM and SFF may inspire new SSM for analyzing CAV safety using field data generated by automated driving companies such as Waymo.

由于CAV由算法控制，其安全性能在很大程度上取决于控制算法被设计得有多保守（即安全）。将适当的安全原则纳入CAV控制算法，并彻底评估其安全性能变得非常重要。Shalev-Shwartz等人（Mobileye，2018年）提出了一种称为责任敏感安全（RSS）概念，这是一个技术中立的框架，包括五个安全原则，任何CAV制造商都可以采用这些原则设计CAV控制算法，以确保安全一致性。在这个框架下，可以利用各种SSM来评估CAV的安全性。Weng等人（2020年）提出了一种名为模型预测瞬时安全度量（MPrISM）的方法，用于建模自动驾驶车辆的安全性。MPrISM是一个高维度的模型预测TTC度量，估计当其他道路用户表现非常激进时的TTC，而自动驾驶车辆则尽其所能进行纵向和横向的机动（与大多数先前研究仅涉及纵向相比）。Nister等人（2019年）开发了一个称为安全力场（SFF）模型作为CAV控制系统的基础。类似于MPrISM，SFF还考虑了一个高维度（例如纵向和横向）的模型预测方法来估计碰撞风险，这种方法可以用来开发新的SSM。如果CAV的感知系统正常工作，SFF可以保证安全。Winner等人（2019年）讨论了PEGASUS项目（建立普遍接受的质量标准、工具和方法以及场景和情境的项目）。正如其名称所示，该项目侧重于评估CAV安全所需的标准、程序、测试场景等。此外，RAND的Fraade-Blanar等人（2018年）最近发布了一份关于评估CAV安全框架和措施的报告。其中一些研究并不直接涉及开发新的SSM（例如RSS、RAND报告、PEGASUS），但它们可以帮助我们理解面临的CAV安全挑战，以及如何采用现有的SSM和/或开发新的SSM来评估CAV安全性。特别是高维度的MPrISM和SFF可能会激发利用Waymo等自动驾驶公司生成的实地数据来分析CAV安全性的新SSM。

5. Conclusions

SSM are important for safety performance evaluation, since crashes are rare events and historical crash data does not capture near-crash events that are also critical for improving site safety. SSM have been researched for years and have been widely used in simulation-based CAV safety studies. This paper focuses on reviewing SSM and their applications in CAV safety studies. The main contributions of this paper are three folds. First, we provide a comprehensive review of significant SSM and categorize them into two major categories, SSM and SSM-based models, based on how they are developed and how they estimate the severity of an interaction. Second, we summarize field and simulation based safety studies using SSM. We further discuss various SSM applications in simulation-based CAV safety studies, including safety impacts evaluation and safety-oriented trajectory optimization. Third, we identify and discuss a series of issues related to SSM for CAV safety studies and point out some directions for future research. We hope the findings can help researchers and practitioners understand the pros and cons of existing SSM and choose the most appropriate one(s) for their safety studies. Also, the analyses may help researchers avoid duplicative research and inspire innovative ideas for future SSM research.

SSM在安全性能评估中至关重要，因为碰撞是罕见事件，历史碰撞数据无法捕捉到对提升场地安全同样关键的接近碰撞事件。多年来，SSM已经得到广泛研究，并在基于仿真的CAV安全研究中得到广泛应用。本文重点回顾了SSM及其在CAV安全研究中的应用。本文的主要贡献有三个方面。首先，我们全面回顾了重要的SSM，并根据它们的开发方式和如何评估交互作用的严重性将它们分类为两大类，即SSM和基于SSM的模型。其次，我们总结了基于实地和仿真的使用SSM的安全研究。我们进一步讨论了在基于仿真的CAV安全研究中各种SSM的应用，包括安全影响评估和面向安全的轨迹优化。第三，我们确定并讨论了与CAV安全研究中的SSM相关的一系列问题，并指出了未来研究的一些方向。我们希望这些发现能帮助研究人员和从业者理解现有SSM的优缺点，并选择最适合其安全研究的方法。此外，这些分析可以帮助研究人员避免重复研究，并激发未来SSM研究的创新思路。

As road users change (e.g., aging driver population) and new users are introduced (e.g., CAV with different levels of automation), there will be interesting and oftentimes challenging research problems. For example, in mixed autonomy traffic HDV could behave differently than in traditional traffic environment, and conventional SSM may not be valid and cannot be adopted without modification. This raises a number of questions, such as “Is single SSM good enough for CAV of different levels of automation and connectivity?”, “Can we find a universal SSM for mixed autonomy traffic?”, “What SSM are capable of describing the crash risk for a vehicle platoon and individual vehicles in the platoon?” and “What SSM are better for trajectory optimization to improve safety?” These are some of the questions that the authors believe the traffic safety research community should address in the near future before CAVs are widely deployed.

随着道路使用者的变化（例如，老龄驾驶员群体的增加）和新使用者的引入（例如，不同自动化级别的联网和自动驾驶汽车（CAV）），会出现一些有趣且具有挑战性的研究问题。例如，在混合自主交通中，人工驾驶车辆（HDV）的行为可能与传统交通环境中不同，而传统的安全代理度量（SSM）可能不再适用，需要进行修改。这引发了一系列问题，例如：“单一的SSM是否适用于不同自动化和联网级别的CAV？”、“我们能否找到一个适用于混合自主交通的通用SSM？”、“哪些SSM能够描述车辆编队及编队内个别车辆的碰撞风险？”以及“哪些SSM更适合轨迹优化以提高安全性？”这些都是作者认为在CAV广泛部署之前，交通安全研究社区应当解决的问题。

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From： https://blog.csdn.net/qq_32939117/article/details/140800347