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Testing Scenario Library Generation for Connected and Automated Vehicles, Part I: Methodology

Shuo Feng, Yiheng Feng, Chunhui Yu, Yi Zhang, Henry X. Liu

arXiv:1905.03419v3eess.SYcs.RO

TL;DR

CAV testing lacks a systematic way to generate scenario libraries across different ODDs, CAV models, and performance metrics. This paper proposes a unified TSLG framework using criticality-guided scenario search and theoretically justifies accurate evaluation with fewer tests than on-road testing. Its strongest scope boundary is that ideal zero-variance conditions require the surrogate model to match the test CAV exactly.

  • Problem

    CAV testing lacks a systematic framework for generating testing scenario libraries across different ODDs, CAV models, and performance metrics.

  • Method

    The framework combines exposure frequency from naturalistic driving data with maneuver challenge from a surrogate CAV model, then searches for critical scenarios using optimization and sampling methods.

  • Results

    Theoretical analysis establishes unbiased performance-index estimation and zero estimation variance under specified conditions, supporting accurate evaluation with fewer tests than on-road testing.

  • Takeaways & Limitations

    Scenario libraries can integrate criticality-based search with CAV evaluation across ODDs, CAV models, and multiple performance metrics.

  • Takeaways & Limitations

    Zero-variance ideal results require the surrogate model to be exactly the same as the test CAV, a condition the paper says cannot hold completely.

Abstract

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Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs), and yet there is no systematic framework to generate testing scenario library. This study aims to provide a general framework for the testing scenario library generation (TSLG) problem with different operational design domains (ODDs), CAV models, and performance metrics. Given an ODD, the testing scenario library is defined as a critical set of scenarios that can be used for CAV test. Each testing scenario is evaluated by a newly proposed measure, scenario criticality, which can be computed as a combination of maneuver challenge and exposure frequency. To search for critical scenarios, an auxiliary objective function is designed, and a multi-start optimization method along with seed-filling is applied. The proposed framework is theoretically proved to obtain accurate evaluation results with much fewer number of tests, if compared with the on-road test method. In part II of the study, three case studies are investigated to demonstrate the proposed methodologies. Reinforcement learning based technique is applied to enhance the searching method under high-dimensional scenarios.

I. INTRODUCTION

CAV testing requires scenario libraries that efficiently evaluate safety and broader driving performance across operational design domains. The paper proposes a unified TSLG framework that prioritizes scenarios by both maneuver challenge and real-world exposure frequency.

  • Motivation: On-road testing is realistic but may require hundreds of millions of miles to validate CAV safety at human-driven-vehicle levels.Simulation is cost-effective but difficult to model exactly, while closed-facility testing offers greater control and efficiency.
  • Motivation: A testing scenario library is a critical subset of the millions of scenarios possible within a given operational design domain.The library is intended to support evaluation against predefined performance metrics.
  • Research Gap: Existing TSLG research addresses scenario description, metric design, library generation, and CAV evaluation, but prior methods remain limited in ODDs, CAV models, or performance metrics.The paper identifies low-dimensional scenarios, specific CAVs, and safety-only evaluation as examples of these limitations.
  • Proposed Framework: The proposed unified framework integrates scenario parameterization, incremental metrics, critical-scenario search, and CAV evaluation within one TSLG process.Its metrics include safety, functionality, mobility, and rider’s comfort.
  • Proposed Framework: Scenario criticality combines maneuver challenge and exposure frequency, using a CAV surrogate model, naturalistic driving data, auxiliary optimization, and seed-filling.This definition differs from approaches that usually overvalue worst-case scenarios.
  • Theoretical Basis: Theoretical analysis establishes unbiased performance-index estimation and zero estimation variance under certain conditions, supporting accuracy and efficiency claims.The analysis also informs the selection of criticality thresholds and sampling-policy parameters.

III. PROBLEM FORMULATION

The formulation represents scenarios through ODD-constrained decision variables and evaluates CAVs across safety, functionality, mobility, and rider’s comfort. It defines the testing target as a critical subset of feasible scenarios.

  • A. Decision Variables: A scenario consists of temporal development among scenes containing stationary scenery and dynamic elements such as pedestrians and vehicles.The formulation adopts the paper’s scene and scenario terminology from prior work.
  • A. Decision Variables: ODD parameters θ specify conditions such as lanes, road type, and weather, while remaining scenario parameters form the decision-variable vector x.The feasible set X is constrained by the ODD, including speed, acceleration, and perception ranges.
  • A. Decision Variables: The TSLG task is to determine a critical subset Φ of the ODD-feasible set X for CAV evaluation.The cut-in example parameterizes scenarios using relative distance and relative speed at the cut-in moment.
  • B. Performance Metrics: The framework evaluates safety, functionality, mobility, and rider’s comfort rather than focusing only on safety.These metrics represent incremental expectations for CAV evaluation.
  • B. Performance Metrics: Safety is assessed through outcomes such as disengagement or accidents resulting from the CAV’s response to scenario actions.The cut-in example links the outcome to decision variables including cut-in distance and speed difference.
  • B. Performance Metrics: Functionality measures whether a CAV completes a specified driving task within the scenario’s requirements.A conservative vehicle may fail a required lane change before a freeway exit despite maintaining safety distance.
  • B. Performance Metrics: Safety and functionality are both treated as critical because a CAV must complete driving tasks safely without human intervention.The paper connects this capability to potential public acceptance.
  • B. Performance Metrics: Mobility measures travel efficiency, while rider’s comfort measures passengers’ physical and psychological feeling; case studies of both are deferred to future work.These metrics are included for higher-level requirements but are not developed through case studies here.

C. Performance Index Estimation

The section describes estimating CAV performance indices from scenario outcomes and improving efficiency through importance sampling and a criticality-based scenario library.

  • CAV performance indices quantify metrics such as accident rate for safety and failure rate for functionality.
  • On-road estimation samples scenarios from the ODD distribution and estimates the event probability from observed outcomes.
  • Rare accidents require an intolerably large number of tests for reasonable estimation accuracy under ordinary Monte Carlo estimation.
  • Importance sampling improves efficiency by assigning higher probability to critical scenarios during testing.
  • The scenario library is intended to construct the importance function by including scenarios whose criticality exceeds a threshold.

E. Assumptions Made for TSLG

The framework assumes rare events and shared generic CAV behaviors, then defines and searches for critical scenarios using exposure, maneuver challenge, optimization, and seed-fill expansion.

  • E. Assumptions Made for TSLG: The framework assumes the evaluated event is rare on-road and that tested CAVs share generic behavioral features.
  • E. Assumptions Made for TSLG: Generic behavioral features include maintaining safe distances and interacting safely with surrounding vehicles, despite manufacturer-specific differences.
  • A. Definition of Criticality: Scenario criticality combines exposure frequency estimated from naturalistic driving data with maneuver challenge estimated by a surrogate CAV model.
  • A. Definition of Criticality: The surrogate model uses human driving data because open CAV data are scarce, making human critical scenarios meaningful testing scenarios for CAVs.
  • A. Definition of Criticality: Higher-occurrence and more challenging scenarios receive higher evaluation priority, unlike approaches that overvalue extremely rare worst-case scenarios.
  • B. Critical Scenario Searching: An auxiliary objective guides search when most scenarios have zero criticality and zero criticality gradient.
  • B. Critical Scenario Searching: Multi-start optimization finds local critical scenarios, while seed-fill expands from those seeds to identify additional critical scenarios.
  • B. Critical Scenario Searching: The search threshold is theoretically analyzed, and reinforcement learning can enhance search for high-dimensional scenarios after structural dimension reduction.

V. CAV EVALUATION WITH THE LIBRARY

CAV evaluation with the generated library samples testing scenarios, conducts specified tests, and estimates performance indices from the results.

  • The evaluation process obtains scenarios by sampling from the library, conducts CAV tests, and estimates performance indices.
  • The generated library supplies the testing scenarios used in the evaluation process.
  • The process is illustrated in Fig. 3.

A. Scenario Sampling

The framework balances exploitation of high-criticality scenarios with exploration outside the library, then uses importance sampling to estimate performance indices from repeated CAV tests.

  • A. Scenario Sampling: Sampling exploits scenarios according to normalized criticality while allowing exploration outside the library to reduce missed critical scenarios caused by surrogate–test-CAV dissimilarity.The ϵ-greedy policy selects outside-library scenarios randomly with probability ϵ > 0.
  • A. Scenario Sampling: The greedy policy samples only from the library, whereas ϵ-greedy sampling explores feasible scenarios outside the library with equal probability.The choice creates a direct trade-off between concentrating tests on critical scenarios and retaining coverage beyond the generated library.
  • A. Scenario Sampling: The sampling distributions construct the importance function q(x), incorporate CAV and naturalistic-driving knowledge, and apply to both low- and high-dimensional scenarios.The method also provides a way to progressively improve the importance function.
  • A. Scenario Sampling: Testing uses sampled scenario initial conditions and background-vehicle maneuvers in simulation or a closed facility, with test counts determined by required precision and confidence.The number of tests depends on the estimation variance, expectation, confidence level, and a predefined relative-error bound.
  • A. Scenario Sampling: The performance index is estimated by weighting testing outcomes with exposure frequency divided by the selected importance function, and the estimator is proved unbiased.The sampling policy determines which importance function is used, while testing estimates P(A|x_i, θ).

VI. THEORETICAL ANALYSIS

The theoretical analysis examines the proposed method’s evaluation accuracy and efficiency and uses those results to guide its hyper-parameter choices.

  • VI. THEORETICAL ANALYSIS: The analysis validates accuracy and efficiency theoretically while discussing the critical-scenario threshold and ϵ as hyper-parameters.The pre-determined parameters θ are omitted from the simplified notation used in the analysis.

A. Accuracy Analysis

The accuracy analysis establishes unbiased performance-index estimation for ϵ-greedy sampling and for greedy sampling under an additional condition.

  • A. Accuracy Analysis: Theorem 1 states that the proposed evaluation method obtains an unbiased performance-index estimate under either specified sampling condition.The conditions are greedy sampling with zero test-CAV performance outside the library, or ϵ-greedy sampling.
  • A. Accuracy Analysis: ϵ-greedy sampling supports the theorem through positive sampling probability for every scenario and Monte Carlo estimation under the resulting distribution.The Central Limit Theorem is used to characterize the estimator approximately by a normal distribution when the sample size is large.
  • A. Accuracy Analysis: Greedy sampling preserves unbiasedness only when all scenarios outside the library have zero performance contribution for the test CAV.Under that condition, the feasible decision-variable set can be reduced from X to Φ without loss of accuracy.
  • A. Accuracy Analysis: Because the zero-contribution condition may fail across diverse CAVs in real-world applications, the analysis suggests ϵ-greedy sampling.This recommendation retains a nonzero probability of sampling outside-library scenarios.

B. Efficiency Analysis

The efficiency analysis links testing efficiency to estimation variance, showing that variance can reach zero only under strict alignment conditions between the surrogate and test CAV.

  • B. Efficiency Analysis: The proposed method is efficient because its estimation variance is small or zero under certain conditions, reducing the minimum number of required tests.The analysis identifies estimation variance as the quantity determining the minimal test count.
  • B. Efficiency Analysis: Theorem 2 states that estimation variance is zero under greedy sampling, no contribution outside the library, and proportional surrogate and test-CAV performance functions.The condition is expressed as V ar(ˆµ) = σ2/n = 0.
  • B. Efficiency Analysis: Zero estimation variance would reduce the minimum number of tests to one, but the required exact surrogate–test-CAV match is impossible to achieve completely in practice.The analysis attributes evaluation variance to dissimilarity between the surrogate model and the specific test CAV.
  • B. Efficiency Analysis: Theorem 2 provides a basis for selecting the ϵ-greedy exploration probability and the criticality threshold.These choices are connected to the conditions governing estimation variance.

C. Choices of Hyper-parameters

The section establishes variance results for epsilon-greedy sampling and explains how hyper-parameters affect library size, estimation variance, and threshold selection.

  • ϵ-greedy sampling separates estimation variance into two parts under Theorem 2’s condition (3).
  • The choice of ϵ in Eq. (22) does not increase estimation variance for scenarios included in the library.
  • Theorem 3 derives an upper bound for estimation variance using the critical-scenario set Φ and the threshold γ.
  • A larger constant m decreases library size but increases the upper bound of estimation variance.
  • Determining γ requires recursion because the number of critical scenarios N(Φ) depends on γ; practical use may relax γ to mµ_S/N(X).

VII. CONCLUSIONS

The paper proposes a unified TSLG framework for CAV evaluation across ODD types, performance metrics, and CAV models. It defines scenario criticality using maneuver challenge and exposure frequency, searches with multi-start optimization, and extends the method in Part II to case studies and high-dimensional scenarios.

  • The framework generates testing scenario libraries for different ODD types, performance metrics, and CAV models.
  • Scenario criticality combines maneuver challenge and exposure frequency, while multi-start optimization searches for critical scenarios.
  • A surrogate model containing generic CAV features evaluates maneuver challenge, and theoretical analysis addresses testing accuracy and efficiency.
  • Part II demonstrates the method through cut-in, car-following, and highway-exit case studies and applies reinforcement learning to high-dimensional scenarios.
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