## 1 Introduction
Crash-related studies have demonstrated that the primary factor determining the passenger injury level is the subjected force during the crash, which can be estimated based on multiple severity parameters, such as the velocity change (\(\Delta\)V) and energy equivalent speed (EES) [20]. When combined with the crash characteristics, only a few indicators are sufficient to obtain accurate results in predicting the severity outcomes [21; 22]. However, the main drawback of these parameters is that their initial formulations are derived from the post-crash consequence, which limits the applications to the reduction in potential risk before crash [23]. To fulfill this requirement, [PERSON] adopted a new a priori factor to measure the energy dissipation of a vehicle during a crash and evaluated its effect in injury assessment [24]. [PERSON] presented a theoretical Extended Delta-V as a measure of conflict severity in site-based observations and validated its performance in identifying severe traffic events [8]. The other variables, such as closing velocity (Vr), crash momentum index (CMI), and crash severity index (CSI), are proposed in a priori formulations, which measure the impact speed and eccentricity of the potential crashes [25]. A single crash-related indicator cannot be expected to capture all risk-relevant information considering the variability of crash dynamics. In cases of multiple alternative crash indicators, the severity-variable relationships must be further explored. Hence, the aim of this study was to explore several pre-crash indicators (PCIs) based on in-depth crash datasets that fully consider the impact of crash mechanism with adequate data samples. From the perspective of assessment methods, machine learning (ML) has been widely employed in the roadway safety field, especially for complex crash modeling, such as causation analysis and risk assessment [26; 27; 28]. ML models have displayed advantages in dealing with the limitations in data generalization and prediction performance compared with traditional statistical methods. The hidden associations between risk factors and model results can be effectively explained through novel post hoc analysis, thus guiding roadway safety [29]. ML has been successfully applied in risk modeling. [PERSON] employed a classification and regression technique to identify the important factors affecting driving risk in terms of driver, vehicle, and road environment [13]. [PERSON] compared the performance of light gradient boosting and extreme gradient boosting models in risk prediction and quantified the importance, total effect, and main and interaction effects of risk factors by Shapley additive explanation (SHAP) [30]. The novel visualization methods can effectively measure the evident distribution between crash characteristics and severity probabilities, providing detailed interpretation of the results [31]. To this end, this study attempts to explore the nonlinear associations between crash indicators and severity levels using ML and interpretation methods. Therefore, the key factors may be extracted from the model results, and efficient suggestions are correspondingly presented for road safety. This study proposes a framework combining the PCIs and ML models to explore relevant factors of IR with full consideration of the impact mechanics and the a priori information. The formulations of several PCIs are proposed on the basis of the impulse-momentum theory, and six ML models were applied with a fusion dataset containing adequate crash cases. The model results are further investigated to identify the intrinsic crash patterns for different impact types with proper interpretation methods. This framework provides a major overview of the benefits and drawbacks of several PCIs, showcases their applicability in understanding the complex crash patterns, and explores favorable predictive methods for IR assessment in pre-crash scenarios.