Numerical Reconstruction of Cyclist Impact Accidents: Can Helmets Protect the Head-Neck of Cyclists?

Cyclists are vulnerable road users and often suffer head-neck injuries in car-cyclist accidents. Wearing a helmet is currently the most prevalent protection method against such injuries. Today, there is an ongoing debate about the ability of helmets to protect the cyclists' head-neck from injury. In the current study, we numerically reconstructed five real-world car-cyclist impact accidents, incorporating previously developed finite element models of four cyclist helmets to evaluate their protective performances. We made comparative head-neck injury predictions for unhelmeted and helmeted cyclists. The results show that helmets could clearly lower the risk of severe (AIS 4+) brain injury and skull fracture, as assessed by the predicted head injury criterion (HIC), while a relatively limited decrease in AIS 4+ brain injury risk can be achieved in terms of the analysis of CSDM0.25. Assessment using the maximum principal strain (MPS0.98) and head impact power (HIP) criteria suggests that helmets could lower the risk of diffuse axonal injury and subdural hematoma of the cyclist. The helmet efficacy in neck protection depends on the impact scenario. Therefore, wearing a helmet does not seem to cause a significant neck injury risk level increase to the cyclist. Our work presents important insights into the helmet's efficacy in protecting the head-neck of cyclists and motivates further optimization of protective equipment.

Numerical investigation of the rider's head injury in typical single-electric self-balancing scooter accident scenarios.

As the use of electric self-balancing scooters (ESSs) increases, so does the number of related traffic accidents. Because of the special control method, mechanical structure and driving posture, ESSs are prone to various single-vehicle accidents, such as collisions with fixed obstacles and falls due to mechanical failures. In various ESS accident scenarios, the rider's head injury is the most frequent injury type. In this study, several typical single-ESS accident scenarios are reconstructed via computational methods, and the risk of riders' head/brain injury is assessed in depth using various injury criteria. Results showed that two types of ESSs (solo- and two-wheeler) do not have clear differences in head kinematics and head injury risks; the head kinematics (or falling posture) and ESS accident scenario exhibit a distinct effect on the head injury responses; half of the analysed ESS riders have a 50% probability of skull fracture, a few riders have a 50% risk of abbreviated injury scale (AIS) 4+ brain injury, and none has a diffuse axonal injury; the ESS speed plays an important role in producing the head/brain injury in ESS riders, and generally, higher ESS speed generates higher level of predicted head injury parameters. These findings will provide theoretical support for preventing head injury among ESS riders and data support for developing and legislating ESSs.

Methods for fusing uncertain results obtained from different models in accident reconstruction.

Considering that almost all existing solutions of fusing different reconstructed results require experts' opinions and the issue of how to fuse probabilistic results and mixed results has not been discussed. Two solutions are proposed. The first is based on the Monte Carlo Method (FMCM), while the second is based on the Sub-Interval Technique (FSIT). The method based on FMCM generates sample points according to the distribution of each uncertain result firstly, and then gives out the cumulative distribution function of the final fused result by statistical analysis. The method based on FSIT gets the result fusion interval set according to lower and upper bounds of all interval results and a given length d of each sub-interval firstly, and then calculate the weighted matrix of the result fusion interval. As a result, the cumulative distribution function of the final fused result can also be given out by statistical analysis. Finally, three real accidents are given to demonstrate the methods of FMCM and FSIT, the results of which show that both work well in practice.

Potential benefits of controlled vehicle braking to reduce pedestrian ground contact injuries.

Protecting struck pedestrians during the ground contact phase has been a challenge for decades. Recent studies have shown how ground related injury is influenced by pedestrian kinematics. In this paper we further developed this approach by assessing the potential of controlling vehicle braking to reduce pedestrian ground contact injuries. Applying a recently proposed Simulation Test Sample, a series of simulations were run using the MADYMO software environment. The approach considered 6 vehicle shapes, 4 pedestrian models, 3 impact velocities and 2 pedestrian gaits and each case was considered with two different vehicle braking approaches. The first was full braking, while the second applied controlled braking, for which a strategy based on pedestrian kinematics was applied. The effect of vehicle braking was evaluated using the Weighted Injury Cost (WIC) of overall pedestrian injuries and the pedestrian-ground impact velocity change. The proximity of the vehicle and pedestrian at the instant of ground contact was also evaluated to assess the potential of future vehicle based intervention methods to cushion the ground contact. Finally real-world videos of pedestrian collisions were analyzed to estimate the available free vehicle stopping distances. Results showed substantial median reductions in WIC and head impact velocity for all vehicle shapes except the Van. The proximity of the pedestrian to the vehicle front at the instant of ground contact under controlled braking is less than 1.5 m in most cases, and the required stopping distance for the vehicle under controlled braking was within the available stopping distance estimated from the video footage in about 74% of cases. It is concluded that controlled braking has significant potential to reduce the overall burden of pedestrian ground contact injuries, but future efforts are required to establish an optimized braking strategy as well as a means to handle those cases where controlled braking is not beneficial or even harmful.

A case-oriented approach for analyzing the uncertainty of a reconstructed result based on the evidence theory.

Uncertainty analysis is an effective methodology to improve the reliability of an accident reconstruction result. Many existing methods can be employed in this field, which can confuse a practicing engineer who does not know these methods well. To make the selection easier, a case-oriented approach was proposed based on the evidence theory. Users only need to input uncertain traces and a selected accident reconstruction model to calculate the uncertainty of reconstructed results using the proposed approach. Three basic steps of the case-oriented approach are as follows: first, all types of input traces should be transformed into their evidence form; then, focal elements of the reconstructed result and their corresponding basic probability assignment (BPA) need to be calculated; finally, the belief function (Bel) and plausibility function (Pl) of the reconstructed results are calculated. Three common conditions, which are accidents with all interval traces, accidents with all probabilistic traces, and accidents with interval and probabilistic traces, were discussed based on the basic steps of the case-oriented approach. Furthermore, methods for how to transform different traces to their evidence form, how to calculate the interval of the response efficiently, and how to fuse high conflict evidence were presented. Numerical cases showed that the approach worked well in all conditions. Finally, a vehicle collisions accident case was presented to demonstrate the application of the proposed approach in practice.

Methods for describing different results obtained from different methods in accident reconstruction.

There is always more than one method can be employed to reconstruct a traffic accident and then more than one result can be obtained. How to describe these different results becomes an issue. Two solutions were given, the first is to fuse different results to one result, while the other is to rank different results according to their credibility. Methods based on the Ordered Weighted Averaging (OWA) operator and Uncertain Ordered Weighted Averaging (UOWA) operator were proposed to fuse different certain results and different interval results to one result, respectively. And methods based on the Combination Weight Arithmetic Average (CWAA) and OWA operators were proposed to rank different certain or interval results. Finally, a true vehicle-motorcycle accident was given to demonstrate these proposed methods, results showed that all methods work well in practice. If the calculation uncertainty was not considered, the fused result 64.56km/h and a ranked vector can be obtained; if the calculation uncertainty was considered, the fused result [62.13, 68.13]km/h and a ranked interval number set can be obtained. Because that all final results were obtained by employing widely used mature operators, they deserve to be trusted. The research provides more reliable choices to describe different results obtained from different methods in accident reconstruction.

Injury Source and Correlation Analysis of Riders in Car-Electric Bicycle Accidents.

The knowledge about the injury source and correlation of riders in car-electric bicycle accident will be helpful in the cross validation of traces and vehicle safety design. In order to know more information about such kind of knowledge, 57 true car-electric bicycle accidents were reconstructed by PC-Crash and then data on injury information of riders were collected directly from the reconstructed cases. These collected data were validated by some existing research results firstly, and then 4 abnormal cases were deleted according to the statistical method. Finally, conclusions can be obtained according to the data obtained from the remaining 53 cases. Direct injuries of the head and right leg are from the road pavement upon low speed; the source laws of indirect head injuries are not obvious. Upon intermediate and high speed, the injuries of the above parts are from automobiles. Injuries of the left leg, femur, and right knee are from automobiles; left knee injuries are from automobiles, the road pavement and automobiles, respectively, upon low, intermediate, and high speed. The source laws of indirect torso injuries are not obvious upon intermediate and low speed, which are from automobiles upon high speed, while direct torso injuries are from the road pavement. And there is no high correlation between all parts of the injury of riders. The largest correlation coefficient was the head-left femur and left femur-right femur, which was 0.647, followed by the head-right femur (0.638) and head-torso which was 0.617.

Methods for analyzing the uncertainty of a reconstructed result in a traffic accident with interval and probabilistic traces.

In order to make the reconstructed result more reliable, a method named improved probabilistic-interval method was proposed to analyze the uncertainty of a reconstructed result in a traffic accident with probabilistic and interval traces. In the method, probabilistic traces are replaced by probabilistic sub-intervals firstly; secondly, these probabilistic sub-intervals and those interval traces will be combined to form many new uncertainty analysis problems with only interval traces; thirdly, the upper and lower bound of the reconstructed result and their probability were calculated in each new uncertainty analysis problem, and an algorithm was proposed to shorten the time taken for this step; finally, distribution functions of the upper and lower bound of the reconstructed result were obtained by doing statistic analysis. Through 2 numerical cases, results obtained from the proposed method were almost the same as results obtained from the Monte Carlo method, but the time taken for the proposed method was far less than the time taken for the Monte Carlo method and results obtained from the proposed method were more stable. Through applying the proposed method to a true vehicle-pedestrian accident, not only the upper and lower bound of the impact velocity (v) can be obtained; but also the probability that the upper bound and the lower bound of v falls in an arbitrary interval can be obtained; furthermore, the probability that the interval of v is less than an arbitrary interval can be obtained also. It is concluded that the proposed improved probabilistic-interval method is practical.

A Taylor-Affine Arithmetic for analyzing the calculation result uncertainty in accident reconstruction.

In order to analyze the uncertainty of a reconstructed result, the Interval Algorithm (IA), the Affine Arithmetic (AA) and the Modified Affine Arithmetic (MAA) were introduced firstly, and then a Taylor-Affine Arithmetic (TAA) was proposed based on the MAA and Taylor series. Steps of the TAA, especially in analyzing uncertainty of a simulation result were given. Through the preceding five numerical cases, its application was demonstrated and its feasibility was validated. Results showed that no matter other methods (The IA, AA, the Upper and Lower bound Method, the Finite Difference Method) work well or bad, the TAA work well, even under the condition that the MAA cannot work in some cases because of the division/root operation in these models. Furthermore, in order to make sure that the result obtained from the TAA can be very close to the accurate interval, a simple algorithm was proposed based on the sub-interval technique, its feasibility was validated by two other numerical cases. Finally, a vehicle-pedestrian test was given to demonstrate the application of the TAA in practice. In the vehicle-pedestrian test, the interval [35.5, 39.1]km/h of the impact velocity can be calculated according to steps of the TAA, such interval information will be more useful in accident responsibility identification than a single number. This study will provide a new alternative method for uncertainty analysis in accident reconstruction.

Two Simple Formulas for Evaluating the Lower Bound of the Impact Velocity in Vehicle-pedestrian Accidents.

Formulas for evaluating the lower bound of the impact velocity are valuable in vehicle-pedestrian accident reconstruction. The theory of classical mechanics and four hypotheses were employed to derive formulas; the research results and simulation/accident tests were employed to validate their feasibility. Then, two simple formulas were developed according to the distance between the rest positions of the vehicle and the pedestrian and the flight-phase distance. The results showed that the evaluated results by the two proposed formulas are inferior to the existing results. The influence of a roadside step on the impact velocity, which decreased with an increase in the flight-phase distance and a reduction in the road slope, was evaluated. Based on a real accident, the study concludes that the lower bound can be easily obtained with the proposed formulas, which can be used to determine the evaluated impact velocity during simulations.

A simple algorithm for analyzing uncertainty of accident reconstruction results.

In order to analyzing the uncertainty in accident reconstruction, based on the theory of extreme value and the convex model theory, the uncertainty analysis problem is turn to an extreme value problem. In order to calculate the range of the dependent variable, the extreme value in the definition domain and on the boundary of the definition domain are calculated independently, and then the upper and lower bound of the dependent variable can be given by these obtained extreme values. Based on such idea and through analyzing five numerical cases, a simple algorithm for calculating the range of an accident reconstruction result was given; appropriate results can be obtained through the proposed algorithm in these cases. Finally, a real world vehicle-motorcycle accident was given, the range of the reconstructed velocity of the vehicle was calculated by employing the Pc-Crash, the response surface methodology and the new proposed algorithm, the range was [66.1-67.3] km/h. This research will provide another choice for uncertainty analysis in accident reconstruction.

Response surface methodology and improved interval analysis method--for analyzing uncertainty in accident reconstruction.

Methods used to calculate intervals of accident reconstruction results are research hotspot in the word. The response surface methodology-interval analysis method (RSM-IAM) is a useful method for analyzing uncertainty of simulation results in this field, but there are two problems in this method because of the interval extension problem and inaccurate response surface models. In order to tackle these two problems, based on subinterval analysis thought and response surface methodology, an improved interval analysis method (RSM-IIAM) is proposed. In RSM-IIAM, the stepwise regression technique is used to obtain a reasonable response surface mode of the simulation model; and then, intervals of uncertain parameters are divided into several subintervals; after that, intervals of simulation results in accident reconstruction are calculated according to these subintervals. Finally, four numerical cases were given. Results showed that the RSM-IIAM is simple and high accuracy, which will be useful in analyzing uncertainty of simulation results in accident reconstruction.

Analyzing the uncertainty of simulation results in accident reconstruction with Response Surface Methodology.

This paper is focused on the uncertainty of simulation results in accident reconstruction. The Upper and Lower Bound Method (ULM) and the Finite Difference Method (FDM), which can be easily applied in this field, are introduced firstly; the Response Surface Methodology (RSM) is then introduced into this field as an alternative methodology. In RSM, a sample set is firstly generated via uniform design; secondly, experiments are conducted according to the sample set with the help of simulation methods; thirdly, a response surface model is determined through regression analysis; finally, the uncertainty of simulation results can be analyzed using a combination of the response surface model and existing uncertainty analysis methods. It is later discussed in detail how to generate a sample set, how to calculate the range of simulation results and how to analyze the parameter sensitivity in RSM. Finally, the feasibility of RSM is validated by five cases. Moreover, the applicability of RSM, ULM and FDM in analyzing the uncertainty of simulation results is studied; the phenomena that ULM and FDM can hardly work while RSM can is found in the latter two cases. After an analysis of these five cases and the number of simulation runs required for each method, both advantages and disadvantages of these uncertainty analysis methods are indicated.

Analysis and application of relationship between post-braking-distance and throw distance in vehicle-pedestrian accident reconstruction.

Through theoretical analysis and introduction of some empirical parameters, the relationship between post-braking-distance and throw distance was studied concentratedly. Here, the post-braking-distance is the distance a vehicle will travel from the impact position to when it comes to a complete stop. Two useful formulas which are meaningful in vehicle-pedestrian accident reconstruction were finally obtained. The first one can be used to calculate impact speed according to throw distance, while the other one can describe the relationship between post-braking-distance and throw distance. Their feasibility has been validated by comparing with other scholars' empirical formulas and simulation results of software Pc-Crash, respectively. The relationship between post-braking-distance and throw distance has very bright application perspective in vehicle-pedestrian accident reconstruction such as helping policemen obtain more useful evidences, validating credibility of the throw distance, judging whether the vehicle is fully braked or not, determining the impact position etc. Finally its application was demonstrated by three cases, in which the impact speed was also calculated. All results until now have shown that conclusions obtained in this article are feasible and helpful in vehicle-pedestrian accident reconstruction.

Two non-probabilistic methods for uncertainty analysis in accident reconstruction.

There are many uncertain factors in traffic accidents, it is necessary to study the influence of these uncertain factors to improve the accuracy and confidence of accident reconstruction results. It is difficult to evaluate the uncertainty of calculation results if the expression of the reconstruction model is implicit and/or the distributions of the independent variables are unknown. Based on interval mathematics, convex models and design of experiment, two non-probabilistic methods were proposed. These two methods are efficient under conditions where existing uncertainty analysis methods can hardly work because the accident reconstruction model is implicit and/or the distributions of independent variables are unknown; and parameter sensitivity can be obtained from them too. An accident case is investigated by the methods proposed in the paper. Results show that the convex models method is the most conservative method, and the solution of interval analysis method is very close to the other methods. These two methods are a beneficial supplement to the existing uncertainty analysis methods.