**1. Introduction**

For more than 20 years, devices resembling aircraft's "black boxes" and generally referred to as EDRs (Event Data Recorders) have been in use in motor transport. They are intended to record the parameters that describe vehicle motion, driver's activities, state of vehicle's systems, and sometimes current environmental conditions. The objective is to provide data concerning the course of road accidents (incidents), including the data useful for accident reconstruction.

Their scope of operation may be different, although some minimum requirements for the devices of this class have been set down by various normative documents and legal instruments. In this area, a fundamental role is played by a document issued under the auspices of NHTSA in the USA as early as 2006 [1], where the requirements for such devices have been laid down. In that document, the term EDR has been defined as follows: "*(* ... *) a device or function in a vehicle that records the vehicle's dynamic time-series data during the time period just prior to a crash event (* ... *) or during a crash event (* ... *)*". Although without obligatorily requiring, that extensive document recommends vehicles to be equipped with such devices. In 2012, the NHTSA proposed a regulation [2], according to which EDRs should be installed in light-duty vehicles from 2014 on; however, it withdrew it in 2019 [3] with justifying that by the fact that an overwhelming majority of vehicles are already provided with EDRs meeting the requirements of [1]. In Europe, the legal regulations concerning this issue are just being implemented. Pursuant to Regulation (EU) 2019/2144 of the European Parliament [4], new vehicles will have to be equipped with EDR (from

**Citation:** Guzek, M.; Lozia, Z. Are EDR Devices Undoubtedly Helpful in the Reconstruction of a Road Traffic Accident? *Energies* **2021**, *14*, 6940. https://doi.org/10.3390/ en14216940

Academic Editors: Stefania Santini and Mario Marchesoni

Received: 14 September 2021 Accepted: 19 October 2021 Published: 21 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

mid-2022 on). It should also be remembered that now EDRs are already installed in almost all new vehicles (in 2017, 99.6 % of all the light-duty motor vehicles newly manufactured in the USA were provided with EDRs, according to the document [3] mentioned above).

As already mentioned, the EDRs record the parameters that describe vehicle motion, driver's operations on vehicle controls, state of vehicle's systems, and sometimes current ambient conditions in the pre-, during- and post-collision phase. As regards vehicle motion, the basic signals recorded are those representing vehicle acceleration components, rotational speeds of vehicle wheels, data defining the angular position of the vehicle body (angles or components of the angular velocity of the vehicle body solid). The knowledge of these quantities, both in a direct and an appropriately processed form, makes it possible to obtain information about the dynamics and kinematics of motor vehicle motion in specific phases of the accident situation. The authors were mainly interested in the vehicle motion phase, which may be understood as the potential pre-accident situation. The main objective of the study was to estimate the possible accuracy of reconstruction of the timeseries data that are important from the point of view of the analysis of motion, i.e., time histories of vehicle velocity and trajectory. The analysis has been carried out by taking into consideration the typical existing EDR solutions as regards the number of the parameters recorded that describe the motion of the vehicle body solid and the typical elements of vehicle manoeuvres (braking, lane-change, entering a turn, motion along a curve). The tests were carried out for a typical medium-class compact passenger car.

Many titles can be found in the literature that addresses the issues related to the accuracy of using EDR records. Most of them show a high usefulness of such solutions for accident analysis and present examples of their applications; see, e.g., [5–8].

There are also a few publications directly dealing with the accuracy of determining the parameters that describe the vehicle motion, but they mainly concern the strict collision phase and the determining of the vehicle velocity immediately before and after the collision or the vehicle velocity change during the collision, denoted by ΔV. As examples of such publications, [9–16] may be mentioned. A review of the materials showing the errors that occur when the pre- and post-impact velocities and ΔV are determined has been provided in [17], indicating the possible reasons for the inconsistencies having occurred.

Legal and technical issues related to using the EDRs have been discussed in [18] in the context of continuously rising vehicle autonomisation levels.

Also noteworthy are the publications describing research works in which the behaviour of drivers or the functioning of vehicle safety systems was assessed based on the EDR records of actual events. As an example, an attempt was made in the work reported in [19] to estimate the effectiveness of the operation of LDW (Lane Departure Warning) and LDP (Lane Departure Prevention) systems. A method of analysing the left-turn crashes with taking into account driver's actions and based on EDR records of such incidents (as an input database) has been presented in [20]. In [21], EDR records of intersection crashes were used to propose an IADAS (Intersection Advanced Driver Assistance System).

There are only a few publications dealing with the vehicle motion in the pre-accident phase, i.e., in the phase when a hazardous situation is just arising. In [20], a trajectory approximation was used for the purposes of space-time analysis of a left-turn crash based on EDR records. EDR records of angular speeds of vehicle wheels, used as a basis for estimating the vehicle speed, have been analysed in [22]. The possibility of using this signal as a reliable source of information about the vehicle speed during braking has been highlighted. The research work was carried out for a vehicle provided with an air braking system. In [23], the velocity values obtained from EDR records were compared with the vehicle velocity measured by a self-contained device (V-Box). The velocity values obtained from CAN (EDR) were found to be in good conformity with the reference velocity. Similar conclusions can be found in [24]. In [25], the authors compare the EDR records with the V-box records during movement with rotation on a low friction road surface.

As regards the all-embracing analysis of vehicle motion based on EDR records of the motion dynamics, the [26] paper may be highlighted, where 3D transformations and integration of the accelerations recorded have been discussed as a method of obtaining information about the time histories of vehicle velocities and trajectory. Such a possibility has been shown, with potential difficulties having been emphasised. This possibility confirms to some extent the conclusions formulated by the authors of this paper in [27,28]. This paper presents the methods of determining the vehicle velocities and trajectory from EDR records on the one hand and, on the other hand, computational examples showing how some simplifications in EDRs' design can affect the accuracy of the time curves being reconstructed. In these terms, the research works reported here are a direct continuation of those described previously in [27–30], but updated mathematical models of the test specimens adopted have been used in this case.

The fact that EDRs of various types are commonly used in present-day motor vehicles and the possibility of using their records for the reconstruction of vehicle motion and, on the other hand, scanty literature addressing these issues fully justify the undertaking of research in this field.

#### **2. Materials and Methods**

In the research presented, simulation calculational methods were used, where an experimentally verified model of motor vehicle dynamics and models of EDR records and of record processing algorithms were employed. A block diagram of the method has been shown in Figure 1. In the method adopted, the motion simulation results are taken as accurate (reference) values, and EDR records are simulated on these grounds (EDR model). Based on these records, time histories of the parameters describing the vehicle motion (velocity, position) are reconstructed with data processing algorithms (denoted by DPM, i.e., Data Processing Methods) being used. The difference between the reconstructed and accurate values is a measure of the reconstruction error. Individual elements of the method (vehicle dynamics model, EDR records model, and EDR record processing method, i.e., DPM) will be presented in subsequent subsections).

**Figure 1.** Method of estimating the accuracy of reconstruction of vehicle motion, based on EDR records (a, V, ω, r, Λ—component vectors of: acceleration, velocity, angular velocity, position, angles, respectively).

### *2.1. Vehicle Dynamics Model*

The tests were carried out for a KIA Ceed SW motor car, provided with a McPherson strut front suspension system with an antiroll bar. The suspension system (together with steering system components) is fastened to a subframe, which in turn is fixed to the car body solid. The left and right rear wheel suspension systems are independent of each other (apart from being coupled together by an antiroll bar). Each of them consists of a spring element (helical spring), shock absorber, two transverse arms, trailing arm, and lateral control rod. On both sides, the wheel suspension systems are fixed in a part to a steel drawpiece, which plays the role of a subframe.

A simulation model of this vehicle has been presented in publications [31–33] (Figure 2). It consists of 9 mass elements: vehicle body solid (treated as a rigid body), 4 material particles O1, O2, O3, and O4, where the vehicle's "unsprung masses" have been concentrated (including road wheels in their translational motion), and 4 solids representing the rotating road wheels (exclusively in their rotational motion).

**Figure 2.** Physical model of a two-axle motor vehicle with independent front and rear wheel suspension systems, together with the coordinate systems adopted.

The following coordinate systems have been adopted:


To describe the translational motion of the solids and material particles of the model, the positions of the centres of mass (OC, O1, O2, O3, O4) of the said solids are used.

The axes Oiξi, Oiηi, Oiζ<sup>i</sup> (i = C, 1, 2, 3, 4) are treated as the principal central axes of inertia of the corresponding rigid bodies.

The rotation of the vehicle body solid about the fixed point OC has been described with the use of "aircraft angles", also referred to as "quasi-Euler angles" [34–38]:


The sequence of rotations has been adopted as identical to their listing order. The axes of individual rotations are treated as the principal central axes of inertia of the vehicle body solid.

The equations of motion have been derived with Lagrange equations of the second kind having been used. Prior to this, the following 14 generalised coordinates were adopted:


In the model, the steering system flexibility and directional stability of road wheels have been taken into account. The tyre-road contact forces and moments have been described with the HSRI-UMTRI model [39,40] having been used, extended by adding the IPG-Tire model of transient states of tyres [41] in the form as adopted in paper [37].

The model has been experimentally verified as satisfactorily applicable to typical vehicle motion tests recommended by ISO or ECE, including the calculational part of the steady-state circular driving tests (ISO 4138, [42]), tests with step input applied to the steering wheel (ISO 7401, [43]), straight-line braking tests (UN ECE Regulation No 13, [44]), with the ABS being inactive.
