Innovative Methodology for Generating Representative Driving Profiles for Heavy-Duty Trucks from Measured Vehicle Data

Abstract

The imperative for electrification of road transport, driven by global climate targets, underscores the need for innovative powertrain systems in heavy-duty vehicles. When developing new electric drive modules, individual operational requirements need to be considered instead of generalized usage profiles, as heavy-duty vehicles experience significantly differing loads depending on their field of operation. Real driving data, representing the demands of different application scenarios, offers great potential for digital replication of driving conditions at different stages of simulation and physical validation. Application- and vehicle-specific longitudinal requirements during operation are particularly relevant for the dimensioning of powertrain components. Road gradient and mass estimation assist in the description of these operating conditions, allowing for detailed modeling of the real load conditions. An incorporation of real driving data instead of solely relying on standardized cycles has the potential of tailoring components to the target lead users and applications. While some operating conditions can be recorded by vehicle manufacturers, these are usually not accessible by third parties. In this paper, the authors present an innovative methodology of estimating vehicle parameters for the generation of representative driving profiles for implementation into a consecutive powertrain design process. The approach combines the measurement of real driving data with state estimation. The authors show that the presented methodology enables the generation of driving profiles with less than 25% deviation from the original data set.

1. Introduction

At nearly eight gigatonnes (Gt) of CO₂ in 2022, global mobility-related emissions represent a significant share of the 36.8 Gt total CO₂ emissions [1]. Road freight transport in particular makes up 1.8 Gt (22.5%) [2]. The electrification of commercial vehicles therefore offers promising opportunities to reduce both local and global CO₂ emissions. At the same time, it presents one of the greatest challenges for vehicle manufacturers, suppliers, and customers. Aspects such as range, charging speed, reliability, and durability are even more important in the commercial vehicle segment for economic operation than for passenger cars [3]. In order to design and optimize new electric heavy-duty vehicles to their specific requirements, new methods are required. Currently, the design of electric powertrains is mainly based on reference data and load collectives available internally to the vehicle manufacturers or standardized efficiency cycles, e.g., from the Vehicle Energy Consumption Calculation Tool (VECTO) [4], but less publicly available real driving data or derived requirements that can be shared openly. Application-specific powertrain design is inconceivable without representative driving profiles, as heavy-duty vehicles experience a wide range of different operation conditions, influencing load profiles, efficiency, and the lifetime of the powertrain components.

The challenges of electric powertrain design for heavy-duty vehicles are the subject of numerous research endeavors. While some approaches already exist, these use either standardized driving cycles [5,6], static performance requirements [7], measured or synthetic velocity profiles [8], or state-based driving cycles [9]. However, for application-specific holistic powertrain concept design, detailed information on the usage profile of a vehicle is required. Standardized driving cycles, such as the VECTO cycles, are intended for energy demand estimations for vehicle certification [4]. They offer a basis for comparison but lack usage-individual information as well as peak operation points for powertrain design. Static performance requirements, such as maximum velocity and different gradeabilities, are important for load-dependent powertrain component design. These are known from manufacturer experience [7] or need to be derived from measured data. As dynamic driving behavior has a relevant share in real load collectives, static information is not sufficient to be representative alone. State-based driving cycle generation, as presented in [9], delivers synthetic driving profiles based on statistical evaluation of real velocity profiles. However, additional load-relevant information, such as road gradient and vehicle mass, is required for representing the driving behavior of heavy-duty trucks. Therefore, an innovative methodology of generating representative driving profiles from real driving data, incorporating road gradient and estimated vehicle mass, as initially presented in [10], is developed for integration into holistic powertrain concept design.

2. General Methodology

In order to assist the process of powertrain electrification for heavy-duty trucks, a methodology of holistic powertrain concept design has been developed at the Institute for Automotive Engineering (ika) of RWTH Aachen University [11]. The full development process is shown in Figure 1. The additions presented within this paper (Figure 1, left) focus on the integration of real driving data to derive application-specific design requirements for the subsequent powertrain design and concept evaluation (Figure 1, right).

Within this methodology, the first step focuses on defining a conventional reference vehicle, which is to be electrified or substituted by a requirement-appropriate vehicle with an electric powertrain. From the reference vehicle, static base and application-dependent requirements are derived, and requirements specific to the vehicle type and segment are defined. The second step in the design process consists of collecting real driving data during normal operation. From the measured real driving data, the vehicle and driving states are estimated. From here, representative driving profiles are generated for the reference vehicle, which serve as a basis to derive load collectives for designing the electric powertrain components. With the derived requirements and load collectives, a modular holistic powertrain design process is carried out, resulting in viable powertrain concepts ready for longitudinal simulation and later prototypic assembly.

2.1. Measurement of Real Driving Data

For the measurements, a real reference vehicle and a target vehicle for the powertrain concept design are defined. The reference vehicle may be a single vehicle or part of a vehicle fleet whose operating behavior is to be recorded for a certain duration. The data logging phase depends on the diversity of the individual vehicle usage profile and is therefore not fixed. Within the data logging phase, the general operating behavior should be widely covered for the best possible design of the application-specific powertrain concepts. Since additional factors such as market and regulatory requirements are also taken into account in the later process of determining requirements and generating load spectra, incomplete coverage of the operation profile is uncritical.

The target vehicle can either be a digital twin of the reference vehicle for which an electric powertrain is to be designed or a not-yet-existing, theoretical concept. Alternatively, a different, existing, or theoretical target vehicle can be defined. In both cases, the parameters relevant for describing the longitudinal dynamic behavior are required. These are given in

Table 1. Parameters defining the reference vehicle.

Parameter	Symbol	Unit
Vehicle curb mass	mveh	kg
Aerodynamic drag coeff.	cd	/
Frontal area	A	m2
Rolling resistance coeff.	cr	/
Dynamic wheel radius	rdyn	m

.

Parameters such as the aerodynamic drag coefficient or rolling resistance coefficient are not constant under all conditions in real operation. For simplification and due to the minor influence of changes during operation compared to, for example, the variable payload mass, these parameters are assumed constant based on the reference vehicle.

The vehicle and driving behavior are measured during real operation for the subsequent powertrain concept design. Here, the assessment is reduced to longitudinal dynamic behavior, as the influences of lateral and vertical dynamics on the powertrain performance are assumed negligible. This allows the driving behavior to be approximated using the differential equation of motion from (1) and resistance forces from (2) to (4):

$$\ddot{x}={\displaystyle \frac{1}{{(m}_{veh}+m_{pl}+m_{rot})}}\cdot \left[{\displaystyle \frac{T_{wheel}}{r_{dyn}}}-\left(F_r+F_{cl}+F_{air}\right)\right],$$

(1)

$$F_r=c_r\cdot {(m}_{veh}+m_{pl})\cdot g\cdot cos(\alpha ),$$

(2)

$$F_{cl}={(m}_{veh}+m_{pl})\cdot g\cdot sin(\alpha ),$$

(3)

$$F_{air}={\displaystyle \frac{{\rho }_{air}}{2}}\cdot c_d\cdot A\cdot {\dot{x}}^2,$$

(4)

which represent the relation between acceleration $\ddot{x}$, drive torque at the wheel $T_{wheel}$ and driving resistances. Here, $m_{pl}$ is the payload mass, $m_{rot}$ the sum of equivalent rotational masses of the powertrain and $F_r$,$F_{cl}$, and $F_{air}$ are rolling resistance, climbing resistance and aerodynamic drag, respectively. The resistance forces are calculated with the gravitational acceleration constant $g$ ($g=9.81 \mathrm{m}{\mathrm{s}}^{-2}$), road gradient $\alpha$, vehicle velocity $\dot{x}$ and air density ${\rho }_{air}$, which is assumed constant at $\rho =1.2 \mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$. Wind speed is neglected for simplification.

While many parameters are already defined by the reference vehicle, the following remain to be measured or estimated: vehicle velocity, vehicle acceleration, payload mass, and road gradient. To describe a truck’s driving behavior adequately, using both measurement equipment for reading vehicle communication via the Controller Area Network (CAN) along with external sensors to measure environmental conditions is a suitable approach. For this, a dedicated data logger has been developed and built up at ika. A Raspberry Pi 4 forms the basis of the first prototype. It combines a USB-to-CAN interface with the sensors listed in

Table 2. Sensor list of the developed data logger.

Sensor	Product	Data Rate (Hz)
Air pressure	STMicro LPS25HB	25
Humidity and temperature	STMicro HTS221	12.5
Inertia (x-, y-, and z-axis)	STMicro LSM9DS1	up to 1000
GPS	DFRobot UBX-G7020-KT	10

.

The CAN interface is connected non-invasively with the on-board diagnosis (OBD) socket as well as the fleet management system (FMS) interface to request and read communication via the OBD II and SAE J1939 protocols [12]. From CAN communication, signals such as vehicle velocity and driver requested torque are recorded.

During vehicle operation and measurement, communication requests are sent at a rate of approximately 30 Hz while sensor data is logged at the sensors’ individual sample rate. Only the GPS receiver sends a position update at only 1 Hz, which is below its specified data rate. The given data rates of sensors and recorded CAN communication are sufficiently high resolution to describe the vehicle and driving status adequately.

2.2. Estimation of Vehicle and Driving States

In order to describe the vehicle and driving state adequately, vehicle velocity, vehicle acceleration, payload mass, and road gradient are required. While vehicle velocity can be measured directly, and acceleration can be derived accordingly, road gradient and payload mass have to be estimated instead.

2.2.1. Robust Road Gradient Estimation

Various approaches exist for approximating road gradient. The first considered approach matches the vehicle position history with digital elevation models, such as the Shuttle Radar Topography Mission (SRTM), as explained in [13]. Here, the absolute elevation is identified for the GPS position recording of the vehicle. The road gradient can be calculated from the determined elevation profile according to (5):

$$\tan \alpha ={\displaystyle \frac{dh}{ds}},$$

(5)

where $h$ is the determined elevation and $s$ is the driven distance. An alternative method involves calculating elevation directly using the international elevation formula, which is given in (6):

$$h={\displaystyle \frac{288.15K}{0.0065\frac{K}{m}}}\cdot \left(1-{\left({\displaystyle \frac{p\left(h\right)}{1013.25hPa}}\right)}^{{\displaystyle \frac{1}{5.255}}}\right),$$

(6)

where $p\left(h\right)$ is the height dependent air pressure. Road gradient is also calculated according to (5). Within a third method, road gradient can be calculated from the acceleration force measured by an inertia measurement unit (IMU), using (7):

$$\alpha =\arcsin \left({\displaystyle \frac{a_x-\ddot{x}}{g}}\right),$$

(7)

where $a_x$ is the acceleration measured by the IMU with the longitudinal vehicle acceleration $\ddot{x}$ being the derivative of vehicle velocity (cf. (1)). However, it was shown in [14] that the calculated gradient based on the acceleration approach deviates strongly from reality with the measurement equipment used so far. The differences can be explained by the difficult positioning of the sensor as well as filter sensitivity. Therefore, only the estimated gradients from the map matching approach and the barometric height formula are used for now. These approaches are fused in order to obtain a robust estimation. A weighting function was chosen to combine the height and gradient profiles of both approaches, which is given in (8):

$${\alpha }_{fused}={\displaystyle \frac{w_{\alpha ,GPS}\cdot {\alpha }_{GPS}+w_{\alpha ,baro}\cdot {\alpha }_{baro}}{w_{\alpha ,GPS}+w_{\alpha ,baro}}},$$

(8)

where ${\alpha }_{fused}$ is the fused gradient, $w_{\alpha ,GPS}$ and ${\alpha }_{GPS}$ are the weighting factor and gradient, respectively, of the map-matching results, while $w_{\alpha ,baro}$ and ${\alpha }_{baro}$ are the weighting factor and gradient, respectively, of the barometric approach. To calculate these weighting factors, potential influencing parameters were investigated. For the map matching approach, the horizontal and vertical accuracies could be identified, which provide a solid estimate of GPS quality. For the barometric approach, influences of temperature and wind were investigated, but no significant correlation could be proven. Due to the overall good quality of the barometric approach as shown in [15,16], a constant weighting factor of 0.7 is assumed for now, while the map matching approach receives a weighting factor between 0 and 1 based on a linear function of horizontal and vertical accuracy. An example of the current state of the developed road gradient fusion approach is shown in Figure 2 for a tunnel transit.

It can be seen from Figure 2 that the tunnel begins at approximately 1850 m of distance travelled, as the map matching weighting factor drops, while at the same time the height profiles diverge considerably. This behavior is attributed to the digital elevation model providing the absolute elevation of the terrain at a given GPS position, not necessarily the elevation of the road. In the case of this exemplary tunnel transit, a delta of up to 40 m exists results between the vehicle’s actual elevation and the estimated elevation from GPS results. Here, the dynamic weighting of the sensor fusion function dampens or eliminates inaccurate values originating from GPS from the fused height and road gradient profiles. However, the weighting sensitivity of the map matching approach shows further optimization potential and shall be revised with more available data.

2.2.2. Payload Mass Estimation

In addition to the road gradient, payload mass is also a decisive factor of the load profile for heavy-duty trucks. While truck curb weight is defined based on the vehicle specifications, payload mass may vary during operation. This is not necessarily monitored continuously. In some vehicles, the axle load is calculated, e.g., via the air pressure of the air suspension and provided directly via the FMS interface. However, not all vehicles are equipped with an FMS interface or air suspension. Alternatively, the total mass can be approximated with a model-based estimator. Here, vehicle mass, including payload mass, is calculated based on the equation of longitudinal motion as given in (1). To solve the equation, the rolling resistance and drag coefficients are set by the reference vehicle and assumed to remain constant during operation, as well as air density. Since the total vehicle mass can be assumed to be approximately constant over a driving segment, a method for determining a scalar value based on vectors of noisy measured values is required. Several methods can be used for this purpose. The following algorithms are considered for mass estimation: Least squares (LS), Recursive Least Squares (RLS), and the Levenberg–Marquardt algorithm (LM) [16,17,18].

The LS approach aims at a minimization of the estimation parameter through the sum of error squares. For this purpose, the normal form of the least squares method is constructed, which is given in (9):

$$\hat{\mathsf{\Theta }}={\left(H^{T}H\right)}^{-1}\cdot H^T\cdot y,$$

(9)

where $\hat{\mathsf{\Theta }}$ is the estimated parameter vector, $H$ is the regression vector, and $y$ is the measurement vector. For the estimation of mass only, the following conditions apply, as defined in (10):

$$\widehat{\mathsf{\Theta }}=m_{veh}+m_{pl},H=\ddot{x}+g\cdot \sin \left(\alpha \right)+c_r\cdot g\cdot \cos \left(\alpha \right),y={\displaystyle \frac{T_{wheel}}{r_{dyn}}}-{\displaystyle \frac{\rho }{2}}\cdot c_d\cdot A\cdot {\dot{x}}^2,$$

(10)

The RLS algorithm is an online parameter estimation method. Unlike the LS, the RLS updates its estimates recursively, as new data becomes available, making it suitable for real-time applications as well as dynamically changing behavior. The recursive form is given in (11):

$$\widehat{\mathsf{\Theta }}\left[k\right]=\widehat{\mathsf{\Theta }}\left[k-1\right]+K\left[k\right]\cdot (y\left[k\right]-H^T\left[k\right]\cdot \widehat{\mathsf{\Theta }}\left[k-1\right]),$$

(11)

where $k$ is the time step, $\widehat{\mathsf{\Theta }}\left[k\right]$ is the new estimation, $\widehat{\mathsf{\Theta }}\left[k-1\right]$ is the previous estimation, $K\left[k\right]$ is the gain vector, and $y\left[k\right]$ is the new measurement data. The gain vector is calculated according to (12):

$$K\left[k\right]=P\left[k-1\right]\cdot H\left(k\right)\cdot {\left(\lambda +H^T\left[k\right]\cdot P\left[k-1\right]\cdot H\left[k\right]\right)}^{-1},$$

(12)

where $P\left[k-1\right]$ is the covariance matrix from the previous time step and $\lambda$ is the forgetting factor. The forgetting factor ($0<\lambda \le 1$) controls how quickly previous data is forgotten. Here, $\lambda =1$ weighs all data equally, while lower values of $\lambda$ gradually discount previous data in the weighting. The covariance matrix is calculated as of (13):

$$P\left[k\right]={\displaystyle \frac{1}{\lambda }}(P\left[k-1\right]-K\left[k\right]\cdot H^T\left[k\right]\cdot P\left[k-1\right]),$$

(13)

The LM algorithm extends the RLS to handle non-linear least squares problems by incorporating a damping factor and using the Jacobian matrix for gradient-based updates. The formula for the regularized covariance matrix is given in (14):

$$P_{reg}\left[k\right]={\displaystyle \frac{1}{\lambda }}\left(P\left[k-1\right]-K\left[k\right]\cdot H^T\left[k\right]\cdot P\left[k-1\right]\right)+\mu \cdot I,$$

(14)

where $\mu$ is the added dampening factor and $I$ is the identity matrix, ensuring numerical stability by preventing the covariance matrix from becoming singular.

As road gradient, the estimated and fused road gradient is used, and for simplification, the equivalent rotational mass is neglected in all approaches. Additionally, the following constraints from [19] are applied for filtering the measured data:

• Vehicle is in operation and velocity is above 5.5 m/s;
• Acceleration is above 0.1 m/s²;
• Motor torque is above 500 Nm.

These constraints filter out non-dynamic and low load driving segments from the measured data, as the algorithms require some dynamic behavior for reliable operation. In Figure 3, a comparison of the different mass estimation algorithms is displayed. Here, the mass is estimated for a simulated constant driving situation, where noise is applied to the output signals at 16 s.

The comparison shows the lack of stability of the LS when the driving status changes and due to noise caused by e.g., measurement inaccuracies. It therefore does not provide a sufficient basis to be further considered as an algorithm for mass estimation. Both RLS and LM indicate close matching with the real vehicle mass. However, the LM algorithm demonstrates a marginally faster convergence to the real value than the RLS while also not being influenced by the applied noise. Therefore, the LM algorithm is chosen for the mass estimation in the following steps.

2.3. Generation of Driving Profiles and Load Collectives

According to [20], the basic principle of driving profile generation follows three steps:

• Recording driving data during normal real-world operation,
• Analyzing the recorded data to describe or characterize the driving conditions,
• Develop representative driving cycles for the recorded conditions.

The first two steps are fulfilled with the measurements and the estimations of mass and road gradient distribution. Various methods exist for generating driving profiles, which can be categorized into deterministic and stochastic approaches [21]. Driving cycle generation methods, which operate deterministically, show the same results when repeated with unchanged input data. In contrast, stochastically generated cycles vary despite identical input data. However, statistical characteristics, such as the distribution of velocities and accelerations, are identical or very similar for all stochastic cycles.

A stochastic method is chosen to synthesize and consequently generalize driving profiles representing the longitudinal characteristics from the measured driving data. For this purpose, a Markov chain-Monte Carlo (MCMC) technique is utilized, which is based on the methodology presented by [22]. Using 2D Markov chains, the state and transition probabilities of $\dot{x}$, $\alpha ,$ and $m_{pl}$ are determined from the measured data. Therefore, each state combines a synthesized velocity, gradient, and payload mass class with a probability for the state in the next time step. To apply this 2D method in three dimensions, the gradient and payload mass classes are combined into one class, increasing its size substantially but not increasing matrix dimensions. Synthesizing velocity and gradient through 2D Markov chains takes into account their interdependencies, allowing unrealistic driving behavior, such as increasing velocity with increasing gradient or changing gradients during a standstill, to be eliminated in advance. The Monte Carlo sampling method is based on a Poisson distribution created from the measured driving data. Here, repeated random sampling allows for the generation of new samples, functioning as a random number generator. A sample is selected in each time step over a predefined length of the final driving profile. After each selection, the probability matrices are updated, which improves the resulting cycle, as the distribution characteristics asymptotically approach the original distributions if the timespan is set long enough. However, the cycle length is chosen to be relatively short for later longitudinal dynamics simulations and is far shorter than the length of the original data. Therefore, the asymptotic behavior is only utilized to a limited extent. Another issue with the high divergence of the time lengths in this stochastic method is the large scatter of the resulting cycles regarding their characteristics. For this reason, the maximum deviations from the original characteristics are limited by the following criteria:

• Deviation of mean, standard, and maximum velocity ≤ 10%,
• Deviation of mean, standard, minimum, and maximum gradient ≤ 15%,
• Deviation of mean, standard, minimum, and maximum acceleration ≤ 15%.

These boundary conditions limit the amount of synthesized cycles but still allow for several valid results. An evaluation function, which is given in (15), is implemented to select the result that represents the original data best from the generated cycles:

$$w_{cycle}={\displaystyle \frac{1}{n_{crit}}}{\sum }_{i=1}^{n_{crit}}{\displaystyle \frac{{\sigma }_i}{{\sigma }_{i,max}}}\in [0,1],$$

(15)

where $n_{crit}$ is the number of deviation criteria, ${\sigma }_i$ is the resulting deviation per criterion, and ${\sigma }_{i,max}$ is the allowed maximum deviation per criterion. The generated cycle with the lowest evaluation coefficient $w_{cycle}$ and therefore the smallest total deviation from the measured data set is selected from the generated results.

Representing the most fitting driving profile, the selected cycle provides not only an additional source for application-specific load points but also their distribution, relevant for the derivation of load collectives for the reference vehicle. In a first step, these are calculated statically at the wheel, as the powertrain topology is unknown at this stage of development. The load collectives provide an indication of frequent operating points, to which the individual powertrain components are subsequently to be designed in terms of safety, lifetime, and efficiency.

2.4. Powertrain Concept Design and Vehicle Simulation

Based on the generated driving profiles and the reference vehicle parameters, powertrain concepts can be designed. To accomplish this task, a modular, holistic concept design methodology for electric powertrains has been developed at ika, as presented in [23,24]. This design method comprises the definition of requirements, the individual design of the components (electric machine, inverter, and transmission), and concludes with the validation of prototypes on test benches. The method is specifically designed for electric powertrain design. Its modularity allows for systematic development from scratch as well as targeted component optimization. The primary goals, similar to the metaheuristic algorithms that form the basis of the design method, are a substantial reduction in development time and costs by automatically synthesizing and evaluating powertrain concepts to determine those for further investigation early in the process.

To assess energy demands during operation, a longitudinal dynamics model of the truck is simulated. The architecture of the forward calculating model implemented in MATLAB/Simulink is shown in Figure 4.

Contrary to simulations for passenger vehicles, cycle data for trucks are typically given as a function of distance. For this reason, an additional signal resembling the stop time for standstill is necessary. Furthermore, the driver cannot be represented by a PI controller alone to follow the demanded velocity signal. Therefore, the driver model includes distinctive states, e.g., standstill, to account for the requirements resulting from the aforementioned cycle properties. A state machine is implemented to manage the transitions in between these states. Interfaces to the HV architecture are included to connect the on-board charger (OBC) and an electric power take off (ePTO) to supply power (e.g., for a refrigerated body) or for dynamic charging (e.g., with a pantograph).

3. Results

The current state of development of the methodology presented was exemplarily demonstrated to provide conclusions on the plausibility of the processes. For this purpose, a DAF XD 450 FAN (model year 2023) was defined as the reference vehicle. The characteristic properties of the vehicle, such as aerodynamic drag and rolling resistance coefficient, were provided by the manufacturer within the project. The vehicle was equipped with the prototypic data logger, and a short test drive was conducted, which is displayed in Figure 5.

The minimum velocity is 0 km/h, while the maximum velocity is 76 km/h. The average velocity is 34.09 km/h, with a standard deviation of 14.18 km/h. The high standard deviation can be attributed to the dynamic velocity of the driving segment. This is an advantage for the mass estimation, as described before. The height profile shown in Figure 5 is the integration of the robust gradient estimation. For mass estimation, the LM algorithm is parametrized with a forgetting factor $\lambda$ of 0.9985 and an initial mass value of 8818.8 kg, which equals the unladen mass of the truck. The comparison of estimated mass from the vehicle, the LM algorithm, as well as the real mass is displayed in Figure 6.

The real total vehicle mass was measured before the test drive at 22,007.4 kg. It can be observed that the algorithm is unstable until it has received sufficient usable data points for estimation. The mass is estimated close to the real measured value for several hundred seconds, but drifts off around 700 s into the data set. This behavior can be attributed to the lower dynamics and therefore lower load and torque values in the later segment of the data set, which is not beneficial for the estimation. Overall, the mass estimation using the LM algorithm shows a closer approximation to the real vehicle mass than the vehicle’s own estimation read from the CAN bus. Therefore, the estimated mass is used for further cycle generation while still showing potential for further optimization.

With the given velocity, gradient, and mass profile, the cycle generation process according to chapter 2.3 is performed. Here, a workstation featuring an Intel^® Core™ i9-12900 processor and 128 GB random access memory is used, and the algorithms are implemented in MATLAB. The resulting cycle is shown in Figure 7.

The generated cycle fulfills the boundary conditions set in chapter 2.3 for velocity, gradient, and acceleration. The generated mass profile deviates more significantly from the input mass profile, especially regarding the standard deviation criterion, mainly due to the high selected step size of 1000 kg. This step size was chosen due to current computational limitations, predominantly limited memory, and will be re-evaluated in the future. The generated cycle is rated with an evaluation score of 1.39 (cf. (14)), meaning that it deviates on average over all evaluation criteria at the same weighting by 39%. This again can be mainly attributed to the high deviation in mass, especially its standard deviation and minimum value evaluation. Removing the mass-related evaluation criteria from the total evaluation score results in a remaining deviation of 24.51%.

4. Discussion and Outlook

Within this paper, the authors have presented a novel approach to measured data-based generation of representative driving profiles for heavy-duty trucks, considering the velocity, gradient, and mass profiles. With a prototypic data logger, relevant vehicle, and environmental data to describe vehicle operation was measured. From the measured data, next to vehicle velocity, gradient and mass over time were individually estimated. With the dataset consisting of directly measured and estimated vehicle parameters, driving cycles are generated using 2D Markov chains. First results have proven the methodology plausible while at the same time pointing out further optimization potentials. While the estimation of road gradient from barometric data and a GPS-matched elevation model delivers reliable results, the estimation of vehicle mass using the Levenberg–Marquardt algorithm as a state estimator deviates from the real measured values. Here, further investigations within a parameter study for the filter criteria as well as the state estimator settings are required. With a closer estimation of the vehicle mass, load collectives for the powertrain components can be derived, and powertrain concept design can be performed. Further optimization of the estimation algorithms is required to identify positive effects on the powertrain development process in terms of development time and costs.