## 4 Review of Current Methodologies against the Background of Calibration Challenges
### Synthetically Designed Cycles Based on (Regionally) Relevant Driving Behavior
Using measurement data with real emissions allows flexibly changing the target of the investigation without the requirement of adjusting existing or building new models for the emission formation. Due to this, a big advantage is provided toward the potential implementation of new exhaust gas components. The demand for usage-relevant test cycles is covered by the approach of statistical analysis of the collected data. On the one hand, a huge amount of data (e.g., robustness measurements and fleet data) is used for the calculation of probability distributions and targets for reference values describing the overall dynamics and power demands, such as v-a\({}_{\text{pos95}}\), RPA or DrCE (distance related cycle energy) [82]. These can be used for the rating of how relevant a certain drive profile is in the general context of real-world usage of the vehicle and the decision of which targets shall be applied for a new test cycle. On the other hand, the signal traces are analyzed for similarity with the detected critical events [65], using a dynamic time warping approach [108]. By explicitly searching for similar signal patterns of all critical events in the complete amount of available real-world driving data, the statistical relevance of each event can be evaluated. Applying the methodology to hybrid vehicles requires only small adjustments. While the derivation of statistical distributions remains untouched, it may be extended by additional characteristic values. These may include e.g., the duration or distance of operation with an active or inactive internal combustion engine. Comparing the traces of signals for the identification of most relevant events remains unchanged. The set of features used for the comparison can be either supplemented or replaced by relevant signals for hybrid operation. The knowledge about relevance of specific measurement data and driving styles allows shifting the focus from \"worst-case\" driving cycles that do not necessarily reflect a realistic behavior on public roads to a critical \"most relevant\" cycle. Here, the critical sequences are combined with their appearance under normal use conditions, leading  
Figure 8: Schematic overview of the process for statistically supported RDE test cycle generation. to a cycle that is not only relevant with respect to key values describing the totality of the profile, but also relevant regarding the local traces. Using a cost function, control inputs (Figure 8 \"Required Inputs\") can be applied to weight between the potential targets of the critical pollutant species, the intensity and statistical relevance of the emission events to be used, the overall driving dynamics and the characteristics to be achieved. Distances and distance shares can be explicitly specified with respect to the final definition of the legislation. For the application on hybrid use-cases, additional information of e.g., statistically representative durations and distances with and without use of the internal combustion engine or typical load distributions can be considered within the cost function as well. The reproduction of such inputs although requires supplementary algorithms and models. With additional degrees of freedom or hybrid powertrain, a detailed system prediction will become necessary to achieve the desired operation behavior on the chassis dynamometer or test bench. The extension of the approach is currently being developed and will be described in [109]. For the actual generation of the cycle (Figure 8 \"Event Combination\"), adjustments of simplified models are carried out based on the use case and the input data. Basic models for the engine map and transmission are required to support the acceleration profile generation and ensuring a drivable speed profile for the individual vehicle. The previously selected events are placed in the cycle considering the input values for distance shares and speed targets and are connected by synthetically generated parts.