## 1 **Introduction**
### HiL-Based Virtual Calibration and Validation  
The majority of the current HiL systems focus on functional hardware and software testing [27; 28]. The main aim of the investigations and analyses presented in this work is to broaden this conventional scope with the incorporation of virtual engine control unit (ECU) calibration. This is achieved by the extension of a conventional HiL platform to a closed-loop system simulation of the complete powertrain, as already described in several studies. A considerable number of HiL-based virtual calibration applications for light-duty vehicles in the field of diesel emission calibration have already been presented by [PERSON] et al. [29; 30; 31; 32] and [PERSON] et al. [33]. HiL-based applications for heavy-duty diesel engines are discussed by [PERSON] et al. [34]. For petrol engines, initial studies on HiL and driving cycle-based emission calibration have already been carried out by [PERSON] et al. [35], [PERSON] [36] and [PERSON] et al. [37]. A study on HiL-based driveability calibration and validation was conducted by [PERSON] et al. [38].  
A closed-loop HiL system allows coupling of various control units--e.g., the ECU and Transmission Control Unit (TCU)--with real-time capable models for the simulation of a complete powertrain. Due to stringent real-time requirements of the respective powertrain models [39], the trade-off between model accuracy and computing time needs to be carefully balanced [40]. This is especially challenging when modelling complex physical phenomena, such as engine raw emissions and emission conversion mechanisms inside a TWC. Real-time simulation approaches for modelling these mechanisms and their application for HiL-based virtual calibration are currently being researched. [PERSON] [41] and [PERSON] et al. [42] published approaches for the real-time simulation of engine-out emissions from a gasoline engine based on neural networks, whereby [PERSON] achieved a relative deviation of <5% for all EU6d-relevant emissions components in WLTC operation.  
[PERSON] et al. developed a real-time simulation approach for engine-out emissions from a diesel engine, taking into consideration the detailed chemistry of the emission formation [43]. Real-time capable simulation models for the exhaust gas aftertreatment system are presented, for example, by [PERSON] [44; 45] (KNN-based approach) and [PERSON] [46] and [PERSON] [47] (control-oriented models).  
To reap the efficiency benefits associated with HiL-based virtualization, it is essential to accompany the powertrain development process with a seamless integration of virtual processes. [PERSON] et al. [35] divide the HiL support during the powertrain development process into two major phases: While \"HiL stage #1\" facilitates support of calibration tasks in the scope of base calibration at the engine dynamometer test bench (as, e.g., described by [PERSON] [48]), \"HiL stage #2\" enables drive cycle-based calibration including tailored emission simulation for the target powertrain [35; 49]. The feasibility study presented in this paper is carried out during \"HiL stage #2\". To enable HiL stage #2, a real ECU with a high maturity dataset regarding its base calibration, as well as a prototype vehicle for validation purposes, should be available. In addition, a significant amount of steady-state and dynamic measurement data should be on hand for parameterization of the respective dynamic emission and TWC models.