## 1 **Introduction**
### Case Example--Technical Fundamentals  
In order to evaluate the transferability of OBD engineering tasks from a vehicle to a HiL platform, this study presents a case example that includes the diagnoses for monitoring the status of the TWC and the oxygen sensor downstream TWC (Heated Exhaust Gas Oxygen-sensor, HEGO) in the EATS.  
The diagnoses of the corresponding components take place during an active rich/lean adjustment of the fuel-air mixture that is triggered by the ECU. Due to the active adjustment of the air-fuel mixture and the subsequent loading and unloading of the oxygen storage of the TWC, the so-called parallelization influences the tailpipe emission results during drive cycle operation. The target of the parallelization is to combine diagnoses that use the same active adjustment of the air-fuel mixture event. With this measure, the total diagnosis time and thus the emission influence is lowered.  
The task of the TWC diagnosis is to give a statement about the ageing status and, therefore, the emission conversion capability of the component. This is achieved by determining the oxygen storage capacity (OSC) of the TWC. The OSC is calculated by the ECU according to Equation (1) [50].  
\[OSC=\dot{m}_{Exh}\cdot(\lambda-1)\cdot\!0.23\cdot\Delta t \tag{1}\]  
where \(\dot{m}_{Exh}\) represents the exhaust gas mass flow, \(\lambda\) the air-fuel ratio upstream TWC and \(\Delta t\) the time of the lean event of the parallelization. The value 0.23 represents a fixed value for the mass ratio of oxygen in the exhaust gas.  
The task of the HEGO sensor diagnosis is to give a statement about the response behavior of the HEGO sensor voltage \(U_{HEGO}\). A dynamically slow HEGO sensor can lead to falsified OSC results and to prolonged rich and lean phases during the parallelization event that is negatively impacting tailpipe emissions. The dynamic behavior, or the so-called latency, of the HEGO sensor voltage \(\tau_{HEGO,lat}\) is represented as a PT1 behavior and determined as well as quantified by the ECU using Equation (2). A high latency value corresponds to a slow and, therefore, faulty sensor.  
\[\tau_{HEGO,lat}=\Delta t\cdot\frac{U_{HEGO,ref}-U_{HEGO,1}}{U_{HEGO,2}-U_{HEGO,1}} \tag{2}\]  
In Equation (2), \(U_{HEGO,ref}\) represents a fixed reference value indicating the corresponding sensor voltage that determines the start and the end of the transition time check lean-rich (or rich-lean, depending on the case). Furthermore, \(U_{HEGO,1}\) represents the HEGOvoltage at the start of the calculation and \(U_{HEGO,2}\) the HEGO voltage at the end of the calculation. \(\Delta t\) is the time between \(U_{HEGO,1}\) and \(U_{HEGO,2}\).  
Figure 1 provides an overview of the typical signal profile of the relevant sensor signals for a parallelization event both for so-called OK systems--considering a new catalyst and new oxygen sensors--and so-called not OK (nOK) systems--considering an aged TWC as well as an aged HEGO sensor.  
The typical \(\lambda\)-signal profile upstream TWC is displayed in the UEGO (universal exhaust gas oxygen) sensor diagram; the HEGO sensor voltage downstream TWC is displayed in the HEGO sensor diagram.