## 3 Results--HiL-Based Calibration and Validation of TWC and HEGO Diagnoses
### Phase #2--Diagnostic Run with an Not OK System  
Referring to Figure 4a, the quality of simulation of the signals relevant for the release conditions have already been presented in Figure 5, since for a noK system they do not differ from an OK system significantly for the considered case example.  
For the diagnostic run (Figure 4b), however, the modelling environment should be able to simulate the failure patterns that correspond to the respective diagnoses. In Figure 8, the diagnostic run of the parallelization is shown for an aged TWC. To simulate the failure pattern of an aged TWC, the parametrization of the TWC model is changed accordingly. The oxygen de- and adsorption rates and the respective OSC map are fitted to those of an aged TWC. Also, the system behavior using an aged TWC model is in line with that of a corresponding vehicle measurement.  
Figure 9 shows the parallelization for a noK HEGO sensor. To simulate the failure pattern of a latent HEGO sensor signal in the direction from rich to lean, the HEGO sensor voltage is PT1 filtered on model side (with a time constant of 800 ms) and matches the rich to lean behavior of a noK HEGO sensor from a vehicle measurement quite well.  
Beyond the correct reproduction of the diagnostic run of a noK system in one engine operating point, Figure 7 shows that the OSC and HEGO latency results for the respective system exhibit reproducible diagnostic results over the entire operating range (ref. Figure 4c). The diagnostic results obtained in the HiL simulation are in the same order of magnitude as those compared to vehicle measurements over the entire operating range.  
Figure 7: Comparison of mappings performed on the HiL and on the vehicle—OSC (**a**) and HEGO latency (**b**) results over the entire relevant exhaust gas mass flow range for an OK and a noK system for both TWC and HEGO sensors.  
By simulating the respective fault patterns accordingly, the so-called fault paths in the ECU can be validated. It depends on the legislation, according to which prerequisites a fault is stored in the fault code memory of the ECU and whether the malfunction indicator light (MIL) is activated. Figure 10 shows six consecutive HiL simulations of WLTC driving cycles. Cycles 1-3 are executed with an aged TWC model (nOK system). Cycles 4-6 are executed with a stabilized TWC model (OK system). In cycle 7, only the engine start is executed (stabilized TWC). For the example shown in Figure 10, the MIL is activated when a nOK system is detected for the third time in a row (MIL phase). The status check of the diagnosis changes within one driving cycle as soon as the diagnostic has run through successfully and a diagnostic result is available. After MIL activation, a virtual TWC change is performed, followed by a healing phase of three consecutive WLTC driving cycles. In Figure 10, the healing phase is completed when an OK system is detected three times in  
Figure 8: Comparison of HiL and chassis dynamometer measurement—Diagnostic run of the parallelization for a nOK system with an aged TWC at \(\hat{m}_{Exh}=90\frac{kg}{h}\) and \(T_{TWC}=700\) \({}^{\circ}\)C.  
Figure 9: Comparison of HiL and chassis dynamometer measurement—Diagnostic run of the parallelization for a nOK system with an aged HEGO sensor at \(\hat{m}_{Exh}=90\frac{kg}{h}\) and \(T_{TWC}=700\) \({}^{\circ}\)C.  
succession. Then, the MIL is deactivated at the beginning of the fourth cycle. For this example, MIL activation after three consecutive failure detections and MIL deactivation after three successful healing cycles is according to the respective EU6d legislation. The example described demonstrates the feasibility of enabling fault path testing on a HIL platform, including fault entry (MILing) and fault healing, in compliance with legislation.