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Modern turbo-charged downsized engines reach high values of specific power, causing a significant increase of the exhaust gas temperature. Such parameter plays a key role in the overall powertrain environmental impact because it strongly affects both the catalyst efficiency and the turbine durability. In fact, common techniques to properly manage the turbine inlet gas temperature are based on mixture enrichment, which causes both a steep increase in specific fuel consumption and a decrease of catalyst efficiency. At the test bench, exhaust gas temperature is typically measured using thermocouples that are not available for on-board application, and such information is processed to calibrate open-loop look-up-tables. A real-time, reliable, and accurate exhaust temperature model would then represent a strategic tool for improving the performance of the engine control system.

Knock is a non-deterministic phenomenon and its intensity is typically defined by a non-symmetrical distribution, under fixed operating conditions. A statistical approach is therefore the correct way to study knock features. Typically, intrinsically deterministic knock models need to artificially introduce Cycle-to-Cycle Variation (CCV) of relevant combustion parameters, or of cycle initial conditions, to generate different knock intensity values for a given operating condition. Their output is limited to the percentage of knocking cycles, once the user imposes an arbitrary knock intensity threshold to define the correlation between the number of knocking events and the Spark Advance (SA). In the first part of the paper, a statistical analysis of knock intensity is carried out: for different values of SA, the probability distributions of an experimental Knock Index (KI) are self-compared, and the characteristics of some percentiles are highlighted.