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Over the last decade or so, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. The fact that the origins of these techniques can be traced back to notions of belief propagation in the statistical physics literature lends a certain mystique to the area for many statisticians. Our goal in this work is to present the main ideas of AMP from a statistical perspective, to illustrate the power and flexibility of the AMP framework. Along the way, we strengthen and unify many of the results in the existing literature.

The development of combustion engines is heavily influenced by environmental regulations and efficiency. Since the environmental regulation have influenced engine design already with special combustion system and exhaust gas treatments, efficiency and the greenhouse gas CO2 has become a major issue for further development. CO2 emissions and fuel efficiency are linked and are directly influenced by the internal friction of the combustion engine. One major part of this internal friction is coming from the crank train bearings. Since we have to consider different operating conditions for the crank train bearings like hydrodynamic and mixed friction (hydrodynamic in combination with boundary contact), working principles as well as different engine operating conditions like full load, idle, start stop etc. different measures need to be employed for a friction reduced crank train. The optimal dimensioning of the bearings in combination with oil viscosity reduction are already known to a certain extent. Nevertheless they result in changes of bearing loads and may in consequence increase the share of boundary friction. Therefore, only looking on these two optimization steps is not enough. In addition the friction coefficient between bearing and shaft as well as the interaction between bearing surface and lubricant need to be addressed to reduce friction loss. In order to gain a complete picture, influences and the interaction of • geometric properties and bearing dimensions, • friction coefficient of bearings in combination with crankshaft materials, • oil formulation, viscosity and their interaction with engine application and duty cycle as well as • losses caused by the lubrication system design and components are investigated and analyzed based on simulation and testing. At first the different steps are investigated individually and secondly combinations and interactions are derived on basis of parameters derived on tribological tests and material data. Oil viscosity as major driver during hydrodynamic operation but also the influence of additive packages during mixed friction is roughly estimated on basis of tribological investigations. Since the overall friction system and its optimization are very complex, an example for a truck engine in different applications shows advantages and disadvantages of the different approaches. Also border lines given by operational risk and improvement limits are explained. The improvement options given by bearing materials and special coatings are explained in combination with different engines and engine applications. Further development activities, ways of collaboration between engine manufacturer and bearing supplier and an outlook on up-coming bearing system are completing the picture for a holistic approach on friction reduction in crank train bearings.