Metamodel Development Based on a Nonparametric Isotropic Covariance Estimator and Application in a V6 Engine

This paper presents the utilization of alternative correlation functions in the Kriging method for generating surrogate models (metamodels) for the performance of the bearings in an internal combustion engine. Originally, in the Kriging method an anisotropic exponential covariance function is developed by selecting optimal correlation parameters through optimization. In this paper an alternative nonparametric isotropic covariance approach is employed instead for generating the correlation functions. In this manner the covariance for spatial data is evaluated in a more straightforward manner. The metamodels are developed based on results from a simulation solver computed at a limited number of sample points, which sample the design space. An integrated system-level engine simulation model, consisting of a flexible crankshaft dynamics model and a flexible engine block model connected by a detailed hydrodynamic lubrication model, is employed in this paper for generating information necessary to construct the metamodels. For both metamodels an optimal symmetric latin hypercube algorithm is utilized for identifying the sampling points based on the number and the range of the variables that are considered to vary in the design space. The initial clearance between the crankshaft and the bearing at each main bearing, and the oil viscosity comprise the varying parameters. The maximum oil pressure and the percentage of time (the time ratio) within each cycle that a bearing operates with oil film thickness less than a user defined threshold value constitute the performance variables of the system. Results from the two types of metamodels are compared with the results from the actual solver for a large number of evaluation points.