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Metamodel Development Based on a Nonparametric Isotropic Covariance Estimator and Application in a V6 Engine
ISSN: 0148-7191, e-ISSN: 2688-3627
Published March 08, 2004 by SAE International in United States
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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.
CitationWang, J., Vlahopoulos, N., and Gorsich, D., "Metamodel Development Based on a Nonparametric Isotropic Covariance Estimator and Application in a V6 Engine," SAE Technical Paper 2004-01-1142, 2004, https://doi.org/10.4271/2004-01-1142.
Reliability and Robust Design in Automotive Engineering
Number: SP-1844 ; Published: 2004-03-08
Number: SP-1844 ; Published: 2004-03-08
- Bochner, S., “Harmonic Analysis and the Theory of Probability”, University of California Press, Los Angeles, (1955).
- Cheng B. and Titterington D. M., “Neural Networks: A Review from a Statistical Perspective”, Statistical Science, Vol.9, n1, pp. 2-54, (1994).
- Craven, P., Wabba, G., “Smoothing Noisy Data with Spline Functions: Estimating the Correct Degree of Smoothing by the Methods of Generating Cross-Validation”, Numerical Mathematics, Vol.31, pp. 377-403, (1978).
- Cressie, N., “Spatial Prediction and Ordinary Kriging”, Mathematical Geology, Vol.20, n4, pp. 405-421, (1988).
- Cressie, N., “Statistics for Spatial Data”, john Wiley & Sons, New York, (1993).
- Currin, C., Mitchell, T., Morris, M., and Ylvisaker, D., “A Bayesian Approach to the Design and Analysis of Computer Experiments,” ORNL Technical Report 6498, available from the National Technical Information Service, Springfield, VA, 22161, (1988).
- Dyn, N., Levin, D., and Rippa, S., “Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions”, SIAM Journal of Scientific and Statistical Computing, Vol.7, n2, pp. 639-659, (1986).
- Ebrat, O., “Detailed Main Bearing Hydrodynamic Characteristics for Crankshaft-Block Dynamic Interaction in Internal Combustion Engines”, Ph.D. Thesis, The University of Michigan, (2002).
- Ebrat, O., Mourelatos, Z.P., Hu, K., Vlahopoulos, N., and Vaidyanathan, K., “Structural Vibration of an Engine Block and a Rotating Crankshaft Coupled Through Elastohydrodynamics Bearings,” SAE, 03NVC-145, (2003).
- Ellacott, S.W., Mason, J.C., and Anderson, I.J., “Mathematics of Neural Networks: Models, Algorithms, and Applications”, Kluver Academic Publishers, Boston, MA, (1997).
- Gorsich, D.J. and Genton, M.G., “On the Discretization of Nonparametric Isotropic Covariogram Estimator”, (2003).
- Hajela, P. and Berke, L., “Neural Networks in Structural Analysis and Design: An Overview”, 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, Cleveland, OH, AIAA 2, pp 901-914, AIAA-92-4805-CP, (1993).
- Hu, K., Mourelatos, Z., and Vlahopoulos, N., “A Finite Element Formulation for the Coupling Rigid and Flexible Body Dynamics of Rotating Beams”, Journal of Sound and Vibration, Vol.253, n3, pp. 603-630, (2002).
- Hu, K., “A Finite Element Formulation for Coupled Rigid and Flexible Dynamic Analysis of an Internal Combustion Engine Crankshaft System”, Ph.D. Thesis, The University of Michigan, (2002).
- Iman, R.L., and Conover, W.J., “Small Sampling Sensitivity Analysis Techniques for Computer Models, With an Application to Risk Assessment” (with discussion), Communications in Statistics, Part A-Theory and Methods, Vol.9, pp. 1749-1874, (1980).
- Jansen, M., Maifait, M., and Bultheel, A., “Generalized Cross Validation for Wavelet Thresholding,” Signal Processing, Elsevier, n56, pp. 33-44, (1996).
- Johnson, J., Moore, L., and Ylvisaker, D., “Minimum and Maximum Distance Designs”, J. Statist. Plann. Inference, Vol.2, pp. 131-148, (1990).
- McKay, T., Beckman, R., Conover, W., “A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, pp. 239-246, (1979).
- Morris, M., Mitchell, T., “Exploratory Design for Computer Experiments”, J. Statist. Plann. Inference, Vol.43, pp. 381-402, (1995).
- Park, J.-S., “Optimal Latin-Hypercube Designs for Computer Experiments”, J. Statist. Plann. Inference, Vol.39, pp. 95-111, (1994).
- Rumelhart, D. E., Widrow, B. and Lehr, M. A., “The Basic Ideas in Neural Networks”, Communications of the ACM, Vol.37, n3, pp. 87-92, (1994).
- Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P., “Design and Analysis of Computer Experiments”, Statistical Science, Vol.4, n4, pp.409-435,(1989)(a).
- Sacks, J., Welch, W.J., and Schiller, S.B., “Designs for Computer Experiments”, Technometrics, Vol.31, n1, pp.41-47,(1989)(b).
- Shewy, M., Wynn, H., “Maximum Entropy Design”, Journal of Applied Statistics, Vol.14, n2, pp. 165-170, (1987).
- Stein, M., “Large Sample Properties of Simulation Using Latin Hypercube Sampling”, Technometrics, Vol.29, pp.143-151, (1987).
- Wang, J., “Probabilistic and Sensitivity Analyses for the Performance Characteristics of Engine Bearings due to Variability in Bearing Properties”, Ph.D. Thesis, The University of Michigan, (2003).
- Yaglom, A.M., “Some classes of random fields in n-dimensional space, related to stationary random processes”, Theory of Probability and its Application, Vol.2, pp.273-320, (1957).
- Ye, K.Q., Li, W., and Sudjianto, A., “Algorithm Construction of Optimal Symmetric Latin Hypercube Designs”, Journal of Statistical Planning and Inference, Vol.90, pp.145-159, (2000).