In simple optimization problem, direct searching methods are most accurate and practical enough. However, for more complicated problem which contains many design variables and demands high computational costs, surrogate model methods are recommendable instead of direct searching methods. In this case, surrogate models should have reliability for not only accuracy of the optimum value but also globalness of the solution. In this paper, the Kriging method was used to construct surrogate model for finding aerodynamically improved three dimensional single stage turbine. At first, nozzle was optimized coupled with base rotor blade. And then rotor was optimized with the optimized nozzle vane in order. Kriging method is well known for its good describability of nonlinear design space. For this reason, Kriging method is appropriate for describing the turbine design space, which has complicated physical phenomena and demands many design variables for finding optimum three dimensional blade shapes. To construct airfoil shape, Prichard topology was used. The blade was divided into 3 sections and each section has 9 design variables. Considering computational cost, some design variables were picked up by using sensitivity analysis. For selecting experimental point, D-optimal method, which scatters each experimental points to have maximum dispersion, was used. Model validation was done by comparing estimated values of random points by Kriging model with evaluated values by computation. The constructed surrogate model was refined repeatedly until it reaches convergence criteria, by supplying additional experimental points. When the surrogate model satisfies the reliability condition and developed enough, finding optimum point and its validation was followed by. If any variable was located on the boundary of design space, the design space was shifted in order to avoid the boundary of the design space. This process was also repeated until finding appropriate design space. As a result, the optimized design has more complicated blade shapes than that of the baseline design but has higher aerodynamic efficiency than the baseline turbine stage.

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