Development of a deviation package method for low-cost robust optimization in compressor blade design

Manufacture variations can greatly increase the performance variability of compressor blades. Current robust design optimization methods have a critical role in reducing the adverse impact of the variations, but can be affected by errors if the assumptions of the deviation models and distribution parameters are inaccurate. A new approach for robust design optimization without the employment of the deviation models is proposed. The deviation package method and the interval estimation method are exploited in this new approach. Simultaneously, a stratified strategy is used to reduce the computational cost and assure the optimization accuracy. The test case employed for this study is a typical transonic compressor blade profile, which resembles most of the manufacture features of modern compressor blades. A set of 96 newly manufactured blades was measured using a coordinate measurement machine to obtain the manufacture variations and produce a deviation package. The optimization results show that the scatter of the aerodynamic performance for the optimal robust design is 20% less than the baseline value. By comparing the optimization results obtained from the deviation package method with those obtained from widely-used methods employing the deviation model, the efficiency and accuracy of the deviation package method are demonstrated. Finally, the physical mechanisms that control the robustness of different designs were further investigated, and some statistical laws of robust design were extracted.

Breaking the geometry-performance tradeoff in compressor deviation modeling:Nested principal component analysis

Uncertainties in the aerodynamic performance of compressors,introduced by manufac-turing variations,have received more and more attentions in recent years.The deviation model plays a crucial role in evaluating this uncertainty and facilitating robust design.However,current deviation models with a few variables cannot simultaneously achieve a precise geometric approxi-mation of deviation and provide an accurate assessment of performance uncertainty.This paper introduces a novel deviation modeling method named Nested Principal Component Analysis(NPCA)to break this tradeoff.In this method,both geometry-based and performance-based modes are utilized to describe manufacturing variations.By considering aerodynamic sensitivity,surface deformations that significantly impact aerodynamic performance can be extracted for deviation modeling.To demonstrate the superiority of this newly proposed method,ninety-eight newly man-ufactured compressor rotor blades were measured using a coordinate measurement machine,and both NPCA and Principal Component Analysis(PCA)were employed to model the real manufac-turing variations.The results indicate that,in comparison to the PCA method,the NPCA method achieves an equivalent level of accuracy in geometric reconstruction and evaluation of mean perfor-mance.Furthermore,the same level of accuracy can be obtained with eight NPCA modes and fifty PCA modes when assessing the scatter in aerodynamic performance.Finally,the working mecha-nism of the NPCA method for accurate uncertainty quantification was further investigated.

High-performance low-leakage regions of nano-scaled CMOS digital gates under variations of threshold voltage and mobility

We propose a modeling methodology for both leakage power consumption and delay of basic CMOS digital gates in the presence of threshold voltage and mobility variations. The key parameters in determining the leakage and delay are OFF and ON currents, respectively, which are both affected by the variation of the threshold voltage. Additionally, the current is a strong function of mobility. The proposed methodology relies on a proper modeling of the threshold voltage and mobility variations, which may be induced by any source. Using this model, in the plane of threshold voltage and mobility, we determine regions for different combinations of performance (speed) and leakage. Based on these regions, we discuss the trade-off between leakage and delay where the leakage-delay-product is the optimization objective. To assess the accuracy of the proposed model, we compare its predictions with those of HSPICE simulations for both basic digital gates and ISCAS85 benchmark circuits in 45-, 65-, and 90-nm technologies.