Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points

A centrifugal compressor is required to increase aerodynamic efficiency, ensure structural integrity, and reduce processing costs. This paper presents a dimension reduction technique based on proper orthogonal decomposition (POD) in combination with an adaptive sampling method to reduce computational costs. Design of experiment (DOE) is first used to choose initial sampling points. Then, parts of the sampling points are selected to format the snapshot matrix. Subsequently, the number of principal components to be retained is determined after POD analysis. An adaptive sampling point adding approach is used to increase new sampling points. The approach places more points around the regions of initial optimum designs by learning the information from previous data through POD analysis. Finally, the POD coefficients are selected to act as new design variables in the following multidisciplinary design optimization process. The method is first tested by three mathematical benchmark functions. The proposed method is then used to optimize a centrifugal compressor, of which the results are verified by tests. A normalized isentropic efficiency improvement of 3.7% and 3.0% in the maximum speed state and cruise state has been obtained after optimization. Additionally, the processing costs are reduced by about 30% owing to the number of blades reduced.

Download Full-text

Reduced-order models for radiative heat transfer of hypersonic vehicles

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020926730 ◽

2020 ◽

Vol 234 (11) ◽

pp. 1836-1848

Author(s):

Xiaoxuan Yan ◽

Jinglong Han ◽

Haiwei Yun ◽

Xiaomao Chen

Keyword(s):

Proper Orthogonal Decomposition ◽

Interpolation Method ◽

Reduced Order Modeling ◽

Orthogonal Decomposition ◽

Hypersonic Vehicles ◽

Reduced Order ◽

Discrete Empirical Interpolation Method ◽

Empirical Interpolation Method ◽

Proper Orthogonal ◽

Discrete Empirical Interpolation

Aerothermoelastic analysis of hypersonic vehicles is a complex multidisciplinary coupling problem. Thus, accurate modeling of varying disciplines with low computational cost is necessary. This work developed a tractable approach-based reduced-order modeling technology to solve the radiative thermal transfer problem in a hypersonic simulation. A method that combines proper orthogonal decomposition and unassembled discrete empirical interpolation method is developed to construct the reduced-order modeling. First, high-dimensional original systems are projected on the optional basis generated by proper orthogonal decomposition, and the nonlinear term is further approximated by unassembled discrete empirical interpolation method. Then, a numerical integration method for the solution of the reduced system of nonlinear differential equations is provided. Case studies that use a classical hypersonic control surface model, in which the time history and spatial distribution of the thermal load are known a priori, are conducted to validate the accuracy and efficiency of the reduced-order modeling methodology and to assess the robustness of the reduced-order modeling for thermal solution. Results indicate the ability of reduced-order modeling to reduce the nonlinear system size with reasonable accuracy.

Download Full-text