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Gradient-enhanced universal kriging with polynomial chaos as trend function
Zuhal L.R.a, Zakaria K.a, Palar P.S.a, Shimoyama K.b, Liem R.P.c
a Institut Teknologi Bandung, Indonesia
b Institute of Fluid Science, Tohoku University, Sendai, 980-8577, Japan
c The Hong Kong University of Science and Technology, Hong Kong
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In this paper, we propose a new formulation of gradient-enhanced universal Kriging that uses sparse polynomial chaos expansion (PCE) as trend functions. In this regard, the gradient information is used to improve both the trend function and the Gaussian process part. The optimal set of polynomial terms is selected based on the least angle regression algorithm. We tested the performance of the proposed gradient-enhanced polynomial chaos Kriging (GEPCK) in several algebraic and non-algebraic test cases and compared it with ordinary Kriging (OK) and ordinary gradient-enhanced Kriging (GEK). Results show that GEPCK consistently outperformed other methods or at least competitive to the best performing method on both algebraic and non-algebraic problems. This indicates that the performance of the conventional GEK can be further improved by incorporating sparse PCE as trend functions.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Gaussian Processes,Gradient informations,Least angle regressions,Ordinary kriging,Polynomial chaos,Sparse polynomials,Trend functions,Universal kriging[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]Pramudita Satria Palar and Lavi Rizki Zuhal were funded in part through the Program Penelitian, Pengabdian Kepada Masyarakat, dan Inovasi (P3MI) 2019-2020 administered by Lembaga Penelitian dan Pengabdian Kepada Masyarakat, Institut Teknologi Bandung, Indonesia. Part of the work was also carried out under the Collaborative Research Project 2019 of the Institute of Fluid Science, Tohoku University.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.2514/6.2020-1865[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]