arXiv subjects

Zhenping Feng

Publications and source records attributed to Zhenping Feng.

4 recordsLinked to original sources

arXiv2026

A Novel Multi-fidelity Surrogate for Efficient Turbine Design Optimization

To solve the turbine design optimization problems efficiently, surrogate-based optimization (SBO) algorithms are frequently used. To further reduce the cost of turbine design, the multi-fidelity surrogate (MFS) based optimization is proposed by the researchers, who resort to augmenting the small number of expensive high-fidelity (HF) samples by a large portion of low-fidelity (LF) but cheap samples in surrogate modeling and optimization process. Nonetheless, according to our observations, the MFS based optimization sometimes can only have better convergence rate at the early stage of optimization process, but yielding worse final solution than the single-fidelity surrogate (SFS) based optimization that uses high-fidelity samples alone. The reason behind can be explained as follows. With the increase of HF samples in the optimization process, the LF samples can cause negative effect and therefore misleading the optimization search. To address the above issue, an ensemble weighted multi-fidelity surrogate (EMFS) is proposed. Specifically, the density-based spatial clustering of applications with noise (DBSCAN) is used to detect the region where the MFS cannot build a more accurate surrogate, and a local SFS is built there. Then, an EMFS is built by combining the MFS and SFS with adaptive weights, which is used to guide the optimization process. The related algorithm is named as multi- and single-fidelity surrogate fused optimization, i.e., MSFO. Through tests on GE-E3 blade optimization and the film cooling layout design of a turbine endwall, the effectiveness of proposed MSFO is well demonstrated.

physics.flu-dyn↗

arXiv2026

A Novel Multi-fidelity Surrogate for Turbomachinery Design Optimization

Turbomachinery design optimization involves expensive black-box problems. Sample-efficient multi-fidelity optimization (MFO) offers an efficient solution. By utilizing multi-fidelity surrogates (MFS), the MFO algorithm can use fewer high-fidelity samples aided by low-fidelity samples to establish an accurate surrogate model. However, when MFS is used in sequential sampling optimization, it has been observed that the final optimal solution obtained by single-fidelity optimization (SFO) is better than that of MFO, even though MFO performs better at the early stages. This can be attributed to the assumption of an even and nested distribution of samples, which is incorrect when using a sequential adding strategy. To address these issues, we propose a novel algorithm called multi-single-fidelity optimization (MSFO) to overcome the limitations of the conventional MFO procedures. In the surrogate establishment of MSFO, we use the density-based spatial clustering of applications with noise (DBSCAN) method to detect local areas where low-fidelity samples are no longer effective. A combination of both global MFS and local single-fidelity surrogate model, built using high-fidelity samples alone, is used to establish an ensemble, which improves the anti-interference ability of the algorithm against misleading low-fidelity data. The effectiveness of the MSFO algorithm is verified first on numerical benchmark functions. Then, the algorithm is used to optimize the aerodynamic profile of a turbine and the film cooling layout design of a turbine endwall. Here, high-fidelity sample sources are obtained from fine-mesh CFD simulations, whereas low-fidelity sample sources are obtained from the same simulations run on a coarser mesh. The results demonstrate that our MSFO algorithm performs significantly better than the conventional SFO and MFO processes, with a higher level of robustness.

physics.flu-dyn↗

arXiv2022

Classification of solutions to equations involving Higher-order fractional Laplacian

In this paper, we are concerned with the following equation involving higher-order fractional Lapalacian \begin{equation*} \left\{\begin{aligned} &(-\Delta)^{p+{\frac{\alpha}{2}}}u(x)=u_+^\gamma~~ \mbox{ in }\mathbb{R}^n,\\ &\int_{\mathbb{R}^n}u_+^\gamma dx<+\infty, \end{aligned}\right. \end{equation*} where $p\geq 1$ is an integer, $0<\alp<2$, $n> 2p+\alpha$ and $\gamma \in (1,\frac{n}{n-2p-\alp})$. We establish an integral representation formula for any nonconstant classical solution satisfying certain growth at infinity. From this we prove that these solutions are radially symmetric about some point in $\R^n$ and monotone decreasing in the radial direction via method of moving planes in integral forms.

math.AP↗

arXiv2022

Classification of solutions to several semi-linear polyharmonic equations and fractional equations

We are concerned with the following semi-linear polyharmonic equation with integral constraint \begin{align} \left\{\begin{array}{rl} &(-\Delta)^pu=u^\gamma_+ ~~ \mbox{ in }{\mathbb{R}^n},\\ \nonumber &\int_{\mathbb{R}^n}u_+^{\gamma}dx<+\infty, \end{array}\right. \end{align} where $n>2p$, $p\geq2$ and $p\in\mathbb{Z}$. We obtain for $\gamma\in(1,\frac{n}{n-2p})$ that any nonconstant solution satisfying certain growth at infinity is radial symmetric about some point in $\mathbb{R}^{n}$ and monotone decreasing in the radial direction. In the case $p=2$, the same results are established for more general exponent $\gamma\in(1,\frac{n+4}{n-4})$. For the following fractional equation with integral constraint \begin{equation*} \left\{\begin{array}{rl} &(-\Delta)^sv=v^\gamma_+ ~~ \mbox{ in }{\mathbb{R}^n},~~~~\\ &\int_{\mathbb{R}^n}v_+^{\frac{n(\gamma-1)}{2s}}dx<+\infty,~~~~~ \end{array}\right. \end{equation*} where $s\in(0,1)$, $\gamma \in (1, \frac{n+2s}{n-2s})$ and $n\geq 2$, we also complete the classification of solutions with certain growth at infinity. In addition, observe that the assumptions of the maximum principle named decay at infinity in \cite{chen} can be weakened slightly. Based on this observation, we classify all positive solutions of two semi-linear fractional equations without integral constraint.

math.AP↗