基于高斯过程回归和深度强化学习的水下扑翼推进性能寻优方法

Processing math: 100%

杨映荷, 魏汉迪, 范迪夏, 李昂

Optimization Method of Underwater Flapping Foil Propulsion Performance Based on Gaussian Process Regression and Deep Reinforcement Learning

YANG Yinghe, WEI Handi, FAN Dixia, LI Ang

表2 GPR常用核函数

Tab.2 Common kernel functions for GPR

核函数	函数关系式
Matern 3/2	k(x_i, x_j\|θ)=σ²exp $(1 + \frac{\sqrt{3 r}}{σ_{l}})$ exp $(- \frac{\sqrt{3 r}}{σ_{l}})$ , r= $\sqrt{(x_{i} - x_{j})^{T} (x_{i} - x_{j})}$
Matern 5/2	k(x_i, x_j\|θ)=σ² $(1 + \frac{\sqrt{3 r}}{σ_{l}} + \frac{5 r^{2}}{3 σ^{2}})$ exp $(- \frac{\sqrt{5 r}}{σ_{l}})$
ARD Matern 3/2	k(x_i, x_j\|θ)=σ²(1+ $\sqrt{3 r}$ )exp(- $\sqrt{3 r}$ ), r= $\sqrt{\overset{d}{\sum_{m = 1}} \frac{(x_{i m} - x_{j m})^{2}}{σ_{m}^{2}}}$
ARD Matern 5/2	k(x_i, x_j\|θ)=σ² $(1 + \sqrt{5} r + \frac{5 r^{2}}{3})$ exp(- $\sqrt{5 r}$ )
Squared exponential	k(x_i, x_j\|θ)=σ²exp $[- \frac{1}{2} \frac{(x_{i} - x_{j})^{T} (x_{i} - x_{j})}{σ_{l}^{2}}]$
Absolute exponential	k(x_i, x_j\|θ)=σ²exp $(- \frac{r}{σ_{l}})$ , r= $\sqrt{(x_{i} - x_{j})^{T} (x_{i} - x_{j})}$