benchmarkfcns.multifidelity.borehole

benchmarkfcns.multifidelity.borehole(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the multi-fidelity Borehole function. SCORES = borehole(X) computes the value of the Borehole function at point X. multifidelity.borehole accepts a matrix of size M-by-8 and returns a matrix SCORES of size M-by-2. Properties (High-fidelity):

• Dimensions: 8

• Recommended domain: rw in [0.05, 0.15], r in [100, 50000], Tu in [63070, 115600], Hu in [990, 1110], Tl in [63.1, 116], Hl in [700, 820], L in [1120, 1680], Kw in [9855, 12045].

Mathematical Definition

\[\begin{aligned}\]

f_{hf}(mathbf{x}) &= frac{2pi T_u (H_u - H_l)}{ln(r/r_w) left[ 1 + frac{2 L T_u}{ln(r/r_w) r_w^2 K_w} + frac{T_u}{T_l} right]} \ f_{lf}(mathbf{x}) &= frac{5 T_u (H_u - H_l)}{ln(r/r_w) left[ 1.5 + frac{2 L T_u}{ln(r/r_w) r_w^2 K_w} + frac{T_u}{T_l} right]} end{aligned}

Visualization

No visualization available for this function.