Bound-constrained nonstationary Gaussian process regression for ventilated cavitation prediction

TY - JOUR

T1 - Bound-constrained nonstationary Gaussian process regression for ventilated cavitation prediction

AU - Bai, Tian

AU - Chen, Kuangqi

AU - Wang, Dianpeng

N1 - Publisher Copyright: © 2026 Elsevier Ltd.

PY - 2026/7

Y1 - 2026/7

N2 - This research is motivated by the need to predict cavity length in ventilated cavitation experiments. Given the freestream velocity and ventilation rate, the underlying physical mechanism gives rise to informative bounds and distinct shedding regimes, which in turn induce nonstationarity in the system. In this paper, we propose a novel nonstationary bounded Gaussian process regression model that simultaneously incorporates nonstationarity and bound constraints. We adopt the Gaussian process projection framework to enforce the bound constraints and propose a mixture of bounded Gaussian processes to capture nonstationarity, where each component models a locally stationary behavior consistent with the constraints. The model parameters and mixture components are estimated through a two-stage procedure. Importantly, the proposed model reveals latent physical mechanisms by identifying distinct components, thereby offering deeper scientific insights into the input-output relationship. Numerical results across test functions and the ventilated cavitation experiments validate the superiority of the proposed method. Specifically, the proposed method effectively captures the evolution of ventilated cavity structures, thereby significantly enhancing the adaptability and operational reliability of high-speed underwater vehicles under complex environmental conditions. Codes are available on https://github.com/tbai114/Nonstationary-bounded-Gaussian-process .

AB - This research is motivated by the need to predict cavity length in ventilated cavitation experiments. Given the freestream velocity and ventilation rate, the underlying physical mechanism gives rise to informative bounds and distinct shedding regimes, which in turn induce nonstationarity in the system. In this paper, we propose a novel nonstationary bounded Gaussian process regression model that simultaneously incorporates nonstationarity and bound constraints. We adopt the Gaussian process projection framework to enforce the bound constraints and propose a mixture of bounded Gaussian processes to capture nonstationarity, where each component models a locally stationary behavior consistent with the constraints. The model parameters and mixture components are estimated through a two-stage procedure. Importantly, the proposed model reveals latent physical mechanisms by identifying distinct components, thereby offering deeper scientific insights into the input-output relationship. Numerical results across test functions and the ventilated cavitation experiments validate the superiority of the proposed method. Specifically, the proposed method effectively captures the evolution of ventilated cavity structures, thereby significantly enhancing the adaptability and operational reliability of high-speed underwater vehicles under complex environmental conditions. Codes are available on https://github.com/tbai114/Nonstationary-bounded-Gaussian-process .

KW - Bounded regression

KW - Gaussian process

KW - Mixture models

KW - Nonstationarity

UR - https://www.scopus.com/pages/publications/105027628457

U2 - 10.1016/j.ress.2026.112222

DO - 10.1016/j.ress.2026.112222

M3 - Article

AN - SCOPUS:105027628457

SN - 0951-8320

VL - 271

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

M1 - 112222

ER -