A PC-Kriging-HDMR integrated with an adaptive sequential sampling strategy for high-dimensional approximate modeling

High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality, resulting in decreased modeling accuracy as the design parameter space expands. Furthermore, the lack of a parameter decoupling mechanism hinders the identification of couplings between design variables, particularly in highly nonlinear cases. To address these challenges and enhance prediction accuracy while reducing sample demand, this paper proposes a PC-Kriging-HDMR approximate modeling method within the framework of Cut-HDMR. The method leverages the precision of PC-Kriging and optimizes test point placement through a multi-stage adaptive sequential sampling strategy. This strategy encompasses a first-stage adaptive proportional sampling criterion and a second-stage central-based maximum entropy criterion. Numerical tests and a practical application involving a cantilever beam demonstrate the advantages of the proposed method. Key findings include: (1) The performance of traditional single-surrogate models, such as Kriging, significantly deteriorates in high-dimensional nonlinear problems compared to combined surrogate models under the Cut-HDMR framework (e.g., Kriging-HDMR, PCE-HDMR, SVR-HDMR, MLS-HDMR, and PC-Kriging-HDMR); (2) The number of samples required for PC-Kriging-HDMR modeling increases polynomially rather than exponentially as the parameter space expands, resulting in substantial computational cost reduction; (3) Among existing Cut-HDMR methods, no single approach outperforms the others in all aspects. However, PC-Kriging-HDMR exhibits improved modeling accuracy and efficiency within the desired improvement range compared to PCE-HDMR and Kriging-HDMR, demonstrating robustness.Comment: 17 pages with 7 figures and 9 table

Global sensitivity analysis based on DIRECT-KG-HDMR and thermal optimization of pin-fin heat sink for the platform inertial navigation system

In this study, in order to reduce the local high temperature of the platform in inertial navigation system (PINS), a pin-fin heat sink with staggered arrangement is designed. To reduce the dimension of the inputs and improve the efficiency of optimization, a feasible global sensitivity analysis (GSA) based on Kriging-High Dimensional Model Representation with DIviding RECTangles sampling strategy (DIRECT-KG-HDMR) is proposed. Compared with other GSA methods, the proposed method can indicate the effects of the structural and the material parameters on the maximum temperature at the bottom of the heat sink by using both sensitivity and coupling coefficients. From the results of GSA, it can be found that the structural parameters have greater effects on thermal performance than the material ones. Moreover, the coupling intensities between the structural and material parameters are weak. Therefore, the structural parameters are selected to optimize the thermal performance of the heat sink, and several popular optimization algorithms such as GA, DE, TLBO, PSO and EGO are used for the optimization. Moreover, steady thermal response of the PINS with the optimized heat sink is also studied, and its result shows that the maximum temperature of high temperature region of the platform is reduced by 1.09 degree Celsius compared with the PINS without the heat sink.Comment: 34 pages, 18 figures, 5 table

Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing complexity. We use analytic models of various levels of complexity, then demonstrate performance on two engineering-scale problems: a single-physics nuclear reactor neutronics problem, and a multiphysics fuel cell problem coupling fuels performance and neutronics. Lastly, we demonstrate sensitivity analysis for a time-dependent fuels performance problem. We demonstrate the application of all the algorithms in RAVEN, a production-level uncertainty quantification framework