Multi-fidelity (MF) surrogate models for incorporating multiple non-hierarchical low-fidelity (LF) datasets, whose rank of fidelity level is unknown, have attracted much attention in engineering problems. However, most of existing approaches either need to build extra surrogate models for LF datasets in the fitting process or ignore the cross-correlations among these LF datasets, resulting in accuracy deterioration of an MF model. To address this, a novel multi-fidelity cokriging model is proposed in this article, termed as MCOK, which can incorporate arbitrary number of non-hierarchical LF datasets without building extra LF surrogate models. A self-contained derivation of MCOK predictor and its mean square error are presented. It puts all the covariances between any two MF datasets into a single matrix and introduces additional parameters “gamma” to account for their cross-correlations. A novel method for tuning these additional parameters in a latent space is developed to deal with the problem associated with non-positive definite correlation matrix. The proposed MCOK method is then validated against a set of numerical test cases and further demonstrated via an engineering example of aerodynamic data fusion for FDL-5A flight vehicle. Results from current test cases show that MCOK outperforms existing non-hierarchical cokriging, linear regression MF surrogate model, and latent-map Gaussian processes model, with more accurate and robust predictions, which makes it more practical for engineering modeling problems.

For real-world engineering design optimizations, it is of great significance to find approximate optimal designs with least number of expensive functional evaluations. This paper proposes to use a surrogate-based multi-objective evolutionary algorithm (SBMO) to address this type of problems. The basic idea is to decompose a multi-objective optimization problem into a number of scalar optimization subproblems and to optimize them simultaneously in a simple-to-implement manner, in which global surrogate models are used to enable full cooperation between subproblems. First, initial samples are selected by design of experiments and expensive simulations are conducted to evaluate them. Second, global surrogate models for objective (and constraint) functions are built through the sampled data and the optimization subproblems are solved simultaneously to suggest new samples. Third, the surrogate models are updated and the optimization proceeds to the next generation. This process is repeated until satisfactory Pareto-front solutions are found. Thanks to decomposition strategy, the infill-sampling criteria and constraint handling dedicated for a single-objective optimization can be directly used in a SBMO. The difference between SBMO and the existing methods such as MOEA/D-EGO is that a combined infill-sampling strategy and dedicated constraint handling are used. Benchmark test cases have demonstrated that SBMO is efficient, robust and has good capability of constraint handling. SBMO has been applied to multi-objective aerodynamic shape optimization of a transonic airfoil. It has been shown that SBMO is well suited for engineering design problems where expensive numerical simulations are employed.

The complex nonlinear dynamics of tilt-rotor aircraft has consistently limited their applications due to substantial challenges in transition flight safety. The aerodynamic characteristics of tilt-rotor aircraft wings are studied in this paper. Systematic wind tunnel tests focused on the coupling propeller, angle of attack, aileron, and flap are first conducted. Important aerodynamic forces, moments, and coefficients are derived through the distributed engagement of multiple measuring balances. The results show that although the amplitudes of the aerodynamic coefficients of the wings are affected by the nacelle and propeller slipstream, their evolution trends are similar to those of a basic airfoil. Based on this finding, a simple but effective aerodynamic characterization method is proposed based on wind tunnel test data, which achieves a straightforward polynomial approximation of the aerodynamic coefficients under high angles of attack in full transition processes. This work provides a solid foundation for future control law design and the simulation of tilt-rotor aircraft.