Many industrial design problems are characterized by a lack of an analytical expression defining the relationship between design variables and chosen quality metrics. Evaluating the quality of new designs is therefore restricted to running a predetermined process such as physical testing of prototypes. When these processes carry a high cost, choosing how to gather further data can be very challenging, whether the end goal is to accurately predict the quality of future designs or to find an optimal design. In the multi-fidelity setting, one or more approximations of a design’s performance are available at varying costs and accuracies. Surrogate modelling methods have long been applied to problems of this type, combining data from multiple sources into a model which guides further sampling. Many challenges still exist; however, the foremost among them is choosing when and how to rely on available low-fidelity sources. This tutorial-style paper presents an introduction to the field of surrogate modelling for multi-fidelity expensive black-box problems, including classical approaches and open questions in the field. An illustrative example using Australian elevation data is provided to show the potential downfalls in blindly trusting or ignoring low-fidelity sources, a question that has recently gained much interest in the community.

The paper addresses a critical challenge in System-of-Systems (SoS) simulations arising from the different granularity levels in SoS simulations, integrating non-coupled Discrete Element Method results into SoS-level Discrete Event Simulations using surrogate modeling. Illustrated with a wheel loader bucket use-case in mining, it enhances early design decision-making and lays the groundwork for improving SoS simulations in construction equipment design. This paves the way for broader research and application across diverse engineering design domains.

Losses induced by tip clearance limit decisive improvements in the system efficiency and aerodynamic operational stability of aero-engine axial compressors. The tendency towards even lower blade heights to compensate for higher fluid densities aggravates their influence. Generally, it is emphasised that the tip clearance should be minimised but remain large enough to prevent collisions between the blade tip and the casing throughout the entire mission. The present work concentrates on the development of a preliminary aero-engine axial compressor casing design methodology involving meta-modelling techniques. Previous research work at the Institute for Turbomachinery and Flight Propulsion resulted in a Two-Dimensional (2D) axisymmetric finite element model for a generic multi-stage high-pressure axial compressor casing. Subsequent sensitivity studies led to the identification of significant parameters that are important for fine-tuning the tip clearance via specific flange design. This work is devoted to an exploration of the potential of surrogate modelling in preliminary compressor casing design with respect to rapid tip clearance assessments and its corresponding precision in comparison with finite element results. Reputed as data-driven mathematical approximation models and conceived for inexpensive numerical simulation result reproduction, surrogate models show even greater capacity when linked with extensive design space exploration and optimisation algorithms.

Compared with high-fidelity finite element simulations, the reductions obtained in computational time when using surrogate models amount to 99.9%. Validated via statistical methods and dependent on the size of the training database, the precision of surrogate models can reach down to the range of manufacturing tolerances. Subsequent inclusion of such surrogate models in a parametric optimisation process for tip clearance minimisation rapidly returned adaptions of the geometric design variables.

The research focuses on the design space optimisation of National Advisory Committee for Aeronautics (NACA) submerged inlets through the formulation of a hybrid data fusion methodology. Submerged inlets have drawn considerable attention owing to their potential for good on-design performance, for example during cruise flight conditions. However, complexities due to the geometrical topology and interactions among various design variables remain a challenge. This research enhances the current design knowledge of submerged inlets through the utilisation of data mining and Computational Fluid Dynamics (CFD) methodologies, focusing on design space optimisation. A two-pronged approach is employed where the first step encompasses a low-fidelity model through data mining and surrogate modelling to predict and optimise the design parameters, while the second step uses the Design of Experiments (DOE) approach based on the CFD results for the candidate design geometry to construct a surrogate model with high fidelity for design refinement. The feasibility of the proposed methodology is demonstrated for the optimisation of the total pressure recovery of a NACA submerged inlet for the subsonic flight regime. The proposed methodology is found to provide good agreement between the surrogate and CFD-based model and reduce the optimisation processing time by half in comparison with conventional (global-based) CFD optimisation approaches.

Surrogate models are widely used for dataset correlation. A popular application very frequently shown in public literature is in the field of engineering design where a large number of design parameters are correlated with performance indices of a complex system based on existing numerical or experimental information. Such an approach allows the identification of the key design parameters and their impact on the system’s performance. The generated surrogate model can become part of wider computational platforms and enable optimisation of the complex system without the need to run expensive simulations.

In this paper, a number of design point simulations for a combined gas-steam cycle are used to generate a response surface. The generated response surface correlates a range of cycle’s key design parameters with its thermal efficiency while it also enables identification of the optimum overall pressure ratio and the high pressure level of the raised steam across a range of recuperator effectiveness, pinch temperature difference across the heat recovery steam generator and the pressure at the condenser. The accuracy of a range of surrogate models to capture the design space is evaluated using root mean square statistical metrics.

The ability to quickly fabricate small unmanned aircraft system (sUAS) through Additive Manufacturing (AM) methods opens a range of new possibilities for the design and optimisation of these vehicles. In this paper, we propose a design loop that makes use of surrogate modelling and AM to reduce the design and optimisation time of scientific sUAS. AM reduces the time and effort required to fabricate a complete aircraft, allowing for rapid design iterations and flight testing. Co-Kriging surrogate models allow data collected from test flights to correct Kriging models trained with numerically simulated data. The resulting model provides physically accurate and computationally cheap aircraft performance predictions. A global optimiser is used to search this model to find an optimal design for a bespoke aircraft. This paper presents the design loop and a case study which demonstrates its application.