Computer-simulated experiments have become a cost effective way for engineers to replace real experiments in the area of product development. However, one single computer-simulated experiment can still take a significant amount of time. Hence, in order to minimize the amount of simulations needed to investigate a certain design space, different approaches within the design of experiments area are used. One of the used approaches is to minimize the time consumption and simulations for design space exploration through response surface modeling. The traditional methods used for this purpose are linear regression, quadratic curve fitting and support vector machines. This paper analyses and compares the performance of four machine learning methods for the regression problem of response surface modeling. The four methods are linear regression, support vector machines, M5P and random forests. Experiments are conducted to compare the performance of tree models (M5P and random forests) with the performance of non-tree models (support vector machines and linear regression) on data that is typical for concept evaluation within the aerospace industry. The main finding is that comprehensible models (the tree models) perform at least as well as or better than traditional black-box models (the non-tree models). The first observation of this study is that engineers understand the functional behavior, and the relationship between inputs and outputs, for the concept selection tasks by using comprehensible models. The second observation is that engineers can also increase their knowledge about design concepts, and they can reduce the time for planning and conducting future experiments.

In engineering, design analyses of complex products rely on computer simulated experiments. However, high-fidelity simulations can take significant time to compute. It is impractical to explore design space by only conducting simulations because of time constraints. Hence, surrogate modelling is used to approximate the original simulations. Since simulations are expensive to conduct, generally, the sample size is limited in aerospace engineering applications. This limited sample size, and also non-linearity and high dimensionality of data make it difficult to generate accurate and robust surrogate models. The aim of this paper is to explore the applicability of Random Forests (RF) to construct surrogate models to support design space exploration. RF generates meta-models or ensembles of decision trees, and it is capable of fitting highly non-linear data given quite small samples. To investigate the applicability of RF, this paper presents an approach to construct surrogate models using RF. This approach includes hyperparameter tuning to improve the performance of the RF's model, to extract design parameters' importance and \textit{if-then} rules from the RF's models for better understanding of design space. To demonstrate the approach using RF, quantitative experiments are conducted with datasets of Turbine Rear Structure use-case from an aerospace industry and results are presented.

The design of aircraft engines involves computationally expensive engineering simulations. One way to solve this problem is the use of response surface models to approximate the high-fidelity time-consuming simulations while reducing computational time. For a robust design, sensitivity analysis based on these models allows for the efficient study of uncertain variables’ effect on system performance. The aim of this study is to support sensitivity analysis for a robust design in aerospace engineering. For this, an approach is presented in which random forests (RF) and multivariate adaptive regression splines (MARS) are explored to handle linear and non-linear response types for response surface modelling. Quantitative experiments are conducted to evaluate the predictive performance of these methods with Turbine Rear Structure (a component of aircraft) case study datasets for response surface modelling. Furthermore, to test these models’ applicability to perform sensitivity analysis, experiments are conducted using mathematical test problems (linear and non-linear functions) and their results are presented. From the experimental investigations, it appears that RF fits better on non-linear functions compared with MARS, whereas MARS fits well on linear functions.

The use of decision-making models in the early stages of the development of complex products and technologies is a well-established practice in industry. Engineers rely on well-established statistical and mathematical models to explore the feasible design space and make early decisions on future design configurations. At the same time, researchers in both value-driven design and sustainable product development areas have stressed the need to expand the design space exploration by encompassing value and sustainability-related considerations. A portfolio of methods and tools for decision support regarding value and sustainability integration has been proposed in literature, but very few have seen an integration in engineering practices. This paper proposes an approach, developed and tested in collaboration with an aerospace subsystem manufacturer, featuring the integration of value-driven design and sustainable product development models in the established practices for design space exploration. The proposed approach uses early simulation results as input for value and sustainability models, automatically computing value and sustainability criteria as an integral part of the design space exploration. Machine learning is applied to deal with the different levels of granularity and maturity of information among early simulations, value models, and sustainability models, as well as for the creation of reliable surrogate models for multidimensional design analysis. The paper describes the logic and rationale of the proposed approach and its application to the case of a turbine rear structure for commercial aircraft engines. Finally, the paper discusses the challenges of the approach implementation and highlights relevant research directions across the value-driven design, sustainable product development, and machine learning research fields.