**1. Introduction**

The aviation industry faces great sustainability challenges associated with global warming and climate change [1,2]. It has been estimated that approximately 920 million tons of CO2 emissions were produced by the aviation industry worldwide in 2019 only [3]; a doubling or even tripling of said emissions is forecasted to occur by 2050 unless radical changes have been implemented [4]. Therefore, the development of sustainable approaches and solutions with regard to future aviation technologies and applications is of utmost importance. To this end, the utilization of low-density polymeric composites for weight reduction represents a major goal for the aviation sector, given that weight considerations are very critical compared to other transportation sectors [5,6]. In this context, carbon fiber reinforced plastics (CFRPs) have been extensively used for lightweight aircraft applications towards achieving better fuel efficiency and, consequently, lowering the associated environmental burden of the aviation sector. Despite the excellent specific properties of CFRPs, issues such as the great environmental and economic impact of their production, as well as difficulties linked to their recyclability, remain open challenges that need to be addressed [5,7]. It is worth noting that currently, approximately 98% of CFRP waste is

**Citation:** Markatos, D.N.; Malefaki, S.; Pantelakis, S.G. Sensitivity Analysis of a Hybrid MCDM Model for Sustainability Assessment—An Example from the Aviation Industry. *Aerospace* **2023**, *10*, 385. https:// doi.org/10.3390/aerospace10040385

Academic Editor: Doni Daniel

Received: 21 February 2023 Revised: 23 March 2023 Accepted: 20 April 2023 Published: 21 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

landfilled [8]. Until today, recycled composites are not being used for mass production in aviation; only demonstrators or prototypes have been developed, targeting secondary aviation applications (e.g., seat armrests, side-wall interior panels) [9,10].

When considering the use of recycled material in aviation, the concern of circular economy (CE) principles is of great importance as it represents an integral part of sustainability. Therefore, apart from the assessment of the environmental impact as well as the economic viability of the recycled components, the dimension of circularity also needs to be examined. In addition, when focusing on high-performance applications, the technological quality features of the recycled component need to be evaluated as the components under consideration must meet specific mechanical performance limits and manufacturing requirements [11]. To this end, new tools are required to support decision-making towards CE practices and sustainability goals; in this frame, multi-criteria decision-making (MCDM) tools can be of aid in supporting decision-makers reach a satisfying solution, especially when conflicting criteria are present. MCDM belongs to a variety of techniques able to determine a preference ordering among alternative solutions whose performance is scored against a series of criteria. MCDM has been used in many fields, including the aviation sector, although the vast majority is focused on the airlines and aircraft level as it occurs from an extensive recent review paper involving MCDM-related studies in the aviation field; among the MCDM methods applied in the aviation sector, AHP, SAW, TOPSIS, ELEC-TRE, VIKOR, as well as hybrid methods integrating combinations of them, appear to be the most widely used ones, with AHP and TOPSIS being the first choice for decisionmaking [12]. However, regardless of the choice of the MCDM, it occurs that the sensitivity and robustness of the proposed tools are not systemically examined. Moreover, in cases where a robustness assessment has been conducted, it consists of a sensitivity analysis of the weights' variation, while the sensitivity of the MCDM tool to the data variation appears to be generally neglected. The latter becomes clear from the representative cited works of Table 1, incorporating MCDM methodologies within the aviation sector.


**Table 1.** Representative works from the aviation sector implementing MCDM methodologies.

Conducting a sensitivity analysis of MCDM is particularly important in the aviation sector, given the complex and safety-critical nature of decision-making in this industry. Therefore, a data sensitivity analysis is crucial for the reliability of the tool as it helps to identify and manage uncertainty in data inputs (such as measurement error, sampling error, or missing data), leading to more accurate and reliable predictions and better-informed decisions. In this context, the implementation of a reliable and robust MCDM tool can be useful for selecting the most appropriate material, design component, and manufacturing process in the conceptual design and design phase of a product. For a given engineering application, the attention focus lies on the proper selection of criteria and metrics rather than on the selection of the most appropriate MCDM methodology [21].

In the present study, a hybrid MCDM tool, introduced by the authors in [22], to support the policy decision of selecting a sustainable material for aircraft components has been applied, and its robustness has been examined towards ensuring its reliability as a decision support tool. The research questions that will be addressed in the present work include: (1) What is the level of sustainability of virgin and recycled CFRP components, and how do they compare to each other? (2) How reliable is the assessment of sustainability through MCDM? Based on the above research questions, the work aims to support policy decisions by providing decision-makers with a reliable and robust tool that can aid in the selection of sustainable materials in the aviation industry. The studied tool combines the analytic hierarchy process (AHP) and a weighted sum model (WSM) to obtain the final output. In this context, the influence of the data normalization method, as well as the sensitivity to the weights and data variation, is evaluated. For this purpose, a case study has been considered, aiming to assess the sustainability potential of CFRP recycled composites in aviation with regard to the type of fuel utilized within aircraft operation. In this frame, kerosene, as well as liquid hydrogen from conventional and renewable sources, have been considered. The proposed MCDM tool integrates environmental, economic, and circular economy criteria, as being the most relevant aspects representing sustainability, according to the authors. The output of the model is a weighted sum that can be understood as a metric of sustainability. The results demonstrate that the proposed tool provides an effective and robust method for the evaluation of the sustainability of aircraft components.

## **2. Methodology**

#### *2.1. Basic Considerations*

As mentioned above, a case study from the aviation industry involving recycled CFRP components has been considered to assess the robustness of the proposed tool. For the sake of the present study, the geometrical features of the considered components, with the exception of weight, are assumed to be identical. The recycled components comprising of either randomly or aligned fibers are compared against a virgin woven CFRP. To enable comparison and be in compliance with the design requirements, the stiffness of the virgin and recycled components must be identical. To this end, to compensate for the variation of stiffness among the considered components, thickness (and consequently mass) has been treated as a variable that has to be adjusted to achieve equal stiffness. Equal stiffness has been considered an appropriate criterion for the comparison of different materials/components [15]. The expected mass ratio (Rm) between the virgin and the recycled components is calculated based on the following approximate formula [23–25]:

$$\mathbf{R\_m} = \frac{\mathbf{m\_{recycled}}}{\mathbf{m\_{virgin}}} = \frac{\mathbf{P\_{recycled}}}{\mathbf{P\_{virgin}}} \left(\frac{\mathbf{E\_{virgin}}}{\mathbf{E\_{reycle}}}\right) \tag{1}$$

where m (kg) and p (kg/m3) represent the mass and the density of the components under comparison, respectively, while E (N/m2) is the elastic modulus of the components.
