Multi-objective design optimization of sustainable commercial a-ircraft: performance and costs

Abstract

The present work deals with a multi-objective optimisation approach to incorporate up-to-date financial models in the multidisciplinary conceptual design of a commercial aircraft. Design optimisations based on financial objective functions are compared to standard performance-based optimal solutions. The main novelty is in the extension of the financial models to the long-term investments of a wider group of stakeholders. The rationale underlying this research stems from two considerations: (i) the environmentally sustainable development of the air transportation system in the next 20 years is subordinate to breakthrough technologies, since the consolidated ones have reached their saturation point; (ii) the economic impacts of highly innovative concepts on the stakeholders chain is still uncertain. The problem is addressed at the conceptual design level and the analysis is performed within a comprehensive multidisciplinary framework, adopting all the technical constraints required in aeronautical design. The Pareto fronts obtained using performance and financial merit factors, reveal that the proposed financial model yields highly efficient, technically sound concepts. The design space point corresponding to the negative cash flows minimum turned out to be very close to the one corresponding to minimum acoustic emissions, confirming that the financial model drives the optimiser towards environment-friendly designs.

Keywords:

• Eco-design
• engineering design for sustainable development
• environmental issues
• sustainable aircraft technologies
• Multidisciplinary Conceptual Design Optimization (MCDO)
• multi-objectives optimizations
• Pareto optimality

1. Introduction

The paper deals with the integration of economic considerations in the conceptual design of environment-friendly commercial aircraft. The concept of eco-friendly aircraft is nowadays recurring in most of the mid- and long-term research plans for the civil aviation development. The definition of this apparent oxymoron is certainly a questionable matter and may be the object of an endless debate. After all, a noisy machine burning tons of fuel for each mission can be hardly considered as friendly to environment. In the context of the present paper, we will refer to environment-friendly aircraft as those that satisfy the mission requirements in terms of performance, payload and safety, fulfilling, at the same time, all the strict constraints in green-house gases emission and noise level foreseen for the next two decades. The ultimate goal of the research is the assessment of the long-term financial implications induced by the highly innovative, unconventional concepts expected to be introduced in the near future to cope with the environment challenge. Specifically, the present work aims at the identification of a design strategy suitable to ensure the sustainable development of the civil aviation avoiding unaffordable financial penalisation for the stakeholders involved. Indeed, according to all analysts, a substantial growth in air traffic demand is expected in Europe in all possible socio-political scenarios. The average yearly growth rate foreseen spans from a minimum of 0.7% in the unlikely fragmented world scenario, up to about 4% in the global growth scenario, with local peaks above 6% in those European areas with the highest expected rate of development (Eurocontrol 2013). The translation of these rates into numbers of flights reveals that a doubling of the air traffic in the European skies is a more than a plausible forecast. In such a context, the environmental targets can be accomplished only through a substantial reduction of the emissions of noise and nitrogen oxides, indicated by ACARE (Advisory Council for Aeronautic Research and Innovation in Europe) in a reduction relative to year 2000 of 75% in CO₂ emission, 90% in NO_x emissions and 65% of perceived noise (ACARE 2011). Unfortunately, technical advancements are becoming more and more difficult, as the conventional technologies are reaching a saturation point. Any further evolutionary improvement is becoming more costly and time consuming, thus making the introduction of breakthrough concepts a mandatory enabling factor to face the environmental challenge in a constantly growing market. During the last decade, several unconventional configurations have been introduced, each one characterised by specific revolutionary solutions. Just to give to the reader an idea of the level of innovation we are talking about, Figure 1 shows two of these concepts, the boxed-wing and the blended-wing-body.

Figure 1. Pictorial renderings of a boxed-wing configuration (left) and the blended-wing-body concept (right).

Even the simple visual inspection of these renderings reveals how these unconventional solutions require a substantial adaptation of the manufacturing, operational and maintenance procedures, imposing, in some cases, the revision of the existing regulations and significant infrastructural investments to all the stakeholders involved. From this point of view, a realistic estimate of the commercial attractiveness of these solutions is subordinate to an update of the standard life-cycle cost models used to estimate the profitability of the current aircraft. A viable strategy to address the situation lies on the integration of updated financial models in the conceptual multidisciplinary design, and adopting a multi-objective approach to take into account the interests of all the stakeholders involved. It is worth noting that the value-based approach to the conceptual design of a commercial aircraft is definitely not new. Although an extensive review of the substantial literature in the field is beyond the scope of the present paper, it is worth mentioning at least the papers that, in the authors’ opinion, represent the primary reference for the present work. A first approach to the value-based multi-disciplinary conceptual optimisation of commercial airplanes was presented in Markish and Willcox (2003), where performance, cost and revenue models were integrated to estimate the value of a family of aircraft. In that paper, the analysis is based on the management of the uncertainty level of the future operational scenario, and includes a preliminary exercise on the program value of a BWB family. The possibility of including, at the conceptual design level, the environmental footprint of an aircraft as an optimisation objective was discussed in detail in Antoine and Kroo (2005). That interesting work describes in details the comprehensive optimisation framework used, and demonstrates, in a multi-objective context, the feasibility of such an approach in substantially decreasing the impact of the civil aviation in terms of noise and emissions. Furthermore Hall et al. (2013) explores future aircabins comparing optimisation and win–win scenarios, moving the focus from technical and design considerations to a customer-driven approach, in order to take into account final consumers’ needs, and value all stakeholders involved. Another work of high relevance to the objectives of the present research is Peoples and Willcox (2006), where the attention is focused on the assessment of the business risk associated to the financial uncertainties. The work presented here is closely related to that approach. The same design philosophy has been implemented in the Multidisciplinary Conceptual Design Optimization (MCDO) framework FRIDA (FRamework for Innovative Design in Aeronautics), developed by the authors and their collaborators during the last decade. The financial models have been updated on the basis of the aforementioned considerations, also including the estimate of the equivalent cost of noise following the most recent achievements on the topic (Schipper 2004; Iemma and Diez 2005; Grampella et al. 2013). Taking advantage of the all the features implemented in FRIDA, the final results have been obtained using two derivative-free global optimization methods: the Particle Swarm Optimization (PSO) method (Kennedy and Eberhart 1995; Campana et al. 2013; Diez et al. 2014), and the Multi-Objective Genetic Algorithm (MOGA) (Deb et al. 2002).

Section 2 introduces the cost model used in the present work within the context of the expected future scenarios and includes remarks about its relationship with the models used in the literature. The multi-objective optimisation problem is formalised in Section 3, whereas the preliminary numerical results are presented in Section 4. Here, the analysis is limited to conventional aircraft concepts in order to validate the basic assumptions on well-assessed concepts. Section 5 closes the paper with some concluding remark about the work presented and an outline of the developments foreseen in the near future.

2. Cost model and the future scenario

The air traffic is expected to witness a significant growth in the long run. The European Organisation for the Safety of Air Navigation (Eurocontrol 2013), an intergovernmental organisation with 41 Member States, produced a set of different scenarios of the European air traffic long-term forecast. Based on the political orientation of Europe, depending on whether it will be addressed towards an economic adaptability, in a world where the majority of GDP growth is expected to come from regions other than Europe, and whether it will adopt an inward or outward perspective, four different scenarios have been developed whose more likely ones forecast an air traffic movements increase in 2050, compared to 2012, ranging from 90 to 170%. Moreover, nearby airport facilities, the expansion of urban areas is occurring. These two factors raised the interest around life quality of communities of these areas which are impacted by chemical and acoustic emissions. Within this context, it is understandable why the European Community allocated funds to scientific projects focusing on novel technologies and procedures to handle this issue.

Currently, based on flight time and class of the plane, according to the International Civil Aviation Organization (ICAO) policies (ICAO 2012), several airports charge airlines noise fees, which have to be reinvested to continue the application of noise alleviation or prevention measures. It is worth noting that these charges are applied as air navigation fees when a flight is operated. A few speculations around future developments of these initiatives foresee that noise taxes could be ruled, this way adding airlines a burden related to the ownership of noisy planes, not any longer to its employment. However, despite the value of this hypothesis, a deep political analysis goes beyond the purpose of this paper and entails several other complications like, for instance, the agreement between countries to determine which one should collect this tax.

Whatever development of noise fees one envisions, it is clear that an economic interest among airline companies has already emerged. On top of that, legislative pressures are expected to be exercised. In fact, political interest has surfaced through the concept of Balanced Approach to managing the problem of noise, introduced in 2001 by ICAO, the United Nations agency in charge of codifying principles and techniques of international air navigation and fostering the planning and development of international air transport to ensure safe and orderly growth. This approach is based on identifying a noise problem in a specific place and analysing the possible options to mitigate it. Simultaneously, the European Community has created ACARE, an agency dealing with the improvement of the competitive situation of the European Union in the field of aeronautics. ACARE has launched the Community objectives for noise mitigation. Air traffic growth, urban areas expansion, economic and political interests are likely to determine a more significant economic impact of noise fees.

Financial implications from the viewpoint of manufacturer have been deeply explored and an excellent analysis is proposed by Markish and Willcox (2003). Therefore, design and manufacturing costs have been widely studied and modelled. Nevertheless, marketability of a product strongly depends on the demand side, too.

We propose to analyse the market from a different perspective which embraces several stakeholders considerations, including the airline’s one. On one hand, even though in the aeronautical industry, according to Porter’s five forces analysis, suppliers have the strongest negotiation power, airline companies started providing manufacturers with their proposals for the future planes. On the other hand, airline companies constitute the joining link between manufacturers and airports.

What does an airline company need in order to decide whether to invest in a new airplane? A financial analysis whose output is the Net Present Value (NPV) of the investment itself. This implies that the initial investment and positive and negative cash flows throughout the airplane’s life and discount rate have to be assessed. Positive cash flows are obviously related to revenues, while negative ones are associated with financial direct operating costs. Revenues are related to the number of passengers and ticket prices. Both variables are determined by laws of supply and demand in the transportation industry and are affected, especially in such a long term due to technical innovation, by uncertainty. For the sake of simplicity, in this paper, on top of the initial investment, only cash outflows have been included, which have been calculated over a one-year time-frame and considered as constant. According to IATA (Ferjan 2014), airliner operating cost structure follows in Figure 2. In this analysis, top three direct cost categories have been considered (fuel, aircraft ownership, maintenance) since they account for 53% of operational costs and 77% of direct operational costs. In addition, airport charges, even if their incidence is limited (5%), have been comprised since they include noise fees which are expected to become more impacting in the future.

Figure 2. Airline operational costs breakdown.

In the last quarter of century, life-cycle costs have been linked to two main stages: design and operational ones as proposed by Markish and Willcox (2003). These cost categories have been associated to the fuel-weight and empty-weight of the plane. However, from an airline perspective it is critical to determine the acquisition price P_AC and, since the commercial planes market is regulated by the laws of supply and demand, price is not determined by the cost of design. Of course, from a manufacturer viewpoint, selling price is the source of revenue which has to recover manufacturing costs, including design ones. This implies that acquisition price is limited but not determined by the cost of design and it is defined by the value delivered and perceived by the customer, which strongly depends on the performance of the aircraft. In order to include the added-value, valuable previous works (Markish and Willcox 2003) have considered that an operating costs increase was offset by a proportional selling price decrease and vice versa, in a zero-sum approach. A different cost analysis approach is proposed, in order to determine the most valuable solutions. Indeed, in this paper, acquisition price has been related to features determining performance and to characteristic driving profits. The first set is composed of maximum speed and balanced field length BFL, while the second one consists of the number of seats, the width and pitch seat which determine the comfort of the passengers, therefore, the price they can be available to pay for the flight, which is connected to the revenues of the airline company. The price of the aircraft has been then calculated according to an empirical formula as highlighted by Ferreri (2003),

(1)

Being N_S the number of seats, V_max the maximum aircraft speed, P_S the seat pitch (i.e. the space between two consecutive rows of seats), W_S the seat width and BFL the balanced field length. Fuel cost is the most relevant and impacting cost category which currently accounts for 33% of operational costs according to IATA (Ferjan 2014). In order to estimate it, an average mission and an average number of missions have been determined. This way, the total annual distance flown by the aircraft can be calculated. Furthermore, considering the fuel average price and the consumption of the aircraft, the annual fuel cost can be determined.

Maintenance accounts for 9% of operational costs (Ferjan 2014) and has been historically considered directly proportional to the acquisition price since the high value of an item would imply high costs of spare parts and skilled labour. For the sake of simplicity, this approach has been adopted. It is worth noting that different considerations can be valuable, too. For instance, manufacturers could charge a higher price, if they could guarantee limited maintenance interventions since the sold product not only would require reduced expenses but it would also be potentially more profitable for its higher availability.

Moreover, considering the continuously growing interest towards negative externalities, despite their limited current financial impact, noise fees have been included in this analysis. Acoustic emissions have a meaningful impact on the boroughs nearby airport facilities since they cause a decrease in value of the properties in these areas. These values are therefore determined by internal characteristics and external factors. Hedonic pricing methods, including willingness to pay, have been thoroughly developed by Schipper (2004), and Grampella et al. (2013) further enhanced his analysis proposing a method to calculate the monetary impact of the aforementioned external factors in terms of properties loss of value. More specifically, such a cost can be formalised as follows

(2)

where ANE expresses the Average Noise Exposure which is the SEL average value measured in approach, flyover and lateral points as defined by ICAO certification. Political decisions can of course go beyond the resulted value, however, this one should be considered the fairest approach to determine the fees that airlines should pay, being based on a zero-sum approach.

Finally, negative cash flows are calculated as it follows:

(3)

being C_F the fuel cost, C_M the maintenance one and C_N, as described by the Equation (2(2) ), the monetary impact of sound emissions.

3. The multi-objective optimization problem

In order to identify the most valuable configuration from an airline company viewpoint, one has to narrow down its analysis on a specific airplane class (single-aisle or twin-aisle jet) on a consistent average mission (short-haul, medium-haul and long-haul flight) and on an average number of missions. Afterwards, a multi-optimization problem is defined aiming to identify the trade-off solution between the minimum initial investment and the recurrent outflows.

(4)

being J(x) the k-th objective function with x the vector containing the N_x design variables bounded by and in the design space D, g_i(x) the N_q inequality constraints and h_j(x) the N_h equality constraints. The set of x in the n-dimensional design space D which satisfies the constraints is called the feasible set. Specifically, in the multi-objective optimization problems (MOP), the solution consists of a set of alternatives, being the latter optimal if a better solution within the variables domain does not exist. The optimality criterion, especially in the event that there are more conflicting objectives, can be found in the possibility that exists a set of solutions such that it is possible to further minimise one objective solely at the expense of one other: such solutions are non-dominated and constitute the Pareto front.

The results presented below concern the choose of the optimal wing system of a single-aisle aircraft. With the aim of analysing the impact of acquisition price P_AC on the negative cash-flows NCFs, the objective functions, in compliance with the cost modelling described above, are the following ones:

(5)

The optimisation variables, summarised in Table 1, are related to the shape of the wing in terms of span, chords and thickness ratio. The fuselage size is imposed by the aircraft class (164-pax) and the tail geometry is assumed fixed.

Table 1. Design variables related to the 164-pax aircraft: reference value, lower bound and upper bound.

Design Variable	Reference	Lower bound	Upper bound
Half–span [m]	17.05	10.00	35.00
Root Chord [m]	5.100	4.000	10.00
Tip Chord [m]	1.600	1.000	4.000
Thickness Ratio (root)	0.152	0.050	0.200
Thickness Ratio (tip)	0.108	0.050	0.200

The mission profile, shown in Figure 3, is modelled on 100-min flight, a typical European air travel: the cruise altitude is 10.000 metres and the cruise Mach number is around 0.77, whereas both the take-off and approach procedures are regulations compliant.

Figure 3. Mission characteristics as a function of the flight duration. (a) Geometric altitude h_g and kinematic altitude h_k = v²/2 g and (b) True airspeed v_t and vertical velocity v_v = v_t sinγ, with γ the ramp angle.

For the reference configuration (see Table 1), the high-lift devices settings combined with the fuselage angle of attack ensure both the vertical equilibrium and the stall prevention at the same time during the entire mission, and the engines operating points are such that the overspeed is never exceeded and the rotational speed never passes under the idle condition. Notwithstanding, it is worth noting that, since the change in the wing geometry gives rise to modifications in the aerodynamic, structural and inertial characteristics of the aircraft, the following constraints must be imposed during the optimisation

(6)

being α_max the stall angle (function of the high-lift devices settings), N1_os and N1_i respectively the engine overspeed and idle condition (in revolution per minute), v_max = min[v_f,v_NE] the maximum acceptable velocity (with v_f the flutter velocity and v_NE the never-exceed velocity, in compliance with the FAR regulations), σ_max the maximum normal stress at the root of the wing.

4. Numerical simulations

In this work, a pseudo objective function is used to take into account the optimisation constraints. The pseudo objective is defined using an external penalty function, proportional to the square of the ratio of the violated constraint value to a reference value (quadratic penalty function). As aforementioned, the minimisation is carried-out using two gradient-free methods. The first is the Particle Swarm Optimization (PSO), introduced by Kennedy and Eberhart (1995), as deterministic implementation (MODPSO) developed by the Resistance & Optimization team of the CNR-INSEAN (Campana et al. 2013), whereas the second one is a Multi-Objective Genetic Algorithm (MOGA) and the exploited algorithm is based on the NSGA-II, exhaustively described by Deb et al. (2002).

The optimisation analysis has been carried out within the framework FRIDA – FRamework for Innovative Design in Aeronautics (for details, see the Appendix). The minimisation problem was solved making use of 1000 iterations and 50 particles for the PSO, and 50 individuals over 1000 generations for the MOGA (50000 objective function evaluations for both the algorithms). The normalised solutions with the Pareto front evolution through iterations is presented in Figure 4, and the optimal Pareto solutions in Figure 5.

Figure 4. Multi-objective optimization aimed at minimising the acquisition price P_AC and the annual negative cash flows NCFs: normalised solutions (with respect to PSO algorithm first feasible generation) and Pareto front evolution obtained with the PSO and the NSGA-II algorithms.

Figure 5. Multi-objective optimization aimed at minimising the acquisition price P_AC and the annual negative cash flows NCFs: Pareto optimal solutions (the generic Pareto optimal solution, shown by the arrow, is the closest to the utopia point) obtained with the PSO and the NSGA-II algorithms.

On the Pareto front, the solutions corresponding to the minimum of both the acquisition price P_AC and negative cash flows NCFs, and a generic optimal solution along the Pareto front (see Figure 5) have been selected: the resulting wing systems are characterised by the geometrical variables of Table 2.

Table 2. Results of the optimisation analysis aimed at the minimisation of the aircraft price P_AC and the negative cash flows NCFs.

Design variable	Min [PAC]	Min [NCFs]	Generic OPT
Half–span [m]	16.77	21.31	17.52
Root Chord [m]	5.64	4.036	4.153
Tip Chord [m]	1.817	1.038	2.581
Thickness Ratio (root)	0.074	0.068	0.075
Thickness Ratio (tip)	0.112	0.052	0.077

As shown in Figure 6, the minimum price solution is less performing in terms of fuel consumption, since the induced drag contribution is greater for having a greater reference surface and a smaller aspect ratio. This solution is also more impacting as for acoustic emissions having a greater wet surface. It is worth noting that even though this configuration is clearly less efficient, lying on the Pareto front, it is an optimal solution which an airline company could take into consideration.

Figure 6. Multi-objective optimization aimed at minimising the acquisition price P_AC and the annual negative cash flows NCFs: optimal wing systems. (a) Minimum aircraft acquisition price PAC, (b) Minimum airline negative cash flows NCFs, and (c) Trade-off solution (closer to the utopia point).

The traditional conceptual design approach mainly focuses on performance features, whereas the one proposed in this paper is enriched with the financial consideration. Therefore, the authors with the purpose of investigating the relationship between the airline company financial implications and the aircraft performance, conducted another multi-objective optimization analysis: such optimisation is aimed to minimise the average noise exposure level ANE (see Equation (2(2) )) and the fuel W_f consumed during the entire mission, i.e. the objective functions are now

(7)

and the constraints are the same defined by the Equation (6(6) ). The used minimisation algorithms are the same of the previous problem, as well as the number of objective function evaluations, i.e. 1000 iterations and 50 particles for the PSO and 50 individuals over 1000 generations for the MOGA.

The wing geometrical characteristics, in terms of optimisation variables, for the solutions corresponding to the minimum of average noise level ANE and fuel consumed W_f, and for the generic optimal solution are presented in Table 3.

Table 3. Results of the optimisation analysis aimed at the minimisation of the average noise level ANE and the fuel consumed W_f.

Design variable	Min [ANE]	Min [Wf]	Generic OPT
Half–span [m]	23.39	23.34	23.37
Root Chord [m]	4.001	4.213	4.002
Tip Chord [m]	1.002	1.001	1.001
Thickness Ratio (root)	0.058	0.051	0.057
Thickness Ratio (tip)	0.073	0.058	0.072

The normalised solutions and the Pareto front evolution through iterations are presented in Figure 7, whereas the optimal Pareto solutions in Figure 8.

Figure 7. Multi-objective optimization aimed at minimising the noise level ANE and the fuel consumption W_f: normalised solutions (with respect to PSO algorithm first feasible generation) and Pareto front evolution obtained with the PSO and the NSGA-II algorithms.

Figure 8. Multi-objective optimization aimed at minimising the average noise level ANE and the fuel consumption W_f: Pareto optimal solutions (the generic Pareto optimal solution, shown by the arrow, is the closest to the utopia point) obtained with the PSO and the NSGA-II algorithms.

The results have revealed that the Pareto front solutions, shown in Figure 8 (the Pareto front evolution through generations are presented in Figure 7) bring to a wing system consistent with the Figure 9(b), i.e. it looks that the design choices leading to environmental pollution abatement, in terms of acoustical emissions, are aligned with the ones that guarantee the minimum of the annual negative cash flows for the airline company.

Figure 9. Multi-objective optimization aimed at minimising the noise level ANE and the fuel consumption W_f: optimal wing systems. (a) Minimum noise level ANE, (b) Minimum fuel consumption W_f, and (c) Trade-off solution (closer to the utopia point).

It is worth noting that the Paretial optimal solutions in the performance space (ANE-W_f) lie close to the Pareto front of the financial problem. Instead, financial optimal solutions lie within the range of the performance problem, not on the front, as shown in Figure 10.

Figure 10. Comparison of performance solutions to financial solutions. (a) Minimum average noise level ANE and minimum fuel consumed W_f solutions in the financial problem normalised space (P_AC-NCFs) and (b) Minimum aircraft price P_AC and minimum airline negative cash flows NCFs solutions in the performance problem normalised space (ANE-W_f).

This implies that designing an aircraft only according to technical-performance consideration could determine unsustainable economic situations.

Considering the achieved outcomes, it is appropriate to leverage on the expertise gained through EC-funded SEFA (Sound Engineering For Aircraft, FP6, 2004–2007) and COSMA (Community Noise Solutions to Minimise aircraft noise Annoyance, FP7, 2009–2012) projects on unconventional configurations.

5. Concluding remarks

Conventional configurations of tube-and-wings aircraft have been analysed, through a set of simulations and optimisation analyses.

The first set of simulations explores the impact of acquisition price P_AC on the negative cash-flows NCFs, determining the optimal wing system of a single-aisle aircraft. The minimum price solution defines a configuration being less performing as for fuel consumption, because of the greater induced drag contribution for a greater reference surface and a smaller aspect ratio. Moreover, its greater wet surface implies a stronger impact in terms of acoustic emissions.

The second set investigates the relationship between the airline company financial implications and the aircraft performance, that is to say the trade-off between average noise exposure level ANE (see Equation (2(2) )) and the fuel W_f consumed during the entire mission. The results show that the configuration leading to acoustical emissions abatement is aligned with the one that guarantee the minimum of annual negative cash flows of an airline company.

As aforementioned, the consolidate technology has approached a saturation point, therefore the model has to be extended and it is worth noting that innovative configurations are currently under analysis.

Furthermore, novel aircraft are likely to require infrastructural enhancements which will necessitate corresponding investments. Even though they are not going to be directly incurred by airline companies, air passenger carriers are charged airport improvement fees by airport management firms. For this reason, the current method has to be enriched to include these charges in addition to the analysed subset of financial direct operational costs.

In order to have a complete overview of potential investments in innovative configuration airplanes, the current analysis has to be integrated with the increase and decrease in cash outflows, with the estimation of cash inflows and the determination of a proper discount rate. This way, Net Present Value (NPV) over the useful life of an aircraft can be calculated.

Finally, this analysis deals with forecasts and long-term designs based on a high level of technological innovation. This long-run perspective is unavoidably typified by aleatory ‘uncertainties’ associated with variables which include both stochastic (e.g. the cost of oil or demand/offer air traffic), and epistemic uncertainties, related with variables whose value is not known due to lack of knowledge (future technologies, future policy decisions). Consistently, the model has to be enhanced in order to take into account and manage these uncertainties.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Umberto Iemma is an associate professor of Aerospace Structures and Design currently in charge of the courses in Engineering Mechanics for the bachelor degree in Mechanical Engineering and Multidisciplinary Aircraft Design for the master’s degree in Aeronautical Engineering, at the Roma Tre University. His primary research interests are the multidisciplinary design optimisation of eco-friendly aircraft, the theoretical and numerical modelling in acoustics, aeroacoustics and aerodynamics. He coordinates the activity of the Aircraft Design Laboratory at Roma Tre University. He also coordinates the development of the multidisciplinary aircraft design optimisation toolbox FRIDA (FRamework for Innovative Design in Aeronautics), successfully adopted as primary analysis platform in many FP7, Clean Sky and H2020 projects. Member of the NATO expert panels AVT-252 (Stochastic Design Optimisation) and AVT-233 (Aeroacoustics of Engine Installation). Author of more than 130 scientific papers published on peer-reviewed scientific journal or presented at international conferences.

Fabio Pisi Vitagliano has a PhD in Mechanical Engineering with a thesis on multisciplinary conceptual design of eco-friendly commercial aircraft. He obtained the International MBA at the IE Business School, one of the top-ranked programmes in the world according to Financial Times standings. Currently is a professor Human Resources Management, Leadership and Communication at the Rome Business School for both postgraduate and MBA programmes. His professional background includes experiences as a Corporate Trainer, Program Manager, Business Developer and Strategy Consultant at worldwide leading companies.

Francesco Centracchio has a PhD in Mechanical and Industrial Engineering with a research on physical modelling of musical instruments for real-time simulations. Has developed a highly multidisciplinary teaching experience in flight dynamics, aircraft technologies, engineering mechanics, aircraft design, piano technique, music theory in academia and high school. He is currently research fellow in the group of multidisciplinary design optimisation of aircraft at the Roma Tre University. His primary research interest is the optimal design of unconventional, highly innovative low-noise aircraft. He is currently the main developer of the design optimisation toolbox FRIDA (FRamework for Innovative Design in Aeronautics).

Appendix

The MCDO framework FRIDA

The Multidisciplinary Conceptual Design Optimization (MCDO) framework, FRIDA (FRamework for Innovative Design in Aeronautics), has been used for the optimisation analysis presented in this work. FRIDA can thoroughly outline the aircraft and it utterly fits when the application requires a multidisciplinary approach, such as the aircraft configuration definition, the environmental impact (taking into account both the acoustical and chemical emissions) combined with financial considerations.

Figure A1. FRIDA (FRamework for Innovative Design in Aeronautics) is the tool developed at Roma Tre University, integrated with models for the estimate of life-cycle costs and infrastructural investments.

The algorithms used for the aircraft analysis are, whenever possible, prime-principle based, since the main goal of the formulation is the assessment of innovative aircraft configurations, for which the designer cannot rely on past experience or literature data.

The multi-objective minimization algorithms implemented in FRIDA are two gradient-free methods: PSO, introduced by Kennedy and Eberhart (1995) and NSGA-II, described by Deb et al. (2002). The PSO implementation peculiarity lies on the particles deterministic distribution. A detailed analysis of the impact on the solution due to the initial particles position can be found in Campana et al. (2013). Furthermore, Iemma et al. (2014) compared this algorithm efficiency to the NSGA-II one.

The search for an optimal wing system implies, for each iteration of the optimisation process, the aerodynamic coefficients computation which could require burdensome simulations. On the other hand, being FRIDA developed to perform the conceptual design, the trade-off between model accuracy and computational resources is crucial, for this reason, it is necessary to have an accurate and fast tool for the aerodynamic analysis. Accordingly, the aerodynamic module of FRIDA make use of a zeroth-order Boundary Element Method (BEM) starting from an integral formulation based on a quasi-potential flow (Morino 1993). The formulation is coupled with a boundary-layer integral model to take into account the effects of viscosity providing an adequate estimation of the viscous drag, which is essential for the study of flight mechanics and performance analysis.

At each iteration, the total aircraft weight is also evaluated: the structural weight evaluation is addressed starting from the knowledge of the characteristic dimensions of the wing and tail elements (spars, stringers, ribs and coverings), as well as the fuselage geometric sketch: in the aftermath, the weights of engines, landing gear and fixed equipment are added. An accurate analysis of masses distribution, including payload, crew, fuel and operational items, allows the estimation of the centre of gravity of the actual aircraft configuration.

The changing in the wing system for the search of the optimum also requires the compliance with the structural constraints: a 6-D.O.F. torsional-bending beam equivalent model of the wing is built in FRIDA, and the nodal generalised forces due to the aerodynamic loads are computed. The structural module also evaluates approximate modes of vibration and the natural frequencies of the beam representing the wing.

The aeroelasticity model makes possible the flutter and divergence speeds estimation, which represents a further constraint of the analysis presented in this work. To carry out an efficient aeroelastic analysis, a reduced order model (ROM) based on a finite-state approximation is employed for the evaluation of the matrix collecting the aerodynamic forces (Morino et al. 1995).

The set-up of the minimisation problem presented in this work imposes the simulation of on entire mission: since an aerodynamic analysis at each sample of the trajectory would be too expensive in terms of computational costs, suitable corrections are applied in order to take into account the aerodynamic effects of high-lift devices (flaps and slats), air-brakes and landing gears (Raymer 1992). Simultaneously, the flight mechanics is solved in order to guarantee the static longitudinal stability, fundamental requirement for each flight condition, by imposing that the derivative of the pitching moment with respect to centre of gravity is less than zero.

The analysis of the entire mission also requires the knowledge of the engine operating points at each sample of the trajectory. To this aim, a semi-empirical turbofan model, based on both prime-principle and available experimental data, is implemented within FRIDA. For a given flight condition, knowing the engine features, such a model provides the rotational speeds of respectively low-pressure and high-pressure spools starting from the knowledge of the over-speeds and idle conditions in terms of revolutions per minute. For each flight condition, the jets velocity is calculated through the momentum equation and their temperatures are estimated with the energy balance. Thereafter, the amount of fuel consumed is also estimated.

The noise emissions assessment is made possible using the aeroacoustic module within FRIDA: the implemented models allow the estimation of both the airframe (Fink 1976, 1977) and the propulsion noises,(Morfey and Fisher 1970; Heidmann 1979), as a function of the distance from the observers, the directivity angles and the actual aircraft configuration, in terms of wet surfaces and engine operating-point, the latter evaluated as detailed above. For the calculation of the 1/3 octave band Sound Pressure Level (SPL), the algorithms also take into account the Doppler effect and the atmospheric absorption (Sutherland et al. 1974). Through a proper post-processing, the Sound Exposure Level (SEL) and the Effective Perceived Noise Level (EPNL) are also estimated. Moreover, FRIDA includes an innovative sound-quality assessment method (Iemma, Diez, and Marchese 2006; Diez and Iemma 2012; Iemma et al. 2014), developed during progression of EC-funded SEFA (Sound Engineering For Aircraft, FP6, 2004–2007) and COSMA (Community Noise Solutions to Minimise aircraft noise Annoyance, FP7, 2009–2012) projects.

The financial module, introduced in this work, allows the estimation of financial implications from an airline company perspective. It implements the model previously described. The initial investment, i.e. the acquisition price, maintenance and fuel costs, the most relevant financial direct operating cost categories, and noise charges are calculated. The price of the aircraft P_AC has been related to its performance and profitable characteristics and then calculated according to an empirical formula as highlighted by Ferreri (2003). The cost of fuel has been computed considering the consumption over a defined mission, the number of missions and the average price of fuel. Maintenance is directly proportional to the value of the aircraft. Noise has a social impact on the properties in areas nearby airports facilities: this negative externality is converted into an economic loss of value according to a method developed by Grampella et al. (2013).