Comparative reliability analysis of electric aircraft versions for NASA’s X-57 based on Lz-transform method

As the goals of air transport shift towards more-electric or all-electric airplanes, different drive train configurations have been explored recently. A major goal on the way towards the inclusion in commercial air traffic is high reliability. One of the experimental electric airplanes is NASA’s X-57 “Maxwell”, which consists of fourteen electric motors powered from a battery pack. The aim of this paper is to assess the reliability of the proposed design of the X-57 by using the Lz-transform approach, as well as to propose several alternative designs to its electric drive train, in order to use less vehicle mass on the motors and more on the battery pack, without sacrificing the original availability and expected performance, with a final goal to increase the flight range. The reliability analyses show that the replacement of X-57’s three-phase motors with six-phase ones greatly improves availability of the electric drive train due to the use of fault-tolerant electric machines. Additionally, all of the further proposed alternative designs have higher availability than the X-57. The alternatives with CHB inverter topologies generally achieved higher availability values and higher expected performance than the B6 variants. Finally, the use of a distributed propulsion system with smaller take-off motors leads to a motor-mass advantage compared to more conventional drive train designs.


Introduction
The European Union's climate action plan aims to reduce greenhouse gas emissions and become completely climate neutral by the year 2050 [17].One of the steps towards achieving net zero carbon emissions is the electrification of the transport sector, with a long term goal to completely replace combustion engines with electrical engines.A shift towards the use of electrical drives is recently seen in aviation, from hybrid-electric to all-electric projects.An all-electric aircraft is around two to three times more energy efficient compared to its fossil fuel counterpart [27].In addition to the improved efficiency and reduced carbon emissions, electrified aviation can also contribute to noise reduction.The main limitation of an all-electric aircraft is the flight range, as the current battery technology, in combination with available volume and weight within the aircraft, allows for a total flight duration of only about 60 min [25,23].
NASA is developing a battery powered electric airplane X-57 "Maxwell" with an innovative distributed propulsion system, which allows for a reduction in wing area, while providing the same lift with less motor power [40,8].A similar distributed propulsion system is featured in the "ECO-150-300" [43] and the "DRAGON" [44] electric airplane models, as well as in the hybrid-electric plane design exploration in [36].
In order to become a part of commercial transportation, electric airplanes need to get certified by an airplane safety organisation such as EASA (European Union Aviation Safety Agency) or FAA (Federal Aviation Administration).The standards for certifying electric airplanes are still in the making, however there are some preliminary documents or conditions in use (such as SC E-19 by EASA).High aircraft reliability is one of the main issues in its inclusion in the air transportation system.Different analytical methods can be used to assess system reliability, one of which is the Lz-transform method, suitable for complex multi-state systems.It was firstly introduced by Lisnianski in [34], as an extension of the widely used Universal Generating Function method, which can only be used for steady-state processes.In [33] Lisnianski explains the application of the Lz-transform to dynamic reliability analysis of a multi-state system.This method is often applied in reliability analyses of traction systems of ships [21] and helicopters [20], as well as manufacturing systems [49].
Reliability analysis can be a mathematically challenging task, especially in the case of complex multi-state systems.Modelling of continuous-time stochastic processes often requires a vast number of differential equations, which are usually computationally demanding and timeconsuming to solve.The Lz-transform method allows for a quicker and simpler analysis of multi-state systems.

Lz-Transform Fundamentals
The Lz-transform of a discrete-state continuous-time Markov process G(t) is mathematically represented as: where p i is a probability that the process G is in a certain state i, out of k possible states, at a time instant t.Performance of the states is quantified with exponents g i .As a process cannot be in more than one state at one time instant, the events are mutually exclusive and the sum of probabilities is equal to 1. [35] In order to obtain all the probabilities across the desired time frame, it is necessary to solve a system of differential equations given by: where x is the respective matrix entry in the diagonal.The diagonal terms represent the "departing" transitions from each state of a Markov chain, whereas each of the remaining elements represent one single transition from and to a state defined in its index (see Figure 1).To connect two elements in a series connection, the following Ushakov operator is applied, imposing a "min" function on the exponents of the two Lz-transforms: When it comes to a parallel connection of redundant elements, Ushakov operator imposes a "sum" function on the exponents: The final Lz-transform of a complete multi-state system can be directly used for calculating important parameters which give an insight about the reliability of the system [35].
Availability is calculated as the sum of all probabilities of the exponents that fulfil the criterion, i.e. are greater or equal than the defined w, shown in equation (6).Availability is a quantity used to describe the ability of a system to function without failures, as well as the ability of the external environment to repair the system in case of failure, to bring it back to the healthy state [32].Furthermore, it is the ability of the system to function after a failure, due to its fault tolerance.
Expected performance is a sum of the products of probabilities and the exponents: 3. NASA's X-57 "Maxwell" In the recent years, NASA has been developing an experimental (X) electric aircraft called X-57 Maxwell, with a distributed propulsion system.It is based on Tecnam P2006T plane, whose internal combustion motors have been removed in order to test the electric propulsion systems through the four defined project stages.The idea behind the distributed propulsion system lies in increasing aerodynamic lift by the use of thrust from light motors spread across the wings, therefore allowing for a reduction of the size of wings for a more efficient cruise.[38] IC

X-57 Specifications
The modification IV of the X-57 airplane utilises a distributed propulsion system which consists of: • two 47 kW h battery packs, • two 60 kW cruise motors and propellers, and • twelve 10.5 kW high lift motors (HLM) and foldable propellers.[38] All fourteen motors are used at take-off and climb, and only the two cruise motors are used in cruise mode, when the propellers of HLM fold to reduce drag.More on specific flight phases can be found in [25,7].Duration of the flight is 3400 s, or approximately 57 min.Two flight phases/demands are considered within this paper: • the Roll phase, which demands 240 kW for 10 s and • the Climb1 phase, which demands 210 kW for 90 s as the other phases from [7] represent a demand too low for a representative comparison of the availability functions.
The battery itself weighs more than the rest of the propulsion system with a total mass of 390 kg.Mass of cruise motors is reportedly 22.2 kg each [14], whereas one HLM has a motor mass of 2.34 kg [24].Total mass of all motors is 72.5 kg, which will be important in comparison with alternative drive trains.Total aircraft mass is 1360 kg [38].It is important to note that this aircraft is still in the process of development, which means that documents and specifications have changed throughout the process.
The propulsion system was simplified to the following main components: battery packs, inverters, motors and propellers, which will be covered with respect to reliability in the following sections.A reliability analysis was performed by means of the Lz-transform method.The calculated reliability indices will be used for comparison with proposed alternative propulsion system designs.

X-57 Cruise Motors and Propellers
The two cruise motors on the ends of the wings are 60 kW three-phase PMSM air-cooled outrunner motors, produced by Joby Aviation [14].Cruise propellers in use are of variable-pitch, consisting of three blades [9].
A three phase motor is considered as a two-state Markov process, named "M", (shown in Figure 2), as any phase failure results in total failure of the motor, since it requires all three phases to run.As it operates at its nominal power of 60 kW, the Markov process states for the cruise motor are 60 and 0. This element is represented with Lz-transform as shown in equation (8).Failure and repair rates chosen for this process are from [3] for a three phase machine: λ M = 0.09 y −1 and µ M = 113 y −1 .
The propeller is also considered as a two-state process, named "P", with states 60 and 0, represented with Lz-transform in (9).The failure rate is chosen from propeller data in NASA's General Aviation Aircraft Reliability Study [39] to be λ P = 0.066 y −1 .The repair rate for a variable-pitch propeller is µ P = 95 y −1 sourced from [5].This source used a very similar failure rate of 0.06 y −1 , comparably to the aforementioned chosen one.Performance of the healthy state g, as well as the transition rates depend on the element.

X-57 High Lift Motors and Propellers
X-57 is special due to its distributed propulsion system, which uses the small motors placed across the wing to increase lift, to therefore use narrower wings [24].Such design is meant to also increase efficiency of operation, providing more degrees of freedom in control, redundancy, and noise reduction.[30] X-57 Maxwell uses twelve 10.5 kW motors only during take-off and landing.The propellers are foldable to reduce drag when not in use [24].Both HLM and its propeller are treated as twostate processes "m" and "p", respectively, with performance values of 10.5 and 0. Lz-transform of these two elements is shown in equations ( 10) and (11).
The failure and repair rates for these two components are the same as for the cruise motor and cruise propeller, summarised in equations ( 12) and (13).

X-57 Battery System
The battery system is made of two parallel battery packs, each consisting of eight modules.One module has 320 single NCA 18650-30Q cells, connected in a 20p16s configuration.Total battery system useful capacity is 47 kW h, it weighs 390 kg and the nominal voltage is 461 V. NASA's top level battery requirements [25] are to provide the maximum of 132 kW for 45 s, 74 kW for 3 min, and continuous power of 60 kW.A Markov model is defined per battery pack, according to the previously mentioned NASA requirements.Since the 74 kW per pack are insufficient to power neither Roll nor Climb1 phase, a three-state model of "Pack" is considered, the performance values of states being 132, 60 and 0, as graphically shown in Figure 3 and mathematically in equation (14).
Choosing the failure rates was a challenging task, as there is little data on M T T F of battery packs in electric vehicle and aircraft applications.An option could be to use warranty period as M T T F , which differs across the manufacturing companies.Studies on reliability of electric airplanes have used failure rates of 0.08 y −1 in [5], 150 FIT or 0.0013 y −1 in [2], 0.438 y −1 in [20].Furthermore, 2.4 • 10 −6 h −1 or 0.021 y −1 was calculated in [45] and the value gets even as low as 0.0006 y −1 in [13].
On the other hand, there is extensive research on effect of cycle depth, temperature, discharge voltage and current on capacity fade, and therefore ageing.One must also take into account calendar ageing, storage conditions, and charging.Data sheet of the Samsung 18650-30Q predicts 250 or 300 cycles to reach the end-of-life at maximum current discharge (15 A).The authors of [41] report an average cycle life of 517, [16] reported 1024, and the average cycles to failure in [47] for two different types of cells were 587 and 724 under 1C discharge.If the value of 1024 is considered, at 1C discharge, it would take 2048 h −1 to failure (with 2 h in total to charge and discharge).Which means that a single cell would fail around 4.3 times a year.From experience it is known that our smartphone or laptop batteries last at least 1.5 years, Tesla provides warranty of 8 years, Nissan of 2 years, even Samsung's own single-cell warranty is 18 months.It is clearly noticeable that a connection between cycle life experiments and real-life capacity fade is not distinguishable.
However, a dissertation on ageing of EV battery by Keil [29] provides more insight on specific parameters and their effect on capacity fade.Cycle depth was a dominant factor on cycle life, leading to a distinctly faster capacity fade compared to the effect of temperature, voltage, dynamics etc.A long-term discharge test showed that a 61% depth of discharge caused the capacity fade to 80% after 850 days, or 2.33 years.A test to compare dynamic driving mode and constant current mode, with the same average current, gave similar capacity fade results.
In relation to the load profile of X-57, high power modes Roll and Climb1 discharge a total of 13% of the total capacity in 100 s (other flight phases are not taken into account), which is considered a low depth of discharge.Therefore, double the power output will be assumed not to have a significant impact on the cycle fade and therefore will be assigned the same approximated time to failure as in the rest of the phases.
To conclude, the failure rates of the battery used in this analysis will be based on the period of 850 days to failure, resulting in λ Pack = 461 y −1 from the average repair rate of batteries, found in [6].When it comes to the RBD of X-57, the representation of the battery system is a simplification of the real scheme, since both batteries provide half the power to each of the cruise motors.As this kind of configuration does not allow for a series-parallel RBD, a simple parallel connection of the two packs powering the whole system was chosen as the best approximation.Full traction scheme is available in [8,1].

X-57 Inverter
It is briefly mentioned in [8] that each of the two power trains, consisting of three half-bridge modules, provides half the torque in a cruise motor, with the use of Cree's CAS300M12BM2 halfbridge chips.No further inverter information was found in NASA's literature.Since [10] used the same module in reliability calculations, the adapted failure rate of λ INV = λ inv = 0.0316 y −1 will be used in the later reliability calculations.The value was adapted with the use of provided equations for three CAS300M12BM2 per module instead of the six considered in the study.The repair rate was chosen from [5], with the value of µ INV = µ inv = 584 y −1 .
As two inverters are used in a redundant structure to power the cruise motors, they will be connected in parallel in the respective RBD (see Figure 4).Additionally, it is assumed that only one such inverter powers the HLM.
The inverters for a cruise motor ("INV") and the inverters for HLM ("inv"), are two-state processes, as it is described in Fig. 2. Due to the redundant structure, there will be two parallel "INV" elements connected to the "M", each having half the branch performance -30 and 0. The HLM inverter "inv" will have states 10.5 and 0. See the Lz-transforms of the two inverter elements in (15) and (16).

Alternative Electric Propulsion System Units
Several alternative designs of the propulsion system are proposed with a lower total number of motors with more fault-tolerant and redundant elements, while meeting the power requirements.
An additional goal was to achieve a lower total mass of the motors than the X-57.This way, the difference in mass could be used for the battery system, which could increase the flight range.Two different inverter technologies are proposed and discussed, as well as the use of faulttolerant machines.These are combined in different drive train configurations, whose reliability is analysed and compared amongst each other, as well as with the X-57.

Considered Inverter Technologies
A simple half-bridge inverter used in X-57 has the advantage of a low number of semiconductors, taking up less volume and mass, and being controlled in a simpler manner compared to more complex inverter topologies.However, it lacks fault tolerance, which is very important for the availability of an electric aircraft drive train.A cascaded H-bridge (CHB) inverter is a multilevel inverter which offers a large scale of fault tolerance, depending on the number of levels, i.e. the number of modules used.The authors of [4] compared a CHB to a conventional B6-bridge in an electric helicopter and found a significantly smaller power ripple in the CHB topology during a single phase failure, as well as better fault tolerance, especially for multi-phase machines.
When it comes to failure rates, a simple and common strategy is to calculate the values relatively to the number of components, based on the values from the Military Handbook [46].In some cases the base rates are adapted with experimental test results.A consequence of using this approach is that the inverters with a lower number of components tend to have lower failure rates compared to the more branched or modular topologies.However, simple structures lack the fault tolerance.To compare the approaches, two different inverter topologies will be used in the analysis: B6-bridge and 5-level CHB.Each variant will be assessed with two different base failure rates: one theoretical, based on the number of components and their individual failure rates, and one more practical, based on the results of available experimental studies.

B6-bridge:
This configuration includes one B6-bridge per three phases of a motor, allowing a multi-phase machine to operate as a multiple of three phases, i.e. a nine-phase machine would operate as a triple three-phase machine.The total number of switches of this configuration is 2m, with m denoting the machine's number of phases, as there are 6 switches per three-phases in a B6-bridge.The chosen approach includes with one DC link for all the modules in the parallel connection, similarly as in the case of the X-57 cruise motor.
This topology is represented in an RBD as a parallel connection of m/3 branches, as depicted in Figure 5.Each inverter element, named "B6", has two states, since a failure of one switch in a module leads to a failure in the whole module.The performance values are defined as P Mm and 0, as each branch needs to be capable of carrying the full motor power P Mm in case of failure of any of the other branches.The practical failure rate was calculated by the formulae and data provided in [10] for one capacitor and three half-bridge modules, equals to λ B6 = 0.0316 y −1 .The same value was used for the X-57 cruise inverter (see Section 3.5).Similarly, the repair rate is µ B6 = 584 y −1 from [5].

5-level CHB:
A 5-level CHB consists of two H-bridge modules per phase.Each module has its own separate source of energy.For that purpose, the original X-57 battery system requires reallocation and division into smaller units.Instead of using the two parallel battery packs, as in the B6 topology, each CHB module is powered from one small battery block.With this approach, the total battery system is physically split into 2N independent blocks, with N representing the total number of motor phases in the system.
If one of the two inverter modules fail with the other still functioning, that phase stays functional too, with an overload on the remaining inverter module.All phases are operated independently, but if one phase fails, the fault tolerance of multi-phase machines allows for continued operation with one phase less.To model this behaviour as precisely as possible with Markov models, each battery-inverter phase branch will be represented with a three-state "CHB" element in series with a three-state battery block ("BB") element.This is a minor simplification, as there are two modules of the inverter per phase and two sources.However, using three states for one element simulates the above mentioned failure degradation within the phase.If both modules fail, the third (failed) state is reached, meaning that the whole phase has failed.
The "BB" and "CHB" branches which power one motor are all connected in parallel with each other, then continue in series with the multi-phase machine (see Figure 6).Generally, one CHB module would technically have states P Mm /m and 0, as it needs to be able to power one phase individually, if the other module fails.However, when the two modules are evaluated as one reliability element, as previously elaborated, the three states are 2P Mm /m, P Mm /m and 0, shown in equations ( 18) and (19).
Similarly, the "BB" element is defined with three states as well, to fully power one phase.Its Lztransform is presented in equation (20).Newly calculated states of these battery blocks depend on the fraction of the total power which a branch provides and on the number of phases of the motor in the branch.A general formula on how to define new states of "BB" is provided in equation (21).As this formula is related to the original states of X-57 battery pack, the reader can revise the values in equation (14).
... The failure rate for one "CHB" reliability element is calculated by using the data and equations of [26] for two capacitors, eight switches and eight diodes, resulting in λ CHB 23 = 0.206 y −1 .This value is used for the first transition.However, due to the increased current as a consequence of one module failure, the functional one gets overloaded, which shortens its remaining lifetime.The current becomes two times higher, and the heating losses, therefore, increase four times, according to Joule's law.With these consequences in mind, the new failure rate is calculated as four times the first transition, λ CHB 23 = 0.824 y −1 .For a focus on failure comparability of the two topologies, the repair rate of one "CHB" element is equally defined as for the B6 inverter, i.e. µ CHB 21 = µ B6 = 584 y −1 , which covers just the repair after the first failure.The repair after the second failure, which involves two modules, meaning that the repair rate is half the first value: µ CHB 31 = 292 y −1 .

Fault-Tolerant Electric Motors
Multi-phase electric motors are considered fault-tolerant as a failure in one phase minimally obstructs the function of the machine.As shown in [3], higher number of phases means an increase in availability, with immediate repairs done after every phase failure.However, a failure of a phase may lead to a reduced amount of torque.Besides fault tolerance, multi-phase machines have reduced harmonic content of the air gap, which leads to reduced torque ripple [12].They require lower DC-link capacitors and have a higher efficiency compared to conventional threephase motors.Additionally, development of inverter technologies and modulation techniques allowed for more research to be conducted and more frequent application of the multi-phase machines in both industry and academia.[22] The two motor choices for the alternative drive train configurations are six-and nine-phase machines.As previously mentioned, these can run each-phase independently or in groups of three, acting as a multiple of a three-phase machine.Different inverter topologies of multi-phase machines are discussed in [12,15,4,31].
The authors of [28] proposed a methodology for defining the states of a multi-phase machine as a Markov process.This paper covers detailed instructions on determining the number and performance values of states, depending on the performance demands.With the use of this method, and a condition that a minimum of half of the machine power needs to be provided after an occurred failure.A six-phase machine will have five states: g M6 = {100%, 83%, 66%, 50%, 0} P M6 whereas a nine-phase machine will have six states: The Lz-transform of the "M6" and "M9" elements is shown in equations ( 22) and (23), respectively.Time dependency is considered in the Lz-transforms, but will be omitted in writing from this point on, due to the lack of horizontal space.

Proposed Alternative Topologies
This section introduces different alternatives to the X-57 design.The idea is to use a lower number of parallel drive train branches, with more fault-tolerant structures and topologies.The drive topologies are named in a way to provide a hint on the structure of the topology, for example "X" meaning a distributed propulsion system (similar to X-57) and the numbers combined with a "P" refer to the motors' phase numbers.The 6PX, copies the design of X-57, but replaces three-phase with six-phase motors, while all remaining component definitions stay unchanged.Other alternatives, being 9P6PX, 6P6 and 9P4, will use four to eight electric motors, distributed across the wings.Aerodynamic performance is neglected in this analysis.
A crucial assumption needed to be made ahead of the analysis related to the specific power of motors.The reported active mass of Joby's 60 kW cruise motor used in X-57 is 22.2 kg, with a specific power of 2.7 kW/kg.HLM's active mass of 2.34 kg and 10.5 kW give a specific power of approximately 4.5 kW/kg.El Refaie and Osama [42] overviewed different electric motors in aero and land vehicle applications, where the motors between 10 kW and 100 kW have power densities in the range of 2.4 and 5 kW/kg.A smaller motor of 10 kW was designed in [18] using lightweight stator construction and HiperCo50 magnet to result in 6 kW/kg specific power with only 1.67 kg.A 60 kW five-phase IPMSM was reported in [48] achieving 3.12 kW/kg.A six-phase electric aircraft motor was assessed in [37], resulting in 10.6 kW/kg for active parts (6.4 kW/kg considering total weight).Additionally, Da Rosa and others [11] and Fleitas and others [19] showed that a multi-phase machine may not differ in mass from the three-phase machine and can even have a lower value, due to the lower volume of conductive material required.
In order to approximate the total motor mass in different alternative configurations, the specific power of motors up to 30 kW is taken as 4.5 kW/kg, otherwise, for powers higher than 30 kW, it is taken as 3.12 kW/kg.This limit was taken as an assumption based on overview of the air-cooled motors between 10 kW and 100 kW in [42].
Table 1 gathers all the failure and repair rates used for solving the systems of differential equations of Markov processes-elements in the drive train of X-57 and in the alternative drive trains.

6PX Drive Topology
This alternative uses the same design (position and mass of motors) as the original X-57 (see Fig. 7), however, includes six-phase instead of three-phase motors.An additional adaptation is the use of two B6 inverters per motor, applying also to the HLM, in order to properly run every six-phase motor.7: 6PX representation across the wings.The power distribution is the same as in X-57 only with six-phase motors.
The difference to X-57 in Lz-transform is found in the B6 inverters and motors.The new expressions are given in equations ( 24)-( 27), where the "M6" stands for the new cruise motor, "m6" for the new take-off motor, "B6 M " is cruise inverter and "B6 m " take-off branch inverter.

9P6PX Drive Topology
A similar distributed propulsion system is used in this alternative, utilising two nine-phase 60 kW cruise motors.There are six instead of twelve take-off motors of 21 kW each, all six-phase (see Fig. 9).With the previously mentioned specific power assumptions, total motor mass of this alternative is estimated at 66.5 kg.The Lz-transform for the 9P6PX of nine-phase, six-phase motors, and propellers are listed in equations ( 28)- (31), the battery packs and B6 inverters are given in equations ( 32)-( 34), and lastly CHB with "BB" in equations ( 35)- (38).The "Pack" equation for this and all the remaining alternatives is identical to the equation ( 14) and will not be repeated in the upcoming IC-MSQUARE-2023 Journal of Physics: Conference Series 2701 (2024) 012130 When speaking of the total motor mass comparison, only the 9P6PX alternative has a lower estimated value (66.5 kg) than the 72.5 kg of the X-57 motors.Finally, adding the expected performance and the total motor mass into consideration, the 9P6PX-CHB could be considered as a slightly better design.

Conclusion
The reliability analyses show that the replacement of X-57's three-phase motors with sixphase ones, with their suitable B6 inverters, as defined in the 6PX alternative, greatly improves availability of the electric drive train due to the use of fault-tolerant electric machines.Furthermore, all of the further proposed alternative designs (9P6PX, 6P6 and 9P4) have higher availability than the X-57 at the demands of 240 kW and 210 kW.Alternatives with CHB inverter topologies generally achieve higher availability values and higher expected performance than the B6 variants, due to the fault-tolerant inverter configuration.More specifically, 6P6 and 9P6PX with the CHB inverter topology were chosen as the most reliable systems of this comparative analysis.When analysing the estimated mass of the alternatives, according to the stated specific power assumptions, the 9P6PX alternative was the only design with a lower total motor mass than the one of the X-57, with a 6 kg advantage.However, if this mass advantage would be used to increase the battery mass, it would only bring about an insignificant increase in the flight range, with respect to the total battery mass of 390 kg.According to the presented statistical data, where the motors with a few dozen kW of power have a higher specific power than the ones closer to 100 kW, it is concluded that a distributed propulsion system with, two larger multi-phase cruise motors and a number of small multi-phase motors used at roll and take-off, provides a potential for a weight reduction, compared to conventional propulsion system designs.
There are some issues to be covered in future work with regard to this topic.First, the propulsion system can be analysed with cruise motors having more than nine phases.Second, a more detailed Markov process description of the system components, including the ageing process and scheduled maintenance as transition functions.Finally, a system analysis for nonrepairable systems can be conducted for the drive train alternatives presented within this paper, since for the mentioned flight scenarios, a mid-operation repair is typically not feasible.

Figure 1 :
Figure 1: Markov chain representation for an n-state process

Figure 2 :
Figure 2: Markov chain representation for two state elements of X-57: INV, inv, M, m, P, p.Performance of the healthy state g, as well as the transition rates depend on the element.

Figure 3 :
Figure 3: Markov chain representation for a single battery pack

Figure 4 :
Figure 4: RBD of X-57.Capital letters are for the Cruise motor branch elements, small letters for the HLM branches.There are twelve HLM branches and two cruise branches.

Figure 5 :
Figure 5: Partial RBD example of the B6 topology with a nine-phase machine

Figure 6 :
Figure 6: Partial RBD for CHB implementation for an m-phase machine

Figure 9 :
Figure 9: 9P6PX representation across the wings.It uses distributed propulsion system with less motors than X-57.

Table 1 :
Elements of X-57 (upper block) and of the alternative drive train configurations (lower block), their number of states, and chosen failure and repair rates in y−1