Utafiti huu unatengeneza architecture ya Prognostics and Health Management (PHM) kwa ajili ya kufuatilia pad wear ya electro-mechanical brakes (E-Brake) katika flights na kutabiri Remaining Useful Life (RUL) kwa brakes zinazolengwa kutumika baadaye katika small na business-class aircraft.

Tatizo kuu ni kwamba katika aviation systems, real “run-to-failure” datasets ni very limited. Kwa kuwa safety-critical aircraft parts kwa kawaida huingizwa kwenye maintenance au kubadilishwa kabla ya kufikia catastrophic failure, inakuwa difficult kutengeneza sufficient training data kwa artificial intelligence au data-driven life-prediction models zinazotegemea historical field data pekee.

Watafiti wanajaribu kutatua tatizo hili kwa structure ya high-fidelity multiphysics simulation + physics-based wear model + particle filter + “landing repository” inayohifadhi flight history.

Brake inayochunguzwa ina four Electro-Mechanical Actuators (EMA) zinazobana multi-disc brake mechanism kwenye main-landing-gear wheel. Kila EMA ina brushless DC motor, single-stage reducer, ball screw, force sensor na motor-position feedback. System inatumia ukweli wa kifizikia kwamba kadiri brake pad inavyovaa, clearance kati ya pad na disc huongezeka, hivyo actuator lazima itembee zaidi ili kutoa braking force ileile.

Health indicator yenye nguvu zaidi katika study imechaguliwa kuwa maximum angular position ya electric motor. Pearson correlation coefficient kati ya variable hii na pad wear ilihesabiwa kuwa `1,00`; SNR ilikuwa `53,71` kwa %20 wear na `54,99` kwa %40 wear. Kwa maneno mengine, katika simulation environment ya study, kadiri pad inavyovaa, maximum rotational motion inayofanywa na motor huongezeka systematically na strongly.

Particle-filter prognostic algorithm ilijaribiwa kwenye 40 separate simulated fault-to-failure processes na particle counts zinazobadilika kati ya 50 na 5000. Katika sample analyses zenye 5000 particles, filter iliweza kufuatilia simulated real wear progression kutoka fault detection hadi end of service life; predicted RUL distributions zilikaribia simulated real End of Life (EOL) value.

Katika average ya 40 simulation sequences, Relative Accuracy (RA) iliripotiwa kwa ujumla kubaki juu ya %80 threshold iliyotumiwa na watafiti. Hata hivyo, results hizi hazionyeshi success ya pad-life prediction iliyopimwa kwenye real aircraft. Wear na RUL validation katika study yote inategemea simulated fault-to-failure data.

Kwa mtazamo wa Uturuki: Study haikufanywa kwenye specific aircraft au brake system inayotumika nchini Uturuki. Hata hivyo, approach iliyotengenezwa ni PHM methodology inayoweza kuzingatiwa katika research za aviation, electro-mechanical actuators, landing gear, predictive maintenance, digital twins na airworthiness nchini Uturuki. Hasa, kuunga mkono maintenance decision si kwa periodic visual inspection pekee bali pia kwa health indicators zinazotolewa kutoka existing motor-position na current sensors ni important research direction. Lakini kabla ya kutumika kwenye real aircraft nchini Uturuki, brake material, disc geometry, EMA architecture, runway conditions, aircraft mass, thermal cycles na real wear coefficients lazima zithibitishwe experimentally kwa platform hiyo.

Kwa nini electro-mechanical aircraft brake?

Katika more-electric-aircraft approach, sehemu ya conventional hydraulic na pneumatic subsystems hubadilishwa na electrically driven systems. Electro-mechanical brakes zina potential ya kuondoa hydraulic lines, kurahisisha system architecture na kutoa system signals nyingi zaidi zinazoweza kufuatiliwa digitally.

Kwa upande mwingine, reliability ya components nyingi za electro-mechanical kama electric motors, transmission elements, sensors, power electronics, ball screws na brake materials huwa critical.

Kwa hiyo, lengo la study si braking pekee, bali kutengeneza system inayoweza kuendelea kukadiria brake imevaa kiasi gani na ni landing ngapi za useful life zinaweza kuwa zimebaki.

Aircraft na brake architecture iliyochunguzwa

Target platform ni small business-class aircraft yenye takeoff mass karibu 5,5–6,1 tonnes. Kuna E-Brake moja kila upande wa kulia na kushoto kwenye main landing gear.

Kila brake ina multi-disc structure na four separate Electro-Mechanical Actuators zinazoweka force parallel kwenye brake pads.

Brake command hupitia chain hii:

Pilot brake command → Brake Control Unit (BCU) → anti-skid control → four EMA → brake pads → discs → wheel braking torque.

BCU ina touchdown protection functions zinazozuia braking kabla ya wheel kugusa runway. Anti-skid system humodulate braking force kwa kuzingatia wheel speed na runway conditions.

Kuna nini ndani ya EMA?

Kila Electro-Mechanical Actuator ina brushless DC motor. Rotational motion ya motor hubadilishwa kuwa linear force kwenye brake pad kupitia single-stage reduction system na ball-screw mechanism.

Kila actuator ina:

• force sensor inayopima applied force,
• resolver inayotoa motor position,
• motor phase currents,
• force na current control loops

.

PHM system ni muhimu hasa kwa sababu watafiti wanalenga kutumia sensors ambazo tayari zipo ndani ya brake-control system badala ya kuongeza dedicated wear sensor mpya.

High-fidelity model inajumuisha nini?

Model ambayo watafiti wanaiita “high-fidelity” si transfer function moja tu. Mechanical, electrical na thermal subsystems zimemodeliwa pamoja.

Main components ni:

• longitudinal aircraft motion,
• wheel rotational dynamics,
• tire–runway contact,
• anti-skid behavior,
• electro-mechanical actuators,
• brushless DC motor,
• PWM-controlled power electronics,
• reducer na transmission elasticity,
• ball screw,
• brake-pad–disc friction,
• brake temperature,
• pad wear.

Tire–runway friction ilimodeliwaje?

Slip ratio imefafanuliwa kama:

\[ \lambda = \frac{V-\omega_wR}{V} \]

. Hapa \(V\) ni aircraft linear speed, \(\omega_w\) ni wheel angular speed, na \(R\) ni effective rolling radius.

Instantaneous tire–runway friction coefficient huhesabiwa kwa modified Burckhardt model:

\[ \mu=\mu_0(\lambda)\mu_{max}(p_{tire},v_{air}) \]

Kwa hiyo, braking behavior haitegemei brake mechanism pekee, bali pia slip ratio, tire pressure, aircraft speed, tire type na runway conditions.

Katika second-order surface fit ya model kwa experimental reference data, \(R^2\) values ziliripotiwa kuwa 0,9976 kwa dry asphalt, 0,9941 kwa treaded tire–wet asphalt na 0,9892 kwa smooth tire–wet asphalt.

Kwa nini brake temperature ni muhimu kwa PHM?

Katika braking, sehemu kubwa ya mechanical energy hubadilishwa kuwa heat. Katika source model, brake power:

huhamishwa kwenda thermal system kupitia disc–pad friction, huku pad temperature \(T_{brake}\) na brake-case temperature \(T_{case}\) zikifuatiliwa kama separate thermal nodes.

Simplified thermal balance imewakilishwa na:

\[ P_{fr} - \frac{T_{brake}-T_{case}}{R_{br,c}} = C_{brake}\frac{dT_{brake}}{dt} \]

na:

\[ \frac{T_{brake}-T_{case}}{R_{br,c}} - \frac{T_{case}-T_{amb}}{R_{amb,c}} = C_{case}\frac{dT_{case}}{dt} \]

.

Kwa simplification, model inachukulia braking power yote kuwa heat; secondary loss mechanisms kama noise na vibration zimepuuzwa.

Pad wear inamodelliwaje?

Pad wear imeingizwa kwenye model kama increase ya free stroke inayohitajika kufikia disc.

Wear increment huhesabiwa kama:

\[ \Delta x_{thr} = \int f_{wear}(T) K_{wear}(T) v(t) p(t)\,dt \]

.

Hapa wear inahusishwa na physical variables kama temperature, pad–disc sliding speed na contact pressure.

Hata hivyo, wear coefficients zilizotumiwa hazikutolewa kutoka real tribological tests za prototype brake pad hii. Kwa kuwa experimental data ya specific material bado haipo, literature values za similar friction pairs zilitumika kama msingi na coefficients zikashughulikiwa kama stochastic variables katika simulation.

Ni uncertainties gani zipo katika simulation?

Badala ya ideal landing moja, watafiti walitengeneza operating conditions nyingi. Variables ni pamoja na:

• aircraft mass wakati wa landing,
• runway temperature,
• runway wetness,
• tire type,
• tire pressure,
• approach speed,
• normal au emergency braking,
• manufacturing tolerances,
• pilot reaction time,
• sensor noise

.

Aircraft mass ilisampleiwa kutoka uniform distribution karibu 5,5–6,1 tonnes, approach speed kutoka normal distribution yenye mean 110 knot na standard deviation 5 knot, na tire pressure kutoka distribution yenye mean 200 psi na standard deviation 30 psi.

Pilot reaction delay ilibadilishwa kati ya 0,1–0,5 seconds.

Runway conditions zinaathirije braking distance?

Values hizi si real field braking distances za target aircraft; ni distributions zilizotengenezwa na high-fidelity simulation.

Brake temperatures

Kutokea kwa higher brake temperatures kwenye dry runway licha ya shorter braking distance kunaendana na tire–runway system kuweza kuhamisha braking power kubwa zaidi.

Health indicator ilichaguliwaje?

Kwa kuwa PHM algorithm haina dedicated sensor inayopima wear moja kwa moja, health indicator inayobadilika regularly na wear ilitafutwa ndani ya existing brake signals.

Candidate features zilitathminiwa kwa Pearson correlation pamoja na Signal-to-Noise Ratio (SNR), inayowakilisha robustness kwa external operating conditions.

Kwa nini maximum motor angle ni indicator yenye nguvu sana?

Kwa kuwa mechanism inatumia ball screw, motor rotation ina direct relation na actuator linear motion. Kadiri brake pad inavyokuwa thin, initial clearance kati ya pad na disc huongezeka.

Katika hali hii, actuator lazima itembee distance kubwa zaidi kabla braking haijaanza. Ikiwa ball screw lazima ifanye linear motion kubwa zaidi, electric motor pia lazima izunguke zaidi.

Kwa hiyo:

Pad wear ↑ → disc–pad clearance ↑ → EMA free stroke ↑ → ball-screw motion ↑ → motor maximum angular position ↑

relation hutokea.

Advantage ya indicator hii si high correlation pekee. Source Figure 13 inaonyesha kwamba licha ya different runway, tire na braking conditions, values zilibaki kwenye approximately linear trend ileile kulingana na wear ratio.

Kwa nini particle filter ilichaguliwa?

Study ilichagua particle filter badala ya fully data-driven models kama LSTM. Main reason ni kwamba hakuna large physical run-to-failure dataset kwa real prototype brake.

Large black-box model iliyotrainiwa kwa synthetic data pekee ina risk ya kujifunza assumptions za simulation model badala ya physical brake.

Particle Filtering huunganisha physical wear-progression model na measured health indicator katika Bayesian framework. Pia inaweza kuwakilisha nonlinear degradation processes ambazo si lazima zifuate Gaussian distribution kwa particle distributions.

Basic structure ya particle filter

State probability distribution huwakilishwa approximately kwa number fulani ya particles na weights zake:

\[ p(x_t|y_{1:t}) \approx \sum_i w_t^i \delta(x_t-x_t^i) \]

Katika SIR approach, particle weights huupdate kulingana na likelihood ya new measurement:

\[ w_t^i \propto w_{t-1}^i p(y_t|x_t^i) \]

Katika study, process model ya particle filter iliundwa kama:

\[ x_{N+1} = K_{wear}(E_{brake,N}) + x_N + \omega(N) \]

na measurement model:

\[ y_{N+1} = f(x_{N+1},\nu(N)) \]

.

\(x_N\) inawakilisha pad-wear state, \(y\) motor maximum angular position, na \(E_{brake,N}\) total energy indicator iliyoprocessiwa na brake katika Nth landing.

Brake energy ya landing moja

Brake-energy indicator huhesabiwa kupitia forces za actuators nne na wheel angular speed:

\[ E_{brake,N} = r_{ebrake} \int_{t_0}^{t_{end}} \sum_{i=1}^{4} F_i\omega_w\,dt \]

.

Value hii huandikwa kwenye “landing repository” baada ya kila landing.

Landing repository ni nini?

Structure hii ni mojawapo ya elements zinazovutia zaidi katika study. Algorithm haihesabu future service life kwa fixed assumption kwamba “every landing is the same”.

Baada ya kila flight, database inaweza kuongezewa:

• braking energy,
• runway conditions,
• aircraft mass,
• tire information,
• brake temperature,
• relevant aircraft-level operating information

.

Wakati long-term RUL prediction inafanywa, possible future landings husampleiwa randomly kutoka historical usage distributions hizi. Hivyo remaining life hutokana si na fixed mission profile moja, bali na aircraft yenyewe growing operational history.

RUL inafafanuliwaje?

Algorithm huendeleza wear state mbele kwa wakati na kuunda probability distribution ya remaining number of landings zinazohitajika kufikia defined End of Life region.

Relative Accuracy huhesabiwa kama:

\[ RA = 1- \frac{|RUL_r-RUL|}{RUL_r} \]

.

Hapa \(RUL_r\) ni simulated real remaining life, huku \(RUL\) ni remaining life iliyotabiriwa na algorithm.

Prognostic Horizon hutathminiwa kupitia point ambapo prediction inaingia kwa mara ya kwanza ndani ya ±%20 band ya real RUL value.

Model na prognostic algorithm hazikufanywa intentionally kuwa identical

Kama important methodological detail, high-fidelity wear model inayozalisha fault-to-failure data na wear model inayotumiwa na particle filter si identical.

Wakati simulation data inatengenezwa, wear coefficient inategemea variables kama instantaneous temperature na contact pressure. Katika particle filter, simplified wear law inatumika na wear coefficient inakuwa mmoja wa stochastic parameters wanaoestimated online.

Choice hii ilifanywa kuzuia particle filter isihesabu tu model iliyoiunda na kujaribu behavior yake chini ya structural model mismatch.

Mbinu na Matokeo ya Utafiti

Simulation infrastructure

High-fidelity dynamic model, electrical, mechanical na thermal subsystems, pamoja na particle-filtering structure zilitengenezwa na kusimulated katika MATLAB R2022a/Simulink.

Physical E-Brake prototype inaendelea kutengenezwa ili baadaye iintegrate kwenye Iron Bird ground-test system. Kwa hiyo, katika stage hii hakuna large-scale run-to-failure database iliyopatikana kutoka real prototype.

Database creation

Emergency-braking maneuvers zilitumika hasa kutengeneza basic behavior database. Sababu ni kupunguza variable effect ya pilot command katika emergency braking na kuchunguza dynamics za E-Brake system yenyewe katika controlled manner zaidi.

Normal braking pia ilitathminiwa ili kuangalia effect ya operating conditions kwenye health indicator.

Health-indicator selection

Kwa feature selection, simulations ziliendelea hadi karibu %50 cumulative wear level na correlations za candidate signals na wear zikachunguzwa.

Motor maximum angular position:

• Pearson correlation: 1,00
• SNR, %20 wear: 53,71
• SNR, %40 wear: 54,99

ikawa main selected health indicator.

Fault-to-failure tests

Prognostic algorithm ilitathminiwa kwenye 40 different simulated fault-to-failure processes.

Particle count:

\[ N_p=50\ldots5000 \]

ilibadilishwa.

Katika detailed examples zenye 5000 particles, particle distribution ilionyesha progression inayolingana na simulated ground-truth wear values kutoka fault detection hadi region ya approaching end of service life.

RUL distribution inaonyesha nini?

Source Figure 17 inaonyesha RUL distributions katika different times kwa sample fault-to-failure process ambapo EOL imewekwa kuwa 600 landings.

Katika example, predictions zilirecalculate baada ya:

• 60th landing,
• 192nd landing,
• 357th landing,
• 522nd landing

.

Kadiri aircraft service life inavyoendelea, predicted RUL distribution hukaribia real simulated EOL point. Kulingana na source, real EOL value inabaki ndani ya displayed prediction distributions.

RA na CRA results

Relative Accuracy na Cumulative Relative Accuracy results zilizopatikana kutoka 40 simulated landing sequences zimeonyeshwa katika source Figure 19.

Watafiti wanaeleza kwamba mean RA kwa ujumla ilibaki juu ya %80 acceptance threshold na CRA values pia zilionyesha high levels.

Hata hivyo, source haitoi single final “mean accuracy = X%” value kwa results hizi. Kwa hiyo, approximate number haijasomwa kutoka graph na kutumiwa hapa kama exact result.

Matokeo yanayoungwa mkono na utafiti

• PHM algorithm iliweza kutengenezwa kwa prototype-stage E-Brake kwa kutumia high-fidelity simulation data.
• Katika simulation environment, extremely strong relation ilipatikana kati ya pad wear na electric motor maximum angular position.
• Selected health indicator ilionyesha high robustness kwa runway na braking conditions kuliko candidate nyingine.
• Particle filter iliweza kufuatilia hidden pad-wear state parallel na simulated ground-truth.
• RUL probability distributions zilikaribia simulated EOL point katika sample fault-to-failure process.
• Mean RA performance ya 40 simulation sequences iliripotiwa kwa ujumla kuwa juu ya %80 threshold.
• Kwa kuwa existing EMA position na current measurements zinaweza kutumika kwa PHM, dedicated additional wear sensor inaweza kutohitajika.
• Landing repository approach inaweza kuingiza historical aircraft usage conditions kwenye future stochastic RUL prediction.

Matokeo ambayo utafiti haujathibitisha

• Haijathibitishwa kwamba algorithm itatoa RUL accuracy ileile kwenye real aircraft.
• Physical run-to-failure experiments na real E-Brake prototype bado hazijafanywa.
• Pad-wear coefficients hazijacalibrated kutoka real tribological tests za target prototype.
• Haijaonyeshwa kwamba selected motor-angular-position indicator ni universal health indicator kwa all electro-mechanical aircraft brakes.
• System yenye multiple simultaneous fault types haijavalidated comprehensively.
• Disc wear si main target ya current prognostic state model.
• Operational benefit katika real flight operations, maintenance personnel na certification processes bado haijapimwa kwa field testing.

Main scientific limitations

Limitation muhimu zaidi ni kwamba PHM-system performance evaluation inategemea synthetic fault-to-failure data.

Ingawa high-fidelity model inajumuisha physical knowledge kwa upana, simulation si real system yenyewe. Hasa kutokuwa na experimentally determined wear coefficients specific kwa pad material bado ni important uncertainty ya real wear rate.

Pia, selected health indicator ina direct dependence na EMA–ball-screw–pad geometry. Electro-mechanical brake systems zenye architecture tofauti zinaweza kuhitaji indicators tofauti.

Source pia inasema kwamba classical Sequential Importance Re-sampling approach inayotumiwa katika particle filter ina limitations katika representing probability distributions, hasa tail regions. Watafiti wanaona method hii kuwa sufficient kwa preliminary study katika stage hii.

Future work

Experimental validation imefafanuliwa kama mandatory next step mara physical test system itakapopatikana.

Katika future, pia imepangwa:

• model calibration kwa real brake-wear data,
• kuongeza disc wear kwenye system,
• management ya multiple simultaneous fault modes,
• Bayesian data fusion,
• kuingiza future weather/runway conditions kulingana na operating region katika landing-repository sampling

.

Maelezo ya Chanzo na Mbinu

Jina kamili asilia la utafiti: A Simulation Study on Wear Monitoring and Prognosis in Electro-Mechanical Brakes for a Small Passenger Aircraft

Waandishi: Riccardo Achille; Andrea De Martin; Antonio Carlo Bertolino; Giovanni Jacazio; Massimo Sorli.

Corresponding author: Riccardo Achille.

Taasisi: Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy.

Aina ya chanzo: Peer-reviewed research article.

Jarida: Actuators.

Mchapishaji: MDPI.

Publication: 2026, Volume 15, Article 161.

Submission date: 19 January 2026.

Revision date: 6 March 2026.

Acceptance date: 8 March 2026.

Publication date: 11 March 2026.

DOI: 10.3390/act15030161.

Official link:https://doi.org/10.3390/act15030161

Leseni: Creative Commons Attribution (CC BY).

Relation na previous work: Article ni revised na expanded version ya “Development of a PHM system for electrically actuated brakes of a small passenger aircraft” iliyowasilishwa katika 8th European Conference of the Prognostics and Health Management Society iliyofanyika Prague tarehe 3–5 July 2024.

Funding: Research ilifadhiliwa kupitia project ya “Electromechanical Landing Gear System Integration for Small Aircraft” (E-LISA), grant agreement 887222, chini ya European Commission Horizon 2020 Framework Programme.

Ethics committee: Not applicable.

Informed consent: Not applicable.

Data availability: Access to data is restricted. Data zilitolewa na E-LISA Consortium na zinaweza kupatikana kutoka kwa authors kwa permission ya consortium.

Conflict of interest: Waandishi waliripoti hakuna conflict of interest. Imeelezwa kwamba funder hakuwa na role katika study design, data analysis na interpretation, manuscript preparation au publication decision.

Method summary: Study inaunganisha mechanical, electrical na thermal behavior za electro-mechanical aircraft brake katika high-fidelity simulation environment ili kutengeneza synthetic fault-to-failure processes za pad wear. Operating conditions hubadilishwa stochastically; wear-related health indicators huchaguliwa kwa Pearson correlation na SNR; motor maximum angular position hutumika kama main health indicator, na state estimation pamoja na RUL prediction hufanywa kwa particle filter inayotegemea Sequential Importance Re-sampling.

Critical note kuhusu experimental validation

Kutumia “high-fidelity model” katika study hii na kuwa “PHM system iliyovalidated kwenye real physical E-Brake” si kitu kilekile.

Article inaeleza wazi kwamba physical prototype bado iko development stage na hakuna historical run-to-failure dataset. Kwa hiyo, all 40 fault-to-failure processes na RUL ground-truth values zilitengenezwa na simulation.

Kwa hiyo, results zinaunga mkono applicability na potential ya algorithm-design approach katika simulation environment; hazithibitishi certification-level prognostic accuracy kwenye real aircraft.

Critical note kuhusu wear model

Pad-wear coefficients hazikutolewa experimentally kutoka specific friction material ya target E-Brake prototype. Source study inaeleza wazi kwamba parameters hizi zilitolewa kutoka literature kuhusu similar friction pairs na kushughulikiwa stochastically.

Kwa hiyo, absolute pad life au remaining number of landings hazipaswi kutumika kama validated service-life values za real target brake.

Critical note kuhusu RUL performance

Source Figure 19 inaonyesha kwamba mean Relative Accuracy kwa ujumla iko juu ya %80 threshold; lakini study hairipoti final performance kama single precise mean percentage. Kwa hiyo, approximate numbers hazijatolewa kutoka graph na kuwasilishwa kama scientific data.

Vivyo hivyo, source Figure 17 ina specific simulation example yenye EOL = 600 landings. Value hii ya 600 landings ni end-of-life point ya specific synthetic fault-to-failure example; si certified au general service life ya aircraft brake inayochunguzwa.