22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 Coparing structural airfrae aintenance strategies based on probabilistic estiates of the reaining useful service life. WAG a, C.GOGU b,.biaud b, C.BES b a. ISA de Toulouse, Institut Cléent Ader, yiwang@insa-toulouse.fr b. Université Toulouse III, Institut Cléent Ader, christian.gogu@univ-tlse3.fr b. Université Toulouse III, Institut Cléent Ader, nicolas.binaud@univ-tlse3.fr b. Université Toulouse III, Institut Cléent Ader, christian.bes@univ-tlse3.fr Abstract: Structural airfrae aintenance is a subset of aircraft aintenance, which is often perfored at scheduled intervals to detect and repair cracks that would otherwise affect the safety of the aircraft. With the progress of structural health onitoring (SHM) techniques, which uses on-board sensors and actuators to assess daage status, condition-based aintenance (CBM) is considered as an alternative to traditional scheduled aintenance. By applying SHM techniques, CBM can access daages status as frequently as needed and unscheduled aintenance can be asked once the daage exceeds a particular threshold. Due to the harsh working environent and sensor liitation, the easureent data acquired fro SHM is often quite noisy. In this paper, Extended Kalan filter is used to filer the noise to provide an accurate estiation of crack size and crack growth paraeters together with their associated uncertainty. This knowledge is used to obtain a probabilistic estiate of the reaining useful service life of the structure. Based on these estiates, two aintenance philosophies are developed and further copared in ters of aintenance stop nuber or replaced panel nuber. The results indicate that both these two strategies reduce considerably the aintenance stop nuber copared to scheduled aintenance. Key words: Structural health onitoring, Scheduled aintenance, Conditionbased aintenance, Extended Kalan filter, Reaining useful service life 1 Introduction Aircraft aintenance can be classified into airfrae aintenance and engine aintenance. The airfrae aintenance that deals with non-structural ites such as furniture and electronic systes is called non-structural airfrae aintenance [1] while the one that concerns the cracks in the structural section (such as fuselage panels) which grows due to loading/unloading cycles during takingoff/landing and have the risk of leading to panel fatigue failure is called structural airfrae aintenance. This paper focuses on structural airfrae aintenance.
22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 Traditionally, aircraft aintenance is scheduled. For a typical short-range coercial aircraft (e.g. A320, B737) the first aintenance occurs at 20000 th flight cycle and consecutive aintenance is perfored every 4000 cycles until its end of life, which is 60000 cycles. The aintenance schedule for coercial aircrafts is designed to be conservative to ensure a very low probability of failure, which iplies that there are no critical cracks being detected on an aircraft s fuselage panels during the scheduled aintenance tie in the early life of the aircraft. With the progress of structural health onitoring (SHM) technique, condition-based aintenance (CBM) is considered an alternative strategy to scheduled aintenance. Through the help of on-board sensors and actuators of SHM syste, CBM evaluates the daage status as frequently as needed and asks unscheduled aintenance whenever the crack size exceeds a particular threshold. One proble is that the crack size easureent data acquired fro SHM syste can be quite noisy due to the harsh environent and sensor liitations. An efficient filtering technique is necessary to filter the noise and get a uch ore accurate estiate for the crack size and the crack growth paraeters. Extended Kalan filter (EKF) is proposed here since it is a coonly used algorith for recursive nonlinear state estiation due to its excellent filtering properties. In practice, CBM strategy is yet to be ipleented in coercial aircrafts. One of the issues preventing its widespread ipleentation is that CBM is considered too disruptive to traditional aintenance process. Another downside of pure CBM is that daage assessent by on-board SHM is less accurate than DI techniques used for scheduled aintenance, CBM would lead to a lower level of reliability than scheduled aintenance [2]. It is then likely that CBM would benefit fro working in tande with traditional scheduled aintenance. ou [3] developed a fraework to integrate CBM with scheduled aintenance. Fitzwater cobined CBM with traditional scheduled aintenance and applied the proposed aintenance strategy on an F-15 fighter aircraft [4]. Pattabhiraan presented a hybrid aintenance strategy to skip unnecessary scheduled structural airfrae aintenance using an on-board structural health onitoring syste and argued that the hybrid strategy has the potential to lead to substantial cost saving over the lifetie of an aircraft [2]. The ai of the present paper is to propose and copare new structural airfrae aintenance strategies based on a probabilistic estiate of the reaining useful servicing life of the structural airfrae parts. The paper is organized as follows. Section 2 introduces the crack growth odel and the developed procedure for EKF estiation of the crack size and crack growth paraeters based on noisy SHM data. Section 3 presents two aintenance strategies that are proposed that take advantage of the EKF estiations. Section 4 copares the two strategies in ter of aintenance stops and nuber of replaced panels by a case study. Conclusions are drawn in section 5. 2. Crack size estiation using EKF During the lifetie of an aircraft, loading and unloading cycles occur due to repeated pressurization/depressurization of the fuselage and can lead to fatigue cracks in the fuselage panels. Cracks or daages in this paper refer to existing flaws on the fuselage panel of an aircraft. Typically, a fuselage is odeled as a hollow unifor cylinder while cracks in the fuselage panel are odeled as through-the-thickness center straight cracks in an infinite plate. This assuption is well verified if the crack size is sall copared to the distance between fuselage stiffeners. For larger crack sizes the odel can be adjusted by considering corrective ters in the calculations of the stress intensity factors to account for boundary conditions effect of stiffeners. The life of an aircraft can be viewed as consisting of daage propagation cycles, interspersed with inspection and repair. Crack propagation can be odeled in yriad ways depending on different phenoena to which the critical crack site is subject [5-7]. Based on airfrae fatigue tests on various ilitary aircrafts, Molent et al. concluded that a siple crack growth odel adequately represented a typical crack growth [8]. In this work, the
22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 celebrated Paris law is selected to describe the crack growth behavior since it is coonly used for fatigue analysis due to its siplicity. The Paris law is given by [9]: da C( K) d (1) where a is the half-crack size in eters, is the nuber of load cycles. da/d is the crack growth rate in eters/cycle. C and are the Paris law paraeters which are associated with aterial properties. K is the range of stress intensity factor in MPa, which is approxiated in Eq.(2) as a function of the pressure differential (p), fuselage radius (r) and panel thickness (t). The coefficient A in Eq.(2) is a correction factor that copensates for odeling the fuselage as a hollow cylinder (thus ignoring the effect of stringers and stiffeners). K= A pr a (2) t Syste dynaics is discretized such that a discrete-tie EKF can be used. Euler ethod is eployed to discretize Eq.(1). The discrete Paris law can be written in a recursive for at each flight cycle k a k a f ( a k 1 k 1 C( K) ) w k 1 where wk 1 is the additional process noise. Here wk 1 is assued to be 0. Since the crack size is easured by sensors, the easured crack size always contains noise due to the easureent environent and sensor liitations. The easureent data is odeled as z h( a ) v (4) k k k in which h is the easureent function and v k is the easureent noise such that vk ~ (0, R ). In this paper, the easureent function h is identity. Eq.(3) and Eq.(4) are called the syste equation and easureent equation respectively. In the aforeentioned crack growth odel, and C are the unknown paraeters that need to be estiated. A two-diensional paraeter vector is defined as [ C, ] T (5) Appending to the state variable, that is crack length a, the augented state vector is defined as x [ a C] T (6) aug Using subscript aug to denote all the augented variables, the extended syste is represented in Eq.(7). xaug, k faug ( xaug, k 1) waug, k 1 (7) z h ( x ) v aug, k aug aug k aug, k aug, k where v, is the augented easureent noise vector including v ak,, vk, and v Ck,, which represent respectively the uncorrelated easureent noise of each state variable with a zero ean and a variance of Ra, R, RC. The augented easureent noise covariance atrix R aug could be written as Raug diag ( Ra, R, RC) (8) The details of the EKF algorith can be found in [10,11]. We use the sybol " " to represent an estiate and subscript ''k'' to denote the tie step. Sybols ''-'' and ''+'' in the upper right corner are used to indicate a priori estiate and a posteriori estiate respectively. For exaple, xˆaug, k represents the a priori estiate of the augented state vector at tie step k while xˆaug +, k denotes the posteriori estiate at the sae tie. Siilar, P k + is the a priori estiate for state error covariance atrix at tie step k while P k - is the a posteriori one. The EKF algorith will be used next to deterine for each aircraft panel the associated aterial paraeters governing crack growth and C as well as their associated estiation uncertainty (P k + covariance atrix). Given this uncertainty in and C, various (3)
22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 possible siulations of the crack growth can be carried out, which will be used in the aintenance strategies that we propose next. 3 Maintenance strategies 3.1 CBM The condition-based aintenance strategy tracks daage as frequently as needed (typically every couple of dozen or few hundred flight cycles) and requests aintenance whenever the crack size is found to be large enough to threaten structural integrity. The daage status evaluation is called aintenance assessent. Figure 2 illustrates the flowchart of the proposed condition based aintenance strategy. Maintenance assessent is ipleented every 100 cycles. At each assessent, on-board SHM syste acquires crack size data on each panel. Here EKF is eployed to incorporate this noisy data into the Paris law to output an optial posterior estiate for crack size. If the axial crack size of an aircraft panels exceeds a particular threshold (a aint ), unscheduled aintenance is asked iediately and this aircraft is sent to the aintenance hangar, in which place all panels on this aircraft are inspected and for each of the a decision of whether replacing or not (called IfReplace decision) is ade. A straightforward idea for IfReplace decision is that panels with crack size greater than a second threshold a rep are replaced [2]. In this case, a rep should be assigned a sall value (uch saller than a aint ), aking the aintenance strategy too conservative. This is the basis of traditional condition based aintenance. ote however that the two aterial property paraeters and C are different fro panel to panel, which iply that the crack in each panel will propagate with its own rate in the future flight cycles. Based on this fact we seek a less conservative probabilistic ethod to ake a new IfReplace decision. Based on the existing knowledge of each individual panel at current flight cycle (i.e. crack size, and C given by EKF), we predict for each panel the future crack size distribution after a certain nuber of flight cycles, say I SHM flight. If we have, for exaple, 95% confidence that in the future I SHM flight cycles the crack in a panel will not exceed a aint, then this panel will not be replaced at the present aintenance stop. The selection for I SHM can be deterined in several ways. It is generally designed to aintaining a desired frequency of unscheduled aintenances or it can be just chosen based on the existing experiences of scheduled aintenance interval that recoended by certification authorities or aircraft anufacturers. The optiization of paraeter I SHM taking into consideration of boundary conditions like frequency of unscheduled aintenance and aintenance cost is the future work to be researched. In this paper, I SHM is set to be 4000 for initial attepts referring to the scheduled aintenance interval of a short-range coercial aircraft. The detailed process of the new CBM aintenance strategy, called CBM new, is presented in Figure 1. 3.2 CBM-Skip based strategy CBM-Skip is a hybrid strategy proposed in [2] that cobines the scheduled aintenance with the traditional CBM approach. CBM-Skip has the sae objective as pure CBM in ter of reducing unnecessary aintenance stops. However, CBM-Skip ensures as uch as possible that aintenance activities are carried out in scheduled aintenance interval. As in section 3.1 we propose to odify CBM-skip here to take into account the panel to panel variability and use a probabilistic estiate of the crack propagation to deterine the necessary aintenance actions. The idea of CBM-Skip is described as follow. The aintenance assessent is carried out at scheduled aintenance tie as well as every 100 cycles for unscheduled aintenance. At every scheduled aintenance stop, for each panel the crack size evolution fro current stop up to next scheduled aintenance stop is predicted by using Monte Carlo siulation. If the 95% of percentile of crack size exceeds the threshold a aint then this panel is replaced. The Flight cycles between two consecutive scheduled aintenance stop is noted by I sch, which is generally selected fro the scheduled aintenance interval according to the
In aintenance hangar, ake IfReplace decision 22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 corresponding aircraft type. If no panel needs to be replaced at this scheduled tie, then CBM-Skip recoends skipping this structural airfrae aintenance. If a crack issed at the tie of scheduled aintenance grows critical between two consecutive scheduled aintenances, CBM-Skip will recoend structural airfrae aintenance to be perfored iediately when this crack exceeds the threshold a aint. This calls for unscheduled aintenance, which is costlier but guarantees safety. The nuber of flight cycles fro current unscheduled aintenance until next scheduled aintenance stop is denoted by I SHM. At each unscheduled aintenance stop, we predict the crack propagation in the future I SHM cycles by Monte Carlo ethod. If the 95% of percentile of crack size exceeds a aint then this panel is replaced. ote that I SHM is distinct fro I SHM that was used in the CBM strategy. In CBM strategy, I SHM is optiized satisfying soe certain constrains like a desired reliability level and lowest cost. Once it is deterined, it keeps constant. While in CBM-Skip, I SHM is a variable depending on how any flight cycles are left fro current cycle to next schedule aintenance tie. The new CBM- Skip procedure, called CBM-Skip new, is shown in Figure 2. Start Set initial flight cycle k=0 Airplane in service (Daage grows) k=k+100, ipleent aintenance assesseent For state vector of each panel, x aug,k =[a k k C k ] T, get its eanμ=x + aug,k and covarianceσ=p + k fro EKF If axial crack >=a aint Unscheduled aintenance asked. Aircraft sent to aintenance hangar iediately Initialize panel counter i=1 Draw saples of state vector based on the ultivariate noral distribution, x aug,k ~(μ,σ) Grow the crack size of each saple I SHM cycles. Obtain the distribution of crack size Calculate the 95% quantile of the saples, denoted by a_quantile If a_quantile>a aint Panel Replace i++ Aircraft go to next service If i<=total nuber of panel If end of life? Stop Figure 1 Flowchart for the CBM new strategy
In aintenance hangar, ake IfReplace decision In aintenance hangar, ake IfReplace decision 22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 Start Set initial flight cycle k=0 Airplane in service (Daage grows) k=k+100, ipleent aintenance assesseent For state vector of each panel, x aug,k =[a k k C k ] T, get its eanμ=x + aug,k and covarianceσ=p + k fro EKF If at the tie of scheduled aintenance? Initialize panel counter i=1 Draw saples of state vector based on the ultivariate noral distribution, x aug,k ~(μ,σ) If axial crack >=a aint Unscheduled aintenance asked. Aircraft sent to aintenance hangar iediately Grow the crack size of each saple I sch cycles. Obtain the distribution of crack size Calculate the 95% quantile of the saples, denoted by a_quantile Initialize panel counter i=1 Draw saples of state vector based on the ultivariate noral distribution, x aug,k ~(μ,σ) If a_quantile>a aint Panel Replace i++ Grow the crack size of each saple I SHM cycles. Obtain the distribution of crack size Calculate the 95% quantile of the saples, denoted by a_quantile If i<=total nuber of panel If nuber of replaced panel==0? If a_quantile>a aint Panel Replace i++ Skip this scheduled aintenance Aircraft go to next service If end of life? Stop If i<=total nuber of panel Figure 2 Flowchart for CBM-Skip new strategy 4 Coparison between CBM and CBM-Skip based strategies In this section, the two aintenance strategies will be copared in ters of the nuber of aintenance stops and nuber of panels replaced. A typical short-range coercial aircraft (e.g. A320, B737) is considered here. The schedule aintenance for this kind of aircraft is that the first aintenance happens at 20000 flight cycle and consecutive aintenance is ipleented every 4000 cycles until its end of life, which is 60000 cycles. A fleet of 100 aircrafts is siulated. Each aircraft is assued to have 500 fuselage panels and each panel is assued to have an initial crack. The values in Table 1 are used in this case study. The coparison results are shown in Table 2. The CBM is copletely rando in nature, eaning that aintenance stop can occur any tie within the lifetie of the aircraft. The proposed CBM new strategy indicates that on average an aircraft
22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 undergoes very few aintenance stops during their lifetie copared with scheduled aintenance (10 aintenance stops). However, the pure CBM strategy always requires unscheduled aintenances, which can be quite disruptive of the airline s traditional service planning and can thus be quite costly. CBM-Skip has a little higher average aintenance stop than pure CBM, however it has alost no unscheduled aintenances. This strategy incorporates the advantages of scheduled aintenance and CBM. It reduces the aintenance stops and reduces the cost of unscheduled aintenances copared to CBM because the nuber of unscheduled aintenance is negligible here. Table 1 Panel-to-panel uncertainties Paraeter otation Type Value Initial crack size a 0 Lognoral Ln (0.2e-3, 35%COV) Mean value of Deterinistic 3.8 Standard deviation of Deterinistic 0.27 Mean value of C C Deterinistic Log 10 (1.5e-10) Standard deviation of C Deterinistic 0.16 C Correlation coefficient of and C Deterinistic -0.8 Paris law paraeter 0 Multivariate (,, C, C, ) Paris law paraeter C 0 noral Individual panel uncertainties used in EKF Estiated initial crack length â 0 Unifor U[a 0-25% a 0, a 0 +25% a 0 ] Estiated initial ˆ 0 Unifor U[ 0-25% 0, 0 +25% 0 ] Estiated initial C Ĉ 0 Unifor U[C 0-25% C 0, C 0 +25% C 0 ] Initial error covariance atrix P 0 Deterinistic diag (1e-4,1,1e-10) Measureent noise variance Ra Deterinistic (30% a 0 ) 2 Measureent noise variance R Deterinistic (50% 0 ) 2 Measureent noise variance RC Deterinistic (50% C 0 ) 2 Aircraft geoetry paraeters Fuselage radius r Deterinistic 1.95 Panel thickness t Deterinistic 2e-3 Correction factor A Deterinistic 1.25 Paraeters related to aintenance Unscheduled aintenance threshold a aint Deterinistic 39.5e-3 Paraeter in SHM strategy I SHM Deterinistic 4000 Paraeter in CBM-Skip strategy I sch Deterinistic 4000 Maintenance strategy Table 2 Coparison of the two aintenance strategies Average o. of Average o. of Average o. of panel aintenance stops per unscheduled replaced aircraft aintenance stops per aircraft CBM new 1.28 1.28 3.4 CBM-Skip new 4.64 0 6.7 5 Conclusions This paper presents two kinds of condition-based aintenance strategies based on structural health onitoring. The easureent uncertainty of SHM syste is considered and the noisy SHM data is incorporated into a deterinistic Paris law odel using extended Kalan filter to iprove the accuracy of the crack size estiation. Based on the estiated crack size, new CBM and CBM-Skip strategies are developed. The proposed CBM new strategy is designed copletely rando without
22 èe Congrès Français de Mécanique Lyon, 24 au 28 Août 2015 considering scheduled aintenance tie. Unscheduled aintenance can be required at any tie in the aircraft s lifetie. This strategy is thus uch ore disruptive to traditional aintenance organization. CBM incurs uch fewer aintenance stops than that of scheduled aintenance but the aircraft safety has been reduced. By contrast, CBM-Skip new incorporates both the advantages of CBM and scheduled aintenance, which reduces unnecessary aintenance stops (although a little bit higher than CBM but still uch lower than scheduled aintenance) as well as guarantees aircraft safety. Furtherore, by applying CBM-Skip, alost all aintenance stops occur during one of the ten scheduled interval when engine and non-structural aintenance are ipleented. This is likely to have a beneficial role in ters of lifetie aintenance costs. References [1] S. Pattabhiraan, C. Gogu,.H. Ki, et al. Synchronizing Condition-based Maintenance with ecessary Scheduled Maintenance. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynaics and Materials Conference, 2012 [ 2 ] S. Pattabhiraan, C.Gogu, a H. Ki, et al. Skipping unnecessary structural airfrae aintenance using an on-board structural health onitoring syste. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 226.5 (2012): 549-560. [3] M.ou, G.Meng. A odularized fraework for predictive aintenance scheduling. Proc IMechE, Part O: J Risk and Reliability 2012; 228(4) 380-391. [4] L. Fitzwater, C. Davis, T.Torng, et al. Cost/benefit analysis for integration of non-deterinistic analysis and in-situ onitoring for structural integrity. USAF condition-based aintenance plus (CBM+) initiative AFLMA Report LM200301800 (2003). [5] C.E.HARRIS, J.C.EWMA, R.S.PIASCIK, Analytical ethodology for predicting widespread fatigue daage onset in fuselage structure. Journal of Aircraft, 35.2 (1998) 307-317. [6] K.F.ILSSO, Elasto-plastic odels for interaction between a ajor crack and ultiple sall cracks. In : FAA-ASA Syposiu on the Continued Airworthiness of Aircraft Structures, Atlanta, GA, Proceedings. 1996. p. 197-224. [7] J.R.MOHAT, B.B.VERMA, P.K.RA, Prediction of fatigue crack growth and residual life using an exponential odel: Part I (constant aplitude loading). International Journal of Fatigue, 31.3 (2009) 418-424. [ 8 ] L.MOLET, S.A.BARTER, A coparison of crack growth behaviour in several full-scale airfrae fatigue tests, International Journal of Fatigue. 29.6 (2007) 1090-1099. [9] P.C.PARIS, F.ERDOGA, A critical analysis of crack propagation laws, Journal of Fluids Engineering. 85.4 (1963) 528-533. [10] M.S.GREWAL, A.P.ADREWS, Kalan filtering: theory and practice using MATLAB. John Wiley & Sons, 2011. [11] G.WELCH, G.BISHOP, An introduction to the Kalan filter,1995.