Feng LU ,Chunyu JIANG ,Jinqun HUANG ,*,Xiojie QIU

a Jiangsu Province Key Laboratory of Aerospace Power System,College of Energy and Power Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

b Aviation Motor Control System Institute,Aviation Industry Corporation of China,Wuxi 214063,China

KEYWORDS Aero-engine;Cubature information filter;Performance degradation;Sensor fusion;State estimation

Abstract Gas-path performance estimation plays an important role in aero-engine health management,and Kalman Filter(KF)is a well-known technique to estimate performance degradation.In previous studies,it is assumed that different kinds of sensors are with the same sampling rate,and they are used for state estimation by the KF simultaneously.However,it is hard to achieve state estimation using various kinds of sensor measurements at the same sampling rate due to a complex network and physical characteristic differences between sensors,especially in an advanced multisensor architecture.For this purpose,a multi-rate sensor fusion using the information filtering approach is proposed based on the square-root cubature rule,which is called Multi-rate Squareroot Cubature Information Filter(MSCIF)to track engine performance degradation.Soft measurement synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple sampling rates of measurement,and a fault sensor is isolated by maximum likelihood validation before state estimation.The contribution of this paper is to supply a novel multi-rate information filter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor system.Tests are conducted for aero-engine performance degradation estimation with multiple sampling rates of sensor measurement on both digital simulation and semi-physical experiment.Experimental results illustrate the superiority of the proposed algorithm in terms of degradation estimation accuracy and robustness to sensor failure in a multi-sensor system.

1.Introduction

Condition-based maintenance has been widely promoted in the field of aero-engine manufacturing,Maintenance,Repair,and Overhaul(MRO)in recent years.1,2A maintenance schedule formulated by current health condition brings improved operability and safety as well as reduced cost.The performance of an aero-engine gradually deteriorates over time due to fouling,corrosion,and erosion on major rotating components.Besides,accidental events resulted from Foreign Object Damage(FOD)or Domestic Object Damage(DOD)will impact a quick degradation in gas path performance.3,4The ingestion of birds and ice relates to the FOD,and the vane to ablate or fracture relates to the DOD.5Health parameters are defined by the changes of gas path component efficiencies and flow capacities,and they are generally utilized to represent gradual or abrupt performance degradation.Health parameters are unmeasurable from engine sensors,and different kinds of sensor measurements are introduced to calculate them.6-8A precise estimation of health parameters from available measurements plays an important role in gas-path performance analysis of Engine Health Management(EHM),and it has received more attentions.

Some approaches have been developed to gain the engine health condition from sensor measurements,such as weighted least squares,Kalman Filter(KF),genetic algorithm,sparse Bayesian,gray relation theory,neural networks,and sparse kernel method.9-15The KF-based approach is one of the most commonly used methods for estimating aero-engine degradation,since it relies on an engine physical performance model from classical aero-thermodynamics principle.16,17More physical characteristics of engine components are contained in the KF-based approach,and they are hardly interrupted by measurement noise and little depend on prior samples of a degradation dataset.Among these KFs,a linear KF is employed for state estimation of a linear dynamic system,and extended to a nonlinear dynamic system by the Extended KF (EKF),Unscented KF(UKF),and Cubature KF(CKF).18-20The EKF is with a first-order Taylor series expansion,while both of the UKF and CKF with a second-order expansion.The former nonlinear filtering algorithm produces more state estimation errors than those of the latter two due to a missed high-order term.The CKF has been developed in the last ten years as the closest ever known direct approximation of a Bayesian filter.Compared to the UKF,use of less state variable points in the CKF leads to less computational consumption without sacrificing accuracy.Hence,the CKF might be a better candidate for estimating performance degradation of aircraft engines.

The rapid development of sensor measurement technology promotes more kinds of sensors used to estimate engine performance degradation.Engine sensor measurements,like spool speeds,gas path temperature,and pressure,are collected and fused in various improved KF algorithms.21,22A bank of hybrid KFs with multiple sensors improves performance anomaly detection rates in EHM applications.23,24More sensor measurements used will advance the reliability of performance degradation estimation.However,some of the sensors operate in different sampling rates,which inevitably leads to a multi-rate state estimation issue in a sensor fusion process.That is to say,the complication of health estimation increases due to not only the number increase of sensor measurements but also the filtering synchronization in a multi-sensor system.Thus,a novel KF algorithm with data buffers was introduced to gas path health estimation with different rates of sensor acquisition.20The stability computation of the KF random Riccati equation was proven with partly missed observation,25and the KF stability analysis was presented as Markov packet losses.26An optimal sensor fusion state estimation method was discussed for multi-sensor systems with disordered measurements.27These studies presented the KF stability margin for state estimation in a multi-sensor system with different sampling rates,and mainly focused on the Linear Kalman Filter(LKF)in a linear system.

Reliable sensor measurements are the key for a KF estimator to calculate a state variable.However,it is hard to acquire real engine performance degradation if one of the sensor measurements deviates from the nominal value.It cannot ensure that the involved sensors run normally all time for state estimation,especially in the harsh operating circumstance of an aircraft engine.To address this gap,a novel multi-rate nonlinear filter methodology is proposed using sensor fusion and square-root cubature rule from previous studies of KF algorithms, which is named Multi-rate Square-root Cubature Information Filter(MSCIF).An information filter is utilized to describe state estimation with sensor fusion,since it brings easier expressions of time update and measurement update in a multi-sensor architecture. Multi-rate state estimation is achieved in the MSCIF by the soft measurement synchronous,and sensor measurements are divided into three subsets depending on various kinds of speed,pressure,and temperature with their own sampling rates.A Maximum Likelihood test combined to the MSCIF(ML-MSCIF)is designed to isolate an anomalous sensor by χ2test running in each sensor subset.Both digital simulations and semi-physical experiments are carried out to evaluate the involved algorithms for abrupt and gradual degradation estimation of aero-engine performance in a multiple-sampling rate measurement system, besides the combination of sensor fault tolerance is also addressed.Test results indicate that the proposed algorithm owns a satisfactory estimation accuracy with various sampling rates in a multi-sensor system.

The rest of this paper is organized as follows.Section 2 raises the problem of aero-engine health estimation using a state estimator based on sensor fusion with different sampling rates.In Section 3,the ML-MSCIF algorithm is explained in detail for multi-rate state estimation.Section 4 gives digital simulations and semi-physical experiments on a turbofan engine,followed by discussions are.Section 5 draws conclusion remarks and gives suggestions for further work.

2.Problem formulation

A dual-spool turbofan engine is studied in this paper,which includes an inlet,a fan,a compressor,a bypass,a combustor,a High-Pressure Turbine (HPT), a Low-Pressure Turbine(LPT),a mixer,and a nozzle.The inlet supplies airflow into the fan,and then air is divided into two streams:one flowing into the compressor and the other passing through the bypass.Air leaving the compressor moves to the combustor,and fuel is burnt to produce hot gas to drive turbines.The fan and the compressor are driven by the LPT and the HPT,respectively.Gas from the LPT and air from the bypass mix in the mixer,and then leaves the engine through the nozzle.A mathematical model of the engine is built on the basis of component-level modeling theories,20,28and it is expressed as

where xori(t),u(t),c(t),and y(t)are successively the engine original state variables,input variables,atmosphere variables,and sensor measurements.The input parameters of the engine model are the fuel flow Wfand the nozzle area A8,and the original state variables include the low-pressure spool speed NLand the high-pressure spool speed NH.The nonlinear function f(·)is the engine state transition function,and g(·)is the measurement function.The sensor measurements for engine degradation estimation are the fan outlet temperature T22,the fan outlet pressure P22,the compressor outlet temperature T3,the compressor outlet pressure P3,the HPT outlet temperature T43,the HPT outlet pressure P43,the LPT outlet temperature T5,and the LPT outlet pressure P5besides NLand NH.

The health parameter vector h=[SE1,SW1,SE2,SW2,SE3,SW3,SE4,SW4]Tis used to depict engine performance degradation from an ideal condition,and its element is defined by

where ηi,Wiare the real component efficiency and flow capacity,respectively,andare their ideal values.SE1,SE2,SE3,and SE4are the efficiency coefficients of the fan,the compressor,the HPT,and the LPT,respectively,and SW1,SW2,SW3,and SW4are separately their mass flow coefficients.The variations of unmeasurable health parameters of interest will result in sensor measurement changes.A Kalman filter is employed to estimate state variables from sensor measurements,so health parameters are added to the original state variables to be estimated.Then augmented state variables are rewritten by x=[xori,hT]T=[NL,NH,SE1,SW1,SE2,SW2,SE3,SW3,SE4,SW4]T.Fig.1 gives a sensor distribution diagram of an aero-engine29in a multi-sampling rates system.

In the multi-sensor system,the sensor measurements are classified into N subsets by the sensor kinds.In this study,engine physical parameters are normalized correction to standard atmosphere condition,and thus the atmosphere variable c is not involved in the nonlinear engine expression.Provided that the same sensor kind has a uniform sampling rate,the discretized equation of the engine model is summarized from Eq.(1)as follows:

where k is time index,and subscript is the i-th sensor subsets.yi(k)is the observation vector of the i-th sensor subset.The process noise term w(k)and the measurement noise term vi(k) are uncorrelated Gaussian white noises with E(wi,wj)=Q·δij,and E(wi,vj)=0,whereotherwise,δij=1;E(·)is the function for mathematical expectation and Q is variance matrix of process noise.

Suppose that the sampling rate of the i-th sensor subset is Si.For simplification and generality of sampling rate differences in various sensor subsets,N sensor subsets sampling rates follow

where Niis a known positive integer.An example of a multisensor system with different sampling rates is illustrated in Fig.2,and there are totally three sensor measurement subsets.Measurement data is collected in sensor subset 1 at each step,sensor subset 2 every second step,and sensor subset 3 every third step.That is to say,all sensor measurements are obtained from three sensor subsets separately with sampling rates of first step,second step,and third step,and it completes one global sampling cycle using six steps.

Fig.1 Aero-engine multiple-sensor distribution diagram for degradation estimation.29

Fig.2 Multi-sensor system of three sensor subsets with different sampling rates.

3.Multi-rate information filter algorithms

The state-space formulation of a state estimator is from the engine component level model,which is developed from a virtual turbofan engine from General Gas Turbine Simulation(GGTS).30It is programmed using C language,and packaged by a dynamic link library to be called by MATLAB software.Thus,the state-space formulation of the KF estimator is nonlinear.The computer hardware used for the simulation is CPU i5-3470@3.20 GHz and RAM 4 GB.The sampling time of the examined engine is 0.02 s.

An information filter is presented in the terms of an inverse information covariance matrix of a plain KF algorithm,and it is the mathematical equivalence to the plain-state estimator.20,31The information variables and covariance of the information filters bring easier expressions of time update and measurement update in the multi-sensor fusion system.An Extended Information Filter(EIF)and a Cubature Information Filter(CIF)are presented in this study,and a soft measurement synchronization is designed and combined with the involved information filter algorithms to perform degradation estimation for aircraft engines.

3.1.Multi-rate extended information filter

The EIF algorithm is derived from the plain EKF for state estimation of the nonlinear system in a multi-sensor system.The EIF is interested in the information state vectorand the information matrix PF(k|k )rather than the state estimateand the error covariance P(k|k )in the EKF.The detailed EIF algorithm is as follows.

The prior information state vectorand the prior information matrix PF(k |k-1)are given as

where P( k|k-1)is the prior error covariance,and φ(k)is the Jacobian expression of the nonlinear process equation in Eq. (3) at k, i.e.,is the posterior error covariance,and Q(k-1)is the process noise covariance at k-1.The prior state variableis obtained by

The posterior information state vectorand the information matrix PF(k|k )are updated as

where i (k)is the information state modification,and I(k)is the associated information contribution matrix,defined by

where υ(k) is the innovation vector,is the covariance matrix of measurement noise at time k,and H(k)is the Jacobian matrix of the nonlinear measurement equation,

Consider sensor fusion with different sampling rates during EIF state estimation,a soft measurement synchronization is designed and combined into the Multi-rate EIF(MEIF).When three sensor subsets are used to stream measurements for state estimation in the multi-sensor system as given in Fig.1,the posterior information variables of MEIF with the soft measurement synchronization are rewritten by

where mod (k ,Ni)=0 denotes k divided by Niwith no remainder,and moddenotes that k cannot be completely divided by Ni.

3.2.Multi-rate square-root cubature information filter

As was mentioned earlier,the CKF is a state-of-the-art nonlinear filtering algorithm,and there are 2n cubature points to be calculated for state estimation in the CKF at each step.Less computational efforts are paid by the CKF without estimation accuracy sacrifice compared to the UKF.The MSCIF is developed from the conventional CKF,and it deals with state estimation using multiple-sampling rate sensor measurement fusion.Square-root processing of the information contribution matrix in the MSCIF is to preserve the matrix positive definitiveness,and symmetry to improve the numerical stability during filtering iteration behavior. In addition, the MSCIF algorithm combined with a sensor fault tolerant criterion is discussed,and it is presented in detail in the following section.

In the MSCIF algorithm,the parameter of interest is the square-root of the information matrix SF(k|k )rather than the information matrix itself.SF(k|k )is derived from the factorization of the information matrix as

The number of cubature points is 2n as n state variables to be estimated.The l-th posterior cubature point X(l;k-1|k-1)at k-1 and the l-th prior cubature point X(l;k|k-1)at current step k are computed as

The predicted cubature state and its square-root of the error covariance are given as

where Tria(·)denotes the QR decomposition of the matrix,while SQ(k -1) is a square-root factor of Q(k -1), andThe weighted cubature state matrix is defined by

Similar to the corporation of EIF measurement equations in Eq.(3),a pseudo measurement matrix Hs(k)is introduced to MSCIF as

where the information covariance Pxy(k|k-1)is calculated from the weighted cubature state matrix Xs(k |k-1)and the measurement matrix Ys(k |k-1).With the help of the pseudo measurement matrix Hs(k),the information state modification i(k)and its information contribution matrix I(k)are expressed as

The information contribution matrix is factorized as I(k)=SI(k)( SI(k))T.Thus,the square-root factor SI(k)of the information contribution matrix is expressed as

where SR(k)denotes a square-root factor of R-1(k)so that R-1(k)=SR(k)(SR(k))T.Then,the updated cubature information state at step k is rewritten as

The updated information matrix is factorized at step k as follows:

The square-root matrix of the updated information is obtained by

In order to make the square-root CIF algorithm to achieve state estimation using different sampling rates measurement for the multi-sensor system,the calculation of soft measurement synchronization is also used to form the MSCIF.That is to say, the MSCIF algorithm is developed from the square-root CIF,and further extended to the applications of multi-rate state estimation in a sensor fusion configuration with information feedback.The posterior information variables of MSCIF with soft measurement synchronization are rewritten in three subsets of the multi-sensor system by

The MSCIF algorithm for sensor fusion of multiple sampling rates includes three parts:local information filtering estimation,soft synchronization module,and master information filter.The former one implements in the local field,and the latter two run in the fusion center.As three sensor subsets are involved,the speed sensor measurements are denoted by subset 1,pressure by subset 2,and temperature by subset 3.Each local information relates to one sensor subset,and measurements are collected in local information filters in different sampling rates.The local information variables are matched by the sampling rate,and streamed by the i-th channel triggered in soft synchronization.The local information state vectors and information contribution matrices are calculated real-time in the local field,and then transmitted to the fusion center for fusion calculation.

In the fusion center,the estimated local information variables are used in fusion calculation of the master information filter only when the measurement update completes in the local field.The master information filter produces global state estimates by time update and prediction steps,and it runs at the highest sampling step.The predicted information variables play the roles of the prior states in both the local field and the fusion center.The global information variables are feedback to each local information filter at the same time for the local estimates at the next step.The sensor fusion framework of the MSCIF algorithm is illustrated for a multi-sensor network in Fig.3.

Since the failure probability of a multi-sensor system increases as more sensors are utilized for state estimation,sensor fault detection and isolation capacity are critical to cut anomalous sensor data for improving the reliability of sensor fusion filtering estimation.Maximum likelihood validation is introduced and combined to check whether the sensed data fault or not for the MSCIF,and it is defined by the MLMSCIF.It is achieved by comparing the real to the predicted measurement,and accepting only those lie within a predetermined bound.The statistical χ2test is expressed by

where Ri(k)is the measurement noise covariance related to i-th sensor subset,λi(k)is the i-th sensor subset fault indicator,and niis the innovation vector dimension of the i-th local filter.The anomalous threshold of sensor measurement λi,maxis empirically selected by the statistical characteristics of sensor measurement noise.The sensor data is rejected as λi(k)＞λi,maxfor successively three steps,and λi(k),λi,maxare dimensionless parameters. As we know, the sensor measurements are redundant for the engine Full Authority Digital Electronic Control(FADEC),and there are usually dual-channel structures to ensure the system reliability.The redundant channel of sensor measurement runs in hot standby.In this paper,we assume that the sensor measurements in channel A are normally used for performance degradation estimation,and the measurements in channel B will work as sensor anomaly recognized.

Fig.3 Framework of MSCIF algorithm for a distributed multi-rate sensor network.

4.Experiments and discussion

4.1.Comparison of degradation estimation accuracy

The proposed methodology is assessed by systematical experiments using multi-rate sensor fusion for gas path degradation estimation of aircraft engines.Three physical sensor kinds are employed for engine performance estimation,and denoted by a speed sensor subset y1=[NL,NH],a pressure sensor subset y2=[P22,P3,P43,P5], and a temperature sensor subset y3=[T22,T3,T43,T5].Sensor measurements of various physical kinds own different sampling rates,and sensor faulty like anomaly bias is considered in the network.The MSCIF with a maximum likelihood test achieves to detect the combination anomaly of performance degradation and sensor faulty.Provided that subset 1 has a sampling rate S1=20 ms,the rest two sensor subsets have S2=40 ms and S3=60 ms.The covariance matrices of measurement noise in different sensor subsets follow R1=0.00152I2×2, R2=0.00152I4×4, and R3=0.0022I4×4.

Monte Carlo simulation of ten tries is performed to test gradual degradation and abrupt degradation of gas turbine engine performance.Root Mean Square Error(RMSE)and Root Mean Square Deviation(RMSD)are used as performance indicators to illustrate estimation accuracy of the proposed algorithms,and they are separately defined as

where Nqis the data series length of one test,and Npis the health parameter number of sensor subset.andare the estimated value,true value,and estimated average value of health parameters at time k in the j-th simulation run,respectively.

Engine performance gradual degradation is expressed by health parameters generally deviated from their nominal values in the course of its lifetime.The engine is health when every element of health parameter vector equals to 1.The health parameters are dimensionless.The health parameters start from 1 at t=0 s,and move to the magnitudes at the end t=10 s as:-2.18%on SE1,-2.85%on SW1,-6.71%on SE2,-8.99%on SW2,-3.22%on SE3,+2.17%on SW3,-0.808%on SE4,and+0.3047%on SW4.20Four typical abrupt degradations are involved:fan degradation(-2%on SE1and-2%on SW1),compressor degradation(-2%on SE2and-2%on SW2),HPT degradation(-2%on SE3and+2%on SW3),and LPT degradation(-2%on SE4and+2% on SW4). The deviations of health parameters are injected at t=2 s to simulate abrupt degradation.

The RMSEs by the MEIF with synchronous sampling of 40 ms and multi-rate sensor fusion are separately 0.0342 and 0.0311,and those by the MCIF are 0.0250 and 0.0231 in the case of gradual deterioration affecting all major components at the same time.Besides,typical operating points are selected to evaluate the proposed methodology in a flight envelope in cases of abrupt degradation,and they are labelled Point 1,Point 2,and Point 3.Operating Point 1 is at ground(Height H=0,Mach number Ma=0,Wf=2.48 kg/s),and it owns the corrected NL100%.Operating Point 2 is also at ground(H=0,Ma=0,Wf=1.95 kg/s),but its corrected NLis 90%. Operating Point 3 is at the cruise condition(H=10000 m,Ma=0.7,Wf=1.13 kg/s),and its corrected NLis 100%.Comparison results of estimation accuracy by the MEIF and the MSCIF are presented in Table 1,and RMSEs and RMSDs are involved in the cases of abrupt degradation and gradual degradation.

As seen from Table 1,RMSEs and RMSDs of the MSCIF are lower than those of the MEIF no matter which type of abrupt fault modes is examined at the three flight operating conditions.Likewise,the MSCIF has lower RMSEs than those of the MEIF during gradual deterioration simulations.Sincegradual deterioration impacts all components while abrupt degradation impacts one(at most two)component at a time,the former degradation estimation produces higher RMSEs than those of the latter one.It indicates that the MSCIF provides better health estimation accuracy and is less fluctuant around the real degradation compared to the MEIF.Hence,only the MSCIF is chosen and further assessed to state estimation performance with regard to sensor fault tolerance in digital simulations.

Table 1 Comparison results of estimation accuracy by MEIF and MSCIF at typical operations.

4.2.Sensor-fault-tolerant degradation estimation

The health parameter tracked by the MSCIFs is discussed under gradual deterioration with one sensor faulty during sensor fusion in a multi-sampling system.As was mentioned earlier,λ1,λ2,and λ3refer to the fault indicators of the speed,pressure,and temperature subsets,and fault thresholds of the three engine sensor subsets are selected by statistical measurement noise.32The fault thresholds of the three subsets are λ1,max=7.5,λ2,max=5,and λ3,max=5.The total cycle number is 2000 in the simulation.A magnitude 1.5%of sensor bias fault is injected to the LPT outlet pressure sensor P5during 1000-1400 cycles,and the remaining sensors run normally.The same bias magnitude is given to sensor NL,and it means that the sensor subset of the spool speed fails.Fig.4 depicts health performance estimation by MSCIF algorithms during gradual deterioration,and estimated and real values of health parameters are separately depicted by solid and dotted lines.

Four estimated health parameters SW2,SE3,SW3,and SW4by the MSCIF have rapid changes and deviate from their normal values as sensor P5fault injection at 1000 cycles under gradual deterioration in Fig.4(a).From Fig.4(c),the estimated fan flow capacity SW1drops obviously from 98.5%to 96.2%,and the rest health parameters change a little as sensor NLbias occurs.Some deviation of sensor measurements will pollute the health parameters estimates of the MSCIF,and these estimates are no longer suitable for engine performance monitoring.Fig.4(b)and 4(d)give the health estimation by the MSCIF with the maximum likelihood test during gradual degradation,and the fault indicators λ of the three sensor subsets in the ML-MSCIF are given in Fig.5(a)and 5(b).

From Fig.5(a),the fault indicators of spool speed and temperature sensor subsets λ1and λ3move smoothly,while λ2suddenly exceeds the fault threshold value(λ2,max=5)from 1000 cycles to 1400 cycles.The sensor P5breakdown only leads to a clear change on the fault indicator of the pressure sensor subset,and no effect on the other fault indicators.Fault indicator λ1violates its threshold,and the rest indicators λ2and λ3are below their thresholds during the sensor NLbias in Fig.5(b).As was mentioned earlier,the fault sensor will be isolated,and the corresponding sensor signal in Channel B will be triggered for state estimation when the sensor failure of a subset in Channel A is detected.Then the estimates of engine health parameters are calculated by the ML-MSCIF on the basis of the measurement without sensor bias pollution.

Fig.4 Health estimation with one sensor faulty under gradual deterioration by MSCIFs.

Fig.5 ML-MSCIF fault indicators of sensor subsets combined with gradual degradation.

Fig.6 Health estimation under abrupt degradation combined with sensor faulty.

When it comes to abrupt performance degradation,a simulation test of the MSCIFs on fan abrupt degradation and HPT abrupt degradation combined with sensor bias is carried out.The total simulation time is 10 s.The abrupt degradation of components occurs at t=2 s,and a 2%bias of sensor T43and NHare injected from 5 s to 7 s.Comparisons of engine health estimation between the MSCIF and the ML-MSCIF are shown in Fig.6.From Fig.6(a),the estimates of health parameters obviously deviate from their real values between 5 s and 7 s,especially the LPT efficiency suddenly shifts to 109%.It is obtained that the sensor bias results in a deviation of health parameter estimates by the MSCIF without maximum likelihood validation.Similar results can be obtained in Fig.6(c),and some health parameter estimates by the MSCIF clearly deviate from their real magnitudes as sensor NHfault.

The fault indicators λ of the three sensor subsets in the MLMSCIF are shown in component abrupt degradation in Fig.7.From Fig.7(a),the fault indicators of speed and temperature sensor subsets λ2and λ3exceed their thresholds at 2 s,and immediately move back.Only λ3runs above its threshold from 5 s to 7 s.The fault indicators λ2and λ3jump over their thresholds at 2 s,which is resulted from a component performance abrupt change. These indicators rapidly move below the thresholds after 2 s.Based on the maximum likelihood test of the ML-MSCIF,it is not sensor anomaly at 2 s since these fault indicators are not above their thresholds for three successive steps.Hence,the sensor measurement in Channel A will still work for engine health estimation by the ML-MSCIF,and no need of redundant measurements in Channel B.Since the overrun of fault indicator λ3successively occurs during 5 s and 7 s,an anomaly of the temperature sensor subset is detected.Then,the fault sensor subset is isolated,and its redundant sensor subset of temperature is triggered for state estimation.As seen from Fig.6(b),the estimates of health parameters are around 1 before 2 s,and then SE1and SW1move to 0.98,and the rest health parameters are still around 1 after 2 s.In Fig.6(d),SE3moves to around 0.98,SW3to 1.02,and the remaining health parameters are about 1 after 2 s,which indicates that HPT abrupt degradation is reached and tolerant to sensor NHfaulty.Therefore,the ML-MSCIF yields a correct health condition of the aircraft engine in the scenarios of fan and HPT abrupt degradation with one sensor faulty.

The simulation results from Fig.4 to Fig.7 reveal that the health parameters estimates can well track to their real changes of health condition under fan abrupt degradation with sensor T43fault and HPT abrupt degradation with sensor NHfault.In order to comprehensively evaluate the health estimation performance of the ML-MSCIF in a multi-sensor system,tests in various combinations of component degradation with faulty sensors are performed at ground design operation.The magnitudes of sensor bias in speed,pressure,and temperature are 1.5%,1.5%,and 2%,respectively.Table 2 shows the RMSEs and RMSDs of the ML-MSCIF in cases of four rotating components with one sensor deviation from its normal value.

The maximum RMSEs of fan,compressor,HPT,and LPT degradation are respectively 0.0229,0.0231,0.0235,and 0.0221 from Table 2,which indicate that health parameter estimates by the ML-MSCIF algorithm could give a good tracking accuracy in the examined component performance abrupt degradation.The RMSDs of four abrupt degradations are all below 0.0217,so the ML-MSCIF estimation results are relatively steady around the real health status.From the simulations above,we conclude that the ML-MSCIF algorithm can provide a satisfactory performance of health estimation in both gradual deterioration and abrupt degradation combined with sensor faulty.

Fig.7 ML-MSCIF fault indicators of sensor subsets under component abrupt degradation.

4.3.Semi-physical experiment and analysis

In order to further verify the health estimation performance of the proposed algorithm using sensor fusion with different sampling rates,tests are performed in a semi-physical experimental system of aircraft engine rotating component health monitoring.This experimental system is developed from an engine health monitoring rapid prototype system,33and the hardware equipment and block diagram for the engine degradation estimation semi-physical experiment are presented in Fig.8.The semi-physical experimental system contains an aircraft engine simulator,a controller rapid prototype,real I/O interfaces,a fuel servo system,and a health estimation module.

A virtual aircraft engine model regarded as a real engine runs in the engine simulator in real time on the National Instrument(NI)PXIe module,and the sampling frequencies of various sensors are set as digital simulation.One hardware NI CompactRIO(CRIO)plays the role of health estimation unit to track component performance and sensor fault isolation in real time.Another NI CRIO is used as a controller rapid prototype to calculate fuel flow from the residuals of the command and sensor measurement.The actuator of the examined system is achieved by an electro-hydraulic servo module,which is driven by a small inertia motor simulating the engine Low-Pressure(LP)spool.

Fig.8 Semi-physical experiment platform for engine health estimation.

Fig.10 Health estimation of ML-MSCIF in abrupt degradation on semi-physical experiment platform.

The analog signal of engine fuel consumption sensed by a turbine flowmeter with a sampling rate of 20 ms is transformed to a digital signal,and it is then sent into the engine simulator for engine model computation.The digital signal of the LP rotor speed is transformed to an analog signal to make a small inertial motor follow this spool speed,and it drives the fuel pump to supply fuel for the control system by a power shaft at the same time.The rotating speed is measured by a speed sensor installed on the motor,and transformed to a digital signal to stream into both of the controller and the health estimation module.

Fig.11 Semi-physical experimental results of ML-MSCIF health estimation under single health parameter degradation.

Gradual degradation and abrupt degradation of gas path performance are tested on the semi-physical experimental platform,with a closed-loop control of the LP rotor speed at the design operation.33,34The data sampling rates are 20 ms,40 ms,and 60 ms in the speed sensor subset,pressure sensor subset,and temperature sensor subset using a dual-channel mode.The control variables and sensor measurements are normalization and dimensionless before filtering calculation.The change rule of the engine health parameters is the same as that during gradual degradation in the digital simulation above,and sensor P5in Channel A is failed with a 2%bias from 500 to 700 cycles.Fig.9 presents the system parameters of engine health estimation during gradual deterioration on the semi-physical experimental platform.The control variable Wfand the plant output NLare given in Fig.9(a),and the estimates of engine health parameters are shown in Fig.9(b).

As seen from Fig.9(a),fuel flow measured by the sensor of the turbine flowmeter increases slowly along with performance gradual deterioration,while parameter NLis almost not changed.More fuel is consumed to make actual NLto follow the control command as the component performance degradation.From Fig.9(b),the actual change rules of health parameters follow the dot lines,which are similar to those in Fig.4(b).The estimated health parameters move around the dot lines,and the maximum deviation of health parameters by the ML-MSCIF is below 0.9%.The standard deviations in the digital test are less than those in the semi-physical test due to the higher noise level and the fuel actuator included in the latter test.Consequently,the ML-MSCIF yields the estimated health parameters well tracking real degraded magnitudes of gas path performance using sensor fusion with different sampling rates.

The abrupt performance degradations of four rotating components by the ML-MSCIF are tested combined with a 2%bias on sensor NHusing an asynchronous sample of sensor measurements.An abrupt degradation on components occurs at 2 s,and the sensor bias from 5 s to 7 s.Anomaly tracking results are shown in Fig.10,wherein health parameters estimates in the cases of fan degradation in Fig.10(a),compressor degradation in Fig.10(b),HPT degradation in Fig.10(c),and LPT degradation in Fig.10(d).

The estimates of health parameters SE1and SW1by the ML-MSCIF begin to deviate-2%from 1 at 2 s,and each health parameter follows its real value change denoted by a dot line in Fig.10(a).Fan degradation is then recognized from Fig.10(a)at 2 s since-2%on both SE1and SW1relates to fan degradation.The estimates of health parameters SE3and SW3deviate-2%and 2%from 1 at 2 s,and the rest estimates track their real parameters well in the whole 10 s in Fig.10(c).From Fig.10(b)and Fig.10(d),we can separately find compressor degradation and LPT degradation from 2 s,which indicates that the ML-MSCIF could give accurate estimates of gas path performance changes.The effect of health parameters on the control variables is extended to the semi-physical experiment in the NLclose-loop system,and Fig.11 gives examined parameters results by the ML-MSCIF under single fan health parameter degradation.

Fig.12 Semi-physical experimental results of ML-MSCIF health estimation under fan+HPT abrupt degradation.

The engine runs at the design operation,and a deviation of-3%on SE1occurs at 4.5 s.From Fig.11(b),all health parameter estimates move around 1.00,and only the SE1estimate has a sharply shift to 0.97 from 4.5 s.Since the fan efficiency decreases,the fuel flow increases to about 1.04 to maintain NLin Fig.11(a).Fig.11(c)and 11(d)show the effect of the fan mass flow coefficient SW1on the fuel flow in the NLclose-loop system.The SW1estimate steps to about 0.98 at 2.5 s and tracks its actual value from Fig.11(d).It illustrates that SW1degradation in the fan leads to less fuel consumption for a given NL.Although NLcan still be maintained,the power reduces due to a decrease of the air mass flow.That is to say,performance degradation in any of the components does not always result in more fuel consumption for a given NL,and a given NLis only one of the key factors to reflect the power requirement.

In order to further evaluate the health estimation performance of the ML-MSCIF on multiple-component degradations,one typical abrupt degradation on double components is carried out combined with sensor NHbias using an asynchronous sample of sensor measurements.This combination of component degradation is fan-plus-HPT abrupt degradation,in which the fan degrades at t=2 s and the HPT at t=6 s successively.A bias magnitude of 2%on sensor NHoccurs from 8 s,and semi-physical experiment results by the ML-MSCIF are shown in Fig.12.

The fuel flow Wfdecreases a little from 2 s and then clearly increases from 6 s in Fig.12(a).Fan degradation leads to a decrease of power consumption in the LP spool,and an air mass flow coefficient reduction plays the dominant role for the fuel flow decrease after 2 s.Although a fan efficiency reduction will increase the fuel flow,a fan flow capacity reduction will more obviously decrease the fuel flow from the previous simulation and discussion.The power driving the spool to rotate will reduce as HPT degradation.Compared to fan degradation,HPT degradation dominates the power change with the same degradation magnitudes on efficiency and flow capacity.Hence,more fuel will be consumed to maintain the spool speed unchanged as the combination degradation on fan and HPT from 6 s.Although the LP spool speed NLfluctuates at about 2 s and 6 s as component degradation,it can move back and along 1.00 in the whole 10 s in Fig.12(a).The health parameter estimates follow the desired deviation of gas path health performance by the ML-MSCIF from Fig.12(b).In a word,the health estimation performance of the ML-MSCIF is validated using sensor fusion with multiple sampling rates from the semi-physical experiment, and it acquires similar results achieved by digital simulations.

5.Conclusions

This paper has proposed a new multi-rate state estimation method based on information filters for aero-engine degradation estimation.The novelty of this methodology lies in the development of ML-MSCIF algorithms using sensor subsets fusion with asynchronous measurement,and the maximum likelihood validation strategy to address the issues of combination anomaly detection of component degradation and onesensor faulty.The methodology is evaluated on a dual-spool turbofan engine for gas path abrupt and gradual degradation estimations by digital simulation and semi-physical experiment.Experimental results show that the involved information filters with soft measurement synchronization can achieve multi-rate state estimation by sensor fusion.The MSCIF has better state tracking performances than those of the MEIF at typical operations in a flight envelope from systematic comparisons.Besides,sensor fault tolerant health estimation is completed by the ML-MSCIF using maximum likelihood validation, and it provides satisfactory accuracy of health estimation.

This research introduces a novel multi-rate filtering algorithm for aero-engine health estimation with asynchronous measurement.There are several important topics for future research that are related to this work.The information filtering methodology developed in this paper runs in a partly sensor fusion structure,and the same kinds of sensor are classified into one sensor subset.Further studies can extend to a comprehensive sensor fusion system,and sensors of the same kind in one subset could own different sampling rates.In addition,the evaluation of the proposed methodology is limited to digital simulation and semi-physical experiment,and it will be of more practical significance to examine these involved algorithms on a rig test of an aero-engine at more typical operations in a full flight envelope.

Acknowledgements

We are grateful for the financial supports of the National Natural Science Foundation of China(No.61304113),the Fundamental Research Funds for the Central Universities,China (No. NS2018018), and Qinglan Project of Jiangsu Province.