Onboard Engine FDI in Autonomous Aircraft Using Stochastic Nonlinear Modelling of Flight Signal Dependencies

Transcription

1 Onboard Engine FDI in Autonomous Aircraft Using Stochastic Nonlinear Modelling of Flight Signal Dependencies Dimitrios G. Dimogianopoulos, John D. Hios and Spilios D. Fassois Stochastic Mechanical Systems & Automation (SMSA) Group Department of Mechanical & Aeronautical Engineering University of Patras, GR 65 Patras, Greece Internet: sms European Control Conference, July -5, 7, Kos, Greece Research supported by the European Commission [FP6 STREP project No on Innovative Future Air Transport System (IFATS) ]. Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 1 / 1

2 Talk Outline 1 Introduction & Aim of the Work The Aircraft Engine and the Faults 3 FDI Scheme Operation Principles 4 Results 5 Concluding Remarks Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 / 1

3 1. Introduction & Aim of the Work The General Problem Effective Fault Detection & Isolation (FDI) in aircraft engines by using existing onboard resources. Motivation & Significance Modern aircraft must achieve high reliability/safety at the lowest possible cost. Aircraft component FDI traditionally based on physical redundancy = increases cost/weight = NOT well suited to future aircraft. Aircraft systems and electronics increasingly complex: Increasing need for self-monitoring. Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 3 / 1

4 1. Introduction & Aim of the Work (cont d) State of the Art Nonlinear physical modelling of gas turbine engine dynamics & FDI using engine singnals & statistical hypothesis testing (Bassevile 98, Wu et al. 4). Interactive Multiple Models (IMM): Kalman filters for healthy and faulty aircraft engine configurations; selection of the correct model at each instant by means of a probabilistic principle (Kobayashi et al. 3). Multiple Models (MM): Similar to IMM principle; Takagi-Sugeno type fuzzy models may be used for healthy and faulty aircraft engine configurations (Diao et al. 4). Non-model based FDI (Tumer et al. 99, Samara et al. 7). Aircraft engine dynamics are Technical Difficulties complex = linear system modelling NOT well suited operating-point-dependent = may achieve good results locally but not globally (entire flight regime). Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 4 / 1

5 1. Introduction & Aim of the Work (cont d) Aim of the Work The design and assessment of an FDI scheme that: (a) is effective over an entire flight regime and under various flight conditions, and, (b) may be, possibly, based on global and available flight quantities. Approach -stage stochastic pooled nonlinear modelling of relationships among measured flight signals (identification). Statistical decision making techniques for checking the validity of these relationships for an aircraft in unknown state (FDI). Expected Advantages Pooled nonlinear modelling yields global models that are compact & accurate over an entire flight regime Scheme relies on available global signals (NOT on internal engine quantities, such as rotor speed, turbine pressure etc) = fewer sensors Stochastic framework accounts for modelling & measurement uncertainties Easy to adapt to any kind of aircraft Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 5 / 1

6 . The Aircraft Engine and the Faults d 1 d Mach[t] Alt[t] Throttle[t] + Engine Dynamics + Thrust[t] Figure 1. Generic representation of the engine subsystem (d 1 and d designate entering faults). Table 1. The faults considered Type Description Magnitude Component Interpretation F A k Incorrect Mach readings k =.5, sensor faulty sensor (k fraction of value entering left engine). F B k Noisy left engine thrust k = 1 engine wear in blades - deficiency (with noise variance k) in compressor airflow F C k Total loss of left engine k = 1, engine engine shutdown due to (within k sec from fault occurence) 6 fast internal deterioration Faults accounted for in the FDI scheme: F A k, F B k (modelled faults). Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 6 / 1

7 . The Aircraft Engine and the Faults (cont d) Y-axis (m) Flight details t= s t=3 s X-axis (m) Flight Regime: Initial Altitude: clean 1 5 ft Initial Mach:.4 Turbulence: low slowly varying heading deg, commanded roll = 3 deg Thrust (kg) Thrust (kg) Thrust (kg) 4 x 14 5 x x 14 F A.5 Healthy F B 1 Healthy F C 1 Healthy time (s) 5 3 Figure. Total engine thrust signals: (a) Healthy versus F.5 A affected aircraft; (b) healthy versus F1 B affected aircraft; (c) healthy versus F 1 C affected aircraft x 1 4 (all faults occurr at 15 s). (a) (b) (c) Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 7 / 1

8 3. FDI Scheme Operation Principles Autopilot inputs Turbulence Wind Aircraft Ay[t] β[t] Rudder[t] NARX predictor model Thrust[t] + _ e[t] Thrust [t t-1] Inverse ARMA filtering ε[t] Statistical processing Autopilot inputs Aircraft Attitudes Angular rates Body Axis Decision Making Module Accelerations Figure 3. The fault detection and isolation scheme and detail of the aircraft simulator. Main idea: FDI is based on changes on a residual sequence ε[t] obtained by driving the current flight signals through predetermined pooled (global) models: FDI is accomplished by detecting changes in the residual variance σ ε Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 8 / 1

9 3. FDI Scheme Operation Principles (cont d) How to obtain the residuals ε[t]? Two-stage pooled nonlinear modelling (identification) of the dependencies among common flight signals available from aircraft sensors. Stage 1: Modelling the major nonlinear dynamics b/w inputs (lateral acceleration A y, side-slip angle β, rudder moment) and output (total engine thrust) by means of a CCP-NARX representation. Stage : Modelling of CCP-NARX residuals by means of a CCP-ARMA representation to capture remaining information. A y[t] β[t] Rudder[t] Thrust[t] Residual generation via CCP-NARX e[t] Residual generation via CCP-ARMA ε[t] 1 st stage pooled nonlinear modelling nd stage pooled modelling Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 9 / 1

10 3. FDI Scheme Operation Principles (cont d) The CCP-NARX (Constant Coefficient Pooled - Nonlinear AutoRegressive with exogenous excitation) model: Noise Covariance: Noise Distribution: output {}}{ y j[t] = L θ i i= regressor {}}{ p i,j[t] + noise {}}{ e j[t] E{e j[t] e κ[t τ]} = γ e[j, κ] δ[τ] e j[t] NID (, σ e(j)) }{{} Normally Independently Distributed j: variable indicating current flight Constant Coefficient Pooled: θ i constant & valid j ( flight) p i,j[t]: cross products between lagged output and inputs or their powers Advantages of -stage CCP modelling Provides a global and compact model valid for all flights (within a flight regime). Statistically optimal use of all available signals simultaneously. Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 1 / 1

11 3. FDI Scheme Operation Principles (cont d) How to identify a CCP-NARX model? Assume M flights covering an entire flight regime: Input/Output Data Records A ltitude (ft) 4.5 x Flight Envelope Mach Number um,1[t] y1[t] t t um,[t] y[t] t t um,m[t] ym[t] t t Pooling model parameters θi are constant and valid for every flight ej[t] is a zero mean i.i.d. over time but contemporaneously correlated random variable with: Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 11 / 1

12 3. FDI Scheme Operation Principles (cont d) Structure selection: CCP-NARX model identification Structure selection: which terms p i,j should be included? Parameter estimation: how to estimate θ i s? Section signals into multiple overlapping segments. Select regressors for each segment via a Forward Orthogonal Search algorithm (FOS; Korenberg et al. 88). N samples Flight No. # 1 # # M N s N s N s segmentation = reduced computational burden overlap = smooth transition from local dynamics of each segment Merge all regressor sets = Extended Regressor Set (ERS). Omit statistically insignificant terms from ERS via bootstrapping (Kukreja et al. 4) = obtain confidence intervals of θ i s by re-sampling noise terms Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 1 / 1

13 3. FDI Scheme Operation Principles (cont d) Parameter estimation: 1 Rewrite CCP-NARX model as a linear regression: y j [t] = φ T j [t] θ + e j [t] with φ j [t] = [p,j [t]... p L,j [t]] T and θ = [θ... θ L ] T. Stack N data samples from j-th flight: 3 Stack data from M flights: y j [1] φ T j [1] e j [1]. =. θ +. y j [N] φ T j [N] e j [N] }{{}}{{}}{{} y j ej y 1. y M } {{ } ȳ = Φj Φ 1. Φ M } {{ } Φ θ + e 1. e M } {{ } ē 4 Estimate θ via a Weighted Least Squares (WLS) based scheme. Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 13 / 1

14 3. FDI Scheme Operation Principles (cont d) Fault Detection: Set up the statistical hypothesis testing problem: H : σ u σ null hypothesis - healthy engine H 1 : σ u > σ alternative hypothesis - faulty engine σ : residual variance of healthy engine σ u : residual variance of engine in unknown state Form the statistic: Under H : F = (l 1) σ u σ u (l 1) (l 1) σ σ (l 1) F l 1,l 1 central F-distribution with (l 1), (l 1) degrees of freedom l: data samples for estimation of σ u l : data samples for estimation of σ F = X 1/n 1 X /n F n1,n if : X 1 χ n 1 X χ n and mutually independent Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 14 / 1

15 3. FDI Scheme Operation Principles (cont d) F = σ u σ F l 1,l 1 Hence the proper hypothesis is selected as: at the risk level α: = probability of accepting H 1 although H is true - false alarm Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 15 / 1

16 4. Results A) Modelling (identification) Results Flight Regime: clean Turbulence: low Aircraft Weight: 31, 85 lbs Number of flights M: 168 Signal Length N: 7, 51 ( 3 sec) Sampling Frequency f s: 5 Hz slowly varying heading deg, commanded roll = 3 deg Thrust (kg) β (rad) 4 x x time (s) A y (m/s ) Rudder Moment (kg m) time (s) CCP-NARX structure (1 st stage modelling) p 1 [t] = u 1 [t 5]u 3 [t ] p 7 [t] = y[t ] p [t] = u 3 [t 1]u 3 [t 3] p 8 [t] = y[t 3] p 3 [t] = u 3 [t 1]u 3 [t 4] p 9 [t] = y[t 3] p 4 [t] = u 3 [t 3] p 1 [t] = y[t 3]y[t 4] p 5 [t] = u 3 [t 5] p 11 [t] = y[t 5] p 6 [t] = y[t 1] u 1 [t]: y-axis acceleration A y u [t]: β angle u 3 [t]: rudder moment y[t]: thrust Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 16 / 1

17 4. Results (cont d) Performance of the identified model (case 1): Thrust (kg) 1 st stage modelling residuals nd stage modelling residuals.5 x actual CCP-NARX prediction time (s) Figure 4. Two stage model assessment: (a) Actual thrust versus one-step-ahead CCP-NARX(5,8) prediction, (b) one-step-ahead CCP-NARX(5,8) prediction errors, and (c) one-step-ahead CCP-ARMA(15,5) prediction errors. (a) (b) (c) Y-axis (m) t= s t=3 s X-axis (m) Flight details Initial Altitude: 7 5 ft Initial Mach:.5 1 st Stage Modelling: RSS= nd Stage Modelling: RSS= Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 17 / 1

18 4. Results (cont d) Performance of the identified model (case ): Thrust (kg) 1 st stage modelling residuals nd stage modelling residuals x actual CCP-NARX prediction time (s) Figure 5. Two stage model assessment: (a) Actual thrust versus one-step-ahead CCP-NARX(5,8) prediction, (b) one-step-ahead CCP-NARX(5,8) prediction errors, and (c) one-step-ahead CCP-ARMA(15,5) prediction errors. (a) (b) (c) Y-axis (m) x Flight details t= s t=3 s X-axis (m) x 1 4 Initial Altitude: 5 ft Initial Mach:.4 1 st Stage Modelling: RSS= nd Stage Modelling: RSS= Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 18 / 1

19 4. Results (cont d) B) FDI Results I Flight Regime: clean Turbulence: low Number of flights: 54 with roll command: 3 deg 54 with roll command:.5sin(.1πt) deg test quantity F test quantity F Healthy (a) F A.5 F B 1 (c) time (s) test quantity F test quantity F F C 6 (b) (d) time (s) Figure 6. Typical FDI results (horizontal lines designate statistical limits at risk level α faults are detected when F[t] exceeds statistical limits). Fault Detection Rates (%) Fault Isolation Rates (%) Monitored signal for FDI: CCP-ARMA 5-step-ahead residuals ε[t] (provides robust FDI results) Risk level: α = 1 7 Fault detection: Test quantity F[t] exceeds horizontal bar Fault isolation: Check F[t] pattern after fault detection % 98.5 % 99.4 % 99.1 % Healthy A B C F F F k k k (Mach sensor fault) (noisy thrust) (loss of thrust) 1 % 1 % A B F F k k (Mach sensor fault) (noisy thrust) Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 19 / 1

20 4. Results (cont d) B) FDI Results II Flight Regime: clean Turbulence: medium Number of flights : 336 with roll command: 3 deg 336 with roll command:.5sin(.1πt) deg test quantity F test quantity F time (s) Healthy F A time (s) (b) test quantity F F B time (s) Figure 7. Typical FDI results (horizontal lines designate (a) (c) Fault Isolation Rates (%) Fault Detection Rates (%) % 87. % 8.1 % Healthy A F k B F k (Mach sensor fault) (noisy thrust) 1 % 1 % A F k B F k statistical limits at risk level α faults are detected when (Mach sensor fault) (noisy thrust) F[t] exceeds statistical limits). Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 / 1

21 5. Concluding Remarks An FDI scheme for aircraft engine faults was designed & tested. Design principles: (a) Pooled nonlinear stochastic and two-stage modelling of the dynamics. (b) Fault detection based on statistical hypothesis testing. (c) Only global and available flight signals are used. The FDI scheme: 1. Proved effective with hundreds of flights under the clean flight regime and light turbulence.. It clearly suggested that local engine signals and dedicated sensors are not necessary. 3. Its performance deteriorated under substantial turbulence conditions. It is expected that this can be corrected by proper re-design. 4. The scheme is simple and suitable for on-line implementation. Dimogianopoulos et al. (University of Patras) Onboard Engine FDI ECC 7 1 / 1