Smart Icing Systems Research Organization Technologies Core Aerodynamcs Control and Aircraft Flight Human and Sensor Icing Mechanics Factors Propulsio

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1 Flight Controls and Sensors Investigators: Tamer Baοsar (CSL/ECE) Principal Perkins Λ (CSL/ECE) William Petros Voulgaris (CSL/AAE) Graduate Students: Li (NASA Support) Wen Melody Λ (CRI Support) James Eric Schuchard (Fellowship) Undergrad Students: Keller (NSF Support) Eric Hillbrand (Fellowship) Thomas Eduardo Salvador (NSF Support) * presenting 4-

2 Smart Icing Systems Research Organization Technologies Core Aerodynamcs Control and Aircraft Flight Human and Sensor Icing Mechanics Factors Propulsion Integration Technology IMS Functions Characterize Operate and Envelope Adaptive Icing Effects Monitor IPS Protection Control Safety and Economics Simulation Flight Demonstration Trade Study 4-2

3 Flight Controls and Sensors Develop fast and reliable methods and algorithms for inflight ) of aircraft flight dynamics. identification based on the identified parameters. Evaluate performance methods to timeliness and accuracy of icing characterization. according Improve the safety of aircraft in icing conditions. Goal: smart systems to improve ice tolerance. Develop Objectives: Develop robust ice detection and classification methods and algorithms 2) that incorporate identified parameters and other avail- sensor information. able Investigate utility of control reconfiguration to maintain flight 3) characteristics in the presence of icing. Approach: Apply existing parameter identification techniques to parameter identification of flight dynamics. Investigate detection 4-3

4 Smart Icing Systems Research Longitudinal LTI Detection Dynamics Longitudinal LTI ID Dynamics and Drag Sensor Integration Charact. Longitudinal LTV Detection Dynamics Longitudinal LTV ID Dynamics Dynamics Nonlinear Development - Linear, Time-Invariant LTI - Linear, Time-Varying LTV 6-axis Nonlinear Detection Dynamics 6-axis Nonlinear ID Dynamics Adaptation/Handling Recovery Event CONTROL AND SENSOR THE GROUP INTEGRATION Eric Keller, Eduardo Salvador, Prof. Baοsar Thomas Hillbrand, Prof. Baοsar Wen Li, Prof. Voulgaris Characterizaton Jim Melody, Prof. Baοsar Eric Schuchard, Prof. Perkins Flight Simulation Adaptation 4-4

5 Flight Controls and Sensors Outline Recursive Algorithm: H Ice detection & characterization overview Identification during maneuver Batch Algorithm Recursive Algorithm: EKF Neural network detection & classification during maneuver Identification during steady level flight Summary & Conclusions Future Plans 4-5

6 Ice Characterization Block Diagram ID Algorithm(s) Detection Ice Sensor Fusion & Prot Envelope IPS I/F & Flight χ parameters Controller ^χ parameter estimates Flight Pilot input + Dynamics output (depend on χ) ^χ Pilot IPS IMS other sensors 4-6

7 Icing Characterization Philosophy Icing detection will also incorporate aerodynamic sensors steady-state characterization hinge moment sensing ) Sensor Integration Icing matters to the extent that it affects the flight dynamics. Effect of icing on flight dynamics is captured by parameter χ. By observing behavior of dynamics, can infer the value of χ Parameter Identification (ID) ) From estimated parameter ^χ(t), detect and classify icing effects. external environmental sensors Inform pilot of icing directly and via envelope protection 4-7

8 Longitudinal Flight Dynamics Model u forward velocity w downward velocity where angle of attack q pitch rate ff pitch angle ffi E elevator angle trim conditions (i.e., linearization point) U, Clean Iced Linearized model of longitudinal flight dynamics _u = g cos( ) +(X u + X Tu )u + X ff ff + X ffie ffi E _w Uq = g sin( ) + Z u u + Z ff ff + Z _ff _ff + Z q q + Z ffie ffi E _q = M u u + M Tu u + M ff ff + M Tff ff + M _ff _ff + M q q + M ffie ffi E and fm Λ, Z Λ, X Λ g are stability and control (S/C) derivatives. v.0 clean and iced ( ice = ) S/C derivatives: Model ff M ffie M q Z ff Z ffie Z q X ff X u + X Tu M other derivatives are invariant to icing. Extensive simulation for this model has shown that only M ff, M ffie, and possibly M q are useful for icing characterization. 4-8

9 x + n = x = [q ff u] T state where v = ffi E n(t) represents inaccuracies in the measurement, instrument accuracy limitations e.g., w(t) represents unknown excitation of the flight dynamics, turbulence, modeling error e.g., unknown exogenous signals n(t) and w(t) limit accurately of parameter estimated ID Framework Parameter Review May 8-9, 999 NASA Smart Icing Systems Let χ := [M ff ; M ffi E ; M q; Z ff ; Z ffi E ; Z q; X ff ; (X u + X T u )]T parameters to identify and convert flight dynamics to be _x = A(x; v)χ + b(x; v) + w z input measured output z state disturbance (a.k.a., process noise) w measurement noise n system excitation is necessary for identification 4-9

10 Parameter ID Algorithm Categorization Given some information, Ω, (e.g., input, output, and Objective: measurements) identify χ accurately in the presence of w and n. state solve matrix equation no solution when dim(x)» dim(χ) Batch algorithms: static algorithms that process measurements batches: ^χ(t m ) depends on Ω ft mk ; ::: ;t m ;t mg in Recursive algorithms: parameter estimate is based on past and measurements: ^χ(t) depends on Ω [0;t] present characterized by differential equations with i.c.'s convergence rate is a function of excitation level Static algorithms: parameter estimate at any instant, ^χ(t n ), is solely on measurements at that instant, Ω t n. based noise sensitivity depends on excitation level and batch period 4-0

11 Full state derivative information (FSDI): input, state, and state derivative are available, Noise perturbed full-state information (NPFSI): input and noisy measurement state are available, of Noise perturbed partial-state information (NPPSI): input and noisy of only part of the state are available measurement Parameter ID Information Structures ID algorithm depends on type of information available Ω t := (x(t); _x(t);u(t)) i.e., n = 0 and ( _q, _ff, _u) and (q,, ff, u) are measured Full state information (FSI): input and state are available, Ω t := (x(t);u(t)) i.e., n = 0 and (q,, ff, u) are measured Ω t := (z(t);u(t)) i.e., n 6= 0 Ω t := (z(t);u(t)) where z = Cx + n, e.g., ff is not measured. 4-

12 n and w are zero-mean white Gaussian noise, hence Assume: characterized by their covariances completely only ff is directly affected. ) Assume noise covariance equal to energy of _ff for a 5 ffi doublet ff _q ff q ff _ff ff _u ff q ff ff ff ff u Characterization Noise Review May 8-9, 999 NASA Smart Icing Systems of w: Covariance Consider turbulence as a vertical velocity perturbation 0 ffi /s 2 0 ffi /s ffi /s 0 knot/s of n: Covariance Instrument resolution specifications for NASA Twin Otter: ffi /s ffi ffi knot 4-2

13 Identification during Maneuver Longitudinal LTI Detection Dynamics Longitudinal LTI ID Dynamics and Drag Sensor Integration Charact. Longitudinal LTV Detection Dynamics Longitudinal LTV ID Dynamics Dynamics Nonlinear Development - Linear, Time-Invariant LTI - Linear, Time-Varying LTV 6-axis Nonlinear Detection Dynamics 6-axis Nonlinear ID Dynamics Adaptation/Handling Recovery Event CONTROL AND SENSOR THE GROUP INTEGRATION Eric Keller, Eduardo Salvador, Prof. Baοsar Thomas Hillbrand, Prof. Baοsar Wen Li, Prof. Voulgaris Characterizaton Jim Melody, Prof. Baοsar Eric Schuchard, Prof. Perkins Flight Simulation Adaptation 4-3

14 Icing Scenario Maneuver Review May 8-9, 999 NASA During a period of steady level flight, ice accretes but lack of limits parameter ID effectiveness. excitation Afterwards, a maneuver is performed during which parameter ID place. takes Begin ID simulations at beginning of maneuver Parameters assumed constant over the maneuver Maneuver is modeled as an elevator doublet Use simple threshold (mean of clean and iced parameters) for Smart Icing Systems Icing Scenario: Model of Scenario: and dirty evaluation of algorithms quick Must also consider ID of clean aircraft for false alarms" Question: Is there a reliable indication of icing in a reasonable amount of time? 4-4

15 Static Least-Squares FSDI ID Assume that _x(t), x(t), and u(t) are known, and take w(t) equal its mean, i.e., w(t) 0. to At each time instant, t, we have the system of n linear equations r unknowns, χ: in A(x t ;v t )χ = _x t b(x t ;v t ) () where x t 2 IR n and χ 2 IR r. Solve directly for ^χ(t) using matrix least squares: ^χ = h A T Ai AT ( _x t b) (2) Solution will not exist if the rank of A is less than r, e.g., if r > n. 4-5

16 Batch Least-Squares FSDI ID t ;v t )χ = _x t b(x t ;v t ) A(x t2 ;v t2 )χ = _x t2 b(x t2 ;v t2 ) A(x. tm ;v tm )χ = _x tm b(x tm ;v tm ) A(x 9 >= >; ) A m χ = _X m B m Excitation ) nondegenerate equations for t, t2, :::, t m rank of A m is r with sufficient number of measurements, m. ) ^χ(t m ) = A T m A m Λ A T m _ X m B m If the system is poorly excited, or if the batch period is small, the error can very sensitive to w. be Collect several measurements in batch and concatenate equations Solve directly for ^χ(t m ) using matrix least squares: By including disturbances, the error in the estimate, ~χ(t m ), is given by ~χ(t m ) = A T m A mλ A T m W m with W T m := w(t) T w(t2) T w(t m ) T Λ. 4-6

17 Batch Least-Squares FSI ID With x(t) and v(t) known, integration yields x = μ At χ + μ bt + μw t where t = A(x(t);v(t)), _ μ bt = b(x(t);v(t)), and _μw t = w(t). _μa Then ~χ = μ A T μa Λ μa t χ = x t μ bt. tm χ = x tm μ btm μa ; ) μ Aχ = X μ B NPFSI? use measurement z in place of x, but sensitive to measurement noise. ) Extend to FSI case via integrating prefilter. Pure integrator is not stable. In order to stabilize, include pole at < 0 t = μ At + A(x(t);v(t)); μ Affi = 0 _μa t = μ bt + b(x(t);v(t)); μ bffi = x ffi _μb Apply matrix LS to prefiltered equation 9 = μ AT W where W is concatenated prefiltered noise _μw t = μw t + w(t); μw ffi = 0 4-7

18 LS Results: Clean & Iced w/ no Batch Noise Measurement Smart Icing Systems Batch LS FSI Algorithm with T b = 8 s, = 0, and sampling rate 30 Hz 5 ffi doublet maneuver over 0 seconds with process noise but no measurement noise.2.2 Iced Aircraft Clean Aircraft.5.5 Normalized Estimates M ff M ffi E Normalized Estimates M ff M ffi E time (s) time (s) Notice: A reliable indication of icing is not given for either M ffi E or M ff. 4-8

19 LS Results: Clean & Iced w/ no Batch Noise Measurement Smart Icing Systems Batch LS FSI Algorithm with T b = 8 s, = 0, and sampling rate 30 Hz ffi doublet maneuver over 0 seconds with process noise but no measurement noise.2.2 Clean Aircraft Iced Aircraft Normalized Estimates M ffi E Normalized Estimates M ffi E M ff M ff time (s) time (s) Notice: A reliable indication of icing is not given for either M ffi E or M ff. 4-9

20 LS Results: Clean & Iced w/ no Batch Noise Measurement Smart Icing Systems Batch LS FSI Algorithm with T b = 8 s, = 0, and sampling rate 30 Hz 5 ffi doublet maneuver over 0 seconds with process noise reduced by a factor of 00 in energy and no measurement noise.2.2 Iced Aircraft Clean Aircraft.5.5 Normalized Estimates M ff M ffi E Normalized Estimates M ff M ffi E time (s) time (s) Notice: A reliable indication of icing for both M ffi E and M ff is available in s. 4-20

21 Recursive Parameter ID Algorithms guaranteed disturbance attenuation between disturbances and parameter error estimation persistency of excitation results in asymptotic convergence of estimate time-invariant parameters for Extended Kalman filter (EKF): augment the state with the parameters and estimate this augmented state can accommodate both state disturbance and measurement noise estimate may diverge, a.k.a. lose lock" can be generalized to time-varying parameters very common in practice H identification: generalization of recursive least-squares (RLS) and least-mean-squares (LMS) can accommodate both state disturbance and measurement noise can be generalized to time-varying parameters 4-2

22 H FSDI Algorithm Guaranteed disturbance attenuation level fl for any fl greater than some fl Λ where k k Q _^χ = ± A(x; v) T [ _x A(x; v)^χ b(x; v)] ; ^χ(0) = ^χ ffi _± = A(x; v) T A(x; v) fl 2 Q(x; u); ±(0) = Q ffi However, Q(x; v) := A(x; v) T A(x; v) fl Λ = fl = ) generalized LMS estimator: ) = Q ffi A(x; v)t [ _x A(x; v)^χ b(x; v)] _^χ Smart Icing Systems 2 kχ ^χkq(x;v) ^χ 2 j 2» fl 2 Q kwk jχ ffi + ffi is an L 2 norm with a chosen weighting function Q(x; v) 0 and j j Qffi is a weighted Euclidean norm with Q ffi > 0. x, _x, and v are known. For fl > fl Λ parameter estimate ^χ is given by where ±(t) 2 IR r r. Generally, fl Λ is unknown and may be infinite. If fl " the limiting filter is the RLS estimator. 4-22

23 » _^x _^χ NPFSI Algorithm H Review May 8-9, 999 NASA» A 0 0 0» I 0 0 fl 2 Q + ± It can be shown that Q := ± T 2 ± 2 yields fl Λ =, where ± 2 2 IR n r is off-diagonal of ±. portion Smart Icing Systems input is known, but only noisy state measurement z = x + n is available. Guaranteed disturbance attenuation level fl > fl Λ, 2 kχ ^χkq(x;v) 2 + jχ ^χ 2 j 2 Q kwk + jx ffi ^x ffi j 2» fl 2 P + knk ffi ffi ffi where x ffi is actual initial state, ^x ffi is initial state estimate, and P ffi > 0. Both the state and the parameter must be estimated. For fl > fl Λ : b 0 I 0» ^x^χ» + ±» = (z ^x) ; + ±; 0 A 0 0 ±» = _±» 0 0 T 0 A I ±» with ±(t) 2 IR (n+r) (n+r) and ±(0) = diag(p ffi ;Q ffi ). 4-23

24 Recursive H : Iced, No Measurement Noise Using simple threshold, both M ff and M ffi E Notice: indication in < s. give H FSDI Algorithm with fl = 3 and Q ffi = ( 0 6 )I 5 ffi doublet maneuver over 0 seconds with process noise but no measurement noise.2 Normalized Estimates M ffi E M ff time (s) 4-24

25 Recursive H : Clean, No Measurement Noise Notice: M ff and M ffi E H FSDI Algorithm with fl = 3 and Q ffi = ( 0 6 )I 5 ffi doublet maneuver over 0 seconds with process noise but no measurement noise false alarm scenario with various initial parameter estimation errors.03 ff parameter estimates M ffi E M.03 parameter estimates Normalized Estimate Normalized Estimate time (s) time (s) estimates never yield false alarms using simple detection threshold. 4-25

26 M ffi E Using simple threshold, both M ff and M ffi E Notice: indication in < s. give Recursive H : Iced, w/ Measurement Noise H NPFSI Algorithm with fl = 3 and Q ffi = ( 0 7 )I 5 ffi doublet maneuver over 0 seconds with process noise and measurement noise.25 Normalized Estimates M ff time (s) 4-26

27 Notice: M ff and M ffi E Recursive H : Clean, w/ Measurement Noise H NPFSI Algorithm with fl = 3 and Q ffi = ( 0 7 )I 5 ffi doublet maneuver over 0 seconds with process noise and measurement noise false alarm scenario with various initial parameter estimation errors.03 ff parameter estimates M ffi E M.03 parameter estimates Normalized Estimate Normalized Estimate time (s) time (s) estimates never yield false alarms using simple detection threshold. 4-27

28 Using simple threshold, both M ff and M ffi E Notice: give indication in < s. again Recursive H : Iced, w/ Measurement Noise H NPFSI Algorithm with fl = 3 and Q ffi = ( 0 7 )I ffi doublet maneuver over 0 seconds with process noise and measurement noise.25 Normalized Estimates M ffi E M ff time (s) 4-28

29 Notice: M ff Notice: M ffi E Recursive H : Clean, w/ Measurement Noise H NPFSI Algorithm with fl = 3 and Q ffi = ( 0 7 )I ffi doublet maneuver over 0 seconds with process noise and measurement noise false alarm scenario with various initial parameter estimation errors.03 ff parameter estimates M ffi E M.03 parameter estimates Normalized Estimate Normalized Estimate time (s) time (s) gives false alarm for large estimates never cross the initial estimation errors. threshold. 4-29

30 Recursive EKF ID Algorithm Kalman filter provides state estimate. Recast the parameter ID problem into state estimation problem: a In the Kalman filter framework, the state disturbance, measurement noise, initial state, y ffi, are assumed to be Gaussian with: and fw(t)g 0 E fn(t)g 0 E fn(t);n(fi)g = R(t)ffi(t fi) cov fy ffi ;y ffi g = Q ffi cov w(t) and n(t) are assumed to be uncorrelated: Furthermore, fw(t);n(fi)g 0 cov For linear systems Kalman filter provides minimum-variance, unbiased state estimate.» w 0 _x = Aχ + b + w )» 8 x y := >< χ ) v)χ + b(x; v) A(x; 0 _y =» + _χ = 0 >: z = [I 0] y + n E fy ffi g = μy ffi cov fw(t);w(fi)g = P (t)ffi(t fi) However, augmented system is always nonlinear ) extended Kalman filter. 4-30

31 Extended Kalman filter: linearize the system about an estimated (augmented) trajectory. state» v)^χ + b(^x;v) A(^x; 0» (t) 0 ^P 0 0 A(^x; b(^x; v) ^R(t) = R(t); ^P (t) = P (t); & ±(0) = Qffi Recursive EKF ID Algorithm (cont'd) The resulting algorithm is: _^y = + ±(t)h T ^R(t) [z H^y] _±(t) = D(^y; v)±(t) +±(t)d(^y; v) T + μ P (t) ±(t)h T ^R(t) H±(t) where, ± 2 IR (n+r) (n+r), H = [I 0], # μp (t) = ; and; D(^y; v) = A(^x; v) T 0 For a linear system, ^P (t) = P (t) and ^R(t) = R(t) optimal, but not for a nonlinear system. Hence, ^P (t) = ^P (t)t 0, are = ^R(t) T > 0, and Q ffi = Q T ffi 0 are used as algorithm design parameters. ^R(t) 4-3

32 Using the simple threshold, both Notice: ff and M ffi E give an indication in < 2 s. M Recursive EKF Results: Iced EKF Algorithm with ^P (t) 0:I and ^R(t) ( 0 5 )I 5 ffi doublet maneuver over 0 seconds with process noise and measurement noise.25 Normalized Estimates M ff M ffi E time (s) 4-32

33 Recursive EKF Results: Clean EKF Algorithm with ^P (t) 0:I and ^R(t) ( 0 5 )I 5 ffi doublet maneuver over 0 seconds with process noise and measurement noise false alarm scenario with various initial parameter estimation errors M ff parameter estimates M ffie parameter estimates Normalized Estimate Normalized Estimate time (s) time (s) Notice: Using simple threshold, both M ff and M ffie give false alarms for all initial errors. 4-33

34 Notice: Using simple threshold, only M ffie Recursive EKF Results: Iced EKF Algorithm with ^P (t) 0:I and ^R(t) ( 0 5 )I ffi doublet maneuver over 0 seconds with process noise and measurement noise.25 Normalized Estimates M ff M ffie time (s) yields a reliable indication of icing. 4-34

35 Recursive EKF Results: Clean EKF Algorithm with ^P (t) 0:I and ^R(t) ( 0 5 )I ffi doublet maneuver over 0 seconds with process noise and measurement noise false alarm scenario with various initial parameter estimation errors M ff parameter estimates M ffie parameter estimates.5.5 Normalized Estimate Normalized Estimate time (s) time (s) Notice: Using simple threshold, both M ff and M ffie give false alarms for all initial errors. 4-35

36 Detection and Classification during Maneuver Longitudinal LTI Detection Dynamics Longitudinal LTI ID Dynamics and Drag Sensor Integration Charact. Longitudinal LTV Detection Dynamics Longitudinal LTV ID Dynamics Dynamics Nonlinear Development - Linear, Time-Invariant LTI - Linear, Time-Varying LTV 6-axis Nonlinear Detection Dynamics 6-axis Nonlinear ID Dynamics Adaptation/Handling Recovery Event CONTROL AND SENSOR THE GROUP INTEGRATION Eric Keller, Eduardo Salvador, Prof. Baοsar Thomas Hillbrand, Prof. Baοsar Wen Li, Prof. Voulgaris Characterizaton Jim Melody, Prof. Baοsar Eric Schuchard, Prof. Perkins Flight Simulation Adaptation 4-36

37 Given parameter estimate, ^χ(t), and other sensor information, reliably Objective: the presence of icing and classify its severity in a timely manner. detect Train neural networks (NN) to recognize correlations between parameter estimates, other sensor information, and icing. NN will take advantage of trends in parameter estimates, improving over detection. threshold Detection and Classification Formulation Approach: Activate the NN at beginning of maneuver Feed batch of sampled parameter estimates to NN. Use separate detection and classification networks for efficiency Results to date: NN have been applied to H NPFSI identification. Other sensor information has not yet been incorporated. 4-37

38 NN are layered networks of interconnected nodes. Nodes ) activation functions, lines ) weights, multiple lines are summed. Weighted sum of inputs to node plus a bias are input to activation function. sigmoidal activation functions are used. Often, For a given structure (# of layers and nodes) training refers to optimization biases and weights based on a suite of test cases. of NN are general enough to recognize complex nonlinear relationships, such as our sensor information and icing. between Networks Neural Review May 8-9, 999 NASA Smart Icing Systems Neural Network Sigmoidal Activation Function 0.8 Output Nodes Input Nodes Sigmoidal activation functions generalize discrete switching. 4-38

39 For detection based on parameter estimates alone, NN will take advantage any consistent temporal patterns in parameter estimates. of If no consistent trends, NN will not perform better than thresholding at the estimate sample. final Evaluate consistency of trends by running same simulations for various noise realizations: Neural Network vs. Threshold.6.2 Recursive H NPFSI M ffie estimates Batch LS M ffie parameter estimates Normalized Estimate Normalized Estimate time (s) time (s) 4-39

40 Network Results Detection five seconds of M ffie and M ff estimates as input using Recursive H Detection Network elevator input doublets varying from ffi to 0 ffi and from 5s to 5s 0.9 Actual Icing Level ice mark fl indication clean iced 0. ψ smaller amplitude doublets simulation case # 4-40

41 Classification Network Results Four-level five seconds of M ffie and M ff estimates as input using Recursive H Classification Network elevator input doublets varying from ffi to 0 ffi and from 5s to 5s 0.9 Actual Icing Level ice mark ice class. 0 fl /3 2 2/3 + Λ 0. ψ smaller amplitude doublets simulation case # 4-4

42 Identification during Steady-Level Flight Longitudinal LTI Detection Dynamics Longitudinal LTI ID Dynamics and Drag Sensor Integration Charact. Longitudinal LTV Detection Dynamics Longitudinal LTV ID Dynamics Dynamics Nonlinear Development - Linear, Time-Invariant LTI - Linear, Time-Varying LTV 6-axis Nonlinear Detection Dynamics 6-axis Nonlinear ID Dynamics Adaptation/Handling Recovery Event CONTROL AND SENSOR THE GROUP INTEGRATION Eric Keller, Eduardo Salvador, Prof. Baοsar Thomas Hillbrand, Prof. Baοsar Wen Li, Prof. Voulgaris Characterizaton Jim Melody, Prof. Baοsar Eric Schuchard, Prof. Perkins Flight Simulation Adaptation 4-42

43 Steady-Level Flight Icing Scenario During steady level flight the clean aircraft passes through a cloud" of icing and ice accretes continuously. conditions Assume that airplane flies through icing cloud" in time T c, and that the LWC flight path has raised-cosine shape. along Then A c E as a function of time is the solution of d dt A ce = ν 2 [ cos (2ßt=T c)] ; A c E(0) = 0 assumed value of ice (T c ) determines ν from where ice (t) = Z (n)a c E(t)+Z 2 (n)[a c E(t)] 2 Can parameter ID augment steady-state characterization during Question: turbulence? moderate Icing Scenario: Model of Scenario: Use A c E accretion model with freezing fraction n = 0:

44 T c d A ce ο LWC ο cos(2ßt=t c ) dt ) ) ice (t) = Z (n)a c E(t)+Z 2 (n)[a c E(t)] 2 T c T c Steady-Level Flight Icing Scenario (cont'd) freezing fraction n = 0:2 Assume: icing cloud length T c and ice (T c ) Choose: LWC A c E(t) R dt c E(t) ο t T c 2ß sin(2ßt=t c) A ice (T c ) ice (t) 4-44

45 Recursive H Time-varying Algorithm H and K are assumed to be known and d is (unknown) parametric where disturbance. For fl > fl Λ _^χ = H ^χ +± A T [ _x A^χ b] ; ^χ(0) = ^χ ffi _± = ±H H T ± ±KK T ± + A T A fl 2 Q(x; u); ±(0) = Q ffi In this case, H = 0 and K can be calculated from Z (n), Z 2 (n), and the S/C ice -coefficients. derivative Note: M ffie The actual parameters are allowed to vary with time, according to _χ = Hχ + Kd For the FSDI case, we have guaranteed disturbance attenuation level fl > fl Λ, 2 ^χ(t)k kχ(t) Q(x;v) 2 2 jχ ^χ ffi j 2» fl 2 Q kwk + kdk + ffi the algorithm is is an input coefficient and cannot be estimated without input. 4-45

46 Recursive H Results: Moderate Icing minute icing cloud with final icing value of ice = 5 process noise but no measurement noise with H FSDI Algorithm with fl = :000, Q = A T A, and Q ffi = ( 0 4 )I.02 Actual and Estimated M ff Normalized Mff Estimate ^M ff (t) M ff (t) actual M ff estimated M ff classification levels classification delays ice Level Delay 7 s s s s 0.8 > 00 s time (min) 4-46

47 Recursive H Results: Rapid/Severe Icing minute icing cloud with final icing value of ice = :5 2 process noise but no measurement noise with H FSDI Algorithm with fl = :000, Q = A T A, and Q ffi = ( 0 4 )I.02 Actual and Estimated M ff Normalized Mff Estimate M ff (t) ^M ff (t) actual M ff estimated M ff classification levels classification delays ice Level Delay 2 s s s s s < 80 s time (min) 4-47

48 Recursive H and EKF algorithms yield timely estimates during with measurement noise. maneuver Batch estimation performs poorly with and without measurement noise NN applied to recursive H during maneuver detected tailplane correctly 97% of the time, for doublet inputs greater than ffi. icing NN applied to recursive H during maneuver classified tailplane correctly 97% of cases, for doublet inputs greater than ffi. icing For batch detection and classification, NN will not improve over applied after some fixed period. threshold Smart Icing Systems Conclusions 4-48

49 Term Plans Issues/Near Review May 8-9, 999 NASA Smart Icing Systems Refine turbulence process noise model H NPFSI algorithm during steady-level flight Batch LS algorithm during steady-level flight NN accuracy/excitation/batch time tradeoff ID of lateral dynamics Sliding or expanding window for NN detection during maneuver Detection with parameter ID and steady-state characterization 4-49

50 Smart Icing Systems Future Plans Unified approach to various icing event types: lateral/longitudinal, handling/performance Integrate sensor info into detection and classification Extend ID and detection/classification to full nonlinear dynamics Apply linear-based algorithms to nonlinear model at trim point Develop algorithms based on direct parameterization of non- linear model Investigate adaptive control for handling event recovery, not just prevention Support incorporation of algorithms into Icing Encounter Flight Simulator 4-50

51 Flight Controls and Sensors Waterfall Chart Fiscal Years Federal ID of LTI Dynamics Support IE Flight Simulator ID of LTV Dynamics Ice Detection for LTI Dynamics Ice Detection for LTV Dynamics ID of Nonlinear Dynamics Detection for Nonlinear Dynamics Sensor Integration Adaptation/Event Recovery 4-5