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Asok Asok Ray Ray The Pennsylvania State University University - PowerPoint PPT Presentation

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1 8 5 5 Seminar at Seminar at Nat National Inst onal Institut itute of S e of Standar andards and Technology ds and Technology ANOMALY DETECTION ANOMALY DETECTION AND FAILURE MITIGATION ND FAILURE MITIGATION IN COMPLEX DYNAMICAL SYSTEMS

  1. 1 8 5 5 Seminar at Seminar at Nat National Inst onal Institut itute of S e of Standar andards and Technology ds and Technology ANOMALY DETECTION ANOMALY DETECTION AND FAILURE MITIGATION ND FAILURE MITIGATION IN COMPLEX DYNAMICAL SYSTEMS IN COMPLEX DYNAMICAL SYSTEMS Asok Asok Ray Ray The Pennsylvania State University University Park, PA 16802 Email: axr2@psu.edu Tel: (814) 865-6377 Supported by Army Research Office Grant No. DAAD19-01-1-0646 November 19, 2004

  2. Outline of the Presentation 1 8 5 5 Anomaly Detection in Complex Dynamical Systems � Microstate Information Based on Macroscopic Observables � Thermodynamic Formalism of Multi-time-scale Nonlinearities � Symbolic Time Series Analysis of Macroscopic Observables � Pattern Discovery via Information-theoretic Analysis � Real-time Experimental Validation on Laboratory Apparatuses � Active Electronic Circuits and Three-phase Electric Induction Motors � Multi-Degree-of-Freedom Mechanical Vibration and Chaotic Systems � Fatigue Damage Testing in Polycrystalline Alloys Discrete Event Supervisory Control for Failure Mitigation � Quantitative Measure for Language-based Decision and Control � Real-time Identification of Language Measure Parameters � Robust and Optimal Control in Language-theoretic Setting Future Collaborative Research in Complex Microstructures � Modeling and Control of Hidden Anomalies and their Propagation � Experimentation on Real-time Detection and Mitigation of Malignant Anomalies on a Hardware-in-the-loop Simulation Test Bed

  3. Intelligent Health Management 1 8 5 5 and Failure Mitigating Control of Aerial Vehicle Systems Mission/Vehicle Management Level Mission/Vehicle Management Level (Discrete Even (Discrete Event t Decision Making) Decision Making) Flight Management Level Flight Management Level (Continuous/Discrete Event Decision Making) (Continuous/Discrete Event Decision Making) Avionics and Fli Avionics and Flight Control ght Control Level Level Avionic and Structural Life Extending Control System Health and Usage Monitoring (including Feedforward Control) System (HUMS) . . Analytical Measures Robust Wide range (including real-time NDA) Gain Scheduling of Damage States and Feedback Control System Damage State Derivatives Anomaly Detection Conventional Aircraft Flight Information Fusion and Actuator (e.g., FDI, calibration, data fusion, and Structural Special-Purpose Dynamics Other and redundancy management) Dynamics Sensor Systems Information

  4. Anomaly Detection and Classification: Symbolic Time Series Analysis Symbolic Time Series Analysis 1 8 5 5 Multi-Time-Scale Nonlinear Dynamics Multi-Time-Scale Nonlinear Dynamics � Slow T ow Time Scale: A me Scale: Anomaly Pr omaly Propagat opagation ( on (Non-st on-stat ationary St ionary Stat atist istics) cs) � Fast Fast Time Scale: Process R Time Scale: Process Response (St sponse (Stationar onary Statist y Statistics) cs) Model-based Statistical Model-based Statistical Methods Methods � Modeling w it Modeling w ith Nonlinear Nonlinear St Stocha ochast stic D ic Different fferential Equat ial Equations ons � Ito Equation: � Fokker Planck Equation: � Uncertainties in Model Identification and Loss of Robustness � Stat atistical Mechanical istical Mechanical Modeli Modeling ( ng (Canonical anonical Ensemble Ensemble Approach) proach) � Symbolic Time Series Analysis � Small perturbation stimulus � Self-excited oscillations � Thermodynamic Formalism and Information Theory � Hidden Markov Modeling (HMM) and Shift Spaces

  5. Notion of Symbolic Dynamics Notion of Symbolic Dynamics 1 8 5 5 Symbol Sequence β …… φ χ γ η δ α δ χ …… 10 α χ 8 δ 6 Phase Trajectory 4 3 η φ 0 2 φ α δ ε 0 β γ 1 γ η 1 χ, ε 1 0.5 0.5 2 0 0 -0.5 -0.5 Finite State Machine -1 -1 � Discretization of the Dynamical System in Space and Time � Representation of Trajectories as Sequences of Symbols

  6. State Machine Construction D-Markov Machine 1 8 5 5 State to state transitions from a symbol sequence ∈ Ν � alphabet size = |A| Example ∈ Ν 1-D Ising (Spin-1/2) Model � window size = D U { 0 } Nearest Neighbor Interactions = k k k k � kth word (state)= W w w ... w − 0 0 1 D 1 01 00 1 − − − � kth word value = k D 1 i 0 D 1 ∑ 0 ( w ) A 1 = i i 0 1 11 0 10 k k k w w .......... w 1 − 0 1 D 1 + p 00 1-p 00 0 0 k k 1 w 0 w + + + k 1 k 1 k 1 − w w ........ w 1 D − 0 0 p 01 1-p 01 0 1 D 1 In In Out p 10 1-p 10 0 0 0 0 p 11 1-p 11 + = + + + k 1 k 1 k 1 k 1 � (k+1)th word = W w w ... w |A|=2; D=2; A D = 4 − ( 0 1 D 1 ) − + k k D 1 k 1 � (k+1)th word value = − + W w A A w − 0 D 1

  7. State Space Construction via D-Markov Machine 1 8 5 5 � Computationally efficient for anomaly measure � Fixed depth D and alphabet size A � Only the state transition probabilities to be determined based on symbol strings derived from time series data or wavelet-transformed data � States represented by an equivalence class of strings whose last D strings are identical

  8. Anomaly Measure Based on the D-Markov Machine Based on the D-Markov Machine 1 8 5 5 State Transition Matrix Construction State Transition Matrix Construction � Banded structure � Separation into irreducible subsystems � Stationary state probability vector � Information on the dynamical system characteristics � Chaotic motion, period doubling, and bifurcation State Probability Vector State Probability Vector � Reference Point: Nominal Condition p (τ ο ) � Epochs { τ k } of Slow Time Scale { p( τ k )} Anomaly Measure at Slow -Time Epochs Anomaly Measure at Slow -Time Epochs M (τ k ; τ ο ) = d(p( τ k ), p( τ ο ))

  9. Comparison of Epsilon Machine and D-Markov Machine 1 8 5 5 Epsilon Machine [Santa Fe Institute] � A priori unknown machine structure � Optimal prediction of the symbol process � Maximization of mutual information (i.e., minimization of conditional entropy) I[X;Y] = H[X] – H[X|Y] � Analogous to the class of Sofic Shifts in Shift Spaces D-Markov Machine � A priori known machine structure (Fixed order fixed structure with given |A| and D ) � Excess states yielding redundant reducible matrices (Perron-Frobenius Theorem) � Suboptimal prediction of the symbol process � Analogous to the class of Finite-type Shifts in Shift Spaces

  10. Anomaly Detection Procedure 1 8 5 5 � Forward (Analysis) Problem : � Characterization of system dynamical behavior � Parametric and non-parametric anomalies � Evolution of the grammar in the system dynamics � Representation of dynamical behavior as formal languages � Thermodynamic formalism of anomaly measure � Inverse (Synthesis) Problem � Estimation of feasible ranges of anomalies � Fusion of information generated from responses under several stimuli chosen in the forward problem

  11. Summary of Anomaly Detection Procedure 1 8 5 5 Dynamical System Time Series Data Current, Voltage or Anomaly omaly D Detect tection and C ion and Classificat assification on other Signals � Signal Conditioning and Decimation Signal � Denoising Conditioning Sampling and Quantization; � Embedding Denoising, and � Symbol Sequence Generation Decimation � Phase space partitioning Pre- � Wavelet space partitioning Processing Wavelet Transform � Markov Modeling of Symbol Dynamics � Epsilon machine (sofic shift) 00011000110101 … � D-Markov machine (finite type shift) Symbol Generation Partitioning of Wavelet � Thermodynamic Formalism of 1 0 Coefficients Generated Information 00 01 0 0 1 1 Pattern 10 11 D-Markov Machine Representation 1 HMM Construction 0 Anomaly Real-time Analytical Detection Prediction

  12. Externally Stimulated Duffing Equation w ith a single slow ly varying parametric anomaly 1 8 5 5 Governing Equations: Externally 2 Applied Force d y ( t ) dy ( t ) + θ + + α 3 ( t ) y ( t ) y ( t ) s ( ω t 2 dt A Cos ) dt ∈ o ∞ = ω t [ t , ) A Cos ( t ) T & [ y ( t ) y ( t )] Random Initial Conditions Mass T ∈ & [ y ( t ) y ( t )] B δ ( 0 ) o o Slowly Nonlinear Varying ∈ o ∞ Spring t fast time t [ t , ) Damping t slow time s Parameters: α = δ = = ω = 1 ; 0.01 ; A 22; 5.0

  13. Electromechanical Systems Laboratory Anomaly Detection Apparatus for 1 8 5 5 Hybrid Electronic Circuits Externally Stimulated Duffing Equation Computer and Data Acquisition System A Sin( ω t)

  14. Electromechanical Systems Laboratory Phase-plane Plots under Nominal 1 8 5 5 and Anomalous Conditions 4.0 4.0 Phase Variable dy/dt θ = 0.27 Phase Variable dy/dt 3.0 θ = 0.10 3.0 2.0 2.0 1.0 1.0 0.0 0.0 -1.0 -1.0 -2.0 -2.0 -3.0 -3.0 -4.0 -4.0 -2 -1.5 -1 -0.5 0.0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0.0 0.5 1 1.5 2 2.5 Phase Variable y Phase Variable y 4.0 Phase Variable dy/dt 2.5 θ = 0.28 2.0 3.0 θ =0.29 Phase Variable dy/dt 1.5 2.0 1.0 1.0 0.5 0.0 0.0 -0.5 -1.0 -1.0 -2.0 -1.5 -3.0 -2.0 -2.5 -4.0 -1 -0.5 0.0 0.5 1 1.5 -2 -1.5 -1 -0.5 0.0 0.5 1 1.5 2 2.5 Phase Variable y Phase Variable y 2.5 Phase Variable 2.0 Blue Green 1.5 θ = 0.10 θ = 0.27 1.0 0.5 0.0 Red Black -0.5 -1.0 θ = 0.28 θ = 0.29 -1.5 -2.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time

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