FACT 10/99 Vanderbilt / ISIS Fault-Adaptive Control Technology FACT Gabor Karsai, Gautam Biswas (VU/ISIS) Gabor Peceli (TUB)

FACT 10/99 Vanderbilt/ISIS Objective ä Develop and demonstrate FACT tool suite ä Components: ä Discrete Diagnosis and Mode Identification System ä Hybrid Diagnosis and Mode Identification System ä Dynamic Control Synthesis System ä Transient Management System

FACT 10/99 Vanderbilt/ISIS FACT Application Architecture Simulator Diagnosis Engine Dynamic Control Synthesis Transient Manager Configuration Manager Active Model Hypothesis Set Active Model Hypothesis Set Reconfigurable Monitoring and Control System Plant Hybrid Diagnosis Discrete Diagnosis and Mode Identification Supervisory Control and Execution Manger Model Update Framework

FACT 10/99 Vanderbilt/ISIS Hybrid Diagnosis Scheme Complex Systems ä Mode Identification and Fault Isolation in real-time using ä Discrete Models ä Continuous Models ä Integrated Hybrid Fault Isolation: Combining information from the discrete + continuous levels u Mode Identification: OBDD scheme + continuous constraint analysis u Multiple Hybrid Observers for tracking system variables in real time (normal & fault modes) u Parameter Estimation techniques to determine system state & aid controller synthesis and reconfiguration Objective: Isolate the fault source (LRU+failure mode)

FACT 10/99 Vanderbilt/ISIS Discrete Diagnosis: Discrete Fault Model FM1 FM2 FM3 FM4 C1 DY4 DY3 DY6 DY7 DY8 DY5 DY2 DY1 DY9 DY10 DY11 DY12 C2 Failure ModeDiscrepancy“Alarmed” Discrepancy F1 F3F2

FACT 10/99 Vanderbilt/ISIS International Space Station Fault Detection, Isolation and Recovery Modeling

FACT 10/99 Vanderbilt/ISIS Discrete Diagnosis: Relational Formalization

FACT 10/99 Vanderbilt/ISIS International Space Station Fault Detection, Isolation and Recovery Diagnosability Analysis

FACT 10/99 Vanderbilt/ISIS Discrete Diagnosis: Research Issues ä Map: Discrete fault models => relational form ä Efficient reasoning algorithms using OBDDs ä Time-bounds and space-bounds on the algorithm’s complexity ä Design-time analysis of fault models to predict run-time behavior of the algorithm

FACT 10/99 Vanderbilt/ISIS Fault Diagnosis Scheme Dynamic Continuous Systems Binary Decision Source, Type Magnitude

FACT 10/99 Vanderbilt/ISIS Qualitative Approach Fault Isolation ä Qualitative Representation ä magnitude deviations + higher order derivatives. (currently +, 0, -) ä Why Qualitative ? ä Accuracy of models -- structural + difficulty in estimating parameters ä Imprecision of real world numeric models ä computational issues, e.g., convergence problems ä Eventual Goal – Qualitative methods for pruning search + Quantitative parameter estimation methods for fault isolation & impact assessment

FACT 10/99 Vanderbilt/ISIS Diagnosis Algorithm for Continuous Dynamic Systems detect discrepancy generate faults predict behavior progressive monitoring rrsrs fhfh f h, p frfr Magnitude: low, high Slope:below, above normal discontinuous change e 6 - =>R - leak, I + rad-out, R - hy-blk R - leak --> e 6 = Fault Isolation Algorithm 1. Generate Fault Hypotheses: Backward Propagation on Temporal Causal Graph 2. Predict Behavior for each hypothesized fault: Generate Signatures by Forward Propagation 3. Fault Refinement and Isolation: Progressive Monitoring

FACT 10/99 Vanderbilt/ISIS Prediction by Forward Propagation Signatures Signature: predicted future behavior of measurement variables in response to a fault. Basis for signatures: Taylor’s series expansion of a continuous differentiable function about point of failure, t = t 0 : f(t) = f(t 0 ) + f '(t 0 ) (t- t 0 ) / 1! + f ''(t 0 ) (t- t 0 ) 2 / 2! +…… + f (k) (t 0 ) (t- t 0 ) k / k! How to generate signatures from TCG ? Temporal links imply integrating edges, affects derivative of variable on the effect side > Start with 0-order changes  Every integrating edge increases order by one one Rb nd Order signature of e 7 :

FACT 10/99 Vanderbilt/ISIS Monitoring Implementation ä Progressive Monitoring to track system dynamics after failure ä Higher-order derivatives as a predictor of future behavior (justified by Taylor’s series) ä Activated when there is a discrepancy between predicted and observed value.

FACT 10/99 Vanderbilt/ISIS Model-based Feature Extraction using Signal Analysis Methods Derivative Estimation from Noisy Signal (derivative vs. FIR filter) 1. Fault Detection: Detect discrepancy from noisy signal; check for abrupt (discontinuous change) 2. Feature Extraction: Extract magnitude value, slope, and other model-initiated features from noisy signals for Fault Isolation Signal to Symbol Transformation Abrupt Change Detection Statistical Hypothesis Testing GLR methodology DWT: Daubechies-3 wavelet

FACT 10/99 Vanderbilt/ISIS From Discrete + Continuous Analysis to Hybrid Diagnosis + Reconfiguration ä Extend to Hybrid Diagnosis: Hybrid Observers that can handle controller + autonomous jumps ä Mode Identification: in conjunction with discrete diagnosis system ä Parameter Estimation: to assist in controller synthesis (by selection) and reconfiguration

FACT 10/99 Vanderbilt/ISIS Runtime Hybrid Models Issues ä Hybrid Modeling -- controller actions (embedded systems) + autonomous jumps (attributed to modeling abstractions and simplifications) ä Simplification of complex nonlinear dynamics by creating piecewise simpler behaviors about operating regions ä order reduction in the individual piecewise models by singular perturbation techniques Result: Simpler continuous dynamics but complex discrete transition structures

FACT 10/99 Vanderbilt/ISIS Control Library Dynamic Control Synthesis Dynamic Control Synthesis Active Model Control Library Control Library Control Architecture Variants Hypothesis Set

FACT 10/99 Vanderbilt/ISIS Exploration of the Controller Configuration Space Behavior (Hier. Par. FSM) Algorithms (Hier. Altern.) Resources Binary Encoding Binary Encoding Binary Encoding OBDD Representation OBDD Representation OBDD Representation Design Space (Sym. Rep) Constraints (OCL) Binary Encoding OBDD Representation Pruned Design Space

FACT 10/99 Vanderbilt/ISIS Encoding the Controller Architecture Space C3 C2 C1 C31 C32 C6 C7 C8 C9 R C1 C2 C3 C31 C32 C4 C5 Binary Encoding: C1: c1’  c2’ C2: c1’  c2 C3: c1  c2’ C4: c1’  c2  c3’ C5: c1’  c2  c3 C6: c1  c2’  c3’ C8: c1  c2’  c4’ C7: c1  c2’  c3 C9: c1  c2’  c4 C=c1’  c2’

FACT 10/99 Vanderbilt/ISIS Encoding the Constraints R C1 C2 C3 C31 C32 C4 C5 C6 C7 C8 C9 cc1: c1  c2’  c3’  c1  c2’  c4’ C cc1 = C  cc1

FACT 10/99 Vanderbilt/ISIS Dynamic Control Synthesis Research Issues ä Efficient representation of controller architectures ä Formulation of constraints ä Time bounds on the search process

FACT 10/99 Vanderbilt/ISIS Transient Management  Mode transitions  Reconfiguration ä A reconfiguration method is applied ä defines the way of transforming the realization of the old system to the new one ä Requirements: ä must not influence the processing the input samples ä as soon as possible ä using the available computing resources ä minimize the intermediate disturbances caused by the abrupt change in the system (reconfiguration transients)

FACT 10/99 Vanderbilt/ISIS Transient Management Switched Filter Example First-order Direct Structure First-order Resonator-based Structure

FACT 10/99 Vanderbilt/ISIS (n) (n-3) Transient Management Switched Filter Example Time k-1 k x(n-1) x(n-2) u(n-2) u(n-1) y(n-2) y(n-1) x u(n) u(n+1) u(n+2) y(n) y(n+1) y(n+2) x(n+1) x(n+2) x(n+3) x u(n-3)y(n-3)

FACT 10/99 Vanderbilt/ISIS Transient Management Switched Filter Example First-order Direct Structure First-order Resonator-based Strucure

FACT 10/99 Vanderbilt/ISIS Schedule ä Yearly breakdown: ä Year 1: Laboratory version(sim on workstation) ä Year 2: Embeddable version(soft real-time) ä Year 3: Real-time version(hard real-time) ä Year 4: Analysis technology(analysis workbench)

FACT 10/99 Vanderbilt/ISIS Background Slides

FACT 10/99 Vanderbilt/ISIS Model-Based Diagnosis of Dynamic Systems ä Mathematical or Analytic Redundancy schemes Filtering and Observer-based methods - Generate Residue vectors (Frank 90, Isermann 84,Isermann97, Patton and Chen 97) ä State Estimation ä Parameter Estimation ä Characteristic Quantities ä Topological methods Graph based, Compositional ä System ä Fault Models Problem with Topological models- underconstrained Functional Redundancy Methods

FACT 10/99 Vanderbilt/ISIS Methodology ä Parsimonious topological system models ä Qualitative and Quantitative Analysis ä Transient Analysis of faulty behaviors transients represented as signatures: qualitative higher- order time derivatives ä Tracking of dynamic effects by progressive monitoring scheme ä Signal to Symbol Transformation for Tracking and Monitoring ä Measurement selection

FACT 10/99 Vanderbilt/ISIS Bond Graph and Temporal Causal Graph Two-tank System C1 Rb1 Rb2 R12 C2

FACT 10/99 Vanderbilt/ISIS Generate Fault Hypotheses C1 Rb1 Rb2 R12 C2

FACT 10/99 Vanderbilt/ISIS Feature Extraction from Transients ä Signal Magnitude (+,-): simple filter that avoids fluctuations around zero crossings ä Slope estimation : ä first order difference operator ä piecewise linear approximation ä finite impulse response (FIR) filter FIR coefficients: h(n) = (N-1)/2 - n ; n=0,….,N-1 k=0 N-1 Differentiator: y(n) = S  h(k)x(n-k)

FACT 10/99 Vanderbilt/ISIS Wavelet Detector Statistical Testing No underlying signal model Requires explicit model Comparison of Methods GLR applied to compensatory, inverse, and reverse behavior Hard to link threshold function adaptive threshold plus threshold value, h, To design characteristics, e.g., SNR can be directly linked to false alarm rate

FACT 10/99 Vanderbilt/ISIS Automobile Engine Test Bed and Coolant System Schematics Engine Test bed Setup Coolant System Schematics and Sensors Goal: Develop Monitoring and Diagnosis Methodologies for Complex Continuous Dynamic Systems that work with real, noisy data Engine