2001 muri mathematics of failures in complex systems
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2001 MURI Mathematics of Failures in Complex Systems. Project Title :. Characterization and Mitigation of Service Failures in Complex Dynamical systems Technical Vision and Approach. Program manager : Dr. Robert Launer ([email protected]) - PowerPoint PPT PresentationTRANSCRIPT
2001 MURIMathematics of Failures in Complex Systems
Characterization and Mitigation of Service Failures in Complex Dynamical systems
Technical Vision and Approach
Program manager: Dr. Robert Launer ([email protected])Mathematical and Computer Sciences Division
U.S. Army Research Office, P.O. Box 12211Research Triangle Park, NC 27709-2211
Principal Investigator: Professor Asok Ray ([email protected])The Pennsylvania State University
University Park, PA 16802
Project Title:
Complex System FailuresSoftware Hardware Networks Platforms
Understanding
FailureAchieving
Success
Predict Avoid Adjust Reorganize Fix
SA-6
SA-6
SA-12
SA-6
SA-6
SA-6
C2
Factory
Factory
Factory
Airport
Airport
Train station
SEAD(J1)
RIVET
JOINT
(S2)
T1
T2
T3
R1
R2
R3
UAV(S1)
KC-10
(F1) NEWSAM
C2
AWACs
MITIGATION OF PERVASIVE FAILURESMan & Machine Command & Control
of Battlefield DynamicsRef: DARPA Information Technology Office
PROJECT GOALSPervasive Fault Tolerance of Hierarchically Structured Human-Engineered Systems Failure characterization
Continuous and discrete hardware faults Software faults
Failure Mitigation via active and passive control On-line and off-line system reconfiguration Gracefully degraded operation
Failure Simulation Network Collaboratory Experimental validation of theoretical results with hardware in the loop Collaborative research and training of participants from academia, government, and industry Failure Data and Information Repository
MODELING AND CONTROL OF PERVASIVE FAILURES
Failure Characterization Physics-based dynamic modeling of continuous faults
- Damage in mechanical structures
Semi-empirical Modeling of hard failures and soft faults
- Malfunction of electromechanical and electronic hardware
- Malfunction of communication and control software
- Human-machine operation faults
Integration of physics-based and semi-empirical models
Failure Mitigation Continuously-varying robust estimation & control Discrete-event robust decision & control Hierarchically structured hybrid decision & control
OBJECTIVES OF:Pervasive Failure Modeling
Localization of Potential Failure Source(s): benign and malignant faults
Detection and Identification of Incipient Failures: malignant faults
Failure and Damage Prediction under Anticipated Operation: prognosis
Failure-Accommodating Robust Decision & Control: graceful degradation
PHYSICS-BASED MODELINGOF FAILURES
Nonlinear Stochastic Dynamics of (Inhomogeneous) Complex Processes
Multi-Scale Nonstationary Features of Temporal and Spatial Parameters
Non-Colocated Sensory Information
Real-time Information Filtering
Computer Systems Software and Hardware Performability and survivability analysis
Software aging and rejuvenation
Discrete- and continuous-state representation
Electromechanical and Electronic Hardware
Fault Manifestation Analysis
Statistical Failure Analysis
SEMI-EMPIRICAL MODELING OF FAILURES
TECHNICAL CHALLENGES:INTEGRATION OF PHYSICS-BASED AND
SEMI-EMPIRICAL FAILURE MODELS
Nonstationary Statistics of Discrete Events Exciting Nonlinear Dynamics
Complexity of Stochastic Analysis via Monte Carlo Simulation
Robustness of Multi-Scale Nonstationary Distributed Decision & Control Systems
Real-time Information & Control Systems
TECHNIQUES OF APPLIED MATHEMATICS
Systems Sciences: Functional Analysis Nonlinear time-varying dynamical systems Fractal geometry and fractional-dimensional processes Wavelet decomposition of nonstationary random signals Stability analysis and decision & control synthesis Resource-bounded optimization Markov and semi-Markov failure processes
Computer Sciences: Automata & Languages Finite-state automata and regular languages Discrete-event systems and hybrid control Discrete and continuous (stochastic) Petri nets
TECHNICAL APPROACH:
Multi-Scale Nonstationary Modeling
Identification and Quantification of Failure Behavior
Information Fusion of Non-Colocated Sensor Data and Faulty Process Model
Fatigue Cracks in Tube Walls
Creep Thinning in Tube Walls
TYPICAL DAMAGE IN MECHANICAL STRUCTURES
RANDOM FATIGUE TEST DATA Ghonem and Dore (1987)
.
Three sets of 60 carefully controlled tests on specimens made of 7075-T6 alloy
Pmax (kN) RTest
1
2
3
22.79
22.25
15.19
0.6
0.5
0.4
25.4
160.33
25.4
9.525 DIA
6 Holes
Thickness 3.175
All Dimensions in mm
320.67
14.288
Material: 7075-T6 alloy
24
8
10
12
14
16
18
20
22
0 2 4 6 8 10 12 14x104Number of Cycles
Cra
ck L
engt
h (m
m)
60 SpecimensSmax = 70.65 MPaR = 0.6
Frequencyof Loading10 hz
DYNAMICS OF CHAOTIC MOTIONForced van der Pol Equation
)2/sin(25.0
)101(7.0 2
txy
yxyx
Five response cyclesFrom t=0 to t=45.16
Steady-state numerical solutionApproximately 22.5 response cycles
Subharmonic Number 50/22.5 2.2
Dilated Self-similar Waveform(Deterministic)
Statistically Scale-invariant Process(Identical Distribution)
First Order Autoregressive Process(NOT Statistically Scale-invariant)
Self-similarity and Scale-invariance
Scaling Property:
FF sss HH
Self Similarity with Parameter H:
)()(~)()( ttH
tt XXXX
MULTIRESOLUTION WAVELET ANALYSISDecomposition of Chirpy Noise Signal Using the db 4 Orthogonal Wavelet
S=a1+d1=(a2+d2)+d1= = a6+d6+d5+d4+d3+d2+d1
MULTI-SCALE NONSTATIONARY DETERMINISTIC FAILURE MODELING
Failure Model Formulation and Order Reduction
System identification in time and/or frequency domain
Inverse modeling under ill-posed conditions
Recurrent neural network (with simulation data)
Singular perturbation for model order reduction
Nonlinear Time-Varying Dynamics of Fault Propagation
Chaotic behavior of the fault propagation process
Identification of fractal attractors and repellers
Sensitivity to the initial state of fault(s)
MULTI-SCALE NONSTATIONARY STOCHASTIC MODELING
Fractional Brownian Motion (fBm) Random fractal representation of fault characteristics • Potentially benign faults • Potentially malignant faults
Long-memory processes with self-similar disturbances
Nearly 1/f signals with fractional Gaussian noise (fGn)
Statistical wavelet analysis and synthesis Statistical self-similarity of propagated faults
• Scale invariance
Wavelet shrinkage for fault characterization
Multivariate wavelet density estimation
IDENTIFICATION AND QUANTIFICATION OF FAILURE BEHAVIOR
Quantification of Damage Measure Translation-variant -finite deterministic measure
Hausdorff measure for fractional dimensional spaces
Continuous and discrete probabilistic measure
Identification of Failure Events Multi-level hypotheses testing
Pattern matching and scene analysis
Robust identification of uncertainty dynamics
Event generation for discrete-event modeling
SYSTEM DEPENDABILITY
Performability Reliability + Availability + Performance
Survivability Reliability + Availability + Service
Safety
Security
AchievingSYSTEM DEPENDABILITY
Fault Forcasting
Fault Prevention
Fault Accommodation
Fault Removal
ANALYSIS OFSYSTEM DEPENDABILITY
Model-based Evaluation of System Dependability Fault-tree analysis Markov, Markov regenerative, and semi-Markov analysis Stochastic Petri net Statistical inference
Self Similarity of Network Traffic Modeling via fractional Brownian motion (fBm) Multi-scale signal decomposition via wavelet transform
MITIGATION OF PERVASIVE FAILURES
MITIGATION OF PERVASIVE FAILURES
Discrete-Event Decision & Control of Multiple Entities
• Robust and failure-accommodating decision & control
• Game-theoretic approach to systems engaged against others
Hybrid (i.e., continuous and discrete-event) Control of Interacting Entities over Wide Ranges of Operation
Continuously-Varying Control of a Single Entity
• Failure diagnosis and prognosis
• Discrete-time robust output feedback control
Passive Control of Software, Hardware, and Electronic and Electromechanical Components
Discrete-Event System (DES) Decision & Control Synthesis
Qualitative control of discrete event systems
Focusing on the order of event occurrence instead of the specific instant of their occurrence
Failure–accommodating controlled operation
Guaranteeing that the system meets the desired logical goals although operating in a (possibly) degraded mode
DISCRETE EVENT SUPERVISORY CONTROL SYNTHESIS
Plant Description
Plant FSMModel Go
Plant DFSM Model G
Control Objectives
K ControlSpecifications
Completion of S, i.e., S
SyncCompG||S
Is G||SControllable?
Y N
S is the Controller
Iteration: S’ S
G||S’ controllable
S’ is the Controller
)()()( 00 GLGLGLK Constraint:
A SIMPLIFIED FINITE-STATE AUTOMATON MODEL OF ROTORCRAFT OPERATION
q0 idle and safe q1 searching for target q2 alert (in danger) q3 engaged in combat q4 partially damaged q5 destroyed q6 back to the base
States
a attack the target A alarm b partly damaged C mission completed d destroyed
e escape D success/abort
l landing to base
S/s search enemy/friend
t taking off from base
Events
lt
d
e
A
e
Ab
b
d
a
b
Da
AS/s
a
b
e
A
S/s
C/e
d
d
q4
q6
q0
q2q5q1
q3
PERFORMANCE AND ROBUSTNESSOF CONTROLLABLE SUPERVISORS
A signed real-valued measure partitions an accepted language into positive, negative, and null sets
A distance function between two regular languages is defined based on the measure
A metric space of regular languages is constructed with the distance function
A design problem is to achieve a maximally performing
controllable supervisor for the nominal plant model
A dual problem is to design a supervisor that is maximally
robust, i.e., minimally sensitive to modeling uncertainties
MUTI-LEVEL HIERARCHICALDECISION & CONTROL
Low Level Controller #1
Low Level Controller #2
Low Level Plant #1
Low Level Plant #2
High Level Controller
Fea
ture
Se
lect
or #
1
.
Fea
ture
Se
lect
or #
2
.
Inverse FeatureSelector #1
Inverse FeatureSelector #2
low 1
low 2
lowc 1
lowc 2
highc1
high1 high2
highc2
UNIQUENESS OF THE HIERARCHICAL SUPERVISOR SYNTHESIS METHOD
Abstraction based on the behavior of the lower level
closed-loop (controlled) system;
Extension of the controllability and language measure concept to multi-level hierarchical controller
design;
Control specifications dependent on complexity of the plant model at the corresponding level of controlhierarchy.
DAMAGE MITIGATING CONTROL OF COMPLEX SYSTEMS
DAMAGE MITIGATING CONTROL OF COMPLEX SYSTEMS
Motivation:
To achieve high performance with increased:
Safety Reliability Availability Maintainability
Objective:
To ensure structural integrity by: Reduction of material damage (e.g., fatigue cracking)
Simultaneous enhancement of performance via active control
INGREDIENTS OF REAL-TIMEDAMAGE MITIGATING CONTROL
Damage Sensing Systems Multiple damage sensors ARMA model of damage propagation Information fusion
Modeling uncertainty Sensor noise
Hierarchical Decision & Control Robust performance Intelligent decision-making
Approximate reasoning for damage control Discrete-event decision for operation &
maintenance
Technical Approach To model the dynamics of structural degradation in:
Stochastic fractional-dimensional state-space Discrete-event state space
To synthesize robust decision & control algorithms for: Failure prognosis via statistical wavelets Life extension via active control
Technology Transfer To enhance the science & technology base of:
Rotorcraft and land-based vehicle industry
Gas turbine engine industry
DAMAGE MITIGATING CONTROL OF COMPLEX SYSTEMS
Note: Damage, leading to degradation or loss of vehicle safety, is represented by both continuous-varying and discrete-event states that include faults of electronic components and a variety of degradation in mechanical structures such as fatigue cracking, wear, spalling, and
corrosion. However, damage measures are constructed to be C1-continuous, non-negative, finite, and monotonically increasing.
Flight Control Level
Vehicle Management Level
Mission Management Level
Wide-Range NonlinearDamage Control
Rotorcraft Structural Health and Usage Monitoring System
Robust Linear Parameter-Varying Output Feedback Control
Flight Dynamicsand
Structural Dynamics
Conventional and
Special-PurposeSensor Systems
ActuatorDynamics
Analytical Measuresof Damage States and
State Derivatives
Signal Conditioning andSignal Validation
(FDIR and calibration )
.
Information-Integrated Health Management andDamage Mitigating Control of Rotorcraft
Wide- Range Fuzzy Damage-Mitigating Control
StructuralModel
DamagePrediction
Model
FuzzyDamage
Controller
ReferenceSignal
Generator
LinearGain-
ScheduledController
K(z)
PlantDynamics
SH
ydam(t) ydam(k)
u(t)
u(k)
uff(k)
ufb(k)
ydyn(k)
edyn(k)
ereg(k)
ydyn(t)
yreg(k)
yreg(t)
y ref (k) D(k)
ystr(k)
RR(k)
D(k).
S
S
yset(k)
.+
++
_+
_
H
S Sample
Hold
Nonlinear parts of the control system
Linear parts of the control system
DAMAGE MITIGATING CONTROLOF A FIXED-WING TACTICAL AIRCRAFT
On-line Sensor Data
Str
uctu
ral
stre
sses Damage
vector
Damage Rate
vector
ControlInput
Rigid-Body Aircraft
Dynamic Model
Aeroelastic WingModel
Stochastic State-spaceModel ofFatigue Crack
Damage
Fatigue Crack Damage Model
Aeroelastic Model
Rigid-Body Model
Pil
ot
Com
man
ds
PLA
Lif
e E
xten
ding
C
ontr
olle
r
Actuator Model
Propulsion Model
Atmospheric Model
Damage Mitigating Control System Schematic Damage Prediction System
y w
y b ,y s
zs ,z wzb
x w
x s
x b
V
TACTICAL AIRCRAFT SIMILAR TO F-15
Side
slip
Ang
le (
deg)
0 2 4 6 8 10 12 14-5
-4
-3
-2
-1
0
1
2
3
4
PC DMC1 DMC2
Reference
DMC2
DMC1
PC
Reference
0 2 4 6 8 10 12 14
Time (sec)
-150
-100
-50
0
50
100
Rol
l Rat
e (d
eg/s
ec)
PC DMC1 DMC2
Reference
PC
DMC2
Reference DMC1
-5
0
5
10
15
20
Pitc
h R
ate
(deg
/sec
)
0 2 4 6 8 10 12
Time (sec)
PC DMC1 DMC2
Reference
Reference DMC1 DMC2
PC
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cra
ck L
engt
h (i
n m
m)
PCDMC1DMC2
PC
DMC1
DMC2
AIRCRAFT PERFORMANCE AND DAMAGE UNDER TURN REVERSAL MANEUVER
The Space Shuttle Main Engine (SSME)
SSME PROPULSION SCHEMATIC
0.0
0.5
1.0
1.5
2
2.5x10 -3
0.0 0.2 0.4 0.6 0.8 1.0 1.2Time (sec)
Dam
age
in T
urbi
ne B
lade
s
With Damage Control
Without Damage Control
Pressure Range: 2100 psi to 3000 psi
2000220024002600280030003200
0.0 0.2 0.4 0.6 0.8 1.0 1.2C
ham
ber
Pres
sure
(ps
i)
With Damage Control
Without Damage Control
Reference
Pressure Range: 2100 psi to 3000 psi
0.0 0.2 0.4 0.6 0.8 1.0 1.25.98
6.00
6.02
6.04
6.06
O2/
H2 M
ixtu
re R
atio
With Damage ControlWithout Damage Control
Reference
Pressure Range: 2100 psi to 3000 psi
Oxidant (O2) Turbine
0
0.5
1
1.5
2
2.5x10 -5
0 0.2 0.4 0.6 0.8 1.0 1.2Dam
age
in T
urbi
ne B
lade
With Damage Control
Without Damage Control
Pressure Range: 2100 psi to 3000 psi
Fuel(H2) Turbine
VALIDATION OF NEW DMC CONCEPTSIN LABORATORY ENVIRONMENT
Failure Simulation Laboratory Fatigue Testing Apparatus Aircraft Simulation Testbed Rocket Engine Simulation Testbed Fossil Power Plant Simulation Testbed
Rotorcraft Excellence Center Rotorcraft Simulation Testbed Aeroelasticity Simulation Testbed Health and Usage Monitoring (HUMS) Testbed
Computational Fluid Dynamics Laboratory Combustion Simulation Testbed Gas Turbine Engine Simulation Testbed Rocket Engine Simulation Testbed
Break
COMPLEX SYSTEM FAILURES
Understanding
Failure Predict Fix Avoid Adjust Reorganize
Achieving
Success
Software Hardware Networks Machinery
MATHEMATICAL MODELING OF FAULT GENERATION AND PROPAGATION
Fault Propagation Models Physics-based modeling Semi-empirical modeling
Measures of Pervasive Fault Tolerance Physics-based measures Information-theoretic measures
Hierarchically Supervised Automata Hybrid decision & control for failure mitigation Quantitative evaluation of robust performance
An example of System Complexity:INTELLIGENT BATTLEFIELD AUTOMATION
NOISE/UNCERTAINTY ACCOMMODATION
Sensor information validation and calibration
Noise modeling at the interface level
Noise masking for event/action Generators
PLANT/CONTROLLER INTERFACE
Event/action generators serving as continuous/discrete interfaces
Accommodation of multiple controllers with various plant subsystems
HIERARCHICAL AGGREGATION
Feature selector for generating meta- language for the supervisory Controller
Inverse feature selector for control actions
CONTROL SYNTHESIS AUTOMATION
Assuring controllability, observability, scalability, and hierarchical consistency JAVA-based controller synthesis tools
PLANT DYNAMICS, CONTROLLER, AND INFORMATION GENERATOR
Hierarchical Controller
Plant (Simulator)
Control
Decision Support InterfaceController Interface
Dispatcher (Simulation Interface and Control)
Platform Simulation Platform Simulation Platform Simulation
Event GeneratorAction
Generator
Routing Clustering
Plant State Filter
Discrete Event
Hierarchical Discrete Event Controller
(Simulated) Plant Dynamics
Information Generator
Events
Decision Support InterfaceController Interface
Dispatcher (Plant Interface with Control)
Plant Information
Plant Control
Event Generator
Action Generator
Routing Clustering
InformationFilter
Supervisory Controller
Plant Information
Aircraft Controller
Other WeaponSystem Controller
Platform SimulationPlatform Simulation Platform Simulation
Filtered Information
DAMAGE MITIGATING CONTROL
High performance with increased:
Fault tolerance Damage tolerance
Synergistic combination of:
Systems Science Computer Science Mechanical Science Material Science
Enhanced reliability and safety via: Reduced structural damage Information-based maintenance