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 (launer@arl.aro.army.mil)Mathematical and Computer Sciences Division

U.S. Army Research Office, P.O. Box 12211Research Triangle Park, NC 27709-2211

Principal Investigator: Professor Asok Ray (axr2@psu.edu)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