Chapter 8. Management Strategy & Resilience-Driven System Design 8... · 2019. 3. 18. · Chapter 8. Management Strategy. Maintenance Management. 1) Maintenance? • A work process

Seoul National University

Prognostics and Health Management (PHM)

Chapter 8. Management Strategy & Resilience-Driven System Design

Byeng D. YounSystem Health & Risk Management LaboratoryDepartment of Mechanical & Aerospace EngineeringSeoul National University


CONTENTS

2019/1/4 - 2 -

Maintenance Management1Asset Management2Resilience-Driven System Design3

Seoul National University2019/1/4 - 3 -

Chapter 8. Management Strategy

Maintenance Management1)

Maintenance?• A work process that contributes to take care of equipment, respond to its needs, and keep

it in good operating condition

Management?• The organization and coordination of activities aligned with certain policies for the

achievement of clearly defined objectives of an enterprise

Maintenance Management• To help guide the physical performance of maintenance equipment and activities• Maintenance Plan, Materials, Costs, …, etc.

1) Robert M. Williamson, “Asset Management vs. Maintenance Management”, Strategic Work Systems, Inc. 2012



Maintenance Management

Corrective

Preventive

Condition Based

Predictive

Middle Companies

Global Leading

Companies

Future

The cost is main problem according to the survey in Nov. 2014

Most Small Business

Corrective

Maintenance

Preventive

Maintenance

Condition Based

Maintenance

Predictive

Maintenance

Managementmethod

Rely on laborer’s experience

Maintenance guideline

& usage data

Online system monitoring & control

Automaticmanagement of

equipment & system

Technologylevel

Repair and management by field

laborer

Life estimation based on failure history

Anomaly detection,Failure classification,Failure cause analysis

Remaining Useful Life prediction

Enterprise Level Most Small Business

Middle-size Companies

Global Leading Companies Future

PHM Aided



Corrective MaintenanceCorrective Maintenance?• A maintenance task performed to restore an operational condition• Carry out after failure occurrence and detection (action after failure)

Pros and Cons• Pros: no redundancy, no PHM cost• Cons: huge maintenance cost, unexpected opportunity cost, Social risk

Example• Unexpected breakdown of AREX(Airport Railroad Express)

– Corrective maintenance occurred on the power unit of train (redundancy)



Preventive MaintenancePreventive Maintenance?• Perform from time-to-time, along planned guidelines (time-based action)• Carry out in order to avoid suddent breakdown of system

Pros and Cons• Pros: able to avoid expected failure owing to degradation of system• Cons: relatively high waste, occurrence of unexpected failure

Example• Maintenance of main transformer for every 3 years (KEPCO)



Condition Based MaintenanceCondition Based Maintenance?• Perform when one or more indicators show the need of maintenance (action if needed)• Carry out along with the health status of system

Pros and Cons• Pros: no redundancy, capable of handling unexpected failures proactively• Cons: PHM investment cost

Example• Vehicle gas tank, tire pressure, battery SOC, industrial robots, wind turbine, etc.



Predictive MaintenancePredictive Maintenance?• Predict when maintenance should be performed (predict action)• Preparing upcoming maintenance, helping O&M (operation and management)

Pros and Cons• Pros: availing scheduling and management proactively• Cons: investment cost, prediction uncertainty under highly uncertain operation

Example• Industrial bearings, generator windings, etc.



Concept of Asset Management1)

Should one continue improving maintenance strategy or renew the asset?

LCC (Life Cycle Cost) Problem• Maintenance cost• Downtime for maintenance• Asset operation efficiency• Asset operating cost• Quality of operation or service• Safety to staff and the public

<Replacement><Maintenance>

Asset Management

Maintenance Management

1) P J Huggett, “Asset Management – the changing role of Maintenance Management”, The Woodhouse Partnership Ltd, 2012



Concept of Asset ManagementDefinition of Asset Management• ISO 550001)

– Asset management involves the balancing of costs, opportunities and risks against the desired performance of assets, to achieve the organizational objectives.

• PAS 552)

– Systematic and coordinated activities and practices through which an organization optimally and sustainably manages its assets and asset systems, their associated performance, risks and expenditures over their lifecycles for the purpose of achieving tis organizational strategic plan.

Asset Management

𝒎𝒎𝒎𝒎𝒎𝒎 𝐿𝐿𝐿𝐿𝐿𝐿𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒔𝒔𝒕𝒕. 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑟𝑟𝑟𝑟𝑝𝑝…

1) ISO 55000. "ISO 55000." (2013).2) Woodhouse, John. "PAS-55-Asset Management: concepts & practices." 21st International Maintenance Conference, IMC-2006, December. 2006.



Concept of Resilience and RDSDResilience?• (ecology) the ability of the system to maintain its function wen faced with novel

disturbance1)

• (psychology) a dynamic process that individuals exhibit positive behavioral adaptation when they encounter significant adversity2)

• An ability to sustain functionality by resisting and recovering from adverse events3)

𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝜳𝜳 = 𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑹𝑹 + 𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝝆𝝆

Resilience-Driven System Design (RDSD) ? • A new design technique to obtain optimal system and PHM design retaining target

resilience with minimum life-cycle cost

RBDO PHM design

1) Webb, Colleen T. "What is the role of ecology in understanding ecosystem resilience?." BioScience 57.6 (2007): 470-471.2) Luthar, Suniya S., Dante Cicchetti, and Bronwyn Becker. "The construct of resilience: A critical evaluation and guidelines for future work." Child development 71.3 (2000): 543-562.

3) Yoon, Joung Taek, et al. "A newly formulated resilience measure that considers false alarms." Reliability Engineering & System Safety 167 (2017): 417-427.



Motivation of RDSDConventional Approaches

Reliability-based Design Optimization Prognostics & Health Management

• Design-stage technique to obtain optimal

design ensuring target reliability with

minimum cost

• Operation-stage technique to monitor health

states to adaptively prevent potential

failures and maximize system availability

*RBDO: reliability-based design optimization; *PHM: prognostics & health management;



Motivation of RDSDRBDO and PHM on Engineering System

• RBDO and PHM are complementary• Separate implementation: No consideration of interaction• Conservative or failure-prone design High Life-Cycle Cost

HealthIndex

FailureTime

PHM approach

RBDO-approach

How to cohesively incorporate RBDO with PHM

to minimize Life-Cycle Cost?



Resilience-Driven System Design1)

Hierarchical RDSD Framework

Minimize system life-cycle cost Allocate reliability, PHM efficiency, redundancy Satisfy a target system resilience

Resilience Allocation Problem(Top Level)

System Design

PHM unit design (hardware & algorithm) Sensor Network Design

System RBDO Satisfy an allocated reliability

System RBDO(Bottom Level 1)

System PHM Design(Bottom Level 2)

*M/R: Maintenance/Recovery1) Youn, Byeng D., Chao Hu, and Pingfeng Wang. "Resilience-driven system design of complex engineered systems." Journal of Mechanical Design 133.10 (2011): 101011.



Resilience-Driven System Design1)

Top Level: Resilience Allocation Problem



System Design








Resilience-Driven System DesignTop Level: Resilience Allocation Problem• RAP formulation

minimize 𝐿𝐿𝐿𝐿𝐿𝐿(𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡 ,𝐦𝐦)

subject to Ψ 𝜓𝜓 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡,𝐦𝐦 ≥ Ψ𝑡𝑡

0 ≤ 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡 ≤ 1

𝑟𝑟𝑗𝑗𝐿𝐿 ≤ 𝑟𝑟𝑗𝑗 ≤ 𝑟𝑟𝑗𝑗

𝑈𝑈 𝑗𝑗 = 1, … ,𝑁𝑁

𝐿𝐿𝐿𝐿𝐿𝐿 = 𝐿𝐿𝐼𝐼 + 𝐿𝐿𝑃𝑃𝑀𝑀 + 𝐿𝐿𝐶𝐶𝑀𝑀 + 𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀

PHM development

Initial development

pred./corr.Maintenance

Life-Cycle Cost1-2)

Resilience analysis

Ψ 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡,𝐦𝐦 = �𝑗𝑗=1

𝑁𝑁𝜓𝜓𝑗𝑗

𝜓𝜓𝑗𝑗 = 1 − 1 − 𝑟𝑟𝑗𝑗𝑡𝑡𝑚𝑚𝑗𝑗 1− 𝜆𝜆𝑗𝑗𝑡𝑡

𝑚𝑚𝑗𝑗

Note: this formula is for a series-parallel system

• Cost Analysis– Development cost 𝐿𝐿𝐼𝐼

𝐿𝐿𝑗𝑗𝐼𝐼 = 𝑝𝑝𝑗𝑗𝐼𝐼 𝑟𝑟𝑗𝑗𝑡𝑡 𝑟𝑟𝑗𝑗 + exp𝑟𝑟𝑗𝑗

4,

𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑗𝑗𝐼𝐼 𝑟𝑟𝑗𝑗𝑡𝑡 = 𝛼𝛼𝑗𝑗𝐶𝐶 −𝑇𝑇

𝐼𝐼𝑟𝑟 𝑟𝑟𝑗𝑗𝑡𝑡

𝛽𝛽𝑗𝑗𝐶𝐶

– Preventive maintenance cost 𝐿𝐿𝑃𝑃𝑀𝑀

𝐿𝐿𝑃𝑃𝑀𝑀 = �𝑗𝑗=1

𝑁𝑁

𝑟𝑟𝑗𝑗𝜆𝜆𝑗𝑗𝑡𝑡 1 − 𝑟𝑟𝑗𝑗𝑡𝑡 𝐿𝐿𝑗𝑗𝑃𝑃𝑀𝑀

– Corrective maintenance cost 𝐿𝐿𝐶𝐶𝑀𝑀

𝐿𝐿𝐶𝐶𝑀𝑀 = �𝑗𝑗=1

𝑁𝑁

𝑟𝑟𝑗𝑗 1 − 𝜆𝜆𝑗𝑗𝑡𝑡 1 − 𝑟𝑟𝑗𝑗𝑡𝑡 𝐿𝐿𝑗𝑗𝐶𝐶𝑀𝑀

– PHM development cost 𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀

𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀 = �𝑗𝑗=1

𝑁𝑁

𝛼𝛼𝑃𝑃𝑃𝑃𝑀𝑀 −𝑇𝑇

𝐼𝐼𝑟𝑟 𝑟𝑟𝑗𝑗𝑡𝑡

𝛽𝛽𝑗𝑗𝑃𝑃𝑃𝑃𝑃𝑃

1) Dhingra, A. K., “Optimal Apportionment of Reliability and Redundancy in Series Systems under Multiple Objectives,” IEEE Trans. Device Mater. Reliab. (1992)2) Youn et al., “Resilience-driven System Design of Complex Engineered Systems,”, J. Mech. Design (2011)


1st subsystem𝜓𝜓1 = 99.98%𝑟𝑟1 = 2 (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟)

𝑟𝑟11 = 90%𝜆𝜆11 = 85%

𝑟𝑟12 = 90%𝜆𝜆12 = 85%

3rd subsystem𝜓𝜓3 = 99.98%𝑟𝑟3 = 2

𝑟𝑟31 = 90%𝜆𝜆31 = 75%

𝑟𝑟32 = 90%𝜆𝜆32 = 75%

2nd subsystem

𝑟𝑟21 = 90%𝜆𝜆21 = 0

𝑟𝑟23 = 90%𝜆𝜆23 = 0

𝑟𝑟22 = 90%𝜆𝜆22 = 0

𝜓𝜓2 = 99.9%𝑟𝑟2 = 3

2019/1/4 - 17 -


Resilience-Driven System DesignTop Level: Resilience Allocation Problem• RAP formulation

minimize 𝐿𝐿𝐿𝐿𝐿𝐿(𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡 ,𝐦𝐦)

subject to Ψ 𝜓𝜓 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡,𝐦𝐦 ≥ Ψ𝑡𝑡

0 ≤ 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡 ≤ 1

𝑟𝑟𝑗𝑗𝐿𝐿 ≤ 𝑟𝑟𝑗𝑗 ≤ 𝑟𝑟𝑗𝑗

𝑈𝑈 𝑗𝑗 = 1, … ,𝑁𝑁

𝐿𝐿𝐿𝐿𝐿𝐿 = 𝐿𝐿𝐼𝐼 + 𝐿𝐿𝑃𝑃𝑀𝑀 + 𝐿𝐿𝐶𝐶𝑀𝑀 + 𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀

PHM development

Initial development

pred./corr.Maintenance

Life-Cycle Cost1-2)

Resilience analysis

Ψ 𝐫𝐫𝑡𝑡,𝝀𝝀𝑡𝑡,𝐦𝐦 = �𝑗𝑗=1

𝑁𝑁𝜓𝜓𝑗𝑗

𝜓𝜓𝑗𝑗 = 1 − 1 − 𝑟𝑟𝑗𝑗𝑡𝑡𝑚𝑚𝑗𝑗 1− 𝜆𝜆𝑗𝑗𝑡𝑡

𝑚𝑚𝑗𝑗

Note: this formula is for a series-parallel system

• Example result (Ψ = 99.82%)

• Relation to bottom level design problems

Bottom Level 2: System PHM Design

Optimum Component PHM- Efficiency λt

Bottom Level 1: System RBDO

Optimum Component Reliability rt

1) Dhingra, A. K., “Optimal Apportionment of Reliability and Redundancy in Series Systems under Multiple Objectives,” IEEE Trans. Device Mater. Reliab. (1992)2) Youn et al., “Resilience-driven System Design of Complex Engineered Systems,”, J. Mech. Design (2011)



Resilience-Driven System DesignBottom Level 1: System RBDO

System Design









Resilience-Driven System DesignBottom Level 1: System RBDO• RBDO formulation • RBDO procedure

• Relation to bottom level PHM design

Bottom Level 2: System PHM Design

Optimum Component Design 𝐝𝐝𝑗𝑗𝐶𝐶

d2

0

Failure SurfaceG1(d)=0

Infeasible Region Gi(d)>0

d1

Feasible RegionGi(d)≤0Initial Design Failure Surface

G2(d)=0

DeterministicOptimum

RBDOOptimum

𝐸𝐸𝑗𝑗𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = �𝑠𝑠=1

𝑛𝑛𝑐𝑐𝑗𝑗𝐺𝐺𝑗𝑗𝑠𝑠 𝐱𝐱𝑗𝑗C;𝐝𝐝𝑗𝑗C ≤ 0

…

…

success event forith constraint

Series System

Parallel System

System success event

𝐸𝐸𝑗𝑗𝑝𝑝𝑝𝑝𝑠𝑠𝑝𝑝𝑝𝑝 = �

𝑠𝑠=1

𝑛𝑛𝑐𝑐𝑗𝑗𝐺𝐺𝑗𝑗𝑠𝑠 𝐱𝐱𝑗𝑗C;𝐝𝐝𝑗𝑗C ≤ 0

Initial Development Cost

Reliability Analysis

minimize 𝐿𝐿𝑗𝑗𝐼𝐼(𝐝𝐝𝑗𝑗C)

subject to 𝑟𝑟𝑗𝑗 𝐝𝐝𝑗𝑗C ≥ 𝑟𝑟𝑗𝑗𝑡𝑡;𝐝𝐝𝑗𝑗C,L ≤ 𝐝𝐝𝑗𝑗C ≤ 𝐝𝐝𝑗𝑗

C,U;



Resilience-Driven System DesignBottom Level 2: System PHM Design

System Design









Resilience-Driven System DesignBottom Level 2: System PHM Design• PHM design formulation • PHM design variables dPHM

minimize 𝐿𝐿𝑗𝑗𝑃𝑃𝑃𝑃𝑀𝑀(𝐝𝐝𝑗𝑗𝑃𝑃𝑃𝑃𝑀𝑀) + 𝐿𝐿𝑗𝑗𝑀𝑀(𝐝𝐝𝑗𝑗𝑃𝑃𝑃𝑃𝑀𝑀)

subject to 𝜆𝜆𝑗𝑗 𝐝𝐝𝑗𝑗PHM ≥ 𝜆𝜆𝑗𝑗𝑡𝑡

𝐝𝐝𝑗𝑗PHM,L ≤ 𝐝𝐝𝑗𝑗PHM ≤ 𝐝𝐝𝑗𝑗

PHM,U

PHM Development Cost Maintenance Cost

PHM Efficiency

𝜅𝜅𝑗𝑗: 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝 𝑟𝑟𝑤𝑟𝑟 𝑀𝑀/𝑅𝑅 𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟Λ𝑃𝑃𝑗𝑗: 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝑝𝑝𝑟𝑟𝑝𝑝𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟Λ𝐷𝐷𝑗𝑗: 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟

Hardware 𝐝𝐝𝑃𝑃/𝑊𝑊𝑃𝑃𝑃𝑃𝑀𝑀

: sensor types, sensor numbers, and sensor location

𝐹𝐹𝐹𝐹

# of sensors

Prob.

𝑀𝑀𝐹𝐹

acc.

Software 𝐝𝐝𝑆𝑆/𝑊𝑊𝑃𝑃𝑃𝑃𝑀𝑀

: algorithm type, algorithm parameters

SVM

Prob.

ANN LDA

𝑀𝑀𝐹𝐹𝑡𝑡𝐹𝐹𝐹𝐹𝑡𝑡

:𝐹𝐹𝐹𝐹 :𝑀𝑀𝐹𝐹<SVM> <ANN>

- Physics-based- Data-driven

𝜆𝜆𝑗𝑗 ≡ 𝜅𝜅𝑗𝑗 � 𝛬𝛬𝑃𝑃𝑗𝑗 � 𝛬𝛬𝐷𝐷𝑗𝑗



Case Study: Electro-Hydrostatic Actuator (EHA)Problem Description• Closed-loop, hydrostatic control system• Compositions: electronic control unit, electric motor, pump, hydraulic piston actuator

Compositions of EHA

Mechanical Schematic of an EHA model



Case Study: Electro-Hydrostatic Actuator (EHA)Top Level: Resilience Allocation Problem



System Design








Case Study: Electro-Hydrostatic Actuator (EHA)Top Level: Resilience Allocation Problem• Assumption

– The failure times all components considered in the example are exponentially distributed, leading to constant failure rates.

– PHM will detect critical system health states and predict system RUL through health diagnostics and prognostics

– The redundancy level of each subsystem should be no more than nine due to subsystem weight and volume constraints.

– All the components and PHM units fail independently. An observed failure is due to the loss of resilience, i.e., the failures of both a component and its associated PHM unit

• Model Parameters for the EHA case study

minimize 𝐿𝐿𝐿𝐿𝐿𝐿 = �𝑗𝑗=1

4

(𝐿𝐿𝑗𝑗𝐼𝐼 + 𝐿𝐿𝑗𝑗𝑃𝑃𝑀𝑀 + 𝐿𝐿𝐽𝐽𝐶𝐶𝑀𝑀 + 𝐿𝐿𝐽𝐽𝑃𝑃𝑃𝑃𝑀𝑀)

subject to Ψ = �𝑗𝑗=1

4

[1 − 1 − 𝑟𝑟𝑗𝑗𝑡𝑡𝑚𝑚𝑗𝑗 1− 𝜆𝜆𝑗𝑗𝑡𝑡

𝑚𝑚𝑗𝑗] ≥ Ψ𝑡𝑡

𝟎𝟎 ≤ 𝐫𝐫𝒔𝒔,𝝀𝝀𝒔𝒔 ≤ 𝟏𝟏

𝟏𝟏 ≤ 𝒎𝒎𝒔𝒔 ≤ 𝟗𝟗 𝒔𝒔 = 𝟏𝟏, … ,𝟒𝟒

• RAP formulation– Four subsystems Subsystem 𝜶𝜶𝒔𝒔𝑪𝑪 × 𝟏𝟏𝟎𝟎−𝟓𝟓 𝜷𝜷𝒔𝒔𝑪𝑪 𝑪𝑪𝒔𝒔𝑷𝑷𝑷𝑷 𝑪𝑪𝒔𝒔𝑪𝑪𝑷𝑷 𝜶𝜶𝒔𝒔𝑷𝑷𝑷𝑷𝑷𝑷 × 𝟏𝟏𝟎𝟎−𝟔𝟔 𝜷𝜷𝒔𝒔𝑷𝑷𝑷𝑷𝑷𝑷

1 0.5 1.5 2.5 7.5 3.3 1.5

1 0.8 1.5 5.0 15.0 5.3 1.5

2 1.0 1.5 6.5 19.5 6.7 1.5

3 0.7 1.5 12.5 37.5 4.7 1.5



Case Study: Electro-Hydrostatic Actuator (EHA)Top Level: Resilience Allocation Problem• Result and Discussion

– Ψ𝑡𝑡 is set as 0.90, 0.95, 0.99– In order to meet higher target system resilience level, more components are

used with higher component-reliabilities and PHM efficiencies– Compared with the traditional design, the RDSD still yields optimum designs

with much lower LCCs by considering PHM in the early design stageSubsystem Traditional design (without PHM) RDSD (with PHM)

𝜳𝜳𝒔𝒔 = 𝟎𝟎.𝟗𝟗𝟎𝟎 𝒓𝒓𝒔𝒔𝒔𝒔 𝒎𝒎𝒔𝒔 𝝀𝝀𝒔𝒔𝒔𝒔 𝑳𝑳𝑪𝑪𝑪𝑪 𝜳𝜳 𝒓𝒓𝒔𝒔𝒔𝒔 𝒎𝒎𝒔𝒔 𝝀𝝀𝒔𝒔𝒔𝒔 𝑳𝑳𝑪𝑪𝑪𝑪 𝜳𝜳

1 0.7371 3 0 73.6301 0.9000 0.6291 2 0.6721 38.3416 0.9000

2 0.8088 2 0 - - 0.6412 2 0.6682 - -

3 0.7287 3 0 - - 0.6519 2 0.6732 - -

4 0.8292 2 0 - - 0.7363 1 0.7679 - -

𝜳𝜳𝒔𝒔 = 𝟎𝟎.𝟗𝟗𝟓𝟓

1 0.7901 3 0 82.2774 0.9500 0.6152 2 0.6448 45.9357 0.9500

2 0.7731 3 0 - - 0.6437 2 0.6644 - -

3 0.7872 3 0 - - 0.6846 2 0.6677 - -

4 0.8574 2 0 - - 0.7539 2 0.7423 - -

𝜳𝜳𝒔𝒔 = 𝟎𝟎.𝟗𝟗𝟗𝟗

1 0.8102 4 0 111.6017 0.9900 0.6488 3 0.6772 55.0199 0.9900

2 0.7745 4 0 - - 0.6483 3 0.7049 - -

3 0.7850 4 0 - - 0.6567 2 0.8014 - -

4 0.8411 3 0 - - 0.7720 2 0.7678 - -



Case Study: Electro-Hydrostatic Actuator (EHA)Bottom Level 1: System RBDO

System Design









Case Study: Electro-Hydrostatic Actuator (EHA)Bottom Level 1: System RBDO• RBDO formulation

minimize 𝐿𝐿 𝐱𝐱 = 𝜔𝜔 � 𝑉𝑉𝑠𝑠 𝑟𝑟𝑝𝑝, 𝐼𝐼𝑠𝑠 + 1 −𝜔𝜔 � 𝑉𝑉𝑠𝑠 𝑟𝑟𝑠𝑠 , 𝐼𝐼𝑠𝑠

𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝜔𝜔 = 0.098,𝑉𝑉𝑠𝑠 = 𝐼𝐼𝑠𝑠 � 𝜋𝜋 𝑟𝑟𝑝𝑝/2 2,𝑉𝑉𝑠𝑠 = 𝐼𝐼𝑠𝑠 � 𝜋𝜋 𝑟𝑟𝑠𝑠/2 2

subject to 𝑟𝑟𝑆𝑆𝑆𝑆𝑆𝑆 = Pr 𝐸𝐸𝑆𝑆𝑆𝑆𝑆𝑆 = Pr �𝑠𝑠=1

4𝐺𝐺𝑠𝑠 𝐱𝐱 ≤ 0 ≥ 𝑟𝑟𝑡𝑡

subject to 𝐺𝐺1 = �0

2𝑌𝑌 𝑟𝑟 − 𝑌𝑌𝑠𝑠𝑠𝑠𝑟𝑟 𝑟𝑟 𝑟𝑟𝑟𝑟 − 𝑟𝑟𝑛𝑛𝑐𝑐

subject to 𝐺𝐺2 = 𝑟𝑟𝑟𝑟𝑝𝑝 𝑟𝑟𝑟𝑟𝑟𝑟0.5≤𝑡𝑡≤2

𝑌𝑌 𝑟𝑟 − 𝑌𝑌𝑠𝑠𝑠𝑠𝑟𝑟 𝑟𝑟 ≤ 𝜀𝜀𝑡𝑡𝑡𝑡𝑝𝑝,𝑠𝑠 − 𝑟𝑟𝑐𝑐,𝑠𝑠

subject to 𝐺𝐺3 = �2

4𝑌𝑌 𝑟𝑟 − 𝑌𝑌𝑠𝑠𝑠𝑠𝑟𝑟 𝑟𝑟 𝑟𝑟𝑟𝑟 − 𝑟𝑟𝑝𝑝𝑐𝑐

subject to 𝐺𝐺4 = 𝑟𝑟𝑟𝑟𝑟𝑟2≤𝑡𝑡≤4

𝑌𝑌 𝑟𝑟 − 𝑌𝑌𝑠𝑠𝑠𝑠𝑟𝑟 𝑟𝑟 − 𝜀𝜀𝑡𝑡𝑡𝑡𝑝𝑝,𝑠𝑠subject to 𝐺𝐺5 = 𝜂𝜂 − 𝑟𝑟𝑠𝑠/𝑟𝑟𝑝𝑝

minimize 𝐿𝐿 𝐱𝐱 = 𝜔𝜔 � 𝑉𝑉𝑠𝑠 𝑟𝑟𝑝𝑝, 𝐼𝐼𝑠𝑠 + 1 −𝜔𝜔 � 𝑉𝑉𝑠𝑠 𝑟𝑟𝑠𝑠 , 𝐼𝐼𝑠𝑠

𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝜔𝜔 = 0.098,𝑉𝑉𝑠𝑠 = 𝐼𝐼𝑠𝑠 � 𝜋𝜋 𝑟𝑟𝑝𝑝/2 2,𝑉𝑉𝑠𝑠 = 𝐼𝐼𝑠𝑠 � 𝜋𝜋 𝑟𝑟𝑠𝑠/2 2

subject to 𝑟𝑟𝑆𝑆𝑆𝑆𝑆𝑆 = Pr 𝐸𝐸𝑆𝑆𝑆𝑆𝑆𝑆 = Pr �𝑠𝑠=1

4𝐺𝐺𝑠𝑠 𝐱𝐱 ≤ 0 ≥ 𝑟𝑟𝑡𝑡

(normal control error) subject to G1 = �0

2dt

(stabilization time) subject to G2 = arg min0.5≤t≤2

(diturbed control error) subject to G3 = �2

4dt

(disturbed steady state error) subject to G4 = min2≤t≤4

(rod to piston diameter ratio) subject to G5 = η − dr/dp



Case Study: Electro-Hydrostatic Actuator (EHA)Bottom Level 2: System PHM Design

System Design









Case Study: Electro-Hydrostatic Actuator (EHA)Bottom Level 2: System PHM Design• Prognostic Data Generation

– Failure mode : Cross-line leakage on actuator

𝛽𝛽 𝑟𝑟 = 𝛽𝛽0 + 𝑟𝑟𝐸𝐸 exp 𝑟𝑟𝐸𝐸𝑟𝑟 − 1

𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝛽𝛽0: 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑝𝑝𝑟𝑟 𝑝𝑝𝑝𝑝𝑟𝑟𝑝𝑝𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝐸𝐸 𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝐸𝐸:𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑤𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟: 𝑝𝑝𝑟𝑟𝑝𝑝𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

– Failure mode : Cross-line leakage on actuator

• Description of Prognostic Algorithm– Data-driven prognostic algorithm– M. I: Similarity-based interpolation

(SBI) + Relevance vector machine– M. II: SBI + Support vector machine– M. III: SBI with least-square

exponential fitting– M. IV: Bayesian linear regression– M. V: Recurrent neural network

• Prognostic ResultAlgorithm Prognostic accuracy Distri. Type Parameters for non-normal distributions

M. I 0.480 Weibull 𝛼𝛼1 = 49.22,𝛽𝛽1 = 4.15

M. II 0.430 Weibull 𝛼𝛼2 = 60.10,𝛽𝛽2 = 4.12

M. III 0.550 Normal −

M. IV 0.125 Weibull 𝛼𝛼4 = 63.82,𝛽𝛽4 = 5.31

M. V 0.790 Weibull 𝛼𝛼5 = 55.17,𝛽𝛽5 = 4.35


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2019/1/4 - 30 -


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