Computational and Mathematical Challenges in Modeling ... · Equivalent to about 7% of current...

Interdisciplinary Center for Applied Mathematics

Computational and Mathematical Challenges in Modeling, Design, Optimization and Control of Energy Efficient Buildings

VT – I. Akhtar, J. Borggaard, J. Burns, E. Cliff, T. Herdman, L. ZietsmanUTRC – S. Ahuja, C. Jacobson, S. Narayanan, A. Surana

Workshop on Future Directions in Applied MathematicsNorth Carolina State University

March 10 – 11, 2011

Air Flow in aHospital Suite

Room with Disturbance

Who Cares About Energy Efficiency

Future Directions in Applied Mathematics 2

You Just look at your electric or gas bill - $ Save the planet

Department of Energy (EERE & DOE SCIENCE Its their job - $$ Greenhouse gasses

Department of Defense Biggest government user of energy (electricity $$$ National security

National / Industry / Universities Look at electric or gas bill - $$$$ Energy independence - Economic growth and “survival”

National Security & Economics


ECONOMIC GROWTH & POLLUTION

• To sustain a growth rate of ~ 10%/yr, China is adding nearly 1 coal-fired power plant per week - has overtaken the US as the largest polluter

• In order for India to sustain its growth rate of ~ 8%/yr, India must increase its power generation and industrial output by an order of magnitude (also in GHG emissions

DOD

• Has over 500,000 buildings

• Currently the “electric bill” is ≈ 12 % of DOD budget

• Prewar – the electric bill was ≈ 22 % of DOD budget

LIMITS $$$ THAT COULD BE USED BY THE WARFIGHTER

Climate Goals & Renewable Energy


To Get 1 Gigaton Reduction


Install 1,000 sequestration sites like Norway’s Sleipner project (1 MtCO2/year) Only 3 sequestration projects of this scale exist today

Geologic Sequestration

Build 273 “zero-emission” 500 MW coal-fired power plantsEquivalent to about 7% of current global coal-fired capacity of 2 million MW

Coal-Fired Power Plants

Convert a barren area about 2 times the size of the UK (over 480,000 km2), using existing production technologies

Biofuels

Install about 750 GW of solar PV

Roughly 125 times current global installed capacity of 6 GW*

Solar Photovoltaics

Actions that Provide One Gigaton CO2/ Year of Mitigation or OffsetsTechnology

Convert a barren area greater than the combined size of Germany and France (over 900,000 km2)

CO2 Storage in New Forest

Install about 270,000 1 MW wind turbines

Roughly 3 times the global total installed wind capacity at end of 2007.Wind Energy

Deploy 273 million new cars at 40 miles per gallon (mpg) instead of 20 mpg New “CAFÉ” rules would accomplish about half that

Efficiency

Build 136 new nuclear 1 GW power plants instead of coal-fired without CCSEquivalent to about one third of existing worldwide nuclear capacity of 375 GW

Nuclear

Source: Climate Change Technology Program Strategic Plan, September 2006.

To Get 1 Gigaton Reduction


Install 1,000 sequestration sites like Norway’s Sleipner project (1 MtCO2/year) Only 3 sequestration projects of this scale exist today

Geologic Sequestration

Build 273 “zero-emission” 500 MW coal-fired power plantsEquivalent to about 7% of current global coal-fired capacity of 2 million MW

Coal-Fired Power Plants

Convert a barren area about 2 times the size of the UK (over 480,000 km2), using existing production technologies

Biofuels

Install about 750 GW of solar PV

Roughly 125 times current global installed capacity of 6 GW*

Solar Photovoltaics

Actions that Provide One Gigaton CO2/ Year of Mitigation or OffsetsTechnology

Convert a barren area greater than the combined size of Germany and France (over 900,000 km2)

CO2 Storage in New Forest

Install about 270,000 1 MW wind turbines

Roughly 3 times the global total installed wind capacity at end of 2007.Wind Energy

Deploy 273 million new cars at 40 miles per gallon (mpg) instead of 20 mpg New “CAFÉ” rules would accomplish about half thatEfficiency

Build 136 new nuclear 1 GW power plants instead of coal-fired without CCSEquivalent to about one third of existing worldwide nuclear capacity of 375 GW

Nuclear

Source: Climate Change Technology Program Strategic Plan, September 2006.

Energy and Buildings

WHYBUILDINGS

7Future Directions in Applied Mathematics

Energy and Buildings

ANDNOT THIS


WHYBUILDINGS

Building Energy Demand


Buildings consume • 39% of total U.S. energy• 71% of U.S. electricity • 54% of U.S. natural gas

Building produce 48% of U.S. Carbon emissions

Commercial building annual energy bill: $120 billion

The only energy end-use sector showing growth in energy intensity• 17% growth 1985 - 2000• 1.7% growth projected through 2025

Sources: Ryan and Nicholls 2004, USGBC, USDOE 2004

Energy Intensity by Year Constructed Energy Breakdown by Sector

Impact of Energy Efficient Buildings

• A 50 percent reduction in buildings’ energy usage would beequivalent to taking every passenger vehicle and small truck in theUnited States off the road.

• A 70 percent reduction in buildings’ energy usage is equivalent toeliminating the entire energy consumption of the U.S.transportation sector.

HUGE





HUGE

? WHY ?

84% of energy consumed in buildingsis during the use of the building

DESIGN, CONTROL AND OPTIMIZATION OF WHOLE BUILDING SYSTEMS IS THE ONLY WAY TO GET THERE





HUGE

? WHY ?

84% of energy consumed in buildingsis during the use of the building

REQUIRES COMBINING - MODELING, COMPLEX MULTISCALE DYNAMICS, CONTROL, OPTIMIZATION, SENSITIVITY, HIGH PERFORMANCE COMPUTING …

DESIGN, CONTROL AND OPTIMIZATION OF WHOLE BUILDING SYSTEMS IS THE ONLY WAY TO GET THERE


Technical Challenge


The general technical challenge was issued by the U.S. Secretary of Energy, Dr. Steven Chu:

“We need to do more transformational research at DOE … including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.”

Secretary of Energy Dr. Steven Chu, House Science Committee Testimony, March 17, 2009

THE EMPHASIS IS ON DESIGN – CONTROL – OPTIMIZATION TOOLS

NOT

“OPEN-LOOP SIMULATION”

Technical Challenge


The general technical challenge was issued by the U.S. Secretary of Energy, Dr. Steven Chu:

“We need to do more transformational research at DOE … including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.”

Secretary of Energy Dr. Steven Chu, House Science Committee Testimony, March 17, 2009

THE EMPHASIS IS ON DESIGN – CONTROL – OPTIMIZATION TOOLS

NOT

“OPEN-LOOP SIMULATION”

NOT

“SIMULATION BASED DESIGN”

Existence Proof


Existence ProofEnergy Retrofit

10-30% Reduction

Very Low Energy>50% Reduction

LEED Design20-50% Reduction

Tulane Lavin BernieNew Orleans LA

150K ft2, 150 kWhr/m2

1513 HDD, 6910 CDDPorous Radiant Ceiling, Humidity Control Zoning, Efficient Lighting,

Shading

Cityfront SheratonChicago IL

1.2M ft2, 300 kWhr/m2

5753 HDD, 3391 CDDVS chiller, VFD fans, VFD pumps

Condensing boilers & DHW

Deutsche PostBonn Germany

1M ft2, 75 kWhr/m2

6331 HDD, 1820 CDDNo fans or Ducts

Slab coolingFaçade preheat

Night cool

• Different types of equipment for space

conditioning & ventilation

• Increasing design integration of

subsystems & control

Courtesy of Clas Jacobson UTC16Future Directions in Applied Mathematics

Existence ProofEnergy Retrofit

10-30% Reduction

Very Low Energy>50% Reduction

LEED Design20-50% Reduction

Tulane Lavin BernieNew Orleans LA

150K ft2, 150 kWhr/m2

1513 HDD, 6910 CDDPorous Radiant Ceiling, Humidity Control Zoning, Efficient Lighting,

Shading

Cityfront SheratonChicago IL

1.2M ft2, 300 kWhr/m2

5753 HDD, 3391 CDDVS chiller, VFD fans, VFD pumps

Condensing boilers & DHW

Deutsche PostBonn Germany

1M ft2, 75 kWhr/m2

6331 HDD, 1820 CDDNo fans or Ducts

Slab coolingFaçade preheat

Night cool

• Different types of equipment for space

conditioning & ventilation

• Increasing design integration of

subsystems & control

Courtesy of Clas Jacobson UTC17Future Directions in Applied Mathematics

ONE OFF PROJECTSNO GENERAL DESIGN TOOLS

&REQUIRES NEW PARADIGM

HP2C SPECIFICALLY FOR DESIGNOPTIMIZATION & CONTROL

MODEL REDUCTION

Even LEEDS May Not be “Efficient”


Design Intent: 66% (ASHRAE 90.1); Measured 44%

Design Intent: 80% (ASHRAE 90.1); Measured 67%

Source: Lessons Learned from Case Studies of Six High-Performance Buildings, P. Torcellini, S. Pless, M. Deru, B. Griffith, N. Long, R. Judkoff, 2006, NREL Technical Report.

Failure Modes Arising from Detrimental Sub-system Interactions

• Changes made to envelope to improve structural integrity diminished integrity of thermal envelope

• Adverse system effects due to coupling of modified sub-systems:

• changes in orientation and increased glass on façade affects solar heat gain

• indoor spaces relocated relative to cooling plantaffects distribution system energy

• Lack of visibility of equipment status/operation, large uncertainty in loads leads to excess energy use

Current Software Tools …


System Requirements

Economic analysis

Architectural ModelBuilding Loads

Equipment Performance

Product catalogs

Engineering performance

Synthesis ProcessExpert systems

Building Control Automation

Zone schedules

Equipment setpoints

System Analysis with Building Dynamics

gap

existing

existing

Current software and computational infrastructure•Cannot address physics of low energy buildings (natural ventilation)•Cannot address dynamics and controls•Cannot address design (optimization, scalability)•Cannot address embedded systems validation & verification

BIG Science with Hugh Impact


MATHEMATICS OF ENERGYEFFICIENT BUILDINGS

BUILDING SYSTEMS ARE COMPLEX, MULTI-SCALE, NON-LINEAR, UNCERTAIN, INFINITE DIMENSIONAL DYNAMICAL SYSTEMS WITH 100’S OF COMPONENTS …

WHY IS THIS TRUE ?

Whole Building Systems

Loads

Electrical

Information Management

Distribution

Weather

Heating, Ventilation,Air Conditioning

Lighting Lights &Fixtures

EnvelopeStructure

BuildingInsulation

Building Operating Conditions

Safety & Security

Information Thermal Power Link that is not always exploited

Building ManagementSystem

Cost Utilities

Thermostat

MotionSensors

IT Network

BuildingGeometry

Grid

On-Site Gen

Distribution (Fans, Pumps)

Heating & ACEquipment

Other LoadsWater HeatingOffice Equipment

Facilityaccess

Fire / Smoke Detection and Alarm Video


Multi-Scale in Time and Space


Whole Buildings Are Complex SystemsA whole building system is a complex system because:

1. The system components do not necessarily have mathematically similar structures and may involve different scales in time or space;

2. The number of components may be large, sometimes enormous;3. Components can be connected in a variety of different ways, most often

nonlinearly and/or via a network. Furthermore, local and system wide phenomena may depend on each other in complicated ways;

4. The behavior of the overall system can be difficult to predict from the behavior of individual components. Moreover, the overall system behavior may evolve along qualitatively different pathways that may display great sensitivity to small perturbations at any stage.







In addition to the above definition, even a single room can be a complex system if one is concerned with multi-physics dynamics such as coupled (chemically reacting) air flows, thermal profiles, energy flows, air quality, room geometry and the supervisory (closed-loop, possible human in the loop) control.







In addition to the above definition, even a single room can be a complex system if one is concerned with multi-physics dynamics such as coupled (chemically reacting) air flows, thermal profiles, energy flows, air quality, room geometry and the supervisory (closed-loop, possible human in the loop) control.

MATHEMATICAL DEFINITIONOF A COMPLEX SYSTEM

David L. Brown, John Bell, Donald Estep, William Gropp, Bruce Hendrickson, Sallie Keller-McNulty, David Keyes, J. Tinsley Oden and Linda Petzold, Appled Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future, DOE Report LLNL-TR-401536, May 2008.


Math and Computing Opportunities


MATHEMATICAL MODELINGNUMERICAL ALGORITHMSCOMPUTATIONAL TOOLS

SPECIFICALLY FOR

PDE OPTIMIZATION & CONTROLMODEL REDUCTION

HIGH FIDELITY SIMULATION OF WHOLE BUILDING SYSTEMS OPERATING UNDER

FEEDBACK CONTROL

Control Sciences Embrace Computing


CONTROL COMMUNITYNOW UNDERSTANDS

“The Amazing Power of Numerical Awareness”

ARTICLE MOTIVATED BY FEEDBACK CONTROL

PROBLEMS IN THERMAL PROCESSES

FLUID FLOW INFLATABLES

MATERIALS SCIENCE …PDE SYSTEMS

Building Sciences Embrace Computing








Building Sciences Embrace Computing








IN GENERAL THE BUILDING SECTORHAS NOT FULLY EMBRACED COMPUTING - NOR

MODEL BASED DESIGN, CONTROL AND OPTIMIZATIONNOR

HOLISTIC OPTIMIZATION & CONTROLNOR

ADVANCED MODEL REDUCTIONNOR

HIGH PERFORMANCE COMPUTING SO

WHY DO WE THINK THINGS WILL AND CAN CHANGE ?

New Technologies & Ideas


CHP: Combined Cooling, Heating & Power (PureComfort™ Integrated Energy Solutions)

Technical Challenges


Technical Challenges


MODELING AND SIMULATION TOOLS THAT CAPTURE THE CORRECT BUILDING PHYSICS AT ALL KEY TIME AND SPATIAL SCALES ARE ESSENTIAL

HOWEVER, BUILDING SIMULATION ALONE IS NOT SUFFICIENT

MATHEMATICAL AND COMPUTATIONAL TOOLS MUST BE DEVELOPED SPECIFICALLY TO ALLOW INTEGRATION AND TO INTERFACE WITH:

DESIGN – CONTROL – OPTIMIZATION –SENSITIVITY – UNCERTAINTY TOOLS

ALSO, REVOLUTIONARY ADVANCES WILL OCCUR ONLY IF THE ALGORITHMS AND COMPUTATIONAL TOOLS …

ENABLE “PLUG-AND-PLAY” FOR NEW COMPONENT TECHNOLOGIESARE BASED ON STATE OF THE ART COMPUTATIONAL SCIENCEHAVE USER INTERFACES SUITABLE FOR BROAD BUILDING STOCKSBE BUILT ON OPEN SOURCE SOFTWARETAKE ADVANTAGE OF MODERN COMPUTER AND COMPUTER SCIENCE TECHNOLOGY INCLUDING HIGH PERFORMANCE COMPUTING


1. EXISTING BUILDING SIMULATION AND ENERGY TOOLS ARE NOT SUITABLE FOR DESIGN, OPTIMIZATION AND CONTROL OF WHOLE BUILDING SYSTEMS

• THEY WERE NOT DESIGNED FOR THESE PURPOSES

• THEY WERE DESIGNED TO RUN ON PC TYPE PLATFORMS AND HENCE FORCED TO USE CRUDE MODELS OF THE PHYSICS - CHEMISTRY

• DO NOT TAKE ADVANTAGE OF STATE-OF-THE ART ALGORITHMS AND NEW COMPUTER PLATFORMS

• OFTEN IGNORE SPATIAL FEATURES AND TIME SCALES THAT ARE ESSENTIAL TO OPTIMIZATION AND DESIGN TOOLS

2. EXISTING MODELS DO NOT ADDRESS UNCERTAINTY, MULTI-SCALE DYNAMICS AND REAL-TIME REQUIREMENTS

3. EXISTING SOFTWARE IS OFTEN BASED ON CRUDE MODELS, DOES NOT ALLOW FOR EASY INTEGRATION OF DESIGN AND CONTROL TOOLBOXES AND GUI’s / USER INTERFACES DO NOT EXIST – “USED ONLY BECAUSE IT IS FREE”

Barriers and Misconceptions


IF I CAN SIMULATE A SYSTEM, THEN I CAN OPTIMIZE OR CONTROL IT or

I MUST BE ABLE TO CONDUCT HIGH FIDELITY SIMULATIONS BEFORE I CAN DESIGN, OPTIMIZE OR CONTROL A SYSTEM

• DESIGN, OPTIMIZATION AND CONTROL MAY REQUIRE 1,000’s OF SIMULATIONS

• SIMULATION ASSUMES ALL PARAMETERS, INPUTS, DISTRUBANCES ARE GIVEN

• CONTROL DESIGN IS THE PROCESS OF FINDING OPTIMAL INPUTS

• DESIGN AND CONTROL IS OFTEN DONE WITH REDUCED ORDER MODELS

CONCATENATING THE “BEST SIMULATION TOOL” WITH THE “BEST DESIGN TOOL” PRODUCES THE BEST DESIGN OR CONTROL TOOL

IF I CAN SIMULATE THE OPEN-LOOP SYSTEM, THEN I CAN SIMULATE THE CLOSED-LOOP SYSTEM

THERE ARE NO THEORIES TO DEAL WITH MULTI-SCALE DISTRIBUTED PARAMETER CONTROL SYSTEMS

1. EXISTING BUILDING SIMULATION AND ENERGY TOOLS ARE NOT SUITABLE FOR DESIGN, OPTIMIZATION AND CONTROL OF WHOLE BUILDING SYSTEMS

• THEY WERE NOT DESIGNED FOR THESE PURPOSES

• THEY WERE DESIGNED TO RUN ON PC TYPE PLATFORMS AND HENCE FORCED TO USE CRUDE MODELS OF THE PHYSICS - CHEMISTRY

• DO NOT TAKE ADVANTAGE OF STATE-OF-THE ART ALGORITHMS AND NEW COMPUTER PLATFORMS

• OFTEN IGNORE SPATIAL FEATURES AND TIME SCALES THAT ARE ESSENTIAL TO OPTIMIZATION AND DESIGN TOOLS

2. EXISTING MODELS DO NOT ADDRESS UNCERTAINTY, MULTI-SCALE DYNAMICS AND REAL-TIME REQUIREMENTS

3. EXISTING SOFTWARE IS OFTEN BASED ON CRUDE MODELS, DOES NOT ALLOW FOR EASY INTEGRATION OF DESIGN AND CONTROL TOOLBOXES AND GUI’s / USER INTERFACES DO NOT EXIST – “USED ONLY BECAUSE IT IS FREE”

Barriers and Misconceptions

New DOE HUB


The U.S. Department of Energy announced the establishment of a researchhub for energy-efficient building technologies at the Navy Yard in SouthPhiladelphia. The Energy-Efficient Building Systems Design Hub’s missionwill be to develop new energy efficient components for integration into wholebuilding systems, new mathematical models and computer design tools thatcan be used for design and control of new buildings and to retrofit existingbuildings. It also will analyze the role of policy, markets and behavior in theadoption and use of energy technology in buildings.

New DOE HUB


Interdisciplinary Center for Applied Mathematics

Task 1: MODELING AND COMPUTATIONAL TOOLS SPECIFICALLY FOR DESIGN, OPTIMIZATION AND CONTROL OF HIGH PERFORMANCE BUILDINGS ….

The U.S. Department of Energy announced the establishment of a researchhub for energy-efficient building technologies at the Navy Yard in SouthPhiladelphia. The Energy-Efficient Building Systems Design Hub’s missionwill be to develop new energy efficient components for integration into wholebuilding systems, new mathematical models and computer design tools thatcan be used for design and control of new buildings and to retrofit existingbuildings. It also will analyze the role of policy, markets and behavior in theadoption and use of energy technology in buildings.

HUB Partners


1. Penn State University (Lead)2. Carnegie Mellon University3. Drexel University4. Morgan State University5. Princeton University6. Purdue University7. Rutgers University8. University of Pennsylvania9. University of Pittsburgh10. Virginia Tech

UNIVERSITIES1. Bayer Material Science2. IBM Corp.3. Lawrence Livermore

National Laboratory4. PPG Industries5. Turner Construction6. United Technologies Corp

INDUSTRY & LABS

OTHER PARTNERS1. Ben Franklin Technology Partners of Southeastern PA2. Collegiate Consortium3. Delaware Valley Industrial Resource Center4. NJI’s Philadelphia Industrial Development Corp.5. Wharton Small Business Development Center


NEW MATHEMATICAL AND COMPUTATIONAL TOOLS SPECIFICALLYFOR DESIGN – CONTROL - OPTIMIZATION – SENSITIVITY – UNCERTAINTY

BASED ON STATE OF THE ART COMPUTATIONAL SCIENCE

DEAL WITH MULTI-SCALE PHYSICS, CHEMISTRY AND COMPLEXITY

HAVE USER INTERFACES SUITABLE FOR BROAD BUILDING STOCKS

BE BUILT ON OPEN SOURCE SOFTWARE

38

Computational & Mathematical Issues


HP2C ENABLED MODEL REDUCTION

WHOLE BUILDING MODELING, SIMULATION AND HOLISTIC DESIGN

HP2C FOR PARALLEL OPTIMIZATION & DESIGN

PREDICTIVE MODELING AND SIMULATION OF CLOSED-LOOP DYNAMICSENABLE “PLUG-AND-PLAY” FOR NEW COMPONENT TECHNOLOGIES

SHOULD “SOLVE” NON-STANDARD EQUATIONS –

NON-LOCAL (IN SPACE) COUPLED SYSTEMS

PDE SYSTEMS IN HIGH SPATIAL DIMENSION ( ≥ 6) ALLOW FOR DATA DRIVEN COMPUTATION

UNCERTAINTY QUANTIFICATION

NEW MATHEMATICAL AND COMPUTATIONAL TOOLS SPECIFICALLYFOR DESIGN – CONTROL - OPTIMIZATION – SENSITIVITY – UNCERTAINTY

BASED ON STATE OF THE ART COMPUTATIONAL SCIENCE

DEAL WITH MULTI-SCALE PHYSICS, CHEMISTRY AND COMPLEXITY

HAVE USER INTERFACES SUITABLE FOR BROAD BUILDING STOCKS

BE BUILT ON OPEN SOURCE SOFTWARE

39

Computational & Mathematical Issues

POSSIBLE ROLES OF HIGH PERFORMANCE COMPUTING

Traditional HVAC System


HP2C Enabled Model Reduction


HP2C ENABLEDMODELING

&COMPUTER DESIGN TOOLS

Building Description• Architecture, Materials• HVAC, Loads, Lights …• Occupancy• Sensors, Actuators …

Cluster, Grid, Cloud

High PerformanceHigh Productivity

Computing

designmodel

HierarchalReduced – Order Design & Control

Models

High Fidelity Physics-Based Simulation

Tools

BUILDING PHYSICSDESIGN

PARAMETERS

ADVANCED MODEL

REDUCTION METHODS

INTERACTIVE

INTEROPERABLE

COMPUTERDESIGN TOOL

Disturbance Rejection: ICAM CUBE


Boussinesq equations; k-ε model• Grid: 6.6 x 104 nodes• Re = 2.2x104 (w.r.t. room h=3m, diffuser vel.=0.1m/s)• Gr = 4.7x109 (w.r.t. room h=8m)• Re2/Gr = 0.1 < 1 => buoyancy dominated• Time-step = 2 sec

Small room (4m x 4m x 3m) withdisplacement ventilation and chilled ceiling

Inputs• Control: chilled ceiling heat flux• Disturbance: floor heat flux

Outputs• Temperature measurements, on two walls parallel to the XY planes• Occupied zone averaged temperature (used to define LQR cost)

Disturbance Rejection: ICAM CUBE


( ) ( ) ( )r r rz(t) A z t B u t G v t= + +

( )r(t) Dz tξ =

( ) ( ) ( )y(t) C z t Ew tq= +

“RAW” HP2C REQUIREMENTS


“RAW” HP2C REQUIREMENTS


NOT POSSIBLE UNLESS ADVANCES ARE MADE IN

NEW ALGORITHMS&

MODEL REDUCTIONSPECIFICALLY FOR DESIGNOPTIMIZATION & CONTROL


HPC Model Reduction Design

REDUCED BASIS 1

TYPICAL ROOM LEVEL 32 PROCESSOR DOMAIN DECOMPOSITION

REDUCED BASIS 2

FEEDBACK CONTROLLER

GAIN COMPUTED WITH

REDUCED BASIS

Parallel Implementation


GRID SOLUTION

32 PROCESSORS

ALSO USED FOR PARALLEL MODEL REDUCTION

High Performance Computing for:

Future Directions in Applied Mathematics 48REDUCED BASIS 1

Model reduction

REDUCED BASIS 2

CHILLED BEAMS

NATURAL VENTILATION

UNDERFLOOR HEATING

High Performance Computing for:


Holistic control design - optimal sensor placement

Shape sensitivity analysis and uncertainty

Ω

1Γ

DΩ

( )qΩOBSERVER

FUNCTIONAL GAINSENSOR ON LOWER

SIDE WALL

SENSITIVITY WITH RESPECT TO WALL MOVEMENT

“Holistic” Approaches

( ) 2( , ) ( , ) ( , ) ( , ) ( ) ( )tC T t v t T t T t g v tρ κ∂∂ + ∇ = ∇ +x x x x x

1( , ) | ( ) ( )T t b tuΓ =x x

Ω1Γ

ξΩ

= ⋅ = ∫∫∫

( ) ( , ) ( ) ( , )D

t DT t d T t dx x x

u(t) = Temperature of inflow

DΩControlled region

BOUNDARY CONTROL


Sensor Location Issues

( ) 2( , ) ( , ) ( , ) ( , ) ( ) ( )tC T t v t T t T t g v tρ κ∂∂ + ∇ = ∇ +x x x x x

1( , ) | ( ) ( )T t b tuΓ =x x

( )( ) ( ) ( , ) ( ) ( , ) ( )

qy t C T t c T t w tq d

Ω= ⋅ = +∫∫∫ x x x

Ω1Γ

ξΩ

= ⋅ = ∫∫∫

( ) ( , ) ( ) ( , )D

t DT t d T t dx x x

u(t) = Temperature of inflow

DΩControlled region

( ) :xq q δΩ = ∈Ω − <x( )qΩ

Sensor region

BOUNDARY CONTROL


Dynamic Controller

( ) ( ) ( ) ( , )Tu t z t T tK dkΩ

= − = −∫∫∫ x x x

( ) ( )[ ( ) ( ) ( )]e e ez (t) A z t F y t C zq q t= + −

[ ( ) ]( ) ( , )Tq qfF y y=x x OBSERVERFUNCTIONAL GAINS

( ) ( ) ( ) ( , )ˆ Te et z t Tu tK k dΩ

= − = −∫∫∫ x x x


? WHAT DO THESE FUNCTIONAL GAINS TYPICALLY LOOK LIKE ?

Functional Gains

FEEDBACKFUNCTIONAL GAIN

OBSERVERFUNCTIONAL GAIN

SENSOR ON TOP WALL

( ) ( ) ( , )Tt t dk TuΩ

= −∫∫∫ x x x

SΩ

PLACE SENSOR ON DESK

[ ( ) ]( ) ( , )Tq qfF y y=x x

SENSOR ON WALL

WHICH WALLAND WHERE

Sensor on top


Observer Functional Gains


SENSOR ON SIDE WALL

Sensor on centeredon lower side wall


SENSOR ON SIDE WALL

Sensor on lower leftside wall


Observer Functional Gains


SENSOR ON SIDE WALL

Sensor on centeredon lower side wall


SENSOR ON SIDE WALL

Sensor on lower leftside wall

57

PROVIDES ENGINEERING INSIGHTBUT THE SAME RESULT CAN BE

OBTAINED THROUGH FORMAL OPTIMIZATION

….

WITH THE RIGHTCOMPUTATIONAL TOOLS

Future Directions in Applied Mathematics

Requires - Non-Standard Solvers


*( ) ( )( , ) ( , ) ( , )

( ( , )) ( , ) 0

x yp x y p x y p x yp x yq x y

∆ + ∆

−+ =

N

1Γ

2Γ

outΓ

OPTIMAL FEEDBACK CONTROLOF A THERMAL SYSTEM

RICCATI PDES


*( ) ( )( , ) ( , ) ( , )

( ( , )) ( , ) 0

x yp x y p x y p x yp x yq x y

∆ + ∆

−+ =

N

( ( , )) ( , ) ( ) ( ) ( , )p x y p x b b p y d dξ ξ ζ ζ ζ ξΩ×Ω

= ∫N

1Γ

2Γ

outΓ

OPTIMAL FEEDBACK CONTROLOF A THERMAL SYSTEM

RICCATI PDES

NON-LOCAL 2N – DIMENSIONAL PDES

Requires - Non-Standard Solvers

Chandrasekhar Equations


( , ) ( , ) ( , , ) ( , )u t x KT t t x y T t y d yΩ

= − = −∫k

( , , ) 0, ( , , ) ( , )f ft x y t x y c x y= =k h

lim ( , , ) ( , )t

t x y x y→−∞

=k k

*( , )

*

( , , ) ( , , ) ( , )

( , , ) ( , , ) ( , )

x y

T

t x y t x yt

t x y B t x y

∂ = − ∆ ⋅ ⋅ ∂ + ⋅ ⋅

h h

k h

[ ]*( , , ) ( , , ) ( , ) ( , , ) Tt x y B t x y t x yt

∂ = ⋅ ⋅ ∂k h h

Adaptive FE + New Algorithms


1Γ

2Γ

outΓ

GAIN k2

GAIN k1

# CHADRA EQ = 3,189

# RIC EQ = 565,516

Mesh 0

Adaptive FE + New Algorithms


1Γ

2Γ

outΓ

GAIN k2

GAIN k1

Mesh 3 Mesh 5574 Elements, 1231 Nodes, 1063 States

# CHADRA EQ = 3,189

# RIC EQ = 565,516

Mesh 0

Closing Remarks


THESE ARE HARD CS&E PROBLEMS IDEAL FOR HP2CWE NEED A BASIC UNDERSTANDING THE DYNAMICS AND PHYSICS OF THE INTERCONNECTED SYSTEMS IN A WHOLE BUILDINGEXISTING MODELING AND ANALYSIS TOOLS FOR THE TYPE OF COMPLEX SYSTEMS DEFINED BY WHOLE BUILDINGS ARE NOT SUFFICIENT FOR DESIGN AND REAL TIME CONTROL…

NEW PARADIGMS, ALGORITHMS AND COMPUTATIONAL SCIENCES ARE ESSENTIAL

A HOLISTIC APPROACH MIGHT PROVIDE NEW INSIGHTHYBRID AND SIMULATION BASED DESIGN ALGORITHMS WILL PLAY AN IMPORTANT ROLE HIGH PERFORMANCE COMPUTING AND PARALLEL ALGORITHMS ARE ESSENTIAL AT ALL STAGES – DESIGN, OPTIMIZATION, OPERATION…

A WHOLE BUILDING IS AN UNCERTAIN COMPLEX SYSTEMCONTROL (OPTIMAL AND FEEDBACK) WILL BE AN ENABLING SCIENCE FOR HPB DESIGN AND OPERATION OF ENERGY EFFICIENT BUILDINGS…

Closing Remarks






NEED COMPUTATIONAL ALGORITHMS SPECIFICALLY FOR DESIGN, ETC.

NEED MODELING AND MULTI-SCALE COMPUTATIONAL TOOLS

NEED HPC SENSITIVITY AND UNCERTAINTY ANALYSIS TOOLS

Closing Remarks






NEED COMPUTATIONAL ALGORITHMS SPECIFICALLY FOR DESIGN, ETC.

NEED MODELING AND MULTI-SCALE COMPUTATIONAL TOOLS

NEED HPC SENSITIVITY AND UNCERTAINTY ANALYSIS TOOLS

MANY FUTURE DIRECTIONS IN APPLIED MATHEMATICS

WITH APPLICATIONS TO ENERGY EFFICIENT BUILDING DSEIGN AND CONTROL

….

EVEN “PURE” MATHEMATICS


IEEE CDC PAPER

There is no Free Lunch (Energy)



THANK YOUCONTACT INFORMATION

John A. BurnsInterdisciplinary Center for Applied MathematicsWest Campus DriveVirginia TechBlacksburg, VA 24061540 – 231 – [email protected]

Computational and Mathematical Challenges in Modeling ... · Equivalent to about 7% of current...

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