computational and mathematical challenges in modeling ... · equivalent to about 7% of current...
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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 - $$$$ Energy independence - Economic growth and “survival”
National Security & Economics
Future Directions in Applied Mathematics 3
ECONOMIC GROWTH & POLLUTION
• To sustain a growth rate of ~ 10%/yr, China is adding nearly 1 coal-fired power plant per week - has overtaken the US as the largest polluter
• In order for India to sustain its growth rate of ~ 8%/yr, India must increase its power generation and industrial output by an order of magnitude (also in GHG emissions
DOD
• Has over 500,000 buildings
• Currently the “electric bill” is ≈ 12 % of DOD budget
• Prewar – the electric bill was ≈ 22 % of DOD budget
LIMITS $$$ THAT COULD BE USED BY THE WARFIGHTER
Climate Goals & Renewable Energy
Future Directions in Applied Mathematics 4
To Get 1 Gigaton Reduction
Future Directions in Applied Mathematics 5
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
Future Directions in Applied Mathematics 6
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
8Future Directions in Applied Mathematics
WHYBUILDINGS
Building Energy Demand
Future Directions in Applied Mathematics 9
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
10Future Directions in Applied Mathematics
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
? 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
11Future Directions in Applied Mathematics
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
? 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
12Future Directions in Applied Mathematics
Technical Challenge
Future Directions in Applied Mathematics 13
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
Future Directions in Applied Mathematics 14
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
15Future 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 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”
Future Directions in Applied Mathematics 18
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 …
Future Directions in Applied Mathematics 19
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
Future Directions in Applied Mathematics 20
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
21Future Directions in Applied Mathematics
Multi-Scale in Time and Space
Future Directions in Applied Mathematics 22
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.
23Future Directions in Applied Mathematics
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.
24Future Directions in Applied Mathematics
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.
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.
25Future Directions in Applied Mathematics
Math and Computing Opportunities
Future Directions in Applied Mathematics 26
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
Future Directions in Applied Mathematics 27
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
Future Directions in Applied Mathematics 28
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
Future Directions in Applied Mathematics 29
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
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
Future Directions in Applied Mathematics 30
CHP: Combined Cooling, Heating & Power (PureComfort™ Integrated Energy Solutions)
Technical Challenges
Future Directions in Applied Mathematics 31
Technical Challenges
Future Directions in Applied Mathematics 32
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
Future Directions in Applied Mathematics 33
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
Future Directions in Applied Mathematics 34
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
Future Directions in Applied Mathematics 35
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
Future Directions in Applied Mathematics 36
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
Future Directions in Applied Mathematics 37
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
Future Directions in Applied Mathematics 38
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
Future Directions in Applied Mathematics 39
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
Future Directions in Applied Mathematics 40
HP2C Enabled Model Reduction
Future Directions in Applied Mathematics 41
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
Future Directions in Applied Mathematics 42
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
Future Directions in Applied Mathematics 43
( ) ( ) ( )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
Future Directions in Applied Mathematics 44
“RAW” HP2C REQUIREMENTS
Future Directions in Applied Mathematics 45
NOT POSSIBLE UNLESS ADVANCES ARE MADE IN
NEW ALGORITHMS&
MODEL REDUCTIONSPECIFICALLY FOR DESIGNOPTIMIZATION & CONTROL
Future Directions in Applied Mathematics 46
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
Future Directions in Applied Mathematics 47
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:
Future Directions in Applied Mathematics 5151
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
52Future Directions in Applied Mathematics
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
53Future Directions in Applied Mathematics
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
54Future Directions in Applied Mathematics
? 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
55Future Directions in Applied Mathematics
Observer Functional Gains
OBSERVERFUNCTIONAL GAIN
SENSOR ON SIDE WALL
Sensor on centeredon lower side wall
OBSERVERFUNCTIONAL GAIN
SENSOR ON SIDE WALL
Sensor on lower leftside wall
56Future Directions in Applied Mathematics
Observer Functional Gains
OBSERVERFUNCTIONAL GAIN
SENSOR ON SIDE WALL
Sensor on centeredon lower side wall
OBSERVERFUNCTIONAL GAIN
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
Future Directions in Applied Mathematics 58
*( ) ( )( , ) ( , ) ( , )
( ( , )) ( , ) 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
Future Directions in Applied Mathematics 59
*( ) ( )( , ) ( , ) ( , )
( ( , )) ( , ) 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
Future Directions in Applied Mathematics 60
( , ) ( , ) ( , , ) ( , )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
Future Directions in Applied Mathematics 61
1Γ
2Γ
outΓ
GAIN k2
GAIN k1
# CHADRA EQ = 3,189
# RIC EQ = 565,516
Mesh 0
Adaptive FE + New Algorithms
Future Directions in Applied Mathematics 62
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
Future Directions in Applied Mathematics 63
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
Future Directions in Applied Mathematics 64
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…
NEED COMPUTATIONAL ALGORITHMS SPECIFICALLY FOR DESIGN, ETC.
NEED MODELING AND MULTI-SCALE COMPUTATIONAL TOOLS
NEED HPC SENSITIVITY AND UNCERTAINTY ANALYSIS TOOLS
Closing Remarks
Future Directions in Applied Mathematics 65
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…
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
Future Directions in Applied Mathematics 66
IEEE CDC PAPER
There is no Free Lunch (Energy)
Future Directions in Applied Mathematics 67
Future Directions in Applied Mathematics 68
THANK YOUCONTACT INFORMATION
John A. BurnsInterdisciplinary Center for Applied MathematicsWest Campus DriveVirginia TechBlacksburg, VA 24061540 – 231 – [email protected]