B. Eisenhower: Uncertainty and Sensitivity Analysis in Building Energy Models

Uncertainty and Sensitivity Analysis in

Building Energy Models

Bryan Eisenhower

Center for Energy Efficient Design

UCSB

Snowbird, 2011

Motivation – On Average

40% For Buildings

60% Wasted

15% Renewables

End Use 2008 Annual Energy Use (QBTU)

Residential & Commercial Buildings

18.75

Lighting 2.01

Transportation 21.63

Cars 8.83


~30% reduction can be achieved by occupancy based

lighting control (0.8 QBTU)

A 47% reduction in buildings energy use will take ALL

cars off the road!

Source: Buildings Energy Data Book & US EIA

DoD Spends ~3.4Billion Annual on ~1 QBTU


It can be done (1st three examples from recent HPB)!

A Grander View, Ontario Canada

- 22Kft^2 office

- 80% Energy savings as recorded in first year

- Most energy efficient office in CA

David Brower Center, Ontario Canada

- 45Kft^2 office / group meetings

- 42.4 % Energy savings as recorded in 11 months.

The Energy Lab, Kamuela Hawaii

- 5.9Kft^2 Educational

- 75% Energy savings compared to CBECS

- 1st year generated 2x electricity that it used


It will be done…

DoD is the single largest energy user in U.S.

Legislation:

EPA2005:Section 109. Federal Building Performance Standards amended

the Energy Conservation and Production Act11 by adopting the 2004

International Energy Conservation Code, and requiring revised energy

efficiency standards and a 30% reduction in energy consumption of new

federal buildings over the previous standards.

EISA2007: Section 431. Energy Reduction Goals for Federal Buildings

amends the National Energy Conservation Policy Act (NECPA)13 by

mandating a 30% energy reduction in federal buildings by 2015 relative to a

2005 baseline.

EISA2007: Section 433. Federal Building Energy Efficiency Performance

Standards requires 55% reduced fossil energy use in new federal buildings

and major renovations by 2010 relative to a 2003 baseline, and 100% by

2030.

Net Zero will require ~70%

reduction in energy use

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

x 104

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Hours

Power [MW]

Southern CA Edison (2010)

Da

ta: C

A O

AS

IS

Top 25% of power only 2.74% of year.

0 1000 2000 3000 4000 5000 6000 7000 8000 90000.6

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1

1.2

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2.4x 10

4 Load Duration Curves

Hours

Pow

er

[MW

]

Southern CA Edison

Pacific Gas & Elec.

Load Duration Curve

Only used 10 days a

year…

Motivation – On Variance

Some aspects of the

design of the power grid are

based on long tail demand

concerns.

0 100 200 300 400 500 600 700 800 9000

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1400

Hours

Energy [BTU]

Student Resources Building


0 500 1000 15000

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1200

Hours

Energy [BTU]

Life Sciences Building


Motivation – On Variance

Data: Cooling energy for two buildings @ UCSB

Similar long tail distributions are seen at the building

level (no surprise)

Motivation

Pitfalls

[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.] [Frankel 2008]

“….these strategies must be applied

together and properly integrated in the

design and operation to realize energy

savings. There is no single efficiency

measure or checklist of measures to

achieve low-energy buildings. “

“… dramatic improvement in

performance with monitoring and

correcting some problem areas identified

by the metering “

“There was often a lack of control

software or appropriate control logic to

allow the technologies to work well

together “

Modeling

Control

Monitoring

0.5 1 1.5

x 106

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cy

Total Power

Seasonal Consumption - Cooling

0.5 1 1.5 2

x 106

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Fre

qu

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cy

Total Power

Seasonal Consumption - Heating

-1.5 -1 -0.5 00

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Fre

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cy

PMV Avg.

Seasonal Consumption - Cooling

-2 -1.5 -1 -0.5 00

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300

Fre

qu

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cy

PMV Avg.

PMV Avg. - Heating

Sensitivity

Decomposition

methods

Energy Visualization

Uncertainty Analysis

Advanced Energy Modeling

Data analysis toolkits

Energy/Comfort

OptimizationFailure Mode Effect Analysis

Summary

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 1011

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Pumps [J] - Yearly Sum

Fre

quency

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

x 108

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Interior Lighting [J] - Yearly Peak

Fre

quency

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x 1011

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Heating [J] - Yearly Sum

Fre

quency

1600 1650 1700 1750 1800 1850 1900 1950 20000

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Occurr

ences

VAV3 Availability Manager

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

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Occurr

ences

BLDGLIGHT

SCH

Uncertain Inputs

1600 1650 1700 1750 1800 1850 1900 1950 20000

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Occurr

ences


Building Model

Uncertain Outputs

?

Modelling / Analysis

Energy Modeling

Energy models capture both the architectural

components of the building as well as its thermal physics

Typical software contains front-end for drawing

purposes, with mathematical engine for computation

Equations /

Physics / etc.

Building

design

Ryan Casey Erika

Models are built with highschool / undergrad help

Energy Modeling – Uses

Reasons for modeling (entire building)

Compliance

Leadership in Energy and Environmental Design (LEED)

ASHRAE

Rebates for efficient design

Design trades

Usually very few performed in design firm

Academic Studies

Prediction of un-sensed data

Uncertainty / Sensitivity Analysis

Optimization (design / operation)

….

Very little control design / dynamical analysis is performed with

these models at the building level (some work at the component level).

Decades spent on developing energy models

Most are validated on a component basis

At the systems level, the most advanced energy

models, are still do not predict consumption

accurately during the design stage

Actual

Prediction

Energy Modeling & Uncertainty

* Stanford Y2E2 Building

Sensitivity / Uncertainty Analysis

Discrepancy is often introduced because of uncertainty

Commissioning / Operation

Material selection

Usage

… Other unknowns

Sensitivity / Uncertainty Analysis helps manage these

concerns


1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 1011

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Pumps [J] - Yearly Sum

Fre

quency

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

x 108

0

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Interior Lighting [J] - Yearly Peak

Fre

quency

0.5 1 1.5 2 2.5 3 3.5

x 1011

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Fre

quency

1600 1650 1700 1750 1800 1850 1900 1950 20000

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Occurr

ences


0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

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Occurr

ences

BLDGLIGHT

SCH

Uncertain Inputs

1600 1650 1700 1750 1800 1850 1900 1950 20000

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Occurr

ences


Building Model

Uncertain Outputs

?

O(1000) O(10)

Sampling

• O.A.T.

• Monte Carlo

• Latin Hypercube

• Quasi-Monte

Carlo

(deterministic)


Red: In this talk

Uncertainty Analysis

• STD(), VAR()

• COV

• Amplification

factors

Sensitivity Analysis

• Elementary Effects / screening &

local methods

• Morris Method

• ANOVA

• Derivative-based

• Propagation analysis through

decomposition

UA / SA – Historically (Building Sys.)

Author(s) # Param. Technique Notes

Rahni [1997] 390->23 Pre-screening

Brohus [2009] 57->10 Pre-screening / ANOVA

Spitler [1989] 5 OAT / local Residential housing

Struck [2009] 10

Lomas [1992] 72 Local methods

Lam [2008] 10 OAT 10 different building types

Firth [2010] 27 Local Household models

de Wit [2009] 89 Morris Room air distribution model

Corrado [2009] 129->10 LHS / Morris

Heiselberg [2009] 21 Morris Elementary effects of a building model

Mara [2008] 35 ANOVA Identify important parameters for calibration also.

Capozzoli [2009] 6 Architectural parameters

Eisenhower [2011] 1009 (up to 2000)

Deterministic sampling, global derivative sensitivity

‘All’ available parameters in building

Parameter Variation

All numerical design & operation parameters in the model

are varied concurrently (not arch. design)

Parameters organized by type

Type Examples

Heating source (Furnace, boiler, HWGSHP etc)

Cooling source (chiller, CHWGSHP etc)

AHU (AHU SAT setpoint, coil paramters etc)

Air Loop (Fans)

Water Loop (Pumps)

Terminal unit (VAV box, chilled beam, radiant heating floor)

Zone external (Envelope, outdoor conditions)

Zone internal (Usage, internal heat gains schedule, )

Zone setpoint (Zone temp setpoint)

Sizing parameter (Design parameters for zone, system, plant)

1600 1650 1700 1750 1800 1850 1900 1950 20000

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Occurr

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VAV3 Availability Manager 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

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BLDGLIGHT

SCH

nominal10-25%

Parameters varied 10-25% of their mean

Some parameters are of the form a+b < 1

Parameter Variation

Large number of parameters and lengthy simulation time require

efficient parameter selection (for parameter sweeps)

Deterministic sampling avoids the ‘clumping’ that occurs in Monte

Carlo based sampling

Random

Deterministic

Convergence Properties

Monte Carlo bound ~ 1/sqrt(N)

Deterministic bound ~ 1/N

Example Convergence from Building Simulation

Faster

convergence

means more

parameters can be

studied in the

same amount of

time!

Typical Output Distributions

Key Outputs(E) Gas Facility(E) Electricity Facility(E) Submeters: Heating, Cooling, Pump, Interior Lighting, Interior Equipment

(C) Temperature

(C) PMV

(C) PPD

(C) Setpoint missed

5.3 5.4 5.5 5.6 5.7 5.8 5.9 6

x 1011

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Interior Lighting [J] - Yearly Sum

Fre

quency

* TRNSYS results

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 1012

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Fre

quency

5000 realizations performed to obtain convergence

The ‘control’ mechanisms in the model drive distributions towards Gaussian although others exist as well

Case Studies

DOD Building in Colorado(TRNSYS )

An administration and training facility built in 70’s.

One floor with an area of ~24000 ft2.

Major HVAC systems: 2 constant-air-volume

multi-zone-units, chilled water from a central

plant (May-October), hot water by a gas boiler

(November-April).

Domestic hot water generated by a gas water

heater.

DOE benchmark models

Medium office model in Las Vegas

3 floors, ~50K ft^2, 15 zones

DOD: Atlantic Fleet Drill Hall

6430 m2 (69 K ft^2)

Model developed in EnergyPlus

30 Conditioned zones

1009 uncertain parameters

Case Studies

Model Results - UA

Nominal vs. High Efficiency DesignInfluence of Different Parameter

Variation (size)

B. Eisenhower, et al. The Impact of Uncertainty in High Performance

Building Design Prepared for: International Building Performance

Simulation Association, BuildSim 2011

[E+ Drill Hall] [E+ DOE Models]

Characteristics of the output are considered based on different inputs, or

different models

Model Results - UA

[E+ Drill Hall]

Input Uncertainty @ 20%Input Uncertainty @ 10%

Amplification & Attenuation of uncertainty is quantified on a subsystem and

facility basis

Meta-Modelling

Model created using

Gaussian Kernels

Support Vector Regression used to create a high dimensional model

from the data

Sensitivity Analysis (ANOVA)

Sobol’ decomposition into 2n summands

x: uncertain parameters

f: zeroth, first, second, …

order component

functions

Sobol’, I., 2001

If f(x) is square integrable, fi…n() are square integrable as well

Building

energy

model

For analysis, a meta-model is derived to analytically characterize the

building energy model

Total Variance

Total Sensitivity

Sensitivity Indices

Sensitivity Calculation

L2-norm derivative sensitivity indices can be calculated as

L1-norm derivative sensitivity indices can be calculated as

Average derivatives can be calculated as

22

22where

and is a constant for each distributi

f ( )( ) ,

1 ( ) ( )

on ( )

2

tot i ii

i

i i i i i i i

i i

N dD x

x x x dx x dx

x

xx x

2f ( )

( )tot i ii

i

L dD x

x

x x

2f ( )

( )tot i ii

i

M dD x

x

x x

Three approaches to calculating global sensitivity:

Sobol’, I. and Kucherenko, S., 2009

Zheng O’Neill, Bryan Eisenhower, et al

Modeling and Calibration of Energy Models

for a DoD Building ASHRAE Annual Conference, Montreal 2011

Sensitivity Analysis

Uncertainty Analysis considers the

forward progress of how uncertainty

influences the output.

Sensitivity Analysis identifies which

parameters are causing the most

influence

Identifying key parameters in a building helps in design optimization, continuous commissioning, model calibration, …

[E+ Drill Hall]

System Decomposition

http://www.biomedcentral.com/14712105/7/386/figure/F2?highres=y

What are the essential components of a productive network?

Decomposition provides an understanding of essential production units

and the pathway energy/information/uncertainty flows through the

dynamical system

Integrated Gasification Combined Cycle, or IGCC, is a technology that turns coal into gas into

electricity

Decomposition Methods

What are the essential components of a productive network?

Decomposition provides an understanding of essential production units

and the pathway energy/information/uncertainty flows through the

dynamical system

Integrated Gasification Combined Cycle, or IGCC, is a technology that turns coal into gas into

electricity


[Y. Lan and I. Mezic On the Architecture of Cell Regulation Networks,

BMC Systems Biology 2011]

Dynamical systems on graphs highlights dominating function of network

Mean production units (MPU)

- What are the essential components of a productive network

B. Subtilis chemotaxis network


Action-Angle system describes energy behavior

Jacobian describes energy transfer characteristics

0.01 0.02 0.03 0.04 0.05

0

1

2

3

4

5

6

J

J

J

J

J

J

J

0

1

2

3

4

5

6

J

J

J

J

J

J

J

=

Small Large[Eisenhower and I. Mezic Physical Review E, 2010]

Decomposition Methods - Cascade

Facility

Electricity

Intermediate Consumption

Variables

Input

Parameter

Types

Uncertainty at each node and pathway flow identified for a

heterogeneous building

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Parameter Index

Sen

sitiv

ity In

dex

Electricity:Facility [J] (Annual Total)

All Data

Supply air temp setpoint

Chiller1 reference COP

Drill deck lighting schedule

AHU2 return fan maximum flow rate

AHU2 supply fan efficiency

AHU2 supply fan pressure rise

AHU1supply fan efficiency

AHU1 supply fan pressure rise

Chiller1 optimum part load ratio

Eisenhower et al. Uncertainty and Sensitivity Decomposition of Building

Energy Models Journal of Building Performance Simulation, 2011

Circles: Uncertainty at each nodeLine Thickness: ‘conductance’

Decomposition Methods – Building Energy

Acknowledgements

This work was partially supported under

the contract W912HQ-09-C-0054 (Project Number: SI-1709)

administered by SERDP technology program of the Department

of Defense.

Contributors:

Zheng O’Neill (United Technologies Research Center)

Satish Narayanan (United Technologies Research Center – PL/PM)

Shui Yuan (United Technologies Research Center)

Vladimir Fonoberov (AIMdyn Inc.)

Igor Mezic (University of California, Santa Barbara)

Kevin Otto (RSS)

Michael Georgescu (University of California, Santa Barbara)

B. Eisenhower: Uncertainty and Sensitivity Analysis in Building Energy Models

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