Optimal Prediction, Alarm, and Control in Buildings Using Thermal

282 Pages·2004·1.53 MB·English

Optimal Prediction, Alarm, and Control
in Buildings Using Thermal Sensation Complaints
by
Rodney Alexander Martin
B.S. (Carnegie-Mellon University 1992)
M.S. (University of California at Berkeley 2000)
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Engineering - Mechanical Engineering
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor David M. Auslander, Chair
Professor Alice Agogino
Professor Edward Arens
Fall 2004
The dissertation of Rodney Alexander Martin is approved:
Chair Date
Date
Date
University of California, Berkeley
Fall 2004
Optimal Prediction, Alarm, and Control
in Buildings Using Thermal Sensation Complaints
Copyright 2004
by
Rodney Alexander Martin
1
Abstract
Optimal Prediction, Alarm, and Control
in Buildings Using Thermal Sensation Complaints
by
Rodney Alexander Martin
Doctor of Philosophy in Engineering - Mechanical Engineering
University of California, Berkeley
Professor David M. Auslander, Chair
The management and automation of commercial building HVAC (Heating, Ventilation and Air-
Conditioning)systemsisillustrativeofabusinessthatcanbenefitfromtheinsightfuluseofallavail-
ableinformationsources. ModernHVACsystemsusingdirectdigitalcontrolcanpotentiallyprovide
usefulperformancedata. Buildingoccupantfeedbackcomplaintstatisticsareanuntappedresource,
and can be cultivated from modern maintenance management databases. This thesis will address
theintegrationandapplicationofthesefundamentalsourcesofinformation,usingsomemodernand
novel techniques. The cost and scalability of these techniques can be positively influenced by recent
technologicaladvancesincomputingpower,sensors,anddatabases. However,applicationofthethe-
orythatdrivessomeofthenewertechniquesisstillinitsinfancy,andrequirestremendouscomputing
power. Assuch,animportantthemeinthethesisistoaddresscomputationalefficiencyandpractical
usefulness of the techniques, via some clever approximations. One desired outcome is to make these
newtechniquesmoreaccessibletousersofexistingbuildingcontroltechnology. Itishopedthatthese
users and facility managers as well can benefit from the algorithmic and design-oriented paradigm
2
in which the results are presented.
Professor David M. Auslander
Dissertation Committee Chair
i
Dedicated to my Parents: June Carol and Bartholomew Martin, Jr.
ii
Contents
List of Figures v
List of Tables vii
List of Symbols viii
List of Abbreviations xii
1 Introduction 1
1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Background 7
2.1 Current Industrial Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Historical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Thermal Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Information Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Solutions and Treatment of problems . . . . . . . . . . . . . . . . . . . . . . . 13
Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Thermal Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Current Research Efforts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Passive Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Active Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Thermal Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
General Thermal Comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Solicited Occupant Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Unsolicited Occupant Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Commercial Building HVAC Systems. . . . . . . . . . . . . . . . . . . . . . . 29
2.2.4 Hybrid Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Optimal Alarm 36
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 The Exact Alarm Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Kalman Filtering and Prediction . . . . . . . . . . . . . . . . . . . . . . . . . 45
iii
3.2.3 Approximations for the Exact Alarm Region . . . . . . . . . . . . . . . . . . 48
Two-Dimensional Alarm System Approximation . . . . . . . . . . . . . . . . 48
Multiple Sub-Interval Alarm System Approximation . . . . . . . . . . . . . . 51
Mathematical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Multi-Dimensional Alarm System Approximation . . . . . . . . . . . . . . . . 62
3.3 Example Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.1 Examples 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.2 Examples 3 and 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Results for Examples 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.4.1 Example 1: Svensson Model, Operating Complaints Only . . . . . . . . . . . 79
3.4.2 Example 2: Svensson Model, Both Arrival and Operating Complaints . . . . 82
3.4.3 Discussion of Results for Examples 1 and 2 . . . . . . . . . . . . . . . . . . . 85
3.5 Results for Examples 3 and 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.1 Example 3: Federspiel Model, Operating Complaints Only . . . . . . . . . . . 91
3.5.2 Example 4: Federspiel Model, Both Arrival and Operating Complaints . . . . 92
3.5.3 Discussion of Results for Examples 3 and 4 . . . . . . . . . . . . . . . . . . . 93
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4 Discretization of Level-Crossing Formulae 100
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2.1 Zero-Level Upcrossings of a Zero-Mean Stationary Gaussian Random Sequence101
4.2.2 Level Upcrossings of a Stationary Gaussian Random Sequence . . . . . . . . 106
4.2.3 Level Upcrossings of a Non-Stationary Gaussian Random Sequence . . . . . . 108
4.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3.1 Zero-Level Upcrossings of a Zero-Mean Stationary Gaussian Random Sequence113
4.3.2 Level Upcrossings of a Stationary Gaussian Random Sequence . . . . . . . . 114
4.3.3 Level Upcrossings of a Non-Stationary Gaussian Random Sequence . . . . . . 119
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5 Optimal Alarm Design 128
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.2 Design Metrics for the Optimal Alarm System. . . . . . . . . . . . . . . . . . . . . . 129
5.2.1 Baseline Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Iterative Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2.2 A New Optimal Alarm Design Method . . . . . . . . . . . . . . . . . . . . . . 134
Single Interval 2D Approximation . . . . . . . . . . . . . . . . . . . . . . . . 136
Multiple Sub-Interval Approximation. . . . . . . . . . . . . . . . . . . . . . . 138
Multi-Dimensional Approximation . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6 Optimal Control 155
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2 Optimal Reference Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.2.1 State-Space Representation of Plant . . . . . . . . . . . . . . . . . . . . . . . 160
6.2.2 Propagation of Means of State Space Equations . . . . . . . . . . . . . . . . . 162
6.2.3 Revisions to Predictions and Optimal Alarm System . . . . . . . . . . . . . . 164
6.2.4 Revised Cost Function and The Control Law . . . . . . . . . . . . . . . . . . 168
iv
6.2.5 Conditioning on Complaint and Alarm Information. . . . . . . . . . . . . . . 173
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.3.1 Computational Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.3.2 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7 Practical Implementation 187
7.1 Selecting a Prototype Building/Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.2 Optimal Alarm Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.2.1 Selecting the Optimal P Value and Alarm System Utility . . . . . . . . . . . 188
b
7.2.2 Practical Issues in the Design of Optimal Alarm Systems . . . . . . . . . . . 192
7.2.3 Practical Issues in the Implementation of Optimal Alarm Systems . . . . . . 195
7.3 Optimal Control Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.3.1 Inner Loop Controller Details and Event Asymmetry . . . . . . . . . . . . . . 220
7.3.2 Baseline Setpoint Control Policies . . . . . . . . . . . . . . . . . . . . . . . . 221
7.3.3 Optimal Control Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.3.4 “Alarm-Based Control” System Utility . . . . . . . . . . . . . . . . . . . . . . 242
8 Conclusions and Future Research 247
8.1 Optimal Alarm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
8.2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Bibliography 253
v
List of Figures
1.1 Block Diagram of Integrated System . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Plot of PPD vs. PMV and Space Temperature . . . . . . . . . . . . . . . . . . . . . 12
2.2 Plot of Complaint Process Interaction with Building Temperature . . . . . . . . . . 27
2.3 Sample Thermal Comfort Penalty Function . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Approximation to the 2D Alarm Region for P =0.99 . . . . . . . . . . . . . . . . . 50
b
3.2 Exact Alarm Region for m=3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 Process Realization and Level-Crossing Threshold for Examples 1, 2 . . . . . . . . . 71
3.4 Building and Complaint Process Realizations with Level-Crossings . . . . . . . . . . 78
3.5 Building and Hot Complaint Process Realizations with Zero-Level Crossings . . . . . 79
3.6 Type I/II Errors: Papprox,Pˆexact vs. P . . . . . . . . . . . . . . . . . . . . . . . . . 80
i i bi
3.7 Type I/II Approximation Error, (cid:107)Pˆapprox−Pˆexact(cid:107) vs. Number of Sub-intervals. . 82
1
3.8 Type I/II Errors (Upcrossings): Papprox,Pˆexact vs. P . . . . . . . . . . . . . . . . . 83
i i bi
3.9 Type I/II Approximation Error (Upcrossings), (cid:107)Pˆinterv −Pˆexact(cid:107) vs. Number of
1
Sub-intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.10 Type I/II Errors (Downcrossings): Pˆapprox,Pˆexact vs. P . . . . . . . . . . . . . . . 85
i i bi
3.11 Type I/II Approximation Error (Downcrossings), (cid:107)Pˆinterv−Pˆexact(cid:107) vs. Number of
1
Sub-intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.12 Type I/II Error Comparisons, Operating Complaints Only . . . . . . . . . . . . . . . 90
3.13 Type I/II Errors for Operating Complaints Only . . . . . . . . . . . . . . . . . . . . 92
3.14 Type I/II Errors for Both Arrival & Operating Complaints . . . . . . . . . . . . . . 93
3.15 Type I/II Errors for Both Arrival & Operating Complaints . . . . . . . . . . . . . . 94
4.1 Comparative Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2 Discretization vs. Exact Discrete Level Upcrossings. . . . . . . . . . . . . . . . . . . 106
4.3 Discretization vs. Exact Discrete Level Upcrossings (Courtesy Repeat) . . . . . . . . 113
4.4 Peak Expected Complaints vs. hot correlation, ρ . . . . . . . . . . . . . . . . . . . 115
h
4.5 Cost Function Approximations for Expected Complaints/week vs. µ . . . . . . . . 117
TB
4.6 Approximation Summary: ρ(T ) and Peak E[C] vs. ρ . . . . . . . . . . . . . . . . . 118
s
4.7 Approximation Summary Detail: ρ(T ) and Peak E[C] vs. ρ. . . . . . . . . . . . . . 118
s
4.8 Approximation to the 2D Alarm Region for P =0.99 . . . . . . . . . . . . . . . . . 120
b
4.9 Contour Plots of FOH Approximations for Non-Stationary Expected Complaints . . 123
5.1 Parametrization of P for P(A), P(C(cid:48)|A), and P(A(cid:48)|C) . . . . . . . . . . . . . . . . 131
b
5.2 Solutions to argmin J(cid:48)(P ) for differing γ , γ . . . . . . . . . . . . . . . . . . . . . 133
Pb b 1 2
5.3 f (P )=P(C,A) and f (P )=P(C(cid:48),A) . . . . . . . . . . . . . . . . . . . . . . 133
CA b C(cid:48)A b