4. How do commercial buildings work?
Facility managers (FMs) oversee the day to day operations of a commercial
building.
Used to be a whole team!
Shrinking maintenance budgets and increasing complexity makes this a
challenging problem.
Building operations are automated by Building Management Systems (BMSs).
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5. What is a BMS?
Commercial buildings contain Building Management Systems (BMSs) to
improve indoor environment quality and reduce energy consumption.
A BMS will control heating, cooling, ventilation and lighting systems.
Contain thousands of points for sensors (temperature, humidity), actuators
(fans, motors, dampers) and software (schedule, trend logs, calculations).
A BMS will monitor sensors and adjust actuators based on their readings.
For example, if high temperatures are recorded in a room, dampers will open
and air handlers will modulate to provide cooler air.
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7. How does this work in practice?
Vendor sets up a BMS. The BMS will behave in a certain way based predefined
rules.
BMS systems are costly to implement and to modify. Can require a lot of
coding to change the BMS's behaviour.
The bigger the BMS is the harder it is to find what matters. Locating problems
is difficult and time-consuming.
For example, a heating valve might be locked open. If this isn't detected the
BMS will cool the room to reach the required temperature.
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8. So what can we do?
Help facility managers identify if a BMS is operating optimally.
Buildings Alive's goal is to
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Fault detection
Diagnostics
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Collect BMS data using our E2 device
Analyse and transform data into useful information.
Help guide FM's to find out what's wrong.
Provide timely and actionable information.
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12. Feature generation
Dealing with thousands of unevenly spaced time-series.
Uneven spacing in time-series presents difficulties.
Rather than rounding or imputing data we can generate features and work
with them instead.
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13. What features might be useful?
Feature generation for time-series clustering is discussed in Wang, Smith, and Hyndman (2006). Some
useful features for our case might be
Normalise these features using their median, , and interquartile range, ,
Mean
Standard deviation
Kurtosis
Skewness
Biggest change ( )
Smallest change ( )
Number of "mean crossings" per day
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· { − }maxi
∣
∣yti
yti−1
∣
∣
· { − }mini
∣
∣yti
yti−1
∣
∣
·
M IQR
= .y
∗
y − M
IQR
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16. Dimension reduction and clustering
Too many sensors to visualise easily.
Use dimensionality reduction.
Identify clusters and singletons.
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17. Which clustering algorithm?
Method Advantages Disadvantages
K-means Easy to learn. Outperformed by other algorithms.
Hierarchical clustering
Informative - produces a
dendrogram.
Not suitable for large data sets -
time complexity.
Affinity propagation
Automatically determines number of
clusters.
Not suitable for large data sets - time
complexity.
Spectral clustering Good performance.
See Nadler and Galun (2007). Time complexity
of .
( log(n))n
2
( t)n
2
( )n
3
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19. Obligatory mathematics slide
Spectral clustering
We are given points and a similarity matrix . Define the weight matrix, degree matrix and
graph Laplacian as
where,
Once is determined find the eigenvectors corresponding to the smallest eigenvalues of .
Finally, cluster the rows of using K-means.
n ∈xi ℝ
p
S
W
D
L
= ( ) ∈wij ℝ
n×n
= diag ( )di
= D − W,
is the weight between nodes and based on , and,
is the weighted degree of node .
· wij i j S
· =di ∑
n
j=1
wij i
L m Zn×m m L
Zn×m
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21. Dash
Recently released by Plotly.
Easily build web applications for
data analytics.
Open sourced under the MIT
license.
Works nicely with the existing Plotly
graphing libraries.
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Python equivalent of R's Shiny.·
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26. References
“Comparing Different Clustering Algorithms on Toy Datasets.” 2017. http://scikit-
learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html.
Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. 2001. The Elements of
Statistical Learning. Vol. 1. Springer series in statistics New York.
Murphy, Kevin P. 2012. Machine Learning: A Probabilistic Perspective. MIT Press.
Nadler, Boaz, and Meirav Galun. 2007. “Fundamental Limitations of Spectral
Clustering.” In Advances in Neural Information Processing Systems 19, edited by P B
Schölkopf, J C Platt, and T Hoffman, 1017–24. MIT Press.
Von Luxburg, Ulrike. 2007. “A Tutorial on Spectral Clustering.” Statistics and
Computing.
Wang, Xiaozhe, Kate Smith, and Rob Hyndman. 2006. “Characteristic-Based
Clustering for Time Series Data.” Data Mining and Knowledge Discovery 13 (3): 335–
64.
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