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Coursework: sensor selection
CIVE97052 - Water Supply and Distribution Systems
Filippo Pecci and Ivan Stoianov
Department of Civil and Environmental Engineering, Imperial College London
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Coursework: sensor selection
Pressure sensors were initially placed to be evenly spread.
▶ can we remove some
sensors?
▶ which sensors can be
removed without affecting
model accuracy on test
dataset?
▶ which sensors have the
biggest impact on model
accuracy?
Reservoir
Sensor
3/13
Proposed strategy
Iterative process:
1. remove one sensor at the time from train dataset
2. perform model calibration using the updated train dataset
3. compute model error on test dataset (where all 14 sensors are
considered)
How do we select which sensors to remove? In which order?
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Graph theory
A graph G = (V,E) is a mathematical
structure, where:
▶ V is a set of objects (vertices)
▶ E is a set of edges describing the
relation objects in V
▶ when the edges can be crossed only
in one direction, we call G a
directed graph
▶ otherwise, we say that G is an
undirected graph
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WDNs as graphs
A water distribution network is represented by an undirected graph
G = (V,E), where:
▶ V is the set of network nodes
▶ E is the set of network pipes
Reservoir
Sensor
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Betweenness centrality
Consider an undirected graph G = (V,E).
▶ a shortest path between two nodes s, t ∈ V is defined as a
path connecting s and t with minimum number of edges.
▶ betweenness centrality measures how often each node appears
on a shortest path between two nodes in the graph:
c(u) =
∑
s,t̸=u
ns,t(u)
Ns,t
where ns,t(u) is the number of shortest paths between s and t
that passes through u, while Ns,t is the total number of
shortest paths between s and t.
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Betweenness centrality in STKLnet
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Sensors ranking
▶ compute betweenness centrality of each sensor
▶ rank sensors in ascending order
▶ sequentially remove one sensor at the time from the train
dataset, starting from the sensor with smallest value of
betweenness centrality
▶ obtain 14 different sensor configurations for the train dataset
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Proposed strategy
For each sensor configuration:
▶ formulate the problem of hydraulic model parameter
estimation (calibration) using the updated train dateset
▶ implement the sequential convex programming algorithm to
solve the resulting optimisation problem
▶ evaluate error on test dataset (where all 14 sensors are
considered)
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Tasks and questions
1. implement the proposed strategy (previous slide)
2. consider different ways to visualise the results (boxplots,
cumulative distribution function, etc...)
3. comment on the results and make recommendations on which
sensors should be kept.
4. can you explain why the selected sensors are more important
than others?
5. discuss the relevance of your sensor selection for hydraulic
models of water distribution networks
11/13
We have shared a coursework solution Matlab LiveScript, where
some code lines are missing.
▶ fill-in the blank spaces to carry out the different tasks
▶ add code, text and images necessary to visualize the results,
describe solution method and comment on the results
▶ (optional) explore other solution strategies to indicate which
sensors can be removed from the network
▶ other ranking metric for sensors’ criticality?
▶ other optimisation method for solving the parameter
estimation problem?
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Assessment criteria
▶ 60% correctness of the solution and code quality
▶ 30% discussion and interpretation of the results
▶ 10% effort that goes beyond the requirement of the
coursework (e.g. visualisation, investigation of additional
strategies...)
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Submission
▶ After running the completed LiveScipt, export it to a pdf file.
▶ Submit both the LiveScript and the pdf file to the link posted
on Blackboard
▶ Submission by 10 am on 26/03/2021




















































































































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