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MATLAB代写-CIVE97052

时间：2021-03-16

1/13

Coursework: sensor selection

CIVE97052 - Water Supply and Distribution Systems

Filippo Pecci and Ivan Stoianov

Department of Civil and Environmental Engineering, Imperial College London

2/13

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?

4/13

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

5/13

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

6/13

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.

7/13

Betweenness centrality in STKLnet

8/13

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

9/13

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)

10/13

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?

12/13

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...)

13/13

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

学霸联盟

Coursework: sensor selection

CIVE97052 - Water Supply and Distribution Systems

Filippo Pecci and Ivan Stoianov

Department of Civil and Environmental Engineering, Imperial College London

2/13

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?

4/13

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

5/13

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

6/13

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.

7/13

Betweenness centrality in STKLnet

8/13

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

9/13

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)

10/13

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?

12/13

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...)

13/13

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

学霸联盟