SparseSensors.jl

This repository is an implementation of the core sparse sensor placement with QR factorization and cost-constrained QR factorization algorithms from Manohar, et al., "Data-Driven Sparse Sensor Placcement for Reconstruction", and other papers, in Julia. This is a hobbyist port of the fantastic Python library pysensors in Julia.

All collaborations and contributions are welcome.

Installation

To install, use Pkg. From the Julia REPL, press ] to enter Pkg-mode and run

pkg> add SparseSensors

Example

using SparseSensors
using LinearAlgebra
using Gadfly
using DataFrames

#Setup the experiment
r = 11; # Number of basis modes
n = 1000;
x = collect(0.0:1/n:1.0);
vde_basis = VandermondeBasis(x,r);
Ψ = vde_basis.Ψ; #Get the vandermonde basis matrix from the Basis struct

#Make design matrix
X = copy(transpose(Ψ));
n_samples,n_features = size(X);

#Setup QR pivot sensor placement algorithm
qr_pivot = QRPivot(X);
fit(qr_pivot);
pivots = qr_pivot.pivots;

#Select the top 15 sensor locations
f = abs.(x.^2 .- 0.5);
selected_sensors = get_sensors(pivots,15);
x_sensed = x[selected_sensors];
y_sensed = f[selected_sensors];

#Ground truth
df_true = DataFrame();
df_true[!,"x_true"] = x
df_true[!,"y_true"] = f

#Sensed
df = DataFrame()
df[!,"x_sensed"] = x_sensed;
df[!,"y_sensed"] = y_sensed;

#Plot the results
p1 = plot(df,
    layer(x=:x_sensed,y=:y_sensed,color=["Optimized Sensors"]),
    layer(df_true,x=:x_true,y=:y_true,Geom.line,Geom.point,color=["True Function"]),
    Guide.xlabel("x"),Guide.ylabel("y"))

Dependencies

julia >v1.6. LinearAlgebra, Gadfly and DataFrames for plotting.

Todo:

• Implement high level SSPOR and SSPOC interfaces
• Implement high level basis representation wrapper for SVD, etc.
• Set up compatibility with JuliaML/MLJ.jl/ScikitLearn.jl

References

• Manohar, Krithika, Bingni W. Brunton, J. Nathan Kutz, and Steven L. Brunton. "Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns." IEEE Control Systems Magazine 38, no. 3 (2018): 63-86. [DOI] <https://doi.org/10.1109/MCS.2018.2810460>

• Clark, Emily, Travis Askham, Steven L. Brunton, and J. Nathan Kutz. "Greedy sensor placement with cost constraints." IEEE Sensors Journal 19, no. 7 (2018): 2642-2656. [DOI] <https://doi.org/10.1109/JSEN.2018.2887044>

• de Silva, Brian M., Krithika Manohar, Emily Clark, Bingni W. Brunton, Steven L. Brunton, J. Nathan Kutz. "PySensors: A Python package for sparse sensor placement." arXiv preprint arXiv:2102.13476 (2021). [arXiv] <https://arxiv.org/abs/2102.13476>