# PSE

**Repository Path**: bestwishesws/PSE

## Basic Information

- **Project Name**: PSE
- **Description**: The code is for Probabilistic State Estimation in WDN; see https://arxiv.org/abs/2002.01083.
- **Primary Language**: Unknown
- **License**: EUPL-1.1
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2023-07-17
- **Last Updated**: 2023-07-24

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# PSE
The code is for Probabilistic State Estimation in WDN; see https://arxiv.org/abs/2002.01083.
# Main file
MonteCarloNew.m is the main file.
# Intro
This work is to explore how the uncertainty from demand, measurement noise, and pipe roughness coefficients propagate to the uncertainty of system states, i.e., heads and flows.

AnalycalDistribution_FOSM.m is using the FOSM method and is good for any network.

The .m file with "over" considers an over-determined scenario. The file is only for the 3-node network and would give an error when trying the other networks.

The keyword "Pipe"  in the filename means this file considers the uncertainty from pipe roughness coefficients.

All AnalycalDistribution_MC-based files consider demand uncertainty.

For example, the "AnalycalDistribution_MC_over_pipe.m" considers an over-determined scenario and pipe uncertainty demand uncertainty at the same time

"AnalycalDistribution_Kxx.m" simply means we are using the second version of our derived formula, which is much easier to understand and the no need to construct Vech(Kxx).

# Note
Note that for PES1 Network and BAK network, their unit system is based on LPS. Hence, when linearizing the pipes or pumps in a network, Headloss_pipe_R should be 10.66 instead of 4.727; please be careful on converting unit system, otherwise, the covariance results make no sense and no error or warnings would pop out in our code.

As for how to numerically obtain (i) the probability density function of the linear combinations of independent random variables with different (known or unknown) distributions and (ii) its corresponding confidence interval, please see "PSE/tests/PDF_Sum_Random_Var.m" file.