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Topological Search for Fault Diagnosis

Guides: Profs. Sridharakumar Narasimhan and Shankar Narasimhan, IIT Madras

Won the best undergraduate thesis award

In most urban water distribution systems, nearly 25% of water and revenue is lost due to leaks and water thefts. In this context, we proposed a systematic procedure for locating leaks with minimum sensor probes.
 

  • Reduced the problem to hierarchical graph-partitioning.

  • Proposed a mixed integer programming framework for solving the problem. Solutions can be pre-computed and stored off-line. Hence computational effort is one time.

  • Proposed an approximation algorithm, inspired by spectral clustering, for very large networks.

  • Tested algorithms on real world and benchmark networks which indicated a remarkable reduction in required effort compared to previously used ad-hoc methods.

Conventional RL approaches assume little to no knowledge about the environment, thus leading to a general and domain agnostic framework for learning and decision making.

 

However, such a paradigm fails when dealing with safety critical applications where it is impossible to recover from bad decisions. Conventional RL methods assume infinite number of episodes to learn from mistakes and eventually learn to make good decisions - a luxury not available for many real world applications involving physical systems (e.g. field robotics, chemical reactors etc.).

 

Ideas such as optimism in face of uncertainty, which are meant to encourage exploration, are unintuitive for safety critical problems. We are combining ideas from robust control theory, risk aversion in economics, and Bayesian RL to generate trajectories which are informative for learning, yet safe.

Guide: Prof. Balaraman Ravindran

Safe Exploration for Reinforcement Learning

  • Compared different state estimation algorithms like EKF, UKF, MHE, and URNDDR for simultanious state and parameter estimation in a CSTR case study.

  • Used an augmented state vector approach to simultaniously estimate an unknown model parameter along with states.

  • Observed limitations of EKF like sub-optimal error covariance propagation and inability to pose constraints to get physically meaningful estimates.

  • Studied how the different state estimation algorithms overcome these limitations.

 

Download report here

Guide: Prof. Raghunathan Rengaswamy

(Part of course of modern control theory)

Nonlinear state & parameter estimation
Model Predictive Control & SysID

Guide: Prof. Raghunathan Rengaswamy

(Part of course of modern control theory)

  • Model Predictive Control (MPC) is analogous to a moving horizon optimal control stratergy with a heuristic terminal cost. Hence, it is similar to rollout and MCTS methods in approximate dynamic programming literature.

  • MPC is particularly advantageous when handling input and output constraints (optimization setup); and is robust to model uncertainties (long planning horizons).

  • I used subspace identification techniques (N4SID) to estimate an approximate linear model (LTI) for a nonlinear FCC plant using PRBS and IRS input sequences.

  • Used Kalman filter for state estimation and observed that controller is stable and shows good performance even with plant-model mismatch.

Download report here

Unsupervised learning problems

Guide: Prof. Shankar Narasimhan

(Part of course of Multivariate Data Analysis)

  • Used Kalman filter and multi dimensional splines for estimating vehicle trajectory from GPS data. Report
     

  • Used Indipendent Component Analysis to perform blind source separation. The separation was achieved by maximizing the non-gaussianity of the indipendent signals by using kurtosis. Report
     

  • Used PCA and K-means for clustering of leaves based on images. Report

 

Network topology Identification

An important characteristic of "interpretable" ML models are their structure. When models of particular structural properties are learned, it is possible to attribute meaning to different terms and thus interpret the learned result. In most cases, we do not have a direct parametrized form for the model, and have to work with broad characteristics of the model like non-negativity (NMF) or sparsity (compressed sensing, SPCA).

 

In this work, the objective is to learn a network structure which describes the relationship between different variables. We make use of "flow" data and conservation laws to find network structures which are accurate as well as consistent with physical laws of the process (e.g. mass or energy conservation).

Guide: Prof. Shankar Narasimhan

Cascading failures and Systemic risk

Guide: Prof. Sitabhra Sinha  

(The Institute of Mathematical Sciences, India)

Cascading failures are observed in all large scale networked systems like supply chains, financial networks, power grids, and even social networks (epidemiology). Our work was motivated at finding universal laws for cascading dynamics that are invariant across seemingly different systems.

 

Using Monte Carlo simulations, we showed that random walk betweenness centrality (RWBC) of a unit (node or edge) is a robust indicator of its role in propagating cascades. 

 

This observation has applications in design of resilient networks, where redundancies can be added to maximally reduce RWBC.

Semester-long Course Projects
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