CTMTDS Newsletter 19, August 2023

Advances in Time Series Analysis With Reservoir Computing, Braden Thorne

Reservoir computers have proven to be powerful embedding machines for dynamical systems. However, bridging the gap from their machine learning origins to time series analysis is still relatively new, with great potential for novel discoveries. 

In his talk, Braden outlined what reservoir time series analysis is and why we should care about it amidst the ecosystem of other embedding-based techniques. 

Time Series Analysis with Machine Learning, Michael Small

Michael introduced the concept of Reservoir Time Series Analysis - using a particular flavour of machine learning (reservoir computing) to represent the state of a dynamical system and characterise the dynamical evolution of that state. He identified what can be inferred about the changing behaviour of a system from the internal representation of these states within a reservoir machine learning model.

A second strategy within machine learning for time series analysis is to use the machine learning model as a proxy for the original dynamics. Michael used applications in machine vibration and pump cavitation in industrial processes to illustrate that persistent homology can be used as an effective tool to quantify that structure. 

Tim Pesch, Estimation and Testing with Extended Sequential Order Statistics

Historically the lifetimes of individual units of multi-component systems are modelled as independent and identically distributed. sequential order statistics relax this assumption by allowing component lifetime distributions to change upon failure of another unit.

This assumption is justified when the stress on the surviving units increases, and their respective lifetime expectation consequently reduces as components fail successively. Most load-sharing systems will exhibit such a relationship between components. Take a series of wash tanks that filter an inflow of contaminated products, for example. Each tank experiences a different workload based on its position in the series. Consequently, the tanks have different lifetime expectations, even if they are of the same type.

Tim presented a series of inferential results for extended sequential order statistics. He presented a likelihood ratio test to help determine which model is better suited, the sequential order statistics or the extended sequential order statistics model.

These estimation and testing techniques can achieve meaningful results in real-life applications. They empower system operators to predict failure times better and make educated decisions towards their maintenance schedule and stockpiling strategies.

Dr Shuixiu Lu, Nonlinear Time Series Analysis of Industrial Data with Uncertainty  

Industrial data is often uncertain due to the difficulty in collecting critical measures, the noise contaminating measurements, or the underlying system with non-stationarity in which statistical properties change over time. These factors make accurate prediction and effective maintenance a challenging task. In addressing the challenge, a common assumption is that a stochastic process is responsible for uncertainty. Fitting data by stochastic systems is thus widely used to model uncertainty.?

Shuixiu's presentation focused on data dynamics and whether the data fitting is sufficient to model uncertainty. To achieve that, Shuixiu demonstrated a time domain analysis of the data from a social system and presented the difference between time domain analysis and frequency domain analysis to address uncertainty in engineered systems. She illustrated a method based on a reconstruction of the topology in data, highlighting the importance of fitting the dynamics of data in the modelling of uncertainty.