2023-07-29

2023-07-29

Paper Review

Prognostics and health management via long short-term digital twins - ScienceDirect (sunPrognosticsHealthManagement2023, link, DOI, zolib)

$$ \sigma(t) = \inf{s \in T : s > t} $$ $$ \rho(t) = \sup{s \in T : s < t} $$ The first equation in the image is the definition of the lower semicontinuous envelope of the function s at time t. It is denoted by σ(t) and is defined as the greatest lower bound of all values of s that are greater than t. The second equation is the definition of the upper semicontinuous envelope of the function s at time t. It is denoted by ρ(t) and is defined as the least upper bound of all values of s that are less than t

In mathematics, the infimum (abbreviated inf) of a subset of a partially ordered set is the greatest element in that is less than or equal to each element of if such an element exists. In other words, it is the greatest element of that is lower or equal to the lowest element of . Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup) of a subset of a partially ordered set is the least element in that is greater than or equal to each element of if such an element exists. In other words, it is the least element of that is greater than or equal to the greatest element of . Consequently, the supremum is also referred to as the least upper bound (or LUB)

Time Series Library

GitHub - dream-faster/fold: 🪁 A fast Adaptive Machine Learning library for Time-Series, that lets you build, deploy and update composite models easily. An order of magnitude speed-up, combined with flexibility and rigour. A fast Adaptive Machine Learning library for Time-Series, that lets you build, deploy and update composite models easily. An order of magnitude speed-up, combined with flexibility and rigour. Fold

Adaptive back testing

As opposed to cross validation time series