Framework for Synthesis of Hybrid Automata from Time Series with Time- or State-Dependent Switching Conditions
Authors
Hansen, Jakob Østenkjær ; Kristensen, Alex Immerkær
Term
4. term
Education
Publication year
2023
Submitted on
2023-06-08
Pages
22
Abstract
Many systems combine sudden switches with continuously changing variables. A hybrid automaton is a mathematical model for such systems: it joins a graph of discrete modes (also called locations or states) with continuous dynamics described by differential equations. This thesis introduces an offline learning algorithm that automatically builds a hybrid automaton from time-series data (measurements over time). The algorithm has three stages: segmenting the data, learning the model’s structure (modes and transitions), and identifying both the continuous dynamics within each mode and the conditions that trigger switches. We propose two ways to determine switching conditions: a value-based method for stationary time series (without long-term trends) and a time-based method for time series that exhibit trends. In evaluation, the algorithm learned simple models with accurate graph structure and appropriate dynamics from stationary data using variable-based conditions, and from non-stationary, trending data using timed conditions. However, performance degrades when change-point detection fails to segment the series correctly or when different locations have dynamics that are too similar. In those cases, segments may be misidentified, and the structure learner may be unable to separate locations and to assign segments to the correct locations.
Mange systemer blander pludselige skift med kontinuerlige ændringer. En hybridautomat er en matematisk model til sådanne systemer: den kombinerer en graf over diskrete tilstande (ofte kaldet locations) med kontinuerlig dynamik beskrevet ved differentialligninger. I denne afhandling præsenterer vi en offline-læringsalgoritme, der automatisk konstruerer en hybridautomat ud fra tidsserier (målinger over tid). Algoritmen omfatter tre trin: at segmentere tidsserien, at lære modellens struktur (tilstande og overgange) og at finde både den kontinuerlige dynamik i hver tilstand og de betingelser, der udløser skift mellem tilstande. Vi introducerer to metoder til at bestemme skiftebetingelser: en værdibaseret metode til stationære tidsserier (uden langsigtede trends) og en tidsbaseret metode til tidsserier med trends. Evalueringen viser, at algoritmen kan lære enkle modeller med korrekt grafstruktur og passende dynamik fra stationære data ved hjælp af variablebetingelser, og fra ikke-stationære, trendende data ved hjælp af tidsbetingelser. Ydelsen er dog dårlig, hvis detektionen af skiftpunkter ikke segmenterer dataene korrekt, eller hvis dynamikken i forskellige tilstande er for ens. I sådanne tilfælde kan segmenter blive fejlidentificeret, og strukturindlæringen kan have svært ved at skelne tilstande og knytte segmenter til de rette tilstande.
[This apstract has been rewritten with the help of AI based on the project's original abstract]
Keywords