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Probabilistic State Estimation of Timed Probabilistic Discrete Event Systems via Artificial Neural Networks [Draft Version]

Omar Amri, Carla Seatzu, Alessandro Giua, Dimitri Lefebvre

TL;DR

This work tackles state estimation for Timed Probabilistic DES without explicit models by learning from execution data. It introduces two FFN-based approaches: estimating state probabilities at each new observation and updating them at each clock tick, integrating both logical and temporal features into the input. Empirical results show the observation-based estimator achieving about 80% accuracy (training/validation ~0.80/0.79; test ~0.80) with MAE around 1.5% when compared to a model-based estimator, while the time-based estimator reaches about 73% test accuracy with MAE ~5.15%, demonstrating competitive viability. The study demonstrates that data-driven neural networks can recover state dynamics in TP DES settings and points to future work on deeper architectures and post-processing to further improve reliability and applicability across varying timing distributions.

Abstract

This paper is about the state estimation of timed probabilistic discrete event systems. The main contribution is to propose general procedures for developing state estimation approaches based on artificial neural networks. It is assumed that no formal model of the system exists but a data set is available, which contains the history of the timed behaviour of the systems. This dataset will be exploited to develop a neural network model that uses both logical and temporal information gathered during the functioning of the system as inputs and provides the state probability vector as output. Two main approaches are successively proposed (i) state estimation of timed probabilistic discrete event systems over observations: in this case the state estimate is reconstructed at the occurrence of each new observation; (ii) state estimation of timed probabilistic discrete event systems over time: in this case the state estimate is reconstructed at each clock time increment. For each approach, the paper outlines the process of data preprocessing, model building and implementation. This paper not only proposes groundbreaking approaches but also opens the door to further exploitation of artificial neural networks for the benefit of discrete event systems.

Probabilistic State Estimation of Timed Probabilistic Discrete Event Systems via Artificial Neural Networks [Draft Version]

TL;DR

This work tackles state estimation for Timed Probabilistic DES without explicit models by learning from execution data. It introduces two FFN-based approaches: estimating state probabilities at each new observation and updating them at each clock tick, integrating both logical and temporal features into the input. Empirical results show the observation-based estimator achieving about 80% accuracy (training/validation ~0.80/0.79; test ~0.80) with MAE around 1.5% when compared to a model-based estimator, while the time-based estimator reaches about 73% test accuracy with MAE ~5.15%, demonstrating competitive viability. The study demonstrates that data-driven neural networks can recover state dynamics in TP DES settings and points to future work on deeper architectures and post-processing to further improve reliability and applicability across varying timing distributions.

Abstract

This paper is about the state estimation of timed probabilistic discrete event systems. The main contribution is to propose general procedures for developing state estimation approaches based on artificial neural networks. It is assumed that no formal model of the system exists but a data set is available, which contains the history of the timed behaviour of the systems. This dataset will be exploited to develop a neural network model that uses both logical and temporal information gathered during the functioning of the system as inputs and provides the state probability vector as output. Two main approaches are successively proposed (i) state estimation of timed probabilistic discrete event systems over observations: in this case the state estimate is reconstructed at the occurrence of each new observation; (ii) state estimation of timed probabilistic discrete event systems over time: in this case the state estimate is reconstructed at each clock time increment. For each approach, the paper outlines the process of data preprocessing, model building and implementation. This paper not only proposes groundbreaking approaches but also opens the door to further exploitation of artificial neural networks for the benefit of discrete event systems.

Paper Structure

This paper contains 14 sections, 15 equations, 13 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Timed Probabilistic Discrete Event Systems
  4. Neural Networks
  5. Problem Statement
  6. Assumptions
  7. Cases studied, model development and implementation
  8. State Estimation of TPDES over Observations
  9. Data Description and Data Preprocessing
  10. Model Building and Implementation
  11. State Estimation of TPDES over Time
  12. Data Description and Data Preprocessing
  13. Model Building and Implementation
  14. Conclusions and Perspectives

Figures (13)

  • Figure 1: Two examples of TPDES modeled by LTPA.
  • Figure 2: A simple Neural Network.
  • Figure 4: Model implementation
  • Figure 5: The training and validation accuracy (TPDES state estimation over observations).
  • Figure 6: The probability of state $s_1$
  • ...and 8 more figures

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Remark 1
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5