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Data-driven models for fault detection using kernel PCA: A water distribution system case study

Adam Nowicki, Michał Grochowski, Kazimierz Duzinkiewicz (2012)

International Journal of Applied Mathematics and Computer Science

Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system's framework is followed by...

Decomposition of large-scale stochastic optimal control problems

Kengy Barty, Pierre Carpentier, Pierre Girardeau (2010)

RAIRO - Operations Research

In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework...

Decomposition of vibration signals into deterministic and nondeterministic components and its capabilities of fault detection and identification

Tomasz Barszcz (2009)

International Journal of Applied Mathematics and Computer Science

The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature...

Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

Jiangrong Li, Junmin Li, Zhile Xia (2011)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with the problem of stochastic stability and generalized H₂ control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent...

Design of a model following control system for nonlinear descriptor system in discrete time

Shujing Wu, Shigenori Okubo, Dazhong Wang (2008)

Kybernetika

A model following control system (MFCS) can output general signals following the desired ones. In this paper, a method of nonlinear MFCS will be extended to be a nonlinear descriptor system in discrete time. The nonlinear system studied in this paper has the property of norm constraint | | f ( v ( k ) ) | | ≤ α + β | | v ( k ) | | γ , where α ≥ 0 , β ≥ 0 , 0 ≤ γ < 1 . In this case, a new criterion is proposed to ensure the internal states be stable.

Design of an adaptive controller of LQG type: spline-based approach

Tatiana V. Guy, Miroslav Kárný (2000)

Kybernetika

The paper presents an alternative approach to the design of a hybrid adaptive controller of Linear Quadratic Gaussian (LQG) type for linear stochastic controlled system. The approach is based on the combination standard building blocks of discrete LQG adaptive controller with the non-standard technique of modelling of a controlled system and spline approximation of involved signals. The method could be of interest for control of systems with complex models, in particular distributed parameter systems....

Detection and accommodation of second order distributed parameter systems with abrupt changes in input term: stability and adaptation

Michael A. Demetriou, Marios M. Polycarpou (1998)

Kybernetika

In this note, we employ nonlinear on-line parameter estimation methods based on adaptive neural network approximators for detecting changes due to actuator faults in a class of second order distributed parameter systems. The motivating example is a cantilevered beam actuated via a pair of piezoceramic patches. We examine changes in the control input term, which provide a simple and practical model of actuator failures. Using Lyapunov redesign methods, a stable learning scheme for fault diagnosis...

Determination of the initial stress tensor from deformation of underground opening in excavation process

Josef Malík, Alexej Kolcun (2022)

Applications of Mathematics

A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the...

Determination of the initial stress tensor from deformation of underground opening -- theoretical background and applications

Malík, Josef, Kolcun, Alexej (2023)

Programs and Algorithms of Numerical Mathematics

In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number of a certain...

Deterministic Markov Nash equilibria for potential discrete-time stochastic games

Alejandra Fonseca-Morales (2022)

Kybernetika

In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games and the stochastic...

Deterministic optimal policies for Markov control processes with pathwise constraints

Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma (2012)

Applicationes Mathematicae

This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to...

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