Predictive maintenance for the heated hold-up tank

We present a numerical method to compute an optimal maintenance date for the test case of the heated hold-up tank. The system consists of a tank containing a fluid whose level is controlled by three components: two inlet pumps and one outlet valve. A thermal power source heats up the fluid. The failure rates of the components depends on the temperature, the position of the three components monitors the liquid level in the tank and the liquid level determines the temperature. Therefore, this system can be modeled by a hybrid process where the discrete (components) and continuous (level, temperature) parts interact in a closed loop. We model the system by a piecewise deterministic Markov process, propose and implement a numerical method to compute the optimal maintenance date to repair the components before the total failure of the system.Comment: arXiv admin note: text overlap with arXiv:1101.174

Two simple control policies for a multicomponent maintenance system

Control Systems;Maintenance;controle-systemen

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system

Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems

The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator

Coalescent simulation in continuous space:Algorithms for large neighbourhood size

Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail

Modeling of pipeline corrosion degradation mechanism with a Lévy Process based on ILI (In-Line) inspections

International audienceIn pipelines, one of the primary testing procedures used to identify the e↵ects and evolution of corrosion over time is through In-Line Inspections (ILI). ILI inspections provide detailed information regarding the inner and outer pipeline condition based on the remaining wall thickness. Based on this information, di↵erent approaches have been proposed to predict the degradation extent of the defects detected. However, these predictions are subject of uncertainties due to the inspection tool and the degradation process that poses some challenges for assessing an entire pipeline within the timespan between two inspections. To address this problem, ILI data was used to formulate a degradation model for steel-pipe degradation based on a Mixed Lévy Process. The model combines a Gamma and Compound Poisson Processes aimed for a better description of the degradation reported by the ILI data. The model seeks to estimate corrosion lifetime distribution and the mean time to failure (MTTF) more accurately. The model was tested on an actual segment of an oil pipeline, and the results have been used to support a preventive maintenance program

An aircraft sensor fault tolerant system

The design of a sensor fault tolerant system which uses analytical redundancy for the Terminal Configured Vehicle (TCV) research aircraft in a Microwave Landing System (MLS) environment was studied. The fault tolerant system provides reliable estimates for aircraft position, velocity, and attitude in the presence of possible failures in navigation aid instruments and onboard sensors. The estimates, provided by the fault tolerant system, are used by the automated guidance and control system to land the aircraft along a prescribed path. Sensor failures are identified by utilizing the analytic relationship between the various sensor outputs arising from the aircraft equations of motion