Jaime H. Ortega

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.

Identification of immersed obstacles via boundary measurements

We study the following inverse problem: an inaccessible rigid body D is immersed in a viscous fluid, in such a way that D plays the role of an obstacle around which the fluid is flowing in a greater bounded domain Ω, and we wish to determine D (i.e., its form and location) via boundary measurement on the boundary ∂Ω. Both for the stationary and the evolution problem, we show that under reasonable smoothness assumptions on Ω and D, one can identify D via the measurement of the velocity of the fluid and the Cauchy forces on some part of the boundary ∂Ω. We also show that the dependence of the Cauchy forces on deformations of D is analytic, and give some stability results for the inverse problem.

Fluid dynamics of submerged gas injection into liquid in a model of copper converter

We have numerically studied the fluid dynamic effects on water in a converter-shaped vessel of air injection from a submerged tuyere. The time dependent and three dimensional simulations of the bi-phase system were carried out using the volume of fluid (VOF) and the standard κ-e turbulence models implemented in the commercial solver Fluent. Experimental observation of the phenomena were carried out in a water tank. We have also calculated the standing waves on the surface of a liquid solving the wave equation for potential flow. We study the influence of air inlet velocity on bath dynamic which produced the most favorable results with respect to good mixing in the bath, and minimum splashing

On the detection of a moving obstacle in an ideal fluid by a boundary measurement

In this paper, we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in from the measurement of the velocity of the fluid on one part of the boundary. We show that when the obstacle is a ball, we may identify the position and the velocity of its centre of mass from a single boundary measurement. Linear stability estimates are also established by using shape differentiation techniques.

An example of ɛ-insensitizing controls for the heat equation with no intersecting observation and control regions*

Abstract This article is devoted to the ɛ-insensitizing controllability of the heat equation with disjoint control and observation regions. In the 1-D case and for symmetric regions a positive answer is obtained.

ON THE CONTROLLABILITY OF A COUPLED SYSTEM OF TWO KORTEWEG–DE VRIES EQUATIONS

This paper proves the local exact boundary controllability property of a nonlinear system of two coupled Korteweg–de Vries equations which models the interactions of weakly nonlinear gravity waves (see [10]). Following the method in [24], which combines the analysis of the linearized system and the Banachs fixed point theorem, the controllability problem is reduced to prove a nonstandard unique continuation property of the eigenfunctions of the corresponding differential operator.

Modeling of Brain Shift Phenomenon for Different Craniotomies and Solid Models

This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden models, and hyperelastic Mooney-Rivlin with 2- and 5-parameter models. A pressure on the brain surface at craniotomy region was applied to load the model. The models were solved with the finite elements package ANSYS. The predictions on stress and displacements were compared for three different craniotomies. The difference between the predictions of elastic solid model and a hyperelastic Ogden solid model of maximum brain displacement and maximum effective stress is relevant.

Suicide detection in Chile: proposing a predictive model for suicide risk in a clinical sample of patients with mood disorders

Objective: To analyze suicidal behavior and build a predictive model for suicide risk using data mining (DM) analysis. Methods: A study of 707 Chilean mental health patients (with and without suicide risk) was carried out across three healthcare centers in the Metropolitan Region of Santiago, Chile. Three hundred forty-three variables were studied using five questionnaires. DM and machine-learning tools were used via the support vector machine technique. Results: The model selected 22 variables that, depending on the circumstances in which they all occur, define whether a person belongs in a suicide risk zone (accuracy = 0.78, sensitivity = 0.77, and specificity = 0.79). Being in a suicide risk zone means patients are more vulnerable to suicide attempts or are thinking about suicide. The interrelationship between these variables is highly nonlinear, and it is interesting to note the particular ways in which they are configured for each case. The model shows that the variables of a suicide risk zone are related to individual unrest, personal satisfaction, and reasons for living, particularly those related to beliefs in one’s own capacities and coping abilities. Conclusion: These variables can be used to create an assessment tool and enables us to identify individual risk and protective factors. This may also contribute to therapeutic intervention by strengthening feelings of personal well-being and reasons for staying alive. Our results prompted the design of a new clinical tool, which is fast and easy to use and aids in evaluating the trajectory of suicide risk at a given moment.

ε-Insensitizing controls for pointwise observations of the heat equation

Abstract In this paper, we study the e -insensitizing controllability for the functional given by integrating in time the square of the solution of the heat equation in a finite number of points of the domain Ω⊂ R N , i.e., when the observation set is reduced to a finite set of points. We reduce the controllability problem to a unique continuation property for a cascade system of linear heat equations and we obtain a positive result in the case N ⩽3.

Stationary shapes for 2-d water-waves and hydraulic jumps

A hydraulic jump is a physical phenomenon commonly observed in nature such as in open channel flows or spillways and is dependent upon the relation between the initial upstream fluid speed and a critical speed characterized by a dimensionless number F known as the Froude number. In this paper we prove the existence of hydraulic jumps for stationary water-waves as a consequence of the existence of bifurcation branches of non-flat liquid interfaces originated from each of a sequence of upstream velocities F1 > F2 > ⋯ > Fr > ⋯ (Fr → 0 as r → ∞). We further establish explicitly, for F > 0, F≠Fr, r ∈ ℕ, the existence and uniqueness of the solution of a perfect, incompressible, irrotational free surface flow over a flat bottom, under the influence of gravity; as well as the corresponding hydraulic jump.