A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turn "on" the control during a specific time-window and turn it "off" elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.Comment: 28 page

An investigation of hot forming quench process for AA6082 aluminium alloys

This thesis is concerned with the mechanical properties and microstructure evolution during the novel solution Heat treatment Forming cold die Quenching (HFQ) process. HFQ is a hot sheet forming technology which incorporates the forming and quenching stages to produce high strength and high precision Al-alloy sheet parts. The work in the thesis divided into three main sections: Firstly, viscoplastic behaviour of AA6082 at different deformation temperatures and strain rates was identified through analysis of a programme of hot tensile tests. Based on the results from the hot tensile tests, a set of unified viscoplastic-damage constitutive equations was developed and determined for AA6082, providing a good agreement with the experimental results. SEM tests were carried out to investigate the damage nucleation and failure features of the AA6082 during hot forming process and the results are discussed. Secondly, the viscoplastic-damage constitutive equations were implemented into the commercial software ABAQUS via the user defined subroutine VUMAT for the forming process simulation. An experimental programme was designed and testing facilities were established for the validation of the FE process modelling results. A fairly good agreement between the process simulation and the experimental results was achieved. This confirms that the established FE process simulation model can be used for hot stamping of AA6082 panel parts. Further process modelling work was carried out to identify the optimal forming parameters for a simplified representation of a panel part. Finally, a precipitation hardening model was developed to predict the post-ageing strength of AA6082 panel parts, having varying amounts of forming-induced plastic strain. The model was tested against results of experiments which were carried out to investigate the effect of pre-deformation on the ageing kinetics of AA6082. The model is shown to fit and can be used to explain changes in the strength of the material. This set of equations was implemented in the VUMAT, in combination with the viscoplastic damage constitutive equation set, to model the whole HFQ process. The FE model was tested with experimental ageing and hardness results providing good agreements, which are discussed in light of the future development of the HFQ process

3D direct and inverse solvers for eddy current testing of deposits in steam generator

We consider the inverse problem of estimating the shape profile of an unknown deposit from a set of eddy current impedance measurements. The measurements are acquired with an axial probe, which is modeled by a set of coils that generate a magnetic field inside the tube. For the direct problem, we validate the method that takes into account the tube support plates, highly conductive part, by a surface impedance condition. For the inverse problem, finite element and shape sensitivity analysis related to the eddy current problem are provided in order to determine the explicit formula of the gradient of a least square misfit functional. A geometrical-parametric shape inversion algorithm based on cylindrical coordinates is designed to improve the robustness and the quality of the reconstruction. Several numerical results are given in the experimental part. Numerical experiments on synthetic deposits, nearby or far away from the tube, with different shapes are considered in the axisymmetric configuration.Comment: 3

Thermodynamic analysis of indirect injection diesel engine operation

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Shear Strength of Fiber Reinforced Concrete (FRC) Beams without Stirrups

This paper presents the results of twelve shear tests carried out on simply supported rectangular beams, with a shear span to depth ratio (a/d) of 2.4, under a single concentrated load. Six of the beams contained conventional stirrups and six beams were reinforced with steel fibers as web reinforcement. The parameters were: the effect of fiber volume content (0, 0.5, 1.0, and 1.5%), fiber type (end-hooked or corrugated), and the presence of minimum stirrups. The beam span, beam dimensions, shear span to depth ratio (a/d), and percentage of longitudinal reinforcement were all kept constant. Beam deflection, steel strains, crack propagation, and failure modes were recorded for all the tested beams. The test results showed that the stress at shear cracking and the ultimate shear stress increased with increasing the fiber volume content. When steel fibers with a content of 1.5% were added to the beams with minimum stirrups, the brittle shear failure was changed to ductile flexure failure. The test results were used to evaluate existing empirical equations estimating the shear strength of steel fiber-reinforced concrete beams without stirrups. The evaluation indicated that the equations proposed by Narayanan and Darwish 1987 and Kara 2013 provided the most accurate estimation when compared to the test results

Parareal in time intermediate targets methods for optimal control problem

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.Comment: 14 page

A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements

This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified parametrization of the geometry adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell's equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. Numerical experiments are presented to illustrate the convergence and the efficiency of the method