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A note on trust-region radius update ; Delhez, Eric in SIAM Journal on Optimization (2005), 16(2), 548-562 In classical trust-region optimization algorithms, the radius of the trust region is reduced, kept constant, or enlarged after, respectively, unsuccessful, successful, and very successful iterations. We ... [more ▼] In classical trust-region optimization algorithms, the radius of the trust region is reduced, kept constant, or enlarged after, respectively, unsuccessful, successful, and very successful iterations. We propose here to re. ne the empirical rules used for this update by the definition of a new set of iterations that we call "too successful iterations." At such iterations, a large reduction of the objective function is obtained despite a crude local approximation of the objective function; the trust region is thus kept nearly constant instead of being enlarged. The new update rules preserve the strong convergence property of traditional trust-region methods. They can also be generalized to define a self-adaptive trust-region algorithm along the lines introduced by Hei [J. Comput. Math., 21 (2003), pp. 229-236]. Numerical experiments carried out on 70 unconstrained problems from the CUTEr collection demonstrate the positive impact of the modified update strategy on the efficiency and robustness of quasi-Newton variants of a trust-region solver, when BFGS or SR1 updates of the approximation of the Hessian matrix are carried at all iterations. [less ▲] Detailed reference viewed: 63 (9 ULg)Influence of the Aral Sea negative water balance on its seasonal circulation patterns: use of a 3D hydrodynamic model Sirjacobs, Damien ; Grégoire, Marilaure ; Delhez, Eric et al in Journal of Marine Systems (2004), 47(1-4), 51-66 A 3D hydrodynamic model of the Aral Sea was successfully implemented to address the complex hydrodynamic changes induced by the combined effect of hydrologic and climatic change in the Aral region. The ... [more ▼] A 3D hydrodynamic model of the Aral Sea was successfully implemented to address the complex hydrodynamic changes induced by the combined effect of hydrologic and climatic change in the Aral region. The first barotropic numerical experiments allowed us to produce a comparative description of the mean general seasonal circulation patterns corresponding to the original situation (1956-1960) and of the average situation for the period from 1981 to 1985, a very low river flow period. The dominant anticyclonic circulation suggested by our seasonal simulation is in good agreement with previous investigations. In addition. this main anticyclonic gyre was shown to be stable and clearly established from February to September, while winter winds led to another circulation scenario. In winter, the main anticyclonic gyre was considerably limited, and cyclonic circulations appeared in the deep western basin and in the northeast of the shallow basin. In contrast, stronger anticyclonic circulation was observed in the Small Aral Sea during winter. As a consequence of the 10-m sea level drop observed between the two periods considered, the 1981-1985 simulation suggests an intensification of seasonal variability. Total water transport of the main gyre was reduced with sea level drop by a minimum of 30% in May and up to 54% in September. Before 1960, the study of the net flows through Berg and Kokaral Straits allowed us to evaluate the component of water exchange between the Small and the Large Seas linked with the general anticyclonic circulation around Kokaral Island. This exchange was lowest in summer (with a mean anticyclonic exchange of 222 m(3)/s for July and August), highest in fall and winter (with a mean value of 1356 m(3)/s from September to February) and briefly reversed in the spring (mean cyclonic circulation of 316 m(3)/s for April and May). In summer, the water exchange due to local circulation at the scale of each strait was comparatively more important because net flows through the straits were low. After about 20 years of negative water balance, the western Kokaral Strait was dried up and the depth of Berg Strait was reduced from 15 to 5 m. Simulation indicated a quasi-null net transport, except during the seasonal modification of the circulation pattern, in February and October. A limited, but stable, water exchange of about 100 m(3)/s remained throughout the year, as a result of the permanent superposition of opposite currents. (C) 2004 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 671 (41 ULg)The age as a diagnostic of the dynamics of marine ecosystem models Delhez, Eric ; ; in Ocean Dynamics (2004), 54(2), 221-231 The constituent-oriented age theory (CAT) worked out by Delhez et al. (1999) is a flexible tool that can be applied to diagnose complex models. It is shown here how this can be used to quantify the pace ... [more ▼] The constituent-oriented age theory (CAT) worked out by Delhez et al. (1999) is a flexible tool that can be applied to diagnose complex models. It is shown here how this can be used to quantify the pace at which an ecosystem model works. At the cost of the introduction of one additional evolution equation for each compartment of the ecosystem model, the mean age of the biological material forming these compartments can be computed. The information obtained in this way complements the information provided by the concentration data; while the latter measures the standing stocks, the former provides an integrated assessment of the interaction rates and matter fluxes. The benefits of the method are demonstrated with a simple Lotka-Volterra system and a one-dimensional vertical model of the nitrogen cycle in the Ligurian Sea. The theory can be used to study the biological compartments individually or the ecosystem as a whole. In particular, the age is a valuable tool to quantify the overall cycling rate of nitrogen in the food web. [less ▲] Detailed reference viewed: 37 (7 ULg)Variability of shelf-seas hydrodynamic models: lessons from the NOMADS2 project Delhez, Eric ; ; et al in Journal of Marine Systems (2004), 45(1-2), 39-53 Model simulations at the seasonal time scale are often lacking in any real assessment of the associated error bounds. We use here the results of nine three-dimensional hydrodynamic models covering (at ... [more ▼] Model simulations at the seasonal time scale are often lacking in any real assessment of the associated error bounds. We use here the results of nine three-dimensional hydrodynamic models covering (at least) the Southern and Central North Sea to investigate the range of model variability and model errors. The models are run as they are, i.e. with their usual grid, model domain, equation formulation and numerical details, but in a consistent framework-bathymetry, boundary and initial conditions, meteorological forcing functions interpolated from a common data set-. While the responses of the models are clearly qualitatively similar, large quantitative differences do occur. These differences are often of the same order of magnitude as both the ensemble mean and the sensitivity of the individual results to critical parameters. The direct comparison of the results with measurements from the North Sea Project provides a quantification of the model errors for the salinity and temperature distributions. Using the cost function approach, it is shown that the mean errors (for all the models and all seasons) reach about 70% of the natural variability for the temperature and 90% for the salinity. These errors are larger in summer, when a stratification develops over the Central and Northern North Sea, than in winter. No single model parameter (spatial resolution, turbulence closure scheme, model domain, etc.) can explain the different behaviours of the models. (C) 2003 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 34 (7 ULg)Tracer Methods in Geophysical Fluid Dynamics Delhez, Eric ; Book published by Elsevier Science (2004) Detailed reference viewed: 21 (2 ULg)Structural optimisation of steel frames for industrial applications ; Degée, Hervé ; Habraken, Anne et al in Proceedings of the Inverse Problems Design and Optimization Symposium (2004) The paper reports the first results of a work carried out in close collaboration between Astron Buildings SA, a manufacturer of industrial steel buildings, and different groups of civil engineers and ... [more ▼] The paper reports the first results of a work carried out in close collaboration between Astron Buildings SA, a manufacturer of industrial steel buildings, and different groups of civil engineers and mathematicians of the University of Liège to develop an automatic design method for structures with tapered members. This research aims at improving the current method of trialerror followed by experienced engineers to optimize the frames constrained by a chosen national construction code and the technological constraints of the producer. The main benefit of this collaboration arises through the application of a mathematical algorithm based on the sequential quadratic programming method (SQP) in order to reduce, in the first step, the weight of the building, under the great number of constraints. The second step, not yet started, will be devoted to the minimization of the real cost of the frame. This report introduces the first results of this industrial application. [less ▲] Detailed reference viewed: 132 (19 ULg)Residence time in a semi-enclosed domain from the solution of an adjoint problem Delhez, Eric ; ; in Estuarine Coastal & Shelf Science (2004), 61(4), 691-702 The residence time measures the time spent by a water parcel or a pollutant in a given water body and is therefore a widely used concept in environmental studies. While many previous studies rely on ... [more ▼] The residence time measures the time spent by a water parcel or a pollutant in a given water body and is therefore a widely used concept in environmental studies. While many previous studies rely on severe hypotheses (assuming stationarity of the flow and/or neglecting diffusion) to evaluate the residence time, the paper introduces a general method for computing the residence time and/or the mean residence time without such simplifying hypotheses. The method is based on the resolution of an adjoint advection-diffusion problem and is therefore primarily meant to be used with numerical models. The method and its implications are first introduced using a simplified one-dimensional analytical model. The approach is then applied to the diagnostic of the three-dimensional circulation on the Northwest European Continental Shelf. (C) 2004 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 58 (18 ULg)Symmetry and asymmetry of water ages in a one-dimensional flow ; Delhez, Eric in Journal of Marine Systems (2004), 48(1-4), 61-66 Hall and Haine [J. Mar. Syst., in press] briefly addressed the problem of estimating the age of irreducible fluid elements or water parcels in a one-dimensional flow with constant velocity and diffusivity ... [more ▼] Hall and Haine [J. Mar. Syst., in press] briefly addressed the problem of estimating the age of irreducible fluid elements or water parcels in a one-dimensional flow with constant velocity and diffusivity. Herein further developments are achieved on this subject. The age of every water parcel is set to zero at the moment it passes through the point x = 0, where x is an appropriate space coordinate. As time progresses, the age of the water is seen to increase unboundedly upstream of the point x = 0, and tend to the steady-state value \x/u\ downstream of the point x = 0, where a is the water velocity. By contrast, the age of the water parcels that have touched at least once the point x = 0 is symmetric with respect to the point x = 0 is smaller than the water age at any tune and position, and tends to \x/u\ as time progresses. Asymptotic expansions are derived for large times. (C) 2004 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 31 (12 ULg)A trust region algorithm for automatic identification of elasto-viscoplastic model parameters in metallurgical finite element model Jeunechamps, Pierre-Paul ; ; Duysinx, Pierre et al in Steel Grips 2 (2004), Supplement Metal Forming 2004 Simulation of manufacturing processes, here metal forming, has made major progresses during the last years. The virtual simulation of the manufacturing process being now quite well established, a natural ... [more ▼] Simulation of manufacturing processes, here metal forming, has made major progresses during the last years. The virtual simulation of the manufacturing process being now quite well established, a natural step ahead consists in trying to find automatic procedures to optimize it. Another perspective is also to take care of the influence of the manufacturing constraints upon the design, which is the long term objective of the present research project. It aims at optimizing the design subject to both service constraints (stiffness and strength) and manufacturing constraints. A preliminary stage is to be able to build high fidelity digital models. Complex models require more and more material parameters for behavior laws (e.g. material constitutive and friction laws), which have to be identified numerically from experimental data. In this material parameter identification process, three steps can be identified. At first, an experimental testing is carried out. The second step consists in building a simulation model of the experiment. Finally, the unknown model parameters are determined to match the experimental data. A standard identification procedure consists in minimizing a given norm (here the Euclidean norm) of the error between the model predictions and the experimental results. Even if the identification problem is generally quasi-unconstrained, it has the same complexity as structural optimization problems because of the highly nonlinear and implicit character of the functions, which is especially amplified by the large deformation simulation analysis. In this paper, we use an approach of elastoplastic calculation by finite elements combined with two optimization algorithms: a Levenberg-Marquardt algorithm, which is rather classical in the literature for solving identification problems (see [2]) and a trust-region one (see [1]), which is a rather novel approach at least for structural problems. The results obtained with these two methods are then compared and discussed on two test cases. The first application is an academic test case to validate the identification method. The second one, the compression of a cylinder, takes into account an actual experiment. In this application, the material is assumed to be elasto-viscoplastic and described by a Norton-Hoff behavior law and an isotropic strain hardening law. The parameters to be identified are the coefficients of the Norton-Hoff law. [less ▲] Detailed reference viewed: 50 (9 ULg)Identification of elastoplastic model in large deformation problems Jeunechamps, Pierre-Paul ; Walmag, Jérôme ; Delhez, Eric et al in Cinquini, Carlo (Ed.) Proceedings of the 5th World Congress of Structural and Multidisciplinary Optimization WCSMO5 (2003, May) This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the ... [more ▼] This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the classic Levenberg-Marquardt algorithm. The second one is a trust-region algorithm based on a quadratic model. The two algorithms are compared on two cases, one of them being an actual experiment. [less ▲] Detailed reference viewed: 85 (13 ULg)Global water and salt budget of the Aral Sea from 1960 to 1991. Sirjacobs, Damien ; Grégoire, Marilaure ; Delhez, Eric et al Conference (2003, May) Focusing on the global water and salt budget of the Aral sea from 1960 till 1991, a compilation of data available in the litterature is analysed with simple models and compared to the measured evolution ... [more ▼] Focusing on the global water and salt budget of the Aral sea from 1960 till 1991, a compilation of data available in the litterature is analysed with simple models and compared to the measured evolution of the sea. [less ▲] Detailed reference viewed: 21 (4 ULg)Influence of the Aral Sea negative water balance on its seasonal circulation : use of a 3D hydrodynamic model Sirjacobs, Damien ; Grégoire, Marilaure ; Delhez, Eric et al Conference (2003, May) Detailed reference viewed: 20 (2 ULg)Influence of the Aral Sea negative water balance on its seasonal circulation and ventilation patterns : use of a 3D hydrodynamic model Sirjacobs, Damien ; Grégoire, Marilaure ; Delhez, Eric et al in Geophysical Research Abstracts (2003, April), 5(09052), 2003509052 Within the context of the EU INCO-COPERNICUS program "Desertification in the Aral Sea Region: A study of the Natural and Anthropogenic Impacts" (Contract IAC2-CT-2000-10023), a large-scale 3D hydrodynamic ... [more ▼] Within the context of the EU INCO-COPERNICUS program "Desertification in the Aral Sea Region: A study of the Natural and Anthropogenic Impacts" (Contract IAC2-CT-2000-10023), a large-scale 3D hydrodynamic model was adapted to address specifically the macroscale processes affecting the Aral Sea water circulation and ventilation. The particular goal of this research is to simulate the effect of lasting negative water balance on the 3D seasonal circulation, temperature, salinity and water-mixing fields of the Aral Sea. The original Aral Sea seasonal hydrodynamism is simulated with the average seasonal forcings corresponding to the period from 1956 to 1960. This first investigation concerns a period of relative stability of the water balance, before the beginning of the drying process. The consequences of the drying process on the hydrodynamic of the Sea will be studied by comparing this first results with the simulation representing the average situation for the years 1981 to 1985, a very low river flow period. For both simulation periods, the forcing considered are the seasonal fluctuations of wind fields, precipitation, evaporation, river discharge and salinity, cloud cover, air temperature and humidity. The meteorological forcings were adapted to the common optimum one-month temporal resolution of the available data sets. Monthly mean kinetic energy flux and surface tensions were calculated from daily ECMWF wind data. Monthly in situ precipitation, surface air temperature and humidity fields were interpolated from data obtained from the Russian Hydrological and Meteorological Institute. Monthly water discharge and average salinity of the river water were considered for both Amu Darya and Syr Darya river over each simulation periods. The water mass conservation routines allowed the simulation of a changing coastline by taking into account local drying and flooding events of particular grid points. Preliminary barotropic runs were realised (for the 1951-1960 situation, before drying up began) in order to get a first experience of the behaviour of the hydrodynamic model. These first runs provide results about the evolution of the following state variables: elevation of the sea surface, 3D fields of vertical and horizontal flows, 2D fields of average horizontal flows and finally the 3D fields of turbulent kinetic energy. The mean seasonal salinity and temperature fields (in-situ data gathered by the Russian Hydrological and Meteorological Institute) are available for the two simulated periods and will allow a first validation of the hydrodynamic model. Various satellites products were identified, collected and processed in the frame of this research project and will be used for the validation of the model outputs. Seasonal level changes measurements derived from water table change will serve for water balance validation and sea surface temperature for hydrodynamics validation. [less ▲] Detailed reference viewed: 46 (8 ULg)Identification of elastoplastic model parameters in large deformation problems using gamma methods Jeunechamps, Pierre-Paul ; ; et al in Proceedings of the 5th World Congress on Structural and Multidisciplinary Optimization (2003) This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the ... [more ▼] This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the classic Levenberg-Marquardt algorithm. The second one is a trust-region algorithm based on a quadratic model. The two algorithms are compared on two cases, one of them being an actuel experiment. [less ▲] Detailed reference viewed: 79 (17 ULg)Mécanique Rationnelle - Théorie et Applications Delhez, Eric Book published by Etienne Riga (2003) Detailed reference viewed: 53 (4 ULg)A spline interpolation technique that preserves mass budgets Delhez, Eric in Applied Mathematics Letters (2003), 16(1), 17-26 The usual practice of forcing budget models by linear interpolations of mean data does not produce a forcing whose mean is the data value required. The usual third-order spline is modified into a fourth ... [more ▼] The usual practice of forcing budget models by linear interpolations of mean data does not produce a forcing whose mean is the data value required. The usual third-order spline is modified into a fourth-order spline, called mc-spline, to cope with this issue. The technique provides a smooth and faithful continuous interpolation of the original data that is well suited for its graphical representations or for the forcing of numerical models. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲] Detailed reference viewed: 77 (16 ULg)A note on the age of radioactive tracers Delhez, Eric ; ; Mouchet, Anne et al in Journal of Marine Systems (2003), 38(3-4), 277-286 wThe age of a water mass is often estimated experimentally using the radio-age computed from the distribution of a radioactive tracer (radiocarbon, helium-tritium). Deleersnijder et al. [J. Mar. Syst. 28 ... [more ▼] wThe age of a water mass is often estimated experimentally using the radio-age computed from the distribution of a radioactive tracer (radiocarbon, helium-tritium). Deleersnijder et al. [J. Mar. Syst. 28 (2001) 229.] have shown that the radio-age underestimates the age of the water and is larger than the age of the radioactive tracer used for its evaluation. This result is generalized here to radio-ages computed from the ratio of two radioactive tracers. The differences between the different ages are also studied analytically and numerically as functions of the decay rate of the radioactive tracers. For small decay rates, the difference between the age of the water mass and the radio-age is shown to be proportional to the decay rate. It depends also on the level of mixing in the system; even radioactive tracers with small decay rates can provide poor estimates of the age of the water mass in a strongly diffusive flow. For small half lives, both the radio-age and the age of radioactive tracers decrease as the inverse of the square root of the decay rate. The same analysis applies to some extent to the estimates of the age of a water mass from stable tracers with known time dependent sources (e.g. chloroflurocarbons). (C) 2002 Elsevier Science B.V. All rights reserved. [less ▲] Detailed reference viewed: 36 (16 ULg)CAT, The Constituent-oriented Age Theory, and its application to marine flows ; Delhez, Eric ; Mouchet, Anne et al Conference (2002, May) Detailed reference viewed: 41 (1 ULg)The concept of age in marine modelling II. Concentration distribution function in the English Channel and the North Sea Delhez, Eric ; in Journal of Marine Systems (2002), 31(4), 279-297 The age of seawater and the age of real or idealized tracers are often used as diagnostic tools to better understand complex hydrodynamic flows. In most studies, the focus is on some averages of the ages ... [more ▼] The age of seawater and the age of real or idealized tracers are often used as diagnostic tools to better understand complex hydrodynamic flows. In most studies, the focus is on some averages of the ages of the different particles making up a water parcel. The theory developed in Delhez et al. [Ocean Modell. I (1999) 17] and Deleersnijder et al. [J. Mar. Syst. 28 (2001) 229] provides, however, a more detailed description of the distribution of the ages of these particles through the so-called concentration distribution function. In this paper, the numerical aspects of the resolution of the evolution equation for the concentration distribution function in a five-dimensional space (time x 3D space x age dimension) are developed. Evolution equations for the moments of the concentration distribution function up to any order are also derived. A real case application of this theory to the simulation of the advection-dispersion of tracers (technetium-99) discharged at the nuclear fuel reprocessing plant of Cap de La Hague is described. The comparison of the results with those from previous studies demonstrates the advantages of the new method for the computation of the mean age. In particular, the method provides a detailed description of the temporal variations of the mean age only. The analysis of the full concentration distribution function and of its basic statistics shows that the standard deviation of the age of the different particles is far from negligible and should never be overlooked when analyzing age fields. A simplified analytical example suggests that the standard deviation of the age distribution is a measure of the integrated diffusion undergone by the tracer along its path from the source to the observation point. (C) 2002 Elsevier Science B.V All rights reserved. [less ▲] Detailed reference viewed: 39 (10 ULg)Transient behaviour of water ages in the World Ocean ; Mouchet, Anne ; Delhez, Eric et al in Mathematical & Computer Modelling (2002), 36(1-2), 121-127 The transient behaviour of the age of the water and that of the surface water is studied in the World Ocean. At any time and position, the age of the water, the age and the concentration of the surface ... [more ▼] The transient behaviour of the age of the water and that of the surface water is studied in the World Ocean. At any time and position, the age of the water, the age and the concentration of the surface water are seen to obey a simple algebraic relation. The latter is illustrated by means of results of a three-dimensional World Ocean model and the analytical solution of an idealised, purely-diffusive, one-dimensional problem. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲] Detailed reference viewed: 37 (12 ULg) |
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