Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

Avoiding Overfitting in Inverse Modeling of Chloride Migration in Concrete

Inverse analysis for reactive transport of chlorides through concrete in the presence of electric field is presented. The model is solved using MATLAB’s built-in solvers “pdepe.m” and “ode15s.m”. The results from the model are compared with experimental measurements from accelerated migration test and a function representing the lack of fit is formed. This function is optimised with respect to varying amount of key parameters defining the model. Levenberg-Marquardt trust-region optimisation approach is employed. The paper presents a method by which the degree of inter-dependency between parameters and sensitivity (significance) of each parameter towards model predictions can be studied on models with or without clearly defined governing equations. Eigen value analysis of the Hessian matrix was employed to investigate and avoid over-parametrisation in inverse analysis. We investigated simultaneous fitting of parameters for diffusivity, chloride binding as defined by Freundlich isotherm (thermodynamic) and binding rate (kinetic parameter). Fitting of more than 2 parameters, simultaneously, demonstrates a high degree of parameter inter-dependency. This finding is significant as mathematical models for representing chloride transport rely on several parameters for each mode of transport (i.e., diffusivity, binding, etc.), which combined may lead to unreliable simultaneous estimation of parameters.

Modelling and estimating models of physician labour supply and productivity

Ma thèse s’intéresse aux politiques de santé conçues pour encourager l’offre de services de santé. L’accessibilité aux services de santé est un problème majeur qui mine le système de santé de la plupart des pays industrialisés. Au Québec, le temps médian d’attente entre une recommandation du médecin généraliste et un rendez-vous avec un médecin spécialiste était de 7,3 semaines en 2012, contre 2,9 semaines en 1993, et ceci malgré l’augmentation du nombre de médecins sur cette même période. Pour les décideurs politiques observant l’augmentation du temps d’attente pour des soins de santé, il est important de comprendre la structure de l’offre de travail des médecins et comment celle-ci affecte l’offre des services de santé. Dans ce contexte, je considère deux principales politiques. En premier lieu, j’estime comment les médecins réagissent aux incitatifs monétaires et j’utilise les paramètres estimés pour examiner comment les politiques de compensation peuvent être utilisées pour déterminer l’offre de services de santé de court terme. En second lieu, j’examine comment la productivité des médecins est affectée par leur expérience, à travers le mécanisme du "learning-by-doing", et j’utilise les paramètres estimés pour trouver le nombre de médecins inexpérimentés que l’on doit recruter pour remplacer un médecin expérimenté qui va à la retraite afin de garder l’offre des services de santé constant. Ma thèse développe et applique des méthodes économique et statistique afin de mesurer la réaction des médecins face aux incitatifs monétaires et estimer leur profil de productivité (en mesurant la variation de la productivité des médecins tout le long de leur carrière) en utilisant à la fois des données de panel sur les médecins québécois, provenant d’enquêtes et de l’administration. Les données contiennent des informations sur l’offre de travail de chaque médecin, les différents types de services offerts ainsi que leurs prix. Ces données couvrent une période pendant laquelle le gouvernement du Québec a changé les prix relatifs des services de santé. J’ai utilisé une approche basée sur la modélisation pour développer et estimer un modèle structurel d’offre de travail en permettant au médecin d’être multitâche. Dans mon modèle les médecins choisissent le nombre d’heures travaillées ainsi que l’allocation de ces heures à travers les différents services offerts, de plus les prix des services leurs sont imposés par le gouvernement. Le modèle génère une équation de revenu qui dépend des heures travaillées et d’un indice de prix représentant le rendement marginal des heures travaillées lorsque celles-ci sont allouées de façon optimale à travers les différents services. L’indice de prix dépend des prix des services offerts et des paramètres de la technologie de production des services qui déterminent comment les médecins réagissent aux changements des prix relatifs. J’ai appliqué le modèle aux données de panel sur la rémunération des médecins au Québec fusionnées à celles sur l’utilisation du temps de ces mêmes médecins. J’utilise le modèle pour examiner deux dimensions de l’offre des services de santé. En premierlieu, j’analyse l’utilisation des incitatifs monétaires pour amener les médecins à modifier leur production des différents services. Bien que les études antérieures ont souvent cherché à comparer le comportement des médecins à travers les différents systèmes de compensation,il y a relativement peu d’informations sur comment les médecins réagissent aux changementsdes prix des services de santé. Des débats actuels dans les milieux de politiques de santé au Canada se sont intéressés à l’importance des effets de revenu dans la détermination de la réponse des médecins face à l’augmentation des prix des services de santé. Mon travail contribue à alimenter ce débat en identifiant et en estimant les effets de substitution et de revenu résultant des changements des prix relatifs des services de santé. En second lieu, j’analyse comment l’expérience affecte la productivité des médecins. Cela a une importante implication sur le recrutement des médecins afin de satisfaire la demande croissante due à une population vieillissante, en particulier lorsque les médecins les plus expérimentés (les plus productifs) vont à la retraite. Dans le premier essai, j’ai estimé la fonction de revenu conditionnellement aux heures travaillées, en utilisant la méthode des variables instrumentales afin de contrôler pour une éventuelle endogeneité des heures travaillées. Comme instruments j’ai utilisé les variables indicatrices des âges des médecins, le taux marginal de taxation, le rendement sur le marché boursier, le carré et le cube de ce rendement. Je montre que cela donne la borne inférieure de l’élasticité-prix direct, permettant ainsi de tester si les médecins réagissent aux incitatifs monétaires. Les résultats montrent que les bornes inférieures des élasticités-prix de l’offre de services sont significativement positives, suggérant que les médecins répondent aux incitatifs. Un changement des prix relatifs conduit les médecins à allouer plus d’heures de travail au service dont le prix a augmenté. Dans le deuxième essai, j’estime le modèle en entier, de façon inconditionnelle aux heures travaillées, en analysant les variations des heures travaillées par les médecins, le volume des services offerts et le revenu des médecins. Pour ce faire, j’ai utilisé l’estimateur de la méthode des moments simulés. Les résultats montrent que les élasticités-prix direct de substitution sont élevées et significativement positives, représentant une tendance des médecins à accroitre le volume du service dont le prix a connu la plus forte augmentation. Les élasticitésprix croisées de substitution sont également élevées mais négatives. Par ailleurs, il existe un effet de revenu associé à l’augmentation des tarifs. J’ai utilisé les paramètres estimés du modèle structurel pour simuler une hausse générale de prix des services de 32%. Les résultats montrent que les médecins devraient réduire le nombre total d’heures travaillées (élasticité moyenne de -0,02) ainsi que les heures cliniques travaillées (élasticité moyenne de -0.07). Ils devraient aussi réduire le volume de services offerts (élasticité moyenne de -0.05). Troisièmement, j’ai exploité le lien naturel existant entre le revenu d’un médecin payé à l’acte et sa productivité afin d’établir le profil de productivité des médecins. Pour ce faire, j’ai modifié la spécification du modèle pour prendre en compte la relation entre la productivité d’un médecin et son expérience. J’estime l’équation de revenu en utilisant des données de panel asymétrique et en corrigeant le caractère non-aléatoire des observations manquantes à l’aide d’un modèle de sélection. Les résultats suggèrent que le profil de productivité est une fonction croissante et concave de l’expérience. Par ailleurs, ce profil est robuste à l’utilisation de l’expérience effective (la quantité de service produit) comme variable de contrôle et aussi à la suppression d’hypothèse paramétrique. De plus, si l’expérience du médecin augmente d’une année, il augmente la production de services de 1003 dollar CAN. J’ai utilisé les paramètres estimés du modèle pour calculer le ratio de remplacement : le nombre de médecins inexpérimentés qu’il faut pour remplacer un médecin expérimenté. Ce ratio de remplacement est de 1,2.

Advanced parametrical modelling of 24 GHz radar sensor IC packaging components

This paper deals with the development of an advanced parametrical modelling concept for packaging components of a 24 GHz radar sensor IC used in automotive driver assistance systems. For fast and efficient design of packages for system-in-package modules (SiP), a simplified model for the description of parasitic electromagnetic effects within the package is desirable, as 3-D field computation becomes inefficient due to the high density of conductive elements of the various signal paths in the package. By using lumped element models for the characterization of the conductive components, a fast indication of the design's signal-quality can be gained, but so far does not offer enough flexibility to cover the whole range of geometric arrangements of signal paths in a contemporary package. This work pursues to meet the challenge of developing a flexible and fast package modelling concept by defining parametric lumped-element models for all basic signal path components, e.g. bond wires, vias, strip lines, bumps and balls. © Author(s) 2011. CC Attribution 3.0 License.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Inverse Spectral Methods in Acoustic Normal Mode Velocimetry of High Reynolds Number Spherical Couette Flows

Experimental geophysical fluid dynamics often examines regimes of fluid flow infeasible for computer simulations. Velocimetry of zonal flows present in these regimes brings many challenges when the fluid is opaque and vigorously rotating; spherical Couette flows with molten metals are one such example. The fine structure of the acoustic spectrum can be related to the fluid’s velocity field, and inverse spectral methods can be used to predict and, with sufficient acoustic data, mathematically reconstruct the velocity field. The methods are to some extent inherited from helioseismology. This work develops a Finite Element Method suitable to matching the geometries of experimental setups, as well as modelling the acoustics based on that geometry and zonal flows therein. As an application, this work uses the 60-cm setup Dynamo 3.5 at the University of Maryland Nonlinear Dynamics Laboratory. Additionally, results obtained using a small acoustic data set from recent experiments in air are provided.

On The Use of Genetic Algorithms for Parameter Identification in Anaerobic Digestion Modelling

Anaerobic digestion (AD) of wastewater is a very interesting option for waste valorization, energy production and environment protection. It is a complex, naturally occurring process that can take place inside bioreactors. The capability of predicting the operation of such bioreactors is important to optimize the design and the operation conditions of the reactors, which, in part, justifies the numerous AD models presently available. The existing AD models are not universal, have to be inferred from prior knowledge and rely on existing experimental data. Among the tasks involved in the process of developing a dynamical model for AD, the estimation of parameters is one of the most challenging. This paper presents the identifiability analysis of a nonlinear dynamical model for a batch reactor. Particular attention is given to the structural identifiability of the model, which considers the uniqueness of the estimated parameters. To perform this analysis, the GenSSI toolbox was used. The estimation of the model parameters is achieved with genetic algorithms (GA) which have already been used in the context of AD modelling, although not commonly. The paper discusses its advantages and disadvantages.

A methodological approach for the performance optimization of transient seepage models through inverse analysis

The topic of the Ph.D project focuses on the modelling of the soil-water dynamics inside an instrumented embankment section along Secchia River (Cavezzo (MO)) in the period from 2017 to 2018 and the quantification of the performance of the direct and indirect simulations . The commercial code Hydrus2D by Pc-Progress has been chosen to run the direct simulations. Different soil-hydraulic models have been adopted and compared. The parameters of the different hydraulic models are calibrated using a local optimization method based on the Levenberg - Marquardt algorithm implemented in the Hydrus package. The calibration program is carried out using different types of dataset of observation points, different weighting distributions, different combinations of optimized parameters and different initial sets of parameters. The final goal is an in-depth study of the potentialities and limits of the inverse analysis when applied to a complex geotechnical problem as the case study. The second part of the research focuses on the effects of plant roots and soil-vegetation-atmosphere interaction on the spatial and temporal distribution of pore water pressure in soil. The investigated soil belongs to the West Charlestown Bypass embankment, Newcastle, Australia, that showed in the past years shallow instabilities and the use of long stem planting is intended to stabilize the slope. The chosen plant species is the Malaleuca Styphelioides, native of eastern Australia. The research activity included the design and realization of a specific large scale apparatus for laboratory experiments. Local suction measurements at certain intervals of depth and radial distances from the root bulb are recorded within the vegetated soil mass under controlled boundary conditions. The experiments are then reproduced numerically using the commercial code Hydrus 2D. Laboratory data are used to calibrate the RWU parameters and the parameters of the hydraulic model.

Geometrico-static modelling of continuum parallel robots

In this thesis, we explore three methods for the geometrico-static modelling of continuum parallel robots. Inspired by biological trunks, tentacles and snakes, continuum robot designs can reach confined spaces, manipulate objects in complex environments and conform to curvilinear paths in space. In addition, parallel continuum manipulators have the potential to inherit some of the compactness and compliance of continuum robots while retaining some of the precision, stability and strength of rigid-links parallel robots. Subsequently, the foundation of our work is performed on slender beam by applying the Cosserat rod theory, appropriate to model continuum robots. After that, three different approaches are developed on a case study of a planar parallel continuum robot constituted of two connected flexible links. We solve the forward and inverse geometrico-static problem namely by using (a) shooting methods to obtain a numerical solution, (b) an elliptic method to find a quasi-analytical solution, and (c) the Corde model to perform further model analysis. The performances of each of the studied methods are evaluated and their limits are highlighted. This thesis is divided as follows. Chapter one gives the introduction on the field of the continuum robotics and introduce the parallel continuum robots that is studied in this work. Chapter two describe the geometrico-static problem and gives the mathematical description of this problem. Chapter three explains the numerical approach with the shooting method and chapter four introduce the quasi-analytical solution. Then, Chapter five introduce the analytic method inspired by the Corde model and chapter six gives the conclusions of this work.

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

Optimizing fused deposition modelling: the impact of geometrical slicing parameters on mechanical properties

This comprehensive study explores the intricate world of 3D printing, with a focus on Fused Deposition Modelling (FDM). It sheds light on the critical factors that influence the quality and mechanical properties of 3D printed objects. Using an optical microscope with 40X magnification, the shapes of the printed beads is correlated to specific slicing parameters, resulting in a 2D parametric model. This mathematical model, derived from real samples, serves as a tool to predict general mechanical behaviour, bridging the gap between theory and practice in FDM printing. The study begins by emphasising the importance of geometric parameters such as layer height, line width and filament tolerance on the final printed bead geometry and the resulting theoretical effect on mechanical properties. The introduction of VPratio parameter (ratio between the area of the voids and the area occupied by printed material) allows the quantification of the variation of geometric slicing parameters on the improvement or reduction of mechanical properties. The study also addresses the effect of overhang and the role of filament diameter tolerances. The research continues with the introduction of 3D FEM (Finite Element Analysis) models based on the RVE (Representative Volume Element) to verify the results obtained from the 2D model and to analyse other aspects that affect mechanical properties and not directly observable with the 2D model. The study also proposes a model for the examination of 3D printed infill structures, introducing also an innovative methodology called “double RVE” which speeds up the calculation of mechanical properties and is also more computationally efficient. Finally, the limitations of the RVE model are shown and a so-called Hybrid RVE-based model is created to overcome the limitations and inaccuracy of the conventional RVE model and homogenization procedure on some printed geometries.

Gyrokinetic modelling of plasma transport and investigation on test particle dynamics

Turbulent plasmas inside tokamaks are modeled and studied using guiding center theory, applied to charged test particles, in a Hamiltonian framework. The equations of motion for the guiding center dynamics, under the conditions of a constant and uniform magnetic field and turbulent electrostatic field are derived by averaging over the fast gyroangle, for the first and second order in the guiding center potential, using invertible changes of coordinates such as Lie transforms. The equations of motion are then made dimensionless, exploiting temporal and spatial periodicities of the model chosen for the electrostatic potential. They are implemented numerically in Python. Fast Fourier Transform and its inverse are used. Improvements to the original Python scripts are made, notably the introduction of a power-law curve fitting to account for anomalous diffusion, the possibility to integrate the equations in two steps to save computational time by removing trapped trajectories, and the implementation of multicolored stroboscopic plots to distinguish between trapped and untrapped guiding centers. The post-processing of the results is made in MATLAB. The values and ranges of the parameters chosen for the simulations are selected based on numerous simulations used as feedback tools. In particular, a recurring value for the threshold to detect trapped trajectories is evidenced. Effects of the Larmor radius, the amplitude of the guiding center potential and the intensity of its second order term are studied by analyzing their diffusive regimes, their stroboscopic plots and the shape of guiding center potentials. The main result is the identification of cases anomalous diffusion depending on the values of the parameters (mostly the Larmor radius). The transitions between diffusive regimes are identified. The presence of highways for the super-diffusive trajectories are unveiled. The influence of the charge on these transitions from diffusive to ballistic behaviors is analyzed.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Respostas agudas de parâmetros biomecânicos à utilização de diferentes tamanhos de palmar no nado crawl

Universidade Estadual de Campinas . Faculdade de Educação Física

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.