Socioeconomic Evaluation and Ranking of Infrastructure Projects

For most of the last century, the role of private and public sectors in the infrastructure projects were clear. For instance, public authorities were generally in charge of financing and building new infrastructures. Over the last decade, that position has begun to change. Faced with pressure to reduce public sector debt and, at the same time, expand and improve public facilities, governments and public authorities have looked to private sector finance, and have invited private sector entities to enter into long-term contractual agreements which may take the form of construction or management of public sector infrastructure facilities by the private sector entity, or the provision of services (using infrastructure facilities) by the private sector entity to the community on behalf of a public sector body. This paper deals with the new issues raised by the public-private partnerships system or, more generally, by any system in which the new infrastructure is partially financed by its users. Is there, in this case, a new economic rationality of public authorities? Particularly, is there an optimal way to rank projects? This paper discusses the choice by the public authority of the most efficient investing programme in irrigation water infrastructures. More specifically, it studies the optimal ranking of project implementation when these projects are partially self-financed by their own revenues. In this case, the optimal investment programme must be defined under a constraint of annual subsidies. This paper demonstrates that the optimal ranking is not necessarily the ranking of decreasing socioeconomic internal rate of return. This counter-intuitive result can be demonstrated by a general approach. Analytical calculations are not useful in this discrete problem because each programme is an ordered subset of projects. Therefore, there is no continuous variation linking the various programmes and the usual tools of optimization, such as differential calculus, are useless. Thus, we adopt here a discrete optimization analysis based on standard techniques in the physics area, such as Monte Carlo sampling.

Enhanced Reconstruction of Architectural Wall Surfaces for 3D Building Models

The reconstruction of architectural structures from 3D building models is a challenging task and a lot of research has been done in recent years. However, most of this work is focused mainly on reconstructing accurately the architectural shape of interiors rather than the fine architectural details, such as the wall elements (e.g. windows and doors). We focus specifically on this problem and propose a method that extends current solutions to reconstruct accurately severely occluded wall surfaces

Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method

The main contribution of this thesis is the implementation of manufacturing constraints in shape and topology optimization. Fabrication limitations related to the casting process are formulated as mathematical constraints and introduced in the optimization algorithm. In addition, based on the same theoretical and modelization tools, we propose a novel formulation for multi-phase optimization problems, which can be extended to the optimization of structures with functionally-graded properties. A key ingredient for the mathematical formulation of most problems throughout our work is the notion of the signed distance function to a domain. This work is divided into three parts. The rst part is bibliographical and contains the necessary background material for the understanding of the thesis' main core. It includes the rst two chapters. Chapter 1 provides a synopsis of shape and topology optimization methods and emphasizes the combination of shape sensitivity analysis and the level-set method for tracking a shape's boundary. In Chapter 2 we give a short description of the casting process, from which all our manufacturing constraints derive. We explain how industrial designers account for these limitations and propose a strategy to incorporate them in shape and topology optimization algorithms. The second part is about the mathematical formulation of manufacturing constraints. It starts with Chapter 3, where the control of thickness is discussed. Based on the signed distance function, we formulate three constraints to ensure a maximum and minimm feature size, as well as a minimal distance between structural members. Then, in Chapter 4, we propose ways to handle molding direction constraints and combine them with thickness constraints. Finally, a thermal constraint coming from the solidi cation of cast parts is treated in Chapter 5 using several thermal models. Multi-phase optimization is discussed in the third part. The general problem of shape and topology optimization using multiple phases is presented in detail in Chapter 6. A "smoothed-interface" approach, based again on the signed distance function, is proposed to avoid numerical di culties related to classical "sharp-interface" problems and a shape derivative is calculated. An extension of this novel formulation to general types of material properties' gradation is shown in the Appendix A

Socioeconomic Evaluation and Ranking of Infrastructure Projects

For most of the last century, the role of private and public sectors in the infrastructure projects were clear. For instance, public authorities were generally in charge of financing and building new infrastructures. Over the last decade, that position has begun to change. Faced with pressure to reduce public sector debt and, at the same time, expand and improve public facilities, governments and public authorities have looked to private sector finance, and have invited private sector entities to enter into long-term contractual agreements which may take the form of construction or management of public sector infrastructure facilities by the private sector entity, or the provision of services (using infrastructure facilities) by the private sector entity to the community on behalf of a public sector body. This paper deals with the new issues raised by the public-private partnerships system or, more generally, by any system in which the new infrastructure is partially financed by its users. Is there, in this case, a new economic rationality of public authorities? Particularly, is there an optimal way to rank projects? This paper discusses the choice by the public authority of the most efficient investing programme in irrigation water infrastructures. More specifically, it studies the optimal ranking of project implementation when these projects are partially self-financed by their own revenues. In this case, the optimal investment programme must be defined under a constraint of annual subsidies. This paper demonstrates that the optimal ranking is not necessarily the ranking of decreasing socioeconomic internal rate of return. This counter-intuitive result can be demonstrated by a general approach. Analytical calculations are not useful in this discrete problem because each programme is an ordered subset of projects. Therefore, there is no continuous variation linking the various programmes and the usual tools of optimization, such as differential calculus, are useless. Thus, we adopt here a discrete optimization analysis based on standard techniques in the physics area, such as Monte Carlo sampling

Molding direction constraints in structural optimization via a level-set method

International audienceIn the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not adress the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature

Thickness control in structural optimization via a level set method

International audienceIn the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss diff erent strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity. As can be expected, the resulting optimized shapes are strongly dependent on the initial guesses and on the speci fic treatment of the constraints since, in particular, some topological changes may be prevented by those constraints

Multi-phase structural optimization via a level set method

33 pagesInternational audienceWe consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves jump of discontinuous quantities at the interface which are difficult to numerically evaluate. Therefore we suggest an alternative smoothed interface approach which yields more convenient shape derivatives. We rely on the signed distance function and we enforce a fixed width of the transition layer around the interface (a crucial property in order to avoid increasing "grey" regions of fictitious materials). It turns out that the optimization of a diffuse interface has its own interest in material science, for example to optimize functionally graded materials. Several 2-d examples of compliance minimization are numerically tested which allow us to compare the shape derivatives obtained in the sharp or smoothed interface cases

Modal basis approaches in shape and topology optimization of frequency response problems

International audienceThe optimal design of mechanical structures subject to periodic excitations within a large frequency interval is quite challenging. In order to avoid bad performances for non-discretized frequencies, it is necessary to finely discretize the frequency interval, leading to a very large number of state equations. Then, if a standard adjoint-based approach is used for optimization, the computational cost (both in terms of CPU and memory storage) may be prohibitive for large problems, especially in three space dimensions. The goal of the present work is to introduce two new non-adjoint approaches for dealing with frequency response problems in shape and topology optimization. In both cases, we rely on a classical modal basis approach to compute the states, solutions of the direct problems. In the first method, we do not use any adjoint but rather directly compute the shape derivatives of the eigenmodes in the modal basis. In the second method, we compute the adjoints of the standard approach by using again the modal basis. The numerical cost of these two new strategies are much smaller than the usual ones if the number of modes in the modal basis is much smaller than the number of discretized excitation frequencies. We present numerical examples for the minimization of the dynamic compliance in two and three space dimensions