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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 13 May 2021 21:17:41 GMT2021-05-13T21:17:41ZA general surface reconstruction method for post-processing of topology optimisation results
http://hdl.handle.net/10985/16996
A general surface reconstruction method for post-processing of topology optimisation results
BERTOLINO, Giulia; COSTA, Giulio; MONTEMURRO, Marco; PERRY, Nicolas; POURROY, Franck
In this work, a new semi-automatic surface reconstruction procedure is proposed. The main goal of the method is to reconstruct the boundary surface of a triangulation obtained as a result of a topology optimisation calculation. The reconstruction problem is articulated in two main phases: tessellation mapping and surface fitting. The first phase consists of retrieving a suitable map of the triangulation representing the boundary of the optimised topology. To this purpose, a segmentation of the original triangulation is performed and sub-domains (i.e. patches) are identified by means of a semi-automatic strategy. Then, a shape preserving parametrisation algorithm [1] is used on each patch in order to carry out the mapping and to preserve the real 3D shape of the boundary. The second phase deals with an original approach to the surface fitting problem: the problem is stated as a Constrained Non-Linear Programming Problem (CNLPP) by introducing a constraint on the maximum value of the Gaussian curvature of the boundary surface. In this study, the surface fitting problem is solved in the framework of Non-Uniform Rational Basis Splines (NURBS) surfaces. The main idea is to keep all the parameters defining the NURBS surface as design variables in order to state the surface fitting problem in the most general sense. Nevertheless, this fact implies two consequences of paramount importance, constituting just as many difficulties in solving the related CNLPP. Firstly, when the surface fitting problem is formulated by including the number of control points and the degrees of the basis functions among the unknowns, the overall number of design variables for the problem at hand is not fixed a-priori: hence, the resulting CNLPP is defined over a search space of variable dimension. Secondly, the numerical strategy chosen to face such a problem must be able to handle design variables of different nature and to optimise, at the same time, the dimension of the design domain as well as the value of each constitutive parameter of the NURBS surface. In order to overcome the two aforementioned issues, the surface fitting phase is composed of two optimisation steps. Firstly, the ERASMUS (EvolutionaRy Algorithm for optimiSation of ModUlar Systems) tool [2] optimises both the value and the number of design variables by means of a two-level Darwinian strategy, allowing the simultaneous evolution of individuals and species. Secondly, the optimum solution provided by ERASMUS constitutes the initial guess for the local gradient-based optimization, which aims at improving the accuracy of the fitting surface. The proposed method coupled with the NURBS based SIMP algorithm [3], represents a valid solution for the semi-automatic post-processing of complex 3D shapes resulting from topology optimisation.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/169962019-01-01T00:00:00ZBERTOLINO, GiuliaCOSTA, GiulioMONTEMURRO, MarcoPERRY, NicolasPOURROY, FranckIn this work, a new semi-automatic surface reconstruction procedure is proposed. The main goal of the method is to reconstruct the boundary surface of a triangulation obtained as a result of a topology optimisation calculation. The reconstruction problem is articulated in two main phases: tessellation mapping and surface fitting. The first phase consists of retrieving a suitable map of the triangulation representing the boundary of the optimised topology. To this purpose, a segmentation of the original triangulation is performed and sub-domains (i.e. patches) are identified by means of a semi-automatic strategy. Then, a shape preserving parametrisation algorithm [1] is used on each patch in order to carry out the mapping and to preserve the real 3D shape of the boundary. The second phase deals with an original approach to the surface fitting problem: the problem is stated as a Constrained Non-Linear Programming Problem (CNLPP) by introducing a constraint on the maximum value of the Gaussian curvature of the boundary surface. In this study, the surface fitting problem is solved in the framework of Non-Uniform Rational Basis Splines (NURBS) surfaces. The main idea is to keep all the parameters defining the NURBS surface as design variables in order to state the surface fitting problem in the most general sense. Nevertheless, this fact implies two consequences of paramount importance, constituting just as many difficulties in solving the related CNLPP. Firstly, when the surface fitting problem is formulated by including the number of control points and the degrees of the basis functions among the unknowns, the overall number of design variables for the problem at hand is not fixed a-priori: hence, the resulting CNLPP is defined over a search space of variable dimension. Secondly, the numerical strategy chosen to face such a problem must be able to handle design variables of different nature and to optimise, at the same time, the dimension of the design domain as well as the value of each constitutive parameter of the NURBS surface. In order to overcome the two aforementioned issues, the surface fitting phase is composed of two optimisation steps. Firstly, the ERASMUS (EvolutionaRy Algorithm for optimiSation of ModUlar Systems) tool [2] optimises both the value and the number of design variables by means of a two-level Darwinian strategy, allowing the simultaneous evolution of individuals and species. Secondly, the optimum solution provided by ERASMUS constitutes the initial guess for the local gradient-based optimization, which aims at improving the accuracy of the fitting surface. The proposed method coupled with the NURBS based SIMP algorithm [3], represents a valid solution for the semi-automatic post-processing of complex 3D shapes resulting from topology optimisation.Mathematization of experts knowledge: example of part orientation in additive manufacturing
http://hdl.handle.net/10985/19900
Mathematization of experts knowledge: example of part orientation in additive manufacturing
MBOW, Mouhamadou Mansour; GRANDVALLET, Christelle; VIGNAT, Frederic; MARIN, Philippe Rene; PERRY, Nicolas; POURROY, Franck
The use of expert knowledge by manufacturing companies to support everyday activities has become an emerging practice thanks to the new knowledge management tools. A big set of knowledge is available in the organizations but its profitable use to solve problems and assist decision making is still a challenge. This is the case of CAM operations or preprocessing steps for which various works have been led to involve expertsâ€™ knowledge in the decision-making based on qualitative principles. However, so far, there is no methodology to the quantitative representation of that knowledge for more assistance. This paper introduces an approach for the conversion of knowledge into quantitative mathematical models. The main idea is to go from elicitation data in the form of action rules to simple unitary mathematical images; here desirability functions. The whole process carried out to extract the useful information that help building the desirability functions is exposed and different useful mathematical considerations are proposed. The resulting methodology identifies the categories of concepts in action rules and translate them into codified action rules. Then, through a mathematization process, the desirability functions are built. In short, this new approach allows evaluating the satisfaction level of the rules prescribed by the experts. As an illustration, the model is applied to action rules for CAM operations in additive manufacturing and more precisely to the definition of part orientation. This has shown the robustness of the methodology used and that it is possible to translate elicitation data into mathematical functions operable in computation algorithms.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199002021-01-01T00:00:00ZMBOW, Mouhamadou MansourGRANDVALLET, ChristelleVIGNAT, FredericMARIN, Philippe RenePERRY, NicolasPOURROY, FranckThe use of expert knowledge by manufacturing companies to support everyday activities has become an emerging practice thanks to the new knowledge management tools. A big set of knowledge is available in the organizations but its profitable use to solve problems and assist decision making is still a challenge. This is the case of CAM operations or preprocessing steps for which various works have been led to involve expertsâ€™ knowledge in the decision-making based on qualitative principles. However, so far, there is no methodology to the quantitative representation of that knowledge for more assistance. This paper introduces an approach for the conversion of knowledge into quantitative mathematical models. The main idea is to go from elicitation data in the form of action rules to simple unitary mathematical images; here desirability functions. The whole process carried out to extract the useful information that help building the desirability functions is exposed and different useful mathematical considerations are proposed. The resulting methodology identifies the categories of concepts in action rules and translate them into codified action rules. Then, through a mathematization process, the desirability functions are built. In short, this new approach allows evaluating the satisfaction level of the rules prescribed by the experts. As an illustration, the model is applied to action rules for CAM operations in additive manufacturing and more precisely to the definition of part orientation. This has shown the robustness of the methodology used and that it is possible to translate elicitation data into mathematical functions operable in computation algorithms.An Efficient Hybrid Optimization Strategy for Surface Reconstruction
http://hdl.handle.net/10985/20261
An Efficient Hybrid Optimization Strategy for Surface Reconstruction
BERTOLINO, Giulia; MONTEMURRO, Marco; PERRY, Nicolas; POURROY, Franck
An efficient and general surface reconstruction strategy is presented in this study. The proposed approach can deal with both open and closed surfaces of genus greater than or equal to zero and it is able to approximate non-convex sets of target points (TPs). The surface reconstruction strategy is split into two main phases: (a) the mapping phase, which makes use of the shape preserving method (SPM) to get a proper parametrisation of each sub-domain composing the TPs set; (b) the fitting phase, where each patch is fitted by means of a suitable Non-Uniform Rational Basis Spline (NURBS) surface without introducing simplifying hypotheses and/or rules on the parameters tuning the shape of the parametric entity. Indeed, the proposed approach aims stating the surface fitting problem in the most general sense, by integrating the full set of design variables (both integer and continuous) defining the shape of the NURBS surface. To this purpose, a new formulation of the surface fitting problem is proposed: it is stated in the form of a special Constrained Non-Linear Programming Problem (CNLPP) defined over a domain having variable dimension, wherein both the number and the value of the design variables are simultaneously optimised. To deal with this class of CNLPPs, a hybrid optimisation tool has been employed. The optimisation procedure is split in two steps: firstly, an improved genetic algorithm (GA) optimises both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the solution provided by the GA constitutes the initial
guess for the subsequent deterministic optimisation, which aims at improving the accuracy of the fitting surfaces. The effectiveness of the proposed methodology is proven through some meaningful benchmarks taken from the literature.
Thu, 22 Apr 2021 00:00:00 GMThttp://hdl.handle.net/10985/202612021-04-22T00:00:00ZBERTOLINO, GiuliaMONTEMURRO, MarcoPERRY, NicolasPOURROY, FranckAn efficient and general surface reconstruction strategy is presented in this study. The proposed approach can deal with both open and closed surfaces of genus greater than or equal to zero and it is able to approximate non-convex sets of target points (TPs). The surface reconstruction strategy is split into two main phases: (a) the mapping phase, which makes use of the shape preserving method (SPM) to get a proper parametrisation of each sub-domain composing the TPs set; (b) the fitting phase, where each patch is fitted by means of a suitable Non-Uniform Rational Basis Spline (NURBS) surface without introducing simplifying hypotheses and/or rules on the parameters tuning the shape of the parametric entity. Indeed, the proposed approach aims stating the surface fitting problem in the most general sense, by integrating the full set of design variables (both integer and continuous) defining the shape of the NURBS surface. To this purpose, a new formulation of the surface fitting problem is proposed: it is stated in the form of a special Constrained Non-Linear Programming Problem (CNLPP) defined over a domain having variable dimension, wherein both the number and the value of the design variables are simultaneously optimised. To deal with this class of CNLPPs, a hybrid optimisation tool has been employed. The optimisation procedure is split in two steps: firstly, an improved genetic algorithm (GA) optimises both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the solution provided by the GA constitutes the initial
guess for the subsequent deterministic optimisation, which aims at improving the accuracy of the fitting surfaces. The effectiveness of the proposed methodology is proven through some meaningful benchmarks taken from the literature.