Damir Vučina

NPV-based decision support in multi-objective design using evolutionary algorithms

Optimum design problems are frequently formulated using a single excellence criterion (minimum mass or similar) with evolutionary algorithms engaged as decision-support tools. Alternatively, multi-objective formulations are used with a posteriori decision-making amongst the Pareto candidate solutions. The former typically introduces excessive simplification in the decision space and subjectivity, the latter leads to extensive numerical effort and postpones the compromise decision-making. In both cases, engineering excellence metrics such as minimum mass can be misleading in terms of performance of the respective design in the given operational environment. This paper presents an alternative approach to conceptual design where a compound objective function based on the Net Present Value (NPV) and Internal Rate of Return (IRR) aggregate performance metrics is developed. This formulation models the integral value delivered by the candidate designs over their respective life-cycles by applying value-based NPV discounting to all objectives. It can be incorporated as an a priori compromise and consequently viewed as a weighted sum of individual objectives corresponding to their economically faithful representation over the entire operational life-time of the designs. The multi-objective design optimization is consequently expanded from purely engineering terms to coupled engineering-financial decision support.

Computational procedure for optimum shape design based on chained Bezier surfaces parameterization

Optimum design introduces strong emphasis on compact geometry parameterization in order to reduce the dimensionality of the search space and consequently optimization run-time. This paper develops a decision support system for optimum shape which integrates geometric knowledge acquisition using 3D scanning and evolutionary shape re-engineering by applying genetic-algorithm based optimum search within a distributed computing workflow. A shape knowledge representation and compaction method is developed by creating 2D and 3D parameterizations based on adaptive chaining of piecewise Bezier curves and surfaces. Low-degree patches are used with adaptive subdivision of the target domain, thereby preserving locality. C^1 inter-segment continuity is accomplished by generating additional control points without increasing the number of design variables. The control points positions are redistributed and compressed towards the sharp edges contained in the data-set for better representation of areas with sharp change in slopes and curvatures. The optimal decomposition of the points cloud or target surface into patches is based on the requested modeling accuracy, which works as lossy geometric data-set compression. The proposed method has advantages in non-recursive evaluation, possibility of chaining patches of different degrees, options of prescribing fixed values at selected intermediate points while maintaining C^1 continuity, and uncoupled processing of individual patches. The developed procedure executes external application nodes using mutual communication via native data files and data mining. This adaptive interdisciplinary workflow integrates different algorithms and programs (3D shape acquisition, representation of geometry with data-set compaction using parametric surfaces, geometric modeling, distributed evolutionary optimization) such that optimized shape solutions are synthesized. 2D and 3D test cases encompassing holes and sharp edges are provided to prove the capacity and respective performance of the developed parameterizations, and the resulting optimized shapes for different load cases demonstrate the functionality of the overall distributed workflow.

Flow formulation FE metal-forming analysis with boundary friction via a penalty function

Abstract The flow formulation finite-element (FE) analysis of stationary metal-forming processes is generalized to include strain-history sensitive materials and boundary friction. The strain history at a point is obtained by the determination of the respective point trajectory, along which the strain rate is integrated. Boundary friction is introduced by two different original numerical procedures: (i) by superposing additional frictional velocity-sensitive load on flow elements; and (ii) by introducing the Coulomb friction law as a penalized constraint at the element, edge, or node level at the boundary interface. The resulting 2D FE procedures are developed and applied to materially non-linear analysis of idealized plane-strain rolling and extrusion. There is significant industrial significance in these procedures, since they can be efficiently employed in simulations.

3D shape optimization of fan vanes for multiple operating regimes subject to efficiency and noise-related excellence criteria and constraints

ABSTRACT Fully generic 3D shapes of centrifugal roof fan vanes are explored based on a custom-developed numerical workflow with the ability to vary the vane 3D shape by manipulating the control points of parametric surfaces and change the number of vanes and rotation speed. An excellence formulation is based on design flow efficiency, multi-regime operational conditions and noise criteria for various cases, including multi-objective optimization. Multiple cases of optimization demonstrate the suitability of customized and individualized fan designs for specific working environments according to the selected excellence criteria. Noise analysis is considered as an additional decision-making tool for cases where multiple solutions of equal efficiency are generated and as an additional criteria for multi-objective optimization. The 3D vane shape enables further gains in efficiency compared to 2D shape optimization, while multi-objective optimization with noise as an additional criterion shows potential to greatly reduce the roof fan noise with only small losses in efficiency. The developed workflow which comprises (i) a 3D parametric shape modeler, (ii) an evolutionary optimizer and (iii) a computational fluid dynamics (CFD) simulator can be viewed as an integral tool for optimizing the designs of roof fans under custom conditions.

3D shape acquisition and integral compact representation using optical scanning and enhanced shape parameterization

An efficient computational methodology for shape acquisition, processing and representation is developed. It includes 3D computer vision by applying triangulation and stereo-photogrammetry for high-accuracy 3D shape acquisition. Resulting huge 3D point clouds are successively parameterized into mathematical surfaces to provide for compact data-set representation, yet capturing local details sufficiently. B-spline surfaces are employed as parametric entities in fitting to point clouds resulting from optical 3D scanning. Beyond the linear best-fitting algorithm with control points as fitting variables, an enhanced non-linear procedure is developed. The set of best fitting variables in minimizing the approximation error norm between the parametric surface and the 3D cloud includes the control points coordinates. However, they are augmented by the set of position parameter values which identify the respectively closest matching points on the surface for the points in the cloud. The developed algorithm is demonstrated to be efficient on demanding test cases which encompass sharp edges and slope discontinuities originating from physical damage of the 3D objects or shape complexity.

Efficient shape parameterization method for multidisciplinary global optimization and application to integrated ship hull shape optimization workflow

Abstract Multidisciplinary global shape optimization requires a geometric parameterization method that keeps the shape generality while lowering the number of free variables. This paper presents a reduced parameter set parameterization method based on integral B-spline surface capable of both shape and topology variations and suitable for global multidisciplinary optimization. The objective of the paper is to illustrate the advantages of the proposed method in comparison to standard parameterization and to prove that the proposed method can be used in an integrated multidisciplinary workflow. Non-linear fitting is used to test the proposed parameterization performance before the actual optimization. The parameterization method can in this way be tested and pre-selected based on previously existing geometries. Fitting tests were conducted on three shapes with dissimilar geometrical features, and great improvement in shape generality while reducing the number of shape parameters was achieved. The best results are obtained for a small number (up to 50) of optimization variables, where a classical applying of parameterization method requires about two times as many optimization variables to obtain the same fitting capacity. The proposed shape parameterization method was tested in a multidisciplinary ship hull optimization workflow to confirm that it can actually be used in multiobjective optimization problems. The workflow integrates shape parameterization with hydrodynamic, structural and geometry analysis tools. In comparison to classical local and global optimization methods, the evolutionary algorithm allows for fully autonomous design with an ability to generate a wide Pareto front without a need for an initial solution.

Multi-Regime Shape Optimization of Fan Vanes for Energy Conversion Efficiency using CFD, 3D Optical Scanning and Parameterization

Abstract An enhanced reverse engineering procedure was developed for roof fan re-design. An original numerical workflow for robust shape optimization based on maximum energy conversion efficiency was developed. It operates using a sample of multiple operating regimes coupled with CFD simulations. The initial shape solution was originally obtained in point cloud form by optical 3D scanning and subsequent B-spline based parameterization of shape. The CFD simulation of the scanned shape using 3D RANS based software was shown to agree very well with the measured features, experimentally obtained in our lab with the actual initial-shape fan. By manipulating the control points of parametric curves, the developed evolutionary optimization workflow was subsequently able to create shape-optimized vanes. This original procedure was applied to cases of constant-thickness and profiled single curvature vanes, both for single-regime and robust multi-point operating conditions. The corresponding increase in efficiency gained by our computational procedure was correlated with respective velocity and pressure distributions and suppression of flow separation. The novel numerical procedure developed here therefore provides a numerical framework for generic object geometry to re-shape itself autonomously. The change in shape ensures maximum energy conversion efficiency for a given composition of operating regimes. The gain in efficiency with optimized vane shapes proves to be significant in the wide range of flow rates around the best efficiency point.

Enhanced 3D parameterization for integrated shape synthesis by fitting parameter values to point sets

Enhanced single-patch NURBS (Non-uniform rational B-splines) parameterization is developed based on fitting parameter values, capable of handling dynamically changing shapes. With respect to NURBS and T-splines, the proposed single-patch parameterizations results in lower dimensionality enabling optimizers to operate on geometric parameters. Avoiding subdivision surfaces and continuity problems for piecewise NURBS and reparameterizations for T-splines accelerates optimization. This parameterization may be an approximation or initial solution for piecewise NURBS and T-splines. These numerical benefits are accomplished using a multi-stage methodology. An augmented set of fitting variables is formulated beyond the weight factors and control points with parameter values of data points. This augmented set is structured to possess reasonable dimensionality. The developed non-linear fitting includes gradient-based minimization with respect to the augmented set and evolutionary error minimization using external functions. The benefits and potential difficulties of the procedure are evaluated thoroughly. The methodology is tested on engineering objects of high shape complexity and demonstrated to provide superior single- patch fitting performance compared to standard linear fitting methods. The developed numerical approach provides for the aspired main objective which is sufficiently accurate and numerically efficient dynamic shape parameterizaton using a compact set of shape parameters.

Reverse Shape Synthesis of the Hydropump Volute Using Stereo-Photogrammetry, Parameterization, and Geometric Modeling

An automatic procedure for reverse 3D shape synthesis is proposed. Shape acquisition of an existing object involving stereo-photogrammetry, triangulation, and 3D reconstruction is applied to obtain the point clouds. Subsequent parameterization of the acquired geometry using mathematical surfaces yields a compact set of parameters as shape variables to be used in diagnostics. The developed procedure and several specific computational geometry operators are applied with a hydro-pump casing whose complex shape is processed and related to the volute design and flow theory.

Adaptive re-parameterization based on arbitrary scalar fields for shape optimization and surface fitting

Abstract This paper presents a method for re-parameterization based on an arbitrary scalar field named the relaxation field. The relaxation field is applied to re-distribute the control-points of a parametric surface towards the desired areas. The proposed method was developed for possible application in an intelligent shape optimization procedure where a sensitivity field with respect to an objective function (or some other physical field) would be used for constructing the relaxation field. It could hence contribute to the concentrating the control-points at areas where significant changes in the geometry are expected. The method can easily be used in shape optimization since it keeps the number of variables constant during the redistribution of control-points as opposed to adaptive insertion of control points when using T-spline and similar methods. The same method can also be used in surface fitting by choosing the relaxation field based on the geometric error. This leads to an adaptive iterative fitting method. The method was validated by fitting a single patch B-spline surface to triangulated point clouds. The point-clouds were obtained by 3D scanning or from a CAD model. Examples include several complex engineering objects. The proposed method uses a parameterization method based on a combination of harmonic mapping and a mapping method based on a spring mesh. By relaxation using a spring mesh, the method allocates more parametric space to the regions of interest, thus assigning them more control points. The combination of these two mapping methods provides for increased local control while keeping the global smoothness of the parameterization.