Abstract:An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record.The computation required to organize the file is proportional to kNlogN. The expected number of records examined in each search is independent of the file size. The expected computation to perform each search is proportional-to 1ogN. Empirical evidence suggests that except for very small files, this algorithm is con… Show more
“…In order to increase the efficiency of this search, a multidimensional binary search tree known as KD-tree [22] is employed to find the perturbed element with the closest centroid, which is tested first. If the result is an unsuccessful projection, Barycentric coordinates [23] are used to determine which perturbed element should Figure 3: The centroid C of the original model element OP 1 OP 2 OP 3 is projected onto the perturbed element P P 1 P P 2 P P 3 .…”
Abstract. The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.
“…In order to increase the efficiency of this search, a multidimensional binary search tree known as KD-tree [22] is employed to find the perturbed element with the closest centroid, which is tested first. If the result is an unsuccessful projection, Barycentric coordinates [23] are used to determine which perturbed element should Figure 3: The centroid C of the original model element OP 1 OP 2 OP 3 is projected onto the perturbed element P P 1 P P 2 P P 3 .…”
Abstract. The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.
“…We have conducted tests with other more sophisticated and precise strategies, viz. the Locality-Sensitive Hashing [31], Kd-tree [32], and Cover-tree [33]. Although some improvement can be observed in terms of preserving the neighborhoods of the original space into the transformed space, the magnitude of this gain does not compensate the extra running time imposed by these strategies.…”
“…Given a case base containing descriptions of N cases, the number of case dis- More efficient multidimensional retrieval techniques, such as those based on K-d trees [4], were proposed in [15]. K-d tree uses a multi-dimensional tree for management and retrieval of cases.…”
Section: Fig 1 Generalization Of the Fixed Ontology To The Unspecifmentioning
confidence: 99%
“…Assume that the case c s is mapped to a location (2,3,4) in the hypercube. Then the search will compare the c s with the cases located at (*,3,4), (2,*,4), and (2,3,*), where * denotes any possible value in the respective dimension.…”
Section: Fig 1 Generalization Of the Fixed Ontology To The Unspecifmentioning
Abstract. Traditional CBR approaches imply centralized storage of the case base and, most of them, the retrieval of similar cases by an exhaustive comparison of the case to be solved with the whole set of cases. In this work we propose a novel approach for storage of the case base in a decentralized Peer-toPeer environment using the notion of Unspecified Ontology. In our approach the cases are stored in a number of network nodes that is comparable with the number of cases. We also develop an approximated algorithm for efficient retrieval of most-similar cases. The experiments show that the approximated algorithm successfully retrieves the most-similar cases while reducing the number of cases to be compared.
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