Analysis of Data Point Cloud Preprocessing and Feature Angle Detection Algorithm

Background: The two main stages are utilized for feature extraction, from which the first stage consists of a penalty weight to the neighbor graph’s edges. The edge penalty weights are minimized by the neighbor sub-graph extraction to produce the set of feature patterns. For noisy data, the second stage is helpful. Methodology: In order to realize the measurement of the geometric dimensions of the ship block, this paper uses the theory of computer vision and reverse engineering to obtain the data of the segmented-hull with the method of digitizing the physical parts based on the vision, and processes the data by using the relevant knowledge of reverse engineering. Result: The results show that the efficiency of the edge extraction algorithm based on mathematical morphology is 30% higher than that of the mesh generation method. An adaptive corner detection algorithm based on the edge can adaptively determine the size of the support area and accurately detect the corner position. Conclusion: According to the characteristics of the point cloud of ship hull segment data, an adaptive corner detection algorithm based on the edge is adopted to verify its feasibility.

Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions

Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in $\begin{array}{} {\bf V}_h^p \end{array}$-norm for different parameters h, p (p ⩽ 10) is presented. The method does not require specification of penalty weight function.

A discrepancy-based penalty method for extended waveform inversion

Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.

Optimal cooperative guidance with guaranteed miss distance in three-body engagement

The three-body engagement where a target aircraft protects itself by using a cooperative defender missile to intercept an attacking missile is investigated. It is formulated as a constrained linear quadratic optimal problem. Two different optimal cooperative guidance laws for the target and defender are proposed in two cooperation schemes. Since any control effort to reduce the miss distance to smaller than missile’s lethal radius is wasted, the guidance laws are derived to achieve an upper bound on the missile–defender miss distance. In the two-way cooperation scheme, the target and the defender act as a team. How the target makes a trade-off between aiding the defender and evading the missile is investigated by considering both the missile–target zero-effort miss distance and the control effort into the cost function. Without the penalty weight on the missile–target zero-effort miss distance, the two-way minimum control effort guidance laws are available. In the one-way cooperation scheme, the target uses a known evasion strategy independently. The optimal cooperative guidance law is derived for minimizing the control effort of the defender. Simulation results show that these proposed guidance laws can provide a specified missile–defender miss distance and save the control effort compared with the zero-miss-distance guidance law. Two-way cooperation scheme outperforms one-way cooperation scheme.

Dual Residual in Augmented Lagrangian Coordination for Decomposition-Based Optimization

As system design problems increase in complexity, researchers seek approaches to optimize such problems by coordinating the optimizations of decomposed sub-problems. Many methods for optimization by decomposition have been proposed in the literature among which, the Augmented Lagrangian Coordination (ALC) method has drawn much attention due to its efficiency and flexibility. The ALC method involves a quadratic penalty term, and the initial setting and update strategy of the penalty weight are critical to the performance of the ALC. The weight in the traditional weight update strategy always increases and previous research shows that an inappropriate initial value of the penalty weight may cause the method not to converge to optimal solutions. Inspired by the research on Augmented Lagrangian Relaxation in the convex optimization area, a new weight update strategy in which the weight can either increase or decrease is introduced into engineering optimization. The derivation of the primal and dual residuals for optimization by decomposition is conducted as a first step. It shows that the traditional weight update strategy only considers the primal residual, which may result in a duality gap and cause a relatively big solution error. A new weight update strategy considering both the primal and dual residuals is developed which drives the dual residual to zero in the optimization process, thus guaranteeing the solution accuracy of the decomposed problem. Finally, the developed strategy is applied to both mathematical and engineering test problems and the results show significant improvements in solution accuracy. Additionally, the proposed approach makes the ALC method more robust since it allows the coordination to converge with an initial weight selected from a much wider range of possible values while the selection of initial weight is a big concern in the traditional weight update strategy.

Adaptive Sparse Norm and Nonlocal Total Variation Methods for Image Smoothing

In computer vision and graphics, it is challenging to decompose various texture/structure patterns from input images. It is well recognized that how edges are defined and how this prior information guides smoothing are two keys in determining the quality of image smoothing. While many different approaches have been reported in the literature, sparse norm and nonlocal schemes are two promising tools. In this study, by integrating a texture measure as the spatially varying data-fidelity/smooth-penalty weight into the sparse norm and nonlocal total variation models, two new methods are presented for feature/structure-preserving filtering. The first one is a generalized relative total variation (i.e., GRTV) method, which improves the contrast-preserving and edge stiffness-enhancing capabilities of the RTV by extending the range of the penalty function’s norm from 1 to [0, 1]. The other one is a nonlocal version of generalized RTV (i.e., NLGRTV) for which the key idea is to use a modified texture-measure as spatially varying penalty weight and to replace the local candidate pixels with the nonlocal set in the smooth-penalty term. It is shown that NLGRTV substantially improves the performance of decomposition for regions with faint pixel-boundary.