Set Of Initial Points Research Articles

A partial decomposition cutting method with CF-discrepancy for points selection in stochastic seismic analysis of structures

The probability density evolution method is renowned for its effectiveness in conducting stochastic seismic response analyses of structures with uncertain parameters. Within this method, the points selection strategy, particularly in high-dimensional problems, is of paramount importance to achieving a balance between accuracy and efficiency. This paper proposes a novel point selection method designed to capture the probabilistic response of structural dynamic systems. The method starts by generating an initial uniform point set within a unit cube, using an improved number-theoretical method with a large number size. It then employs a partial decomposition cutting method to select a small number of samples from this initial uniform point set, which are subsequently scaled to the unit cube to serve as the representative points. These representative points are then transformed into the original random-variate space, and the corresponding assigned probabilities are computed accordingly. To enhance accuracy, a characteristic function-based discrepancy is proposed and applied to rearrange the representative points in the original random-variate space. The effectiveness of this method is demonstrated through two numerical examples, along with comparisons to results obtained using Monte Carlo Simulation and other comparable point sets.

BIM-based task planning method for wheeled-legged rebar binding robot

ABSTRACT Building Information Modeling (BIM) data has the advantages of high quality, operability, and parametric capabilities. In recent years, the application of BIM in construction planning for building robots has been increasing. Task planning for rebar binding is an important aspect of construction, and there is a growing trend of using robots to improve the accuracy and efficiency of binding operations. However, the complex and dynamic construction site environment poses significant challenges for task planning in rebar binding. Therefore, this paper proposes a new BIM-based task planning method for a wheeled-legged rebar binding robot, which can quickly generate an optimal task sequence. Firstly, an initial set of rebar intersection points is generated based on BIM data. Then, considering the execution dead zone of the robot and the variable workspace of the binding mechanism, the rebar intersection points set is decomposed and filtered using morphological opening operations. Finally, a constrained genetic algorithm is employed to sort the set of task points. Simulation and real-world experiments were conducted using a wheeled-legged rebar binding robot as the research subject. The results demonstrate that, compared to manual planning, the average binding efficiency is approximately 1500 points per hour, which is 1.97 times higher than manual operation. This validates the applicability and effectiveness of the proposed method.

On Successive Approximations for Compact-Valued Nonexpansive Mappings

We show that for a given initial point the typical, in the sense of Baire category, nonexpansive compact valued mapping F has the following properties: there is a unique sequence of successive approximations and this sequence converges to a fixed point of F. In the case of separable Banach spaces we show that for the typical mapping there is a residual set of initial points that have a unique trajectory.

Robust Pointset Denoising of Piecewise‐Smooth Surfaces through Line Processes

AbstractDenoising is a common, yet critical operation in geometry processing aiming at recovering high‐fidelity models of piecewise‐smooth objects from noise‐corrupted pointsets. Despite a sizable literature on the topic, there is a dearth of approaches capable of processing very noisy and outlier‐ridden input pointsets for which no normal estimates and no assumptions on the underlying geometric features or noise type are provided. In this paper, we propose a new robust‐statistics approach to denoising pointsets based on line processes to offer robustness to noise and outliers while preserving sharp features possibly present in the data. While the use of robust statistics in denoising is hardly new, most approaches rely on prescribed filtering using data‐independent blending expressions based on the spatial and normal closeness of samples. Instead, our approach deduces a geometric denoising strategy through robust and regularized tangent plane fitting of the initial pointset, obtained numerically via alternating minimizations for efficiency and reliability. Key to our variational approach is the use of line processes to identify inliers vs. outliers, as well as the presence of sharp features. We demonstrate that our method can denoise sampled piecewise‐smooth surfaces for levels of noise and outliers at which previous works fall short.

Global convergence of the gradient method for functions definable in o-minimal structures

We consider the gradient method with variable step size for minimizing functions that are definable in o-minimal structures on the real field and differentiable with locally Lipschitz gradients. We prove that global convergence holds if continuous gradient trajectories are bounded, with the minimum gradient norm vanishing at the rate $o(1/k)$ if the step sizes are greater than a positive constant. If additionally the gradient is continuously differentiable, all saddle points are strict, and the step sizes are constant, then convergence to a local minimum holds almost surely over any bounded set of initial points.

D3K: The Dissimilarity-Density-Dynamic Radius K-means Clustering Algorithm for scRNA-Seq Data.

A single-cell sequencing data set has always been a challenge for clustering because of its high dimension and multi-noise points. The traditional K-means algorithm is not suitable for this type of data. Therefore, this study proposes a Dissimilarity-Density-Dynamic Radius-K-means clustering algorithm. The algorithm adds the dynamic radius parameter to the calculation. It flexibly adjusts the active radius according to the data characteristics, which can eliminate the influence of noise points and optimize the clustering results. At the same time, the algorithm calculates the weight through the dissimilarity density of the data set, the average contrast of candidate clusters, and the dissimilarity of candidate clusters. It obtains a set of high-quality initial center points, which solves the randomness of the K-means algorithm in selecting the center points. Finally, compared with similar algorithms, this algorithm shows a better clustering effect on single-cell data. Each clustering index is higher than other single-cell clustering algorithms, which overcomes the shortcomings of the traditional K-means algorithm.

Методы и алгоритмы решения задачи выбора граничных точек районов базирования летательных аппаратов

The paper considers a set of methods and algorithms that allows determining the geodetic coordinates of the vertices of a convex polygon (with the number of vertices not exceeding a given one), limiting the initial set of points with known geodetic coordinates. When solving the problem, we developed the following: an algorithm for determining the geodetic coordinates of the polygon vertices; proposals for improving the methodology for constructing the boundaries of the area where points of the aircraft basing areas are located; algorithms for determining the set of points that are the vertices of a convex polygon that limits the initial set of points; an algorithm for reducing the number of vertices of a convex polygon; methods for selecting points by direction and by range; a method for determining the angle at the vertex of a polygon; a method for determining the geodetic coordinates of the vertices of a polygon that do not belong to the original set of points. To effectively solve the problem, we examined several different algorithms, e.g. the Jarvis March algorithm and the Graham scan. The use of the above methods and algorithms makes it possible to determine the geodetic coordinates of the vertices of a convex polygon (with the number of vertices not exceeding a given one), limiting the initial set of points with known geodetic coordinates, and increases the validity and accuracy of determining the geodetic coordinates of the boundary points of the aircraft basing areas.

On the tracking of shelly carbonate sands using deep learning

It is well known that carbonate sands possess weak mineralogies, complex particle morphologies and porous microstructures. These characteristics lead to very distinct mechanical properties of carbonate sands, such as low shear strength, high crushability and high permeability. This paper presents a novel investigation of the recognition and tracking of intact carbonate sand particles using a deep learning method called PointNet++. The capability of PointNet++ to extract the global and local features of the porous structures of carbonate sand particles enables it to excel in the pattern recognition of porous granular materials. First, for the reconstruction of carbonate sand particles, a set of two-dimensional raw images obtained from X-ray microtomography scanning were handled by a series of image processing techniques such as median filter, segmentation and thresholding algorithms. In particular, a special technique previously developed by the authors was used to treat the abundant intra-particle pores and surface concavities of carbonate sand particles to avoid the problem of image over-segmentation. Second, to prepare the training datasets to be used in the PointNet++ deep learning exercise, a strategy of sampling and grouping was proposed to divide the initial point set of each sand particle into several groups. Next, PointNet++ was utilised to capture the global and local context features of the sand particles at different length scales and shown to successfully recognise and track all of the particles. Finally, a comprehensive comparison between several particle tracking methods reported in the literature was made, and the outstanding advantages of the deep learning-based particle tracking method were summarised.

Microscopic analysis of induced nuclear fission dynamics

The dynamics of low-energy induced fission is explored using a consistent microscopic framework that combines the time-dependent generator coordinate method (TDGCM) and time-dependent nuclear density functional theory (TDDFT). While the former presents a fully quantum mechanical approach that describes the entire fission process as an adiabatic evolution of collective degrees of freedom, the latter models the dissipative dynamics of the final stage of fission by propagating the nucleons independently toward scission and beyond. By combining the two methods, based on the same nuclear energy density functional and pairing interaction, we perform an illustrative calculation of the charge distribution of yields and total kinetic energy for induced fission of $^{240}$Pu. For the saddle-to-scission phase a set of initial points for the TDDFT evolution is selected along an iso-energy curve beyond the outer fission barrier on the deformation energy surface, and the TDGCM is used to calculate the probability that the collective wave function reaches these points at different times. Fission observables are computed with both methods and compared with available data. The relative merits of including quantum fluctuations (TDGCM) and the one-body dissipation mechanism (TDDFT) are discussed.

Data-driven model predictive control design for offset-free tracking of nonlinear systems

We propose a design of data-driven Model Predictive Control (MPC) using a suboptimal trajectory and the linear time-varying (LTV) models from data-driven trajectory optimisation that achieves offset-free tracking. Data-driven constrained differential dynamic programming (CDDP) is exploited to improve the trajectory iteratively without the knowledge of the nonlinear model. A trajectory is divided to the transient and steady state regions, controlled by the Linear time-varying MPC (LTVMPC) and the offset-free linear MPC (LMPC), respectively. We prove the feasibility of the proposed LTVMPC in the transient region, and the offset-free tracking property of LMPC. The proposed scheme is validated to a continuous stirred tank reactor (CSTR) process. Simulation studies show that the suboptimal trajectory and LTV models are generated by CDDP, and the proposed MPC achieves offset-free tracking and disturbance rejection for a set of initial conditions and set points in the operating region.

MODELLING OF SEGMENTS OF ONE-DIMENSIONAL CONTOURS ACCORDING TO THE SPECIFIED CONDITIONS

The formation of one-dimensional contours on the basis on the given conditions is one of the most popular geometric modeling problems. The problem is solved by variative discrete geometric modeling, which assumes the formation of intermediate points for the initial set of condensation points. The discrete model of the curve consists of a point sets, given geometric characteristics and a condensation algorithm.
 A discretely presented curve (DPC) is formed by a condensation of the initial point set of an arbitrary configuration in areas on which it is possible to ensure a monotonic change in the values of its characteristics. Monotone plots are joined at special points. Every three consecutive points of the duodenum define an adjacent plane. Four adjacent planes passing through two consecutive points limit the tetrahedron. The chain of consecutive tetrahedrons defined on all segments is the region of the location of the smooth curve of the constant stroke line interpolating the initial point sets. The torsion on the sections of the DPC is estimated by the value of the ratio of the angle between adjacent adjacent planes to the length of the corresponding chord of the accompanying broken line. The point of thickening is assigned inside the tetrahedron of the DPC. As a result of successive condensations, we obtain a continuous bypass of a constant stroke, at each point of which there is a single position of the main trihedron. The point of condensation is assigned in such a way that the values of the torsion in the duodenum points change monotonically. This ensures that the torsion values are regular at the points of the bypass.
 The imposition of additional conditions on the DPC formed requires the definition of the corresponding region of a possible solution within the DPC arrangement tetrahedron.

Visual Tracking With Object Center Displacement and CenterNet

Modern artificial intelligence systems have revolutionized approaches to scientific and technological challenges in a variety of fields, thus remarkable improvements in the quality of state-of-the-art computer vision and other techniques are observed; object tracking in video frames is a vital field of research that provides information about objects and their trajectories. This paper presents an object tracking method basing on optical flow generated between frames and a ConvNet method. Initially, optical center displacement is employed to detect possible the bounding box center of the tracked object. Then, CenterNet is used for object position correction. Given the initial set of points (i.e., bounding box) in first frame, the tracker tries to follow the motion of center of these points by looking at its direction of change in calculated optical flow with next frame, a correction mechanism takes place and waits for motions that surpass a correction threshold to launch position corrections.

Smoothing Property of Load Variation Promotes Finding Global Solutions of Time-Varying Optimal Power Flow

This article analyzes solution trajectories for optimal power flow (OPF) with time-varying load. Despite its nonlinearity, time-varying OPF is commonly solved every 5–15 min using local-search algorithms. Failing to obtain the globally optimal solution of power optimization problems jeopardizes the grid's reliability and causes financial and environmental issues. The objective of this article is to address this problem by understanding the optimality behavior of OPF solution trajectories. An empirical study on California data shows that, with enough variation in the data, local search methods can solve OPF to global optimality, even if the problem has many local minima. To explain this phenomenon, we introduce a backward mapping that relates the time-varying OPF's global solution at a given time to a set of desirable initial points. We show that this mapping could act as a stochastic gradient ascent algorithm on an implicitly convexified formulation of OPF, justifying the escape of poor solutions over time. This work is the first to mathematically explain how temporal data variation affects the complexity of solving power operational problems.

Multi-objective shape optimization of Francis runner using metamodel assisted genetic algorithm

Nowadays evolutionary optimization techniques become an integral part of the design process of hydraulic turbine runners. For optimization the shape of the runner is parameterized by a set of geometrical parameters. The objective functions of each runner geometry, being the efficiency and cavitation performance, are evaluated through CFD analysis of 3D flow-field. As usual, some kind of genetic algorithm is used for searching the Pareto front, due to its inherent possibility of parallel evaluation of different runner variants within one generation. This approach requires extensive CFD computations of hundreds and thousands of runner variants. In order to speed up the optimization process a metamodel (approximate, surrogate model) can be utilized. The metamodel provides an approximation of true dependency of the objective functions on the design parameters. The metamodel is built based on the known objective functions for some initial set of points randomly taken form the design space. Once built, it can be used to replace time consuming CFD computations during the optimization process. In the present paper a metamodel, based on Gaussian processes, is implemented and integrated into a multi-objective genetic algorithm. The obtained algorithm is applied for shape optimization of the Francis turbine runner. The number of the design parameters varied from 4 to 24. The objective functions are multi-point efficiency and cavitation characteristics. True values of the objective functions are evaluated using Reynolds averaged Navier-Stokes computations of the flow field in a reduced turbine domain, including wicket gate, runner and draft tube. These values are used to train the initial metamodel. In order to enhance predictive capabilities of the metamodel, it is retrained periodically during the optimization loop. The results of metamodel-assisted optimization runs are compared to that obtained without metamodel. It is shown that application of metamodel significantly reduces the number of actual CFD computations even for high number of design parameters and thus speeds up the overall optimization process.

Uncertainty quantification and estimation of closed curves based on noisy data

Estimating closed curves based on noisy data has been a popular and yet a challenging problem in many fields of applications. Yet, uncertainty quantification of such estimation methods has received much less attention in the literature. The primary challenge stems from the fact that the parametrization of a closed curve is not generally unique and hence popular curve fitting methods (e.g., weighted least squares based on known parametrization) does not work well due to initialization instabilities leading to larger uncertainties. First, an initial set of cluster points are obtained by means of a constrained fuzzy c-means algorithm and an initial curve is constructed by fitting a B-spline curve based on the cluster centers. Second, a novel tuning parameter selection procedure is proposed to obtain optimal number of knots for the B-spline curve. Experimental results with simulated noisy data show that the proposed method works well for a variety of unknown closed curves with sharp changes of slopes and complex curvatures, even when moderate to large noises are added with heteroskedastic errors. Finally, a new curvature preserving uncertainty quantification method is proposed based on an adaptation of bootstrap method that provides confidence band around the fitted curve, an aspect that is rarely provided by popular curve fitting methods.

Unsupervised generation of polygonal approximations based on the convex hull

The present paper proposes a new non-optimal but unsupervised algorithm, called ICT-RDP, for generation of polygonal approximations based on the convex hull. Firstly, the new algorithm takes into account the convex hull of the 2D closed curves or contours to select a set of initial points; secondly, the significance levels of the contour points are computed using a symmetric version of the well-known Ramer, Douglas-Peucker algorithm; and, finally, a thresholding process is applied to obtain the vertices or dominant points of the polygonal approximation. Since the convex hull can select many initial points in rounded parts of the contour, an additional deletion process is required to remove quasi-collinear dominant points. Furthermore, an additional improvement process is applied to shift the dominant points in order to increase the quality of the polygonal approximation. Experiments performed on a public available dataset show that the new proposal outperforms other unsupervised algorithms for generation of polygonal approximations.

A hydrodynamic prediction model of throttle orifice plate using space filling and adaptive sampling method

The hydrodynamic prediction model improved design efficiency of the flow control application. A global sampling process with space filling method, adaptive sampling method, and neural network is proposed to generate a hydrodynamic prediction model for the flow control device. The optimized Latin hypercube sampling method is applied to create a uniform set of initial sample points for analysis. An automatic computational fluid dynamics analysis process is developed to provide data for the hydrodynamic objective of the multi-stage throttle orifice plate. By self-learning from previous sample points, the new sample points placed in the region of interest are collected by the adaptive sampling method in several iterations. Two numerical examples and the flow rate modeling for the throttle orifice plate are provided to demonstrate the approximation capability of the proposed process. Ten prediction model cases are established by a back-propagation feed-forward neural network, and the test data show that the model constructed by optimized Latin hypercube sampling and adaptive sampling has 1% mean relative error and 4.85% maximum relative error, which is nearly 25% more accurate than the optimized Latin hypercube sampling model. The proposed global sampling process is efficient to build the hydrodynamic prediction model and shows potential in the flow control design area.

Mismatch Removal Based on Gaussian Mixture Model for Aircraft Surface Texture Mapping

Aiming at the fact of lower efficiency and higher time cost for feature matching in aircraft surface texture mapping process, a novel mismatch removal method based on Gaussian mixture model is proposed to increase correct corresponding feature matching point pairs. The detection and initial point sets for corresponding pairs are carried out, and a vector field is interpolated between the two matching of ORB feature points. The Gaussian mixture model(GMM) is introduced and a prior is taken to force the smoothness of the field, which is based on the Tikhonov regularization in vector-valued reproducing kernel Hilbert space(RKHS). In order to obtain the optimal estimation, the MAP solution of a Bayesian model with latent variables, which could be performed by Expectation Maximization (EM) algorithm, is utilized to determine the correct correspondence. The experimental results show that the algorithm could remove mismatches effectively and the classification for feature points is excellent. The calculation time is greatly reduced, which enhanced real-time performance of aircraft surface texture mapping process.

Extensible Spherical Fibonacci Grids.

Spherical Fibonacci grids (SFG) yield extremely uniform point set distributions on the sphere. This feature makes SFGs particularly well-suited to a wide range of computer graphics applications, from numerical integration, to vector quantization, among others. However, the application of SFGs to problems in which further refinement of an initial point set is required is currently not possible. This is because there is currently no solution to the problem of adding new points to an existing SFG while maintaining the point set properties. In this work, we fill this gap by proposing the extensible spherical Fibonacci grids (E-SFG). We start by carrying out a formal analysis of SFGs to identify the properties which make these point sets exhibit a nearly-optimal uniform spherical distribution. Then, we propose an algorithm (E-SFG) to extend the original point set while preserving these properties. Finally, we compare the E-SFG with a other extensible spherical point sets. Our results show that the E-SFG outperforms spherical point sets based on a low discrepancy sequence both in terms of spherical cap discrepancy and in terms of root mean squared error for evaluating the rendering integral.

Robust Point-to-Set Control of Hybrid Systems with Uncertainties Using Constraint Tightening

This paper proposes a solution to the problem of computing optimized point-to-set control strategies for hybrid systems with mixed inputs and uncertainties in the continuous-valued dynamics as well as the reset functions. The solution is based on the idea to account for the uncertainties by tightening the guard and invariant sets, and thus construct a substitute hybrid automaton with deterministic transition dynamics. It can be ensured that a solution for this new model also solves the problem for the original system, i.e. the latter is robustly transferred between initial point and target set.