Non-uniform B-spline Research Articles

Efficient curvilinear optical proximity correction using non-uniform B-spline curves.

The curvilinear mask has received much attention in recent years due to its better lithography imaging fidelity than the Manhattan mask. As a significant part of computational lithography techniques, the curvilinear OPC optimally designs the mask contour represented by parametric curves to generate a curvilinear mask structure. However, the current curvilinear OPC process is computationally intensive and contains redundant data. In this paper, a curvilinear OPC method using the non-uniform B-spline curve, together with a knot removal process, is proposed to improve the optimization efficiency and reduce the mask file size. The non-uniform B-spline curve is used to characterize curvilinear mask structure without a complex splicing process, which can effectively reduce the computation complexity. To our best knowledge, knot removal theory is for the first time applied to solve the redundant data problem in curvilinear OPC. Simulations and comparisons verify the superior optimization efficiency and data reduction (DRON) rate of the proposed method.

Thermodynamic behavior of high-power inductively coupled plasma quartz tube wall

High-power inductively coupled plasmas are commonly used in planetary entry simulations and are increasingly being used in electric propulsion applications. However, during the operation of the system, the walls of the quartz tube will crack and melt. Its thermodynamic behavior is key to ensuring the safe and reliable operation of the system, which is directly related to the distribution of thermal energy within the discharge volume. In this paper, the temperature and stress distribution of the quartz tube wall of an inductively coupled plasma generator at 27 kW–85 kW are described. A numerical simulation model was established to depict the interaction between the plasma and the quartz tube wall. In the field of experimental research, the temperature of the outer wall of the quartz tube was obtained by using a thermal imager, and a non-uniform B-spline difference method was proposed to fit the outer wall temperature of the quartz tube to eliminate the influence of the induction coil. It is found that the numerical simulation and experimental results show that the temperature is stable region, temperature rise area, temperature drop zone, and the high temperature region of the quartz tube wall is located in the coil area, and the high stress area is also located in this region. On this basis, the outer wall temperature and thermal stress of quartz tubes under different heat fluxes are studied. When the heat flux exceeds 18.6 kW/m2, the stresses in the coil area and downstream of the coil exceed the limit stress. Mechanical failures may occur in areas where the ultimate stresses are exceeded, and these results can provide theoretical data for the optimal design of high-power inductively coupled plasma generators.

Flow Investigation and Optimization Design of a Radial Outflow Liquid Turbine Expander for Liquid CO2 Energy Storage System

Abstract The radial outflow liquid turbine expander (LTEROF) draws increasing attention for enhancing the efficiency of the liquid CO2 energy storage (LCES) system. However, the detrimental cavitation deteriorates the flow behavior, which demands an in-depth study of the flow physics and then effective attenuation. This study aims to effectively mitigate thermosensitive fluid cavitation and reduce energy dissipation. First, a preliminary expander design methodology taking into account the large specific volume variation of working fluid is implemented. Next, the entropy production analysis method (EPAM) is proposed to characterize energy dissipation and cavitation. Furthermore, the improved cavitation and turbulence models are validated through simulating Hord's liquid hydrogen hydrofoil. To suppress the cavitation and energy dissipation, the optimization design method based on the particle swarm optimization (PSO) algorithm together with the Kriging-based adaptive surrogate model is developed. Among them, the nonuniform relational B-splines and free form deformation (NURBS-FFD) method is applied to flexibly deform the profiles of nozzle and rotor, and a novel objective function incorporating vapor volume fraction and local entropy production rate (LEPR) is constructed to capture the cavitation and energy dissipation. During optimization, the optimizer is driven by the objective function to search globally toward the cavitation-resistance and low-dissipation geometry. With the optimization, the LEPR region shrinks and the cavitation is obviously weakened, the performance significantly improves both under design condition and under off-design conditions.

Nonparametric density estimation with nonuniform B-spline bases

Recently, Kirkby et al. introduced a general and efficient nonparametric density estimation procedure for local bases that is based on the statistical Galerkin method. However, the resulting density estimators using the statistical Galerkin method are not guaranteed to be proper, i.e., the density functions are not ensured to be nonnegative and normalized. To address this issue, we present a constrained Galerkin method with B-spline functions for nonparametric density estimation. Furthermore, we also provide a procedure to generate the optimal knot vectors for density estimations with nonuniform B-spline bases, which are based on the cumulative distribution of the feature function. Extensive numerical experiments are conducted to demonstrate the efficiency and accuracy of our framework.

A corotational isogeometric assumed natural strain shell element in updated lagrangian formulation for general geometric nonlinear analysis of thin-walled structures

A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems.

Trajectory planning and control algorithm of industrial robot manipulator

As the industrial robot task becomes more complex, the difficulty of trajectory planning and tracking control of manipulator is gradually increasing. To minimize the vibration during the manipulator motion and improve the planning accuracy, the method of quintic polynomial combined with non-uniform B-spline interpolation is studied for joint space (JS) planning. The trajectory tracking system is easily affected by friction nonlinearity and parameters. So a JS trajectory tracking controller based on based on fuzzy neural network (FNN) is designed. Through simulation experiments, the curve obtained by the planning method studied is smoother and the planning error is minimum. The maximum position error is 0.09 rad, and the speed error is not more than 0.1 rad/s. The controller performance test results under different parameters show that the W^, c^, κ^ parameter in FNN can be adjusted in real time, and the value will not affect the performance of the controller. The fluctuation range of trajectory error of different joints is within ±0.2×10-5rad, which indicates that the performance of AFNNC controller studied is better. And its response time is the shortest and its robustness is better when the load changes suddenly.

Trajectory optimization of wall-building robots using response surface and non-dominated sorting genetic algorithm III

Traditional wall-building robots regard brick masonry as a simple assembly process, ignoring the viscoelastic effect of cement mortar, which leads to poor masonry quality. Therefore, this paper proposes a many-objective trajectory optimization method based on response surface methodology (RSM) and non-dominated sorting genetic algorithm III (NSGA-III). Firstly, a substitution model between the objective functions and the design variables is established using RSM, which solves the problem of difficult construction of cement mortar viscoelastic model. Then, a trajectory optimization model is constructed based on seven times non-uniform B-spline, and it is solved using NSGA-III. Finally, the optimal solution is obtained from the Pareto solution set, and it is compared and analyzed with the standard gate-type masonry solution. The results show that after the trajectory optimization, the masonry error is reduced from 2.62 mm to 0.11 mm, which significantly improves the masonry quality, and other performance indicators are also improved. These results contribute to the construction of walls and promote the development of the smart construction industry.

CNBCC: cubic non-uniform B-spline closed curve for arbitrary shape text detection

CNBCC: cubic non-uniform B-spline closed curve for arbitrary shape text detection

Neural Diffeomorphic Non-uniform B-spline Flows

Neural Diffeomorphic Non-uniform B-spline Flows

Age-groups classification of Irrawaddy dolphins based on dorsal fin geometric morphological features

The Irrawaddy dolphin is a species at the top of the food chain, but its population is currently endangered. Hence, the critical need to take effective conservation measures for Irrawaddy dolphins, particularly in population reproduction. The age structure of Irrawaddy dolphins can be studied to understand the population reproduction status and provide reference for formulating scientific conservation measures. Unlike age estimation methods based on invasive biological tissue detection and individual biological target detection methods based on audio features or image pixel features, this paper proposes the method to extract the Irrawaddy dolphin's dorsal fin geometric morphological features for classifying age-groups by using non-uniform B-spline. Firstly, this method uses non-uniform B-spline method to fit the dorsal fin edge curve of Irrawaddy dolphins. Then the curve is resolved to extract its derivatives, curvature and other features that describe its geometry morphology. Finally, the random forest (RF) was supplemented to classify Irrawaddy dolphins into juvenile, middle-aged and older. Experiments show that the method proposed in this paper could effectively classify older dolphins to an accuracy of 87.36%. The method proposed in this paper is non-invasive not only can help analyze the Irrawaddy dolphin's development trajectory, understand the reproductive maturity, fecundity rates, and survival rates, but also can help understand the changes of the regional ecological environment and protect the aquatic diversity.

Research on Mechanism Design and Kinematic Characteristics of Self-Propelled Photovoltaic Cleaning Robot

A hydraulic drive-based self-propelled photovoltaic panel cleaning robot was developed to tackle the challenges of harsh environmental conditions, difficult roads, and incomplete cleaning of dust particles on the photovoltaic panel surface in photovoltaic power plants. The robot has the characteristics of the crawler wheel drive, rear-wheel-independent turning and three-point-independent suspension design, which makes it adhere to the walking requirements of complex environmental terrains, more flexible in turning and automatically levelling so that the stability of the boom mechanism during walking can be ensured. The kinematics model of the upper arm structure equipped with the end cleaning device was built, and the optimized Circle chaotic map and nonlinear weight factor were introduced to enhance the search ability and convergence speed of the sparrow algorithm. Furthermore, the boom running track was optimized in combination with the seven-order non-uniform B-spline curve. Through optimization, the running time of the boom was reduced by 18.7%, and the cleaning efficiency of photovoltaic panel surface was increased. The effectiveness of self-propelled photovoltaic panel cleaning robot cleaning and the reliability of time-optimal trajectory planning were confirmed through simulation and experiment.

Multi-objective Optimal Motion Planning of Heavy-duty Assembly Robot for Large Spacecraft Entering Cabin

The space inside the space capsule such as the space station sky and the core module is narrow, the size of the depth is large, and the bearing points are scattered and weak, there are some difficulties in loading, large size, different shape, complicated interface, scattered position, difficult position and pose adjustment, high assembly risk, etc.. To solve these problems, a six-DOF heavy-duty assembly robot is proposed in this paper. The robot adopts the combination of linear drive and rotating joint to increase the working space and bearing capacity of the robot. The kinematics and dynamics analysis model of the robot is established, and the path planning is carried out by means of quintic non-uniform B-spline interpolation method, considering fully the space constraints of the assembled equipment, a multi-objective trajectory optimization model based on NSGA2 algorithm is established to obtain the Pareto optimal solution set with time, impact and energy consumption as optimization objectives, prove that the equipment can be efficient and smooth. Reliable installation, with less impact and less power consumption under multi-objective optimization analysis.

FUELING GLOCAL: OPTIMIZATION-BASED PATH PLANNING FOR INDOOR UAVS IN AN AUTONOMOUS EXPLORATION FRAMEWORK

Abstract. Exploration is a fundamental problem in robotics that requires robots to navigate through unknown environments to autonomously gather information about their surroundings while executing collision-free paths. In this paper, we propose a method for producing smooth paths during the exploration process in indoor environments using UAVs to improve battery efficiency and enhance the quality of pose estimation. The developed framework is built by merging two approaches that represent the state of the art in the field of autonomous exploration with UAVs. The overall exploration logic is given by GLocal, a paper that introduces an hybrid, i.e. both sampling-based and frontier-based, framework that is able to cope with the issue of odometry drift when exploring indoor environments due to the absence of absolute localization, e.g. through GNSS. The second paper is FUEL, which introduces a frontier-based exploration methodology which computes the drone’s path as an optimized non-uniform B-Spline. The framework described in this paper borrows the optimized B-Spline trajectory generation from FUEL and implements it in GLocal. The presented system is evaluated in two different simulated environments, which show the pros and the cons of such method.

Adaptive Nonparametric Density Estimation with B-Spline Bases

Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method.

A General Reconstruction Framework for Deflectometric Measurement Based on Nonuniform B-Splines

Phase measuring deflectometry (PMD) is a powerful tool well suited for precision measurement of optical surfaces. However, accurate and efficient surface reconstruction from gradients is challenging for the PMD. Because most reconstruction algorithms are not well adapted to complex surface forms with local undulations, and a large number of tedious operations are demanded for calculating the ray intersections. Besides, the format of the reconstructed data is usually not compatible to the machine tools and additional format conversion is required, which increases the computational effort and lengthens the error propagation chain. Therefore, a general reconstruction framework is proposed for the deflectometric measurement based on the non-uniform B-spline (NUBS), which embeds the NUBS into the PMD framework to enhance the local representativity. The correspondences between the points on the screen, camera and workpiece can be established by the parameter mapping instead of by the ray intersections. Simulations and experiments prove the effectiveness of the proposed method, and the measurement accuracy can achieve a level of one hundred nanometers in practice.

Progressive Iterative Approximation of Non-Uniform Cubic B-Spline Curves and Surfaces via Successive Over-Relaxation Iteration

Geometric iteration (GI) is one of the most efficient curve- or surface-fitting techniques in recent years, which is famous for its remarkable geometric significance. In essence, GI can be thought of as the sum of iterative methods for solving systems of linear equations, such as progressive iterative approximation (PIA) which relies on the theory of Richardson iteration. Thus, when the curve- or surface-fitting error is at a desired level, we want to have as few iterations as possible to improve efficiency when dealing with large data sets. Based on the idea of successive over-relaxation (SOR) iteration, we formulate a faster PIA curve and surface interpolation scheme using classical non-uniform cubic B-splines, named SOR-PIA. The genetic algorithm is utilized to estimate the best approximate relaxation factor of SOR-PIA. Similar to standard PIA, SOR-PIA can also be regarded as a process in which the control points move in one direction, but it can greatly reduce the number of iterations in the iterative process with the same fitting accuracy. By comparing with the standard PIA and WPIA algorithms, the effectiveness of the SOR-PIA iterative interpolation algorithm can be verified.

Cavitation Suppression and Design Optimization in a Cryogenic Liquid Turbine Expander Based on Thermodynamic Cavitation and Entropy Production Analysis

Abstract Cryogenic liquid turbine expanders have emerged quite recently as a replacement of J–T valve for enhancing energy efficiency of industrial systems, such as air separation units (ASUs) and Supercritical Compressed Air Energy Storage systems. In the liquid turbine expander, the rotating impeller-induced swirling flow and cavitation are essentially significant and intensive, which requests some in-depth work toward a thorough understanding flow physics and then effective attenuation. This study aims at effectively mitigating the swirling flow and cavitation. The entropy production analysis method (EPAM) is proposed to characterize the swirling flow and cavitation. It is then incorporated with the improved cavitation and turbulence models and validated through the simulation of the Hord's liquid nitrogen hydrofoil. To mitigate the swirling flow and subsequent cavitation, the design optimization method is developed, in which a novel optimization objective function is constituted by incorporating the local entropy production rate and vapor volume fraction to capture the mechanical energy dissipation and cryogenic cavitating flow physics; the non-uniform relational B-Splines and free form deformation (NURBS–FFD) parametric method is used to facilitate a flexible variation in impeller blade and diffuser vane geometries. It is solved within cfx frame by means of the particle swarm optimization (PSO) algorithm coupling the Kriging-based adaptive surrogate model. With the design optimization, the impeller and vaned diffuser tube geometries are collaboratively fine-tuned, and the mechanical energy dissipation and cavitating flow across both the impeller and vaned diffuser tube is effectively mitigated.

A fourth-order numerical method for solving a class of derivative-dependent nonlinear singular boundary value problems

In this paper, a high order numerical scheme based on quartic B-spline functions is proposed to solve derivative-dependent nonlinear singular boundary value problems. Convergence of the method is analyzed. Five test problems are considered to illustrate the accuracy and efficiency of the method. The results obtained by present method are compared with those obtained by the uniform mesh cubic B-spline collocation (UCS) method [1] and non-uniform mesh cubic B-spline collocation (NCS) method [1]. The CPU time of proposed method is compared with that of the NCS method.

The Development of B-Splines for CAD.

A description is given of the milieu, including people, events, and research activities, surrounding the development of the author's doctoral thesis, "Applications of B-spline Approximation to Geometric Problems of Computer-Aided Design." Although initially slow to become adopted, today nonuniform B-splines have become the international de facto standard representation in the CAD industry.

Numerical solution of coupled 1D Burgers' equation by Non-Uniform Algebraic-Hyperbolic B-spline Differential Quadrature Method

Present paper deals with the numerical solution of coupled 1D Burgers’ equation by implementing the Non-Uniform Algebraic Hyperbolic (NUAH) B-spline Differential Quadrature Method. In the present paper, the spatial variable discretization is done using NUAH B-spline, and the obtained system of ODE is dealt with using the SSP-RK43 scheme. To get the improvised results, the concept of modified cubic NUAH B-spline is incorporated. To test the effectiveness and accuracy of the proposed scheme, numerical examples are discussed. Stability analysis of the proposed scheme is investigated by the matrix stability analysis method. The present regime is worthwhile to deal with some complex natured PDEs, where finding the analytical solution is cumbersome.