Geometry Optimization Algorithms Research Articles

Geometry Optimization of Stratospheric Pseudolite Network for Navigation Applications

A stratospheric pseudolite (SP) is a pseudolite installed on a stratospheric airship. A stratospheric pseudolite network (SPN) is composed of multiple SPs, which shows promising potential in navigation applications because of its station-keeping capability, long service duration, and flexible deployment. Most traditional research about SPN geometry optimization has centered on geometric dilution of precision (GDOP). However, previous research rarely dealt with the topic of how SPN geometry configuration not only affects its GDOP, but also affects its energy balance. To obtain an optimal integrated performance, this paper employs the proportion of energy consumption in energy production as an indicator to assess SPN energy status and designs a composite indicator including GDOP and energy status to assess SPN geometry performance. Then, this paper proposes an SPN geometry optimization algorithm based on gray wolf optimization. Furthermore, this paper implements a series of simulations with an SPN composed of six SPs in a specific service area. Simulations show that the proposed algorithm can obtain SPN geometry solutions with good GDOP and energy balance performance. Also, simulations show that in the supposed scenarios and the specific area, a higher SP altitude can improve both GDOP and energy balance, while a lower SP latitude can improve SPN energy status.

Geometry Optimization Algorithms in Conjunction with the Machine Learning Potential ANI-2x Facilitate the Structure-Based Virtual Screening and Binding Mode Prediction.

Structure-based virtual screening utilizes molecular docking to explore and analyze ligand-macromolecule interactions, crucial for identifying and developing potential drug candidates. Although there is availability of several widely used docking programs, the accurate prediction of binding affinity and binding mode still presents challenges. In this study, we introduced a novel protocol that combines our in-house geometry optimization algorithm, the conjugate gradient with backtracking line search (CG-BS), which is capable of restraining and constraining rotatable torsional angles and other geometric parameters with a highly accurate machine learning potential, ANI-2x, renowned for its precise molecular energy predictions reassembling the wB97X/6-31G(d) model. By integrating this protocol with binding pose prediction using the Glide, we conducted additional structural optimization and potential energy prediction on 11 small molecule-macromolecule and 12 peptide-macromolecule systems. We observed that ANI-2x/CG-BS greatly improved the docking power, not only optimizing binding poses more effectively, particularly when the RMSD of the predicted binding pose by Glide exceeded around 5 Å, but also achieving a 26% higher success rate in identifying those native-like binding poses at the top rank compared to Glide docking. As for the scoring and ranking powers, ANI-2x/CG-BS demonstrated an enhanced performance in predicting and ranking hundreds or thousands of ligands over Glide docking. For example, Pearson's and Spearman's correlation coefficients remarkedly increased from 0.24 and 0.14 with Glide docking to 0.85 and 0.69, respectively, with the addition of ANI-2x/CG-BS for optimizing and ranking small molecules binding to the bacterial ribosomal aminoacyl-tRNA receptor. These results suggest that ANI-2x/CG-BS holds considerable potential for being integrated into virtual screening pipelines due to its enhanced docking performance.

A fast hybrid roundness evaluation algorithm based on computational geometry and particle swarm optimization for profiles with massive points

The advancement of measurement has led to rigorous demands for the accuracy and efficiency of roundness evaluation of minimum zone circle (MZC) for profile with massive points. Existing algorithms struggle to balance efficiency and accuracy in such cases. A fast hybrid roundness evaluation (HCGPSO) algorithm for MZC based on the computational geometry (CG) and particle swarm optimization (PSO) algorithm is proposed, which incorporates a CG-based global best (gBest) selection method into the PSO algorithm and refines the termination criterion. A comparison with the published studies demonstrated that the HCGPSO algorithm were accurate and result are displayed to 10-15 mm. The impact of target accuracy, the harmonic and the number of points contained in profile on the performance of proposed algorithm are analyzed. With sub-nanometer target evaluation precision, HCGPSO enhances efficiency by an average of 64 % for profiles containing the highest harmonics from 30 undulations per revolution (upr) to 500 upr with 1500 points. For profiles with 300 to 4000 points at 150 upr, an average efficiency enhancement of 60 % was observed. For profiles with 4000 points at 500 upr from four workpieces, the calculation time is reduced by 55 % on average compared to the PSO algorithm, with increased accuracy and stability.

Distribution of Bound Conformations in Conformational Ensembles for X-ray Ligands Predicted by the ANI-2X Machine Learning Potential.

In this study, we systematically studied the energy distribution of bioactive conformations of small molecular ligands in their conformational ensembles using ANI-2X, a machine learning potential, in conjunction with one of our recently developed geometry optimization algorithms, known as a conjugate gradient with backtracking line search (CG-BS). We first evaluated the combination of these methods (ANI-2X/CG-BS) using two molecule sets. For the 231-molecule set, ab initio calculations were performed at both the ωB97X/6-31G(d) and B3LYP-D3BJ/DZVP levels for accuracy comparison, while for the 8,992-molecule set, ab initio calculations were carried out at the B3LYP-D3BJ/DZVP level. For each molecule in the two molecular sets, up to 10 conformations were generated, which diminish the influence of individual outliers on the performance evaluation. Encouraged by the performance of ANI-2x/CG-BS in these evaluations, we calculated the energy distributions using ANI-2x/CG-BS for more than 27,000 ligands in the protein data bank (PDB). Each ligand has at least one conformation bound to a biological molecule, and this ligand conformation is labeled as a bound conformation. Besides the bound conformations, up to 200 conformations were generated using OpenEye's Omega2 software (https://docs.eyesopen.com/applications/ omega/) for each conformation. We performed a statistical analysis of how the bound conformation energies are distributed in the ensembles for 17,197 PDB ligands that have their bound conformation energies within the energy ranges of the Omega2-generated conformation ensembles. We found that half of the ligands have their relative conformation energy lower than 2.91 kcal/mol for the bound conformations in comparison with the global conformations, and about 90% of the bound conformations are within 10 kcal/mol above the global conformation energies. This information is useful to guide the construction of libraries for shape-based virtual screening and to improve the docking algorithm to efficiently sample bound conformations.

Theoretical Investigations of the Crystal Structures and Molecular Energetics of High Quality Silicon Carbide (β-SiC) Precursor Compound 1,4-bis(trimethylsilyl)benzene

Over the last decades, the rapidly growing theoretical methods have revolutionized whole scientific paradigm, developed state-of-art analyses, and created substantial computational platforms through the huge support of outstanding mathematical algorithms. The self-consistent-charge density-functional based tight-binding (SCC-DFTB) scheme is one of them that offers versatile and efficient quantum mechanical calculations with some unique features compatible especially to the crystalline solid even at low computational resources. Its effective parametrizations and computational implementations under the Gaussian standardized interface as an "External program" via the users' script (Gaussian- External methodology; GEM) has added an additional value because of which various in-built high-level Gaussian computations are directly accessible. Herewith, the Gaussian offered geometry optimization algorithms and convergence criteria plus the ModRedundant type relaxed potential energy surface (PES) scanning techniques are assessed through the GEM, and characterized the crystal structures with concerned molecular energetics and PES of the experimentally synthesized 1,4-bis (trimethylsilyl) benzene (1,4-BTMSB) compound; a potential precursor for the high quality Silicon Carbide (β-SiC) coating particles, and an ideal "Internal Standard" for the quantitative spectroscopic analyses. The general results reveal that the 1,4- BTMSB molecules in its unit-cell and crystal lattice experience significant non-bonding interactions that induces them to attain the definite molecular geometry with recognizable ring, angle, torsional, and steric strains. The quantitative analyses of its PES depict that the phenylene ring has to overcome multiple yet unidentical energy barriers with the tallest Ea1= 5.3 kcal/mol in order to undergo internal 2π angular rotation around the 1,4-(C-Si) axes. And, exhibiting such type internal rotation of its phenylene ring is energetically highly probable as this compound is widely employed in coating high temperature reactors, and in quantizing analyte in high energy run spectroscopic facilities. The same quantification is referred here in order to underscore the significance of adopting perfectly closed topological molecular architectures while designing/synthesizing amphidynamic type crystalline free molecular gyrotops and their prototypes.

Efficient variable cell shape geometry optimization

A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases the standard optimization methods implemented in popular codes such as Quantum ESPRESSO and VASP. To motivate the variable cell shape optimization method presented in here, the eigenvalues of the lattice Hessian matrix are investigated thoroughly. It is shown that they change depending on the shape of the cell and the number of particles inside the cell. For certain cell shapes the resulting condition number of the lattice matrix can grow quadratically with respect to the number of particles. By a coordinate transformation, which can be applied to all variable cell shape optimization methods, the undesirable conditioning of the lattice Hessian matrix is eliminated.

A spur to molecular geometry optimization: Gradient-enhanced universal kriging with on-the-fly adaptive ab initio prior mean functions in curvilinear coordinates.

We present a molecular geometry optimization algorithm based on the gradient-enhanced universal kriging (GEUK) formalism with ab initio prior mean functions, which incorporates prior physical knowledge to surrogate-based optimization. In this formalism, we have demonstrated the advantage of allowing the prior mean functions to be adaptive during geometry optimization over a pre-fixed choice of prior functions. Our implementation is general and flexible in two senses. First, the optimizations on the surrogate surface can be in both Cartesian coordinates and curvilinear coordinates. We explore four representative curvilinear coordinates in this work, including the redundant Coulombic coordinates, the redundant internal coordinates, the non-redundant delocalized internal coordinates, and the non-redundant hybrid delocalized internal Z-matrix coordinates. We show that our GEUK optimizer accelerates geometry optimization as compared to conventional non-surrogate-based optimizers in internal coordinates. We further showcase the power of the GEUK with on-the-fly adaptive priors for efficient optimizations of challenging molecules (Criegee intermediates) with a high-accuracy electronic structure method (the coupled-cluster method). Second, we present the usage of internal coordinates under the complete curvilinear scheme. A complete curvilinear scheme performs both surrogate potential-energy surface (PES) fitting and structure optimization entirely in the curvilinear coordinates. Our benchmark indicates that the complete curvilinear scheme significantly reduces the cost of structure minimization on the surrogate compared to the incomplete curvilinear scheme, which fits the surrogate PES in curvilinear coordinates partially and optimizes a structure in Cartesian coordinates through curvilinear coordinates via the chain rule.

Real Coded Mixed Integer Genetic Algorithm for Geometry Optimization of Flight Simulator Mechanism Based on Rotary Stewart Platform

Designing the motion platform for the flight simulator is closely coupled with the particular aircraft’s flight envelope. While in training, the pilot on the motion platform has to experience the same feeling as in the aircraft. That means that flight simulators need to simulate all flight cases and forces acting upon the pilot during flight. Among many existing mechanisms, parallel mechanisms based on the Stewart platform are suitable because they have six degrees of freedom. In this paper, a real coded mixed integer genetic algorithm (RCMIGA) is applied for geometry optimization of the Stewart platform with rotary actuators (6-RUS) to design a mechanism with appropriate physical limitations of workspace and motion performances. The chosen algorithm proved that it can find the best global solution with all imposed constraints. At the same time, the obtained geometry can be manufactured because integer solutions can be mapped to available discrete values. Geometry is defined with a minimum number of parameters that fully define the mechanism with all constraints. These geometric parameters are then optimized to obtain custom-tailored geometry for aircraft flight simulation.

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. We describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples. Program summaryProgram title: Kohn-Sham Solver 2.0 (KSSOLV 2.0)CPC Library link to program files:https://doi.org/10.17632/pp8vgvfcv4.1Developer's repository link:https://bitbucket.org/berkeleylab/kssolv2.0/src/release/Licensing provisions: BSD 3-clauseProgramming language:: MATLABNature of problem: KSSOLV2.0 is used to perform Kohn-Sham density functional theory based electronic structure calculations to study chemical and material properties of molecules and solids. The key problem to be solved is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem.Solution method: The KSSOLV 2.0 implements both the self-consistent field (SCF) iteration with a variety of acceleration strategies and a direct constrained minimization algorithms. It is written completely in MATLAB and uses MATLAB's object oriented programming features to make it easy to use and modify.

Development and Evaluation of Geometry Optimization Algorithms in Conjunction with ANI Potentials.

An efficient yet accurate method for producing a large amount of energy data for molecular mechanical force field (MMFF) parameterization is on demand, especially for torsional angle parameters which are typically derived to reproduce ab initio rotational profiles or torsional potential energy surfaces (PESs). Recently, an active learning potential (ANI-1x) for organic molecules which can produce smooth and physically meaningful PESs has been developed. The high efficiency and accuracy make ANI-1x especially attractive for geometry optimization at low cost. To apply the ANI-1x potential in MMFF parameterization, one needs to perform constrained geometry optimization. In this work, we first developed a computational protocol to constrain rotatable torsional angles and other geometric parameters for a molecule whose geometry is described by Cartesian coordinates. The constraint is successfully achieved by force projection for the two conjugated gradient (CG) algorithms. We then conducted large-scale assessments on ANI-1x along with four different optimization algorithms in reproducing DFT energies and geometries for two CG algorithms, CG backtracking line search (CG-BS) and CG Wolfe line search (CG-WS), and two quasi-Newton algorithms, Broyden-Fletcher-Goldfarb-Shanno (BFGS) and low-memory BFGS (L-BFGS). Note that CG-BS is a new algorithm we developed in this work. All four algorithms take the ANI energies and forces to optimize a molecule geometry. Last, we conducted a large-scale assessment of applying ANI-1x in MMFF development in three aspects. First, we performed full optimizations for 100 drug molecules, each consisting of five distinct conformations. The average root-mean-square error (RMSE) between ANI-1x and DFT is about 1.3 kcal/mol, and the root-mean-square displacement (RMSD) of heavy atoms is about 0.35 Å. Second, we generated torsional PESs for 160 organic molecules, and constrained optimizations were performed for up to 18 conformations for each PES. We found that the RMSE of all the conformers is 1.23 kcal/mol. Last, we carried out constrained optimizations for alanine dipeptide with both ϕ and φ angles being frozen. The Ramachandran plots indicate that the two CG algorithms in conjunction with the ANI-1x potential could well reproduce the DFT-optimized geometries and torsional PESs. We concluded that CG-BS and CG-WS are good choices for generating PESs, while CG-WS or BFGS is ideal for performing full geometry optimization. With the continuously increased quality of ANI, it is expected that the computational algorithms and protocols presented in this work will have great applications in improving the quality of an existing small-molecule MMFF.

Variational quantum algorithm for molecular geometry optimization

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum algorithm for finding the most stable structure of a molecule by explicitly considering the parametric dependence of the electronic Hamiltonian on the nuclear coordinates. The equilibrium geometry of the molecule is obtained by minimizing a more general cost function that depends on both the quantum circuit and the Hamiltonian parameters, which are simultaneously optimized at each step. The algorithm is applied to find the equilibrium geometries of the ${\mathrm{H}}_{2},$ ${\mathrm{H}}_{3}{}^{+},$ ${\mathrm{BeH}}_{2},$ and ${\mathrm{H}}_{2}\mathrm{O}$ molecules. The quantum circuits used to prepare the electronic ground state for each molecule were designed using an adaptive algorithm where excitation gates in the form of Givens rotations are selected according to the norm of their gradient. All quantum simulations are performed using the PennyLane library for quantum differentiable programming. The optimized geometrical parameters for the simulated molecules show an excellent agreement with their counterparts computed using classical quantum chemistry methods.

Multi-fidelity evolutionary multitasking optimization for hyperspectral endmember extraction

Endmember extraction plays an indispensable role in hyperspectral image processing, which is also an important step to decompose the mixed pixels in spectral unmixing. Most of the existing methods based on the principle of convex geometry and intelligent optimization algorithms have achieved an excellent result, but they also suffer from the influence of outliers and expensive computation respectively. Furthermore, it is difficult to determine the number of endmembers in a hyperspectral image without any prior conditions. In order to alleviate these problems, we propose a multi-fidelity evolutionary multitasking optimization framework for hyperspectral endmember extraction in this article. In the proposed framework, multiple tasks to extract different numbers of endmembers are uniformly coded into a single population, aiming to process these similar tasks simultaneously with the implicit genetic transfer. Accordingly, our proposed algorithm is capable of extracting the best endmember set within a certain range of the number of endmembers without any prior knowledge. In addition, an ensemble surrogate model is firstly built to approximate the high-fidelity fitness with the low-fidelity fitness in endmember extraction, which greatly alleviates the time-consuming problem of individual evaluation. The experimental results on the simulated and the real hyperspectral data demonstrate the effectiveness of the proposed framework. The accuracy and the efficiency of endmember extraction are greatly improved compared with other classic endmember extraction methods.

PyFLOSIC: Python-based Fermi-Löwdin orbital self-interaction correction.

We present pyflosic, an open-source, general-purpose python implementation of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC), which is based on the python simulation of chemistry framework (pyscf) electronic structure and quantum chemistry code. Thanks to pyscf, pyflosic can be used with any kind of Gaussian-type basis set, various kinds of radial and angular quadrature grids, and all exchange-correlation functionals within the local density approximation, generalized-gradient approximation (GGA), and meta-GGA provided in the libxc and xcfun libraries. A central aspect of FLO-SIC is the Fermi-orbital descriptors, which are used to estimate the self-interaction correction. Importantly, they can be initialized automatically within pyflosic; they can also be optimized within pyflosic with an interface to the atomic simulation environment, a python library that provides a variety of powerful gradient-based algorithms for geometry optimization. Although pyflosic has already facilitated applications of FLO-SIC to chemical studies, it offers an excellent starting point for further developments in FLO-SIC approaches, thanks to its use of a high-level programming language and pronounced modularity.

Concurrent Modelling and Experimental Investigation of Material Properties and Geometries Produced by Projection Microstereolithography.

Projection microstereolithography additive manufacturing (PµSLA-AM) systems utilize free radical photopolymerization to selectively transform liquid resins into accurate and complex, shaped, solid parts upon UV light exposure. The material properties are coupled with geometrical accuracy, implying that optimizing one response will affect the other. Material properties can be enhanced by the post-curing process, while geometry is controlled during manufacturing. This paper uses designed experiments and analytical curing models concurrently to investigate the effects of process parameters on the green material properties (after manufacturing and before applying post curing), and the geometrical accuracy of the manufactured parts. It also presents a novel accumulated energy model that considers the light absorbance of the liquid resin and solid polymer. An essential definition, named the irradiance affected zone (IAZ), is introduced to estimate the accumulated energy for each layer and to assess the feasibility of the geometries. Innovative methodologies are used to minimize the effect of irradiance irregularities on the responses and to characterize the light absorbance of liquid and cured resin. Analogous to the working curve, an empirical model is proposed to define the critical energies required to start developing the different material properties. The results of this study can be used to develop an appropriate curing scheme, to approximate an initial solution and to define constraints for projection microstereolithography geometry optimization algorithms.

Geant4/GATE Comparison of Geometry Optimization Algorithms for Internal Dosimetry Using Voxelized Phantoms

Geant4 Application for Tomographic Emission (GATE) is a Monte Carlo code, including the algorithms integrated inside Geant4 and other specific tools dedicated to tomography. Though, the detailed physical modeling of Geant4 is computationally demanding in order to simulate photon interactions and transport, particularly using voxelized phantoms. To circumvent the relatively slow simulation of voxelized phantoms for radiotherapy applications, GATE offers some relevant optimization methods to minimize the time consumption. In this study, specific absorbed fractions (SAFs) in Golem voxelized phantom using GATE Monte Carlo code for three optimization algorithms: Nested Parametrized Volume, Regular navigation algorithm and Compressed voxels methods have been used to calculate SAFs and compared to the literature data. The computation time has been also compared and discussed for the three methods. Compressed voxels method is more than 16 times faster than the two other parameterization methods for internal dosimetry field.

Constructing Spin-Adiabatic States for the Modeling of Spin-Crossing Reactions. I. A Shared-Orbital Implementation.

In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N2O, singlet-triplet conversion in CH2, and CO addition to Fe(CO)4], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.

Mathematical model of solid-liquid phase transitions applied to thermal energy accumulators

The paper presents a mathematical model for the numerical calculation of the heat flow and the volumetric fraction of the liquid phase of phase change materials (PCM) in containers of thermal energy accumulators of spherical and cylindrical shape, used in air conditioning and ventilation systems. The comparison of the calculated and experimental values for n-octadecane showed good convergence of the results. When using in geometry optimization algorithms of containers and when choosing PCM, the model has an advantage due to the high speed of calculations on it.

Field-Aware Interfaces in Continuum Solvation.

Continuum models of solvation are widespread tools for the prediction of solvation free energies of small molecular compounds from first principles. However, the continuum approximation at the core of these approaches limits their accuracy for the modeling of the aqueous solvation of compounds with highly polarized residue or of charged species. This is due to the fact that straightforward definitions of the continuum interface do not account for the reorganization effects induced by these solutes on the positions of surrounding solvent molecules. This kind of problem is usually overcome by stretching the definition of the continuum model, i.e., by using chemical intuition to adjust (usually shrinking) the size of the solvation interface close to the polarized/charged atoms. Nonetheless, this strategy introduces a significant number of additional parameters that need to be tuned and, at the same time, deters the model's transferability. A transferable solution is instead represented by an improved definition of the continuum interface, able to automatically account for the polarization/charge state of the embedded system. Following recent approaches in the literature, the component of the solute's electric field normal to the interface can be used as an effective proxy for the net charge of the embedded system. Here we show a simple definition of this field-aware approach as applied to the recently proposed soft-sphere continuum solvation (SSCS) method. In this model, each soft sphere composing the interface is allowed to readjust as a function of the value of the field flux through its surface. This effect introduces a complex dependence of the interface function on both the electronic and the ionic degrees of freedom of the solute. To account for this dependence during optimization procedures (e.g., the SCF loop and geometry optimization algorithms), the analytic derivatives of the new interface are reported and validated with their numerical counterparts. Application of the field-aware procedure to molecular compounds showing pathological behaviors with the standard SSCS approach show that significant improvements can be achieved by specifically tuning the newly introduced parameters.

An efficient method for minimum zone cylindricity error evaluation using kinematic geometry optimization algorithm

Cylindricity error evaluation is necessary to verify the cylindrical product function and to control the manufacturing process. This paper proposes a novel method for minimum zone cylindricity error evaluation based on kinematic geometry optimization algorithm (KGOA). The proposed method shows excellent performance in the cylindricity error evaluation process. First, the theoretical basis and representation for the minimum zone programming evaluation model are presented. Next, a new approach for extracting feature points is proposed using projective transformation and convex set construction. Instead of all measured points, the extracted feature points are used for the cylindricity error evaluation. On comparing the proposed method with other existing methods based on some literature data sets, agreement or improved solutions are obtained. The simulation and experiment results show that the proposed method can achieve optimum solutions accurately and improve the implementation efficiency. Compared with the commercial software of Coordinate Measuring Machine, the proposed method can reduce the average calculating time by half while retaining the accuracy of evaluation results. The basis of this method can also be applied for other geometrical error evaluation in engineering metrology.

Gray Box Modeling of Power Transformer Windings Based on Design Geometry and Particle Swarm Optimization Algorithm

Reliable models to predict the fast transient response of transformer windings are categorized into three groups: 1) white box; 2) black box; and 3) gray box models. Each group is applicable to solve a certain problem and includes its own advantages, hardly replacable by another group. The gray box methodology is a compromise between black and white box approaches which is investigated profoundly in this paper. A new method based on design geometry estimation is applied to accomplish transient simulation. The introduced procedure is probed on a noninterleaved double disk winding. Simulation and experimental results confirm that the gray box approach is applicable to both terminal and internal response estimation of a transformer when there is no knowledge of the transformer's internal specifications. The parameter identification of the model is performed by the particle swarm optimization algorithm.