scholarly journals High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 536
Author(s):  
Junjun Shi ◽  
Jingfang Shen ◽  
Yaohui Li
Keyword(s):  
Correlation Function ◽  
High Precision ◽  
Screening Method ◽  
Kriging Model ◽  
Modeling Method ◽  
Evaluation Point ◽  
Sampling Points ◽  
Close Distance ◽  
Candidate Point ◽  
Hybrid Sampling

Finding new valuable sampling points and making these points better distributed in the design space is the key to determining the approximate effect of Kriging. To this end, a high-precision Kriging modeling method based on hybrid sampling criteria (HKM-HS) is proposed to solve this problem. In the HKM-HS method, two infilling sampling strategies based on MSE (Mean Square Error) are optimized to obtain new candidate points. By maximizing MSE (MMSE) of Kriging model, it can generate the first candidate point that is likely to appear in a sparse area. To avoid the ill-conditioned correlation matrix caused by the too close distance between any two sampling points, the MC (MSE and Correlation function) criterion formed by combining the MSE and the correlation function through multiplication and division is minimized to generate the second candidate point. Furthermore, a new screening method is used to select the final expensive evaluation point from the two candidate points. Finally, the test results of sixteen benchmark functions and a house heating case show that the HKM-HS method can effectively enhance the modeling accuracy and stability of Kriging in contrast with other approximate modeling methods.

scholarly journals An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1985
Author(s):  
Yaohui Li ◽  
Junjun Shi ◽  
Zhifeng Yin ◽  
Jingfang Shen ◽  
Yizhong Wu ◽  
...  
Keyword(s):  
Correlation Function ◽  
Dimension Reduction ◽  
Principal Component ◽  
Kriging Model ◽  
Modeling Method ◽  
High Dimensional ◽  
Approximation Process ◽  
Correlation Parameter ◽  
Design Variables ◽  
Low Dimensional

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements.

scholarly journals Geological Modeling Method Based on the Normal Dynamic Estimation of Sparse Point Clouds

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1819
Author(s):  
Tiandong Shi ◽  
Deyun Zhong ◽  
Liguan Wang
Keyword(s):  
Point Cloud ◽  
Minimum Spanning Tree ◽  
Point Clouds ◽  
Original Method ◽  
Modeling Method ◽  
Geological Modeling ◽  
Improved Method ◽  
Normal Estimation ◽  
Sampling Points ◽  
Correct Point

The effect of geological modeling largely depends on the normal estimation results of geological sampling points. However, due to the sparse and uneven characteristics of geological sampling points, the results of normal estimation have great uncertainty. This paper proposes a geological modeling method based on the dynamic normal estimation of sparse point clouds. The improved method consists of three stages: (1) using an improved local plane fitting method to estimate the normals of the point clouds; (2) using an improved minimum spanning tree method to redirect the normals of the point clouds; (3) using an implicit function to construct a geological model. The innovation of this method is an iterative estimation of the point cloud normal. The geological engineer adjusts the normal direction of some point clouds according to the geological law, and then the method uses these correct point cloud normals as a reference to estimate the normals of all point clouds. By continuously repeating the iterative process, the normal estimation result will be more accurate. Experimental results show that compared with the original method, the improved method is more suitable for the normal estimation of sparse point clouds by adjusting normals, according to prior knowledge, dynamically.

scholarly journals A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 149
Author(s):  
Yaohui Li ◽  
Jingfang Shen ◽  
Ziliang Cai ◽  
Yizhong Wu ◽  
Shuting Wang
Keyword(s):  
Global Optimization ◽  
Pareto Frontier ◽  
Kriging Model ◽  
Optimization Method ◽  
Function Evaluation ◽  
Sampling Point ◽  
Constrained Global Optimization ◽  
Multi Objective ◽  
Sample Data ◽  
Sampling Points

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

The performance comparison of typical notched flexure hinges

2019 ◽  
Vol 234 (9) ◽  
pp. 1859-1867
Author(s):  
Wei Ma ◽  
Rongqi Wang ◽  
Xiaoqin Zhou ◽  
Guangwei Meng
Keyword(s):  
High Resolution ◽  
High Precision ◽  
Compliant Mechanisms ◽  
Performance Comparison ◽  
Modeling Method ◽  
Stress Concentrations ◽  
High Demand ◽  
Flexure Hinges ◽  
Matrix Modeling ◽  
Practical Guidelines

Flexure hinges, which serve as the crucial joints in a large number of compliant mechanisms, have been widely applied in a variety of significant fields where there is high demand for the micro/nano motions with high resolution and high precision. Currently, an increasing number of notched flexure hinges with different structures and performances have been rapidly developed, but the existing performance comparisons on different notched flexure hinges were only conducted on seldom typical structures and are far from the comprehensiveness and fairness due to the different comparative conditions and discrepant evaluating indexes. Therefore, the finite beam-based matrix modeling method and nondimension precision factors will be employed in comprehensive comparing and ranking of 13 types of frequently-used notched flexure hinges in terms of their main compliances, motion accuracies, and stress concentrations, further providing useful practical guidelines to develop the compliant mechanisms with excellent overall performances.

scholarly journals An Online Gravity Modeling Method Applied for High Precision Free-INS

Sensors ◽  
2016 ◽  
Vol 16 (10) ◽  
pp. 1541 ◽  
Author(s):  
Jing Wang ◽  
Gongliu Yang ◽  
Jing Li ◽  
Xiao Zhou
Keyword(s):  
High Precision ◽  
Modeling Method ◽  
Gravity Modeling

HDD Slider Air Bearing Design Optimization Using a Surrogate Model

2005 ◽  
Author(s):  
Naozumi Tsuda ◽  
David B. Bogy
Keyword(s):  
Convergence Rate ◽  
Cost Function ◽  
Surrogate Model ◽  
Search Space ◽  
Kriging Model ◽  
Flying Height ◽  
Direct Algorithm ◽  
Air Bearing ◽  
High Convergence Rate ◽  
Sampling Points

This report addresses a new optimization method in which the DIRECT algorithm is used in conjunction with a surrogate model. The DIRECT algorithm itself can find the global optimum with a high convergence rate. However the convergence rate can be much improved by coupling DIRECT with a surrogate model. The surrogate model known as the Kriging model is used in this research. It is determined by using sampling points generated by the DIRECT algorithm. This model expresses the shape of a hyper surface approximation of the cost function over the entire search space. Finding the optimum point on this hyper surface is very fast because it is not necessary to solve the time consuming air bearing equations. By using this optimum candidate as one of the DIRECT sampling points, we can eliminate many cost function evaluations. To illustrate the power of this approach we first present some simple optimization examples using known difficult functions. Then we determine the optimum design of a slider with 5nm flying height (FH) starting with a design that has a 7nm FH.

Surrogate modeling of a 3D scramjet-powered hypersonic vehicle based on screening method IFFD

2016 ◽  
Vol 231 (2) ◽  
pp. 265-278 ◽  
Author(s):  
Chen Boyi ◽  
Liu Yanbin ◽  
Shen Haidong ◽  
Lu Yuping
Keyword(s):  
Vehicle Dynamics ◽  
Screening Method ◽  
Kriging Model ◽  
Surrogate Models ◽  
Hypersonic Vehicle ◽  
Fractional Factorial ◽  
Gap Metric ◽  
Alternative Approach ◽  
Pitch Moment ◽  
The Difference

The emphasis of this paper lies in the development of an efficient approach to reproduce the behaviors of the scramjet-powered hypersonic system with high fidelity. The modeling of the dual-mode scramjet powered hypersonic vehicle dynamics with shock interaction, Ram-to-Scram transition, and finite rate chemistry reaction is firstly introduced. The structure of surrogate model is identified with the implement of iterative fractional factorial design (IFFD). In order to declare the reliability of the surrogate models, ν-gap metric is applied to distinguish the difference among these surrogate models in terms of closed-loop performance. The results show that the influence of Mach number on the aerodynamics should not be overlooked, and the effect of propulsion system to the aerodynamic pitch moment is dramatic. Further, the partial Kriging model appears to have the closest plants throughout the flight envelope compared with the full Kriging model and polynomials model. Nevertheless, considering the briefness of analytical expression, the polynomials model may be an alternative approach for design-oriented modeling.

scholarly journals High-Precision Dynamics Characteristic Modeling Method Research considering the Influence Factors of Hydropneumatic Suspension

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Wenguang Wu ◽  
Hongliang Tang ◽  
Sha Zhang ◽  
Lin Hu ◽  
Fanhao Zhang
Keyword(s):  
Cfd Simulation ◽  
Ride Comfort ◽  
Fluid Dynamic ◽  
Influence Factors ◽  
Kriging Model ◽  
Modeling Method ◽  
Effect Of Temperature ◽  
Oil Viscosity ◽  
Nonlinear Characteristics ◽  
And Control

In recent years, hydropneumatic suspension (HPS) has come into widespread use for improving the ride comfort and handling of mining dump trucks and off-road vehicles. Therefore, it is critical to improve the mathematical modeling accuracy to enhance the design and control efficiency and accuracy of HPS. This paper aims to propose a model for improving the modeling precision by considering the effect of different factors on HPS characteristics. A computational fluid dynamic (CFD) model of a HPS was developed, and the volume of fluid (VOF) method was used for the transient calculations in order to simulate the fluid dynamic characteristics and determine the damping and stiffness forces of HPS. The effect of temperature, oil viscosity, nitrogen dissolution rate, and suspension vibration speed on the nonlinear characteristics of HPS was investigated. A limited number of simulation sample points were designed based on the variation ranges of the above factors using the design of experiment (DOE) method. The corresponding damping and stiffness force of each sample point were calculated by CFD simulation. The obtained simulation data were utilized for the fitting of a Kriging model. The results demonstrated that the Kriging model can provide high accuracy, with a prediction error lower than 5%. The proposed modeling method of the HPS nonlinear characteristics is highly efficient, accurate, and faster than traditional methods.

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