Kriging Basis Functions Research Articles

Surrogate modeling of open-celled metal foam sound absorbers with stepwise property gradients

In this paper, we develop a Kriging-based surrogate model to predict the sound absorption performance of open-celled metal foams with user-defined stepwise relative density gradients. An experimentally validated transfer matrix model is used to generate training data capturing the absorption profiles of metal foams with various geometrical parameters. We deploy a spatial analysis method to create influence surfaces around each sample data point and depict its effect on the observed output by using Kriging's basis functions. The surrogate model has an in-built machine learning framework that uses a genetic algorithm and a maximum likelihood function to tune the weights that define these influence surfaces. Using this approach, we successfully developed a data-fed, supervised prediction model that estimates absorption coefficient of a virtual metal foam sample. Post-validation predicted values for unknown sample configurations show satisfactory agreement with their actual absorption coefficients. Finally, we implement the developed metamodel as an iOS application as a potential low-cost tool to reduce testing costs and enable rapid design iterations for acoustic design problems.

Improved Method for Distributed Parameter Model of Solenoid Valve Based on Kriging Basis Function Predictive Identification Program

In this paper, a method for the improvement of the calculation accuracy of the distributed parameter model (DPM) of electromagnetic devices is proposed based on the kriging basis function predictive identification program (PIP). Kriging is mainly an optimal interpolation method which uses spatial self-covariance, and takes a polynomial as the basis function. The accuracy of the kriging-based surrogate model can be improved by adjusting the related functions and hyperparameters. Based on the DPM of a solenoid valve, there exist certain errors in the estimation. They can be summarized as follows: Firstly, the estimation error of magnetic flux leakage (MFL) permeance is caused directly by the deviation of the magnetic flux tube due to the segmented magnetic field line. Secondly, the estimation error of soft magnetic resistance because of the nonlinearity of the permeability of soft magnetic material leads to the change of soft magnetic resistance alongside the magnetic flux. In this paper, an improved kriging error correction method is applied to modify the leak permeance and soft magnetic resistance calculation. The kriging basis function is adjusted to adapt to the data curve of the MFL permeance error data. The calculated MFL permeance data are compared with the error variation data to select the appropriate basis function. To improve the computational efficiency, the PIP is proposed to select the appropriate basis function. The modified MFL permeance data and soft magnetic resistance are substituted into the DPM for improving the computational accuracy and efficiency of the solenoid valve.

Testing of the Kriging-based Finite Element to Shell Structures with Varying Thickness

A variant of the finite element method with Kriging basis functions has been recently developed and applied to plane, plate bending, and shell elastostatic problems. The main advantage of this novel method is that high degree of basis functions can be easily constructed without additional finite element nodes (such as mid-side and inner nodes). This paper revisits the formulation of the Kriging-based finite element method for analysis of curved shell structures, referred to as K-Shell, and presents new numerical tests to shell structures with varying thickness. The K-Shell was formulated based on degenerated 3D elasticity theory. The basis functions were constructed using a set of nodes covering several layers of triangular elements and were employed to approximate both the displacement and geometry. The quartic polynomial basis was chosen to alleviate shear and membrane locking. The K-Shell has been tested using a series of shell benchmark problems with constant shell thickness. The tests showed that K-Shell performed very well in analyzing moderately thick smooth shells. In this paper the K-Shell is tested using two modified shell benchmark problems with varying thickness, i.e. the modified pinched cylinder and the modified hemispherical shell with 18 degrees cut-off. The converged results of three-dimensional finite element model using commercial software Abaqus were used to assess the convergence of the results. The tests show that the performance of K-Shell in analyzing shells with varying thickness is satisfactory.

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.