Use Of Kriging Models Research Articles

An innovative reliability-based design optimization method by combination of dual-stage adaptive kriging and genetic algorithm

PurposeThis study aims to propose an efficient method for solving reliability-based design optimization (RBDO) problems.Design/methodology/approachIn the proposed algorithm, genetic algorithm (GA) is employed to search the global optimal solution of design parameters satisfying the reliability and deterministic constraints. The Kriging model based on U learning function is used as a classification tool to accurately and efficiently judge whether an individual solution in GA belongs to feasible region.FindingsCompared with existing methods, the proposed method has two major advantages. The first one is that the GA is employed to construct the optimization framework, which is helpful to search the global optimum solutions of the RBDO problems. The other one is that the use of Kriging model is helpful to improve the computational efficiency in solving the RBDO problems.Originality/valueSince the boundaries are concerned in two Kriging models, the size of the training set for constructing the convergent Kriging model is small, and the corresponding efficiency is high.

Application of kriging models for a drug combination experiment on lung cancer.

Combinatorial drugs have been widely applied in disease treatment, especially chemotherapy for cancer, due to its improved efficacy and reduced toxicity compared with individual drugs. The study of combinatorial drugs requires efficient experimental designs and proper follow-up statistical modeling techniques. Linear and nonlinear models are often used in the response surface modeling for such experiments. We propose the use of kriging models to better depict the response surfaces of combinatorial drugs. We illustrate our method via a drug combination experiment on lung cancer and further show how proper experimental designs can reduce the necessary run size. We demonstrate that only 27 runs are needed to predict all 512 runs in the original experiment and achieve better precision than existing analyses.

Optimisation of composite manufacturing processes with computer experiments and Kriging methods

This paper deals with the use of Kriging models in multi-objective optimisation of composite manufacturing processes. A comparative analysis of different optimisation methods was conducted for a case study devoted to resin transfer moulding (RTM) processes. The computerised experiments of composite manufacturing were based on a numerical simulation model of the RTM process. A Latin Hypercube Design (LHD) of the computer experiments was adopted. The computational results from the designed experiments were analysed and a Kriging model was built from the data. Finally, a data envelopment analysis (DEA) was conducted, based on the data generated from the Kriging model to optimise the RTM process. The overall performance of this method was evaluated.

Use of Kriging Models to Approximate Deterministic Computer Models

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization

Response surface methods have been used for a variety of applications in aerospace engineering, particularly in multidisciplinary design optimization. We investigate the use of kriging models as alternatives to traditional second-order polynomial response surfaces for constructing global approximations for use in a real aerospace engineering application, namely, the design of an aerospike nozzle. Our objective is to examine the difeculties in building and using kriging models to create accurate global approximations to facilitate multidisciplinary design optimization. Error analysis of the response surface and kriging models is performed, along with a graphical comparison of the approximations. Four optimization problems are also formulated and solved using both sets of approximation models to gain insight into their use for multidisciplinary design optimization. We end that the kriging models, which use only a constant “global” model and a Gaussian correlation function, yield global approximations that are slightly more accurate than the response surface models.

Use of kriging models to predict 12-hour mean ozone concentrations in Metropolitan Toronto—A pilot study

Ozone concentrations exhibit spatial variability within metropolitan areas, resulting in significantly different personal exposures among individuals. This paper uses the statistical technique, kriging, to explore the 12-h daytime (8am–8pm) ozone spatial variation and to predict mean outdoor ozone levels at home sites within the Toronto metropolitan area. Outdoor ozone measurements taken in the Toronto metropolitan area between June and August 1992 are used in kriging models to predict outdoor ozone concentrations. The performance of the model is evaluated by comparing actual home outdoor measurements with predicted values. Results indicate that kriging predictions are more accurate than using only the closest stationary ambient site measurements for determining home outdoor ozone concentrations within the metropolitan area. The average variogram obtained from pooling data throughout the entire sampling period shows a clear spatial trend in the outdoor ozone variation. Kriging predictions using the parameters from the average variogram perform as well as those using variograms from individual days. An approach for minimizing sample bias can be used to increase the accuracy of the predictions; cross-validation suggests that it is a reasonable procedure.