Taylor Kriging Research Articles

Dynamic PRA-Based Estimation of PWR Coping Time Using a Surrogate Model for Accident Tolerant Fuel

This study proposes an interpolation-based response surface surrogate methodology to manage a large number of scenarios in dynamic probabilistic risk assessment. It adopts the shape Dynamic Time Warping algorithm to cluster the interpolation neighborhood from time series sample data. The interpolation method was adapted from Taylor Kriging to allow a reduced-order model of the Taylor series. In order to demonstrate its applicability to complex issues in risk assessment for nuclear engineering, an example risk response surface to estimate emergency core cooling system (ECCS) criteria for triplex silicon carbide (SiC) accident-tolerant fuel was constructed. The response surface was exploited to estimate the cumulative failure probability of the fuel cladding structure due to the uncertainties in operator actions and safety systems. The functional failures were assessed based on a combination of individual layer failures computed by coupling Risk Analysis Virtual Environment software with a pressurized water reactor 1000-MW(electric) RELAP5 model and the in-house fuel performance assessment module. Results showed that SiC cladding failure probability spiked less than 1 min after a large-break loss-of- coolant accident whenever the current ECCS criteria for Zircaloy-4 (Zr-4) cladding was used. However, it still provides an increased safety margin of three orders of magnitude compared to Zr-4. This positive margin could be utilized to relax active ECCS requirements by allowing deviations of up to 450 s in its actuation time. The proposed surrogate methodology generated a response surface of SiC cladding failure probability reasonably well, with a significant savings of computation time. This methodology is expected to be useful in the analysis of system response with complex uncertainty sources.

Optimal shape design of multi-layered IPMSM using adaptive dynamic Taylor Kriging model

PurposeThis paper aims to propose a numerically efficient multi-objective optimization strategy, which can improve both the efficiency and performance during the optimization process.Design/methodology/approachThis paper discusses the multi-objective optimization algorithm by combining multi-objective differential evolution (MODE) algorithm with an adaptive dynamic Taylor Kriging (ADTK) model.FindingsThe proposed approach is validated through application to an analytic example and applied to a shape optimal design of a multi-layered interior permanent magnet synchronous motor for torque ripple reduction while maintaining the average torque.Originality/valueThe ADTK model selects its basis functions adaptively and dynamically so that it may have better accuracy than any other Kriging models. Through adaptive insertion of new sampling data, it guarantees minimum required sampling data for a desired fitting accuracy.

A Novel Reliability-Based Optimal Design of Electromagnetic Devices Based on Adaptive Dynamic Taylor Kriging

This paper proposes an efficient reliability-based optimization algorithm based on adaptive dynamic Taylor Kriging (ADTK). In the ADTK model, the basis functions are optimally selected by the binary particle swarm optimization algorithm and the minimal number of sampling data with a desired fitting error is decided. To evaluate performance of reliability calculation, the Monte Carlo simulation method is employed, where the performance constraint functions are constructed by the ADTK surrogate model. Overall, an electromagnetic application-superconducting magnetic energy storage device (TEAM problem 22) is used to investigate performances of the proposed method.

A Novel Subregion-Based Multidimensional Optimization of Electromagnetic Devices Assisted by Kriging Surrogate Model

A novel subregion-based optimization strategy utilizing an adaptive dynamic Taylor Kriging (ADTK) surrogate model is developed for a multidimensional optimal design of electromagnetic devices. In the algorithm, the whole design space is divided into a series of subregion, which has its own local ADTK model with optimal set of basis functions. For all subregions, a global optimal solution is found by using particle swarm optimization with the help of the local ADTK models of the objective and constraint functions. The proposed algorithm improves remarkably the accuracy of the ADTK model by reducing the computational complexity. It also significantly reduces the computational cost especially for an optimal design of large-scale multidimensional problems. Finally, the effectiveness of the proposed method is demonstrated through applications to two benchmark problems: TEAM problems 22 and 25.

Genetic algorithm optimized Taylor Kriging surrogate model for system reliability analysis of soil slopes

A Kriging-based surrogate model provides a logically strict and efficient tool to evaluate the system reliability of a slope. However, the constant trend function adopted in the ordinary Kriging (OK) cannot always well capture the nonlinear non-smooth properties of a slope stability problem. Although the universal Kriging (UK) with a linear or a quadratic trend function could be an alternative for some cases, a higher order nonlinear trend function is preferable for some more complicated nonlinear non-smooth cases in the slope stability analysis. To address this problem, a genetic algorithm (GA) optimized Taylor Kriging (TK) surrogate model is proposed for the system reliability analysis of soil slopes in this paper. The proposed surrogate model allows a unified framework of the Kriging, considering different extents of nonlinear properties according to the Taylor expansion order (e.g., can be as high as the fourth order). The GA is introduced to search for the optimal correlation parameters, of which the effectiveness is verified by an analytical example. The feasibility of the proposed surrogate model is then validated by two analytical examples before its application to the practical slope reliability analyses. The results show that the UK model can be incorporated into the TK model, and the TK model provides a higher accuracy and efficiency when facing the highly nonlinear slope stability problems. It is also found that the UK model cannot fully capture the potential nonlinear properties existed in a slope stability model as compared with the higher order TK model.

A Novel Adaptive Dynamic Taylor Kriging and Its Application to Optimal Design of Electromagnetic Devices

An adaptive dynamic Taylor Kriging (ADTK) is developed and combined with the particle swarm optimization algorithm to get a numerically efficient optimization strategy. For given sampling data, the ADTK always minimizes its fitting error without regard to a problem through optimal selection of basis functions among Taylor polynomials. An adaptive sampling method is also proposed based on the fitting error estimation, through which a minimum number of sampling data for a desired level of fitting error can be controlled. The proposed approaches are tested with an analytic function and the TEAM 25.

Cost estimation using ANFIS

ABSTRACTCost function estimation is vital for decision-making in project management. In this article, a novel cost estimator is investigated based on an adaptive neuro-fuzzy inference system (ANFIS). In the numerical studies, ANFIS is tested to modeling pressure vessel cost as a case study. According to the comparative results, ANFIS shows better accuracy than multiple linear regression (MLR), Taylor Kriging (TK), and artificial neural networks (ANNs). Hence, ANFIS can be applicable to various cost function estimation problems.

A Numerically Efficient Multi-Objective Optimization Algorithm: Combination of Dynamic Taylor Kriging and Differential Evolution

A dynamic Taylor Kriging (DTK) is newly developed and combined with a multi-objective differential evolution algorithm to get a numerically efficient multi-objective optimization strategy. In the DTK, basis functions are not predefined but optimally selected so that the fitting error with the given sampling data may be minimized. In the developed multi-objective optimization algorithm, the DTK provides predicted objective function values as an alternative to direct finite-element analysis. The effectiveness of the proposed DTK and multi-objective optimization strategy are verified through applications to analytic example and TEAM 22.

A Global Optimization Algorithm for Electromagnetic Devices by Combining Adaptive Taylor Kriging and Particle Swarm Optimization

This paper presents an efficient optimization strategy which employs adaptive Taylor Kriging and Particle Swarm Optimization (PSO). In this method, the objective function of electromagnetic problem is interpolated by using adaptive Taylor Kriging, in which the covariance parameter is obtained by Maximum Likelihood Estimation (MLE). And then, PSO is used to search for optimal solutions of electromagnetic problem. The proposed algorithm is verified its validity by analytic functions and TEAM (Testing of Electromagnetic Analysis Method) problem 22.

Performance of a physical surrogate in the sequential approximate optimization of space trusses

PurposeThe purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to demonstrate its efficiency in reducing the number of high fidelity (HF) runs in the optimization process.Design/methodology/approachIn this work, surrogate models are built for space truss structures. This study uses functional as well as physical surrogates. In the latter, a grid analogy of the space truss is used thereby reducing drastically the analysis cost. Global and local approaches are considered. The latter will require a globalization scheme (sequential approximate optimization (SAO)) to ensure convergence.FindingsPhysically based surrogates were proposed. Classical techniques, namely Taylor series and kriging, are also implemented for comparison purposes. A parameter study in kriging is necessary to select the best kriging model to be used as surrogate. A test case was considered for optimization and several surrogates were built. The CPU time is reduced when compared with the HF solution, for all surrogate‐based optimization performed. The best result was achieved combining the proposed physical model with additive corrections in a SAO strategy in which C1 continuity was imposed at each trust region center. Some guidance for other engineering applications was given.Originality/valueThis is the first time that physical‐based surrogates for optimum design of space truss systems are used in the SAO framework. Physical surrogates typically exhibit better generalization properties than other surrogates forms, produce faster solutions, and do not suffer from dimensionality curse when used in approximate optimization strategies.

System development and application of Taylor Kriging metamodeling

PurposeThe purpose of this paper is to develop an application software interpolation system based on Taylor Kriging (TK) metamodeling, and apply the developed software system to addressing some engineering interpolation problems.Design/methodology/approachTK is a novel Kriging model where Taylor expansion is used to identify the base functions of drift function in Kriging. The paper explains the methodology of TK, illustrates the development of software, and reports the results of two case studies by comparing TK with several regression methods.FindingsTK has the advantage of interpolation accuracy, and the developed Kriging software system is useful and can be conveniently manipulated by users.Practical implicationsThe developed software system can benefit practical engineering applications that need accurate interpolations under limited observations.Originality/valueThis paper develops an application software interpolation system based on a novel TK metamodel, and the practical engineering applications show that it can provide accurate interpolations under limited observations.

Simulation optimization based on Taylor Kriging and evolutionary algorithm

This paper develops a simulation optimization algorithm based on Taylor Kriging and evolutionary algorithm (SOAKEA) for simulation models with high computational expenses. In SOAKEA, an evolutionary algorithm is used to search for optimal solutions of a simulation model, and Taylor Kriging temporarily serves as a surrogate fitness function of this evolutionary algorithm to evaluate solutions. Taylor Kriging is an enhanced version of Kriging where Taylor expansion is used to approximate the drift function of Kriging, and it improves the interpolation accuracy of Kriging. The structures and properties of SOAKEA are analyzed. A combination correction strategy is created, and it effectively reduces the computational expense of SOAKEA. The empirical comparison of SOAKEA with some other well-known metaheuristics is conducted, and the proposed SOAKEA uses particle swam optimization, a population-based evolutionary algorithm, to solve four simulation problems based on multimodal benchmark functions. The results indicate that SOAKEA has significant advantages in optimizing simulation models with high computational expenses.

Taylor Kriging Metamodeling for Stochastic Simulation Interpolation

This paper applies a novel Kriging model to the interpolation of stochastic simulation with high computational expense. The novel Kriging model is developed by using Taylor expansion to construct a drift function for Kriging, thus named Taylor Kriging. The interpolation capability of Taylor Kriging for stochastic simulation is empirically compared with those of Simple Kriging and Ordinary Kriging according to two stochastic simulation cases. Results show that the interpolation of Taylor Kriging is more accurate than Simple Kriging and Ordinary Kriging. The authors analyze two key factors in stochastic simulation, simulation replications and variance, which influence the accuracy of Kriging interpolation, and obtain some important empirical results.

Prediction of wireless network connectivity using a Taylor Kriging approach

The research aim of this paper is to investigate the effectiveness of a new Kriging model which uses Taylor expansion to predict wireless network connectivity. Wireless network connectivity is measured by the strength of emitted signal power from the tower to the point in question. The prediction results are compared with those from the literature where an Ordinary Kriging model and a neural network are used to conduct the same prediction. Root mean squared error (RMSE) and maximum absolute relative error (MARE) show that the prediction results of the new Kriging model are much better than those obtained before with average differences from 51.56% to 85%. This study shows the promise of the new Kriging model to accurately estimate wireless signal strength.

Prediction of wind speed time series using modified Taylor Kriging method

Wind speed forecasting is critical for the operations of wind turbine and penetration of wind energy into electricity systems. In this paper, a novel time series forecasting method is proposed for this purpose. This method originates from TK (Taylor Kriging) model, but is properly modified for the forecasting of wind speed time series. To investigate the performance of this new method, the wind speed data from an observation site in North Dakota, USA, are adopted. One-year hourly wind speed data are divided into 10 samples, and forecast is made for each sample. In the case study, both the modified TK method and (ARIMA) autoregressive integrated moving average method are employed and their performances are compared. It is found that on average, the proposed method outperforms the ARIMA method by 18.60% and 15.23% in terms of (MAE) mean absolute error and (RMSE) root mean square error. Meanwhile, further theoretical analysis is provided to discuss why the modified TK method is potentially more accurate than the ARIMA method for wind speed time series prediction.

Cost Estimation and Sensitivity Analysis on Cost Factors: A Case Study on Taylor Kriging, Regression and Artificial Neural Networks

This article applies Taylor kriging (TK) to cost estimation. The partial differentiation equation of TK is developed and used to assist in sensitivity analysis on cost factors. The capabilities of cost estimation and sensitivity analysis of TK are compared with those of regression and an artificial neural network (ANN) through application in a case study. The results show that TK can provide more accurate cost estimates than those of regression but worse than those of ANN, and both TK and regression are able to effectively find sensitive cost factors.