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This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level.

Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate.

Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day.

The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

Compared with the low-fidelity model, the high-fidelity model has both the advantage of high accuracy, and the disadvantage of low efficiency and high cost. A series of multi-fidelity surrogate modelling method were developed to give full play to the respective advantages of both low-fidelity and high-fidelity models. However, most multi-fidelity surrogate modelling methods are sensitive to the amount of high-fidelity data. The purpose of this paper is to propose a multi fidelity surrogate modelling method whose accuracy is less dependent on the amount of high-fidelity data.

A multi-fidelity surrogate modelling method based on neural networks was proposed in this paper, which utilizes transfer learning ideas to explore the correlation between different fidelity datasets. A low-fidelity neural network was built by using a sufficient amount of low-fidelity data, which was then finetuned by a very small amount of HF data to obtain a multi-fidelity neural network based on this correlation.

Numerical examples were used in this paper, which proved the validity of the proposed method, and the influence of neural network hyper-parameters on the prediction accuracy of the multi-fidelity model was discussed.

Through the comparison with existing methods, case study shows that when the number of high-fidelity sample points is very small, the R-square of the proposed model exceeds the existing model by more than 0.3, which shows that the proposed method can be applied to reducing the cost of complex engineering design problems.

The purpose of this paper is to investigate strategies for expedited dimension scaling of electromagnetic (EM)-simulated microwave and antenna structures, exploiting the concept of variable-fidelity inverse surrogate modeling.

A fast inverse surrogate modeling technique is described for dimension scaling of microwave and antenna structures. The model is established using reference designs obtained for cheap underlying low-fidelity model and corrected to allow structure scaling at high accuracy level. Numerical and experimental case studies are provided demonstrating feasibility of the proposed approach.

It is possible, by appropriate combination of surrogate modeling techniques, to establish an inverse model for explicit determination of geometry dimensions of the structure at hand so as to re-design it for various operating frequencies. The scaling process can be concluded at a low computational cost corresponding to just a few evaluations of the high-fidelity computational model of the structure.

The present study is a step toward development of procedures for rapid dimension scaling of microwave and antenna structures at high-fidelity EM-simulation accuracy.

The proposed modeling framework proved useful for fast geometry scaling of microwave and antenna structures, which is very laborious when using conventional methods. To the authors’ knowledge, this is one of the first attempts to surrogate-assisted dimension scaling of microwave components at the EM-simulation level.

The purpose of this paper is to explore the predictive validity of two measures of fidelity to the individual placement and support (IPS) approach to supported employment.

A systematic review and meta-analysis was conducted of IPS programs. In total, 30 studies provided information characterizing 69 cohorts and 8,392 participants. Predictive validity was assessed by a precision and negative prediction analysis and by multivariate analysis of deviance.

Fidelity scores on the IPS-15 scale of 60 or less accurately predicted poor outcomes, defined as 43 percent or less of participants commencing employment, in 100 percent of cohorts. Among cohorts with IPS-15 fidelity scores of 61-75, 63 percent attained good employment outcomes defined as 44 percent or more commencing employment. A similar pattern emerged from the precision analysis of the smaller sample of IPS-25 cohorts. Multivariate analysis of deviance for studies using the IPS-15 scale examined six cohort characteristics. Following adjustment for fidelity score, only fidelity score (χ²=15.31, df=1, p<0.001) and author group (χ²=35.01, df=17, p=0.01) representing an aspect of cohort heterogeneity, remained associated with commencing employment.

This study provides evidence of moderate, yet important, predictive validity of the IPS-15 scale across diverse international and research contexts. The smaller sample of IPS-25 studies limited the analysis that could be conducted.

Program implementation leaders are encouraged to first focus on attaining good fidelity, then supplement fidelity monitoring with tracking the percentage of new clients who obtain a competitive job employment over a pre-defined period of time.

The evidence indicates that good fidelity may be necessary but not sufficient for good competitive employment outcomes.

Reliable modeling of induction hardening requires a multi-physical approach, which makes it time-consuming. In designing an induction hardening system, combining such model with an optimization technique allows managing a high number of design variables. However, this could lead to a tremendous overall computational cost. This paper aims to reduce the computational time of an optimal design problem by making use of multi-fidelity modeling and parallel computing.

In the multi-fidelity framework, the “high-fidelity” model couples the electromagnetic, thermal and metallurgical fields. It predicts the phase transformations during both the heating and cooling stages. The “low-fidelity” model is instead limited to the heating step. Its inaccuracy is counterbalanced by its cheapness, which makes it suitable for exploring the design space in optimization. Then, the use of co-Kriging allows merging information from different fidelity models and predicting good design candidates. Field evaluations of both models occur in parallel.

In the design of an induction heating system, the synergy between the “high-fidelity” and “low-fidelity” model, together with use of surrogates and parallel computing could reduce up to one order of magnitude the overall computational cost.

On one hand, multi-physical modeling of induction hardening implies a better understanding of the process, resulting in further potential process improvements. On the other hand, the optimization technique could be applied to many other computationally intensive real-life problems.

This paper highlights how parallel multi-fidelity optimization could be used in designing an induction hardening system.

Extreme support vector regression (ESVR) has been widely used in the design, analysis and optimization of engineering systems of its fast training speed and good computational ability. However, the ESVR model is only able to utilize one-fidelity information of engineering system. To solve this issue, this paper extends extreme support vector regression (ESVR) to a multi-fidelity surrogate (MFS) model which can make use of a few expensive but higher-fidelity (HF) samples and a lot of inaccurate but cheap low-fidelity (LF) samples, named ESVR-MFS.

In the ESVR-MFS model, a kernel matrix is designed to evaluate the relationship between the HF and LF samples. The root mean square error of HF samples is used as the training error metric, and the optimal hyper-parameters of the kernel matrix are obtained through a heuristic algorithm.

A number of numerical problems and three engineering problems are used to compare the ESVR-MFS model with the single-fidelity ESVR model and two benchmark MFS models. The results show that the ESVR-MFS model exhibits competitive performance in both numerical cases and practical cases tested in this work.

The proposed approach exhibits great capability for practical multi-fidelity engineering design problems.

A MFS model is proposed based on ESVR, which can make full use of the advantages of both HF data and LF data to achieve optimal results at same or lower cost.

A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry probe, not only the geometric configuration, but the trajectory and thermal protection system (TPS). In the design optimization, the uncertainties of atmospheric and aerodynamic parameters are taken into account. The probability distribution information of the uncertainties are supposed to be unknown in the design. To ensure accuracy levels, time-consuming numerical models are coupled in the optimization. Multi-fidelity approach is designed for model management to balance the computational cost and accuracy.

Uncertainties which cannot defined by usual Gaussian probability distribution are modeled with degree of belief, and optimized through with multiple-objective optimization method. The optimization objectives are set to be the thermal performance of the probe TPS and the corresponding belief values. Robust Pareto front is obtained by an improved multi-objective density estimator algorithm. Multi-fidelity management is performed with an Artificial Neural Network (ANN) surrogate model. Analytical model is used first, and then with the improvement of accuracy, rather complex numerical models are activated. ANN updates the database during the optimization, and makes the solutions finally converge to a high-level accuracy.

The optimization method provides a way for conducting complex design optimization involving multi-discipline and multi-fidelity models. Uncertainty effects are analyzed and optimized through multi-disciplinary robust design. Because of the micro size, and uncertain impacts of aerodynamic and atmospheric parameters, simulation results show the performance trade-off by the uncertainties. Therefore an effective robust design is necessary for micro entry probe, particularly when details of model parameter are not available.

The optimization is performed through a new developed multi-objective density estimator algorithm. Affinity propagation algorithm partitions adaptively the samples by passing and analyzing messages between data points. Local principle component techniques are employed to resample and reproduce new individuals in each cluster. A strategy similar to NSGA-II selects data with better performance, and converges to the Pareto front. Models with different fidelity levels are incorporated in the multi-disciplinary design via ANN surrogate model. Database of aerodynamic coefficients is updated in an online manner. The computational time is greatly reduced while keeping nearly the same accuracy level of high fidelity model.

The purpose of this study is to describe the development of the 14-item reflective fostering fidelity rating (RFFR), an observational rating system to evaluate model fidelity of group facilitators in the Reflective Fostering Programme (RFP), a mentalisation-based psychoeducation programme to support foster carers. The authors assess usability, dimensionality, inter-rater reliability and discriminative ability of the RFFR.

Eighty video clip extracts documenting 20 RFP sessions were independently rated by four raters using the RFFR. The dimensionality of the RFFR was assessed using principal components analysis. Inter-rater agreement was assessed using the intra-class correlation coefficient.

The proportion of missing ratings was low at 2.8%. A single principal component summarised over 90% of the variation in ratings for each rater. The inter-rater reliability of individual item ratings was poor-to-moderate, but a summary score had acceptable inter-rater reliability. The authors present evidence that the RFFR can distinguish RFP sessions that differ in treatment fidelity.

To the best of the authors’ knowledge, this is the first investigation and report of the RFFR’s validity in assessing the programme fidelity of the RFP. The paper concludes that the RFFR is an appropriate rating measure for treatment fidelity of the RFP and useful for the purposes of both quality control and supervision.

Variable-fidelity optimization (VFO) frameworks generally aim at taking full advantage of high-fidelity (HF) and low-fidelity (LF) models to solve computationally expensive problems. The purpose of this paper is to develop a novel modified trust-region assisted variable-fidelity optimization (MTR-VFO) framework that can improve the optimization efficiency for computationally expensive engineering design problems.

Though the LF model is rough and inaccurate, it probably contains the gradient information and trend of the computationally expensive HF model. In the proposed framework, the extreme locations of the LF kriging model are firstly utilized to enhance the HF kriging model, and then a modified trust-region (MTR) method is presented for efficient local search. The proposed MTR-VFO framework is verified through comparison with three typical methods on some benchmark problems, and it is also applied to optimize the configuration of underwater tandem wings.

The results indicate that the proposed MTR-VFO framework is more effective than some existing typical methods and it has the potential of solving computationally expensive problems more efficiently.

The extreme locations of LF models are utilized to improve the accuracy of HF models and a MTR method is first proposed for local search without utilizing HF gradient. Besides, a novel MTR-VFO framework is presented which is verified to be more effective than some existing typical methods and shows great potential of solving computationally expensive problems effectively.