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To present the models with many model parameters by polynomial chaos expansion (PCE), and improve the accuracy, this paper aims to present dimension-adaptive algorithm-based PCE technique and verify the feasibility of the proposed method through taking solid rocket motor ignition under low temperature as an example.

The main approaches of this work are as follows: presenting a two-step dimension-adaptive algorithm; through computing the PCE coefficients using dimension-adaptive algorithm, improving the accuracy of PCE surrogate model obtained; and applying the proposed method to uncertainty quantification (UQ) of solid rocket motor ignition under low temperature to verify the feasibility of the proposed method.

The result indicates that by means of comparing with some conventional non-invasive method, the proposed method is able to raise the computational accuracy significantly on condition of meeting the efficiency requirement.

This paper proposes an approach in which the optimal non-uniform grid that can avoid the issue of overfitting or underfitting is obtained.

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

The purpose of this study is to decrease the computation time that the large number of simulations involved in a parametric sweep when the model is in a three-dimensional environment.

In this paper, a new methodology combining the PCE and a controlled, elitist genetic algorithm is proposed to design IPT systems. The relationship between the quantities of interest (mutual inductance and ferrite volume) and structural parameters (ferrite dimensions) is expressed by a PCE metamodel. Then, two objective functions corresponding to mutual inductance and ferrite volume are defined. These are combined together to obtain optimal parameters with a trade-off between these outputs.

According to the number of individuals and the generations defined in the optimization algorithm in this paper, it needs to calculate 20,000 times in a 3D environment, which is quite time-consuming. But for PCE metamodel of mutual inductance M, it requires at least 100 times of calculations. Afterward, the evaluation of M based on the PCE metamodel requires 1 or 2 s. So compared to a conventional optimization based on the 3D model, it is easier to get optimized results with this approach and it saves a lot of computation time.

The multiobjective optimization based on PCEs could be helpful to perform the optimization when considering the system in a realistic 3D environment involving many parameters with low computation time.

Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models.

In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels.

To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent.

The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

The high probability of the occurrence of separation bubbles or shocks and early transition to turbulence on surfaces of airfoil makes it very difficult to design high-lift and high-speed Natural-Laminar-Flow (NLF) airfoil for high-altitude long-endurance unmanned air vehicles. To resolve this issue, a framework of uncertainty-based design optimization (UBDO) is developed based on an adjusted polynomial chaos expansion (PCE) method.

The γ ̄Re-θt transition model combined with the shear stress transport k-ω turbulence model is used to predict the laminar-turbulent transition. The particle swarm optimization algorithm and PCE are integrated to search for the optimal NLF airfoil. Using proposed UBDO framework, the aforementioned problem has been regularized to achieve the optimal airfoil with a tradeoff of aerodynamic performances under fully turbulent and free transition conditions. The tradeoff is to make sure its good performance when early transition to turbulence on surfaces of NLF airfoil happens.

The results indicate that UBDO of NLF airfoil considering Mach number and lift coefficient uncertainty under free transition condition shows a significant deterioration when complicated flight conditions lead to early transition to turbulence. Meanwhile, UBDO of NLF airfoil with a tradeoff of performances under both fully turbulent and free transition conditions holds robust and reliable aerodynamic performance under complicated flight conditions.

In this work, the authors build an effective uncertainty-based design framework based on an adjusted PCE method and apply the framework to design two high-performance NLF airfoils. One of the two NLF airfoils considers Mach number and lift coefficient uncertainty under free transition condition, and the other considers uncertainties both under fully turbulent and free transition conditions. The results show that robust design of NLF airfoil should simultaneously consider Mach number, lift coefficient (angle of attack) and transition location uncertainty.

The collocation-based stochastic response surface method (CSRSM) is widely used in geotechnical reliability analyses due to its efficiency and accuracy. Determining the optimal truncated order of the associated polynomial chaos expansion (PCE) is important, as it may strongly affect the practical applicability of CSRSM.

This study investigates the performance of different optimal order selection strategies used in the CSRSM and proposes a new cross-order validation method. First, several methods commonly used for optimal order selection are briefly reviewed, and their merits and limitations for reliability analyses are discussed. Then, an improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed.

In total, ten simple mathematical examples from the literature are employed to perform a preliminary test on the proposed method, and a comparative study is conducted to demonstrate its advantages with respect to some other existing methods.

A total of three typical geotechnical problems are employed to demonstrate the performance of the proposed method in geotechnical practice.

An improved optimal order selection method that achieves a better trade-off between efficiency and accuracy is proposed. The threshold value of the deterministic coefficient used for the proposed method is discussed.

The purpose of this paper is to develop a new formulation using spectral approach, which can predict the wave behavior to uncertain parameters in mid and high frequencies.

The work presented is based on a hybridization of a spectral method called the “wave finite element (WFE)” method and a non-intrusive probabilistic approach called the “polynomial chaos expansion (PCE).” The WFE formulation for coupled structures is detailed in this paper. The direct connection with the conventional finite element method allows to identify the diffusion relation for a straight waveguide containing a mechanical or geometric discontinuity. Knowing that the uncertainties play a fundamental role in mid and high frequencies, the PCE is applied to identify uncertainty propagation in periodic structures with periodic uncertain parameters. The approach proposed allows the evaluation of the dispersion of kinematic and energetic parameters.

The authors have found that even though this approach was originally designed to deal with uncertainty propagation in structures it can be competitive with its low time consumption. The Latin Hypercube Sampling (LHS) is also employed to minimize CPU time.

The approach proposed is quite new and very simple to apply to any periodic structures containing variabilities in its mechanical parameters. The Stochastic Wave Finite Element can predict the dynamic behavior from wave sensitivity of any uncertain media. The approach presented is validated for two different cases: coupled waveguides with and without section modes. The presented results are verified vs Monte Carlo simulations.

This study conducts a comparative study on the performance of reliability assessment methods based on adaptive surrogate models to accurately assess the reliability of automobile components, which is critical to the safe operation of vehicles.

In this study, different adaptive learning strategies and surrogate models are combined to study their performance in reliability assessment of automobile components.

By comparing the reliability evaluation problems of four automobile components, the Kriging model and Polynomial Chaos-Kriging (PCK) have better robustness. Considering the trade-off between accuracy and efficiency, PCK is optimal. The Constrained Min-Max (CMM) learning function only depends on sample information, so it is suitable for most surrogate models. In the four calculation examples, the performance of the combination of CMM and PCK is relatively good. Thus, it is recommended for reliability evaluation problems of automobile components.

Although a lot of research has been conducted on adaptive surrogate-model-based reliability evaluation method, there are still relatively few studies on the comprehensive application of this method to the reliability evaluation of automobile component. In this study, different adaptive learning strategies and surrogate models are combined to study their performance in reliability assessment of automobile components. Specially, a superior surrogate-model-based reliability evaluation method combination is illustrated in this study, which is instructive for adaptive surrogate-model-based reliability analysis in the reliability evaluation problem of automobile components.

The polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.

First, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.

Several examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.

The number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.

The purpose of this paper is performing a global sensitivity analysis for automotive electromagnetic compatibility (EMC) measurements related to the CISPR 25 setup in order to examine the effect of the setup uncertainties on the resonance phenomenon.

An integral equation formulation is combined with Darwin model and special Green’s functions to model the configuration. The method of Sobol’ indices is used to gain sensitivity factors enhanced with a polynomial chaos metamodel.

The proposed model resulted in by orders of magnitude lower number of degrees of freedom and runtime compared to popular numerical methods, e.g. finite element method. The result of the sensitivity study is in good agreement with the underlying physical phenomena and improves the understanding of the resonances.

The fast model supplemented by the sensitivity factors can be used in EMC design and optimization.

The proposed method is original in the sense of combining a polynomial chaos metamodel with a low-cost integral equation model to reduce the computational demand for the sensitivity study.