Efficient sampling methods for global reliability sensitivity analysis

An important problem in structure reliability analysis is how to reduce the failure probability. In this work, we introduce a main and total effect indices framework of global reliability sensitivity. By decreasing the uncertainty of input variables with high main effect indices, the most reduction of failure probability can be obtained. By decreasing the uncertainty of the input variables with small total effect indices (close to zero), the failure probability will not be reduced significantly. The efficient sampling methods for evaluating the main and total effect indices are presented. For the problem with large failure probability, a single-loop Monte Carlo simulation (MCS) is derived for computing these sensitivity indices. For the problem with small failure probability, the single-loop sampling methods combined with the importance sampling procedure (IS) and the truncated importance sampling procedure (TIS) respectively are derived for improving the calculation efficiency. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the calculation methods and illustrating the engineering significance of the global reliability sensitivity indices.     

Non-parametric methods for global sensitivity analysis of model output with dependent inputs

This paper addresses the issue of performing global sensitivity analysis of model output with dependent inputs. First, we define variance-based sensitivity indices that allow for distinguishing the independent contributions of the inputs to the response variance from their mutual dependent contributions. Then, two sampling strategies are proposed for their non-parametric, numerical estimation. This approach allows us to estimate the sensitivity indices not only for individual inputs but also for groups of inputs. After testing the accuracy of the non-parametric method on some analytical test functions, the approach is employed to assess the importance of dependent inputs on a computer model for the migration of radioactive substances in the geosphere.     

Global sensitivity analysis in wastewater applications: A comprehensive comparison of different methods

Three global sensitivity analysis (GSA) methods are applied and compared to assess the most relevant processes occurring in wastewater treatment systems. In particular, the Standardised Regression Coefficients, Morris Screening and Extended-FAST methods are applied to a complex integrated membrane bioreactor (MBR) model considering 21 model outputs and 79 model factors. The three methods are applied with numerical settings as suggested in literature. The main objective considered is to classify important factors (factors prioritisation) as well as non-influential factors (factors fixing). The performance is assessed by comparing the most reliable method (Extended-FAST), by means of proposed criteria, with the two other methods. In particular, similarity to results obtained from Extended-FAST is assessed for sensitivity indices, for the ranking of sensitivity indices, for the classification into important/non-influential factors and for the method's ability to detect interaction among factors and to provide results in a reasonable time.It was found that the computationally less expensive SRC method was applied outside its range of applicability (R²) = (0.3–0.6) < 0.7. Still, the SRC produced a ranking of important factors similar to Extended-FAST. For some variables significant interactions among the factors were revealed by computing the total effect indices S_Ti using Extended-FAST. This means that to obtain reliable variance decomposition and to detect and quantify interactions among the factors, the use of the Extended-FAST is recommended. Regarding the comparison between Morris screening and Extended-FAST a poor agreement was found. In particular, the Morris screening overestimated the number of both important and non-influential factors compared to Extended-FAST for the analysed case study.     

A global sensitivity analysis in structural mechanics

A methodology is developed to evaluate the response sensitivity of structural systems to variations in their design parameters. The sensitivity is evaluated by considering the global behavior of the system response when the parameters vary within a bounded region. The design parameters are characterized by means of baseline values plus fluctuating components, and the sensitivity of the system is measured in terms of the global variability of the response with respect to its baseline response. The methodology is then extended into the context of optimum redesign analysis of structural systems. Application of the method is made to a structural system defined by two-dimensional beam-column elements and to a system defined by plate elements. The numerical implementation of the global sensitivity approach is made by means of the finite element method. Several analyses are performed and the results are discussed. Finally, some extensions of the present work are presented.     

A new variance-based global sensitivity analysis technique

A new set of variance-based sensitivity indices, called W$W$-indices, is proposed. Similar to the Sobol’s indices, both main and total effect indices are defined. The W$W$-main effect indices measure the average reduction of model output variance when the ranges of a set of inputs are reduced, and the total effect indices quantify the average residual variance when the ranges of the remaining inputs are reduced. Geometrical interpretations show that the W$W$-indices gather the full information of the variance ratio function, whereas, Sobol’s indices only reflect the marginal information. Then the double-loop-repeated-set Monte Carlo (MC) (denoted as DLRS MC) procedure, the double-loop-single-set MC (denoted as DLSS MC) procedure and the model emulation procedure are introduced for estimating the W$W$-indices. It is shown that the DLRS MC procedure is suitable for computing all the W$W$-indices despite its highly computational cost. The DLSS MC procedure is computationally efficient, however, it is only applicable for computing low order indices. The model emulation is able to estimate all the W$W$-indices with low computational cost as long as the model behavior is correctly captured by the emulator. The Ishigami function, a modified Sobol’s function and two engineering models are utilized for comparing the W$W$- and Sobol’s indices and verifying the efficiency and convergence of the three numerical methods. Results show that, for even an additive model, the W$W$-total effect index of one input may be significantly larger than its W$W$-main effect index. This indicates that there may exist interaction effects among the inputs of an additive model when their distribution ranges are reduced.     

A comparison of two hierarchical optimization methods

In this note the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared. The vehicle for the comparison is a twelth-order complex counter-current example taken from the literature. The computational load for the two methods is compared qualitatively whereas the convergence characteristics arc tested on the example. A simple condition is also given for the convergence of the interaction prediction method. This is also tested on the example.     

A comparison of two optimization methods for mesh quality improvement

We compare inexact Newton and block coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

A comparison of two parametric surface patch methods

The Bézier and Ferguson methods of representing surfaces are compared. Although there are very clear differences in their mode of use they are closely similar in their mathematical basis.     

两种典型扭振式粘度测头的灵敏度对比分析

针对扭振式粘度测量中,不同测头形状所受到的粘性力不同,进而对测量灵敏度产生影响的问题,基于FBG扭矩微振粘度测量原理,研究柱形与球面两种测头装置的测量精度及灵敏度.通过对不同形状的测头建立数学模型,得出相应的电压-粘度关系式,在实验室环境下通过标定实验确定待定系数,并比较两种测头的测量特性.实验数据表明,柱形测头的测量精度及灵敏度高于球面测头,验证了理论分析.同时,对测量误差来源进行了分析,为后续研究提供了理论基础.     

A comparison of two training methods for improving warning symbol comprehension

This study compared the effectiveness of two different types of training in improving comprehension of warning symbols by younger (aged 20-35 years) and older adults (aged 50-70 years). The verbal label training paired the symbol with a label describing its meaning while the accident scenario training further expanded on the nature of the hazard, the required/prohibited actions, as well as the possible consequences of failing to comply. Contrary to prior research (e.g., [Lesch, M.F., 2003. Comprehension and memory for warning symbols: age-related differences and impact of training. J. Safety Res. 34, 495-505]), there was no difference in comprehension for younger and older adults prior to training, with both groups only obtaining about 40% correct responses. Both types of training improved performance on a subsequent comprehension test. However, the accident scenario training produced a higher percentage of correct responses, greater confidence in those responses, as well as a longer-lasting reduction of reaction times. In order to further improve symbol design, as well as training to address comprehension difficulties, future research should more closely examine symbol characteristics that influence comprehension.     

A comparison of two methods for accelerating the convergence of Fourier series

We compare the epsilon algorithm of Wynn with a generalization of summation by parts for accelerating slowly convergent Fourier series. The series considered are

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and four series that arise from the numerical inversion Summation by parts is shown to be advantageous in the acceleration of Fourier sine series. Both acceleration techniques are shown to lead to approximately the same accuracy in accelerating the series that come from the Laplace transform examples.     

A comparison of two analytical evaluation methods for educational computer games for young children

In this paper we describe a comparison of two analytical methods for educational computer games for young children. The methods compared in the study are the Structured Expert Evaluation Method (SEEM) and the Combined Heuristic Evaluation (HE) (based on a combination of Nielsen’s HE and the fun-related concepts from Malone and Lepper) with both usability and fun heuristics for children’s computer games. To verify SEEM’s relative quality, a study was set up in which adult evaluators predicted problems in computer games. Outcomes based on thoroughness (whether the analytical method finds all problems), validity (whether the analytical method uncovers problems that are likely to be true) and appropriateness (whether the method is applied correctly) are compared. The results show that both the thoroughness and validity of SEEM are higher than the thoroughness and validity of the Combined HE. The appropriateness scores indicate that SEEM gives evaluators more guidance when predicting problems than the Combined HE does.

A comparison between two photographic methods for the determination of relative bidirectional reflectance

Two simple photographic methods have recently been proposed for the measurement of relative bidirectional reflectance (Lillesand and Kiefer 1979, Curran 1980). These two methods were used to calculate the relative bidirectional reflectance of ten contrasting surfaces. The photographic relative bidirectional reflectance so recorded, was then compared with the radiometric bidirectional reflectance for each surface. Two conclusions were drawn: first, that relative bidirectional reflectance can be measured using these simple photographic techniques, and second, that there was no significant difference between the Lillesand and Kiefer and Curran methods for photographically deriving relative bidirectional reflectance.     

A comparison of two methods for reducing take-off delay at London Heathrow airport

This paper describes recent research into the departure process at London Heathrow, with the primary motivation of reducing the amount of fuel used, improving both the economic and environmental costs. Two proposals are considered here. The first proposal considers the practicality and potential benefits of aiding the controller in improving the take-off sequencing. The second proposal aims to absorb some of the inevitable delay for aircraft at the stands, before the engines are started, but also involves a take-off sequencing aspect. Models for the two take-off sequencing problems are presented in this paper, the second of which includes an additional pushback time (or TSAT) allocation sub-problem which has to be solved subsequently. These models have distinctive differences from the models for the take-off and arrival sequencing problems which are usually considered in the literature, since they take into account necessary constraints imposed due to the control problem (whether a sequence can actually be achieved, and how) in each case. As discussed in this paper, the control problem cannot be ignored by the controllers at Heathrow, and so it cannot be ignored by any realistic system to aid them in their tasks. Comparative take-off sequencing results are presented for the two systems, and the potential benefits from providing decision support to the runway controllers or improved TSAT allocation at the stands are considered. The paper ends with some overall conclusions from the research, showing the large potential benefits of these systems. The TSAT allocation system which is discussed in this paper has been developed for implementation at London Heathrow as one element of a major project which focuses upon collaborative decision making.     

Probabilistic sensitivity analysis methods for general decision models

Probabilistic sensitivity analysis has previously been described for the special case of dichotomous decision trees. We now generalize these techniques for a wider range of decision problems. These methods of sensitivity analysis allow the analyst to evaluate the impact of the multivariate uncertainty in the data used in the decision model and to gain insight into the probabilistic contribution of each of the variables to the decision outcome. The techniques are illustrated using Monte Carlo simulation on a trichotomous decision tree. Application of these powerful tools permits the decision analyst to investigate the structure and limitations of more complex decision problems with inherent uncertainties in the data upon which the decisions are based. Probabilistic sensitivity measures can provide guidance into the allocation of resources to resolve uncertainty about critical components of medical decisions.     

Surrogate-assisted global sensitivity analysis: an overview

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering discipli     

Efficient global sensitivity analysis with correlated variables

Existing methods for the computation of global sensitivity indices are challenged by both number of input-output samples required and the presence of dependent or correlated variables. First, a methodology is developed to increase the efficiency of sensitivity computations with independent variables by incorporating optimal space-filling quasi-random sequences into an existing importance sampling-based kernel regression sensitivity method. Two prominent situations where parameter correlations cannot be ignored, however, are (1) posterior distributions of calibrated parameters and (2) transient, coupled simulations. Therefore, the sensitivity methodology is generalized to dependent variables allowing for efficient post-calibration sensitivity analyses using input-output samples obtained directly from Bayesian calibration. These methods are illustrated using coupled, aerothermal simulations where it is observed that model errors and parameter correlations control the sensitivity estimates until coupling effects become dominant over time.     

A multi-point sampling method based on kriging for global optimization

In general, sampling strategy plays a very important role in metamodel based design optimization, especially when computationally expensive simulations are involved in the optimization process. The research on new optimization methods with less sampling points and higher convergence speed receives great attention in recent years. In this paper, a multi-point sampling method based on kriging (MPSK) is proposed for improving the efficiency of global optimization. The sampling strategy of this method is based on a probabilistic distribution function converted from the expected improvement (EI) function. It can intelligently draw appropriate new samples in an area with certain probability according to corresponding EI values. Besides, three strategies are also proposed to speed up the sequential sampling process and the corresponding convergence criterions are put forward to stop the searching process reasonably. In order to validate the efficiency of this method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the higher global optimization efficiency of this method makes it particularly suitable for design optimization problems involving computationally expensive simulations.     

Finite difference methods for viscous incompressible global stability analysis

In the present article some high-order finite-difference schemes and in particularly dispersion-relation-preserving (DRP) family schemes, initially developed by Tam and Webb [Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys. 107 (1993) 262-281.] for computational aeroacoustic problems, are used for global stability issue. (The term global is not used in weakly-non-parallel framework but rather for fully non-parallel flows. Some authors like Theofilis [Advances in global linear instability analysis of non-parallel and three-dimensional flows, Progress in Aerospace Sciences 39 (2003) 249-315] refer to this approach as “BiGlobal”.) These DRP schemes are compared with different classical schemes as second and fourth-order finite-difference schemes, seven-order compact schemes and spectral collocation scheme which is usually employed in such stability problems. A detailed comparative study of these schemes for incompressible flows over two academic configurations (square lid-driven cavity and separated boundary layer at different Reynolds numbers) is presented, and we intend to show that these schemes are sufficiently accurate to perform global stability analyses.