[en] Highlights: • Morris’ extension method was applied to evaluate the combined actions of model inputs. • Study of three types of convergence of combined actions results using formal criteria. • New Morris’ extension indices was proposed to achieve convergent results at lower cost. • Morris’ extension method and total interaction Sobol indices provide the same results. • Convergence of screening and ranking can be reached before sensitivity indices stabilize. -- Abstract: This work aims at studying Morris’ extension method to evaluate the contribution of combined variations of inputs to variations of a model output. There is a lack of studies on the Morris’ extension method concerning crucial choices of the adequate number of trajectories to distinguish influential and non-influential groups of pairs of inputs, rank pairs of inputs according to their relative importance and reach out the stability of sensitivity indices values. The Morris’ extension method was studied regarding the three previous issues via applications on simple and complex models, in comparison with total interaction indices of Sobol. Formal criteria were implemented to assess the convergence of sensitivity analysis results. Sensitivity indices based on the median of mixed elementary effects (MEE) were investigated and found to be competing with classical ones based on the mean of MEE, to achieve convergent results.

[en] A comparison between retrieved properties of the rain drop size distributions (DSDs) from multifrequency cloud radar observations and WRF Model results using either the Morrison or the Thompson bulk microphysics scheme is performed in order to evaluate the model’s ability to predict the rain microphysics. This comparison reveals discrepancies in the vertical profile of the rain DSDs for the stratiform region of the squall-line system observed on 12 June 2011 over Oklahoma. Based on numerical sensitivity analyses, this study addresses the bias at the top of the rain layer and the vertical evolution of the DSD properties (i.e., of D_m and N${}_0^{\ast <!--\; ???\; -->}$). In this way, the Thompson scheme is used to explore the sensitivity to the melting process. Moreover, using the Thompson and Morrison schemes, the sensitivity of the DSD vertical evolution to different breakup and self-collection parameterizations is studied. Results show that the DSDs are strongly dependent on the representation of the melting process in the Thompson scheme. In the Morrison scheme, the simulations with more efficient breakup reproduce the DSD properties with better fidelity. Here, this study highlights how the inaccuracies in simulated D_m and N${}_0^{\ast <!--\; ???\; -->}$ for both microphysics schemes can impact the evaporation rate, which is systematically underestimated in the model.

[en] Highlights: • Preventive strike that can cause random loss of attacking resource is considered. • The trade-off between preventive strike and protection is studied. • The case where false targets can be deployed is also considered. • Both perfect false targets and imperfect false targets are investigated. -- Abstract: Most existing research on system defence is restricted to passive measures such as providing redundancy, protecting system elements, and deploying false elements. Some recent works have considered the launching of preventive strikes, where a preventive strike, if successful, destroys all the attacker's resources. However, in practice, a preventive strike might cause a random loss to the attacker's resources. This paper assumes that the destroyable attacking resources follow a Poisson distribution. Procedures are presented to solve the optimal defence strategies for three cases: (1) where preventive strikes and object protections are the only available defence measures; (2) where false targets can also be deployed, and they are perfect; and (3) where false targets can also be deployed, but they are imperfect. Numerical examples are provided to illustrate the applications, and sensitivity analysis is employed to demonstrate the influence of parameters.

[en] Background and purpose: The impact of differences in the distribution of major cancer sites and stages at diagnosis among 4 European countries on the optimal utilization proportion (OUP) of patients who should receive external beam radiotherapy was assessed within the framework of the ESTRO-HERO project. Materials and methods: Data from Australian Collaboration for Cancer Outcomes Research and Evaluation (CCORE) were used. Population based stages at diagnosis from the cancer registries of Belgium, Slovenia, the Greater Poland region of Poland, and The Netherlands were used to assess the OUP for each country. A sensitivity analysis was carried out. Results: The overall OUP by country varied from the lowest of 48.3% in Australia to the highest of 53.4% in Poland; among European countries the variation was limited to 3%. Cancer site specific OUPs showed differences according to the variability in stage at diagnosis across countries. The most important impact on the OUP by country was due to changes in relative frequency of tumours rather than stage at diagnosis. Conclusions: This methodology can be adapted using European data, thus facilitating the planning of resources required to cope with the demand for radiotherapy in Europe, taking into account the national variability in cancer incidence

[en] This memorandum builds upon Section 3.8 of SRNL (2016) and Flach (2017) by defining key error analysis, uncertainty quantification, and sensitivity analysis concepts and terms, in preparation for the next E-Area Performance Assessment (WSRC 2008) revision.

[en] Highlights: • Global Sensitivity Analysis ranks inputs according to their importance on output. • Random Forests is an efficient non-parametric approach for building meta-models. • Random forests variable importance measure is used to define sensitivity measures. • Provide a comprehensive review paper in sensitivity analysis using random forests. • Focus on connections between random forests and Global Sensitivity Analysis. The understanding of many physical and engineering problems involves running complex computational models. Such models take as input a high number of numerical and physical explanatory variables. The information on these underlying input parameters is often limited or uncertain. It is therefore important, based on the relationships between the input variables and the output, to identify and prioritize the most influential inputs. One may use global sensitivity analysis (GSA) methods which aim at ranking input random variables according to their importance in the output uncertainty, or even quantify the global influence of a particular input on the output. Using sensitivity metrics to ignore less important parameters is a form of dimension reduction in the model’s input parameter space. This suggests the use of meta-modeling as a quantitative approach for nonparametric GSA, where the original input/output relation is first approximated using various statistical regression techniques. Subsequently, the main goal of our work is to provide a comprehensive review paper in the domain of sensitivity analysis focusing on some interesting connections between random forests and GSA. The idea is to use a random forests methodology as an efficient non-parametric approach for building meta-models that allow an efficient sensitivity analysis. Apart its easy applicability to regression problems, the random forests approach presents further strong advantages by its ability to implicitly deal with correlation and high dimensional data, to handle interactions between variables and to identify informative inputs using a permutation based RF variable importance index which is easy and fast to compute. We further review an adequate set of tools for quantifying variable importance which are then exploited to reduce the model’s dimension enabling otherwise infeasible sensibility analysis studies. Numerical results from several simulations and a data exploration on a real dataset are presented to illustrate the effectiveness of such an approach.

[en] Global sensitivity analysis (GSA) is a very useful tool to evaluate the influence of input variables in the whole distribution range. Sobol' method is the most commonly used among variance-based methods, which are efficient and popular GSA techniques. High dimensional model representation (HDMR) is a popular way to compute Sobol' indices, however, its drawbacks cannot be ignored. We show that modified GMDH-NN algorithm can calculate coefficients of metamodel efficiently, so this paper aims at combining it with HDMR and proposes GMDH-HDMR method. The new method shows higher precision and faster convergent rate. Several numerical and engineering examples are used to confirm its advantages. - Highlights: • The GMDH-NN is improved to construct the explicit polynomial model of optimal complexity by self-organization. • The paper aims at combining improved GMDH-NN with HDMR expansions and using it to compute Sobol' indices directly. • The method can be applied in uniform, normal and exponential distribution by using suitable orthogonal polynomials. • Engineering examples, e.g., electronic circuit models can be solved by the presented method.

[en] In this study, the author proposes a jointly setting model for determining the process mean and economic manufacturing quantity (EMQ) under the machine breakdown and deteriorating production process. The system addresses the corrective maintenance, preventive maintenance, and allowable shortage. The quality loss of conforming product is considered and Taguchi’s asymmetric quadratic quality loss function is used for evaluating the product quality. The optimal process mean and economic manufacturing quantity are jointly determined by minimizing the total expected cost of product per unit time including the set-up cost, holding cost, corrective maintenance cost, preventive maintenance cost, shortage cost. A solution procedure is devised to obtain the optimal solution and the sensitivity analysis of key parameters is conducted to investigate the effect on the optimal solution. (paper)

[en] Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

[en] Highlights: • Multi-state system performing multi-attempt mission under random shocks is considered. • After each failed attempt the system, if survived, is repaired to ‘as good as new’ state. • The repair time depends on the system state before the repair. • The mission time is limited. • The optimal number of shocks after which any attempt is aborted is considered. Research on mission abort strategies was mostly devoted to binary systems that can be only in two states, i.e., operable or failed. However, the real-world systems can often operate in intermediate states with different levels of performance. On the other hand, if a mission has been aborted and a system has been successfully rescued, at some instances, the next attempt can be activated, thus forming the multi-attempt framework. In this paper, the possibility of multiple attempts is considered for the first time for multistate systems. After each rescue, a system is repaired to ‘as good as new’ state. The repair time depends on its state before the repair. The objective is to maximize the probability of a mission completion within the fixed time deadline for systems operating in a random environment modeled by shocks. Each shock with a given probability results in a system's transition to the states with the lower values of performance. Mission abort is activated for each attempt when the number of experienced shocks exceeds a predetermined number. This number for each attempt should be determined to maximize the mission success probability. For the considered illustrative example, the detailed sensitivity analysis is performed and the relevant discussion is provided.