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[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] 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] Among the many uses for sensitivity analysis is factor prioritization—that is, the determination of which factor, once fixed to its true value, on average leads to the greatest reduction in the variance of an output. A key assumption is that a given factor can, through further research, be fixed to some point on its domain. In general, this is an optimistic assumption, which can lead to inappropriate resource allocation. This research develops an original method that apportions output variance as a function of the amount of variance reduction that can be achieved for a particular factor. This variance-based sensitivity index function provides a main effect sensitivity index for a given factor as a function of the amount of variance of that factor that can be reduced. An aggregate measure of which factors would on average cause the greatest reduction in output variance given future research is also defined and assumes the portion of a particular factors variance that can be reduced is a random variable. An average main effect sensitivity index is then calculated by taking the mean of the variance-based sensitivity index function. A key aspect of the method is that the analysis is performed directly on the samples that were generated during a global sensitivity analysis using rejection sampling. The method is demonstrated on the Ishigami function and an additive function, where the rankings for future research are shown to be different than those of a traditional global sensitivity analysis. - Highlights: ► A sensitivity index function that apportions output variance as a function of the variance reduction that can be achieved for a given factor. ► A main effect sensitivity index that assumes the portion of a particular factor's variance that can be reduced is a random variable. ► The proposed indices are estimated directly from samples generated during a global sensitivity analysis using rejection sampling. ► Methods are demonstrated on the Ishigami function and an additive function. ► The demonstrations reveal main effect rankings that are different than those of a traditional global sensitivity analysis.
[en] Plasma edge transport codes play a key role in the design of future divertor concepts. Their long simulation times in combination with a large number of control parameters turn the design into a challenging task. In aerodynamics and structural mechanics, adjoint-based optimization techniques have proven successful to tackle similar design challenges. This paper provides an overview of achievements and remaining challenges with these techniques for complex divertor design. It is shown how these developments pave the way for fast sensitivity analysis and improved design from different perspectives. (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] The measured sensitivity of the cavity was evaluated and it is full consistent with the measured values. It was explored that the tuning system (the fog structure) has a significant contribution to the cavity sensitivity. By using ribs or by modifying the rigidity of the fog we may reduce the HWR sensitivity. During cool down and warming up we have to analyze the stresses on the HWR to avoid plastic deformation to the HWR since the Niobium yield is an order of magnitude lower in room temperature
[en] Global Sensitivity Analysis (GSA) can help modelers to better understand the model and manage the uncertainty. However, when the model itself is rather sophisticated, especially when dependence exists among model inputs, it could be difficult or even unfeasible to perform quantitative GSA directly. In this paper, a non-parametric approach is proposed for screening model inputs. It extends the classic Elementary Effects (i.e., Morris) method, which is widely used for screening independent inputs, to enable the screening of dependent model inputs. The performance of the proposed method is tested with three numerical experiments, and the results are cross-compared with those from the variance-based GSA. It is found that the proposed method can properly identify the influential and non-influential inputs from a complex model with several independent and dependent inputs. Furthermore, compared with the variance-based GSA, the proposed screening method only needs a few model runs, while the screening accuracy is well maintained. Therefore, it can be regarded as a practical tool for the initial GSA of high dimensional and computationally expensive models with dependent inputs. - Highlights: • A non-parametric and qualitative global SA approach for screening dependent model inputs is developed. • The independent elementary effects and the full elementary effects are proposed for input screening. • The proposed approach produces similar screening results as the variance-based GSA. • The screening approach takes over 25 times less computational cost than the variance-based GSA. • An efficient screening tool for high-dimensional and computationally expensive models with dependent inputs.
[en] Concepts of nonlinear functional analysis are employed to investigate the mathematical foundations underlying sensitivity theory. This makes it possible not only to ascertain the limitations inherent in existing analytical approaches to sensitivity analysis, but also to rigorously formulate a considerably more general sensitivity theory for physical problems characterized by systems of nonlinear equations and by nonlinear functionals as responses. Two alternative formalisms, labeled the ''forward sensitivity formalism'' and the ''adjoint sensitivity formalism,'' are developed in order to evaluate the sensitivity of the response to variations in the system parameters. The forward sensitivity formalism is formulated in normed linear spaces, and the existence of the Gateaux differentials of the operators appearing in the problem is shown to be both necessary and sufficient for its validity. This formalism is conceptually straightforward and can be advantageously used to assess the effects of relatively few parameter alterations on many responses. On the other hand, for problems involving many parameter alterations or a large data base and comparatively few functional-type responses, the alternative adjoint sensitivity formalism is computationally more economical. However, it is shown that this formalism can be developed only under conditions that are more restrictive than those underlying the validity of the forward sensitivity formalism. In particular, the requirement that operators acting on the state vector and on the system parameters must admit densely defined Gateaux derivatives is shown to be of fundamental importance for the validity of this formalism. The present analysis significantly extends the scope of sensitivity theory and provides a basis for still further generalizations
[en] In this study, a release test bed is designed to evaluate the dynamic behaviors of a coil spring. From the release tests, the dynamic behaviors of a coil spring are analyzed. A lumped parameter spring model was established for numerical simulation of a spring. The design variables of a coil spring are optimized by using the design of experiments approach. Two-level factorial designs are used for the design optimization, and the primary effects of the design variables are analyzed. Based on the results of the interaction analysis and design sensitivity analysis, the level of the design variables is rearranged. Finally, the mixed-level factorial design is used for the optimum design process. According to the optimum design of the opening spring, the dynamic performance of the spring-operated mechanism increases by 2.90