Metamodelling with independent and dependent inputs

Application of the control variate technique to estimation of total sensitivity indices

“…Coefficients of decomposition fα j r g; fβ ij pq g can be found using a regression method or MC or Quasi MC integration. The details of implementation can be found in [11], where a Quasi RS-HDMR (QRS-HDMR) variant of the RS-HDMR method was developed. One of the distinctive characteristics of the QRS-HDMR method is that Quasi MC sampling is used in the metamodel training set.…”

“…The component functions in (11) are expanded in terms of a suitable set of functions depending on the distribution of input variables. Typically in the RS-HDMR and PCE methods orthonormal polynomials are used.…”

“…Over the last decade, global SA has gained acceptance among practitioners in the process of model development, calibration and validation, reliability and robustness analysis, decision-making under uncertainty, quality-assurance, and complexity reduction. There have been many successful improvements in the efficiency of estimating the main effect Sobol' indices ranging from the advanced formulas for small sensitivity indices [3,4] to application of RBD [5] and various metamodelling methods [6][7][8][9][10][11]. However, there have been no similar advances concerning estimation of the total sensitivity indices and the Sobol-Jansen formula [12,13] remains to be the only formula used in the direct computation of the total sensitivity indices.…”

A new approach for multivariate data modelling in orthogonal geometry

“…There are also many scientists who have developed new HDMR-based methods that can be used in constructing solutions for several problems in the literature. Some related research areas are multivariate data modelling [22,30,32], reliability analysis [3,4,9], helicopter aeroelastic analysis [19], laminar burning velocity [36], general formulation of HDMR component functions [14,21], random sampling [15], weight optimization [34], sensitivity analysis [37,38], decision-making [7], black-box models [5,25], nonlinear models [6], air quality [12], metamodelling [39], development fragility curves [35], and stochastic dimension reduction [13]. The numerical results of previous studies show that the HDMR philosophy works well for modelling purely and dominantly additive natures while it becomes worse as the multiplicativity dominancy of the problem increases.…”

Reproducing kernel technique for high dimensional model representations (HDMR)

“…However, high-dimensional model representations (HDMR) [1,2] opens a remarkable opportunity to overcome the curse of dimensionality. By introducing an ansatz that for most physical systems, only relatively low order correlations of the input variables will have an impact on the output [2,9,10], a high-dimensional function used to describe a well-defined physical system can be approximatively viewed as a sum of low-dimensional functions [11][12][13][14][15].…”