دانلود رایگان مقاله الگوریتم نمونه گیری هوشمند از سایت الزویر
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الگوریتم نمونه گیری هوشمند برای توسعه مدل جایگزینعنوان انگلیسی مقاله:
Smart Sampling Algorithm for Surrogate Model Development
سال انتشار : 2015
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مقدمه انگلیسی مقاله:
1. Introduction
Naturally, we grasp the understanding of a complex phenomenon by opting for a simpler format. Similarly, we use process simulators to model, study, and analyze complex and nonlinear physicochemical processes. However, such simulations can be compute-intensive, and running them repeatedly in an optimization/analysis procedure can be computationally prohibitive. Furthermore, numerical models can pose significant hurdles within a continuous optimization algorithm. Therefore, it helps to convert a high-fidelity simulation model into a computationally inexpensive surrogate model that captures its essential features with prescribed numerical accuracy. Surrogate modelling, also known as metamodeling, is a technique to generate a mathematical or numerical representation of a complex system based on some sampled input-output data. Many surrogate modelling techniques have been developed over the past few decades such as Polynomial Surface Response Models (PRSM) (Forrester and Keane, 2009; Myers and Montgomery, 2002; Queipo et al., 2005), Kriging (Cressie, 1990; Forrester et al., 2008a; Martin and Simpson, 2005; Sakata et al., 2003; Simpson, 1998), RadialBasis Functions (RBF) (Hardy, 1971; Hussain et al., 2002), Support Vector Regression (SVR) (Clarke et al., 2005), and Artificial Neural Networks (ANNs) (Yegnanarayana, 2004). The literature (Forrester and Keane, 2009; Henao and Maravelias, 2010, 2011; Queipo et al., 2005; Shan and Wang, 2010; Wang and Shan, 2007) has compared them and discussed their applications to various systems. Irrespective of the technique, building a surrogate model requires sample points. The process of generating such points is known as sampling. We can classify the existing sampling methods into two broad categories: non-adaptive and adaptive. The four types of non-adaptive methods are grid-based, pattern/geometrybased, stochastic, and quasi-random. The grid-based method simply distributes sample points to form a uniform grid (Cartesian grid). The second type employs statistics-driven methods such as the design of experiments to fill space. These include full/half factorial designs (Fisher, 1935), central composite (CC) designs (Box and Wilson, 1951), Box-Behnken (Box and Behnken, 1960), PlackettBurman (Plackett and Burman, 1946), Delaunay triangulations and their dual structures (Delaunay, 1934), and Voronoi tessellations (Voronoï, 1908). These methods work well for low dimensions (N ≤ 3) (Davis and Ierapetritou, 2010); (Crombecq et al., 2009), but become extremely costly for large N as in the case of geometry and factorial designs, or inaccurate due to the lack of spatial coverage as in the case of CC, Plackett-Burman, and Box-Beheken designs. Moreover, these methods rapidly face the curse of dimensionality(Forrester et al., 2008c). The third type of sampling methods relies on stochastic sampling with the aim to fill space. For instance, sampling based on random distribution is the most straightforward. The more sophisticated methods include Monte Carlo sampling (Metropolis and Ulam, 1949) and variations (Koehler and Owen, 1996; Niederreiter, 2010) that combine random sampling and probabilistic filtering; Latin hypercube sampling (McKay et al., 1979) that fills hypercube bins via random placements but subject to projection filters; and orthogonal arrays (Hedayat et al., 2012; Rao, 1946, 1947) that generalize Latin hypercube sampling (Giunta et al., 2003). Finally, the fourth type generates sample points quasirandomly using low-discrepancy sequences such as Hammersley (Hammersley and Handscomb, 1964), Sobol(Sobol’, 1967), and Halton (Halton and Smith, 1964). While these methods manage the sample size much better (Mascagni and Hongmei, 2004; Queipo et al., 2005),they may failto capture the characteristics ofthe space properly at higher N. Typically, the system output is computed from the high-fidelity model at these sample points to generate the required input-output data for surrogate development. If the resulting surrogate does not meet expectations, then the model is reconstructed by adding more sample points.
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