Surrogate Modeling and Optimizing for CCP Etch Process

2014 ◽  
Vol 670-671 ◽  
pp. 548-553
Author(s):  
Wen Rui Duan ◽  
Ling Tian
Keyword(s):  
Process Model ◽  
Surrogate Modeling ◽  
Basis Functions ◽  
Flow Ratio ◽  
Approximation Model ◽  
Global Approximation ◽  
Minimum Area ◽  
Capacitively Coupled ◽  
Process Gas ◽  
Surface Method

In order to analyze performance of the Capacitively Coupled Plasma (CCP) etcher, commercial software like OPTIMUS can be applied to approximate etch process model by Response Surface Method (RSM) or Radial Basis Functions (RBF). Multi-factor parameters are concerned in etch process, like frequencies of the dual Radio Frequency system (RF) and flow rate and flow ratio of the process gas. When facing the multi-dimensional problem, the algorithms would turned to be inefficiency and the optimization process may be trapped in local minimum area or cannot converge because of oscillation. To improve surrogate modeling for the CCP etcher, a self-optimizing RBF (SO-RBF) algorithm is proposed and a process modeling tool is developed. Experiments on a state-of-art dual station CCP etcher shows that based on the global approximation model generated by this algorithm, process parameter optimization can be easily implemented with less error than OPTIMUS.

scholarly journals A Three-Dimensional Numerical and Multi-Objective Optimal Design of Wavy Plate-Fins Heat Exchangers

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 9
Author(s):  
Chao Yu ◽  
Xiangyao Xue ◽  
Kui Shi ◽  
Mingzhen Shao
Keyword(s):  
Heat Exchangers ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Basis Functions ◽  
Approximation Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Colburn Factor ◽  
Heat Exchange Efficiency

This paper presents a method for optimizing wavy plate-fin heat exchangers accurately and efficiently. It combines CFD simulation, Radical Basis Functions (RBF) with multi-objective optimization to improve the performance. The optimization of the Colburn factor j and the friction coefficient f is regarded as a multi-objective optimization problem, due to the existence of two contradictory goals. The approximation model was obtained by Radical Basis Functions, and the shape of the heat exchanger was optimized by multi-objective genetic algorithm (MOGA). The optimization results showed that j increased by 17.62% and f decreased by 20.76%, indicating that the heat exchange efficiency was significantly enhanced and the fluid structure resistance reduced. Then, from the aspects of field synergy and tubulence energy, the performance advantage of the optimized structure was further confirmed.

Surrogate Modeling of Complex Systems Using Adaptive Hybrid Functions

2011 ◽  
Author(s):  
Jie Zhang ◽  
Souma Chowdhury ◽  
Achille Messac ◽  
Junqiang Zhang ◽  
Luciano Castillo
Keyword(s):  
Radial Basis Functions ◽  
Wind Farm ◽  
Surrogate Modeling ◽  
Surrogate Models ◽  
Modeling Method ◽  
Basis Functions ◽  
Sampling Techniques ◽  
Hybrid Functions ◽  
Model Complex ◽  
Radial Basis

This paper explores the effectiveness of the recently developed surrogate modeling method, the Adaptive Hybrid Functions (AHF), through its application to complex engineered systems design. The AHF is a hybrid surrogate modeling method that seeks to exploit the advantages of each component surrogate. In this paper, the AHF integrates three component surrogate models: (i) the Radial Basis Functions (RBF), (ii) the Extended Radial Basis Functions (E-RBF), and (iii) the Kriging model, by characterizing and evaluating the local measure of accuracy of each model. The AHF is applied to model complex engineering systems and an economic system, namely: (i) wind farm design; (ii) product family design (for universal electric motors); (iii) three-pane window design; and (iv) onshore wind farm cost estimation. We use three differing sampling techniques to investigate their influence on the quality of the resulting surrogates. These sampling techniques are (i) Latin Hypercube Sampling (LHS), (ii) Sobol’s quasirandom sequence, and (iii) Hammersley Sequence Sampling (HSS). Cross-validation is used to evaluate the accuracy of the resulting surrogate models. As expected, the accuracy of the surrogate model was found to improve with increase in the sample size. We also observed that, the Sobol’s and the LHS sampling techniques performed better in the case of high-dimensional problems, whereas the HSS sampling technique performed better in the case of low-dimensional problems. Overall, the AHF method was observed to provide acceptable-to-high accuracy in representing complex design systems.

Modeling and Optimization of Process Parameters of a DF-CCP Etcher Chamber

2013 ◽  
Vol 572 ◽  
pp. 213-216 ◽  
Author(s):  
Xia Xu ◽  
Juan Feng ◽  
Ling Tian
Keyword(s):  
Process Parameters ◽  
Process Model ◽  
Orthogonal Design ◽  
Low Frequency ◽  
High Plasma ◽  
Chamber Pressure ◽  
Dual Frequency ◽  
Capacitively Coupled ◽  
Optimization Of Process Parameters ◽  
Center Edge

Dual-frequency capacitively coupled plasma (DF-CCP) etcher has become the mainstream in dielectric etcher. By building a 2D axisymmetric model of 300mm DF-CCP etcher in CFD-ACE+ software, plasma simulation experiments are carried out by orthogonal design. Then a process model based on simulation results is proposed to analysis influence of key process parameters including high frequency voltage, low frequency voltage, and chamber pressure and center/edge flow ratio on chamber plasma characteristics. Finally, to get high plasma uniformity and plasma density, process optimizations are carried out.

scholarly journals Multifidelity surrogate modeling based on radial basis functions

2017 ◽  
Vol 56 (5) ◽  
pp. 1061-1075 ◽  
Author(s):  
Cédric Durantin ◽  
Justin Rouxel ◽  
Jean-Antoine Désidéri ◽  
Alain Glière
Keyword(s):  
Radial Basis Functions ◽  
Surrogate Modeling ◽  
Basis Functions ◽  
Radial Basis

scholarly journals An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 570 ◽  
Author(s):  
Suraj Pawar ◽  
Shady E. Ahmed ◽  
Omer San ◽  
Adil Rasheed
Keyword(s):  
Process Model ◽  
Correction Term ◽  
A Priori ◽  
Basis Functions ◽  
Least Squares Regression ◽  
Physical Processes ◽  
Order Model ◽  
Reduced Order ◽  
Real Time Simulations ◽  
Proper Orthogonal

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then present two variants of correction formula based on the assumption that the observed data are a manifestation of all relevant processes. The first method uses a standard least-squares regression with a quadratic approximation and requires solving a rank-deficient linear system, while the second approach employs a recurrent neural network emulator to account for the correction term. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward real-time simulations, where the full process model is not known a priori.

scholarly journals Selecting the Best Quantity and Variety of Surrogates for an Ensemble Model

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1721
Author(s):  
Pengcheng Ye ◽  
Guang Pan
Keyword(s):  
Surrogate Modeling ◽  
Surrogate Models ◽  
Prediction Performance ◽  
Basis Functions ◽  
Ensemble Model ◽  
Ensemble Models ◽  
Modeling Techniques ◽  
Mathematical Problems ◽  
Ensemble Of Surrogates ◽  
Polynomial Response Surface

Surrogate modeling techniques are widely used to replace the computationally expensive black-box functions in engineering. As a combination of individual surrogate models, an ensemble of surrogates is preferred due to its strong robustness. However, how to select the best quantity and variety of surrogates for an ensemble has always been a challenging task. In this work, five popular surrogate modeling techniques including polynomial response surface (PRS), radial basis functions (RBF), kriging (KRG), Gaussian process (GP) and linear shepard (SHEP) are considered as the basic surrogate models, resulting in twenty-six ensemble models by using a previously presented weights selection method. The best ensemble model is expected to be found by comparative studies on prediction accuracy and robustness. By testing eight mathematical problems and two engineering examples, we found that: (1) in general, using as many accurate surrogates as possible to construct ensemble models will improve the prediction performance and (2) ensemble models can be used as an insurance rather than offering significant improvements. Moreover, the ensemble of three surrogates PRS, RBF and KRG is preferred based on the prediction performance. The results provide engineering practitioners with guidance on the superior choice of the quantity and variety of surrogates for an ensemble.

Algorithmically deconstructing shot locations as a method for shot quality in hockey

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Devan G. Becker ◽  
Douglas G. Woolford ◽  
Charmaine B. Dean
Keyword(s):  
Point Process ◽  
Process Model ◽  
Point Processes ◽  
Learning Algorithm ◽  
Basis Functions ◽  
Cox Process ◽  
Spatial Point Processes ◽  
Professional Basketball ◽  
Spatial Point ◽  
Log Gaussian Cox Process

AbstractSpatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.

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