An ANN-based element extraction method for automatic mesh generation

A systematic optimization approach for assembly sequence planning using Taguchi method, DOE, and BPNN

“…Signal-to-noise:Nominalisbest(-10*Log(s**2)) Tanh_Axon Sigmoid_Axon Liu, Liu, & Zhang, 2001;Maier & Dandy, 1998;Yao, Yan, Chen, & Zeng, 2005). The superiority of a network's functional approach depends on the network architecture and parameters, as well as the problem complexity.…”

A self-learning finite element extraction system based on reinforcement learning

“…The FNN module can learn from the acquired data from the experience extraction module to (1) decide which extraction rule should be applied and (2) determine the position of the newly generated point for a new element when necessary. Its network structure is shown in Figure 17 and mathematically described as follows (Yao et al, 2005):…”

“…The FNN can learn from given samples how to decide which rule should be applied and how to position the new point(s) for a new element when necessary. Yao et al (2005) improved the FREEMESH approach by introducing an artificial neural network (ANN) to learn the element extraction rules from a set of pre-selected samples of good quality quad meshes. The improved method eases the acquisition and application of these rules and could handle more complex domain boundaries.…”

“…(2). The absolute coordinates of all points selected for representing a state will be transformed into a new coordinate system that assumes the reference point P 0 as the origin, and the vector from the reference point to the first neighboring point along the counter-clock direction as the unit vector, along the positive direction of the x -axis (Yao et al , 2005). The transformation (i.e., rotation, scaling, and transit) from the original coordinate system Oxy to the new one O'x'y' is shown in Figure 12, and can be represented as:

Fig.

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“…The FNN module can learn from the acquired data from the experience extraction module to (1) decide which extraction rule should be applied and (2) determine the position of the newly generated point for a new element when necessary. Its network structure is shown in Figure 17 and mathematically described as follows (Yao et al , 2005):where type i is the output type, as shown in Figure 18, which equals to one of the three values (i.e., 0, 1, and 2); P i is the output point, consisting of ( x i , y i ); the input points are the state; and N equals 2 in this paper. The objective function used in FNN is denoted in the following formula:where are the FNN model output for i th input and MSE is the sum of the mean squared errors of these three variables.…”