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Han Ding - One of the best experts on this subject based on the ideXlab platform.

  • second order full Discretization Method for milling stability prediction
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper proposes a second-order full-Discretization Method for milling stability prediction based on the direct integration scheme. The model of the milling dynamics taking the regenerative effect into account in the state-space form is firstly represented in the integral form. After the time period being equally discretized into a finite set of intervals, the full-Discretization Method is developed to handle the integration term of the system. On each small time interval, the second-degree Lagrange polynomial is employed to interpolate the state item, and the linear interpolation is utilized to approximate the time-periodic and time delay items, respectively. Then, a discrete dynamical map is deduced to establish the state transition matrix on one time period to predict the milling stability via Floquet theory. The rate of convergence of the Method is discussed, and the benchmark example is utilized to verify the effectiveness of the presented algorithm. The MATLAB code of the algorithm is attached in the Appendix.

  • a full Discretization Method for prediction of milling stability
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper presents a full-Discretization Method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-Discretization Method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed Method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.

Gabor Stepan - One of the best experts on this subject based on the ideXlab platform.

  • updated semi Discretization Method for periodic delay differential equations with discrete delay
    International Journal for Numerical Methods in Engineering, 2004
    Co-Authors: Tamas Insperger, Gabor Stepan
    Abstract:

    An updated version of the semi-Discretization Method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time-period/time-delay ratios. The convergence of the Method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.

  • semi Discretization Method for delayed systems
    International Journal for Numerical Methods in Engineering, 2002
    Co-Authors: Tamas Insperger, Gabor Stepan
    Abstract:

    SUMMARY The paper presents an ecient numerical Method for the stability analysis of linear delayed systems. The Method is based on a special kind of Discretization technique with respect to the past eect only. The resulting approximate system is delayed and also time periodic, but still, it can be transformed analytically into a high-dimensional linear discrete system. The Method is applied to determine the stability charts of the Mathieu equation with continuous time delay. Copyright ? 2002 John Wiley & Sons, Ltd.

Ye Ding - One of the best experts on this subject based on the ideXlab platform.

  • second order full Discretization Method for milling stability prediction
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper proposes a second-order full-Discretization Method for milling stability prediction based on the direct integration scheme. The model of the milling dynamics taking the regenerative effect into account in the state-space form is firstly represented in the integral form. After the time period being equally discretized into a finite set of intervals, the full-Discretization Method is developed to handle the integration term of the system. On each small time interval, the second-degree Lagrange polynomial is employed to interpolate the state item, and the linear interpolation is utilized to approximate the time-periodic and time delay items, respectively. Then, a discrete dynamical map is deduced to establish the state transition matrix on one time period to predict the milling stability via Floquet theory. The rate of convergence of the Method is discussed, and the benchmark example is utilized to verify the effectiveness of the presented algorithm. The MATLAB code of the algorithm is attached in the Appendix.

  • a full Discretization Method for prediction of milling stability
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper presents a full-Discretization Method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-Discretization Method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed Method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.

John Valasek - One of the best experts on this subject based on the ideXlab platform.

  • Multiresolution state-space Discretization Method for Q-Learning
    2009 American Control Conference, 2009
    Co-Authors: Amanda Lampton, John Valasek
    Abstract:

    For large scale problems Q-Learning often suffers from the Curse of Dimensionality due to large numbers of possible state-action pairs. This paper develops a multiresolution state-space Discretization Method for the episodic unsupervised learning Method of Q-Learning, in which a state-space is adaptively discretized by progressively finer grids around the areas of interest within the state or learning space. Optimality of the learning algorithm is addressed by a cost function. Applied to a morphing airfoil with two morphing parameters (two state variables), it is shown that by setting the multiresolution Method to define the area of interest by the goal the agent seeks, this Method can learn a specific goal within plusmn0.002, while reducing the total number of state-action pairs need to achieve this level of specificity by almost 90%.

  • Multiresolution state-space Discretization Method for Q-learning with function approximation and policy iteration
    2009 IEEE International Conference on Systems Man and Cybernetics, 2009
    Co-Authors: Amanda Lampton, John Valasek
    Abstract:

    A multiresolution state-space Discretization Method is developed for the episodic unsupervised learning Method of Q-learning. In addition, a genetic algorithm is used periodically during learning to approximate the action-value function. Policy iteration is added as a stopping criterion for the algorithm. For large scale problems Q-learning often suffers from the curse of dimensionality due to large numbers of possible state-action pairs. This paper develops a Method whereby a state-space is adaptively discretized by progressively finer grids around the areas of interest within the state or learning space. Policy iteration is added to prevent unnecessary episodes at each level of Discretization once the learning has converged. Utility of the Method is demonstrated with application to the problem of a morphing airfoil with two morphing parameters (two state variables). By setting the multiresolution Method to define the area of interest by the goal the agent seeks, it is shown that this Method can learn a specific goal within ±0.002, while reducing the total number episodes needed to converge by 85% from the allotted total possible episodes. It is also shown that a good approximation of the action-value function is produced with 80% agreement between the tabulated and approximated policy, though empirically the approximated policy appears to be superior.

Xiaojian Zhang - One of the best experts on this subject based on the ideXlab platform.

  • second order full Discretization Method for milling stability prediction
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper proposes a second-order full-Discretization Method for milling stability prediction based on the direct integration scheme. The model of the milling dynamics taking the regenerative effect into account in the state-space form is firstly represented in the integral form. After the time period being equally discretized into a finite set of intervals, the full-Discretization Method is developed to handle the integration term of the system. On each small time interval, the second-degree Lagrange polynomial is employed to interpolate the state item, and the linear interpolation is utilized to approximate the time-periodic and time delay items, respectively. Then, a discrete dynamical map is deduced to establish the state transition matrix on one time period to predict the milling stability via Floquet theory. The rate of convergence of the Method is discussed, and the benchmark example is utilized to verify the effectiveness of the presented algorithm. The MATLAB code of the algorithm is attached in the Appendix.

  • a full Discretization Method for prediction of milling stability
    International Journal of Machine Tools & Manufacture, 2010
    Co-Authors: Ye Ding, Xiaojian Zhang, Han Ding
    Abstract:

    This paper presents a full-Discretization Method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-Discretization Method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed Method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.