An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

Groupoids,Discrete Mechanics,and Discrete Variation

After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection betweengroupoids variation and the methods of the first and second discrete variational principles.

Decentralized PID neural network control for a quadrotor helicopter subjected to wind disturbance

A decentralized PID neural network(PIDNN) control scheme was proposed to a quadrotor helicopter subjected to wind disturbance. First, the dynamic model that considered the effect of wind disturbance was established via Newton-Euler formalism.For quadrotor helicopter flying at low altitude in actual situation, it was more susceptible to be influenced by the turbulent wind field.Therefore, the turbulent wind field was generated according to Dryden model and taken into consideration as the disturbance source of quadrotor helicopter. Then, a nested loop control approach was proposed for the stabilization and navigation problems of the quadrotor subjected to wind disturbance. A decentralized PIDNN controller was designed for the inner loop to stabilize the attitude angle. A conventional PID controller was used for the outer loop in order to generate the reference path to inner loop. Moreover, the connective weights of the PIDNN were trained on-line by error back-propagation method. Furthermore, the initial connective weights were identified according to the principle of PID control theory and the appropriate learning rate was selected by discrete Lyapunov theory in order to ensure the stability. Finally, the simulation results demonstrate that the controller can effectively resist external wind disturbances, and presents good stability, maneuverability and robustness.

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.