Online damage detection of earthquake-excited structure based on near real-time envelope extraction

A robust real-time damage detection technique of earthquake-excited structures based on a new demodulation technique for nonlinear and non-stationary vibration signals through the identification of signal envelopes in real time is presented. In the present work, the need for the detection of envelope in a vibration signal in real time is addressed by reformulating the concept of Hermitian interpolation functions to a recursive Hermitian polynomial, which is a key entitlement of the present work. Once, the near real-time demodulation is achieved, the proposed framework proceeds to the newly developed error-adapted framework by addressing the errors accrued between the standard and generalized eigen perturbation formulation in the context of real-time estimation of proper orthogonal modes and linear normal modes. In the adaptive framework, the error is modeled as a feedback, which is constructed to account for the truncation in the order of eigen perturbation. In addition to the improved accuracy due to the envelope extraction, the proposed error-adapted eigen perturbation further improves the detectability over the currently available eigen perturbation–based real-time algorithms. To ensure robustness of the proposed algorithm, a new real-time damage indicator based on the maximum of principal eigenvector of the evolving transformed covariance matrix is proposed. The proposed modules together not only improve the detectability of the damage detection in real-time but also enhance the overall performance in presence of non-stationary excitation, that often mask the damage information in the higher energy zones of the amplitude and frequency-modulated response. Simulations for the proposed framework is performed by considering a 5 degrees-of-freedom linear and base-isolated nonlinear structural system driven by non-stationary stochastic excitations with damage simulated at intermediate floor at a particular time instant. Evidence of the near real-time demodulation and/or envelope removal from the signal and improved damage identification is also provided. An examination of the proposed framework using experimental data further validates the robustness of the proposed scheme.

General Beam Cross-Section Analysis Using a 3D Finite Element Slice

A formulation for analysis of general cross-section properties has been developed. This formulation is based on the stress-strain states in the classic six equilibrium modes of a beam by considering a finite thickness slice modelled by a single layer of 3D finite elements. The displacement variation in the lengthwise direction is in the form of a cubic polynomial, which is here represented by Hermitian interpolation, whereby the degrees of freedom are concentrated on the front and back faces of the slice. The theory is illustrated by application to a simple cross-section for which an analytical solution is available. The paper also shows an application to wind turbine blade cross-sections and discusses the effect of the finite element discretization on the cross-section properties such as stiffness parameters and the location of the elastic and shear centers.

Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method

A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional do-mains. The Local Hermitian Interpolation (LHI) method is employed for thespatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same resultsare obtained for all the non-linear solvers tested, but better convergence ratesare attained with the Newton Raphson method in a double iteration scheme.

STABILITY OF DAMPED COLUMNS ON A WINKLER FOUNDATION UNDER SUB-TANGENTIAL FOLLOWER FORCES

This study examines the dynamic stability regions of damped columns on a Winkler foundation that are subjected to sub-tangentially distributed follower forces. A nondimensionalized equation of motion for the column subjected to linearly distributed follower forces is firstly derived based on the extended Hamilton's principle. A finite element procedure, using Hermitian interpolation functions, is employed to develop the mass matrix, Rayleigh damping matrix, Winkler foundation matrix, elastic and geometric stiffness matrices due to distributed axial forces, and a load correction stiffness matrix to account for sub-tangential follower forces. Subsequently, a time history analysis using the Newmark-β method and an evaluation method for the flutter and divergence loads of the nonconservative system are presented. Finally, the dynamic stability characteristics of the nonconservative system that display the jumping phenomenon in the second flutter load are explored through a parametric study. In particular, how the stable and unstable regions of the undamped and damped Leipholz columns translate with changes in the Winkler foundation stiffness is demonstrated and discussed.