Output-Only Modal Identification of a Nonuniform Beam by Using Decomposition Methods

Abstract

Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.

Single Output and Algebraic Modal Parameters Identification of a Wind Turbine Blade: Experimental Results

“…In order to derive a method to determine the moment when the algebraic estimator converges to stable calculations, we propose to use a sentinel variable that has a known value of 1, as shown in Figure 14. This unitary variable comes from the characteristic polynomial (11), where the N − th power coefficient of the complex variable s precisely equals 1. The fast and online estimations of the modal parameters are shown in Figures 15 and 16, where the dotted line is the numerical value obtained by the classic off-line peak picking and RFP techniques.…”

“…Since 1996, as reported in [9], several online modal parameter identification schemes have been developed using neural networks and artificial intelligence (AI). It is also important to consider that classical mathematical models for dynamic and vibrating systems are linear assumptions of their dynamic behavior such that it is possible to use basic and well known approaches like least squares and auto-regressive models [3,[10][11][12][13][14]. However, the use of modern materials in structural engineering, high displacements, geometrical restrictions, and complex behavior are now becoming common in modern mechanical structures, resulting in inherent non-linear phenomena (e.g., stiffness, damping, and excitation), and as a result, despite of the numerous advantages of the linearity assumption on mechanical systems, there are cases where the linear methods are no longer effective or even valid, as reported in [15][16][17].…”

Characterizing Wave Behavior in a Beam Experiment by Using Complex Orthogonal Decomposition

“…POD is equivalent to singular value decomposition [9,[11][12][13], and has several different variations for the extraction of different parameters of interest. These variations include mass-weighted reduced-order proper orthogonal decomposition (MWPOD) [14,15], Ibrahim time-domain decomposition [16], smooth orthogonal decomposition (SOD) [15,17,18], state-variable modal decomposition (SVMD) [15,19] and, the topic of this paper, COD. To see the connection between POD and COD, next we will explain POD followed by COD.…”