Operational modal analysis of three-dimensional structures by second-order blind identification and least square generalized inverse

Abstract

Most complex engineering structures are three-dimensional in practice. The process of one-dimensional extending to three-dimensional is a challenge that must be conquered by Operational Modal Analysis (OMA) methods when these methods are applied to complex engineering applications supported by scientific researches. This study put forward a new three-dimensional structure OMA method based on Second-Order Blind Identification (SOBI) and general reversion of least square. Firstly, modal coordinates decomposition of one-dimensional structural vibration response signal with SOBI. Secondly, the reasons that modal parameters identified by SOBI including energy uncertainty, order uncertainty and modal missing are explained in theory. Thirdly, the SOBI algorithm is used to decompose the response signals of displacement of a direction whose vibration response is the largest, then the other two directions are calculated by using the least square generalized inverse algorithm, and the modal parameters of three-dimensional structures are identified by the matrix assembly method. Numerical simulation results in a cylindrical shell demonstrated that this novel method is practical and effective by applied to practice in OMA of three-dimensional structures, and robustness to Gauss measurement noise disturbances.

Isomap-Based Three-Dimensional Operational Modal Analysis

“…e 6th-order modal parameters are not extracted well by Isomap because of their weak nonlinear characteristics. 7Tables [11][12][13][14][15][16][17][18][19] illustrate that, as the real modal ratio increases, the modal shapes, frequencies, and modal ratios become more difficult to identify. is is because a larger damping ratio results in smaller structure responses.…”

“…To reduce the influence of the Gaussian-distributed signal measurement noise, the main and biggest structure's dynamic response dimension is selected in practical engineering cases. Substituting Q(t) into the other twodimensional displacement response signals using the Moore-Penrose matrix inverse in (14), the modal shapes of these two dimensions can be identified.…”

“…Classical linear dimensionality reduction algorithms include principal component analysis (PCA) [8], locality preserving projection (LPP) [9], multidimensional scaling (MDS) [10], and linear discriminant analysis (LDA) [11]. Recently, Wang et al introduced PCA to OMA [12] and proposed PCA and second-order blind identification-(SOB-I-) based three-dimensional OMA methods [13,14]. However, the time invariant engineering structures are often three-dimensional, with damping and small nonlinearity [15].…”

Three-dimensional operational modal analysis based on self-iteration principal component extraction and direct matrix assembly

“…Based on the vibration theory in Eq. (6)- (14), when the structure's natural frequencies of each mode are not equal, the modes vectors are orthogonal:…”

“…However, the PCA model is calculated by EVD and the three-dimensional modal shapes are calculated by reverse matrix substitution, so that method has higher space-time complexity and lower identified accuracy. In 2017, J. Wang et al proposed to use second-order blind identification to solve three-dimensional model [14], and the matrix assembly method is similar to C. Wang's method. This paper proposes a new matrix assembly method for complex three-dimensional structures, and uses SIPCE to solve PCA model.…”