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Signal Processing for Sensing and Monitoring of Civil Infrastructure Systems
Published in Fei Hu, Qi Hao, Intelligent Sensor Networks, 2012
where i and j are the number of the columns and rows in the Hankel matrix, respectively. After building the Hankel matrix, the system matrices are retrieved by using singular value decomposition (SVD) of the Hankel matrix: Π(0)=USVT=[U1U2][S1000][V1TV2T]
On the McMillan degree of full-normal-rank transfer functions
Published in International Journal of Control, 2021
Khaled F. Aljanaideh, Ovidiu Furdui, Dennis S. Bernstein
Other approaches for computing the McMillan degree of G require constructing a controllable or observable realisation of G (Mayna, 1968; Munro & McLeod, 1971; Roberts, 1969). As shown in Roberts (1969) and Mayna (1968), a transfer function matrix with transfer functions of order 6, can require constructing a state space realisation of dimension 150. Moreover, in Gupta and Fairman (1974), to compute the McMillan degree of G, a block-Hankel matrix of size is constructed from the Markov parameters of G, where m, l, and r denote the number of inputs, number of outputs, and the order of the least common multiple of the denominators of G, respectively. The McMillan degree of G is equal to the rank of the constructed block-Hankel matrix.
Detectability conditions for output-only subspace identification
Published in Mathematical and Computer Modelling of Dynamical Systems, 2020
Amirali Sadeqi, Shapour Moradi, Kourosh Heidari Shirazi
The order of an LTI system (here denoted by ) is an inherent and invariant quantity, independent from I/O quantity (magnitude) and quality (distribution). According to the implicit function theorem, it corresponds to the order of governing equations and in dynamical system sense, it is perceived as the minimum independent variables, necessary for describing the state of the system. However, from a data-driven point of view, it is to be said that the rank (see Appendix A4) of state sequences, as well as the rank of transient part of the output sequences in a shift-invariant system, equivalently represents the system order. In a similar manner, one can attribute the order of I/O data, to their signal content as a quantitative measure of the signal quality (i.e. number of independent frequency components or periods) by which the signal can be reconstructed. Therefore, it is assumed the order of any signal to be equivalent the rank of its Hankel matrix. In the following statements, we associate these measures to the system order.
Finite element model of a cable-stayed bridge updated with vibration measurements and its application to investigate the variation of modal frequencies in monitoring
Published in Structure and Infrastructure Engineering, 2022
Wen-Hwa Wu, Chien-Chou Chen, Arief Kusbiantoro, Gwolong Lai
The developed SSI algorithm follows the covariance-driven approach where a Hankel matrix needs to be systematically constructed first from the measured outputs with a chosen time lag parameter i. Two equally divided sub-matrices from the Hankel matrix are then multiplied to obtain the approximation of the so-called Toeplitz matrix. Subsequent performance of singular value decomposition on this matrix would lead to the discretized system matrix in the state space by further selecting a system order parameter n. All the modal parameters can eventually be solved according to the theory of linear systems with the obtained eigenvalues and eigenvectors for the discretized system matrix.