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Research Papers

System Identification Based on Output-Only Decomposition and Subspace Appropriation

[+] Author and Article Information
Amirali Sadeqi

Department of Mechanical Engineering,
Faculty of Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357-83151, Iran
e-mail: a-sadeqi@phdstu.scu.ac.ir

Shapour Moradi

Professor
Department of Mechanical Engineering,
Faculty of Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357-83151, Iran
e-mail: moradis@scu.ac.ir

Kourosh Heidari Shirazi

Professor
Department of Mechanical Engineering,
Faculty of Engineering,
Shahid Chamran University of Ahvaz,
Ahvaz 61357-83151, Iran
e-mail: k.shirazi@scu.ac.ir

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 13, 2018; final manuscript received March 22, 2019; published online May 2, 2019. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 141(9), 091012 (May 02, 2019) (14 pages) Paper No: DS-18-1369; doi: 10.1115/1.4043336 History: Received August 13, 2018; Revised March 22, 2019

Output-only identification methods have been developed on a stochastic framework, but for the first time, a subspace-based approach is proposed without using geometric and statistical tools. This aids the computational efforts to be significantly reduced and the range of input sources to be extended in a much realistic manner for future output-only analyses. The approach encompasses any input type and can properly work for systems excited by inputs with finite periods. It is demonstrated that the row space of the output sequences spanned by column vectors of the decomposed orthonormal matrix is sufficient to reconstruct the observations. The transient and steady-state portions of the output row space, afterward, can be captured to reconstruct an integrated innovation model. The advantages of the algorithm are highlighted through several numerical and experimental examples comparing with the traditional subspace identification algorithms.

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Figures

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Fig. 1

Block diagram of the constructed models: (a) traditional state space described by Eqs. (25) and (26) and (b) integrated innovation described by Eqs. (27) and (28), by considering Bu¯k (and Du¯k) as a unique single matrix

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Fig. 4

Comparison of the estimates for output v of case 9 in Table 1, obtained from different models given in Table 2, and identified by the ODSA and traditional subspace algorithms N4SID

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Fig. 2

Stabilization of the first- and second-order poles associated with nine systems in Table1, versus increasing the Hankel rows

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Fig. 3

Deviation of the estimates from measurements in systems of order 4 with larger second-order poles (dots in case 7 and dash-dots in case 9)

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Fig. 5

Order detection process within the singular values of the output Hankel matrix concerning with a typical tenth-order mechanical system of 5DOF mass-spring-damper undergoing a swept-sine input, for different input frequency bands

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Fig. 6

Variation of the singular values of the output Hankel matrix concerning with the 5DOF mass-spring-damper undergoing a swept-sine input with a particular frequency band of 50–150 Hz for different signal to noise ratio (SNR)

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Fig. 8

Measured output versus estimates obtained from model 3 given in Table 3, (SNR = 20 dB), by ODSA, CVA, and MEOSP in the matlab system identification toolbox

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Fig. 9

Experimental setup including the steel cantilever beam 522 × 31.5 × 6.2 mm, shaker Tira-TV5009, force transducer Kistler 9001a, three accelerometers DJB a/120/vi, and a signal analyzer B&K type 3032A

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Fig. 10

Time histories measured by the accelerometer a3 and estimates obtained from model identified by ODSA and N4SID

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Fig. 7

Biasness of the estimates obtained from models 1–5, given in Table 3, when 10% white noise added to the I/O data

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Fig. 11

Relative errors for the estimates of first eigenvalue obtained by three algorithms ODSA, DSI, and SSI versus input noise and for different level of additive output noise 0% (upper left), 5% (upper right), 10% (bottom left) and 15% (bottom right)

Tables

Errata

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