A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

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An eigensystem realization algorithm for modal parameter identification and model reduction

In this paper a new frequency domain technique is introduced for the modal identification of output-only systems, i.e. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical approach where the modal parameters are estimated by simple peak picking. However, by introducing a decomposition of the spectral density function matrix, the response spectra can be separated into a set of single degree of freedom systems, each corresponding to an individual mode. By using this decomposition technique close modes can be identified with high accuracy even in the case of strong noise contamination of the signals. Also, the technique clearly indicates harmonic components in the response signals.

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Modal Identification of Output-Only Systems using Frequency Domain Decomposition

Computer Solution of Linear Algebraic Systems. By G. Forsythe and C. B. Moler. Pp. xi, 148. 1967. (Prentice-Hall.)

Operational modal analysis deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions. This paper extensively reviews operational modal analysis approaches and related system identification methods. First, the mathematical models employed in identification are related to the equations of motion, and their modal structure is revealed. Then, strategies that are common to the vast majority of identification algorithms are discussed before detailing some powerful algorithms. The extraction and validation of modal parameter estimates and their uncertainties from the identified system models is discussed as well. Finally, different modal analysis approaches and algorithms are compared in an extensive Monte Carlo simulation study.

System Identification Methods for (Operational) Modal Analysis: Review and Comparison

Structural health monitoring and damage detection techniques are tools of great importance in the off-shore, civil, mechanical and aeronautical engineering communities, both for safety reasons and because of the economic benefits that can result. The need to be able to detect damage in complex structures has led to the development of a vast range of techniques, of which many are based upon structural vibration analysis. In the present article, some of the latest advances in Structural Health Monitoring and Damage Detection are reviewed, with an emphasis on composite structures on the grounds that this class of materials currently has a wide range of engineering applications. FOREWORD-It should be noted that this review is not intended to be a general, all-encompassing review covering the whole range of structural health monitoring (SHM); it was planned as the starting point for a study focusing on damage detection, localization and assessment for certain kinds of structure. Thus, the line of thought behind the search and the structure of this review is a result of objectives beyond the scope of the paper itself. Nevertheless, it was considered that, once the above was understood, an updated synopsis such as this could also be useful for other researchers in the same field. ©2006 SAGE Publications.

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A review of vibration-based structural health monitoring with special emphasis on composite materials

A method for the direct identification of vibration parameters from the free response

An algorithm is developed to obtain the free responses of a structure from its random responses, due to some unknown or known random input or inputs, using the random decrement technique without changing time correlation between signals. The algorithm is tested using random responses from a ' 'generalized pay load" model and from the "space shuttle" model. The resulting free responses are then used to identify the modal characteristics of the two systems. The method is limited to structures that are linear or have small nonlinearities. N general, the experimental identification of structural modes of vibration is carried out by measuring the input (or inputs) to the structure under test and the resulting responses due to this input. Some vibration testing techniques, in order to simplify the identification procedure, use the free responses of structures. In such cases, although the input excitation need not be measured, some initial excitation is applied to the structure, and free responses are measured immediately after the initial exciting force is removed. There are situations where controlled excitation or initial excitation cannot be used. For example, if the structure to be tested is in operation, applying any kind of external force may cause undesirable interruption. Another example is the case of in-flight response measurements, where a complete knowledge of the excitation is usually not available. In such cases, the use of the "random decrement signature" technique (a special averaging procedure that is used to determine the step and/or impulse response from the random response) to obtain the free responses is a promising technique. The random decrement signature technique1 has been used successfully for failure detection and damping measurement of structures in single-statio n, single-mode response cases. Application of the random decrement signature technique to a multiple of signals changes the time correlation between the individual signals. If the resulting responses are to be used to identify several modes of a structure, the random decrement signature technique must be modified to keep the time correlation between signals unchanged. In this paper, an algorithm is developed to obtain the free responses of a linear structure from its random responses, due to some unknown or known random input or inputs, using the random decrement technique without changing time correlation between signals. The algorithm is tested by ap- plying it to random responses obtained from two real structures. The first structure is a generalized payload model previously tested using sine sweep method and analyzed by NASA Structural Analysis (NASTRAN). The second structure is the V& -scale space shuttle model with modal parameters previously determined using sine sweep method and fast Fourier transform (FFT). Only responses from four stations on the solid rocket boosters (SRB's) were considered in the case of the space shuttle model. The filtered random responses from these two structures were recorded and

Random Decrement Technique for Modal Identification of Structures

The Experimental Determination of Vibration Parameters from Time Responses

The modal confidence factor (MCF) is a number calculated for every identified mode for a structure under test. The MCF varies from 0.00 for a distorted nonlinear, or noise mode to 100.0 for a pure structural mode. The theory of the MCF is based on the correlation that exists between the modal deflection at a certain station and the modal deflection at the same station delayed in time. The theory and application of the MCF are illustrated by two experiments. The first experiment deals with simulated responses from a two-degree-of-freedom system with 20%, 40%, and 100% noise added. The second experiment was run on a generalized payload model. The free decay response from the payload model contained 22% noise.

S. R. Ibrahim

Papers

A method for the direct identification of vibration parameters from the free response

Random Decrement Technique for Modal Identification of Structures

The Experimental Determination of Vibration Parameters from Time Responses

Modal confidence factor in vibration testing

Statistical theory of the vector random decrement technique