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MACEC

A MATLAB Toolbox for Experimental and Operational Modal Analysis

mode 1 - 1.882Hz - 1.22% mode 1 - 1.882Hz - 1.22%
mode 5 - 6.196Hz - 1.72% mode 5 - 6.196Hz - 1.72%
mode 7 - 7.156Hz - 2.47% mode 7 - 7.156Hz - 2.47%

B15 highway bridge: three modes, extracted from measured data using the CSI/ref method of MACEC.

new MACEC 3.2 released.

The latest version of MACEC has been released on 11 February 2011. Check the manual for the list of new features.

Summary

MACEC is a MATLAB toolbox for modal analysis of structures. This powerful tool enables you to extract eigenfrequencies, damping ratios, mode shapes, and modal scaling factors from measured input-output or output-only vibration data. MACEC provides extensive functionalities for the visualization and processing of the measured data, the identification of system models and the determination and visualization of the structure's modal parameters. The program disposes of a graphical user interface (GUI), what makes it very intuitive and easy to handle. It can also be used without the GUI, as an extensive set of individual MATLAB functions.

Obtaining MACEC

The current version, MACEC 3.2, was released in February 2011. The toolbox can be obtained here.

 

Modal testing of civil and mechanical structures

Modal testing of civil and mechanical structures is recieving considerable interest in an increasing range of applications such as design validation, (ambient) vibration monitoring, damage identification, determination of modal damping, fluid-structure interaction, etc. Unfortunately, in general modal parameters (eigenfrequencies, damping ratios, mode shapes and modal scaling factors) can not be measured directly, but they have to be extracted from measured vibrations in a two-step procedure. In the first step, a model of the structure is identified from the data, e.g., a state-space model or a non-parametric frequency response function. In the second step, the modal parameters of the identified model are calculated and divided into true (physical) modes and spurious modes, that appear due to measurement noise, modelling errors, harmonics, etc.

Depending on the type of structure and the application for which the modal parameters will be used, experimental, operational, or combined experimental-operational modal testing is needed. In Experimental modal analysis (EMA), a structure is excited by one or several measured forces, the response of the structure to these forces is recorded, and the modal parameters are extracted from the input-output data. In Operational Modal Analysis (OMA), only the responses are recorded and the modal parameters are extracted from the output-only data. When a modal test is performed in operational conditions, and when in addition to the operational excitation, one or several measured, artificial forces are applied, it is called a combined experimental-operational or an OMAX test (Operational Modal Analysis with eXogenous inputs). MACEC can be used for experimental, operational, and combined modal testing of structures.

Software description

MACEC 3.2 has the following capabilities:

Data conversion
  Raw time data in ascii, *.ddf, *.f32, *.mat, *.msd, *.tdm and *.wav format can be imported. The data are converted into a MATLAB object. If necessary, sensitivities and amplification factors can be defined and these definitions can be stored and re-used.
Signal processing
  The following operations can be performed: low-, high- and band-pass filtering, resampling, offset removal, deleting a channel, retaining part of the data, integration and concatenation of files. With the GUI, the data can be easily visualized the following domains: time-frequency, autocorrelation-auto power spectral density, frequency repsonse function-coherence and cross power spectral density-coherence.
System identification
  A variety of dynamic system identification methods is available for deterministic, stochastic, and combined deterministic-stochastic system identification:
  • SSI: Classic and reference-based stochastic subspace identification. Both the data-driven and the covariance-driven versions are available. With the covariance-driven version, it is possible to calculated confidence bounds on the identified system and modal parameters;
  • CSI: Classic and reference-based combined deterministic-stochastic subspace identification;
  • FRF: H1 method for nonparametric frequency response estimation. Confidence bounds on the auto and cross FRFs can be calculated;
  • PSD(+): A correlogram and a periodogram method for nonparametric positive power spectral density estimation. Confidence bounds on the auto and cross PSD+ can be calculated for the periodogram method;
  • pLSCF: Poly-reference least squares complex frequency domain estimator. Both the deterministic version, that starts from FRF data, and the stochastic version, that starts from PSD+ data, are available.
Selection of modes
  Depending on the system identification algorithm used, the following modal parameter estimation options are available:
  • Peak picking: Intuitive estimation of eigenfrequencies and operational deflection shapes from nonparametric PSD(+) data using the average normalized power spectral density function.
  • CMIF / FDD: Intuitive estimation of eigenfrequencies and mode shapes from nonparametric FRF or PSD(+) data using the complex mode indication function, also termed frequency domain decomposition.
  • Stabilization diagram analysis: For identified parametric system descriptions, the discrimination between physical and spurious modes is made in the stabilization diagram, which offers a variety of modal validation criteria such as relative differences in frequency and damping ratio, MAC distance, damping range, modal transfer norm, modal phase collinearity, mean phase, and mean phase deviation. When a driving point measurement is available, the modes are automatically mass-normalized.
When a mode is picked, the mode shape is immediately plotted in the complex plane in order to provide feedback to the user.
Visualization
  The GUI offers extensive visual support for the definition of the measurement geometry (creation of grid, slave and beam/surface files), as well as for the visualization and animation of the selected mode shapes.
Logfile
  When running the GUI, an *.m file that contains the corresponding batch commands is created.

More information

The manual contains a detailed description of the program, installation instructions, documentation of all provided MATLAB functions and two extensive tutorials on the use of the GUI.
Some screenshots of the GUI are available as well.

Applications

Steel transmitter mast

References

  • B. Peeters and G. De Roeck. Reference-based stochastic subspace identification for output-only modal analysis. Mechanical Systems and Signal Processing, 13(6):855-878, 1999. Theory reference for the SSI method available in MACEC.
  • B. Peeters and G. De Roeck. Stochastic system identification for operational modal analysis: A review. ASME Journal of Dynamic Systems, Measurement, and Control, 123(4):659-667, 2001. Review and numerical comparison of operational modal analysis techniques.
  • E. Reynders and G. De Roeck. Reference-based combined deterministic-stochastic subspace identification for experimental and operational modal analysis. Mechanical Systems and Signal Processing, 22(3):617-637, 2008. Theory reference for the CSI method available in MACEC.
  • E. Reynders, R. Pintelon, and G. De Roeck. Uncertainty bounds on modal parameters obtained from Stochastic Subspace Identification. Mechanical Systems and Signal Processing, 22(4):948-969, 2008. Theory reference for the computation of the variance of modal parameters estimated with SSI from a single batch of data, available in MACEC.
  • E. Reynders, D. Degrauwe, G. De Roeck, F. Magalhães, and E. Caetano. Combined experimental-operational modal testing of footbridges. ASCE Journal of Engineering Mechanics, 136(6):687-696, 2010. Two case studies on the use of OMA and OMAX for footbridge testing, for which MACEC was used.

Authors

MACEC is developed at the Structural Mechanics division of K.U.Leuven. MACEC 1.0 was developed by Bart Van den Branden, Alexander Laquière, Bart Peeters, and Guido De Roeck. MACEC 2.0 was developed by Bart Peeters and Guido De Roeck. MACEC 3.0, 3.1 and 3.2 were developed by Edwin Reynders, Mattias Schevenels, and Guido De Roeck.