Modal Shortcuts

Modal test and analysis is used to determine the engineering structures’ modal parameters, such as modal frequencies, damping ratios, and mode shapes. The measured excitation and response (or only response) data are utilized in modal analysis, and then dynamic signal analysis and modal parameters identification are processed. The modal test and analysis has been developed for more than three decades, and much progresses have been made. It has been widely applied to the engineering filed, such as the dynamic design, manufacture and maintenance, vibration and noise reduction, vibration control, condition monitoring, fault detection, model updating and model validation.

Operating Deflection Shape

Operating Deflection Shape (ODS) is the simplest way to see how a machine or structure moves during its operation, at a specific frequency or moment in time. There are two types of ODS: time domain ODS (TD ODS) and frequency domain ODS (FD ODS).

TD ODS is based on the multi-channel time history data acquired spatially from a machine or structure. It shows the vibration motion of the machine or structure in a period of time clearly, just like a recorder. You can view a structure’s overall motion, and the motion of one part relative to another. Locations of excessive vibration are easily identified.

FD ODS is based on the frequency response functions (FRFs) or power spectral density functions (PSDs), which can be estimated from multi-channel time history data acquired spatially from a machine or structure. It shows how a structure behaves at a single frequency, helping you to find whether or not a resonance is being excited. In the OROS Modal, you even be allowed to inside the different behaves of repeated frequencies.

Experimental Modal Analysis

In the Experimental Modal Analysis (EMA), the structures are excited by artificial forces, then both the inputs (excitation) and outputs (response) are measured to get the frequency response functions (FRFs) or impulse response functions (IRFs) by digital signal processing. Modal parameters can be identified from FRFs or IRFs by identification algorithms in frequency domain or time domain. EMA tests are usually carried out in the lab, with the advantage of high SNR (Signal to Noise Ratio) and easy to change test status.

EMA identification methods can be classified into time domain (TD) methods and frequency domain (FD) methods according to different identification domain. Also they can be classified into SISO (single input single output), SIMO (single input multiple output), and MIMO (multiple input multiple output) according to different number of input and output.

The FRFs are generally utilized for the EMA in frequency domain, which are estimated from the excitation and response signals. Then the modal parameters are identified by constructing the parametric or nonparametric models of the FRFs and and curve fitting them. While the IRFs are generally utilized for the EMA in time domain, which can be obtained the inverse FFT of FRFs.

Time domain methods are suitable for the global analysis in a broad frequency band, which have good numeric stability. However, there are some limitations too: (1) very difficult to confirm the order of math model, (2) always time consuming, (3) many calculation modes got with the structural modes, and difficult to delete them, (4) many setting and judgment needed, complicated-to-use, (5) not able to taking account of the influence of out-band modes. Contrarily, frequency domain methods are always reliable, rapid, easy-to-use, with the capacity to consider the out-band modes and analysis uneven spaced FRFs, so they are applied widely.

Operational Modal Analysis

Operational Modal Analysis is used for large civil engineering structures, operating machinery or other structures, making use of their output response only. These structures are always loaded by natural loads that cannot easily be controlled and measured, for instance waves loads (offshore structures), wind loads (Buildings) or traffic loads (bridges).

Compared with EMA, OMA has its outstanding advantages. In OMA the structure studied is excited by natural loads instead of some expensive excitation equipments as used in EMA. In fact it is very difficult to excite large structures by artificial means. So OMA is more economic and fast, and endowed by nature with characteristics of multiple-input / multiple-output (MIMO). It could be used to distinguish closely coupled modes. Moreover, all the measured responses come under operational state of structures, and their real dynamic characteristics in operation could be revealed, so OMA is very suitable for health monitoring and damage detection of large-scale structures.

Because there are limited channels and accelerometers in a data acquisition system, you may need to decide how to distribute the many measurement points in several groups, the so-called setups. For each setup you should keep 1 or more accelerators at the same location, which are called reference points. The reference points should be located far away the nodal points of the mode shapes. It is recommended to set 2 or 3 reference points.

Modal software features

• Running on the current mainstream Operating systems: Windows 2000/XP/2003 Server/Vista
• Coding with VC++ language and object oriented programming technique, easy to be maintained and expanded
• Four powerful functions: geometry modeling, project management, dynamic signal processing, and modal analysis
• Convenient data importing interface, not only for time domain signal, but also frequency domain signal
• Direct data acquisition from OR3x series analyzers, performing a modal test easily and rapidly
• Various data format: Modal standard file format, Universal File Format (UFF) and OROS format (res, oxf, or oxl)
• Integrated functions for geometry modeling
  • Import geometry from UFF or IGES files
  • Export geometry to UFF files
  • Create regular 3D geometry objects
  • Create and edit geometry interactively
  • Undo and redo operations for geometry edit
  • Customized geometry library
• Combined with all kinds of data acquisition systems or dynamic signal analyzers to make up advanced modal analysis systems
• Powerful, effective and easy-to-use signal processing based on wizard setting
  • Detrend, decimation and digital filter
  • Customized FFT parameters: FFT length, average times, and overlap percent
  • All kinds of window function: boxcar, hanning, hamming, flattop, exponential, force and so on
  • Power Spectrum Density (PSD) estimation: Auto PSD, Cross PSD, PSD matrix, using Welch’s averaged periodogram technique
  • Single input / multiple output (SIMO) FRF estimation: H1, H2 and Hc methods
  • Multiple input / multiple output (MIMO) FRF estimation with multiple coherence function
  • The signal processing is reversible
• Dealing with not only traditional Experimental Modal Analysis (EMA), but also Operational Modal Analysis (OMA)
• EMA techniques based on both input (excitation force) and output response
  • Select-band SIMO modal analysis technique: SIMO rational fraction orthogonal polynomial (RFOP), to obtain several modes from a selected frequency band by one identification
  • Narrow-band MIMO modal analysis technique, MIMO complex mode indicator function (CMIF), to identify modes one by one
  • Select-band MIMO modal analysis technique: frequency domain poly-reference (FDPR) and MIMO rational fraction orthogonal polynomial (RFPM), to obtain several modes from a selected frequency band by one identification
  • Broad-band MIMO modal analysis technique: EMA broad band frequency domain (EBFD) , to obtain many modes from a broad frequency band by one identification, or even obtain all the modes from the full frequency band by one identification
  • MIMO analysis methods: with capacity to identify heavy close or even repeated modes, ideal methods for experimental modal analysis of large and complicated structures
  • Single reference (SR) and Multiple References (MR) hammer impact modal analysis techniques
• OMA techniques base on output data only
  • Valuable for the large civil engineering structures, operating machinery or other structures which are not easily excited artificially; cheap and fast, without requirement for excitation equipment; able to get the dynamic characters of structures in real operating conditions
  • Narrow-band operational modal analysis technique: frequency spatial domain decomposition (FSDD), to obtain modes one by one from the full output spectrum matrix
  • Narrow-band operational modal analysis technique: complex mode indicator function (CMIF), sharing the same algorithm with EMA Narrow-band, to obtain modes one by one from the half output spectrum matrix
  • Broad-band operational modal analysis technique: OMA broad band frequency domain (OBFD), to obtain many modes from a broad frequency band of the half output spectrum matrix by one identification, or even obtain all the modes from the full frequency band by one identification
• Adopting mode indicator function (MIF) to indicate the existence of structural modes
• Unlimited number of identified modes
• Flexible interface arrangement and various mouse and hotkey operation, thereby greatly improving work efficiency
• Perfect and friendly function for arranging interface, operating and exporting data
  • Multiple language interface: English and Chinese are available, and it’s convenient to develop other language interface
  • Special 2D and 3D graphic control panes, supplemented with other control modes such as mouse, hotkey, and menu operations
  • Flexible 2D curves display and control: showing or hiding gridlines, legends and other components, providing complete measurement information (measurement node, direction, whether driving point or not, and so ) of each plot
  • Multiple curve expressions: magnitude (linear, log, and dB coordinate), phase, unwrapped phase, real part, imaginary part, and Nyquist
  • Flexible 3D graphics display and control: showing or hiding node ID, input / output tags, axis and other components, freely translating, zooming and rotating the object
  • Top, bottom, left, right, front and back view of 3D objects, rendering in the style of frame lines or surface
  • Animation control based on OpenGL: play, stop, previous/next frame, amplitude and speed control functions
  • Exporting the modal results to text or graph
  • Directly saving all the curves or graphics to BMP or JPG files
  • Exporting the mode animation to AVI media files, convenient to generate multimedia presentation

ODS & Modal Analysis

Modal can deal with Operating Deflection Shape (ODS) Analysis and two types of modal analysis: Experimental Modal Analysis (EMA, both input and output data are available) and Operational Modal Analysis (OMA, only output data are available).

You can find out how a machine or structure moves during its operation via ODS, which shows the overall dynamic characters of the structure or machine.

You can get the modal parameters of structures via EMA or OMA, by performing the following four steps: (1)Signal processing to get frequency response functions (for EMA) or output power spectrum matrices (for OMA); (2) Selecting an appropriate identification algorithm;（3）Doing modal identification; (4) Operating the identification results, such as viewing mode shapes, copying, and removing, and so on.

Almost all the algorithms begin with the Modal Indicator Function (MIF).

The following modules are available in Modal: TD ODS, FD ODS, EMA Narband (CMIF), EMA SelBand-SIMO (RFOP), EMA SelBand-MIMO 1 (FDPR), EMA SelBand MIMO 2 (RFPM), EMA BroBand (BBFD), OMA NarBand Full (FSDD), OMA NarBand Half (CMIF), and OMA BroBand (OBFD). A NarBand method means an algorithm performed in a narrow frequency band, who has the biggest advantage of simple and easy to use. You can identify the modes only by picking the peaks of MIF one by one. A SelBand method means an algorithm performed in one or several selected frequency bands. A BroBand method means an algorithm performed in a broad frequency band or even the full frequency band sometimes.

An effective tool Modal Assurance Criterion (MAC) is also provided to validate the result of modal identification.

Modal Analaysis process illustration

Selecting an Algorithm

Before modal identification, you should select an appropriate algorithm according to the analysis type (EMA or OMA) and number of input (SIMO or MIMO). You can select the specified algorithm by mouse click on the corresponding item in the "Workspace" shortcut pane. A message will appear if you success in doing this.

Another appropriate algorithm can be selected for necessary. And you can compare the results from different algorithms. If some selected algorithm is not fit for the current case, you will be prompted to select another one.

Doing Modal Identification

It’s recommended to employ the modal indicator function (MIF) for the modal identification in the frequency domain. The identification process varies according to different type of algorithms.

1. Narrow-Band Identification Algorithm

(1) Open the MIF curves interface by pressing the button in the toolbar, and the following interface will appear:

The interface consists of two mode list views and a tab window view (’MIF’ tab and ’Enhanced’ tab ). The two mode list view is synchronous. You can adjust the separator lines to resize these views.

(2) Press thebutton in the toolbar to begin the NarBand modal identification.

(3) Check the identified results and curve fitting of enhanced curves. All the identified modes will be shown in the two mode list views and output shortcut pane. You can check the relevant enhanced curves and its curve fitting in each setup for each mode. If ideal curve fitting hasn’t been got, you can adjust the fitting band manually, and identify this mode again in the current setup by double clicks.

1. Select-Band Identification Algorithm

(1) Open the MIF curves interface by pressing the button in the toolbar.

(2) Select the identification frequency band. Move the cursors by mouse or keyboard to the frequency point you want, then double click the mouse or press Enter key to select this band. As a result, a tag like "[-]" appears to indicate this selected band. The data in this band will be used for modal identification. Multiple selected bands for the identification are allowed in Modal, and all the data in these bands will be used to identify modal parameters. To delete the latest selected band, you can use the button in the toolbar, or by the mouse’s middle click. To delete all the selected bands, you can use the button in the toolbar, or by the mouse’s middle double clicks.

(3) Specify the modal order in the selected bands. MIF plot can be used to indicate the modes existence efficiently. A peak in this plot means a mode. For example, in the selected band of the following figure, four modes are detected, including two heavily closed modes.

(4) Press the button in the toolbar to begin modal identification with selected algorithm.

(5) Check the results. The synthesized FRF/HPSD curves will appear in the main window after identification, and the result will be shown in the output shortcut pane. At the same time, an item corresponding to the selected identification algorithm will appear under the directory of ’Data\Setup1\Mode’ in the workspace shortcut pane.

Double click on this item will show the identified mode list.

3. Broad-Band Identification Algorithm

The process of Broad-Band algorithms is almost the same with Select-Band algorithms, only that broader or even full frequency band can be set for the Broad-Band identification.

Operating the Results

Detailed information on identified modal frequencies, damping ratios, identification time, if structural mode are displayed in the mode list view. You can sort the modes ascending or descending according to the specified keyword by clicking on this column header. Also you can do many other operations by the toolbar or right click popup menu, such as deleting modes, copying modes, viewing the mode shapes, exporting the modes, and so on.

You can also double click on the icon of ’’ in the front of each row to view the mode shape animations. The mode shape animations are an import criterion of modal identification.

Modal Indicator Function (MIF)

A very important step of modal identification is to determine how many modes are contained in a selected frequency band. MIF plot is a very good tool to achieve this, indicating the modes efficiently.

MIF can be employed in not only EMA, but also OMA. The number of MIFs equals the number of excitations or references. The MIFs consist of the singular values of frequency response function matrix (FRF), output power spectral density matrix (OPSD), or half power spectral density matrix (HPSD).

By the powerful singular value decomposition, the real signal space is separated from the noise space. Therefore, the MIFs exhibit the modes effectively. A peak in the MIFs plot usually indicate the existence of a structural mode, and two peaks at a same frequency point means the existence of two repeated modes. Moreover, the magnitude of the MIFs always implies the strength of a mode.

Sometimes we should note the cross modes, for example

As showed in the above figure, the peak in the second MIF curve doesn’t indicate a mode. It’s formed by the cross of two modes.

Operating Deflection Shape

Time domain ODS

With Modal, you can animate time domain ODS directly from multi-channel data that was acquired spatially from a machine or structure. This is done by sweeping a cursor through a set of time histories. You can stop the animation, back it up, and play it forward to observe in slow motion vibration phenomena that may have taken place very quickly.

Frequency Domain ODS

With Modal, you can animate frequency domain ODS directly from data that was acquired spatially from a machine or structure. This is done by sweeping a cursor through a set of frequency domain measurements, or dwelling at a specific frequency. A FD ODS allows you to see how a structure behaves at a single frequency.

Modal Analysis

Modal identification methods

Modal analysis can be conducted via artificial excitation, e.g. shaker or instrument hammer excitation, and input force and output responses are measured. That is normally called an Experimental Modal Analysis (EMA). Modal analysis can be also accomplished during operational conditions of a mechanical structure via responses measurements due to ambient or natural excitation, or other excitation but without input force measurements. This is called as Operational Modal Analysis (OMA).
Modal identification algorithms can generally be divided into 2 categories: Time domain (TD) techniques and frequency domain (FD) techniques. TD modal identification has the advantage of estimation of all the modes in the frequency band of interests at once. However, all the TD modal identification algorithms have common unfavorable feature, difficulty to distinguish physical (structural) modes from computational (noise) modes. For application to real-world structure, to locate structural modes reliably is the most important task of a modal analysis. This is why only FD techniques are implemented in OM2.

EMA	OMA
EMA approach can be divided into three levels based on Single Input Single Output (SISO), Single Input Multiple Outputs (SIMO), Multiple Input Multiple Outputs (MIMO). Modal is born in MIMO. However, SIMO algorithm is also implemented for preliminary application. MIMO EMA has important advantages: not only consistent results can be obtained, but close spaced and even repeated modes can be identified. A modal Indication function (MIF) is calculated via Singular-Value-Decomposition (SVD) of the frequency Response Functions.	OMA is a powerful tool to extract dynamic characteristics of real world structure from output-only measurements during operational conditions. The output response can be generated by ambient or natural excitation as well as artificial broadband excitation (but without input force measurements). A modal Indication function (MIF) is calculated via Singular-Value-Decomposition of Power Spectrum Density (PSD) matrix or Half Power Spectrum Density (HPSD) matrix.
	OMA Narband Full
	Narrow-band operational modal identification algorithm in frequency domain. Distinguishes structural modes from noise modes much easier compare to TD OMA. Based on modal decomposition of Power Spectrum Density (PSD) matrix. Identifies one mode at a time. Can easily deal with closely spaced or even repeated modes of real word mechanical structures. Easy-to-use. An assumption that singular vector, i.e. mode shapes vector, are orthogonal is made. However, even with this approximation, the modal parameters identified still have enough accuracy to meet engineering need.
EMA Narband	OMA Narband Half
Narrow-band MIMO modal identification algorithm. Identifies one mode at a time. Can easily deal with closely spaced or even repeated modes of real word mechanical structures. Easy to use. As typical spatial domain decomposition technique enough output measurements are required. An assumption that singular vector, i.e. mode shapes vector, are orthogonal is made. However, even with this approximation, the modal parameters identified still have enough accuracy to meet engineering need.	Narrow-band MIMO modal identification algorithm. Based on modal decomposition of Half Power Spectrum Density (HPSD) matrix. Identifies one mode at a time. Can easily deal with closely spaced or even repeated modes of real word mechanical structures. Easy to use. As typical spatial domain decomposition technique enough output measurements are required. An assumption that singular vector, i.e. mode shapes vector, are orthogonal is made. However, even with this approximation, the modal parameters identified still have enough accuracy to meet engineering need.
EMA Selband SIMO
Selected-band SIMO modal identification technique, suitable for the modal test with only one excitation or one reference, e.g., a single shaker or single reference for impact tests. Identifies a few modes at a time at user-selected frequency bandwidth. Based on Rational Fraction Polynomial formulation of frequency response function (FRF). To improve numerical performance, orthogonal polynomial is adopted instead of power polynomial in traditional FRF representation. Can be applied in modal testing with a few response measurements.
EMA Selband MIMO1
Selected-band MIMO modal identification technique. Identifies a few modes at a time at user-selected frequency bandwidth. Can easily deal with closely spaced or even repeated modes of real-world complex mechanical structures. A rank chart is displayed to be sure of the number of modes within the frequency band. All modal parameters within the frequency band will be automatically identified. FRF curve-fitting, i.e. comparison between synthesized FRFs based on identified modal parameters and measured FRFs is applied for validation. Use Singular-Value Decomposition (SVD) of FRF data for distinguish structural modes from noise modes, and Principle Component Analysis (PCA) for data condensation. Easy to use. Normally the number of measurements should be larger than the number of modes.
EMA Selband MIMO2
Selected-band MIMO modal identification technique. Identifies a few modes at a time at user-selected frequency bandwidth. Can easily deal with closely spaced or even repeated modes of real-world mechanical structures. Based on Rational Fraction Polynomial formulation of frequency response function (FRF). To improve numerical performance, orthogonal polynomial is adopted instead of power polynomial in traditional FRF representation. It would be better to limit the number of references DOFs of the FRF matrix, e.g. less than three. Can be applied in modal testing with a few response measurements.
EMA Broadband	OMA Broadband
Broad-band MIMO modal identification technique. Identifies all modes in a broad frequency band or even in the full frequency band. Can easily deal with closely spaced or even repeated modes of real-world mechanical structures. Can deal with heavily damped modes. Can produce clear frequency stabilization chart. Selects the structural poles automatically. It is recommended to identify the rigid body modes along. Can be applied in modal testing with a few response measurements.	Broad-band operational modal identification technique. Based on the Half PSD estimated from output responses. Identifies all modes in a broad frequency band or even in the full frequency band. Can easily deal with closely spaced or even repeated modes of real-world mechanical structures. Can deal with heavily damped modes. Can produce clear frequency stabilization chart. Selects the structural poles automatically. It is recommended to identify the rigid body modes along.

Narband (CMIF)

Complex Mode Indicator Function (CMIF), is an narrow band modal identification algorithm in the frequency domain. CMIF an easy-to-use method. You should use it as the following steps:

Selecting a Peak

Press the button in the toolbar, and click the MIF plot to activate it. A red cross marker ’十’ will appear, who is able to find the local peak automatically. The index and coordinate value of the marker are shown in the top left corner of MIF graph. In the figure below, (99,1):[47.85,3.48e+001] means that the cross cursor is now at the 99th point of the first MIF curve, and the coordinate is (47.85, 34.8).

　

Auto Identification

After selecting the peak, you should double click to finish this identification. The identified results will be shown in the MIF plot, mode list and output shortcut pane. Each identified mode will be marker with a shape symbol. Its middle pane indicates the position of peak, and the line points to the identified frequency. The mode selected in the mode list will be marked yellow in the MIF plot while the others are blue.

Checking curve fitting and Refitting

You can check the quality of curve fitting by selecting some mode in the mode list and then turning to the ’Enhanced’ tab page. Seen from below, the blue one is the enhanced FRF curve, and the red one is its fitting curve. Sometimes the identification result is not good because of the automatically selected band is not the best. Thus you can move the two cursors to select a better band, then double click to identify this mode again.

Selband SIMO (RFOP)

Rational Fraction Orthogonal Polynomials (RFOP), is an SIMO modal identification algorithm in the frequency domain. It is suitable for cases with only one excitation or one reference. RFOP can fit the FRFs or HPSDs in a fairy broad frequency band.

Each parameter is defined as the following：

Input Number

Number of excitations or references. It is automatically displayed by the software, and can only be 1 in the RFOP algorithm.

Output Number

Number of excitations or non-references. It is automatically displayed by the software.

Denominator Order

Rational fraction math model is used in the RFOP algorithm, and the order of denominator is twice of the modal order in the selected frequency band. Generally you can confirm the modal order by the MIF plot. In some cases, the modal order should be increased properly to hold the noisy modes, and the noise modes can be deleted by the criterion on damping ratios and mode shapes.

Modal Order

This parameter varies with the denominator order you set. You should ensure that this value equal or larger than the real modal order in the selected frequency band.

Numerator Order

This parameter varies with the denominator order you set, and keeping equal to it. You are allowed to set this value individually to be larger than the denominator order, for the sake of compensating for the out-band modes.

Selband MIMO1

Frequency Domain Poly-reference (FDPR), is a MIMO modal identification algorithm in the frequency domain. It is suitable for cases with multiple excitations or multiple references. FDPR usually fits the FRFs or HPSDs in a narrow frequency band. The outstanding advantage of FDPR is its highly easy-to-use.

Besides the MIF plot, two another bar graphs are provided for you to confirm the modal order in the selected frequency band according to the bars’ height. The upper graph shows the relative height of each mode, and it indicates the first four modes are greater than others. The lower graph shows the ratio of previous mode vs. next mode. You will find the fourth one is extremely high. It means that there are 4 structural modes, and the rest are ’noisy modes". So, here you should specify the system order to 4.

Each parameter is defined as the following：

Number of Bars

Number of bars shown in the graph, default as 10. The minimum value of this parameter is 2, and the maximum value is the output number of FRFs. You can change this value to view the bas more clearly.

Order of System

Modal order in the selected frequency band. Generally a fairy good value will be automatically set according to the practice. You are also allowed to change this value to get better result.

EMA Selband MIMO2

Rational Fraction Orthogonal Polynomials for MIMO (RFPM), is a MIMO modal identification algorithm in the frequency domain. It is suitable for cases with multiple excitations or multiple references. RFPM can fit the FRFs or HPSDs in a fairy broad frequency band.

Each parameter is defined as the following：

Input Number

Number of excitations or references. It is automatically displayed by the software.

Output Number

Number of excitations or non-references. It is automatically displayed by the software.

Denominator Order

Matrix form fractional fraction math model is used in the RFPM algorithm, and the order of denominator is related with the modal order in the selected frequency band. Generally you can confirm the modal order by the MIF plot. The product of denominator order and input number should be larger than twice of the modal order. When the product of denominator order and input number is larger than the twice of the modal order, noisy modes will be identified, which can be deleted by the criterion on damping ratios and mode shapes.

Modal Order

This parameter varies with the denominator order you set. You should ensure that this value equal or larger than the real modal order in the selected frequency band.

Numerator Order

This parameter varies with the denominator order you set, and keeping equal to it. You are allowed to set this value individually to be larger than the denominator order, for the sake of compensating for the out-band modes.

EMA Broadband (BBFD)

The BroBand modal identification module is based on the algorithm of Polyreference Least Squares Complex Frequency (p-LSCF), developed in 2003. p-LSCF is a frequency MIMO modal identification algorithm which has superior performance compared to most time domain MIMO techniques, such as Polyreference Least Squares Complex Exponential (PRCE or LSCE), Extended Ibrahim Time Domain (EITD), and Eigensystem Realization Algorithm(ERA). BroBand EMA makes use of measured Frequency Response Function (FRF) as source data.

　

Features/Advantages of EMA Broband

EMA BroBand does not suffer from numerical problems, i.e. ill-conditioning problem in computing poles of the system in broadband as most frequency domain modal identification algorithm, e.g. Rational Fraction Orthogonal Polynomial (RFOP) and Frequency Domain Polyreference (FDPR), encountered. Compared to SelBand techniques, BroBand can then be applied to identify all the modes in a wide, including full, frequency band of interest at one time.

Compared to most time domain modal identification techniques, such as well know Polyreference (or Least Squares) Complex Exponential (PRCE, or LSCE) technique, :BroBand yields extremely clear stability diagram, making it much easier to select structural modes, or the physical poles, from which modal frequencies and damping ratios can be readily obtained.

The BroBand modular in OM2 has the feature of automatic modal sorting capability, i.e. BroBand can automatically distinguish structural modes from "noise" modes, or real modes from spurious modes.

Main Procedures for EMA BroBand

Major procedures for modal identification with EMA Broband are as follows:

1. Select a frequency band

The EMA Broband can be used to identify all modes in a broad frequency band, including full band. However, frequency band selection may be advantageous and is suggested in the cases as:

• In the "soft" suspension of test article to simulate free-free boundary condition, so called "rigid-body modes" are sometime weakly excited in low frequency range. In this case, frequency band selection excluding this low frequency range is suggested for identification of flexible structural modes. The "rigid-body modes" can also be obtained with selection of corresponding low frequency band.

• A structure under testing sometimes shows "strong mode" or "global modes" in specific frequency band, and "weak modes", or "local modes" in other frequency band. These "strong/global modes" and "weak/local modes" can be easily observed from Modal Indication Function (MIF) plot based on height of the MIF peaks. In this case, it is suggested to divide the full band into few sub-band which cover "strong/global modes" and "weak/local modes", respectively.

• It is suggested to start the frequency band from a valley of the MIF plots, and end the band at a valley too. According to our experience, such a frequency band can yield better result.

1. Start Identification

Press the button of "Start Identification" in the toolbar to start modal identification.

1. Modal Order determination

Preliminary determination of the number of modes in the selected frequency band according to the MIF plot, and fill it in the edit box of "Preset Modes No." Then the BroBand software will calculate a default "minimum order" according to this number. The relationship between "Preset Modes No." and "Minimum Order" is: minimum order = (preset modes No)*Ni/2, where Ni means the number of input.

Change the number of "Order Span" if necessary. The BroBand software will estimate the poles with a range of system order from "Minimum Order" to "Maximum Order", where Maximum order= Minimum order + Order Span-1. The default order span is 12.

"Start Modal ID"

Press the button of "Start Modal ID" or to obtain frequency stability diagram. This operation might take a little longer time to finish a complex structure with large number of modes and measurement coordinates. In the stability diagram, a shape symbol represents one pole. A pole in this diagram may represent a physical (i.e. structural) mode or a spurious (or noise) mode. It is normally not difficult to distinguish physical/structural) mode from spurious/noise mode by the distribution of poles. Generally speaking, a physical/structural mode can be identified in each proper number of orders, while for a spurious/noise pole it usually is not the case. There are five kinds of symbols to indicate the poles:

Symbol	Description
o	The pole is not stable. (The poles obtained from the first order are always considered as unstable.)
f	The frequency of the pole does not change within the tolerance of 1%.
v	The frequency of the pole does not change within the tolerance of 1%, and the pole vector does not change within the tolerance of 10%.
d	The frequency of the pole does not change within the tolerance of 1%, and the damping of the pole does not change within the tolerance of 10%.
s	Both frequency, damping and vector are stable within the tolerances: the frequency of the pole does not change within the tolerance of 1%; the pole vector does not change within the tolerance of 10%; and the damping of the pole does not change within the tolerance of 10%.

1. "Auto Selection" of structural modes

Press the button of "Auto Selection" or , the OM2 selects the physical/structural modes automatically. While move the mouse cursor on a pole, the modal frequency and damping ratio corresponding to this pole will be shown. You can move the mouse on different poles to check the stability via small change of the modal frequency and/or damping ratio.

You can zoom in to check part of the stabilization diagram by click and drag a rectangle with the mouse.

1. Manually selection of physical/structural poles

A pole can also be manually selected by clicking it or deselected it by same operation. A selected pole will be marked with a shape symbol .

1. Mode shape calculation

Press the button of "Calc. Modeshape" to confirm the pole section and BroBand software start to estimate the mode shapes and to calculate the synthesized FRFs.

1. Inspection of identified modal parameters

Open the view of mode list. Yyou can check the identified result here: modal frequencies, damping ratios, modal A, modal B, and mode shape animations.

1. Continue modal identification in another frequency band

If more than one frequency band is selected, returning to the MIF plot window, and repeat the above operations. The result obtained from previous modal identification can also be loaded by pressing the button of "Load Para.".

On the Toolbar of "BBFD Setting" Diagram

	Display the full band of current curve
	Back to previous display range
	Go to next display range
	Show or hide the graph grid
	Copy contents in current main window to the clipboard
	Save current snapshot to BMP or JPG
	Start modal identification to gain poles
	Select the structural poles automatically
	Delete all the selected poles
	Load the parameters (poles, selected poles, frequency band) of previous modal identification

Modal validation, MAC & COMAC

Modal Assurance Criterion (MAC) values can be used to compare two arbitrary complex vectors. The MAC value between two vectors who have linear relationship is near to one. The MAC value between two linearly independent vectors will be near zero. MAC calculation has two applications in the modal analysis.

First, it can be used to compare two mode shapes obtained from two different modal parameter estimation processes on the same test data. Two similar mode shapes have a high MAC value, and two same mode shapes have a MAC value of 1.

Second, it can be used to check the orthogonality of mode shapes when weighted by the mass matrix. Even when no exact mass matrix is available, the orthogonality of mode shapes is approximately satisfied. We can use it to validate the modal result.

The MAC value table can also be showed by the right click popup menu.

Coordinate Modal Assurance Criterion (COMAC) is an extension of Modal Assurance Criterion (MAC). COMAC attempts to identify which measurement degrees of freedom contribute negatively to a low value of MAC. COMAC is calculated over a set of mode pairs, analytical versus analytical, experimental versus experimental or experimental versus analytical. In Modal, COMAC between modes from different identification algorithms or imported modes can be calculated.

To calculate COMAC, the first step is to set the two sets of modes you want to be compared.

In the second step, the mode pairs should be determined. The process of modes paring will be done by Modal automatically, according to the MAC values between each modes in the two sets. You are also allowed to select part of the mode pairs.

Then the COMAC values table will be displayed.

Import / Export

Data and all kinds of results can be exported or printed, which provides you great convenience to write a report or give a presentation. These functions include: Importing data, exporting data, m exporting table,export graphics, exporting animations, print preview and print].

Import

Geometry

You can import geometry information from UFF 15/82/2412 files and IGES files

Data Files

UFF

You can import measurement data in frequency domain (including Frequency Response Functions and Coherence Functions) or time domain (time histories) from the UFF 58/58b files.

1. Response Type

The type of response to be imported. Generally we use accelerometers, so we specify the type as "Acceleration" here.

1. Data Type

The type of data to be imported. There are three types here: 1) frequency response functions (and coherence functions) for EMA analysis, 2) time histories for EMA analysis, and 3) time histories for OMA analysis.

If FRFs which have been applied with exponential windows are to be imported, you need fill the content of "Exp. Window Coef." to modify the increasing damping caused by the exponential window.

If time histories are to be imported, you need specify the marker to distinguish excitation signal from response signal. Here you have two options: reference DOF (REFDOF) or the unit of Y Axis. When the marker is REFDOF, the measurement information of excitation signal should be defined in the field the reference node and direction. While the marker is the unit of Y Axis, software take the signal block with the unit you specified as excitation signal.

1. Setup Name and UFF Data Files

Then you can specify or modify the "Setup Name" and "UFF data files" for each setup. The wildcards (’*’ or ’?’) is allowed to refer to multiple UFF files. If many files are included, you are recommended to use wildcards manually. The common definition of wildcards is employed: "*" to represent any multiple characters, and ’?’ to represent a single character. For example, the "*.unv" represents all the files whose extension names are "unv" in the same directory of this configuration file.

Note (very important): if you want to import time domain UFF data files for EMA, you’d better use the wildcard. You must put the measurement data of one test (for example, in the IMRT, one test means the measurement of one point) into one UFF file. If you have 20 nodes to measure in an IMRT, then you should have 20 UFF files, such as node01.uff, node02.uff, ... node20.uff. Here you can use "node*.uff" to import all the 20 files.

1. Buttons

Press the "Add/Change" button to confirm this operation, then these data files information will be stored for the specified setup. For an EMA test, you are only allowed to have one setup, no matter whether it is time domain or frequency domain. For an OMA test, you are allowed to add more setups.

Press the "OK" button to write these information to the current configuration file, and the new configuration file will be automatically reloaded to import the data specified.

The following interface will appear after the importing:

You can check or change the information of imported data here, such as the response nodes and directions. You can also unselect the data you don’t like. Click the header of each column, the current list will be sorted. In the right of this dialog, two filters are set for convenience.

OROS Format

You can import measurement data in frequency domain ("*.res", including Frequency Response Functions and Coherence Functions) or time domain ("*.oxf" or "*.oxl", time histories) from the OROS format data files.

The interface for importing OROS format data files is very similar with the one for importing UFF data.

To import the FRFs and COHs from the OROS ".res" files, you don’t need to specify the the "Exp. Window Coef." . Because this information is included in the ".res" file, and will be read by OM2 automatically.

The data files of one modal test may be stored in many different directories, so in this interface you should specify the "Searching Directory", but not the name of files. OM2 will search data files in the specified directory and all its subdirectories.

The same interface which allows you to check and change the information of imported data will appear after the configuration file is reloaded.

Equations

You can import the constrain equations from a ASCII format configuration file. The imported equations will be appended to the current equations list in the project. Please note that the sequence of equations is very important, which might lead to different animation effect.

Modes

You can import identified modes (including frequencies, damps, mode shapes, modal A and modal B) from UFF 55 files. An item called "Imported" will appear in the branch of "Data\Setup?\Mode" in the "Data" page of "Workspace" Panel.

Export

Data and all kinds of results can be exported or printed, which provides you great convenience to write a report or give a presentation.

Data

You can export the modes by corresponding toolbar of the mode list view or the right click menu.

All the mode can be exported to a UFF 55 file (".unv") or ASCII file (".asc").

Data such as input signals, output signal, frequency response functions, power spectrums, and coherences can be exported to UFF files or ASCII files in the "Data" tab page of Workspace shortcut panel.

All the data in the data table view can be exported to an ASCII file.

Table

The identified mode list can be export to Microsoft WORD as an table by the following steps:

1. Copy the Mode List to Clipboard

’Copy’ button in the standard toolbar or ’Copy All’ item in the right click menu of the mode list view can be used to copy all the modes to system’s clipboard. If only part of the modes are needed, please select the items you wanted by ’Shift’ or ’Ctrl’ keys (just like the operations in the Windows’ Explorer), then click on the ’Copy’ item in the right click menu.

1. Paste to WORD and Create the Table

Run WORD and create a new document, and paste the contents in the clipboard into it. Select the pasted lines, and use the Insert Table Command, the a new table containing the modes are created. To prettify this table, you can adjust it furthermore.

If you want to use these tables in Microsoft PowerPoint, you can create the table in WORD first, and then copy it to the PowerPoint.

Graphics

Everything in the main window, including the 2D curves, 3D graphics, data tables and so on, can be captured and saved as BMP or JPG graphic files by the ’Save Snapshot’ button in the standard toolbar.

You can also copy a snap into Windows’ clipboard by the ’Copy’ button in the standard toolbar, and then paste it to the document.

Animations

The animations of mode shapes or ODS in Modal can be saved as AVI media files according to the following steps:

• Make sure that the mode shape or ODS wanted is shown in activated.
• Press the "Record" button in the "3D Display" shortcut panel (or using the right click menu), and enter the wanted file name. The default name can be changed from the dialog of "Set Properties...".
• Saving progress will be displayed in the status bar. You can play this AVI file with some media player, or insert it to the WORD/PowerPoint documents.
• The AVI file is encoded with the CODEC you set in the dialog of " Set Properties...". Some CODECs might fail to work correctly. If this happens, please select another one in the dialog of "Set Properties..."..
• Different CODEC leads to different play quality and different file size, you can select the best after trying all.

Print

Everything displayed in the main window, including the 2D curves, 3D graphics, configuration information, data tables and so on, can be previewed by button or printed by button in the standard toolbar. Of course, you can realize these operations by menu too.

Shortcuts operation

Many shortcuts are provided to help you operate Modal more conveniently. Your efficiency can be greatly improved by these shortcut operations employing the mouse and keyboard.

Shortcut Operations in the Explorer

Double click on a ’.cfg’ file	Run Modal, and open this configuration file
Double click on a ’.wsp’ file	Run Modal, and load this workspace file
Drag a ’.cfg’ file to the software’s mainframe	Open this configuration file
Drag a ’.wsp’ file to the software’s mainframe	Load this workspace file

　

Shortcut Operations in the General Interface

Ctrl+N	Create a new configuration file
Ctrl+O	Open a configuration file
Ctrl+P	Print contents in the current window
Ctrl+C	Copy contents in the current window to the clipboard
Ctrl+V	Insert clipboard contents
Ctrl+Z	Undo the last action
Ctrl+Y	Redo the previous undone action
Ctrl+D	Locate to the setup list box in the standard toolbar, and switch between each setup
F1	Show the online help manual
F5	Reload the current configuration file
F12	Begin a new session of OROSModal2
Double click on a window tab	Close the relevant window
Middle click on a window tab	Close the relevant window

　

Shortcut Operations in the 2D Curve Window

Double click	Select the band between current cursors
Enter	Select the band between current cursors
Middle click	Delete the latest selected band
Backspace or Delete	Delete the latest selected band
Double middle click	Delete all the selected bands
Esc	Delete all the selected bands
Tab	Find the limits between current cursors
←	Move the two cursors to the left simultaneously
→	Move the two cursors to the right simultaneously
↑	Move the two cursors outwards simultaneously
↓	Move the two cursors inwards simultaneously
Page Up	Increase the cursors’ moving step
Page Down	Decrease the cursors’ moving step
Home or End	Make the two cursors return to default positions
F2 ＋ Mouse moving	Move the two cursors with the mouse simultaneously
F3 ＋ Mouse click	Zoom in the range between the two cursors
F4 ＋ Mouse click	Display the full band of current curve

　

Shortcut Operations in the 3D Graphics Window

Ctrl+M	Locate to the mode list box in the toolbar, and switch between each mode
Click and moving	Rotate the model
F2 ＋ mouse moving	Translate the model or selected 3D objects
F3 ＋ mouse moving up or down	Zoom in or out the model or selected 3D objects
F4 ＋ mouse moving	Rotate the model or selected 3D objects
Mouse wheel scroll	Zoom in or out the model or selected 3D objects
Delete	Delete selected items (nodes, lines, polygons, 3D objects)
←	Translate to the left
→	Translate to the right
↑	Translate to the top
↓	Translate to the bottom

　

Shortcut Operations in the Dialog of ’Showed Series’

Double click on the ’Available No.’	Add the selected items to ’Selected No.’
Double click on the ’Selected No.’	Delete the selected items from ’Selected No.’
Right click anywhere	Delete all the items in ’Selected No.’
Middle click anywhere	Delete all the items in ’Selected No.’

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