2020-07-10T10:49:01.000-0400

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Direct YouTube link: https://youtu.be/wwii_JeVVMY

Operational Modal Analysis (OMA) is a technique used to identify the modal parameters (natural frequencies, damping, and mode shapes) of a structure or object during operation. By measuring and understanding the modal parameters, engineers, architects and designers can help create structures, machines and devices that perform better, last longer, and are more comfortable for their users or occupants.

Some terms used in the article:

- OMA: Operational Modal Analysis - Determining mode shapes, dampings, natural frequencies from operational vibration measurements
- EMA: Experimental Modal Analysis - Determining mode shapes, dampings, natural frequencies from Frequency Response Function measurements via measured force inputs
- ODS: Operational Deflection Shapes - Vibration shape at a given operational frequency, not necessarily a natural frequency of the system

1. Overview of Operational Modal Analysis

1.2 Why OMA?

1.3 OMA vs EMA vs ODS

2.2 EMA Approach

2.3 OMA Approach

3. OMA vs ODS

3.2 ODS Approach

Operational modal analysis is one of a family of techniques used to investigate the dynamics of a structure. Other popular methods include:

- Experimental modal analysis (EMA)
- Operational deflection shapes (ODS)
- Impact testing
- Ground vibration testing (GVT)
- Vibration control testing

However, performing the test during operation means the input forces are not able to be quantified as they are in other techniques. OMA is a

There are three main benefits/reasons to perform a modal analysis during operation:

- Real world operational conditions differ significantly from laboratory conditions
- Practical / Size limitations
- Ongoing health monitoring / damage detection

There may also be environmental influences on the structure that cannot be easily replicated in the laboratory. Aero-elastic interactions like wind and air flow over a structure is a common example. This aero-elastic interaction is critical for understanding phenomena like flutter seen in aircraft (Figure 2) and cannot easily be recreated in a lab. Scale models can be tested inside a wind tunnel in this case, but the aero-elastic inputs still go unmeasured.

The table below (Figure 4) summarizes some of the critical differences between EMA, OMA and ODS for structural analysis.

These differences are discussed in detail in the following sections.

Both OMA and EMA are known as “parametric” methods, meaning that measurement data is used to build a mathematical model of the structure’s dynamic characteristics. This math model is then used to extract the modal parameters of the structure in a systematic way known as curve-fitting.

In both methods, the math model of the structure is built using a family of frequency-domain functions calculated from the measurements. These functions express the frequency domain relationship between the references (or inputs) and the responses (outputs) for various locations around the structure (see Figure 5).

In EMA these functions are known as frequency response functions (FRFs), while in OMA the functions are auto-power and cross-power spectra. In both cases, the end result is a complete system matrix ([H] in Figure 5) relating the outputs of the system to the input. The core difference between the methods is in how each arrives at characterizing the system transfer matrix, H. Figure 6 is a summary of both methods and highlights their similarities and differences.

In EMA, the structure under test is excited using some calibrated method of force input: typically an impact hammer or a dynamic shaker equipped with a force transducer. Thus, the input force is applied at a specific location and direction on the structure, and the amount of force applied during each measurement is accurately recorded. By combining this measured input force with the set of response measurements, a family of curves known as frequency response functions (FRFs) can be calculated.

The FRFs are complex frequency domain functions, having both magnitude and phase information. The input force acts as the reference for the FRFs, which are of the form output/input (typically acceleration/force or “A/F”) and describe how the structure moves at each measurement location per unit force at the input location.

The family of FRFs contains the resonance and damping information for all the system modes. The family of FRFs is used for curve-fitting, where individual modes are selected, the math model of the system is generated, and individual FRFs synthesized from the math model. These synthesized FRFs can then be used to generate the mode shapes for each of the identified modes.

One distinct advantage for EMA: having measured the input force allows for the calculation of modal participation factors, and each mode shape can be properly mass-normalized or arbitrarily scaled.

This white noise assumption allows the response signals from the structure to be used to build the math model of the structure and extract its modal parameters without a measured input. However, without a measured reference force, it is impossible to calculate FRFs in the same way as in EMA, so an alternative method of extracting the frequency information must be employed.

In OMA the responses of the structure are used to create time domain functions known as correlation functions. A correlation function is a statistical tool for finding repeating patterns (such as periodic content) hidden in what seem to be random signals (see Figure 8).

An autocorrelation function (ACF) is the result of comparing a signal with a delayed version of itself at increasing time lags. An ACF provides a measure of the amount of correlation between the two signals (a value between -1 and 1). If the original signal contains periodic information (such as natural frequencies), then the delayed version of the signal will have a high amount of correlation with the original signal at certain periodicities (time lags). However, as the delay between the signals gets larger, the correlation should progressively decay to zero since we are exciting it with an assumed random excitation. The early horizon response (small number of time lags) is dominated by the modal response, while further into the future is just random so there cannot be a correlation between the signals.

In this way, the ACF extracts the periodicities that are common between the two signals, and the resulting function can be translated into the frequency domain. Similarly, a cross-correlation function compares a delayed signal to a reference signal, highlighting the periodicities common between signals from two different measurement locations.

In OMA, one or more measurement locations are selected as reference locations. Using the time domain responses measured across the structure, auto correlation and cross-correlation functions are calculated, extracting periods common across all measurement locations. By taking the discrete Fourier transform of the correlation functions, a family of frequency-domain functions called correlograms is generated. This family of correlograms highlight the dominant frequencies common between measurement locations, analogous to the FRFs in EMA. The correlograms are power spectra (auto and cross spectra) and can be curve fit in a manner identical to the approach used in EMA.

Due to the face that the correlation functions produce an unscaled value between -1 and 1, and the input forces are unmeasured, the concepts of modal participation factor or modal scaling do not exist in OMA.

The data acquired from the test structure for OMA and operational deflection shapes (ODS) is identical. Time domain responses (accelerations) are recorded from various parts of the structure during operation, and a reference measurement location is identified. As in OMA, there is no input force available. The difference between OMA and ODS is how the data is processed, and the final product of the analysis (see Figure 9). An OMA is performed to extract the modal parameters inherent to the structure: natural frequencies, mode shapes and damping. The purpose of performing an ODS is to extract (and animate) the structure’s deformation at a specific operating point, frequency or RPM.

Typically, an issue or problem (unwanted noise, excessive vibration) is discovered at a certain operating condition, and a root cause needs to be identified. An ODS analysis provides animations of how the structure or components are moving (or deflecting) at the problematic operating condition. The ODS does not provide any information as to what is causing the deformation of the structure in the problematic way, be it resonances (modes), direct forced response, or a combination of the two. Where an OMA provides a modal model of the structure that identifies structural modes that may be contributing to the operational issue and can separate these effects from forced response, an ODS simply animates the combined result of all influences on the structure when the issue is present. This can, in certain cases, make the ODS result less insightful than an OMA or EMA.

The deflection shapes of an ODS show the result of modal superposition at a particular operating point. In a forced response, the structure will deform as a weighted combination of multiple modes and mode shapes (see Figure 10). When the structure is excited at or near a natural frequency, this forced response will be dominated by the mode shape corresponding to that natural frequency, but will still be a combination of several mode shapes. For structures that have low amounts of damping, and low modal density (natural frequencies are far apart) the ODS and OMA will provide similar results. However, for structures with closely spaced modes, or for structures that are heavily damped, the ODS results will contain much higher levels of participation from neighboring modes and will not provide reliable information on the underlying modes which are driving the deflection shape.

Finally, another advantage of OMA is that modal parameters can be more confidently used to validate numerical models. In many cases, operational models are also available, or the structure is so big that it would be extremely difficult to excite it with a known force. ODS can also be used, but as they depend on the excitation and operating conditions (a modal model does not) they provide a less objective correlation criterion.

Like in OMA, a measurement location is selected as a reference location. As with any operational data, it is optimal to acquire all data simultaneously, in a single run. If the data must be collected in multiple patches, the reference transducer must remain at the original location, and participate in all runs collected. Response data is acquired for all measurement points, and appropriate windowing of the time domain signal is performed to reduce leakage.

Phase-referenced spectra are then calculated for all measurement locations, with the phase reference being provided by the reference transducer. This results in the reference location spectrum having zero phase for the entire frequency spectrum, and all other spectra’s phase calculated relative to the reference location’s phase. This family of phase-referenced spectra can be used directly to animate the operational deflection shapes for any frequency or RPM measured during the test, as the spectra contain all the necessary magnitude and phase information for each spectral line (Figure 11). Note that the amplitude of deflection in the shape is directly related to the amplitude of the spectrum.

Operational modal analysis provides a unique balance between the benefits of lab-based experimental modal analysis and real-world operational deflection shapes. For structures that cannot be moved into a laboratory environment, or for structures that have features that make laboratory measurements unrealistic, operational modal analysis provides a method to extract the modal parameters of the structure in a reliable way. Understanding the natural frequencies, mode shapes and damping of a structure can help engineers create structures that perform as intended, are safe and durable. When structural problems arise, OMA can provide objective guidance as to the resonances and mode shapes that are contributing to the issue, and what may be done to fix it. Operating deflection shapes are quick and relatively easy to obtain, and provide a detailed snapshot of the structural movement/deformation pattern during problematic operating conditions, but may not provide much objective information about what to change on the structure to affect an improvement.

Questions? Post a Reply, email Scott MacDonald macdonald@siemens.com, or contact Siemens Support Center.

- Index of Simcenter Testing Knowledge Articles
- Structural Dynamics
- A Brief History of Modal Testing and Analysis
- Modal Testing: A Guide
- Simcenter Testlab Impact Testing
- Modal Impact Testing: User Defined Impact Sequence
- What modal impact hammer tip should I use?
- Modal Testing: Driving Point Survey
- Modal Tips: Roving hammer versus roving accelerometer
- Attach Modal Shaker at Stiff or Flexible Area of Structure?
- Using Pseudo-Random for high quality FRF measurements
- Multi Input Multi Output MIMO Testing
- Simcenter Testlab MIMO FRF Testing
- Simcenter Testlab MIMO Swept and Stepped Sine
- Ground Vibration Testing and Flutter
- Structural Dynamics and Vibration On-Demand Webinars
- Natural Frequency and Resonance
- What is Frequency Response Function (FRF)?
- Dynamic Stiffness, Compliance, Mobility, and more...
- How to calculate damping from a FRF?
- Getting Started with Modal Curvefitting
- Modal Assurance Criterion
- Correlating Simulation and Modal Test Results with Simcenter 3D
- Simcenter Testlab Modal Analysis: Modification Prediction
- Import CAD into Simcenter Testlab
- Animate CAD Geometry
- Alias Table: Mapping Test Data to Geometry
- Geometry in Simcenter Testlab
- Maximum Likelihood estimation of a Modal Model (MLMM)
- Simcenter Testlab: Multi-Run Modal Analysis
- Difference Between Residues and Residuals?
- What is an Operational Deflection Shape (ODS)?
- Making a Video of a Time Animation
- Modal Testing Seminar
- Modal Analysis and FEA-Test Correlation Seminar
- Modal Analysis YouTube Playlist

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