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.
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
Index: 1. Overview of Operational Modal Analysis
1.1 What is OMA? 1.2 Why OMA? 1.3 OMA vs EMA vs ODS
2. OMA vs EMA
2.1 Overview 2.2 EMA Approach 2.3 OMA Approach 3. OMA vs ODS
3.1 Overview 3.2 ODS Approach
1. Overview of Operational Modal Analysis (OMA) 1.1 What is OMA? 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)
Ground vibration testing (GVT)
Vibration control testing
As the name suggests, OMA focuses on investigating the structural dynamics of a system while it is inoperation. While other techniques are typically performed in a laboratory, on a shaker table, or with highly controlled boundary conditions, OMA is performed in-situ under real-world load conditions (Figure 1). This ensures that the forces acting upon the structure are realistic with respect to level, location/direction of application, as well as frequency/order content.
Figure 1: Structural testing of an aircraft under two boundary conditions. Left: Experimental modal analysis in a laboratory using pneumatic suspension. Right: Operational modal analysis performed in flight.
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 response-only technique, meaning no input forces are measured during the test. This presents some important challenges to consider when acquiring data to be used in an operational modal analysis but makes OMA uniquely powerful when compared to some of the other popular techniques.
1.2 Why use OMA? 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
Real world conditions: Some structures exhibit a high degree of non-linearity when they are tested in a laboratory environment compared to their real-world usage. An example of this phenomena is an automotive suspension. The shock absorbers in the suspension have a high level of static friction when the vehicle is at rest that isn’t present when the vehicle is in motion on the road. This friction not only artificially raises the stiffness of the local structure but can also exhibit non-linear behavior when the friction is overcome, and the suspension begins to articulate. Non-linear behavior can wreak havoc when attempting to accurately measure and analyze structural dynamics data on vehicles in the lab.
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.
Figure 2: A scale model of an aircraft exhibiting flutter in a wind tunnel.
Practical/Size limitations: Some large structures simply cannot be tested in a laboratory environment. Structures like bridges, buildings, wind turbines, etc. are too large to be tested in a lab, and often it is impossible to properly excite the structures using traditional input methods. In these cases, the natural loads found in-situ (traffic loading, natural/wind excitation, pedestrian traffic, etc.) are more realistic and better suited to properly excite the structure. OMA is often the only option for these structures. See Figure 3.
Figure 3: The Millennium Bridge in London experienced vibration from pedestrian traffic when if first opened in June 2000.
Health monitoring & damage detection: Changing modal parameters (such as natural frequency) can be an early sign of increased wear or impending failure of a machine or structure. By monitoring a structure using OMA engineers can assess the health of the structure without removing it from service or interrupting operations. This is especially useful for very large civil structures such as bridges and buildings, particularly after exposure to potentially damaging events like earthquakes.
1.3 EMA vs. OMA vs. ODS The table below (Figure 4) summarizes some of the critical differences between EMA, OMA and ODS for structural analysis.
Figure 4: Comparison summary of EMA vs. OMA vs. ODS
These differences are discussed in detail in the following sections.
2. OMA vs. EMA (Experimental Modal Analysis) 2.1 Overview 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).
Figure 5: Block diagram representing a dynamic system. H is the system matrix, relating outputs (Y) to inputs (X)
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.
Figure 6: Summary of EMA vs. OMA processes
2.2 EMA Approach
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.
2.3 OMA Approach
In OMA, the input forces ([X] in Figure 5) are unknown and not capable of being measured; the only information available is the system’s response [Y]. However, if the input forces are assumed to be of the form of white noise (equal magnitude across the frequency range of interest), and spatially randomly distributed around the structure, then the responses of the structure would contain all the necessary information needed to characterize the system (see Figure 7).
Figure 7: For white noise input, output matrix [Y] is equal to system matrix [H].
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).
Figure 8: Upper: A series of 100 random numbers concealing a sine function. Below: A plot of the autocorrelation function of the random series, showing the hidden sine function. (Credit: Wikipedia)
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.
3. OMA vs. ODS (Operational Deflection Shapes)
3.1 Overview 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.
Figure 9. Summary of OMA vs. ODS processes
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.
Figure 10. Modal super position effect: when structure is excited at the 2nd natural frequency (f2), the deformation shape will be a superposition of contributions from multiple modes: mode 1 (Point B), mode 2 (Point A), and mode 3 (Point C). When the modes are far apart (left) these effects can be small, and mimic an EMA result. When modal density is high (right) the effects of nearby modes will be significant and make an ODS result less helpful.
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.
3.2 ODS Approach 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.
Figure 11. Operating deflection shapes for a simple plate at several frequencies.
4. Summary 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.