Operational Modal Analysis (OMA)
1. Introduction
Operational Modal Analysis (OMA) is a vibration-based system identification technique used to
extract the modal parameters of a structure—namely natural frequencies, damping ratios, and
mode shapes—using only measured structural responses under operational or ambient loading
conditions. Unlike Experimental Modal Analysis (EMA), OMA does not require measurement of
the input excitation forces, making it particularly suitable for large-scale or in-service structures
such as bridges, buildings, towers, and offshore structures, where artificial excitation is
impractical or impossible.
The fundamental idea behind OMA is that structures are continuously excited by environmental
and operational loads such as wind, traffic, wave action, or microtremors. These ambient
excitations, although unmeasured, contain sufficient broadband energy to activate the dynamic
characteristics of the structure. By analyzing the measured response data, the modal properties
can be identified indirectly.
2. Fundamental Assumptions
The theoretical foundation of OMA relies on several key assumptions:
1. Ambient excitation is stochastic and broadband, often idealized as white noise or
approximately white noise within the frequency range of interest.
2. The structural system is linear and time-invariant, allowing the application of linear
system theory.
3. The excitation is spatially distributed, ensuring sufficient participation of multiple
vibration modes.
4. Measurement noise is uncorrelated with structural response, or its influence is
sufficiently small.
Under these assumptions, the output-only response data contain adequate information to
describe the modal behavior of the structure.
3. Mathematical Formulation
The dynamic behavior of a linear multi-degree-of-freedom (MDOF) system subjected to external
excitation can be expressed as:
𝐌𝐱̈ (𝑡) + 𝐂𝐱̇ (𝑡) + 𝐊𝐱(𝑡) = 𝐟(𝑡)
where M, C, and K are the mass, damping, and stiffness matrices, respectively; x(t) is the
displacement response vector; and f(t) represents the unknown ambient excitation.
In OMA, since the input force f(t) is not measured, the analysis focuses on the statistical
properties of the response signals. In the frequency domain, the output power spectral density
(PSD) matrix can be related to the system’s frequency response function (FRF). Peaks in the PSD
correspond to the natural frequencies of the structure, while damping and mode shapes are
inferred through advanced identification techniques.
4. Modal Identification Techniques
Several methods have been developed to extract modal parameters from output-only data.
Commonly used OMA techniques include:
•
Peak Picking (PP): Identifies natural frequencies directly from peaks in the response
spectrum. This method is simple but limited in accuracy, especially for closely spaced
modes.
•
Frequency Domain Decomposition (FDD): Uses singular value decomposition (SVD) of
the spectral density matrix to separate modal contributions and estimate mode shapes.
•
Enhanced Frequency Domain Decomposition (EFDD): Extends FDD by transforming
selected frequency bands back into the time domain to estimate damping ratios.
•
Stochastic Subspace Identification (SSI): A time-domain method that provides robust
estimates of frequencies, damping ratios, and mode shapes, even in the presence of
noise.
Among these, SSI-based methods are widely regarded as the most reliable for structural health
monitoring applications.
5. Advantages and Limitations
The primary advantage of OMA lies in its non-intrusive nature, as it allows modal testing
without interrupting the normal operation of the structure. This makes OMA ideal for long-term
monitoring and condition assessment of existing infrastructure.
However, OMA also has limitations. The assumption of broadband excitation may not always be
satisfied, especially in cases dominated by narrow-band loads. Additionally, the absence of
measured input forces can complicate the interpretation of results, particularly for estimating
absolute modal scaling.
6. Conclusion
Operational Modal Analysis provides a powerful framework for identifying the dynamic
characteristics of structures using ambient vibration data. By eliminating the need for controlled
excitation, OMA enables efficient and realistic modal testing of large-scale structures under real
operating conditions. As such, it has become a key tool in structural dynamics, system
identification, and structural health monitoring.