### 1. Introduction

Modal analysis is the study of the dynamic properties of a structure under vibration excitation. With modal analysis, engineers can extract the modal parameters (dynamic properties) of a structure. The modal parameters, including natural frequency, damping ratio, and mode shape, are the fundamental elements that describe the movement and response of a structure to ambient excitation as well as forced excitation. Knowing these modal parameters helps structural engineers understand a structure’s response to ambient conditions as well as perform design validation.

#### Industry Trends

Two types of modal analysis are performed in industry today: experimental modal analysis and operational modal analysis. Experimental modal analysis, the most commonly used form of modal analysis today, is the traditional method in which engineers use a device, such as a hammer, to excite a structure and then measure the response. Then the engineers calculate the transfer function and use certain modal parameter extraction algorithms to extract the dynamic properties of the structure.

Experimental modal analysis has been effective in design validation and finite element analysis (FEA) verification, but it has not proved useful in monitoring the long-term health of a large structure such as a bridge. For this reason, operational modal analysis has become the focus of innovation. Strictly concerned with the operation of a structure, this type of analysis focuses on monitoring the modal parameters of a structure and looking for trends in the data that may signal warnings for failure. Using operational modal analysis, structural engineers can proactively monitor the health of a bridge to avoid catastrophic failures.

### 2. Experimental Modal Analysis

Experimental modal analysis is the field of measuring and analyzing the dynamic response of a structure when excited by a stimulus. It is useful in verifying FEA results as well as determining the modal parameters of a structure.

Experimental modal analysis is a four-step process to extract the modal parameters:

**Figure 1.** *Experimental Modal Analysis Process*

#### Vibration Sensors (Accelerometers)

Engineers must properly place vibration sensors, known as accelerometers, on a structure to record the vibration response of a structure due to a known excitation by either a shaker system or an impulse hammer. These excitation systems are necessary to properly excite the modes of the system that reveal the modes of the structure. The accelerometers must have the frequency range, dynamic range, signal-to-noise ratio, and sensitivity needed for the specific test scenario. Vendors such as PCB Piezotronics work to help engineers select the proper sensor for the application.

**Figure 2.*** PCB Accelerometer and Impact Hammer for Measuring Vibration*

#### Data Acquisition

Specialized data acquisition hardware is needed to properly acquire these vibration signals. NI offers dynamic signal analyzers (DSAs) that can simultaneously acquire each channel with 24-bit high-resolution delta-sigma analog-to-digital converters (ADCs). These DSA products have antialiasing filters to prevent aliasing and noise from affecting the measurement quality. Finally, they have the proper signal conditioning to power piezoelectric (ICP or IEPE) accelerometers. National Instruments offers a variety of platforms including USB, wireless 802.11g, PXI, and real-time embedded targets.

**Figure 3.** *National Instruments Data Acquisition Hardware*

#### FRF Analysis

The frequency response function (FRF) compares the stimulus and response to calculate the transfer function of the structure. The result of the FRF is the structure’s magnitude and phase response over a defined frequency range. It shows critical frequencies of the structure that are more sensitive to excitation. Those critical frequencies are the modes of the structure under test. An example of the magnitude result from an FRF is shown in Figure 4.

**Figure 4.** *FRF Results for a Test Scenario*

#### Modal Parameter Extraction

Modal parameter extraction algorithms are used to identify the modal parameters from the FRF data. These algorithms include peak picking, least square complex exponential fit, frequency domain polynomial fit, and FRF synthesis. Each of these algorithms performs the same function of identifying the modal parameters; however, each is optimized for a specific test scenario.

**1. Peak picking** is used to extract a mode from a precomputed signal’s FRF. It is a frequency domain single-degree-of-freedom (SDOF) modal analysis method suitable to estimate uncoupled and lightly damped modes. The computation is fast but the result is sensitive to the frequency shift.

**2. Least square complex exponential fit** **(LSCE)** is used to simultaneously extract multiple modes from a precomputed signal’s FRF. It is a time domain multiple-degree-of-freedom (MDOF) modal analysis method suitable for estimating modes in a wide frequency band. It is ideal for lightly damped modes.

**3. Frequency domain polynomial fit (FDPI)** is used to simultaneously extract multiple modes from a precomputed signal’s FRF. It is a frequency domain MDOF modal analysis method suitable to estimate heavily damped modes, particularly for heavily damped modes in a narrow frequency band.

**4. FRF synthesis** is used to create synthetic FRF for testing and evaluation. With computed modal parameters, engineers can compare synthesized FRF and original FRF to verify the resulting estimation.

The end result of each algorithm is the identified mode(s). As explained above, each algorithm is used in a certain scenario. For example, Figure 4 shows a peak around 280 Hz. If a user is interested in identifying that mode, frequency domain polynomial fit is the correct choice because it is a narrow frequency band. The result of the FDPI algorithm is shown in Figure 5.

**Figure 5.** *Frequency Domain Polynomial Fit Test Results*

### 3. Operational Modal Analysis

With more focus on increasing safety, real-time structural monitoring systems have become a necessity to monitor the integrity of bridges and other structures. Operational modal analysis is a specific type of modal analysis primarily used in real-time structural monitoring systems. Just as the name implies, this type of analysis consists of specific algorithms to extract modal parameters from a structure in operation. The stimulus in operation is ambient conditions such as cars, wind, and seismic activity. Because the stimulus is an unknown signal, specialized algorithms such as stochastic subspace identification (SSI) have been developed that do not require knowledge of the stimulus – only the response.

Operational modal analysis requires three steps to extract the modal parameters:

**Figure 6.** *Operational Modal Analysis Process*

#### Vibration Sensors (Accelerometers)

Accelerometers are used as discussed above in the Experimental Modal Analysis section. Most of the requirements are the same including sensitivity, dynamic range, and frequency range. However, there are a few more requirements including corrosion resistance, temperature change sensitivity, and cable length. Each of these requirements is specified by the sensor vendor. Vendors such as PCB Piezotronics work to ensure that engineers choose the proper sensors for their applications.

#### Data Acquisition

Operational modal analysis requires the use of DSA hardware to achieve simultaneous 24-bit resolution acquisition and high dynamic range. The main differences are in the platform requirements:

1. **A real-time operating system** is necessary for developing a deployed system to run embedded locally at the structure. National Instruments has two platforms, CompactRIO and PXI, that take advantage of real-time embedded technology. These systems are capable of acquiring and analyzing the waveform vibration data locally and/or streaming the waveform to a remote PC. That means these systems can either analyze the data locally and transmit only alarming conditions to an operator or stream the vibration data from the structure to a remote operator for in-depth trending analysis.

2. **Distributed synchronization** is necessary to achieve minimal phase mismatch per vibration channel. National Instruments continues to be a pioneer in the use of cabled and/or GPS technology for high-channel synchronization. NI hardware is specified to within 0.1 degree phase mismatch at 1 kHz within a single PXI chassis of up to 272 channels. With GPS technology, National Instruments has benchmarked the same 0.1 degree phase mismatch on multiple chassis at 1 kHz.

An example application of a large, real-time, synchronized structural monitoring system is the Donghai Bridge, the world’s largest bridge. Located in the East China Sea, the Donghai Bridge is monitored 24/7 with NI hardware consisting of 14 PXI systems running real-time operating systems and synchronized through GPS technology (see Figure 7).

**Figure 7.** *Donghai Bridge Monitored by National Instruments Hardware*

#### Modal Parameter Extraction

Modal parameter extraction is a bit more difficult in operational modal analysis because the stimulus is unknown. For that reason, the algorithms listed above (LSCE, FDPI, peak picking) are not applicable. Instead, SSI is used because it is capable of extracting the modal parameters from the time domain data with no knowledge of the stimulus.

View an in-depth explanation of SSI.

### 4. Conclusion

National Instruments offers hardware and software for performing both experimental and operational modal analysis. NI provides high-performance acquisition on platforms from USB and Wi-Fi 802.11g to embedded real-time targets. NI products are capable of simple, portable USB test acquisitions as well as high-channel GPS synchronized online monitoring systems.

Download the Modal Parameter Extraction LabVIEW VIs.

Note: To apply these functions, you need to install LabVIEW 8.6 or later with the LabVIEW Advanced Signal Processing Toolkit and LabVIEW System Identification Toolkit.