15A.8 Transient Analysis

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This Appendix discusses performing transient analysis with the Transient Analysis VIs located on the

Transient Analysis palette.

15A.8.1 Transient Analysis with the Sound and Vibration Toolkit

Transient analysis is the analysis of nonstationary signals. The Transient Analysis VIs offer two different

techniques for extracting information about transient signals. Use the short-time Fourier transform

(STFT) for signals in which the frequency content changes relatively slowly with time. Use the shockresponse

spectrum (SRS) for shock signals.

You can use the STFT VIs to extract frequency information as a function of time directly from the

signal of interest. Additionally, in the case of a rotating machine where a tachometer signal is

simultaneously acquired with the signal of interest, the STFT VIs can extract frequency information as

a function of the rotational speed.

The results generated by the STFT are typically displayed on a waterfall display or on a colormap. The

STFT VIs return the information needed to properly scale the axes of the displays. You can pass the

information directly to a Waterfall Display VI. Use property nodes for the colormap display.

You can use the SVT SRS VI to evaluate the severity of a shock signal. The results generated by the SRS

are typically displayed on an X – Y graph.

Note: Other LabVIEW toolkits are available that provide additional transient analysis capabilities. The

Order Analysis Toolkit is designed for rotating machinery analysis and monitoring. The Signal Processing

Toolkit has tools, such as wavelets and joint timefrequency

analysis (JTFA), for the analysis of fast

transients.

15A.8.2 Performing an STFT vs.

Time

The STFT available in the Sound and Vibration

Toolkit can compute multiple Fourier transforms

on the time-domain signal with or without

overlapping.

For example, analyze a waveform containing

10 sec of data acquired at 51.2 kS/sec. The signal is

a chirp signal with the following attributes:

* Start frequency ¼ 10 Hz

* End frequency ¼ 10,000 Hz

Figure 15A.33 shows the signal corresponding to

the first 200 msec of the waveform.

Figure 15A.34 shows the result of applying a

baseband FFT on the entire waveform.

Note: No window is applied on the signal.

FIGURE 15A.33 Chirp signal.

FIGURE 15A.34 Baseband FFT on a chirp signal.

Virtual Instrumentation for Data Acquisition, Analysis, and Presentation 15-97

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The spectrum is flat from 10 Hz to 10 kHz. Only

noise is measured at frequencies above 10 kHz.

Unfortunately, this measurement does not provide

any information about how the frequency content

of the signal changes with time. However, the

STFT can reveal useful information about the time

dependence of the frequency content.

Instead of computing a single FFT on the whole

data set, you can divide the data set into smaller

blocks and compute FFTs on these smaller data

blocks. For example, divide the signal into

100 msec blocks and perform an FFT on each of the blocks with the SVT STFT vs. Time VI.

Subdivide the time-domain signal by configuring the time segment control displayed in Figure 15A.35.

Leave from [s] and to [s] each equal to 2 1.00 to ensure that the entire signal is used in the STFT

computation. In this particular example, the 2 1.00 setting in both from [s] and to [s] is equivalent to

setting from [s] to 0 and to [s] to 10.

Create a 100 msec time increment by setting time increment to 100.00 and time increment units (%) to

msec. The 100 msec time increment causes the SVT STFT vs. Time VI to compute one FFT every

100 msec. Setting time increment is independent from selecting the FFT block size.

15A.8.2.1 Selecting the FFT Block Size

In addition to the time segment, one can adjust the FFT block size. For example, analyze a chirp signal

having the following attributes:

* Start frequency ¼ 10 Hz

* End frequency ¼ 10,000 Hz

The measurement is performed using the following settings:

* Acquisition time ¼ 10 sec

* Sampling frequency ¼ 51.2 kS/sec

* FFT block size ¼ 1024 samples or 512 lines (400 alias-free lines)

* Time increment ¼ 100 msec.

Based on the sampling frequency of 51,200 Hz, a 1024 sample FFT requires a 20 msec block of data,

leading to a frequency resolution of 50 Hz.

Because the time increment is 100 msec and a 1024 sample FFT only requires a 20 msec block, only

one block out of five is used for computation. Figure 15A.36 shows the result obtained with a 1024

sample FFT.

FIGURE 15A.35 Time segment control.

FIGURE 15A.36 STFT using a 1024 sample block size.

15-98 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

If you select an FFT Block size of 4096 samples, or 1600 alias-free lines, the resolution improves, as

illustrated in Figure 15A.37. However, the increased resolution comes with the expense of extra processing.

15A.8.2.2 Overlapping

Overlapping is a method that uses a percentage of

the previous data block to compute the FFT of the

current data block. When combined with windowing,

overlapping maximizes the use of the entire

data set. If no overlapping is used, the part of the

signal close to the window edges becomes greatly

attenuated. The attenuation of the signal near the

window edges could result in the loss of information

in the region near the window edges.

Note: Set the desired overlapping rate by

specifying % in the time increment units (%) in

the time increment control. Refer to Figure 15A.35

for the location of this control. No overlapping, or 0%, corresponds to a time increment of 100%. An

overlapping of 75% corresponds to a time increment of 25%. An overlapping of 50% corresponds to a

time increment of 50%, and so forth. The advantage of using the time increment control is that one can

specify values greater than 100%. For example, a time increment of 200% corresponds to computing an

FFT on every other block of data.

Figure 15A.38 and Figure 15A.39 illustrate the overlapping process. Figure 15A.38 shows a 50%

overlap.

Figure 15A.39 shows the resulting subdivisions when one uses a 50% overlap and a Hamming

window.

15A.8.2.3 Using the SVT STFT vs. Time VI

The following example illustrates how to use the SVT STFT vs. Time VI. Figure 15A.40 shows the block

diagram.

The example in Figure 15A.40 acquires 10 sec of data at a sample rate of 51.2 kHz. After scaling, the

signal is sent to the SVT STFT vs. Time VI. The result is displayed on the intensity graph in Figure 15A.41.

Note: Use the X scale and Y scale offset and multiplier properties to properly scale the axes of the

intensity graph. In this example, the X scale range is 0 to 10 sec. The Y scale range is 0 to 25,600 Hz. The

Nyquist frequency is 25,600 Hz. You can adjust the Z scale so that only the relevant part of the signal is

displayed. In other words, you can hide noise in the displayed signal by increasing the minimum limit of

the Z-axis. Refer to the LabVIEW Help for information about the offset and multiplier properties for

graph controls.

FIGURE 15A.37 STFT using a 4096 sample block size.

FIGURE 15A.38 50% overlap.

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15A.8.3 Performing an STFT vs. Rotational Speed

Analyzing the frequency content as a function of the rotational speed is helpful when dealing with

measurements on rotating machinery. Use the SVT STFT vs. RPM (analog) VI to analyze the frequency

content as a function of the rotational speed.

FIGURE 15A.39 Subdivisions of the time-domain waveform.

FIGURE 15A.40 Use of the SVT STFT vs. Time VI.

FIGURE 15A.41 STFT vs. time graph.

15-100 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

15A.8.3.1 Converting the Pulse Train to Rotational Speed

Use the SVT Convert to RPM (analog) VI to

convert a pulse train acquired by a tachometer or

encoder to the rotational speed expressed in

rotations per minute (RPM).

Note: For simplicity, the remainder of this

Appendix uses the term tachometer to denote

both a tachometer and an encoder.

In this example, an accelerometer is mounted at

the test location for an engine run-up. A

tachometer is used to measure the speed of the

shaft and returns one pulse per revolution as a

transistor – transistor logic (TTL) signal. Use the

tach info control to specify the characteristics

of the pulses generated by the tachometer.

Figure 15A.42 shows the settings for the tachometer

info control.

Figure 15A.43 shows a simulated tachometer

signal.

You can use the SVT Convert to RPM

(analog) VI to measure the rotational speed in

RPM as a function of time. Figure 15A.44

shows the result obtained with the SVT Convert

to RPM (analog) VI and a simulated tachometer

signal.

15A.8.3.2 STFT vs. RPM

You also can display the STFT of an input signal as

a function of the rotational speed based on the

tachometer signal. Two input signals are needed,

the signal of interest and the signal from the

tachometer. Again, an engine run-up serves as a

good example of computing an STFT as a function

of the rotational speed.

During an engine run-up, the sound pressure

close to the engine is measured with a microphone.

Figure 15A.45 shows the signal acquired by the

microphone.

The signal from the tachometer is also acquired.

The measured tachometer signal is converted to

RPM with the SVT Convert to RPM (analog) VI.

Figure 15A.46 shows the rotational speed as a

function of time, as computed by the SVT Convert

to RPM (analog) VI.

Using the SVT STFT vs. RPM (analog) VI allows

you to measure the frequency content of the signal

as a function of the rotational speed of the engine.

Figure 15A.47 displays the results obtained with

the SVT STFT vs. RPM (analog) VI on an intensity

graph.

FIGURE 15A.42 Tachometer info control.

FIGURE 15A.43 Tachometer signal.

FIGURE 15A.44 Result from SVT convert to RPM

(analog) VI.

FIGURE 15A.45 Microphone signal obtained during

engine run-up.

Virtual Instrumentation for Data Acquisition, Analysis, and Presentation 15-101

© 2005 by Taylor & Francis Group, LLC

15A.8.4 Measuring a Shock Response Spectrum

Obtain the SRS by applying the acquired shock

pulse to a series of single degree of freedom

(SDOF) systems. Plot the system maximum

response as resonance frequency of the system.

An SDOF mechanical system consists of the

following components:

* Mass, whose value is represented with the

variable m

* Spring, whose stiffness is represented with

the variable k

* Damper, whose damping coefficient is

represented with the variable c

The resonance frequency fN, and the critical

damping factor, z; characterize an SDOF system,

where

fN ¼

1

2p

ffiffiffiffi

k

m

s

z ¼

c

2

ffiffiffiffi

km p

For light damping, where z is less than or equal to

0.05, the peak value of the frequency response

occurs in the immediate vicinity of fN and is given

by the following equation, where Q is the resonant

gain:

Q ¼

1

2z

Figure 15A.48 illustrates the response of an

single-DoF system to a half-sine pulse with a 10g

acceleration amplitude and 10 msec duration. The

top graph shows the time-domain acceleration.

The middle graph is the single-DoF system

response with a 50 Hz resonance frequency. The

bottom graph is the single-DoF system response

with a 150 Hz resonance frequency. In both cases, z

is 0.05.

Use the signals shown in Figure 15A.48 to

construct the SRS. For example, the maximax, the

absolute maximum response of the calculated

shock response signal over the entire signal

duration, uses the absolute maximum system

response as a function of the system natural

frequency. Figure 15A.49 illustrates the maximax

SRS for the same half-sine pulse.

Note: Each computed SRS is specific to the pulse used to perform the measurement.

You can use other types of shock spectra depending on the application. These spectra include the

initial shock response from the system response over the pulse duration or from the residual shock

FIGURE 15A.46 Rotational speed as a function of time

during engine run-up.

FIGURE 15A.47 Intensity graph of sound pressure

level for an engine run-up.

FIGURE 15A.48 Single-DoF system response to a halfsine

shock.

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© 2005 by Taylor & Francis Group, LLC

spectrum from the system response after the pulse.

You can use the positive maximum, the negative

maximum, or the absolute maximum response

signal value.

The Sound and Vibration Toolkit uses

the Smallwood algorithm to compute the

SRS. The SVT Shock Response Spectrum

VI also offers the ability to preprocess the

time-domain signal to improve SRS results.

You can remove any DC component or apply

a low-pass filter with a selectable cut-off frequency.

The SVT Shock Response Spectrum VI can

compute the SRS from the absolute acceleration

response or from the relative displacement

response. Use the model control on the SVT

Shock Response Spectrum VI to select the appropriate

response.

Figure 15A.50 shows how to use the SVT Shock

Response Spectrum VI. The example in Figure

15A.50 acquires 1000 samples of data from an

accelerometer during a shock. The shock signal triggers the acquisition. The program stores 100 samples

before the trigger to properly capture the entire shock signal.

Figure 15A.51 displays the acquired time-domain signal and the computed SRS.

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