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# Time Series Analysis Application Areas (Advanced Signal Processing Toolkit)

LabVIEW 2013 Advanced Signal Processing Toolkit Help

Edition Date: June 2013

Part Number: 372656B-01

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Time series occur in many fields. This topic discusses time series analysis applications in the industrial and engineering fields using the LabVIEW Time Series Analysis Tools.

## Fault and Failure Diagnosis

Fault diagnostics are important industrial tools to assess the health of industrial equipment and ensure that the equipment is in proper working condition. Failure or damage detection ensures the integrity of machine elements and structures. Using the time series analysis methods such as dynamic modeling, cepstrum analysis, or bispectrum analysis, you can perform fault and failure diagnosis by analyzing the vibration or acoustic signals from the equipment.

The following figure shows an example of performing fault diagnosis by building an autoregressive-moving average (ARMA) model for a vibration time series from a running engine.

Under normal conditions, the vibration signal from the engine is a stationary time series. If you build an ARMA model for this stationary time series, the modeling errors are usually small. However, if the engine is not running properly due to imbalance or cracks, the vibration signal becomes a nonstationary time series. If you build an ARMA model for this nonstationary time series, the modeling errors increase. In the previous figure, the peaks in the Noise Variance graph show the large variances of the modeling errors and indicate that this engine is not running properly.

If you want to detect a structural failure or damage in a mechanical system, you usually compute and examine the power spectral density (PSD) of the time series that the analyzed system generates. However, in some cases, you cannot get a satisfactory result by computing the PSD. The following figure shows the PSD of the vibration time series from a normal concrete beam and a cracked concrete beam. The differences are subtle, and they do not suggest the presence of a defect in the beam.

Using the Time Series Analysis Tools, you can compute the bispectra of the two time series. Bispectrum analysis is related to the third moment (skewness) of a vibration time series and outperforms traditional PSD analysis in detecting the asymmetric nonlinearity due to structural cracks.

The following figure displays the bispectra of the vibration time series from the cracked beam and the normal beam.

The magnitudes of the peaks in the two bispectra are different. In the Bispectrum of a Normal Beam graph, the magnitudes are small. In the Bispectrum of a Cracked Beam graph, the magnitudes are large. A large magnitude indicates large coupling between frequencies in a time series. In the previous figure, you can see that the bispectrum of the cracked beam contains significant coupling between frequencies due to system non-linearities.

Refer to the Beam Crack Detection VI in the labview\examples\Time Series Analysis\TSAApplications directory for an example that demonstrates the application of computing the bispectrum of a signal to detect cracks of a beam.

## Structural Testing

Structural testing extracts key resonance features of a physical system by estimating the modal parameters of a time series that the system generates. Modal parameters include natural frequencies, damping factors, magnitudes, and phases.

Modal parameters contain information that describes the inherent dynamic properties of a structure. Understanding the vibration behavior of a structure is important in creating robust prototypes and validating structural systems such as cars, aircraft, bridges, and buildings. You can obtain the modal parameters of a structure by performing modal analysis using the time series modeling method.

The following figure illustrates a structural testing experiment that obtains the modal parameters of a steel-reinforced concrete beam. A hammer impacts the beam, and seven acceleration sensors located in different positions on the beam acquire the resulting vibration signals.

Using the Time Series Analysis Tools, you can compute the resonance components, or modes, of the steel-reinforced concrete beam. The following table lists the detected natural frequencies f and damping factors a of each mode of the beam.

First Mode Second Mode Third Mode Fourth Mode
f(Hz) 78.2886 249.407 457.382 579.891
α 0.17 0.16 0.17 0.49

Besides the natural frequency and damping factor, a mode also includes the magnitude and phase information. The following figure shows the modal shapes of the beam computed with the estimated magnitudes and phases of each mode.

Refer to the Modal Analysis of a Plate VI in the labview\examples\Time Series Analysis\TSAApplications directory for an example that demonstrates structural testing with the estimated modal parameters of a time series.

## Data Mining

Data mining extracts important features from data and helps you find interesting patterns, rules, or models. Data mining involves a variety of computational methods and techniques. For example, independent component analysis (ICA) is an effective data mining method in the biomedical, mechanical, and seismological fields. You can use ICA to separate informative signals from noise in signals such as electroencephalogram (EEG) signals and magnetoencephalogram (MEG) signals.

MEG signals are the magnetic signals generated from electric dipoles around a human brain. The following figure shows some MEG signals acquired at a human scalp by 148 sensors. These signals indicate brain activities.

All cognitive activities in the human brain generate magnetic signals. Besides those cognitive activities, heartbeats, eye blinking, and breathing also generate magnetic signals. These signals are superimposed on the measured brain signal in the previous figure. To distinguish the brain signal from other signals, you can perform ICA on the MEG signals to remove the unwanted signals not originating in the brain activities. The following figure shows the result of ICA.

You can see that the Independent Components graph contains a red line, which clearly indicates the signal generated from heartbeats. You can remove the heartbeat signal from the MEG signals and perform further analysis on the residual signals.

Refer to the Magneto Encephalogram (MEG) Signal Analysis VI in the labview\examples\Time Series Analysis\TSAApplications directory for an example of ICA in analyzing MEG signals.

## Industrial Measurement

Industrial measurements involve measuring a variety of physical attributes such as position, speed, and force. In general, you can measure the physical attributes directly with appropriate sensors. However, in some special industrial applications where you cannot apply measuring directly, you have to obtain the physical values using some time series analysis methods, such as correlation.

The following figure illustrates a speed measurement system for a steel rolling mill. The reflected light from the surface of the steel belt is focused onto two photoelectric cells by lens. The two photoelectric cells, located at different positions with a separation of d, convert the waveform signals of the reflected light into voltage signals. The voltage values from the photoelectric cells form two time series Xt and Yt. The two series are acquired on the same position track with a separation of d.

To measure the moving speed of the steel belt, you can perform cross-correlation on Xt and Yt and generate the correlogram, as shown in the following figure.

The correlogram of the two time series contains a maximum point at a lag of τd. To compute the speed v of the steel belt, you can use the following equation: v = dd.

## Model Predictive Control

Model predictive control is an important application of time series analysis in engineering. The model predictive control process includes the following steps:

1. Build models of a time series.
2. Use the models to predict the future values of the time series.
3. Make necessary adjustments to the system that generates the time series to make the predicted values align better with target values.

The following section provides an example of controlling shaft axes positions based on predicted results.

First, you acquire the positions of the rotating shaft axes to form a time series. You then make a prediction for the next position of the moving shaft by building models of the time series. Using the predicted position, you can take actions to reduce the future position error. The following figure shows two time series plots of the shaft axes position with prediction control and without prediction control. The Shaft Axes Position with Control graph shows a smaller variance.

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