# New software supports vibration tests with non-Gaussian distribution

**03.08.16**

**IMV provides training in the new test method**

Body, chassis and the interior of vehicles are constantly exposed to dynamic stress. The performance and stiffness of the components are tested in product tests and simulated transport situations under real-life conditions. So far, the tests frequently were performed with noise excitation for which the normal Gaussian distribution was applied for the amplitude frequency. Now IMV vibration exciters can also be used for non-Gaussian vibration tests. This is made possible by new software which in addition to the conventional features for the traditional noise excitation includes two new parameters: kurtosis (“peakedness“) and skewness.

**Real peaks are often higher**

“The purpose of the non-Gaussian method is to adapt the signals used for excitation in the lab to real-life conditions as much as possible in order to obtain identical stress”, Dipl.-Ing. (FH) Martin Engelke, Marketing and Sales Manager IMV, says. It goes without saying that the test results depend strongly on the type and method of the mechanical stress produced in the lab environment. “Measurements during vehicle tests have shown that, in practice, peak vibrations are often higher and the frequency of the amplitudes follows a different distribution“, Engelke adds.

**Non-Gaussian distribution supplies more realistic picture**

Formerly, sine signals were often used. In the last few years, noise excitation has made ever deeper inroads in the realm of vibration testing because it provides a truer picture of the real stress. The noise excitation is based on normal distribution. For some time now, the non-Gaussian distribution has been preferred. It is important that the test engineer has a good understanding of the nature of the signals. He must take the protection of the test specimen from extreme peaks and the protection of the vibration testing system into account as much as the properties of the non-Gaussian amplitude distribution. In contrast with the uniquely described noise excitation with normal distribution (se, e.g., DIN EN 60068-2-64), these properties are more varied.

Two indices define the properties of tests with traditional noise excitation:

• The power spectral density (PSD) in (m/s²)²/Hz or g²/Hz, and

• The root mean square

Tests with non-Gaussian distribution require two additional parameters:

• Kurtosis (“peakedness“), and

• Skewness.

Both values are specified as integers.

**Probability density function**

The amplitude probability density function shows the distribution of the noise (or “accidental“) vibrations by which the properties of the signal can be evaluated. The diagram below shows the waveform across time rotated by 90 degrees and the amplitude values on the horizontal axis. Then the horizontal axis is divided in fixed intervals (bins). The histogram shows the number of points for each interval.

The histograms cannot be compared with each other because the number of points depends on the length of the time signal, i.e., the number of values becomes larger with longer time signals. For the amplitude probability density function, the histogram is normalised according to the total number of points. In this way, the amplitude probability density facilitates the comparison of different histograms.

**Kurtosis, measure of the amplitude probability density**

The kurtosis (“peakedness“) parameter is a measure of the amplitude probability density in the range of zero (i.e., the mean, in this case). Kurtosis of the Gaussian distribution is “3“. For higher values of kurtosis the probability density in the range of zero and also along the margins is becoming larger. Given below is an example of the amplitude probability density for different values of kurtosis.

Examples of the time response of the signals with Gaussian distribution and kurtosis = 6 and = 10 are shown in the following graph. The higher the kurtosis, the higher the signal peak.

**Skewness, a measure of symmetry**

Skewness is a measure for the symmetry of the amplitude probability density. At skewness “0“, the distribution is symmetrical relative to the mean. At values other than zero, the amplitude probability density is skewed.

Examples of the time response of the signals with different skewness are shown in the following graph.

**Control**

Like with traditional noise, as far as the control of non-Gaussian signals is concerned, the power spectral density (PSD) and the root mean square are controlled so that these values of the control channel agree with the reference values. The values of kurtosis and skewness are controlled, in addition. Therefore, in a noise test with non-Gaussian excitation, the root man square and the power spectral density are the same as the values for tests with Gaussian distribution, the peaks in the time response of the signal are higher, however.

For the exact mapping of the non-Gaussian signals, the control of the time response of the signal was introduced. Before the test starts, the transfer function of the system must be determined:

1. Measurement of the transfer function

2. Adjustment

During the first adjustment, the power spectral density and the root mean square are matched with the set points.

3. Adjustment for non-Gaussian distribution

Now the values for “kurtosis“ and “skewness“ are matched with the set points.

4. Test starts

**Sporadic and stationary peaks**

Even when kurtosis and skewness are specified, the time response of the noise signal is not defined sufficiently. Another differentiation is possible.

• Sporadic peak type

In this case, peaks occur sporadically; only a value for kurtosis can be specified for this type of excitation.

• Stationary peak type

In this case, peaks occur constantly; values for kurtosis and skewness can be specified for this type of excitation.

Examples of the time response of the signals for different characteristics are shown below.

**Vibration testing systems from IMV**

The IMV vibration controller type K2 and the IMV vibration testing systems support tests with non-Gaussian normal distribution. This new method provides an even better representation of real-life situations and the test results are more accurate. The values and characteristics described above can be used for these tests.

(02.08.2016)