**Random Vibration Testing**

In a random vibration test, the shaker is driven by a wide band random signal. Feedback control adjusts this drive signal to generate a response that conforms to a specified test profile. The control algorithm calculates the inverse transfer function between the output drive and the input control channels, which is the composite of the amplifier, shaker, and UUT response. The product of the inverse transfer function and the response profile then gives the output drive spectrum. A phase randomizer and inverse FFT then generate the random drive output time stream.

The test profile is set under the Broadband Profile and Line Limits section of the Test Configuration window. The input channels used for control are selected in the Input Channels settings, and the other channels may be used to monitor responses of other parts of the test unit. If more than one channel is selected as a control channel, the channels will be combined, in an average, maximum, or minimum strategy, to form a composite control signal. The FFT of this signal is the control(f) signal. The controller monitors the deviation of control(f) from the target profile and updates the output drive signal in real-time.

**The Random Control Process**

Random excitation is often used to simulate real world vibration. The purpose of the random vibration control system is to generate a true random drive signal such that, when the signal is applied via an amplifier/shaker to the device under test, the resulting shaker output spectrum will match the user-specified test profile. This reference profile is defined in the frequency domain in units of *(Acceleration)2/Hz*. This signal is to be applied to the UUT for a specified amount of time to verify the device's ability to function in its service environment.

If the series of components being controlled (i.e., the amplifier, shaker, and testing structure) is assumed to be an integrated linear system, then it can be described by a system transfer function H(f) in frequency domain. The frequency spectra of the control and drive signals, Y(f) and X(f), can be linked together by H(f) as:

Y(f) = H(f) X(f)

Or

X(f) = H(f) -1 Y(f)

where H(f)-1 is called the *inverse transfer function*.

If a flat spectrum drive signal excites a shaker/test-article system, the resulting acceleration response spectrum will not be flat. The armature resonances and the dynamics of the test-article react on the system to produce peaks (resonances) and valleys (anti-resonances) in the resultant spectrum.

To apply a specified spectrum to the test article, the drive spectrum must be altered to correct for the dynamics of the shaker/load combination. This process is generally referred to as “Equalization”. The inverse transfer function is calculated continuously while the test is running to monitor any change in the system characteristics. Corrections are applied in real-time.

Given a desired spectrum R(f) (reference spectrum, or profile), the required value for the drive can be calculated as:

X(f) = H(f) -1 R(f)

where X(f) is the spectrum of the required drive signal.

Once the drive spectrum X(f) is known, there are several ways to generate a random output signal in the time domain. This signal must have the following properties:

A spectral shape defined by

*X(f).*Free of discontinuities

A Gaussian amplitude distribution

The algorithm involves these steps:

Digitize the input signals and transform them into frequency domain using the FFT process.

Estimate the inverse system transfer function between the averaged input and output via cross-spectral method.

Generate a reference spectrum with random phase.

Multiply the reference spectrum by the inverse transfer function, and apply an Inverse FFT to the result to generate the output-time waveform.

Output the time waveform through a D/A converter.

All these calculations are completed within the period of one time frame to ensure a very fast control loop time.

**Control Dynamic Range in Random**

One of the key requirements for a random controller is to achieve high control dynamic range. Control dynamic range is a measure to compare the highest and lowest spectrum amplitude in the control signal. Spiders can achieve at least 90dB control dynamic range. This can be measured by a modified Chinese testing standard, JJG-948. The JJG-948 only requires a control dynamic range up to 60dB. By modifying the noise floor to lower quantity we can show much higher control dynamic range.