Static vs. Dynamic data acquisition

I have been asked many times to define Static and Dynamic data. In short, the Static data is sufficiently represented just by one sample. Dynamic data is more complex, and is represented by a data set. For example, if we have a sensor that measures temperature, we can get a sample at any time and each time we get a value that represents the temperature at that moment. However, if we sample a sound wave at any time, we will get a random value that is not representative of the sound intensity or frequency.

Data acquisition is the process of converting an analog signal to data by sampling the signal at certain time intervals. The signal is usually an output of a sensor and represents a physical parameter being measured by the sensor. Depending on the type of the sensor, the data can be sampled at a faster or slower rate providing more or less detailed information. A signal from a temperature sensor, for example, changes slowly and can be sampled at a relatively slow rate without loss of quality. The temperature signal is called static as it represents its corresponding value at any time.

A signal from an accelerometer represents a movement of the machine housing on which the accelerometer is installed. This signal contains a sum of vibrations at different frequencies that are generated in different parts of the machine. Analyzing magnitudes of these vibrations helps detect changes in the machine due to wear, lack of lubrication, imbalance, misalignment, and other mechanical, electrical, or process abnormalities. Because of its dynamic nature the accelerometer signal can’t be sampled at an arbitrary time to yield a meaningful result. The data has to be acquired many times in a rapid succession to obtain a data set.

To obtain a proper set of data for analysis the vibration signal has to be sampled at a relatively high sampling rate. The sampling rate defines the analysis bandwidth, i.e. the highest frequency component that is available for analysis. The length of the data set defines the frequency resolution, i.e. the lowest difference between two frequencies that can be detected. The data set then represents a function of vibration magnitude over time. Using further data processing the software can present the data in many other forms, including a spectrum (magnitude vs. frequency) and calculate various overall and statistical parameters.

Instrumentation - Dynamic Resoluiton

When sensor signals are being converted to data the capabilities of ADC (analog to digital converter) should be considered. The dynamic resolution of an ADC is related to a number of steps the original signal is approximated with. If the ADC has 10 bit resolution, that means that the full input range will be digitized using 2^10 (two to the power of ten) or 1024 steps. For many applications it is too crude, especially if the signal is not amplified. Typically, for vibration measurements ADCs with 16 or even 24 bits of resolution are used. For industrial vibration monitoring a 16 bit ADC is quite enough. A sensor with the sensitivity of 100 mV/g and the signal range of -10/+10V will have the smallest step of 3mg at 16 bit ADC. Dynamic resolution is sometimes listed in dB in device specifications.

If more dynamic resolution is needed, the signal can be amplified, or an ADC with higher resolution can be used. There are trade-offs with either method. An analog amplifier can introduce noise while a higher resolution ADC results in a more expensive device. There is a signal processing technique that can boost dynamic resolution through oversampling.

Instrumentation: Data Acquisition: Sampling Rate

When a dynamic process such as vibration has to be studied it is important to perform measurements correctly. The data acquisition process converts an analog signal obtained from a sensor into a discrete function. This is done by sampling the signal at equal intervals. The speed at which the sampling takes place is called sampling rate. Why do it? Because the resulting data is very convenient to transmit, process and store.

The faster the sampling rate, the closer the digital function is to the original signal. So, what sampling rate is really needed? It depends on the highest frequency of interest. Technically, the sampling rate has to be at least twice the highest frequency of interest. The ratio used in the industry is 2.56, which is called Nyquist factor. This means that if the highest frequency we would like to study is 1000 Hz, the sampling rate has to be at least 2560 samples per second.

Now, how much data do we have to collect to have enough to calculate a spectrum? This depends on the spectrum resolution we are trying to achieve. At 800 lines per spectrum we will need 800*2.56=2048 samples. Here, again we multiply by the same Nyquist factor. Time needed to collect the samples we need is found by dividing the number of samples by the sampling rate: 2048/2560=0.8 seconds. It is easy to see that at lower frequencies and higher spectrum resolution it might take quite a while to collect the data. That is why it is sometimes takes so long to acquire a data set.