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Noise

Filtering topics:

Filtering that is part of
A Guide to Fault Detection and Diagnosis..

Noise is a general term for errors or non-useful variations modifying the “true” values in a stream of data. The purpose of filtering is to reduce the effects of noise. But what is noise, and where does it come from?

Characterization of noise

Noise is often characterized in terms of frequencies. Typical, normal noise is often at high frequencies, higher than the natural frequencies observed in the processes of interest. Low pass filters reduce this noise, allowing mainly low frequency signals to pass through. Low frequency errors occur more slowly than the natural frequencies of the process, for instance, a slow drift in the bias of a sensor. High pass filters can eliminate this noise.  Noise at frequencies that are similar to frequencies of interest in the process are the toughest to eliminate. These arise, for instance, due to a cycling controller. That is true process behavior, but irrelevant for many applications above process control such as plant optimization, because the longer-term average value is correct for the slower time scale of that application.

For convenience in analysis, noise is often modeled as Gaussian (drawn for a random normal distribution). There are multiple reasons why it is popular for analysis: (1) It is reasonable in many cases, because noise may arise as a combination of signals from many sources, and for most kinds of noises, the central limit theorem applies, in that combinations of random variables tend towards a normal distribution. (2) Gaussian noise can be characterized by just two parameters: a mean and a variance (or its square root, the standard deviation). (3), Gaussian noise has the property that linear combinations of Gaussian variables are also Gaussian. This simplifies analysis such as propagating the mean and variance through linearized system models.

The noise introduced by one sensor is usually treated as independent of the noise from any other sensor. Noise is usually treated as independent from one time step to another, and with a mean value of 0. However, when the original noise source passes through some process, that process often introduces autocorrelation, meaning that there is correlation from one time step to the next.

Spikes are sudden large changes in value that only last for a very short time. These are common, yet outside of normal models for noise. The goal is usually to eliminate their effects, usually with specialized logic outside of normal high or low pass filters. The exception would be in fault diagnosis cases where the spike is a typical symptom of a particular fault.

Sources of noise

Two major categories of noise sources are sensor noise and process noise.

Sensor noise is caused by errors in the sensors and the transmission of the signals. Sensor noise includes “spikes” as well as high frequency variations. High frequency variations include “hum” at frequencies that are a multiple of the power supply frequency. Spikes in signals occur from many sources and are picked up by the instrumentation and its wiring. Sudden changes in electrical load caused by events such as motor starts and stops will pass spikes through wiring, and may also generate enough electromagnetic energy that nearby sensors and their wiring may pick it up. Arcs in electric motors, or caused by arc welding can similarly generate spikes. Inadequately shielded sensors or their transmission lines, and variables transmitted through wireless links are vulnerable to radio frequency interference, leading to spikes, and pickup of other noise such as electrical hum. Noise can also be introduced through ground loops.

Process noise is rapid variation that originates in the monitored process itself. This might be true variation in variable values, but might be of such a high frequency that it is of no interest for a particular analysis. In the process industries, examples include noise introduced by turbulence, boiling, or even cyclic variations introduced by badly tuned controllers. In applications such as wind farms or airplanes, wind gusts might be considered process noise. In building management, the brief passing of a cloud that reduces solar energy input might be considered process noise.  In the case of badly tuned controllers, these variations are not at all random. But, relatively high-frequency flow controller cycling might be of little interest when analyzing the behavior of large equipment. A time-averaged value is of more interest when considering steady state models for diagnosis, or even dynamic models when only modeling large equipment.

In monitoring computer system or network behavior, some variables such as CPU utilization or network utilization can vary extremely rapidly.

Diagnostic systems looking at any of these kinds of variables need to use filtering to reduce the effects of high frequency noise and spikes.

Copyright 2010 - 2017, Greg Stanley