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A Guide to Filtering of Single Variables

Diagnosis topics:


Filtering subtopics:


This section describes filtering of noise for individual variables, mainly using digital filters. It is part of
A Guide to Fault Detection and Diagnosis. This page provides a top-level overview of filtering. The complete section can be read as a sequence of pages by clicking on the “next” links at the bottom of each page, starting with the page on Noise.


The purpose of filtering is to reduce noise. But what is noise, and where does it come from? Two major categories of noise are sensor noise and process noise. Please go to the page on Noise.

The purpose and effects of filtering and smoothing

Both filtering and smoothing reduce the effects of noise, improving estimates of the values of variables. Filtering produces an estimate of the current value, while smoothing produces an estimate at a past time. For this discussion, we are mainly concerned with reducing higher frequency noise. There are tradeoffs in selecting filter parameters, because increasing noise rejection also increases the time it takes to diagnose a fault. Please go to the page The purpose and effects of filtering and smoothing.

When to avoid filtering

Some failure modes must be detected with unfiltered variables. While filtering is usually desirable to reduce the effects of noise, it is important to realize that some diagnosis depends on time series analysis, on recognizing the presence or absence of noise, or unusual dynamic behavior, as a symptom of a fault. In many of these cases, the unfiltered data must be used. 

It is also important to realize that there may be “hidden” filtering present in your system. In particular, you must be careful to recognize filtering that is introduced by process data historians and process control system interfaces. Please go to the page When to avoid filtering.

Categorizing filters by their memory of past data

Digital filters that only rely on a fixed number of recent input values are called finite impulse response filters (FIR) in electrical engineering, and also referred to as “moving average” (MA) filters in the terminology of time series analysis. Those that rely on previous output values as well as the most recent input, effectively weight in a little bit of all earlier inputs. They are called infinite impulse response filters (IIR), or “autoregressive filters” (AR). The popular exponential filter is an example of this. Please go to the page Categorizing filters by their memory of past data .

Sampling, aliasing, and analog anti-alias filtering

When analog signals are sampled for digital filtering, if the sampling rate is inadequate, aliasing will make the high frequencies appear as if they were lower frequencies. An analog anti-aliasing filter must be used to prevent this. Supervisory systems like diagnostics are prone to this problem because they are often sampled at a low data rate. Please go to Sampling, aliasing, and analog anti-alias filtering.

Commonly used filters

Separate pages describe some commonly used digital filters. Please see the individual pages for:

Estimating a derivative (rate of change)

We sometimes want to estimate a variable’s rate of change - its time derivative. However, derivative estimation is extremely sensitive to noise. Please see the following:

Filtering strategy and tuning

When setting the filter parameters, a balance must be achieved between noise rejection vs. speed of response. Also, detection of important transients, and symptoms that manifest as high frequency noise must be considered. Please see Filtering strategy and tuning .

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