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The Purpose and Effects of Filtering and Smoothing

Filtering topics:

 

This page describes the purpose and effects of filtering and smoothing for single variables. This page is part of the section on
Filtering that is part of
A Guide to Fault Detection and Diagnosis..

Filtering reduces noise, improving estimates of variables

For systems using sensor data, noise and bias errors are almost always an issue. For this discussion, we focus on filters reducing high frequency noise and “spikes” for single variables. (In electrical engineering terms, we are focusing on “low-pass” filters.) Low frequency errors such as bias errors require analysis using multiple variables and relationships between those variables such as models.

The primary purpose of filtering is to reduce noise. It accomplishes this by combining multiple values of variables sampled over time so that at least some of the noise is canceled out. This way, we produce better estimates of the true variable values in the monitored system. This is generally desirable, so filtering is an important component of an overall diagnostic system because of the prevalence of noise. However, there are cases described later where filtering is not desirable.

A signal from one sensor might be used unfiltered for some analyses, and with several different filters for other purposes. This depends on the types of noise, the process and noise frequencies of interest, and the failure modes being considered.

Filtering vs. smoothing

There is a distinction between “filtering” and “smoothing”. With filtering, we want to obtain the best estimate of the current value of the input signal. With “smoothing”, we want to obtain the best estimate at an earlier time. Because data is already available both before and after the earlier time, smoothing to estimate older values provides more accuracy. Strictly speaking, we can usually can tolerate some delays in diagnosis, so that either filtering or smoothing could be used. However, we generally just use simple filters with the understanding that most filters do in fact introduce lags and delays.

Trading high frequency noise rejection against delays in diagnosis

Most filter outputs change more slowly than the input (measured) values. As a result, when fault detection and diagnosis is based on the outputs of filters, it takes longer to detect real changes. This is easily seen when looking at the response to an input step change, as shown for several types of filters in the text that follows. “Heavier” filtering (longer time constants in the exponential filter case) results in increased noise rejection, but also increased lag in response to changes. So, filter design involves a tradeoff between high frequency noise rejection and delays in diagnosis. To give quick diagnostic results, filtering usually should not get too “heavy”. However, much heavier filtering can be tolerated in diagnostic systems than in feedback control systems. So, typical restrictive guidelines on the amount of filtering in control systems do not apply.

One consideration is how each filtered variable will be used. If a conclusion will be reached by an AND condition between two tests, variables used in the two tests should usually not have drastically different filtering. Otherwise, short term responses in one lightly filtered variable may already have moved to different values by the time another test with heavily filtered variables crosses it’s threshold test.

Copyright 2010 - 2013, Greg Stanley

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