JUL-AUG 2018

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16 INTECH JULY/AUGUST 2018 WWW.ISA.ORG PROCESS AUTOMATION figures will show results of diverse fil- tering methods on the same data. In figure 1, the solid line represents the moving average filter with N=3 and the dashed line with N=30. Note several features: l The MA with N=3 makes a more rapid rise to the new data value, but its vari- ation is larger than the MA with N=30. l The character of an MA filter response to a step change in the signal is a lin ear ramp toward the new value, which lasts N samples. l The response to the one-time out- lier is a pulse that has a duration of N samples and a magnitude of 1/N th of the outlier deviation. An advantage of the MA filter is that the concept of averaging is commonly understood, and the tuning choice of window length N is easily related. For example, moving averages are com- mon in reporting the performance of a company stock. When periodic distur- bances are present, a window length chosen to match the period will result in a signal that moves to the new aver- age in one period. However, the algo- rithm causes some delay in process alarms and process control applica - tions realizing and responding to a sudden process change. The algorithm does not reject data outliers. First-order filter (FoF): A first-order filter has several alternate names, in - cluding exponentially weighted mov- ing average (EWMA) and autoregressive moving average (ARMA). The FoF rep - resents the analog device methods for filtering an electronic resistor-capacitor or pneumatic restriction and bellows, but it can be digitally performed. The advantage is that it is computationally simpler than an MA filter, which must store and process all of the data in the window. The FoF equation is: Here lambda, λ, is the filter factor (it is not related to lambda tuning). It ranges between 0 and 1, 0 < λ < 1. X i is the most recent data measure- ment; X f,i-1 is the prior filtered value; and X f,i is the new filtered value. If one derives the equation as an approxi- mation to the moving average meth- od, essentially: Some vendors use the symbol f for the filter factor, and some switch the λ and (1-λ) weighting. If one derives the FoF from the differential equation rep - resenting a first-order RC circuit, then: where Δt is the sampling interval, and τ is the time constant. With sub- stantial filtering, the time constant is approximately related to the number of data, τ ≅ Δt N . The user needs to be aware of the manner in which the ven- dor presents the filter. The FoF also tempers, but does not Figure 1. Characteristic performance of a moving average filter to a process step change and spike Figure 2. Characteristic performance of a first-order filter to a process step change and spike

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