Integrated absolute error

The integral of the absolute value of the deviation lAE (Integral Absolute Error) was also proposed as a measure for control quality ... 

The PI and PID control ler were tnned to produce a minimum integrated absolute error (lAE). Their response curves are similar in appearance to agaussian distribution curve, but with a damped cycle in the trailing edge. The peak deviation of the PID response curve is only 0.12 times the uncontrolled offset, occurring at O.l Zx the peak deviation of the PI response curve is 0.21 times the uncontrolled offset, occurring at 0.48Zx. These values can be used to predict the load response of any distributed lag whose parameters K and Zx are known or can be estimated as described below. 

Integrated absolute error (lAE) This is a measure of the total area under the response curve on both sides of zero error. It is one of the generally accepted performance criteria. Since the error following a load change eventually disappears, the lAE approaches a finite value for any stable loop. 

Integrated absolute error (lAE) essentially takes the absolute value of the error. Negative areas are accounted for when lAE is used, thus dismissing the problem encountered with IE regarding sinusoidal responses. 

IAE = Integral of the Absolute Error, cost functional for determining quality of control (the higher the value, the worse the control)... 

Several criteria may be used to estimate the quality of control (Stephanopoulos, 1984). One of these is the integral of the time-weighted absolute error (ITAE), where... 

Integral of time-weighted absolute error (ITAE)... 

Third-order results for closed-shell molecules have average absolute errors of 0.6 - 0.7 eV [31]. Transformed integrals with four virtual indices and OV4 contractions for each value of E are required for the U intermediate, which is needed for ionization energy as well as electron affinity calculations. 

Raman spectra in the range 1545-355 cm 1 were selected for data analysis. An average of 27 (461/17) spectra were obtained for each individual with a 3 min integration time per spectrum. Each spectrum was obtained with excitation power 300 mW and integration time equivalent to 3 min. Spectra from each volunteer were analyzed using PLS with leave-one-out cross-validation, with eight factors retained for development of the regression vector. For one subject, a mean absolute error (MAE) of 7.8% (RMSECV 0.7 mM) and an R2 of 0.83 were obtained. 

After experimental work, the value of the activation energy (EA) and the reference permeability (Qref) for a PVA-based (from GKSS) pervaporation membrane and mixture in use have been obtained (see tablel), and the model for the pervaporation process with and without heat integration has been successfully validated. The absolute error between the model and the experimental permeate fluxes is under 8% (see fig.4), and almost insignificant for the water purity in the permeate side (under 0.5%) obtaining a permeate stream with up to 99.9% in water. 

If the experimental errors are underestimated, it can lead to tight but inaccurate distance bounds. Conversely, the overestimated errors can lead to unnecessarily imprecise distance bounds. RANDMARDI takes into account two types of experimental errors relative integration errors and absolute errors due to spectral noise. The first kind can be estimated, for example, by comparing intensities of symmetric peaks below and above the diagonal, and the second type can be estimated as 50-200% of the lowest quantifiable peak, depending on the spectrum quality. 

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