100 200 300 400 500 600 700 800 Coefficient number

Figure 6.59. SPE on different scales of the decomposed faulty batch data. Darker line represents 99% control limit.

charts on important scales can be conveniently used on both detection and diagnosis of abnormal operation, particularly, in the case of small shifts in variable set points. Figure 6.61 represents detection and diagnosis of abnormal operation. Responsible variable(s) are detected by SPE charts and diagnosed correctly by contribution plots (averaged contributions during the period when the process is out-of-control) for this fault case as glucose feed rate (variable 3), glucose (variable 5) and penicillin concentrations (variable 8) in the fermenter. □

Methodology of on-line MSMPCA: Wavelet decomposition by nature is not suitable for on-line monitoring because future measured data is needed to calculate the current wavelet coefficient which introduces a time delay in the computation. This delay can be prevented by making the wavelet filter causal by implementing special wavelet filters named boundary corrected filters at the edges. Another source for time delay in wavelet decomposition is the dyadic downsampling. The signal is decomposed into wavelet coefficients only if it is of dyadic length. For example if the signal has three data points, the decomposition is not executed until the fourth data point is added to the signal. In order to eliminate these disadvantages, an algorithm that includes decomposition of data in a moving window has been

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