Brazilian Journal of Chemical Engineering PLANTWIDE PERIODICAL DISTURBANCES ISOLATION AND ELIMINATION IN A PETROCHEMICAL UNIT

Reducing process variability is crucial to reach a more profitable operating point. Periodical disturbances, however, impose barriers to achieve this goal. Their effect can be strong since one disturbance that appears in a specific loop of a highly coupled plant can be seen in several loops. Thus, isolating their source and diagnosing their cause are essential. In this work, we describe the application of spectral independent component analysis to isolate a periodical disturbance that has a strong impact on the final variability in a polyethylene plant located in Southern Brazil. After the first analysis, the source was detected and the cause identified: valve stiction. To identify the cause (valve, bad tuning, or periodic disturbance), we used the methodology based on higher-order statistics. Once the valve problem had been overcome, the product variance was reduced by 93%.


INTRODUCTION
One frequent cause of poor process performance is the presence of plant-wide periodical disturbances (Thornhill and Horch, 2007) whose effect can spread through the entire plant, inhibiting the process from achieving a more profitable operating point. Nowadays, plants are more coupled and have a large number of recycles because of mass and heat integration. One oscillation that starts in a specific loop can be propagated to the entire process, increasing the product variability. Thus, it is clear that detecting and eliminating plant-wide oscillations are essential to ensure process profitability and reduce product variability. However, the diagnostics of the loop that is the source of the disturbance and the cause of the oscillation is not straightforward. This is the scenario seen in a petrochemical plant located in Southern Brazil. One periodical oscillation affects the product variability and, because of plant recycles, the engineers could not detect either the source or the cause. Our goal is to detect and find the source of the oscillation, eliminating it (if possible) after diagnosing the cause.
The procedure to eliminate plant wide oscillations requires three steps:

METHODOLOGY
This section describes the methodologies used to automatically detect the oscillation, its root cause (source), and the cause of oscillation.

Oscillation Detection
Initially, the oscillation was automatically detected using the integral of the square error, a method proposed by Hägglund (1995).
The idea behind the method is simple: based on time trend zero-crossing, the integral of the absolute error between each zero crossing is computed (IAE C ). It is then compared with a threshold value (IAE LIM ). If IAE C > IAE LIM , then the process has an oscillatory behavior.
The oscillation detection procedure can be summarized as follows: 1. Choose an acceptable oscillation amplitude (a); 2. Compute IAE LIM as 2a/.  is 2/Ti and Ti is the integral time of the controller.
3. Monitor IAE C . Restart it when the control error changes its signal.
4. If IAE C exceeds IAE LIM then the oscillation has occurred.

Detecting the Root Cause (Source) of Oscillation
To detect the root cause of the oscillation, the methodology based on Spectral Independent Component Analysis (SICA) was used . Initially, the time-domain ICA will be described and then the methodology to detect the root cause of oscillations will be explained.
Consider that the plant has m sensors, whose observations are x m .
They are linear combinations of n independent, non-Gaussian source outputs. Each column is called an Independent Component (IC).
The matrix of observations (X) can be written as a linear function of the matrix of ICs (S).

 X AS
( 3) where A is called the mixing matrix (m by n). Each sensor can be decomposed into linear combinations of ICs.
The ICA problem involves the estimation of both A and S. The Fast ICA algorithm (Hyvärinen et al., 2001) was used in this work.
In the spectral ICA model, the rows of X are singlesided power spectra P(f) over a range of frequencies (f) of the same sensor. P(f) can be estimated using Discrete Fourier Transform (DFT) (Oppenheim et al., 1999). The main advantage of using power spectra instead of time series is that the first is blind to the time delays. Besides, SICA can isolate a single peak in each independent component, when multiple oscillations are present in the plant.
The procedure to apply the methodology based on SICA is described below: 1. Compute the power spectra for all measured variables (X).
2. Decompose X into independent components, obtaining A and S (using FastICA).
3. Find the sign of the dominant peak for each IC, denoted by SN j , (j=1…n); 4. Adjust the A and S matrixes using the following relation: Then .

 X BY
Here, the new term, based on matrix B, called the significance index is introduced. It provides the importance of the combined matrix elements. Values close to 1 represent a strong impact from an IC in a power spectrum signature. Smaller values of the significance index show a smaller impact of a given IC.
Then, each IC was adjusted to achieve a maximum significance index equal to 1.
1. Find the maximum absolute value for each column of B ( j , j=1…n); 2. Scale the mixing matrix B and IC matrix Y; Based on the new matrix A, the source of each independent component, or plant-wide disturbance, can be identified. The loop for a given IC whose significance index is close to 1 is probably the root cause of that oscillation.
In the work of , the dominance of each independent component over the plant is analyzed, helping to discover which are the main plant disturbances. However, in our case, a visual analysis showed that the mentioned oscillation (see Fig. 2) appeared in several loops, causing a strong impact in the product variability.

Detecting the Cause of Oscillation
The last step is to diagnose the cause of the oscillation. In this work, we will apply the methodology based on higher-order statistics, proposed by Choudhury et al. (2004). To corroborate the results, the methodology to quantify stiction based on ellipsis interpolation will also be used (Choudhury et al., 2008).
The method proposed by Choudhury et al. (2004) claims that, if the process is locally linear and a nonlinear behavior is present, then the valve is responsible for this behavior. If the loop has an oscillatory behavior and the valve is working properly, the problem can be poor loop performance or other external disturbance (e.g., a disturbance transferred from another loop with oscillatory behavior).
where X(f) is the discrete Fourier transform of any time series x(k) and B(f 1 ,f 2 ) is called the bispectrum in the frequencies f 1 and f 2 . The bispectrum is the third order cumulant in the frequency domain. It is defined as: where * denotes the complex conjugate. One positive feature of bic 2 is that it is bounded between 0 and 1. Assuming that bic 2 at each frequency is a chisquared ( 2 ) distributed variable with 2 degrees of freedom, a modified test formulated by averaging the squared bicoherence over the triangle of the principal domain with better statistical properties will be used to verify signal Gaussianity. The test can be summarized as follows: bîc is the average of the squared bicoherence. If NLI = 0, the process is linear; otherwise the process is nonlinear. If the loop is nonlinear, then the valve "suffers from" stiction.
To corroborate the diagnostics provided by the method based on higher-order statistics, the method based on ellipsis interpolation (Choudhury et al., 2006) will also be used to diagnose and quantify valve stiction. If the process variable (pv) and control output (op) plot has an ellipsis pattern, as shown in Figure 3, then the stiction is confirmed. The apparent stiction can be quantified as the length of the horizontal ellipsis axis (sb).

RESULTS
This section describes the application of the methodologies in the petrochemical plant previously described. The IAE C whole dataset nd 2 nd IAE C ontrollers, as   Figure 4, the eliminated he significan ble 3). The so and PC02, a he impact of in Figure 5.  Based on Figure 8 and Figure 9, we can verify that, in each case, the disturbance vanished. The positive impact on loop variability is corroborated by the comparison between the ratio of the original (when all loops were closed) and the new variance when PC01 and PC02 were opened, as shown in Table 4. Table 4 summarizes the strong impact caused by IC1. Its elimination can reduce the product and the whole plant variability, achieving a more profitable operating point.

CONCLUSIONS
In plants with a high number of recycles, periodical disturbances can strongly affect loop variability, because one oscillating loop can have a widespread effect in the whole plant. Thus, isolating its source and diagnosing its cause are essential to ensure a highly efficient operation. In this work, we illustrate this scenario in a petrochemical plant located in Southern Brazil, where periodical disturbances have a strong influence on product variability.
The procedure followed three steps. Initially, we detected loop oscillation using the methodology based on IAE (Hägglund, 1995). Then, each disturbance was isolated using Spectral Independent Component Analysis . We identified the disturbance whose period we want to isolate and its sources, which were PC01 and PC02. Finally, we diagnosed the cause of the fault in both loops as valve stiction using the methodology based on higher-order statistics (Choudhury et al., 2004).
To verify the theoretical predictions in the industrial plant, each loop was opened for a period, because the valves could not be replaced. The impact was visible: the reduction in the variability of almost all loops was verified and the reduction in product variability was up to 93%.