On-Line Process State Classification for Adaptive Monitoring

Ind. Eng. Chem. Res. 2006, 45, 3095-3107

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On-Line Process State Classification for Adaptive Monitoring Young-Hak Lee Automation and Systems Research Institute and School of Chemical and Biological Engineering, Seoul National UniVersity, Seoul 151-742, Republic of Korea

Hyung Dae Jin Department of Chemical Engineering, Pohang UniVersity of Science and Technology (POSTECH), Pohang, Gyeongbuk 790-784, Republic of Korea

Chonghun Han* School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National UniVersity, Seoul 151-744, Republic of Korea

In process monitoring that is based on statistical models, adaptive monitoring techniques have been developed to reflect frequent changes in the operating conditions. The key to adaptive monitoring of real industrial processes is to distinguish process operating condition changes from variations due to disturbances. This paper proposes a systematic method for detecting process state changes and classifying them as operating condition changes or variations as a result of disturbances. The key idea of the proposed method is to extract process knowledge that is based on if-then rules for detecting the operating condition changes. When a state change is accepted by a defined set of rules, it is classified as an operating mode change. Otherwise, it is classified as a disturbance. A signed digraph and statistical data analysis are used to generate the rules from the process knowledge. A robust cumulative-sum algorithm is used for change detection. The proposed method was validated using a dataset from an industrial process heater. The results showed a classification power of 97%. Adaptive monitoring that is based on the proposed method could significantly reduce the number of false alarms, compared to previous remodeling approaches. 1. Introduction During the past few decades, multivariate data models such as principal component analysis (PCA), partial least squares (PLS), Fisher’s discriminant analysis, canonical variate analysis, and independent component analysis have been widely used to monitor processes and qualities in chemical plants.1,2 Those models easily handle complex correlations of process measurements. They enable one to update a model promptly and avoid fitting a model to noise, and they provide easy-to-interpret information. However, they require frequent model updates, because of time-varying changes such as catalyst deactivation, preventive maintenance and cleaning, seasonal variations, and sensor and process drifting, which degrade the monitoring performance. To handle time-varying changes in terms of multiple operating modes, a model library-based method using various modeling methods such as clustering, super PCA, mixture PCA, and multiple PCA have been presented.3-7 A model library is defined as a bundle of models matched to the operating modes. When a model becomes degraded, it is exchanged for a new model that corresponds to the operating mode. However, the operating modes in a model library are not fixed. This approach still requires updates to the model library. As an approach to adaptive modeling, Wold developed an exponentially weighted moving PCA and PLS, in which the model is dynamically updated by giving more weight to recent samples than to past samples.8 Gallagher and Wise applied an exponentially weighted moving covariance (EWMC) method * To whom all correspondence should be addressed. Tel.: +82-2880-1887. Fax: +82-2-888-7295. E-mail: [email protected].

to monitor microelectronics manufacturing processes.9 The method needs rules for resetting the moving mean when large shifts occur as a result of a change in cleaning or equipment aging. The recursive PCA (RPCA) proposed by Li et al. can handle slow time-varying properties.10 However, RPCA fails to distinguish process-operating-condition changes from the process variations that are due to disturbances. Therefore, the model can adapt to disturbances when recent samples include them.11 Unfortunately, it is not easy for the previous two approaches to cover the complex behavior observed in actual industrial processes. Figure 1 shows the typical process behavior visualized in reduced space with real industrial long-term data. The arrow on the figure represents the direction of time. The process behavior contains the abrupt time-varying changes without the repetition of an operating mode. This characteristic makes both the model library-based approach and the recursive one unstable. Although it holds multiple operating modes, the model librarybased approach has many false alarms in the overlapped operating region. When using the recursive approach, the monitoring performance falls severely when an operating mode changes abruptly. After changing the operating conditions, the process usually represents the stationary behavior in a new operating zone. Our work is focused on presenting a clue for the adaptive monitoring of real industrial processes with time-varying behavior such as that observed in Figure 1. To enhance the monitoring performance and reduce false alarms, an on-line process state classification method is proposed. The key idea of the proposed method is to classify the process state changes using an if-then rule when the process exists outside the

10.1021/ie048969+ CCC: $33.50 © 2006 American Chemical Society Published on Web 03/14/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006

Figure 1. Typical process behavior visualized in reduced space with real industrial long-term data; the arrow on the figure represents the direction of time.

statistical limits. The model update then is performed only if the process change is classified into a new operating mode. The next section describes an industrial fired heater as a typical actual process with complex time-varying behavior. For model updates of such an industrial process, an on-line process state classification method that is based on the if-then rule is proposed in section 3. Section 4 shows the application results for the industrial fired heater. Then, monitoring performance based on the proposed method is compared with a standard one. Finally, conclusions are presented. 2. Process Description: An Industrial Refinery Fired Heater A fired heater in an industrial refinery plant was used to test the proposed method. The fired heater consists of three major components: a heating coil, an enclosure, and combustion equipment. The heating coil consists of tubes connected together in series to carry the charge that is being heated. Heat is transferred to the material passing through the tubes. The enclosure consists of a firebox, which is a steel structure lined with a refractory material to hold the generated heat. Burners create the heat via the combustion of gas or oil. The heating coil absorbs the heat mainly via radiant heat transfer and convective heat transfer from the flue gases. The flue gases are vented to the atmosphere via a stack. For increased heat recovery, an air preheater is installed downstream of the convection section. Instruments are generally provided to control the firing rate of the fuel and air flow through the coils to maintain the desired operating conditions. Figure 2 shows the fired heater configuration used in this work. The three major parameters are controlled and monitored: the fuel pressure, excess air, and the draft in pressure. The feed output temperature provides the set point for the burner fuel pressure controller. If the heater is fired with more than one type of fuel, then one of them is base-loaded and set at a constant firing rate while the second fuel has load fluctuations. Excess air control essentially involves answering the question “How much excess air needs to be provided?” The optimum excess air is dependent on the type of fuel used. Less is better because the minimum excess air reduces the amount of heat lost to the flue gases, minimizes the cooling effect on the flame, and improves the heat transfer. If there is not enough excess air, unburned fuel will begin to appear in the flue gas, because of

insufficient air. The hot flue gases inside the firebox and stack are lighter than the cold ambient air outside, which creates a slightly negative pressure inside the furnace. Combustion air is drawn into the burners and hot gas flows out of the stack, because of this pressure differential. In this system, the air is supplied using a centrifugal fan commonly known as a forceddraft (FD) fan. An induced-draft (ID) fan is provided to draw the flue gases out of the heater. The negative pressure inside the furnace ensures the appropriate air supply to the burners from the atmosphere. A balanced draft system is when both forced- and induced-draft fans are used with the heater. The fired heater used in this study has a balanced draft system. The plant operation database stores various measurements that are related to the following operating conditions: (i) inlet feed conditions, (ii) outlet conditions, (iii) inlet conditions of fuel and air, (iv) flue gas conditions, and (v) combustion conditions within the heating box (temperatures, pressures, excess air, etc.). These data are essential to demonstrate the proposed approach. The important variables for the rule extraction are given in Table 1. The process monitoring model that uses the variables must be frequently validated and updated, because of variations in the heating load, changes in slag/soot deposits, seasonal effects, and so on. These variations cause the process to represent time-varying behavior, as observed in Figure 1. This application is suitable for demonstrating the benefits of the proposed method. 3. On-line Process State Classification for Model Update Chemical processes are operated at a large number of steady states and frequently switch among them. Each steady state is known as an operating mode. The plant undergoes changes from one operating mode to another, and operating-mode changes are quite common in the process industry. Mode changes are normally executed by plant operators who follow predefined standard operating procedures (SOPs). Multivariate statistical monitoring methods should be able to overcome model degradations that are due to operating mode changes. Process disturbances or failures can be misclassified as operating mode changes in performing adaptive statistical monitoring. Such an undesirable effect makes a model adapt to the disturbances. Therefore, it is essential to classify the current process states as “operating-mode changes” or as “others.” The model can be updated when identifying the operating-mode changes. There are few reports for distinguishing between operatingmode changes and disturbances. Kano et al.12 proposed a dissimilarity index that can detect a change in the operating condition by monitoring the distribution of process data. The idea can be used to detect a new operating mode, assuming that the change in the operating mode is matched with that of the distribution of process data. However, the index can be corrupted by many disturbances, even though the assumption is valid, and the use of a set window size causes a smoothing effect to the outliers. Teppola et al.3 mentioned that disturbances and new operating conditions could be discriminated by detecting out-of-control states, followed by contribution plot analysis. It is a weak point that contribution plot analysis is strongly dependent on the process understanding of the analyst. Also, several mode identification methods based on fuzzy C-means clustering,13 hierarchical clustering,4 self-organizing neural networks,14 and fuzzy rule-based identification techniques15 can be found. However, because these methods must (i) update the defined operating modes, according to gradual process changes, or (ii) add an algorithm to isolate disturbances, they are not appropriate to be combined with the model update scheme.

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Figure 2. Schematic of the refinery fired heater used in this study. Table 1. Process Variables for Factor Extraction Based on Statistical Data Analysis variable number

description

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

feed flow rate of crude oil feed flow rate of crude oil fired heater inlet pressure fired heater inlet temperature total feed flow rate of crude oil convection outlet temperature convection outlet temperature convection outlet temperature convection outlet temperature fired heater outlet temperature fuel oil pressure fuel gas pressure fuel gas flow rate air flow rate pressure difference between fuel oil and steam draft pressure O2 concentration in flue gas flue gas temperature flue gas temperature air preheater inlet temperature of flue gas air preheater shell inside temperature fired heater inlet air temperature air preheater outlet temperature of flue gas left fired box temperature right fired box temperature

In fact, the operating mode usually changes because of alterations in the feed flow rate or composition, product specifications, utility supply conditions, and preventive maintenance and cleaning. Statistical models can be degraded because the changes in only a few causes can dominate the mode changes. Operating modes are mainly shifted in a process through set-point changes by plant operators. Therefore, it may be meaningful to identify mode changes focusing on dominant set-point changes. The basic idea of the proposed state clas-

sification method is to identify the mode changes by shifts in the significant factors such as the set points of the process variables, as distinguished from disturbances. If a mode change is not detected using the factors, the process state is classified as a disturbance. Hence, it is extremely important to identify the necessary and sufficient factors. To detect a change in the identified factors, a cumulative-sum (CUSUM) SPC chart is introduced. The CUSUM chart shows efficient performance in detecting slight shifts in the mean of a process.16 Window-size median filtering can be preprocessed before shifts are detected. The median filter has good resistance to random impulse noise.17 As a result, the modes can be detected by observing the CUSUM of the principal factors to the mode changes with a form of if-then rules. A couple of issues must be addressed to generate the rules to detect the mode changes. (1) Key factors that dominate the operating-mode changes should be identified. As previously mentioned, the operating mode can be changed when one or more set points change significantly. For example, a change in the throughput is necessarily accompanied by set-point change(s) in the level or flow rate. To find the set points that are significant to mode change in complex control loops, a qualitative model that can capture the causal structure of the system is proposed. Irrespective of a set-point change, the operating mode can be formed by uncontrollable factors such as the feed composition (e.g., the composition of crude oil in a refinery). For such an operating mode, the mode change cannot be identified by a set-point change but, instead, must be identified using the measurements correlated with the formed mode. Multivariate data analysis based on historical data is used to cope with this difficulty. (2) Disturbances can hinder the detection of mode changes. A change in a principal factor can be falsely detected because of a disturbance. For example, the feed flow rate that governs the process throughput can seriously fluctuate, as a result of

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controller malfunction or valve sticking. The abnormal change may be falsely detected as a mode change. Therefore, conditions to isolate disturbances should be included in the rule. (3) When multiple factors affect the process, a process change in one factor can be canceled out as a result of the others. It might be difficult to identify the mode change with the changes in more than one factor. Although one factor has an effect in the positive direction, other factors can have an effect in the negative direction. Indeed, such changes may not alter the operating mode. Causal analysis tools that can formulate the cause-and-effect relationships of these factors are used to cope with this problem. It is helpful to reveal the interaction among the factors. Also, it ensures the mode change by checking effect variables, followed by a change in factors. (4) Parameters such as the decision limit of a factor for detecting a mode change and the window size for a median filter should be decided. These are closely involved with detectability. The framework for developing a process state classifier for adaptive monitoring is proposed next. It consists of two phases: rule generation for detecting mode changes as distinguished from disturbances and the on-line classification using the rule. As previously mentioned, the rule can be generated via two steps: identification of the factors that dominate mode changes and construction of a mode-change detection method based on if-then rules. The rule generation procedure is depicted in Figure 3. 3.1. Representation of Cause-and-Effect Relations. In this study, a signed digraph (SDG) will be used to represent a causeand-effect relationship. A digraph is a graph with directed arcs between the nodes, and an SDG is a graph in which the directed arcs have a positive or negative sign attached to them. The directed arcs lead from the “cause” nodes to the “effect” nodes. An SDG has nodes that represent events or variables and it describes the causal paths to deviation from the steady state of variables.18 The studies on SDGs so far have focused on fault diagnosis. The majority of the studies have also considered only steady-state situations. Several efforts in applying SDGs to dynamic situations have achieved only very limited success, mainly because of the limitation of the methods used in qualitatively describing the temporal trends of variables. Recently, Li and Wang have presented how fuzzy digraphs can be used for qualitative and quantitative simulation of the temporal behavior of process systems.19 Fortunately, this study does not require the qualitative interpretation of dynamic trends. It just needs a simple signed digraph structure. In this work, SDGs are used to obtain the following information: (i) the main factors that influence the operating-mode change selected as the root nodes in each SDG; (ii) the effect variables consequent to the change in the factors, which are used to ensure the change detection of the factors; and (iii) the interactions among the factors related to the operating-mode change. In particular, the main factors are largely involved with the set points in control loops. Therefore, SDG-based causality of control loops should be analyzed. Chen and Howell proposed a self-validating control-system-based fault detection and diagnosis method. In this approach, fault isolation is achieved through qualitative reasoning about steady-state deviations in measured variables by referring to the SDGs of control systems.20 Within this work, it is noteworthy for our purposes that the way of representing control systems and interactions between them is with SDGs. Only the main idea is given here, and a more comprehensive explanation can be found in Chen and Howell.20

Figure 3. Rule generation procedure for change detection of operating modes.

Figure 4 shows an example of the simplified SDG built using a block diagram of a 2 × 2 system with a single-loop controller. First, the manipulated variables (MV), the set-point variable (SP), and the disturbances (D) in the diagram are assigned as nodes of a SDG. The arcs are then connected to nodes according to the signal flow of the control actions in the block diagram. Finally, when the set points are changed or the disturbances are introduced, the signs on the arcs are determined by considering the changes in the direction of the variables in the nodes. A cascade control system can be treated in a similar way. The set point of the outer-loop controller can be selected as a factor to change the mode, whereas that of the inner loop is not a factor, because it is strongly dependent on that of the outer loop. Hence, the inner loop of a cascade control system can be viewed as a clustered node that consists of several nodes that form a circle. An interesting approach was developed by Mo et al.21 and Lee et al.,22 who treated all the nodes related to a single control loop as a cluster. An SDG with interacting and recycle nodes can be also represented with the clustered nodes in the simplified way.19


Figure 4. (a) Block diagram of a 2 × 2 system with a single-loop controller. (b) Signed digraph (SDG) built using the diagram.

3.2. Identification of the Factors Dominating Mode Changes. 3.2.1. Factor Identification Based on Process Knowledge from the Signed Digraph. Root nodes such as the set-point variables are selected as the main factors influential to operating-mode changes. In the case of a cascade control system with inner and outer loops, only the set points for the outer loop can be decided as a root node, because the set point for the inner loop is strongly dependent on the control output for the outer loop. Also, because the interacting and recycling nodes are treated as a single node in the representation of an SDG, the set point for the inner loop can be included into a clustered node. The nodes with only output arcs are extracted as factor candidates. By considering the interaction among the root nodes, we can identify the final factors. 3.2.2. Factor Identification Based on Statistical Data Analysis. Other factors, which cannot be extracted from SDG analysis, may exist. For example, when the uncontrollable feed composition changes, it is difficult to identify the factor from the SDG that is generated based on the control loops. Such a factor can be captured using historical data analysis. The procedure used to extract these factors is as follows: (1) Collect the data that include various operating modes, according to the time axis, and remove the data in an unstable state such as the oscillation of the controlled variables. Unstable state data can contaminate the results of the data analysis. The data should include the various state variables reflecting the operating modes that cannot be identified using the control variables involved with a set point. The ability to observe the process states determines the ability to identify the hidden factors. (2) With the set-point variables related to the factors defined in the upper section, the resulting data matrix is classified into sub-data matrices, according to the time axis. To identify a subdata matrix with the multiple modes, the concept of entropy is

introduced. The state of data distribution is judged from the value of the entropy. As the entropy increases, the randomness, or degree of disorder, of a dataset increases. For each sub-data matrix, the Shannon entropy is obtained to identify the factors that indicate a mode change. The Shannon entropy (d) is defined as23

d)

-1

L

∑pk log(pk) log(L)k)1

(1)

where the fraction of the total variance (pk) indicates the relative significance of the kth singular value, in terms of the fraction of the overall variation that they capture, and L is the number of variables in the data matrix. A Shannon entropy of d ) 0 corresponds to an ordered and redundant dataset in which all expression is captured by a single singular value, and d ) 1 corresponds to a disordered and random dataset where all singular values are equally expressed. Therefore, the entropy d for a sub-data matrix with multiple modes is smaller than those with a single mode. A data matrix with a single mode shows a random variation around a steady state, in which d has a large value. Therefore, a data matrix that contains a hidden mode change has a relatively small d value. In this step, the data matrices with multiple modes are selected. The threshold value for d (dc) is defined as the maximal value for entropy values for data matrices with the multiple modes to minimize the possibility of missing the main factors. (3) Extract the additional factors from the sub-data matrices selected as those with multiple modes in step 2. A centroidlinkage-based hierarchical clustering24 is applied to distinguish among the modes. Clustering is a procedure used to identify the observations that belong to each operating mode. If the distribution is simple with a multivariate normality assumption for each cluster, nonhierarchical clustering methods can show

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good performance. However, when the observations are significantly distorted with a large number of variables, the efficiency and stability of nonhierarchical clustering methods are degraded. To resolve the difficulty, the popular hierarchical clustering method is introduced. After that, the causes of changes in the modes can be analyzed and the key variable(s) to detect the mode changes are selected. Principal factors caught by step 3 are integrated with the factors defined in the previous section. The insignificant ones, which are subsequent to a root factor, then are removed. The root factor means the causal source that is identified as one of the input nodes of the SDG. 3.3. Construction of Mode Detection Rule. Mode-detection logic based on the extracted factors is built in terms of an ifthen rule. The factors are mutually independent, so the logic to detect mode changes can be made individually. The logic for the individual factors is ordered according to priority. The factors that change more frequently have higher priority. In detecting mode changes, a meaningless logic execution occurs if infrequently changing factors are set in front of the rules. With the predetermined factors, the procedure for defining the rule should cover three main issues: (i) the change detection of the factor, (ii) the removal of disturbance and noise effect for robust change detection, and (iii) the identification of the interference effect among the factors. The cumulative-sum (CUSUM) algorithm16 combined with a window-size-based median filter is introduced to detect any change in a factor promptly. The CUSUM algorithm is more efficient in detecting small shifts in the mean of a process than that of Shewart. The tabular CUSUM works by accumulating derivations from the steady state of a factor according to the following equations:

C+(t) ) max[0, x(t) - (µ0 + K) + C+(t - 1)]

(2)

C-(t) ) max[0, (µ0 - K) - x(t) + C-(t - 1)]

(3)

where x(t) is the current value of a factor, µ0 is a target value for x, and C+(t) and C-(t) are the upper and lower CUSUMs, respectively. K is the allowance filtering trivial changes. If either C+(t) or C-(t) exceed the decision interval (H), the factor is considered to be changed. To lessen the effect of noise or an outlier, x(t) in eqs 2 and 3 is preprocessed with a median filter based on the window size. The median estimate demonstrates a good resistance to random-impulse noise and preserves the edges and discontinuities in the curves.17 The window size is referenced as data size of the period when a manipulated variable significantly changes to reach a steady state after changing a set point. A factor change can be detected by the movement of a manipulated variable. To determine if a factor is changed or not, the data of the period moving the manipulated variable should be needed at least. In this study, the average size of the periods moving the manipulated variable for each factor is used as the window size. Disturbances may result in the false detection of mode changes. The rules should include conditions to isolate the disturbances that might occur in the causal path of each factor. Disturbances can be largely identified via control-loop analysis that is involved in a factor. As an example of the detection methods, the method of control-loop performance assessment (CLPA) described by Desborough and Harris is outlined here.25 The basis of CLPA is that the controller error should have no predictability over some given prediction horizon. That is, the controller error Y is decomposed as Yi ) yˆ i + ri, where yˆ is the predictable component of the controller error and r is the zero-

mean residual. The objective of control is to remove any predictable components. That is, yˆ should be small or zero. Desborough and Harris’s performance index can be expressed as

η )

mse(yˆ i) mse(Yi)

)1-

σr2 mse(Yi)

(4)

where mse(yˆ i) is the mean square value of a predictable component, mse(Yi) the mean square value of the controller error, and σr2 the variance of the residual. The index η is dimensionless and in the range of 0-1. When the control performance is good, controller error has little predictability and the index is zero, because mse(Yi) ) σr2. The opposite is true for a poorly controlled loop in which controller error is predictable. In this work, Desborough and Harris’s performance index is introduced into the proposed rule generation procedure. When more than two factors are independently changed, process operation may be unchanged in a total view. This is due to the interference effect of the factors. For instance, if the heating load in a process is dependent on the feed flow rate and feed temperature, a process load change by feed flow rate can be cancelled out by a change in the feed temperature. To cope with this problem, causal relationships that are required to change the factor are used. Consequences followed by a change in a factor can be identified as a change in the effect nodes linked with the input node (factor) in the SDG. This supports the ensuring the factor change. Changes in those factors are also detected by the CUSUM algorithm, together with the change in the factors. In summary, the if-then rule is composed of the logic for individual factors, and the logic for the jth factor is formed as follows:

Logic j: IF {change of factorj AND change of effect of causal factorj AND identification of no disturbance for change in factorj)} THEN operating-mode change by factorj

(5)

where, if the IF statement in Logic j is not accepted, go to “Logic j+1”. 3.4. Operating-Mode Detection and Disturbance Isolation Procedure. This section describes the classification procedure of the two process-changing states: operating-mode change and variation due to a disturbance. The logic defined in section 3.3 can be used to identify a change after detecting process changes; therefore, process changes must be detected with some indices. The detection of these changes is based on a principal component analysis (PCA) model for multivariate statistical process control (MSPC).26,27 The model is first produced from the reference data. To distinguish between the changes and the normal reference behavior, the statistical confidence limits for the monitoring statistics, such as Hotelling’s T2 statistic and the squared prediction error (SPE), are calculated. The proposed procedure is described as follows: (1) Detect the process changes that exceed the control limits for the MSPC. (2) The outlying data undergo the predefined logical processes. Each rule is applied to detect the changing data according to the priority. If the data are accepted by at least one of the defined conditional statements, a process change is identified as a transition of the operating mode. Otherwise, it is classified as a disturbance.

Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3101 Table 2. Main Controllable Factors and Uncontrollable Factors Factors

Figure 5. Flowchart used to detect an operating-mode change and isolate a disturbance.

(3) When detecting a mode change, the model should be updated. Figure 5 shows a procedure to detect an operating-mode change and isolate a disturbance.

main streams

controllable

uncontrollable (surrounding)

feed stream feed stream feed stream

feed flow rate outlet temperature outlet temperature

feed density (composition) feed temperature feed switching

fuel stream fuel stream

fuel oil flow rate fuel gas flow rate

fuel gas density fuel oil/gas supply ratio

air stream

air flow rate

air temperature

draft draft

draft pressure excess O2

flue gas temperature

4. Results and Discussion 4.1. Identification of the Factors Dominating Mode Changes. 4.1.1. SDG-Based Factor Identification. As mentioned in the previous section, an operating-mode change is mainly caused by a change in the controllable factors. Understanding the control loop in the fired heater is extremely useful for identifying the controllable factors. The fired heater is operated using four main control loops. Table 2 represents the main controllable factors and the surrounding factors that affect them. In the case of the feed stream, various feeding conditions due to changes in feed temperature, feed composition, and feed switching influence on the load of the heater, even though the feed flow rate is well-controlled. Figure 6 shows a block diagram highlighting the transmission interactions among the control loops. In the cascade, the outlet temperature of the fluid in the coil is tightly controlled by adjusting the fuel flow controller set point, which adjusts the valve position. The air flow controller set point is adjusted, depending on the fuel flow. Excess O2 is manually controlled according to the air and oil flow. It is often used as an indicator for monitoring the heater efficiency. The feed flow rate is adjusted according to a level set point in the preflash, which is located in the upper stream. The draft pressure is controlled by adjusting the flue gas flow released through the ID fan. As a transmission interaction, the

Figure 6. Block diagram of the fired heater considering the transmission interactions.

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Figure 7. SDG for the fired heater.

flue gas flow rate affects the air temperature via an air preheater, which influences the outlet temperature. In addition, an increase in the feed flow rate can cause a decrease in the outlet temperature. An SDG was constructed based on the useful process knowledge extracted from Table 2 and Figure 6. In the SDG, the set point, present value, and valve opening variables in the control loops were set as nodes. In addition, the surrounding factors were assigned as nodes. Arcs were generated using the flows within each control loop and among the control loops in Figure 6. The signs were selected by reasoning the cause-andeffect relationship based on the changes in the set points or the surrounding factors that were inducing mode changes. For example, the outlet temperature decreases if the feed density increases. Therefore, the negative sign (-) is marked. Figure 7 shows the SDG of a fired heater based on the control-loop analysis. As a result of the SDG analysis, the feed flow rate, temperature, composition, feed output temperature, and draft pressure were obtained as factor candidates that can influence an operating-mode change. They are the root nodes marked with the symbol “h” in Figure 7. The heater can maintain a consistent heat duty because of the interactions among those, although they do change. To identify the change in the heater duty, the effect as a result of a change in these factors must be observed. When the load changes, the fuel and air flow are directly affected. Because the air flow is not strongly connected to the others, it was selected as an effect variable to ensure the change in the feed condition. In addition, the feed temperature is simultaneously changed with the other variables, such as the feed density, in the switching feed. This means that the feed temperature is dependent on the other variables. Because draft pressure maintains a constant set point, the mode change is not influenced. In conclusion, the feed flow rate, feed density, and outlet temperature were identified as factors, and the air flow rate was identified as an effect variable.

4.1.2. Factor Identification Based on Hierarchical Clustering. To perform the statistical analysis, data over a six-month period were collected. Using the set points of the factors just described, a data matrix was classified according to time. The datasets with more than two steady states were selected by the entropy criterion. The selected datasets may have multiple modes to be identified by other factors. In the datasets, the set points of the predefined factors were constant, but the other factors were altered, which contributed to changing modes. Figure 8 shows a score plot for a selected dataset and a time series plotfor a main contributing variable. Two clusters were identified in the reduced space. The fuel gas density mainly helps to discriminate among the operating modes. This means that the operating modes can be changed according to the various fuel inlet conditions. From the historical data, a new factor influencing the mode changes was identified. Table 3 shows the detection frequency for the individual factors that cause operating-mode changes. 4.2. Rule Formulation for Detection of Operating Mode Changes. According to the detection frequency shown in Table 3, the order of the rules was determined. First, a change in the set point of the outlet temperature means a transition from one mode to another. To detect a change, the following logic was devised: SP Logic 1: IF {|median(TOT,t ) - TSP OT,0| > 0}

THEN an operating-mode change

(6)

SP is the data vector of a window size for an outlet where TOT,t temperature set point at time t, and TSP OT,0 is an outlet-temperature set-point value in the original operating mode. Second, a change in the feed density was detected using the CUSUM algorithm. The air flow rate was selected as an effect variable. An increase of the density induced an increase in the air flow


Figure 8. (a) Score plot of the data matrix with 2 modes. (b) Time-series plot of the main variable influential to division of the modes, fuel gas density. Table 3. Checksheet Representing the Detection Frequency for Individual Factors Causing Operating-Mode Changes

rate. This is why the heat duty in the heater was heavier. The logic for this procedure is as follows:

Logic 2: IF {(CUSUM of median(DF,t) > HDF AND CUSUM of median(FAR,t) > HFAR) OR (CUSUM of median(DF,t) < HDF AND CUSUM of median (FAR,t) < HFAR)} THEN an operating-mode change

(7)

where DF,t is a data vector for the feed density and FAR,t is a data vector for the air flow rate. HDF and HFAR are the decision limits of DF,t and FAR,t calculated from the original mode. Third, the CUSUM algorithm detects a mode change for the feed and air flow rates. A mode change can be falsely detected by considering an arbitrary change in the feed flow rate, such as the controller oscillation, even though CUSUM of the median values was used. Therefore, controller oscillation must be isolated. Desborough and Harris’s performance index, η (see eq 4), was used to detect an oscillation in the control loop. A previous implementation of the index in a refinery had found a

Figure 9. (a) Variable plot for the set point of the output temperature. (b) Standard monitoring chart for a set-point change in the output temperature. (c) On-line mode-detection-based monitoring chart for a set-point change in the output temperature.

target of η e 0.15 to be suitable.28 The corresponding logic was defined as follows:

Logic 3: IF {(CUSUM of median(FF,t) > HFF AND CUSUM of median(FAR,t) > HFAR) OR (CUSUM of median(FF,t) < HFF AND CUSUM of median (FAR,t) < HFAR) AND η e 0.15} THEN an operating-mode change

(8)

where FF,t is a data vector for the feed flow rate and HFF is the decision limit of FF,t from the original mode. Finally, the fuel gas density could not be measured in this case. To detect a change in that factor, the total number of burners firing fuel oil and gas was used. The number of burners consuming fuel gas

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Figure 10. (a) Variable plot for the feed density. (b) Standard monitoring chart for a change in the feed density. (c) On-line mode-detection-based monitoring chart for a change in the feed density.

decreases if the density of the fuel gas entering the fired heater increases while that of the burner for fuel oil increases. Therefore, the number of burners consuming fuel gas or fuel oil is changed, which results in a mode change. The logic for this is as follows:

Logic 4: IF {|median(BG,t) - BG,0| > 0} THEN an operating-mode change

(9)

where BG,t is a data vector of the window size for the number of burners consuming fuel gas at time t, and BG,0 is the number of burners consuming fuel gas in the original operating mode. 4.3. Operating-Mode Detection and Disturbance Isolation. Frequent operating-mode changes are performed in the refinery

Figure 11. (a) Variable plot for the feed flow rate. (b) Standard monitoring chart for a set-point change in the output temperature. (c) On-line modedetection-based monitoring chart for a change in the feed density.

fired heater. The classification and monitoring results of the process states outlying the control limits are described in this section. 4.3.1. Case 1: Mode-Change Detection Resulting from a Set-Point Change in Output Temperature. When two monitoring indices, T2 and SPE statistics, exceed the control limits, one of two actions can be taken: model update or disturbance isolation. Figure 9 shows a variable plot for a set point in output temperature and T2 and SPE charts for a standard monitoring case and a mode-detection-based monitoring case. At the 53rd point, a new mode was detected (Figure 9a). It results from a set-point change in output temperature, which was identified by rule 1 in eq 6. Figure 9a shows that normal states were falsely identified as abnormal states since detecting the mode change.


Figure 12. Monitoring result performed with process state classification.

When considering the detection of the mode change, false alarms can be significantly reduced, as shown in Figure 9b. They detected the disturbance (at the 189th point) in a similar way. 4.3.2. Case 2: Mode-Change Detection Resulting from a Feed Density Increase. In the second case, a mode change was caused by a feed density increase (Figure 10a). The standard monitoring case shows false alarms of ∼70 points after detecting the mode change (Figure 10b), whereas the proposed case shows just a few false alarms (Figure 10c). The disturbance at the 220th point was identically detected in both of them. 4.3.3. Case 3: Mode-Change Detection Resulting from a Feed Flow Rate Increase. Figure 11a shows the feed flow rate increase at the 298th point. The proposed case shows a more robust monitoring result than for the standard case, as seen in Figure 11b and c. The proposed rule was applied to industrial data over a threemonth period, which included 170 process changes to be classified. Table 4 represents the classification results by the proposed approach. It shows the good classification power with a correctly classified rate of 97%. A case was falsely detected as a mode change due to sudden peaks in the set point for the outlet temperature. The peaks can disturb the estimation of the median. The mode changes that were misclassified as disturbances were the outlying data detected near the control limits for T2 and SPE. Very slight mode changes cannot be detected. Indeed, such a mode change has little influence on model degradation. 4.4. Comparison and Discussion. To compare the monitoring effect by the proposed rule-based approach with the standard one, industrial data over a three-month period were collected. Using the operation log, and with operator’s opinion, a total of

69 process changes were identified and classified as 23 mode changes and 46 disturbances. The identified process changes were used to validate the proposed method. The proposed method showed a perfect classification result for the 69 process changes, excluding the unidentified changes, as seen in Figure 12. A model update with process state classification was recursively performed whenever the new operating mode was detected. In this figure, 288 out of 10 000 samples were detected as false alarms (i.e., type I error). Compared with the monitoring results of the proposed method, the standard method without process state classification triggered false alarms in 1660 out of 10 000 samples, as seen in Figure 13. The model update in standard monitoring goes through remodeling after reaching the steady state. It requires at least 30 data samples in terms of the Central Limit Theorem to identify mode changes and construct a statistically significant model. That means that the model update is suspended for the period when the data samples are collected. The proposed method helps extremely to reduce the type I error rate in adaptive monitoring. As a result, the monitoring model can be rapidly adapted to the changing operating conditions by detecting the operating-mode changes. 5. Conclusions This paper proposes a systematic method for detecting and classifying process state changes as an operating-mode change or a variation due to a disturbance. Also, it shows that the rapid and correct identification of an operating-mode change from process changes is essential for adaptive process monitoring. The process knowledge was used to detect operating-mode changes using an if-then rule. The rule was constructed from two steps: (i) identification of the principal factors that influence

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Figure 13. Monitoring result performed without process state classification. Table 4. Classification Results for the Industrial Data, Including 170 Process Changes state

correctly classified rate percentage: 97.00 (165/170)

operating-mode changes Rule 1 Rule 2 Rule 3 Rule 4 disturbances

98.30 (57/58) 97.60 100.00 100.00 100.00 96.40 (108/112)

error analysis set-point peak

detection near thresholds

the operating-mode changes, and (ii) construction of the mode detection logic. A signed digraph (SDG) that was based on process knowledge was used to define the rules. Statistical data analysis was also used to identify the rules that could not be covered by the process knowledge. The CUSUM algorithm with a window-based median filter was used to detect the changes. A change was classified as a variation due to a disturbance if the changing state was not accepted through a defined rule. The proposed approach was applied to an industrial fired heater in a refinery plant. For 170 changing states mixed with operatingmode changes and variations as a result of disturbances, the proposed method showed an classification accuracy of ∼97%. Monitoring based on the proposed approach is expected to reduce the number of false alarms. When large shifts occur as a result of process revamping, equipment changes, etc., the defined rule may be upgraded. After such a significant change can be made, other factors that are influential to a mode change must be searched again, using the corresponding historical data, which can be troublesome.

Acknowledgment The authors gratefully acknowledge the partial financial support of the Korea Science and Engineering Foundation provided through the Advanced Environmental Biotechnology Research Center (R11-2003-006) at Pohang University of Science and Technology and the Brain Korea 21 program initiated by the Ministry of Education, Korea. Nomenclature AR ) air B ) number of burners B ) burner number data vector C- ) lower CUSUM value C+ ) upper CUSUM value D ) density data vector d ) Shannon entropy DR ) draft pressure EXO2 ) excess O2 F ) feed F ) flow rate data vector G ) fuel gas H ) decision interval for change detection K ) allowance filtering trivial changes in CUSUM calculation L ) number of variables OT ) outlet temperature in the fired heater pk ) relative significance of the kth singular value in terms of the fraction of the overall variation r ) zero mean residual SPE ) squared prediction error T ) temperature data vector


T2 ) Hotelling’s T2 statistic t ) time x ) scalar value of a factor Y ) controller error sequence yˆ ) predictable component of the controller error Greek Symbols µ0 ) target value for a factor η ) Desborough and Harris’s performance index σ2 ) variance of a signal sequence Subscripts i ) index of a signal sequence in control loop j ) index of a factor order in logic k ) index of a principal component Literature Cited (1) Ching, L. H.; Russell, E. L.; Braatz, R. D. Fault Detection and Diagnosis in Industrial Systems; Springer-Verlag: London, 2000. (2) Kano, M.; Hasebe, S.; Hashimoto, I.; Ohno, H. Evolution of Multivariate Statistical Process Control: Application of Independent Component Analysis and External Analysis. Comput. Chem. Eng. 2004, 28, 1157. (3) Teppola, P.; Mujunen, S.-P.; Minkkinen, P. Adaptive Fuzzy C-Means Clustering in Process Monitoring. Chemom. Int. Lab. Syst. 1999, 45, 23. (4) Hwang, D.-H.; Han, C. Real-time Monitoring for a Process with Multiple Operating Modes. Control Eng. Pract. 1999, 7, 891. (5) Chen, J.; Liu, J. Mixture Principal Component Analysis Models for Process Monitoring. Ind. Eng. Chem. Res. 1999, 38, 1478. (6) Choi, S. W.; Park, J. H.; Lee, I.-B. Process Monitoring Using a Gaussian Mixture Model via Principal Component Analysis and Discriminant Analysis. Comput. Chem. Eng. 2004, 28, 1377. (7) Zhao, S. J.; Zhang, J.; Xu, Y. M. Monitoring of Processes with Multiple Operating Modes through Multiple Principle Component Analysis Models. Ind. Eng. Chem. Res. 2004, 43, 7025. (8) Wold, S. Exponentially Weighted Moving Principal Components Analysis and Projections to Latent Structures. Chemom. Int. Lab. Syst. 1994, 23, 149. (9) Gallagher, N. B.; Wise, B. M.; Butler, S. W.; White, D. D., Jr.; Barna, G. G. Development and Benchmarking of Multivariate Statistical Process Control Tools for a Semiconductor Etch Process: Improving Robustness through Model Updating. In International Symposium on AdVanced Control of Chemical Processes, Banff, Canada, 1997; p 78. (10) Li, W.; Yue, H.; Valle-Cervantes, S.; Qin, S. J. Recursive PCA for Adaptive Process Monitoring. J. Process Control 2000, 10, 471. (11) Rosen, C.; Lennox, J. A. Multivariate and Multiscale Monitoring of Wastewater Treatment Operation. Wat. Res. 2001, 35, 3402.

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ReceiVed for reView October 25, 2004 ReVised manuscript receiVed February 5, 2006 Accepted February 15, 2006 IE048969+

On-Line Process State Classification for Adaptive Monitoring

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