An intelligent system for multivariate statistical process monitoring and ...

ISA TRANSACTIONS® ISA Transactions 41 共2002兲 255–270

An intelligent system for multivariate statistical process monitoring and diagnosis Eric Tatara, Ali C¸inar* Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, IL 60616, USA

共Received 26 October 2000; accepted 25 May 2001兲

Abstract A knowledge-based system 共KBS兲 was designed for automated system identification, process monitoring, and diagnosis of sensor faults. The real-time KBS consists of a supervisory system using G2 KBS development software linked with external statistical modules for system identification and sensor fault diagnosis. The various statistical techniques were prototyped in MATLAB, converted to ANSI C code, and linked with the G2 Standard Interface. The KBS automatically performs all operations of data collection, identification, monitoring, and sensor fault diagnosis with little or no input from the user. Navigation throughout the KBS is via menu buttons on each user-accessible screen. Selected process variables are displayed on charts showing the history of the variables over a period of time. Multivariate statistical tests and contribution plots are also shown graphically. The KBS was evaluated using simulation studies with a polymerization reactor through a nonlinear dynamic model. Both normal operation conditions as well as conditions of process disturbances were observed to evaluate the KBS performance. Specific user-defined disturbances were added to the simulation, and the KBS correctly diagnosed both process and sensor faults when present. © 2002 ISA—The Instrumentation, Systems, and Automation Society. Keywords: On-line process monitoring; Real-time monitoring; Knowledge-based systems; Multivariate statistical process monitoring; Sensor auditing; Data fusion; Canonical variate analysis; State space models

1. Introduction Statistical methods for detecting changes in industrial processes are included in a field generally known as statistical process control 共SPC兲 or statistical quality control. The most widely used and popular SPC techniques include univariate methods that involve observing a single variable at a given time, obtaining the mean and variance of the variable, and checking its value against upper and lower control limits. While a univariate approach may indeed work for monitoring a small number of process variables that are not correlated, current capabilities in data acquisition hardware allow a *Corresponding author. Tel.: ⫹1-312-567-3637; fax: ⫹1-312-567-75170. E-mail address: [email protected]

large 共several thousand兲 number of variables to be easily measured. Application of univariate statistical process monitoring 共SPM兲 methods to larger multivariable systems becomes difficult, if not impossible, and is often erroneous. This simplified approach to process monitoring requires an operator to continuously monitor perhaps dozens of different univariate charts, which substantially reduces the ability of plant personnel to make accurate assessments about the state of the process. Multivariable statistical process monitoring 共MSPM兲 techniques offer the proper theoretical framework for monitoring multivariable processes. MSPM techniques reduce the amount of raw data presented to an operator and provide a concise set of statistics that describes the process

0019-0578/2002/$ - see front matter © 2002 ISA—The Instrumentation, Systems, and Automation Society.

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Eric Tatara, Ali C¸inar / ISA Transactions 41 (2002) 255–270

behavior. Many of the current MSPM techniques are only valid for data that are independent and identically distributed 共iid兲. The independence assumption means that the data must not be correlated with each other, either in current measurements or lagged values, and that each have similar statistical distributions. This assumption, however, only applies to very idealized data and is not commonly observed in real processes. Correlations in the data include autocorrelation, which indicates a correlation of a single variable with its past observations, and cross-correlation, which indicates a relationship between two or more variables at either the current observations or past observation. Most process data are correlated, such as tray temperature readings in a distillation column or temperature and concentration in a chemical reactor; consequently, it is necessary to utilize MSPM methods capable of monitoring such processes. 关1兴 Data-driven MSPM methods that are capable of handling correlated data include methods based on principal component analysis, projection to latent structures 共PLS兲, and canonical variate and subspace state space modeling. Data-driven techniques are dependent on data collected from a real process in order to formulate a model that describes the variability of that process. System identification methods suitable for linear processes with correlated data such as principal components regression, PLS, canonical variate state space modeling, and subspace state space modeling are described in 关1– 4兴. System identification methodologies that can handle nonlinear systems have also been proposed 关5–7兴. The model developed is used to predict the future values of monitored process variables. The difference between the model predictions and the process measurement is referred to as the model residual. The residuals between the predicted and actual values may be assessed for statistical significance; a significant increase in residuals suggests the presence of abnormal conditions in the process. In addition to measuring the magnitude of the residuals, one may also examine trends in the residuals. Sensor errors in the form of a bias change, drift, or excessive noise may be diagnosed by examining the residuals over time. Periodically performing sensor audits 关2,8,9兴 by examining the residuals for statistically significant changes can greatly enhance the credibility of the data as well as significantly reduce the number of false alarms.

The aforementioned monitoring techniques may be integrated with an automated system to provide real-time process monitoring and diagnosis. Knowledge-based systems 共KBSs兲 or expert systems are computer systems designed in an attempt to emulate the decision-making capabilities and knowledge of a human expert in a specific field. A KBS consists of a knowledge base, decision rules, and an inferencing engine. The knowledge base is comprised of a set of knowledge, data, and facts pertaining to a specific problem and process. Decision rules are rules, developed by human experts based on intimate knowledge about the process, to reach a conclusion given the facts, such as process data. The inference engine processes the rules based on the data and conclusions reached by other rules 共inferences兲 to reach a conclusion such as fault diagnosis. Knowledge-based systems increased in popularity during the early 1980s when many people viewed knowledge-based systems as ‘‘magic bullet’’ solutions to every problem. Unfortunately, the high expectations of knowledge-based systems ultimately led to widespread distrust of the technology after such systems failed to perform as expected. Knowledge-based systems are gradually becoming more popular for performing such tasks as monitoring and diagnosis—tasks that KBSs are able to perform very well. Additionally, current computer hardware and software—technology that was unavailable when the KBS first gained popularity—are ideal for real-time KBS development and run-time platforms. KBSs are useful for solving problems that can only be done by human experts or are repetitive in nature and perform effectively due to their inherently well-defined knowledge space. The advantage over human experts is access to very large databases and fast execution time. While a human expert may need to search volumes of printed text for a piece of information, a KBS can quickly search electronic databases in short time. Knowledge-based systems excel at qualitative processing, which is beneficial in diagnosis of process faults and monitoring applications. Human experts routinely perform qualitative analysis using process specific information and heuristics. Therefore, one can design a KBS to perform a specific task by transferring the knowledge from a human to a computer code. Of course, the ability of the KBS to reason is directly related to the quality of


knowledge supplied by the knowledge engineer. If the KBS is supplied with incorrect or irrelevant knowledge, the performance of the KBS will be poor. Furthermore, if the KBS is designed for a specific application, it typically cannot be applied to a different application without significant modifications to the knowledge base. Several knowledge-based systems for process monitoring and fault diagnosis in areas of chemical engineering have been reported 关8 –16兴. Additionally, several knowledge-based systems for system identification are available 关17–24兴. They are based on linear single-input–single-output or multiple-input–single-output models and typically require significant user input and operate offline. The KBS developed by Norvilas et al. 关25兴 is the predecessor of the work presented in this paper; however, the original KBS did not incorporate sensor validation or subspace identification techniques. While these systems represent the state of technology for KBS-based monitoring and diagnosis, systems that integrate methods of system identification, process monitoring and control, and sensor fault diagnosis have not been reported. A robust system for monitoring and diagnosis of a multivariable process must utilize the powerful MSPM techniques that have been developed for analysis of these processes as well as features of KBS for qualitative reasoning. Such a hybrid system will use the best of both techniques. While commercial monitoring software is gradually incorporating more advanced statistical monitoring techniques, a large portion of the available commercial software for MSPM and KBS is used offline, that is, data are processed and analyzed after an event has occurred or the process operation has ceased. A real-time monitoring and diagnosis system is necessary to detect and diagnose faults as they occur, in order to take immediate corrective measures. The KBS emulates the behavior of a human engineer responsible for interpreting various statistical tests performed on the process data in real time and decides what data are to be used when building models for prediction purposes, selects the type of system identification model building techniques to use, schedules monitoring and diagnosis events, coordinates alarm handling, and suggests corrective actions in the event of a process fault. A process monitoring and fault diagnosis system that combines the strengths of system identifica-

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tion, MPSM, and real-time KBS is reported in this paper. The KBS automatically performs all operations of data collection, identification, and monitoring and sensor fault diagnosis with little or no input from the user. Navigation throughout the KBS is achieved through menu buttons on each user-accessible screen. Selected process variables are displayed on charts showing the history of the variables over a period of time. Multivariate statistical tests and contribution plots are also shown graphically. The KBS was evaluated using simulation studies with a polymerization reactor through a nonlinear dynamic model. 2. System identification, monitoring and diagnosis tasks and modules 2.1. System identification System identification is the process of building an accurate model of a process from collected data for the purpose of monitoring, control, and modeling. The advantages of canonical variate state space 共CVSS兲 modeling over classical PC and PLS regression methods have been discussed 关1,26兴. Canonical variate analysis was initially conceived by Hotelling in 1936 and later refined for use in dynamic systems by Akaike 关27兴 and Larimore 关26兴. CVSS modeling techniques for use in monitoring multivariable dynamic continuous processes were developed by Negiz and Cinar 关1兴. A state space model allows the prediction of onestep-ahead values for the state variables of the model, given the model parameters and the current state values as shown by

xk⫹1 ⫽Axk ⫹B␧k ,

共1兲

yk ⫽Cxk ⫹ ␧k ,

共2兲

where xk is the vector of n state variables at time k, yk is the vector of p output measurements, ␧k is a stochastic input vector 共measurement noise兲 with T zero mean and covariance E ( ␧k ␧k⫹1 ) ⫽⌬ if the lag l⫽0, and 0 otherwise. CVSS realization methods are used for determining the system matrices A, B, C and covariance matrix ⌬ with the minimum number of state variables needed to capture the process dynamics. The state variables defined by the CVSS modeling procedure describe the

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variation in data such that each additional state variable describes the largest fraction of the variation remaining after the portion described by the previously defined state variables. The first few significant state variables can often be used to describe the greatest variation of the process. These state variables are independent of each other at zero lag; hence, they can be used to determine the status of a multivariable process that has timedependent measurements.

UCL T 2 ⫽

2.2. Monitoring 2.2.1. Univariate process monitoring The Shewhart control chart, developed in the 1920s by Walter A. Shewhart, is a graphical means of displaying quality characteristics calculated from industrial process variables 关28兴. Quality characteristics or variables are statistics that are derived from measured data obtained from process sensors. The purpose of the Shewhart chart is to show a plot of the desired quality variable of interest versus time as well as a region bounded by upper and lower control limits that define the incontrol process. The area between the lower and upper control limits represents the natural variation of the data. If each observation of the measured quality characteristic falls between the control limits on the control chart, the data are in a region of normal operation or considered to be in statistical control. If an observation falls outside of the limits, the process is out of control. By using the Shewhart control charts to monitor process variables, one may assign a cause to abnormal conditions by observing which variable or variables have exceeded the control limits. 2.2.2. Multivariate monitoring techniques Shewhart charts only provide information for monitoring the magnitude and variation of single variables. However, the in-control region of many chemical processes is defined by several variables, thereby rendering the univariate control chart inappropriate for monitoring, when used exclusively 关28,29兴. Univariate charts represent quality characteristics in only one-dimensional space, in terms of the possible value of the characteristic. To create a better representation of the state of the process, a multivariable statistic called the Hotelling T 2 statistic is used:

T 2 ⫽ 共 x⫺x ¯ 兲 T S⫺1 共 x⫺x ¯兲,

where x is an observation vector of p state variables. The vector ¯x represents the estimated mean for each state variable, ( • ) T denotes the transpose operation, and S is the estimated covariance matrix. The in-control mean and covariance matrices are computed from a set of n in-control samples. The T 2 statistic may be calculated and plotted for each new observation. The control limit for the T 2 statistic is

共3兲

p 共 n 2 ⫺1 兲 F , n 共 n⫺p 兲 ␣ ,p,n⫺p

共4兲

where F ␣ ,p,n⫺ p is the F -distribution parameter with a confidence of ( 1⫺ ␣ ) percent and ( p,n ⫺p ) degrees of freedom. 2.2.3. Squared prediction error (SPE) chart for model evaluation One-step-ahead predictions of the process outputs based on model equations. 共1兲 and 共2兲, yˆk , may be compared to the actual process outputs yk after the actual process outputs are obtained. The difference between the predicted and actual process outputs is the process residual

ek ⫽yk ⫺yˆk .

共5兲

The process residuals indicate the performance of the model prediction. If the model is a good representation of the process, the residuals will be small, and if the model is a poor representation, the residuals will be large. Large residual values may also represent disturbances in the process. While the T 2 statistic indicates a process disturbance in the state space, the SPE describes the behavior of the process outside of the state space. If a significant deviation from normal operating conditions occurs, the model prediction will differ significantly from the actual process outputs. The residuals, therefore, provide a means to measure the state of the process not described by the state space. The squared prediction error 共SPE兲 statistic is the square of the process residuals and is defined in a manner similar to the T 2 statistic:

SPE⫽ 共 e⫺e ¯ 兲 T S⫺1 ¯兲, e 共 e⫺e

共6兲

where ¯e is the estimated mean of the residuals and Se is the estimated covariance matrix of the residuals. The constants ¯e and Se are obtained from the CVSS process model derived from a set of


in-control data. The SPE statistic may be calculated and plotted for each new observation. The UCL for the SPE statistic is calculated by

UCL SPE⫽

p 共 n 2 ⫺1 兲 F , n 共 n⫺p 兲 ␣ ,p,n⫺p

共7兲

where F ␣ ,p,n⫺p is the F -distribution parameter with a confidence of ( 1⫺ ␣ ) percent and ( p,n ⫺p ) degrees of freedom, p is the number of predicted variables, and n is the number of samples used in the model development. 2.2.4. Contribution plots The T 2 and SPE statistics determine the overall status of the process; however, the individual process variables responsible for the out-of-control condition or the source causes for abnormal operation cannot be determined by the T 2 and SPE charts. Contribution plots are used to determine the process variables that contribute to large T 2 values 关3,25兴. Contribution plots are used to monitor the state variables obtained from the canonical variate state space system identification models. The equation for the contribution from a single state variable and corresponding process variable and lag is

conta, j,l ⫽

xa trana, j,l 共 y j ⫺ ␮ j 兲 , sa

共8兲

where y j is the jth observed process variable, ␮ j is the estimated mean of y j , x a is the ath predicted state variable with variance s 2a , trana, j,l , denotes the appropriate element of the state transition matrix 关2兴, and l is the lag of the process variable for that particular contribution. The total contribution of each process variable to the out-ofcontrol condition may be found by summing the values of contributions that share a sign with the out-of-control state variable. The software alerts the user to investigate large contributions when an out-of-control condition is detected. Contributions can be plotted for assisting a human expert diagnose the source cause of abnormal process operation, or the numerical contribution values can be used directly by fault diagnosis software. 2.3. Sensor auditing The use of multivariate statistical measures to monitor a process requires that the measured data accurately represent the true state of the process.

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Sensor auditing for assessing the correctness of information generated by a sensor is a critical component of process monitoring and diagnosis. Out-of-control operation may indicate either a process fault or a sensor failure. Therefore, sensor auditing is used to determine the source of an outof-control process condition detected by the MSPM techniques described above. Functional redundancy of measured variables can be used to develop sensor auditing methods. Functional redundancy involves using information from various process sensors to determine if a sensor is functioning properly. Abnormality of a sensor may be investigated by evaluating the deviation of the mean and variance of residuals between measurement and predicted sensor readings 关1兴. Data batches collected when the sensor was operating properly can be used to build predictive PC or PLS models. Then, these models are used with new batches of data to determine sensor status. A multipass PLS method was developed to extend this approach to monitor the status of multiple sensors 关30兴. A multipass CVSS technique similar to the multipass PLS algorithm was developed for detecting multiple sensor failures in dynamic processes 关9兴. This is achieved by eliminating successfully the corrupted measurements from the NOC data 共calibration set兲 and future collected data 共test set兲 and building a new model. The model residuals, the difference between the actual process data and that predicted by the CVSS model, are monitored. The algorithm indicates a sensor fault when either the mean or variance of the residuals of the corresponding sensor are out of the statistical limits 共based on t and F probability distributions兲. Since the corrupted variable affects the model predictions of the remaining variables, false alarms may be generated unless the corrupted variable is taken out of both the calibration and the test data sets. The information loss due to taking a variable out of both the calibration and the test data set is not significant since the testing procedures are based on the iid assumption of the residuals and not on the minimum prediction error criterion by the model. The algorithm discards the variable with the highest deviation level by investigating the residual mean and variance values. Since it may be impossible to replace a sensor immediately due to cost or physical system constraints, the sensor audit procedure ensures that a valid CVSS model is

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Fig. 1. Sensor audit procedure.

available for uninterrupted monitoring of the process and remaining sensors and providing estimated values for the variable measured by the faulty sensor. The nature of the sensor fault is diagnosed by determining whether the residual mean, the residual variance, or both exceed their statistical limit. The decision flow chart for the sensor audit procedure is shown in Fig. 1. If only the residual mean exceeds the limit, then the corresponding sensor is subjected to a bias change. If only the residual variance exceeds its limit, then the corresponding sensor is subjected to excessive noise. If both the residual mean and the residual variance exceed their limits, then the corresponding sensor

is experiencing a drift. The likelihood for all of the process sensors to become simultaneously faulty is extremely small. After several successive steps, if the mean and variance of the remaining residuals still indicate significant variation, then it is more likely that a disturbance is active on the system, causing the in-control variability to change significantly. 3. Real-time KBS design 3.1. G2 development software The G2 software 关31兴 is a graphical knowledge base development environment for creating intel-


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such as buttons and slider bars update the values of the user specified variables that pertain to individual controls. The G2 environment provides an excellent shell for the development of a supervisory KBS; however, specific numerically intensive calculations for process simulation and analysis cannot be efficiently implemented in the G2 environment. One may take advantage of more sophisticated programs for numerical analysis and simulation by linking those programs to G2. G2 software provides several options for networking and passing data between external programs. The G2 Standard Interface 共GSI兲 bridge functions as an intermediary between the object-oriented knowledge representation in G2 and code developed using external software. Software routines for system identification and sensor audit were developed in Matlab by Negiz and Cinar 关9兴. The Mathworks provides a Matlab Compiler that converts the standard Matlab m-file format into ANSI C files. Each Matlab C function to be called through GSI is a separate entity in the bridge code. 3.2. KBS operation Fig. 2. KBS control panel for selection of model and sensor audit parameters.

ligent real-time applications. Applications developed in the G2 environment are called knowledge bases 共KBs兲 and may be saved in a format that allows periodic maintenance or modifications. A KB contains workspaces that resemble windows available in most graphical operating systems upon which objects are organized. Workspaces may be arranged in a hierarchical structure providing means for organization of data. Workspaces contain all of the rules, variables, and objects that are used when developing a KB. The G2 programming language is very similar in structure to the English language, allowing for rapid software development. Graphical representation of data in the G2 environment is performed through several different types of charts that are customizable by the user. The displays may be placed on any workspace and the shape, position, and colors of the display may be modified as needed by the user. Charts have real-time capability and can display any type of numerical or symbolic data. Controls

The function of the monitoring KBS is to reduce the time required for manual process monitoring and diagnosis. The rule base in the KBS contains general information as well as process-specific information for monitoring and diagnosis in the form of over 400 rules and procedures. However, this number may be misleading because the G2 software dynamically creates rules based on the structure of the knowledge base. The number of internal rules used by G2 software 共for data handling and updating the graphical displays, for example兲 may be on the order of several thousand and are not typically seen by the developer or the end-user. Data collection and model construction are performed by the KBS in real time. The degree of automation is variable based upon the experience of the user. Engineers and operators who are unfamiliar with the process and/or monitoring will benefit greatly from a fully automated system. The control panel shown in Fig. 2 contains virtual controls to allow the advanced user to override the automated model building features of the software. Default values for the monitoring parameters are given and may be changed as the user deems appropriate. Model development and sensor

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Fig. 3. KBS operations for process and sensor fault detection and diagnosis.

audit are fully automated procedures, though they may be disabled by check boxes on the control panel. Model parameters may also be manually adjusted via type-in boxes. The value of future and past lengths to use for the observation vectors may be specified as well as the number of states to use for model development. In the event that the user chooses a value outside the nominal range determined by the software, a message appears informing the user that his choice may lead to unpredictable model performance and suggests a suitable value. The KBS is structured to minimize the computational expense often encountered with rule base systems. The initial CVSS model development step typically requires less than 10 s of processing time on a 300 MHz PC for a set of 8000 sample data. The KBS is able to handle all other computational requirements on a real-time basis with a maximum sampling frequency of 1 Hz. The process monitoring components of the KBS include code for the calculation of tests such as the T 2 and SPE statistics as well as the display of both univariate and multivariate data. Figure 3 is a flow chart that outlines the sequence of KBS events that occur when a process or sensor fault occurs. When the T 2 or the SPE indicate an out-of-control process condition, the sensor audit is activated by the KBS to first determine if a faulty sensor is responsible. When a faulty sensor is suspected, the KBS

builds a new process model by excluding the suspected faulty sensor. If all of the sensors are found to be working correctly, contribution charts are used to determine the process variables most likely responsible for the out-of-control condition. The most significant variables are used by the rule base to make a diagnosis of the fault. Furthermore, the rule base is subdivided into several categories of rules for each of the monitored process variables. When a specific variable is determined to be involved in the abnormal process operation via the contribution plots, the subsection of the rule base for the identified variable is activated. The modularization of the rule base in this fashion thus provides a computationally efficient method to execute diagnosis rules as only those rules that are directly related to the actual process fault are activated. For example, in a cooled continuous stirred tank reactor 共CSTR兲, if the reactor temperature is found to contribute to an out-of-control condition, the portion of the rule base responsible for temperature-related faults is activated. Fault information is propagated through a series of rules designed to determine the root cause of the process fault, as in a sample rule from the KBS: ‘‘If the reactor temperature is high and the agitator power is normal and the coolant temperature is normal and the coolant flow rate is normal and the feed flow rate is normal, then conclude that the feed temperature is high.’’ The preceding rule is written in a different form than used in the KBS for brevity, although the logic is the same. The rule output is displayed in generated reports that outline the possible sources of the fault as well as a list of corrective measures for the purpose of returning the process to normal operating conditions. 4. Monitoring system and KBS evaluation 4.1. Polymerization reactor simulation The system used for evaluation of the KBS performance is a simulation of the polymerization of vinyl acetate in a CSTR. The simulation, developed by Teymour 关32兴, consists of four ordinary differential equations for the reactor temperature, solvent volume fraction, monomer volume fraction, and the initiator concentration in the reactor, as well as three differential equations for the mo-


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Fig. 4. T 2 and SPE charts in response to a 5% increase in the reactor feed temperature for 60 min. The time of occurrence of the disturbance is indicated by a short vertical bar.

lecular weight moments of the reactor. The moments are functions of the polymer chain reaction kinetics as well as the probabilities of polymer chain propagation, and are used for the calculation of the various polymer molecular weights, polydispersity, and conversion. Variables that are ‘‘measured’’ and displayed by the KBS include the polydispersity, reactor temperature, conversion, and the reactor initiator concentration. The five manipulated variables are the reactor cooling jacket temperature, the initiator concentration in the feed stream, the feed stream temperature, the feed solvent volume fraction, and the residence time. The four monitored system output variables are assumed to be available via analytical methods at 1-min intervals for the physical system. The assumption is valid for the reactor temperature, conversion, and initiator concentration, though the polydispersity measurement in a physical system may take up to 30 min or more to obtain via analytical monitoring techniques. The manipulated variables are modified by adding random fluctuations to each of the inputs. The noise simulates slow changes in the reactor feed conditions, resulting in low-magnitude reactor dynamics. Disturbances may be added by changing the values of manipulated variables. The CSTR simulation is implemented as an external function that solves the reactor ordinary differential equations 共ODEs兲

using CVODE, an ODE solver written in C language. The CVODE software 关33兴 is a set of C libraries that are used with a C function for the ODE equations. G2 software sends reactor data to the ODE solver via the GSI bridge and receives the computed system outputs for the next time interval. 4.2. KBS performance Two case studies are presented. The first case study illustrates monitoring and identification of process variables responsible for inflating the monitoring statistics. These variables can be used by plant personnel or a KBS for fault diagnosis. The second case study illustrates the integration of process monitoring and sensor auditing, demonstrating how an integrated system prevents potential false alarms due to sensor malfunction. 4.2.1. Case study 1 A case study was performed to investigate the response of the T 2 and SPE charts to a moderate disturbance in one of the monitored process variables. A 5% increase in the reactor feed temperature was introduced to the system and maintained for 60 min before returning the feed stream to normal operating conditions. As expected, the multivariate charts are the first indicator of the distur-

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Fig. 5. Shewhart charts of process variables in response to a 5% increase in the reactor feed temperature for 60 min.

Fig. 6. Contribution plots based on data collected after a 5% increase in the reactor feed temperature. Variables shown are reactor initiator concentration 共1兲, reactor conversion 共2兲, reactor temperature 共3兲, and reactor polydispersity 共4兲. Contributions are normalized 共0–1兲.

Fig. 7. Explanation of contribution charts after a 5% increase in the feed temperature.


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Fig. 8. Univariate charts after a bias change is introduced to the reactor conversion sensor. The time of occurrence of the disturbance is indicated by a short vertical bar.

bance on the system. The T 2 statistic exceeds the 99% confidence interval 25 min after the disturbance was introduced 共Fig. 4兲. The SPE statistic exceeds the 99% confidence interval 20 min after the disturbance, earlier than the T 2 chart, in response to the rapidly changing process variables. The initiator concentration in the reactor exceeds the statistical limits of the Shewhart chart after 35 min. Reactor temperature and conversion exceed the statistical limits after approximately 40 min and the polydispersity measurement exceeds the univariate limit after 44 min 共Fig. 5兲. The contribution chart 共Fig. 6兲 shows the normalized contribution of each variable to the out-of-control states. The contributions of each variable from 共8兲 are summed and the ratio of the contribution from each variable to the sum of the total contributions is plotted. The bars in Fig. 6 represent the percent-

age contribution of each variable to the out-ofcontrol T 2 value. The KBS automatically displays a message that the reactor temperature contributes to over 99% of the out-of-control T 2 value 共Fig. 7兲. The case study shows that the multivariate statistical tests reveal that the process is out of control significantly earlier than the univariate Shewhart chart in Fig. 5. The SPE statistics performs somewhat better than the T 2 , while the contribution charts correctly explain that the reactor temperature is responsible for causing the multivariate statistics to exceed their respective limits. The multivariate statistics outperform the univariate Shewhart charts because the multivariate techniques monitor the squared distance between the current and nominal process variables, whereas

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Fig. 9. T 2 and SPE charts after a bias change is introduced to the reactor conversion sensor. The time of occurrence of the disturbance is indicated by a short vertical bar.

Fig. 10. The residual means and variances 共denoted by ⫻兲 for the test data set and the statistical limits 共solid line兲 after a bias change is introduced to the reactor conversion sensor. Variables shown are reactor initiator concentration 共1兲, reactor conversion 共2兲, reactor temperature 共3兲, and reactor polydispersity 共4兲.


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Fig. 11. T 2 and SPE charts indicating normal operating conditions after sensor 2 is removed from the calibration and test data sets. The time when the new model was developed is indicated by a short vertical bar.

Fig. 12. Univariate charts after sensor 2 is removed from the calibration and test data sets.

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Fig. 13. The residual means and variances 共denoted by ⫻兲 for the test data set and the statistical limits 共solid line兲 after sensor 2 is removed from the calibration and test data sets. Variables shown are reactor initiator concentration 共1兲, reactor conversion 共2兲, reactor temperature 共3兲, and reactor polydispersity 共4兲.

the univariate chats can only monitor a single variable at a time. 4.2.2. Case study 2 The first case study is designed to examine the performance of individual features of the KBS. Case study 2 is performed to examine the synergy between the multivariable charts and the sensor audit routine. A bias is added to the reactor conversion measurement with a magnitude of about 5% of the current reactor conversion 共sensor 2兲. Immediately after the bias change is introduced to the sensor, both the univariate chart for reactor conversion 共Fig. 8兲 and the multivariate T 2 and SPE charts 共Fig. 9兲 indicate an out-of-control condition. The KBS automatically begins the sensor validation routine to determine the source cause of the inflated T 2 and SPE. Fig. 10 illustrates that the residual mean for sensors 1 共initiator concentra-

tion兲, 2 共reactor conversion兲, and 4 共polydispersity兲 have exceeded the in-control statistical limits. Sensor 2 has the highest ratio of the residual mean to the limit and is therefore removed from the calibration set and test data sets and a new CVSS model is developed automatically by the software. After the new CVSS model is constructed, the T 2 and SPE statistics immediately return to within the NOC limits 共Fig. 11兲. The statistical limits for the T 2 and SPE are automatically recalculated by the KBS, depending on the number of sensors monitored by each statistic. The univariate chart for the reactor conversion continues to indicate the process is operating out of control 共Fig. 12兲. However, the sensor audit routine has successfully shown that only the reactor conversion measurement is biased, and the remaining sensors are operating correctly as indicated by the in-control re-


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duces the amount of data that must be continuously analyzed by process operators. Consequently, process faults may be detected more rapidly and consistently by the integrated KBS than by using statistical or knowledge-based techniques exclusively.

References

Fig. 14. Explanation of a sensor fault after a bias change is introduced to the reactor conversion sensor.

sidual means and variances after sensor 2 is removed from the model and test data sets 共Fig. 13兲. The KBS reveals that the reactor conversion 共sensor 2兲 is corrupted by a bias change 共Fig. 14兲. 5. Conclusions A process monitoring and fault diagnosis system integrating multivariate statistical techniques with knowledge-based techniques was developed. Use of MSPM charts such as T 2 and SPE results in improved monitoring of the multivariable process when compared to the use of univariate SPM techniques. Contribution plots are able to select the variables causing the disturbances in the T 2 chart, and through the use of process knowledge stored in production rules, the root cause of the disturbances can be diagnosed on-line. The system gives the user access to model-based monitoring tools and knowledge-based diagnosis techniques integrated in a real-time system with an easy user interface. Sensor auditing was developed for multivariable continuous processes based on functional redundancy generated by a state space process model. The method can detect and discriminate between bias change, drift, and noise. The method can be implemented to run repeatedly at frequent intervals based on data sets collected for a sufficiently long period and warn plant personnel about incipient sensor faults. The integration of statistical tools with knowledge-based techniques re-

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Eric Tatara received his B.S. and M.S. in chemical engineering from Illinois Institute of Technology in 1997 and 1999, respectively. He is currently a Ph.D. candidate in the Process Modeling, Monitoring and Control Group in the department of Chemical Engineering at Illinois Institute of Technology. His research interests include statistical process control, artificial intelligence, and modeling and monitoring of complex systems. Ali Cinar has received his Ph.D. in chemical engineering from Texas A&M University in 1976. He is currently Professor of chemical engineering and Dean of the Graduate College at Illinois Institute of Technology. His research interests include statistical process monitoring and fault diagnosis, supervisory control of process operations by integrating, system theoretical, statistical and artificial intelligence–based techniques, and modeling and monitoring applications in biomedical engineering.