Detection of faults in Batch Processes: Application to an industrial fermentation and a steel making process Abstract Introduction

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1 Detection of faults in Batch Processes: Application to an industrial fermentation and a steel maing process Barry Lennox *, Gary Montague + and Ognjen Marjanovic * * Control Technology Centre Ltd, School of Engineering, University of Manchester, UK + Dept. of Chemical and Process Engineering, University of Newcastle-upon-Tyne, UK Abstract This paper describes the application of multivariate statistical process control to two industrial case studies. These two studies involve the monitoring of a fed-batch fermentation process and a LD Converter, which forms part of a steel maing process. For the fed-batch fermentation process it is demonstrated that Principal Component Analysis enables the early detection and isolation of process faults. It is further shown that Partial Least Squares is able to provide an indication of final product quality in both the fermentation and steel maing process. This is particularly important as in both systems, it is not possible to measure product quality using on-line sensors. Introduction The ability to detect and isolate the cause of process faults is of great importance in the process industries. It has been estimated that poor management of process faults loses the US petrochemical industry $20 billion per year (Vedam, 999). Accurate early detection and isolation of fault conditions has the potential to provide operators and engineers with valuable information that could help them to better manage such situations. Statistical Process Control (SPC) is one tool that can provide process operators and engineers with early warnings of fault conditions. The concept of SPC is that current operating conditions, measured in terms of the mean and variation of product quality variables, are compared with the conditions that were recorded when the process was nown to be operating free from faults. Any change in the statistical nature of the product quality measurements indicates abnormal conditions which should then be investigated. Despite its successful application to industrial process monitoring there are several limitations of SPC. Typical industrial processes can contain hundreds of sensors. For monitoring purposes SPC requires each sensor to have its own monitoring chart, which is impractical in situations where there exist many tens or hundreds of sensors. A further limitation of SPC is that an underlying assumption of the approach is that all the process variables are independent of one another. This is rarely the case with complex processes and can cause the technique to fail to identify fault conditions. A more appropriate method of detecting and isolating process faults is to utilise multivariate statistical process control (MSPC) approaches (Wise and Gallagher 996; MacGregor and Kourti, 995). MSPC relies primarily on two statistical projection techniques, Principal Component Analysis (PCA) (Jacson, 99) and Partial Least Squares (PLS) (Geladi and Kowalsi, 986). In terms of its application to industry, MSPC has been demonstrated in several studies to be a very capable tool for the detection and isolation of fault conditions. In this paper details are provided regarding two industrial case studies aimed at evaluating the suitability of MSPC techniques to provide condition monitoring capabilities. The two case studies involve a fed-batch fermentation process, operated by Biochemie Gmbh and a LD Converter, operated by SSAB Oxelösund (Swedish Steel), which forms part of a steel manufacturing process. Multivariate Statistical Process Control Principal Component Analysis (PCA) Although there maybe tens or even hundreds of plant variables that are recorded on any given process plant, there tend to be a much smaller number of underlying characteristics that actually drive the process. PCA is a technique that can be used to identify a new set of variables that reflect these characteristics. These new variables, termed scores, are linear combinations of the original plant variables. The expectation is that there will be fewer scores than plant variables and therefore the plant can be monitored with much greater ease by simply considering these new variables. Process monitoring is achieved through PCA by developing a PCA model on process data that is free from faults. This model then acts as a template which new operating data can be compared with. Deviations from the template indicate the presence of abnormal conditions, possibly resulting from a process fault. As with SPC methods, process monitoring with PCA is achieved through the construction of control charts. There are many different control charts that have been proposed for use with PCA, the most frequently applied being T 2 and SPE charts. T 2 and SPE are two univariate parameters that are able to characterise new data. The T 2 variable indicates how close to the mean

2 operating conditions the plant is currently operating and the SPE provides a measure of how closely the relationships that were present in the original data, used to develop the PCA model, hold in the current conditions. Partial Least Squares (PLS) High levels of collinearity between process variables can cause problems when attempting to identify models of process systems using standard approaches, such as Ordinary Least Squares (OLS). PLS is an identification tool that is suitable for use in such situations. PLS firstly divides the process variables into cause and effect factors. Then lie PCA, it identifies the underlying features in the cause and effect variables. Unlie PCA, however, PLS identifies the features in the cause variables that can most accurately describe the effect variables. Although, PLS can be used in a similar way to PCA for process monitoring, in this wor it is used for or on-line prediction of difficult to measure quality variables. The mathematics involved in PCA and PLS is provided, briefly, in the appendix. Multi-way MSPC MSPC techniques were initially developed for application to continuous processes. The case studies that are reported in this paper, however, are batch in form. This represents two major problems for the application of MSPC techniques. The first is that batch processes tend to be highly non-linear and operate around pre-specified trajectories, rather than fixed levels. The second problem is that batch data sets are typically stored in 3-dimensional arrays, with the three dimensions being number of variables, number of observations and number of batches. To resolve these problems, Nomios and MacGregor (994) proposed multi-way MSPC. In this technique the 3-dimensional array is unfolded into a 2- dimensional array as illustrated in figure. The unfolded matrix in then scaled, such that each column has zero mean and unit variance. In the studies reported in this paper, the effect variables are single measurements of product quality measured at the end of the batch. These measurements are collated into a single column array. Sample mx Batch nb nx Variable Original X Unfolded X nb nx * mx Figure : Unfolding Technique Following the unfolding of the 3-dimensional array, PCA and PLS can be applied. Process monitoring using the unfolded array allows deviations from nominal trajectories to be considered. The unfolding procedure also removes the major non-linearities from the data. Case Study : Biochemical fermentation systems are highly sensitive to abnormal changes in operating conditions. To ensure that the maximum possible yield of product is obtained from the system it is necessary to ensure that conditions within the fermenter remain closely fixed around a pre-specified trajectory. In many industrial fermentation systems process operators use their experience and nowledge of the fermentation process to detect potential problems and mae modifications when necessary. The importance of effective operator control cannot be underestimated as the performance of a fermentation is very much dependant upon the ability to eep the system operating smoothly. A fermentation that is free from major upsets is liely to be more productive than one subject to significant disturbances. Therefore, the earlier a potential problem to the system can be detected, the less severe its influence on the system will be and the resulting corrective action will consequently be more restrained. The aim of this project was to develop a process monitoring system for an industrial fed-batch fermentation system. A multi-way PCA model was initially developed from historical data from ten high yield industrial batches, referred to as nominal batches. The reason for using data collected from high-yield batches only is that the purpose of the monitor is to identify if any subsequent batches deviate from the conditions that are expected of a high yield batch. The T 2 and SPE charts produced

3 by this PCA model for the nominal batches are displayed in figure 2. Figure 2: Control Charts for Reference Batches The ability of this model to monitor a number of subsequent batches was then determined. Some of these batches operated smoothly whilst others were affected by disturbances. Figure 3 shows the control charts that were calculated by the PCA model during a batch that contained a fault. The fault that occurred during this batch was an intermittent drift on a ph sensor. This drift occurred between sample numbers 40 and 70 and 00 and 50. Figure 3 demonstrates that this sensor fault is detected by violations of the SPE confidence limit. determined by analysing the contribution that each variable maes to the SPE statistic. In this example, this correctly identified the ph sensor as the liely cause of the fault. The effect variable in this application is the concentration of biomass in the fermenter. Unfortunately, this value is measured through a laboratory assay and is therefore only available at infrequent intervals during the batch. This represents a problem to operations staff as for long periods of time they have no direct measurement of the quality of the batch. To help provide this information, a multi-way PLS model was used as a prediction tool to estimate the end concentration of biomass in the fermenter. In this way, the PLS model acts as a classification system and can be used to indicate if the current batch is more consistent with high or low yield batches, as such the nominal data used to develop the PLS model contained measurements recorded during both high and low yield batches. Figure 4 shows an example of a multi-way PLS monitoring chart. This chart shows the final biomass concentration (solid line), estimated at each sample time during the batch, 95% confidence limits (dashed line) and the actual final concentration of biomass (thin solid line). It can be seen from figure 4 that for this batch, which proceeded upset free, the PLS estimate of the final product concentration was reasonably accurate throughout. The accuracy of the PLS model displayed in figure 4 was consistent with that produced for several other batches. This level of accuracy maes the PLS model a useful tool for monitoring the progress of the fermentation system for this particular application. Figure 3: Control Chart for Test Batch The reason that the fault is not identified in the T2 chart is that this chart is able to detect significant changes in operation and high impact faults. A fault such as this, a small drift on a sensor is unliely to be detected in the T 2 chart. The cause of this fault can be Prediction Actual Conf Limit Sample Time Figure 4: PLS Monitoring Chart Although it is difficult to identify the exact financial benefits of employing MSPC technology on a fed-

4 batch fermentation process, it is worth considering that the contents of a given fermentation may be worth in excess of $500,000. If a fault can be detected and acted upon before it is able to affect the progression of the batch then there is a clear benefit to the adoption of MSPC. MDC Technologies estimate that the typical benefits of applying MSPC tools is approximately $250,000 to $,000,000 pa *. Case Study 2 The second application involves a batch operated process that forms part of a SSAB Oxelösund (Swedish Steel) steel-maing plant. The process, termed a LD converter reduces the carbon levels in iron by blowing oxygen into a bath to form low carbon steel. Two inert gases, Ar and N 2, are blown from the furnace bottom to mix the bath. The blowing process taes approximately 20 minutes per batch and is split into three phases. During the first phase, which lasts between 3-6 minutes, Si, Mn and Fe are oxidised and lime is dissolved to form slag. The second phase taes approximately 5 minutes and commences after the Si has been oxidised. The decarburisation rate is almost constant during this stage, and decreases rapidly during the brief third phase due to carbon depletion in the metal, which results in heavy Fe oxidation. The briefness of the third phase, typically less than two minutes, maes it difficult to stop the oxygen blowing at the correct time. More accurate timing of the oxygen shut-off would allow the carbon target to be achieved more closely and lead to a reduction in average blowing time and an increase in product consistency. If the FeO content in the slag could be measured then it be used to define the batch endpoint and thus indicate when to cease oxygen blowing. Unfortunately, harsh conditions within the process mean that it is not possible to tae any direct measurements of FeO content in the slag. The alternative to measuring the FeO content in the slag is to attempt to infer it using the measurements that are taen on this process. The objective for this case study was therefore to provide an on-line prediction of FeO content in the slag. Static measurements of FeO, along with many other concentrations, are available at the end of each batch. The first problem encountered in this application was that the multi-way MSPC approach requires that the run-length of each bath be the same. Whilst this was true for the fermentation process, the run-length varied by a magnitude of three in this process. Although more complicated methods exist, such as dynamic time warping of data (Kassidas et al, 998), the standard approach to coping with variable run lengths is to simply determine the shortest run length and then ignore the data collected after this time in all batches. For the LD Converter this approach is unsuitable because it is the data collected towards the end of the batch, the third phase of operation that is of particular concern. The method that was adopted in this study was to ignore the dynamic data collected at the start of the batch and to use the static data, collected at the start of the run, along with the dynamic data collected during the latter stages of each batch. It was found that if the final 50 samples were used from each batch then this encompassed the third phase of operation for each batch. In all, 35 static variables were included and 5 dynamic variables, with a window length of 50 and a sample interval of 6 seconds, giving a total of 285 variables in the unfolded matrix. After initial evaluation, records of 9 batches were included in the analysis. The first 80 batches were used for PLS modelling and the remaining batches used for evaluation. The prediction accuracy of the approach is illustrated in figure 5. The PLS model that is used to generate these predictions contained 5 latent variables. In this figure the first 80 measurements were used to develop the PLS model, with the remainder being used to evaluate it. It is evident from figure 5 that the model is far from perfect, however, it is capable of identifying the major trends in the FeO measurement. The quality of prediction is viewed very favourably by SSAB who at present have no comparable method of identifying FeO content on-line. There are many measurements that are recorded on this process. The majority of these measurements are static and relate to the analysis of materials entering the bath. The remaining measurements can be considered to be dynamic and include the flow-rate of oxygen into the bath and the decarburisation rate. *

5 FeO * * Predicted FeO Actual FeO Batch Number Figure 5: PLS Prediction of FeO Clearly, in an on-line implementation, the endpoint of the data is not nown in advance, therefore it is not nown what data from the current batch should be used in the model. So, for the purposes of on-line FeO prediction, the model is run over a moving window of fifty samples, which provides a rolling estimate of the iron oxide concentration. It is envisaged that the endpoint would be declared, and oxygen blowing ceased, when the predicted FeO concentration reached a pre-defined level. Figure 6 shows a simulated run of the on-line predictor using a typical batch from the evaluation set Figure 6: On-line FeO Prediction Figure 6 shows that the initial predictions of FeO are poor. This is because the model was developed on data from the end of batches and thus cannot reproduce the behaviour of the first stage of the blowing process. As the batch progresses, the predictions improve and tend towards the endpoint value. The PLS model, reducing the prediction problem from 285 variables to five latent variables thus provides an accurate on-line indicator of FeO concentration from which the endpoint of the batch may be more accurately predicted. Conclusions This paper has provided details of two successful industrial applications of multivariate statistical technology. The applications described in this study, a fed-batch fermentation and a steel maing plant, both operate in batch mode. Batch is seen as a particularly relevant area to wor in at present as there is an increasing shift to batch as customer requirements change from low quality, high production to high quality, reduced production. In the fermentation process, it was shown that Principal Component Analysis could be used to detect and isolate the cause of process faults. It was further shown that Partial Least Squares was able to provide on-line inference of product quality. This technique was extended to the steel maing plant where it was shown that Partial Least Squares could also infer product quality. Such measurements can be used to improve product quality and efficiency. References Geladi, P. and Kowalsi, B.R., 986, Partial least squares regression: a tutorial, Anal. Chim. Acta., 85, -7 Jacson, J.E., 99, A User s Guide to Principal Components (Wiley) Kassidas, A., MacGregor, J.F. and Taylor, P.A., 998, Synchronisation of batch trajectories using dynamic time warping, AIChE Journal, 3-25 MacGregor, J.F. and T. Kourti, 995, Statistical process control of multivariate processes, Contr. Eng. Pr., 3 (3), Nomios, P. and MacGregor, J.F., 994, Monitoring batch processes using multi-way principal component analysis, AIChE Journal, 40 (8), Vedam, H. and Venatasubramanien, V., 999, PCA- SDG based process monitoring and fault detection, Contr. Eng. Pr., 7, Wise, B.M., Gallagher, N.B., 996, The process chemometrics approach to process monitoring and fault detection, Journal of Process Control, 6 (6), Wold, S., 978, Cross-validatory estimation of the number of components in factor and principal components models, Technometrics, 34,

6 Appendix: Mathematics of PCA and PLS Principal Component Analysis PCA transforms a matrix containing measurements from n process variables, Z, which is typically scaled to zero mean and unit standard deviation., into a matrix of mutually uncorrelated variables, t (where = to n). These variables, called principal components (PCs), are transforms of the original data into a new basis defined by a set of orthogonal loading vectors, p. The individual values of the principal components are called scores. The transformation is defined by: np T [ Z ] t p + E = < = n () The loadings are orthonormal, and hence become the eigenvectors of the data covariance matrix, Z T Z. The t and p pairs are ordered so that the first pair captures the largest amount of variation in the data and the last pair capture the least. In this way it is generally found that a small number of PCs (np) can account for much of the variation in the data, with the remaining PCs constituting the error term, E. When eqn. is applied to a single vector of new process measurements, z T, the resulting term E is called the prediction error. There are several methods for determining the suitable value for np. One method is to continue to add PCs until the variation explained in the retained PCs exceeds a particular value, however a more suitable approach, and the technique that is adopted in much of this wor, is to use cross validation (Wold, 978). Partial Least Squares PLS is a tool that can be applied whenever plant variables can be partitioned into cause (X) and effect (Y) values. The method may be used for regression and, lie with PCA for the reduction of the effective dimensionality of data. The approach wors by selecting factors of cause variables in a sequence which successively maximises the explained covariance between the cause and effect variables. Given a matrix of cause data, X, and effect data, Y, a factor of the cause data, t, and effect data, u, is evaluated, such that np< nx np< nx T T t p + E and Y = uq + = = X = These equations are referred to as the outer relationships. The vectors t are mutually orthogonal. These vectors and the u are selected so as to maximise the covariance between each pair, (t, u ). Linear regression is performed between the t and the u, to produce the inner relationship, such that: u = bt + ε where b is a regression coefficient, and ε refers to the prediction error. The PLS method provides the potential for a regularised model through selecting an appropriate number of scores, or latent variables, u in the model. Furthermore, it is often found that a relatively small number of the low-index latent variables can explain the greater part of the variation in both the cause and effect variables. As with PCA, cross validation can be used to select the necessary number of latent variables. F *