Single channel event (SCE) for managing sensor failures in MSPC

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Abstract

This paper makes use of the single channel event (SCE) index for managing sensor failures. The SCE index provides prior information how and if a sensor failure is detected in multivariate SPE and D control charts. Furthermore, the SCE index can be used as a diagnostic tool for multivariate monitoring schemes of industrial processes. These features of the SCE index attribute to improved abnormal situation management. The usage of the SCE index is demonstrated for the Tennessee Eastman continuous process.

Introduction

Multivariate statistical tools have been applied successfully to monitor industrial processes (continuous and batch). This is not only proved by the number of scientific articles that have been published so far. Also the development of commercial software applications that make use of multivariate tools for process monitoring purposes has increased. This includes software applications developed by large companies such as Aspen Tech. Numerous case studies and industrial applications showed that multivariate process monitoring is well suited for process improvement. These improvements lead to safer, cleaner and more cost effective production. In the near future, more companies will use multivariate monitoring methods to improve their processes.

One of the goals of multivariate statistical process control (MSPC) is to detect disturbances. Disturbances can cause process operations to deviate from their normal operating conditions (NOC). These disturbances may result in, e.g. loss of production/quality or dangerous situations. Therefore, it is very important to detect abnormal situations as fast as possible. A common abnormal event is the failure of a sensor that records the ongoing of the process. Consider a temperature sensor placed inside a polymer reactor that is broken for some reason. Will the broken sensor be detected in the multivariate charts? Besides, this also depends on the physical value that the sensor produces when it is broken. It might be true that deviations from the set point are too small in order to be detected in the multivariate charts. In that case, the broken sensor will fail to detect a dangerous runaway of a reactor. As a result, the polymer hardens inside the reactor and all its piping. This leads to a great economic loss. In serious cases, the abnormal situation may endanger human life.

One aspect of managing unknown process disturbances is to investigate a signal that is induced in one of the multivariate charts. It is important to understand the cause of this event. This is commonly referred to as fault isolation. A commonly used fault isolation approach (based on multivariate statistical models) are contribution plots (Miller, Swanson, & Heckler, 1998). In case of a sensor failure, the contribution plot ideally reveals one variable that contributes most significant to the multivariate signal in, e.g. the SPE chart. For more complex faults such as fouling or set-point changes, contribution plots are more difficult to interpret. Dunia and Qin (1998) suggested a method for fault isolation via reconstruction. This method enables separation of faulty sensor from the remaining ones. Another approach to interpret multivariate signals is to make use of fault signatures. The current multivariate event is compared to a database of reference fault signatures. An overview of such methods is presented by Yoon and MacGregor, 2001, Yoon and MacGregor, 2000.

In order to further improve the management of sensor failures in multivariate monitoring schemes, a power analysis tool is presented based on the “single channel event” (SCE) index. First, the SCE index provides a quick answer to the question how and if a sensor failure is detected. This provides an added diagnostic value to undertake corrective actions. If these answers are not satisfying, a strategy is proposed to improve detection of sensor failures. Second, the SCE index can be used for MSPC model validation, e.g. what sensors should be included or removed from the MSPC model. The SCE index can be used a priori, that is, prior to monitoring the current process. Furthermore, the SCE index does not require a library or database of know process disturbances. The effects of the MSPC model parameters to the SCE index are studied and applied to the Tennessee Eastman continuous process.

Section snippets

Geometry of sensor failures

Multivariate statistical monitoring is generally based on a set of raw process data and a principal component analysis (PCA) model. Assume that the process data is derived under NOC. For various reasons, it is worthwhile to describe the NOC data by so-called latent variables. To do this, the original variable space is transformed into a latent variable space. This is what the PCA model is used for. The latent variable space constructed with PCA is represented by the loadings, scores and

Single channel event index

In this section, the mathematical derivation of the SCE index is described. The term “single event” refers to the situation of a failure of one sensor. More important, the sensor is not included in a control loop. Therefore, fault propagation in the presence of feedback is not applicable. The term “channel” is used as a more common term for “process variable”. The SCE index can be calculated for the SPE and D chart and represents the magnitude of a sensor failure that is required to exceed the

SCE index for the Tennessee Eastman process

The usage of the SCE index is demonstrated for a well-known industrial process: the Tennessee Eastman process. This process involves two simultaneous gas–liquid exothermic reactions. A detailed description of the process is given in the paper by Downs and Vogel (1993). The process has five major unit operations: the product condenser, a vapor–liquid separator, a recycle compressor and a product stripper. The process produces two products (G and H) from four reactants (A, C, D and E).

Discussion of the results

Once the SCE index is calculated, the values can be compared to the physical value that a broken sensor produces. From this, it can be established whether the monitoring charts are capable of detecting sensor failures. This provides valuable information that plays an important role in fault detection management. Unfortunately, these physical values are unknown for the Tennessee Eastman data.

The results that are found for the SCE index can also be used as a diagnostic tool to investigate the

Conclusions

In this paper, the SCE index is introduced. The SCE index proved to be a helpful tool to manage sensor failures in the SPE and D chart. The values of the SCE index can be compared to the physical values that a broken sensor records. This provides valuable information to increase safety of productivity. Furthermore, the SCE index is helpful to investigate the diagnostic properties of the SPE and D chart prior to monitoring new samples. If these properties are unsatisfying, solutions are

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