1. Introduction

Process monitoring, fault detection and isolation (FDI) is an essential issue in the field of process control. At first FDI deals with the determining whether the process is under normal condition or not then it is responsible for locating source of the fault (Venkatasubramanian V, etal. 2003). Most of the processes are multivariate and complicated which defy the model based process monitoring approach, hence methods based on statistical process monitoring (SPM) has become one of the active research areas (Joe Qin S. 2003).

An important characteristic of chemical processes is that they are multivariate with huge amount of measured data but with poor information. PCA which is a multivariate statistical process monitoring method deals with this kind of problem and is used in process monitoring. In real chemical processes, however, difficulties may arise because the PCA method is linear and processes are nonlinear. Therefor non-linear principal component analysis (NLPCA) is presented as remedy which generalizes PCA to nonlinear processes (Dong, D., J. McAvoy, T. 1994). NLPCA is implemented in different ways; including using artificial intelligence or most specifically in this study Neural Networks (NN) is used. There are two types of NLPCA based on neural networks; Input training neural networks (IT-NN) and Auto-associative neural networks (AANN). Owing to some inherent useful specifications of the AANN especially in the field of sensor fault diagnostics, this types of neural network is preferred.

The basic idea of SPM based on auto-associative neural networks is to find a NLPCA model for a set of correct data from a healthy system and healthy measurements. Then apply PCA transformation to a testing data. We consider the system to be healthy if this set of testing data complies with the original calibration AANN model (Najafi N., etal. 2004).

Generally, there are three types of faults; process faults, actuator faults and sensor faults. Sensor fault is the most important, because making control decision based on non-accurate measurements may lead to disastrous results and control system becomes unreliable. For supplying the data needed for a fault tolerant system and locating the source of the fault, there needs redundant sensors. However, introducing redundant sensors is expensive because of the cost of the extra sensors and their maintenance. It also imposes a levy on control hardware and software (Najafi N., etal. 2004) and (Sing H., 2004). Sensor FDI is a field which focuses on detection and isolation of sensor faults. In this paper we present an auto-associative neural network based algorithm which is able to detect, isolate and also reconstruct single and multiple sensor faults. The algorithm is based on the inherent characteristic of AANN. Sensor faults are errors which occurred in sensors due to calibration, biasing, drifting, etc.

AANN is used in Enhanced-AANN algorithm (Najafi N., etal. 2004) for single FDI, but we go further and propose an algorithm for multiple FDI which is a novelty introduced in this paper.

AANN structure and its specifications are explained in section 2. Fault detection using AANN is described in section 3.Section 4 is devoted for describing the main algorithm for single fault. Extending the algorithm for multiple faults is done in Section 5. The case study used for testing the algorithms and data generation is described in section 6.In section 7 results and discussions are presented and finally our conclusions are presented in section 8.

2. Auto-associative neural networks

Auto-associative neural networks are five layer feed forward networks including: input layer, mapping layer, bottleneck layer, de-mapping layer and output layer. The network outputs are trained to imitate the inputs. The network inputs are the process variables (including process input or output variables) which have a degree of correlation.  Number of nodes in the input and output layers are equal to process variables and number of nodes in the other layer is determined by trial and error based on network performance (Dong, D.J.McAvoy T., 1996). The hidden layers do the role of maintaining the correlation of variables based on the training data. Figure 1 illustrates the AANN structure.

Figure1

AANN structure (Najafi N., etal. 2004)

AANNs have some intrinsic specifications which have made it useful for sensor fault diagnostics, as follows:

1. AANN has identity mapping which is essential for sensor fault diagnostic.
2. Correlation between the variables is captured into the network weights during the training. This is used for faulty sensor reconstruction.
3. AANN can do a degree of noise reduction (Mathisen M.L., 2010)
   1. Fault detection using AANN

After determining the AANN structure, it is trained using normalized healthy data and monitoring statistics such as Squared Prediction Error (SPE) or Hotelling T² are calculated. This paper analyses SPE for process monitoring, because the SPE may have lower changes to give false alarms in process monitoring (T.R. Borgan., 2011). Then normalized faulty data is presented to AANN and SPE statistic is calculated using AANN output. If one of the variables is faulty then control limit of SPE is exceeded and the fault is detected. SPE and T² and their control limits are elaborated in reference (Thissen U., 2001). After a fault is detected it should be isolated (localized), which will be explained in the following section.

3. Self-reconstructing AANN (S-AANN) algorithm for single fault isolation

Due to interrelation between the process variables and the fact that AANN captures the correlation in its weights, if one of the sensors goes out of calibration or fails, the output of AANN will show an estimation of the corrected value of the sensor. In  real  cases,  as  Kramer  has  explained  in  his  original  paper  (Kramer M.A., 1991), when  we  have  a  faulty  measurement  in  one  of  the  sensors,  all  of  the  AANN output  values would  be  distorted.  However,  we  are  able  to  single  out  the  faulty  sensor  by  analyzing  the residue  vector  between  the  input  and  output,  because  it  is  expected  that  the  maximum absolute value of residue is in the faulty sensor (Kramer, M.A 1991). After finding the faulty sensor, the next step is to feed the estimated value of the faulty sensor to AANN input. After several iterations, all of the residues will approach to zero and we reconstruct the value of the faulty sensor. This procedure has been shown in the diagram of figure 2.

Figure2

reconstruction of a faulty sensor using S-AANN algorithm (M. Sharifi, 2009)

Difference between input and output of the algorithm is calculated. Mean of the difference for faulty sensor is nonzero and hence the faulty sensor is localized.

4. Extending the S-AANN for multiple-faults

The above algorithm is for isolation of single faulty sensor. The S-AANN algorithm can be extended to be applicable in multiple-fault condition. The procedure is the same as the above algorithm, but reconstruction is repeated for all the sensors, respectively. The sensor with the higher index k is reconstructed first.

5. Case study

An open loop Dimerization process is used to test the algorithms. One of the most economic methods for producing butene-1 is the catalytic dimerization of ethylene. The industrial ethylene dimerization reactor operates in a liquid phase at bubble point conditions.  Fresh ethylene and homogenous catalyst are fed continuously to the reactor where the heat of the exothermic reaction is removed by means of an external cooler. The cooler is installed on the recycle pipelines. The recycle returns portion of the product back to the reactor. The ethylene dimerization process is strongly nonlinear. According to industrial practice, extreme regular monitoring of the process variables is necessary (E. Ali and K. Al-humaizi, 2004). Sensors and measuring instrument are very essential in this process and need regular maintenance and monitoring, because the measured values are used for the process control and they should be reliable. Figure 2 illustrates this process which is occurred in a Continuous Stirred Tank Reactor.

Figure 3

Schematic of the Dimerization reaction process (E. Ali and K. Al-humaizi, 2004).

There are seven possible variables used for process monitoring namely, the coolant flow rate Wc, the feed flow rate Fe, the catalyst concentration in the feed Ak, the feed temperature Tf, the recycle ratio β, the produced Butene concentration Bc, and the reactor temperature T.

5.1. Data generation

Using the Dimerization process model, about 2000 sample data was generated. Each sample data contains 7 variables which were introduced in the above section. About 1% white noise is induced to the dataset to be close to real situation. The dataset is normalized and then is randomized and 1500 samples are selected randomly for training the AANN and the remaining 500 samples are used as the test set. We introduce two types of faults (drift and shift) to the test set and use it for testing the algorithms.

6. Results and discussions

Structure of the AANN for the algorithm is decided to be 7-10-3-10-7 by trial and error. We changed this structure to various numbers of hidden layers and compared the SPE for a known faulty sensor and found that the best structure is 7-10-3-10-7. Scaled conjugate gradient (scg) was adopted as training algorithm. Figure 3 show the normalized training set and Figure 4 shows the normalized test set.

Figure 4

Normalized training set (sorted), X axis is sample number.

Figure 5

Normalized test set (sorted, X axis is sample number.

6.1. S-AANN results for single shift fault

Shift error of 10% is introduced to the sensor number 7 which is a thermocouple, measuring the temperature of the product. The fault is occurred in sample 200 and continues to sample 400. Figure 6 show sensor 7 which has shift error.

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Figure 6

Sensor 7 output, before and after contamination (shift fault)

Fault is detected using SPE statistic (Figure 6). Figure 7 shows sensor 7 output before and after reconstruction. The difference (error) between the S-AANN input and output is shown in Figure 8, and the mean of the difference is shown in figure 9.

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Figure 7

Fault detection using SPE plot

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Figure 8

Sensor 7 output before contamination, after inducing shift error, and after reconstruction by S-AANN

Figure 9

The difference between S-AANN input and output. The input data had shift error. (X axis is sample number)

Figure 10

The mean of the difference between input and output of the S-AANN for shift fault

The results show that the algorithm has reconstructed and isolated sensor 7 as faulty sensor, properly.

6.2. S-AANN results for single drift fault

Drift error is introduced to the sensor number 1 which is an orifice plate, measuring flow rate of the coolant (Figure 11). The fault is occurred in sample 100 and continues to sample 500.

Figure 11

Sensor 1 output, before and after contamination

SPE plot detects the occurred fault (Figure 12)

Figure 12

Fault detection using SPE plot

Figure 12 shows the sensor 1 in different conditions.

Figure 13

Sensor 1 before contamination, after inducing drift error, and after reconstruction by S-AANN

The difference (error) between the S-AANN input and output is shown in Figure 13, and the mean of the difference is shown in figure 14.

Figure 14

The difference between S-AANN input and output. The input data had drift error

Figure 15

The mean of the difference between input and output of the S-AANN for drift fault

From the above results it is clear that although reconstruction is not accurate, but the algorithm has localized the faulty sensor, properly.

The S-AANN has low computational time with respect to E-AANN (Najafi N., etal. 2004). Table 1 show the measured time for a single FDI using the two algorithms.

Table 1

Comparison of computational time for the reconstruction algorithms (drift fault)

6.3. Multiple-fault condition

Multiple-fault is condition in which more than one sensor is contaminated simultaneously. Here we have contaminated three sensors simultaneously from sample 200 to 500. Sensor 2 has drift fault, sensor 6 and sensor 7 have 10% shift fault. The Extended S-AANN discussed in section 5 is applied. Fault detection using SPE plot is illustrated in figure 15.

Figure 16

The SPE plot in multiple-fault condition

Figures 16, 17 and 18 illustrate the sensors in different conditions.

Figure 17

ensor 2 output, before and after contamination and after reconstruction in multiple faults condition

Figure 18

ensor 6 output, before and after contamination and after reconstruction in multiple fault condition

Figure 19

Sensor7 output, before and after contamination and after reconstruction in multiple fault condition

Figures 19 and 20 are the result of the Extending S-AANN algorithm for fault isolation.

Figure 20

The difference between input and output of the algorithm, in multiple-fault condition

Figure 21

The mean of the difference in multiple-fault condition

It is clear that the algorithm has identified sensors 2, 6 and 7 as source of the faults because mean of the differences for these sensors are non-zero.

7. Conclusions

Introducing additional sensors to control system for fault isolation is expensive and may also be taxing on control software and hardware. Therefore fault diagnostic algorithms which are able to isolate the occurred faults have a particular attraction. In this paper we proposed a new algorithm based on auto-associative neural networks (AANN) which reconstructs and isolates the faulty sensor. This algorithm which is called self-reconstructive AANN was extended to be applicable in multiple faults conditions. The algorithms were tested on a Dimerization process. By trial and error we found that, in multiple fault conditions the algorithm can work properly when less than half of variables are faulty which is a limitation for S-AANN. This limitation is related to correlation of variables. The algorithm was shown to be able to isolate the faulty sensors, properly. Due to low computational burden, the algorithm is a suitable candidate for online application. In the future research we are going to improve the E-AANN to obtain a new algorithm with low computational time and more accurate than S-AANN.

Acknowledgment

This research paper is supported by National Iranian Oil Company (NIOC) and Iranian Offshore Oil Company (IOOC)

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