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- 1. Research article A method to remove chattering alarms using median ﬁlters Yongkui Sun a, c , Wen Tan b, * , Tongwen Chen c a School of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan, PR China b School of Control & Computer Engineering, North China Electric Power University, Beijing, PR China c Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Alberta, Canada a r t i c l e i n f o Article history: Received 31 March 2016 Received in revised form 17 May 2017 Accepted 11 December 2017 Available online 27 December 2017 Keywords: Chattering alarms Median ﬁlters Alarm systems a b s t r a c t Chattering alarms are the most found nuisance alarms that will probably reduce the usability and result in a conﬁdence crisis of alarm systems for industrial plants. This paper addresses the chattering alarm reduction using median ﬁlters. Two rules are formulated to design the window size of median ﬁlters. If the alarm probability is estimated using process data, one rule is based on the probability of alarms to satisfy some requirements on the false alarm rate, or missed alarm rate. If there are only historical alarm data available, the other rule is based on percentage reduction of chattering alarms using alarm duration distribution. Experimental results for industrial cases testify that the proposed method is effective. © 2017 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Alarm systems form the essential part of the operator interfaces in large modern industrial facilities such as chemical plants, power stations and oil reﬁneries. An alarm indicates potential problems, and directs the operator's attention towards plant conditions requiring immediate assessment or corrective action. Therefore, alarm systems play an important role in preventing, controlling and mitigating the effects of abnormal situations [1,2]. According to EEMUA [1], every alarm presented to an operator should be useful and an operator should not receive more than six alarms per hour during normal operation of a plant. However, this is the rare case in practice. Alarm variables, on the one hand, are very easily implemented in modern industrial plants that are usually equipped with computerized monitoring systems such as distributed control systems and supervisory control and data acquisition systems. Generally the more alarm variables are conﬁgured, the more safety is deemed to be improved. Therefore, the number of conﬁgured alarm variables has increased exponen- tially [3], and there are tens, hundreds or even thousands of alarms raised per hour. As a result, many existing industrial alarm systems have far too many alarms to be handled by plant operators. Per- formance metrics of existing industrial alarm systems are summarized in Table 1 [4], which are based on a study of 39 in- dustrial plants ranging from oil and gas, petrochemical, power and other industries. The benchmarks in EEMUA [1] are provided for reference. Obviously, the actual alarm rates in the various in- dustries exceed the recommended number of alarms in the EEMUA [1] benchmarks. Alarms can be classiﬁed into nuisance alarms and correct alarms. A nuisance alarm is one that does not require a speciﬁc action or response from operators [1,4]. An alternative deﬁnition of a nuisance alarm is an alarm that annunciates excessively, unnec- essarily, or does not return to normal after the correct response is taken [2]. Hence, nuisance alarms are the ones that do not affect the process, even if these alarms are ignored by operators. A correct alarm is the one that requires operators to pay attention or to take action in prompt manner [4]. However, according to industrial surveys provided by Rothen- berg [4] and Bransby and Jenkinson [5], a majority of alarms that operators of industrial plants received are nuisance alarms. Therefore, nuisance alarms considerably weaken the usability of alarm systems, and often lead to a conﬁdence crisis of alarm systems. Chattering alarms, which are caused by noise or disturbance, are the most found nuisance alarms and may account for 70% of alarm occurrences [3]. A chattering alarm is an alarm that is activated and cleared many times within a short time period. Rothenberg [4] deﬁnes chattering alarms as the ones that activate ten or more times within 1 min, and alarms repeating more than three or more times in 1 min are chattering alarms in the ISA standard [2]. * Corresponding author. E-mail addresses: yksun@swjtu.edu.cn (Y. Sun), wtan@ncepu.edu.cn (W. Tan), tchen@ualberta.ca (T. Chen). Contents lists available at ScienceDirect ISA Transactions journal homepage: www.elsevier.com/locate/isatrans https://doi.org/10.1016/j.isatra.2017.12.012 0019-0578/© 2017 ISA. Published by Elsevier Ltd. All rights reserved. ISA Transactions 73 (2018) 201e207
- 2. Because different types of process variables have different time scales in terms of variation dynamics, there is not a unanimous deﬁnition for chattering alarms in the literature. In this context, considering the sampling period of process variables and general- izing the rule of thumb from the ISA standard [2], for a process variable with the sampling period T, chattering alarms are deﬁned as alarms that repeat more than three times in the duration of sixty times of the sampling period T. Clearly, eliminating the chattering alarms can improve the ef- ﬁciency of an alarm system. Consequently, how to reduce chatter- ing alarms has recently been receiving much attention among engineers and researchers. EEMUA [1] and ISA [2] suggest that some methods be used in practice, such as, ﬁlters, deadbands, delay timers, and shelving, to remove chattering alarms. Izadi et al. [6] presented a procedure based on the Receiver Operating Charac- teristic (ROC) framework to design optimal ﬁlters, deadbands, delay timers by considering two major trade-offs between the false alarm rate and missed alarm rate, and between latency and accuracy. Hugo [7] proposed an adaptive alarm deaband method to reduce the number of chattering alarms via an ARIMA model based on process variable measurement. Naghoosi et al. [8] studied the relation between alarm deabands and optimal alarm limits, and estimated the optimal threshold with respect to the deadband and history of the process variable. In order to quantify the degree of chattering, Kondaveeti et al. [9,10] deﬁned a chattering index based on the run lengths of alarms, and Naghoosi et al. [11] developed a method to estimate the chattering index based on the statistical properties of the process variable as well as alarm parameters, and derived an alarm chattering formula for alarm deadbands to aid in optimal design. Wang and Chen [12] revised the chattering index and proposed an online method to detect the repeating alarms due to oscillation and exploited two mechanisms to reduce the number of chattering alarms. To overcome the drawbacks of the above- mentioned chattering indexes, Wang and Chen [13] formulated two rules to detect chattering and repeating alarms using alarm durations and intervals, and proposed an online approach to remove chattering alarms, using three performance indices, namely, the false alarm rate (FAR), missed alarm rate (MAR) and averaged alarm delay. An efﬁcient design strategy was provided to select an appropriate delay timer using the historical alarm data [14]. Median ﬁlters are nonlinear digital ﬁltering techniques and have been widely used to remove noises in the ﬁeld of signal processing [15]. Median ﬁlters outperform linear ﬁlters in environments where the assumed statistics deviate from Gaussian models and are possibly contaminated with outliers [16]. A method to remove chattering alarms using median ﬁlters is proposed in this paper. Two rules to design the window size for median ﬁlters are formulated. If the past samples of the process variable in the normal and abnormal conditions are available, according to the maximum probability of alarms in 60T (T is the sampling period), a window size is chosen for a median ﬁlter to satisfy the re- quirements on FAR, or MAR. If only alarm data is available, ac- cording to the cumulative distribution function of alarm duration distribution, a window size is chosen to satisfy the reduction per- centage of alarms. The advantages of the proposed graphic design method are its simplicity and ease in implementation, which are desirable for ﬁeld engineer. The rest of this paper is arranged as follows: Section 2 in- troduces some preliminaries for the paper. Section 3 gives a brief introduction to median ﬁlters and discusses its performance. Sec- tion 4 addresses the design steps of median ﬁlters using process data, and presents the simulated results. Section 5 gives a design method based on alarm data, and presents the design example. Finally, some concluding remarks are given in Section 6. 2. Preliminaries This section introduces some terminology used later in the paper. An abnormal situation is deﬁned as an event disturbing a pro- cess that requires the operators to intervene to supplement the control system. This deﬁnition speciﬁcally is used to distinguish among normal, abnormal and emergency situations from the perspective of console operations [1,2]. Assume a process variable xðtÞ has a probability distribution function (PDF) pðxÞ at normal situation, a PDF qðxÞ at abnormal situation, and the high-alarm trip point xtp is shown in Fig. 1, then the deﬁnition of the FAR and MAR are [6]: FAR ¼ Z∞ xtp pðxÞdx (1) MAR ¼ Zxtp À∞ qðxÞdx (2) A chattering index j is an index to measure chattering alarms, which is presented by Kondaveeti et al. [9,10] based on run length distributions: j ¼ X r2N Pr 1 r (3) where r is a run length, which is the time difference between two consecutive alarms on the same tag. Pr represents the probability and Pr ¼ nr , P r2N nr ; c r2N, where nrrepresents the alarm count Table 1 Cross-industry activation study. EEMUA Oil & Gas PetroChem Power Other Average alarms per day 144 1200 1500 2000 900 Peak alarms per 10 min 10 50 100 65 35 Average alarms per 10 min 1 6 9 8 5 Fig. 1. Probability density functions of normal and abnormal data and high-alarm trip point. Y. Sun et al. / ISA Transactions 73 (2018) 201e207202
- 3. for any run length r. The chattering index j of an alarm can be perceived as the mean frequency of annunciation of that alarm. The higher the chatter index is, the higher the amount of chattering alarms. According to ISA standard [2], a reasonable cutoff on j to identify the worst chattering alarms is jcutoff ¼ 0:05. Suppose that the process variable xðtÞ is with high alarm trip point xtp, then the alarm signal xaðtÞ is generated as [12]. xtp ¼ & 1; if xðtÞ ! xtp 0; if xðtÞ < xtp (4) The alarm duration, denoted as L, is the time duration of adja- cent ‘1's for xaðtÞ in (4), that is L ¼ t2 À t1 þ 1 (5) where xaðt1 À 1Þ ¼ 0, xaðt2 þ 1Þ ¼ 0, Pt2 t¼t1 xaðt2 þ 1Þ ¼ t2 À t1 þ 1, for t2 > t1. 3. Median ﬁlters 3.1. Deﬁnition of median ﬁlters For a set of n numbers fx1; x2; /; xng, if they are arranged in order such that xð1Þ xð2Þ/ xðnÞ (6) Then xðiÞ is the ith-order statistic (i ¼ 1; /; n) of fx1; x2; /; xng. The median of n numbers x1; x2; /; xn is the ðv þ 1Þth-order statistic, where v ¼ ðn À 1Þ=2, if n is odd. It is denoted by xðvþ1Þ ¼ mediannðx1; x2; /; xnÞ: (7) For even n, v ¼ n=2or v ¼ n=2 À 1, the deﬁnition differs only slightly, which will not be discussed in this paper. Let fxigði ¼ 1; 2; /Þ be sample data of a process variable xðtÞ at sample instant t ¼ 1T; 2T; /, where T is the sampling period. A median ﬁlter is a discrete-time dynamic system with fxig and output fyig, where yi ¼ median n ðxiÀ2v; /; xiÀv; /; xiÞ; ði ¼ 1; 2; /Þ (8) The median ﬁlter deﬁned in (8) is slight different from the one in the literature, e.g., [17]. Because (8) is causal and is easy to realize in practice. 3.2. Performance of median ﬁlters Consider a process signal xðtÞ with high-alarm trip point. That is, an alarm raises if xðtÞ exceeds or equals xtp, and clears if xðtÞ is smaller than xtp. Without loss of generality, the following analysis assumes that the process signal xðtÞ ¼ x0ðtÞ þ nðtÞ, and where x0ðtÞ is a deterministic signal, and x0ðtÞ is always less than xtp, nðtÞ is the noise or disturbance signal, and nðtÞ is independent. There is only nðtÞ to activate the alarms, thus, all the alarms are false alarms. We suppose each of sample data is independent variable with cumulative distribution function Fxð,Þ and xiði ¼ 1; 2; /Þ denotes the sampling value of a process signal xðtÞ at time instant i, let process signal xi be great than or equal to the trip point xtp with probability p i.e., p ¼ 1 À FxðxtpÞ, and the median ﬁlter (8) is applied to signal xi, then, there is no alarm for the output yi if and only if the number of alarms within the window n is less than half of window size v ¼ ðn À 1Þ=2, that is, less than or equal to v, i.e. the probability of yi xtp has a binomial distribution. P À yi xtp Á ¼ Xv i¼0 n i pi ð1 À pÞnÀi (9) For simplicity, let Pðyi xtpÞbQðn; pÞ, the false alarms rate (FAR) is given by FAR ¼ 1 À Qðn; pÞ (10) Eq. (10) relates FAR to the window size and the alarm probability of the process signal xðtÞ, FAR for some different values of window size n and alarm probability p are shown in Fig. 2. It is observed from Fig. 2: (1) FAR gradually decreases and tends to zero when window size increases, if the process variable xðtÞ is in the alarm state with probability p 0:5. (2) FAR gradually increases and tends to one when window size increases, if the process variable xðtÞ is in the alarm state with probabilityp 0:5. (3) FAR equals 0.5 regardless of window size if the process var- iable xðtÞ is in the alarm state with probability p ¼ 0:5. Remark 1. The median ﬁlter can be used to remove the chattering alarm on condition that the process variable is in the alarm state with probability p 0:5. For example p ¼ 0:3, window size n ¼ 15, FAR ¼ 0.05. Remark 2. According to Eq. (9), given an alarm duration length L, this alarm can be removed if the window size n is chosen to be at least twice of the alarm duration length L, for odd n, n ¼ 2L þ 1. Remark 3. If the process variable xðtÞ is in the alarm state for a majority of time, p 0:5, the trip point can be considered as a low- alarm trip point, i.e., it is reasonable to accept that the process variable should be in the alarm state. If the median ﬁlter is applied to signal xðtÞ, the output value yðtÞ at time instant t will be in the alarm state, if and only if the number of alarms within the window centered at time instant is more than half of number of points in the window, that is, more than v ¼ ðn À 1Þ=2, i.e. the probability of yðtÞ xtp in the window is given by Fig. 2. FAR for different p and window size n. Y. Sun et al. / ISA Transactions 73 (2018) 201e207 203
- 4. P À yðtÞ xtp Á ¼ Xn i¼vþ1 n i pi ð1 À pÞnÀi (11) Let PðyðtÞ xtpÞbQ 0 ðn; pÞ, the missed alarms rate (MAR) is given by MAR ¼ 1 À Q 0 ðn; pÞ (12) where Q 0 ðn; pÞ ¼ Pn i¼vþ1 n i pið1 À pÞnÀi ¼ Pv i¼0 n i pnÀið1 À pÞi . 4. Design of median ﬁlters using process data This section will propose a design method for median ﬁlters to reduce chattering alarms by using the process data, while the re- quirements on FAR, or MAR are satisﬁed. The chattering index in Section 2 is used to quantify chattering alarms. The following are assumed to be hold: A1. The past samples of the process variable xðtÞ in the normal and abnormal conditions are available. A2. The alarm signal is independently, identically distributed (IID) and there exist chattering alarms. A3. The alarm signal xaðtÞ is in the non-alarm state for the ma- jority of time, i.e.,p 0:5 The past samples of xaðtÞ in assumption A1 are used to estimate the probability of chattering alarms. Assumption A2 is a statistical requirement for (9)e(10). Many cases satisfy this assumption in practice, e.g., the process variable xðtÞ ¼ x0ðtÞ þ nðtÞ is disturbed by IID noise nðtÞ, where x0ðtÞ is a deterministic signal. Assumption A3 can be veriﬁed because the alarm state is often less than normal state in practice. If assumption A3 does not hold, the proposed method requires minor modiﬁcations; see Remark 6 presented later in this section. The proposed method consists of ﬁve steps: Step 1. Calculate the chattering index j of an alarm signal xaðtÞ. Step 2. If the chattering index j is more than the cutoff threshold 0.05, estimate the maximum probability of alarm in sixty times of sampling period. Otherwise, stop. Step 3. Choose the minimum window size n to satisfy the re- quirements on FAR according to (10). Step 4. Filter the process variable using the median ﬁlter with the chosen window size n and obtain the alarm signal x 0 aðtÞ of the ﬁltered process variable xðtÞ. Step 5. Calculate the chattering index j of alarm signal x 0 aðtÞ, if j 0:05, stop and n is window size of median ﬁlter, Otherwise, increment n by 2 and turn to step 2. There are three remarks for the above steps. Remark 4. In step 2, we estimate the maximum probability of alarms in sixty times sampling period. This choice is based on chattering alarm deﬁned in Section 1, which considers the sampling period and generalizing the rule of thumb from ISA standard. Remark 5. The proposed method needs step 5. (10) only relates the window size of standard median ﬁlters to FAR. Since the moving median ﬁlters are applied to the process variable, alarms close to each other may still remain. Remark 6. If assumption A3 does not hold, i.e. p 0:5, the alarm signal xaðtÞ is in the alarm state for a majority of time, the proposed method needs to be modiﬁed as follows: The complement of alarm data xaðtÞ is used to calculate the chattering index in step 2, i.e. ‘1' of xaðtÞ is substituted by ‘0’, and ‘0’ of xaðtÞ by ‘1’. The window size n to be chosen is to satisfy the requirement on the MAR as in (12). One simulation example and one industrial example are pre- sented here to illustrate the proposed method. Example 1. Consider the continuous stirred tank heater (CSTH) with closed loop control [18]. The CSTH of conﬁguration is shown in Fig. 3 and the temperature in tank is the process variable xðtÞ, which is measured by a type J metal sheathed thermocouple. The simu- lation data N ¼ 10000. Let the temperature xðtÞ be disturbed by a random noise with uniform distribution in ½0:1; 0:2, and the alarm probability of xðtÞ equal to p ¼ f0:1; 0:2; 0:3g, that is the alarm is triggered by noise. Fig. 4(a)-(c) show the temperature xðtÞ, the alarm xaðtÞ corre- sponding to high-alarm trip point xtp ¼ 10:6 and the run length distribution of alarms for the normal situation. The chattering in- dex is j ¼ 0:01, so the alarm is not chattering. Fig. 5(a)-(c) present the run length distribution of alarm xaðtÞ for the three probabilities. When p increases, there are more and more alarms with short run lengths and the chattering indexes are increasing, i.e. j1 ¼ 0:15, j2 ¼ 0:23, j3 ¼ 0:26 for p1 ¼ 0:1, p2 ¼ 0:2, p3 ¼ 0:3, respectively. If the requirement on the FAR in step 3 is FAR 0.05, according to (10), the median ﬁlter window size N1 ¼ 3, N2 ¼ 7, N3 ¼ 17 are chosen for p1 ¼ 0:1, p2 ¼ 0:2, p3 ¼ 0:3, respectively. For p3 ¼ 0:3, window size N3 ¼ 21 is chosen instead of N3 ¼ 17, see Remark 5 in this section. The alarm x 0 aðtÞ is generated by the ﬁltered data, and Fig. 6(a)-(c) shows the run length distribution of alarm signal x 0 aðtÞ. From Fig. 6, it is clear that there are a few alarms with short run lengths, and the distribution is almost uniform for each existing run lengths. The chattering indexes j 0 1 ¼ 0:04, j 0 2 ¼ 0:049, j 0 3 ¼ 0:037 are less than jcutoff ¼ 0:05. For comparison, the chattering indexes for moving average ﬁl- ters using the same windows are given in Table 2. The indexes for median ﬁlters are less than jcutoff ¼ 0:05, and the indexes for moving average ﬁlters are more than jcutoff ¼ 0:05, that is, the chattering alarms caused by noise are not completely removed. Suppose the temperature xðtÞ is disturbed by an auto-correlated noise, which is generated by the random noise passing through a linear time invariant system s2 s2þ ﬃﬃﬃ 2 p sþ1 . Median ﬁlters are used and the chattering indexes are in Table 3. Compared with the inde- pendent noise, the chattering indexes caused by auto-correlation noise are smaller except alarm probability p ¼ 0:1. For alarm Fig. 3. The continuous stirred tank heater. Y. Sun et al. / ISA Transactions 73 (2018) 201e207204
- 5. probability p ¼ f0:1; 0:2g, the chattering index for the ﬁltered xðtÞ is more than jcutoff ¼ 0:05, and the chattering alarms are totally removed for the p ¼ 0:3. Fig. 7 and Fig. 8 show the run length distribution for unﬁltered and ﬁltered xðtÞ, respectively. It is shown that median ﬁlters can still reduce the chattering index under auto- correlated noise. Example 2. An industrial data was studied in Ref. [13]. The pro- cess variable xðtÞ is a temperature of stator outlet pipes for a power generator, which is measured by 54 temperature sensors. xtp ¼ 8 degree is a high-alarm trip point. Due to the existing noise, there are many chattering alarms in the temperature alarm signal xaðtÞ. Fig. 9 shows the process variable xðtÞ with 1155 alarms in 24h; and the run length distribution is given in Fig. 9(c). There are many alarms with short run length and the chattering index j ¼ 0:11. The maximum alarm probability of temperature samples in sixty times of sampling period is estimated as ~pmax ¼ 0:23, thus, N ¼ 7 is the window size of median ﬁlter for stratifying FAR 0.05. The result of ﬁltered x 0 ðtÞ is shown in Fig. 10. From Fig. 10(c), there are only 20 alarms left and the run length distribution is uniform with one alarm count for each run length, and the chattering index j 0 ¼ 0:02. 5. Design of median ﬁlters using alarm data Sometimes it is not possible to obtain enough process data to estimate the alarm probability in industrial practice for the following reasons: Firstly, the abnormal operation conditions in reality are very rare; even if an alarm is raised, it is difﬁcult to distinguish if the alarm is caused by normal or abnormal Fig. 4. (a) Temperature xðtÞ(solid) and alarm trip point xtp(dash), (b) alarm signal xaðtÞ, (c) run length distribution for xaðtÞ. Fig. 5. Run length distributions for xðtÞ with p ¼ 0:1 (a), p ¼ 0:2 (b), p ¼ 0:3 (c) (unﬁltered). Fig. 6. Run length distributions for xðtÞ p ¼ 0:1 (a), p ¼ 0:2 (b), p ¼ 0:3 (c) (ﬁltered). Table 2 Chattering indices for different ﬁlters. Alarm probability window size median moving average p ¼ 0:1 3 0.04 0.06 p ¼ 0:2 7 0.049 0.089 p ¼ 0:3 21 0.037 0.1 Table 3 Chattering indexes for CSTH with auto correlation noise. alarm probability unﬁltered median p ¼ 0:1 0.18 0.07 (window size ¼ 3) p ¼ 0:2 0.19 0.07 (window size ¼ 7) p ¼ 0:3 0.23 0 (window size ¼ 21) Fig. 7. Run length distributions for xðtÞ with auto correlated noise p ¼ 0:1 (a), p ¼ 0:2 (b), p ¼ 0:3 (c) (unﬁltered). Y. Sun et al. / ISA Transactions 73 (2018) 201e207 205
- 6. conditions. Secondly, due to limitation of storage media, the pro- cess data is always stored based on some down sampling technique, there are few process data at the original sampling frequency of the controller. Furthermore, most process control systems only store alarm event data. Finally, ﬁeld engineers are more concerned with the number reduction of chattering alarms, rather than its quan- titative description. In addition, when the median ﬁlter is applied to an alarm signal xaðtÞ, it is a type of generalized delay-timers with k out of n delay-timer, this is, in the consecutive n samples, an alarm is to be raised if and only if there are at least v þ 1 alarms, and an alarm is cleared if and only if there are at most v alarms, where n is the window size and n ¼ 2v þ 1. According to Remark 2, the alarm with alarm duration length L can be removed if the window size of the median ﬁlter is at least twice of the he alarm duration length L. Therefore, the method to design the median ﬁlter using historical alarm data in term of percentage reduction of chattering alarms is proposed in this section. The proposed method consists of the following steps: Step 1. Identify chattering alarms of the historical alarm data. Step 2. Plot the duration distribution of alarms for each alarm tag. Step 3. Plot the cumulative distribution function of the duration distribution. Step 4. According to a reduction percentage of alarms, ﬁnd the duration length L of the alarm. Then the minimum of window size nmin is equal to 2L þ 1. Step 5. Apply the median ﬁlter with nmin to the alarm data. If the reduction percentage of alarms is not satisﬁed, increase the window size, and return to step 5 again. Two industrial examples are presented here to illustrate the proposed method. Consider Example 2 in Section 4; the red dash line in Fig. 11 shows the cumulative distribution function repre- sented by the blue bars. The duration length of all the alarms is less than or equal to 5 s. If we choose the window size nmin ¼ 11, all these alarms can be removed. The duration length of over 97% alarms is less than or equal to 2 s, i.e. we use the median ﬁlter with wind size nmin ¼ 5, there are more than 95% alarms reduced. The black line in Fig. 11 shows the percentage of reduction in chattering alarms using the median ﬁlter with different window size. Consider the industrial data with sampling period T ¼ 1 minute shown in Fig. 12(a), which is used in Ref. [12], Fig. 12(b) shows the run length distribution. It is shown that there exist many chattering alarms. In this case, the cumulative distribution function is represented by the red dash line, and the percentage reduction in chattering alarms by median ﬁlters with different window sizes is showed in Fig. 8. Run length distributions for xðtÞ with auto-correlated noise p ¼ 0:1 (a), p ¼ 0:2 (b), p ¼ 0:3 (c) (ﬁltered). Fig. 9. (a) Process variable xðtÞ(solid) and alarm trip point xtp(dash), (b) alarm signal xaðtÞ, (c) run length distribution for xaðtÞ. Fig. 10. (a) Filtered process variable xðtÞ(solid) and alarm trippoint xtp(dash), (b) alarm signal x 0 aðtÞ, (c) run length distribution for x 0 aðtÞ. Fig. 11. Design of median ﬁlter using the alarm and duration distribution. Y. Sun et al. / ISA Transactions 73 (2018) 201e207206
- 7. black line. More than 94% alarm repeated within 6T can be considered as chattering alarms, using the black curve in Fig. 13, we obtain easily that over 93% alarms are reduced using a median ﬁlter with window size n ¼ 13. 6. Conclusion This paper discussed the performance of median ﬁlters in alarm rationalization and applied them to remove chattering alarms to improve the performance of alarm systems. This work is mainly based on the fact that chattering alarms repeatedly and rapidly change between alarm and normal states in a short time period and have short alarm duration lengths, and the median ﬁlter with window size n(for odd n) can remove alarms whose duration lengths are less than or equal to v ¼ ðn À 1Þ=2. Two design methods of median ﬁlters were proposed and two rules for choosing the window size of median ﬁlters are formulated in this paper. If the past samples of process variable xðtÞ in the normal and abnormal conditions are available, the maximum alarm probability in sixty times sampling period can be used to choose the window size to satisfy the FAR or MAR. Otherwise, if there is only alarm data available, the alarm duration length distribution can be used to determine the window size which satisﬁes a given percentage of reduction of chattering alarms. The industrial case studies illus- trated the effectiveness of the proposed method. Acknowledgments This work was partially supported by National Natural Science Foundation of China under Grant 61733015, U1730105, 61433011, 61603316 and 61773323, China Scholarship Council and Natural Sciences and Engineering Research Council of Canada. References [1] EEMUA-191: alarm systems a guide to design, management and procurement. London: Engineering Equipment and Materials Users Association; 2007. [2] ANSI/ISA-18.2: management of alarm systems for the process industries. North Carolina: International Society of Automation; 2009. [3] Holliﬁeld BR, Habibi E. The alarm management handbook: a comprehensive guide: practical and proven methods to optimize the performance of any alarm management system. Houston: PAS; 2010. [4] Rothenberg D. Alarm management for process control. Momentum Press; 2009. [5] Bransby ML, Jenkinson J. The management of alarm systems. Shefﬁled: Health and Safety Executive; 1998. [6] Izadi I, Shah SL, Shook DS, Kondaveeti SR, Chen T. A framework for optimal design of alarm systems. In: Proceedings of 7th IFAC symposium on fault detection, supervision and safety of technical processes; 2009. p. 651e6. [7] Hugo A. Estimation of alarm deadbands. In: Proceedings of 7th IFAC sympo- sium on fault detection, supervision and safety of technical processes; 2009. p. 663e7. [8] Naghoosi E, Izadi I, Chen T. A study on the relation between alarm dead-bands and optimal alarm limits. In: Proceedings of American control conference; 2011. p. 3627e32. [9] Kondaveeti SR, Izadi I, Shah SL, Shook DS, Kadali R, Chen T. Quantiﬁcation of alarm chatter based on run length distributions. Chem Eng Res Des 2013;91(12):2550e8. [10] Kondaveeti SR, Izadi I, Shah SL, Shook DS, Kadali R. Quantiﬁcation of alarm chatter based on run length distributions. In: Proceedings of 49th IEEE con- ference on decision and control; 2010. p. 6809e14. [11] Naghoosi E, Izadi I, Chen T. Estimation of alarm chattering. J Process Contr 2011;21(9):1243e9. [12] Wang J, Chen T. An online method for detection and reduction of chattering alarms due to oscillation. Comput Chem Eng 2013;54:140e50. [13] Wang J, Chen T. An online method to remove chattering and repeating alarms based on alarm durations and intervals. Comput Chem Eng 2014;67:43e52. [14] Kondaveeti SR, Izadi I, Shah SL, Chen T. On the use of delay timers and latches for efﬁcient alarm design. In: Proceedings of 19th IEEE mediterranean con- ference on control automation; 2011. p. 970e5. [15] Kim J-S, Park HW. Adaptive 3-d median ﬁltering for restoration of an image sequence corrupted by impulse noise. Signal Process Image Commun 2001;16(7):657e68. [16] Barner KE, Arce GR. Order-statistic ﬁltering and smoothing of timeseries: Part ii. Handb Stat 1998;17:555e602. [17] Justusson BI. Median ﬁltering: statistical properties. Springer Berlin Heidel- berg; 1981. p. 161e96. Ch. 5. [18] Thornhill NF, Patwardhan SC, Shah SL. A continuous stirred tank heater simulation model with applications. J Process Contr 2008;18(2):347e60. Fig. 12. (a) The process signal xðtÞ(solid) and its alarm trip point xtp(dash). (b) Run length distribution xðtÞ. Fig. 13. Design of median ﬁlter using the alarms and duration distribution. Y. Sun et al. / ISA Transactions 73 (2018) 201e207 207

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