联合估计异常检测方法的水处理控制.pdf

Environmental Modeling and Assessment 6:77–82, 2001.2001 Kluwer Academic Publishers. Printed in the Netherlands.Water treatment control using the jointestimation outlier detection methodChristine Wright a,∗and David BoothbaDepartment of Management, Western Carolina University, Cullowhee, NC 28723, USAE-mail: cwright@bAdministrative Sciences Department, Kent State University, Kent, OH 44242, USAThe loss of contaminated wastewater into the environment by leakage or other means is a serious problem. This problem is essentially the same as true of the loss of chemical reagents from a chemical production or purification process.The present article shows how the joint estimation method, an outlier detection method for time series analysis, can be used by a facility manager to deal with these problems.Keywords: joint estimation, outlier detection, process control, wastewater control1. IntroductionIn many industries, it is important to determine when the process is out-of-control, (i.e., when significant adverse process changes occur). The idea is to discover these ad-verse process changes while they are still relatively minor, before substandard product or significant pollution is pro-duced. One example of an important chemical process con-trol problem is wastewater treatment. This paper discusses the use of a process control method for the purpose of monitoring wastewater data. The objective of the research was to determine if the out-of-control observations (i.e., abnormal states) could be detected by JE in the period when they first occurred. The process control method reported herein can be used for any compound for which an analytical chemical detection method exists. The method that we consider, Joint Estimation (JE), has the potential to be extremely important to both general pollution control and statistical process con-trol.2. BackgroundIt has been previously shown that pollution producing situations may be recognized through the detection of statistical outliers [1–14]. An outlier is any point that deviates significantly from the underlying process model or time series pattern, indicating a change in the process and thus an out-of-control situation with respect to the process model. Points outside of three standard deviations of the targeted process mean are usually considered to be outliers. Such a point can be identified using statistical methods.If such exist, the process is said to be “out of control” (i.e., there is a significant adverse process change due to an assignable cause which is a cause that can be identified).Otherwise the process is said to be “in control” (i.e., only random variations of output exist within certain control limits).Traditional statistical process control charts as well as most of the other methods currently used are based upon the assumption that the observations in the process time series are independent and identically distributed (IID) about the targeted process mean or targeted value at any time t and that the distribution is normal when the process is in statistical control. Independence implies that there is no particular pattern in the data.Unfortunately, much of the data used in statistical process control is non-IID [15]. Alwan and Radson [15] also note that because of the efforts of G.E.P. Box, the chemical industry has recognized for many years that autocorrelation (i.e., relationships across time) exist in their processes. Bax-ley [16], Berthouex et al. [17], Emer et al. [18], Harris and Ross [19], and Hunter [20] have noted that continuous process industries, such as wastewater plants, often have autocorrelated process data.3.Approaches to SPC when standard methods are not appropriateProcess measures over time are often interdependent (i.e., the observations are autocorrelated). Further, many process time series exhibit a characteristically repetitive pattern, which can be mathematically modeled by an Autoregressive Moving Average [ARMA(p, q)] model. For example, ARMA(1, 1) and other time series models have been empirically found in some cases to be appropriate for modeling a process time series [21]. Under such conditions, traditional SPC procedures may be ineffective and inappropriate for monitoring and controlling the process, perhaps even erroneously indicating an out-of-control situation when the criteria of the traditional control chart are applied [15]. In other words, they are not as effective as they should be in detecting, for example, the escape of pollutants into the environment. Thus, if the process being controlled is one that produces pollutants, these compounds may be introduced into the environment without the producer’s knowledge. Use of time series based process control methods, rather than standard statistical process control methods, is appropriate when data is non-IID or when outlying observations may exist in the data, such as when the materials are particularly valuable or involve critical safety concerns.4. Joint estimation methodThe method considered is successful in handling the problems of general statistical process and pollution con-trol [12,14]. Joint Estimation (JE), a time series procedure, developed by Chen and Liu [22] has been applied to other environmental pollution situations [12]. This method is superior to the one used earlier by Prasad [23] in that (a) outliers are obtained iteratively, based on the adjusted residuals and observations, (b) the procedure does not require intervention models to be estimated to accommodate the outliers，(c) the identification and location of outliers are based on robust parameter estimates, (d) the outlier effects are jointly estimated using multiple regression, and (e) the procedure differentiates between and accommodates for four forms of outliers: Innovational Outliers (IO), Additive Outliers (AO), Level Shifts(LS), and Temporary Changes (TC). These four types of outliers range between the extremes of a one-time change (AO), a permanent shift in the level of a process (LS) and two decaying patterns after the initial impact (IO and TC). This method is proprietary; the details of its algorithms are limited. The JE subroutine is availableon the XUTS Software from Scientific Computing Associates (SCA), Oak Brook, IL.The method is described in appendix. In addition, figure 1 depicts all four types for an ARMA(1, 0) model.The information provided by the JE method with regard to the location of the outlier can increase the effectiveness of detecting the loss of pollutants into the environment. This method was tested by Prasad et al. and found to be very successful with nuclear inventory data as well as general SPC data [2,3]. Wright [14] and Wright et al. [24] show that this method can effectively locate outliers in a time series with as few as 9 observations where the outlier is the last observation in the time series. All outliers are identified as AO when they first occur, this can be seen in figure 1. Furthermore, this method has considerably fewer false alarms than the Exponentially Weighted Moving Average (EWMA) model [12,14,24].Figure 1. AO, TC, LS and IO for an ARMA(1, 0) model.5. Research methodWe utilize the joint estimation (JE) outlier detection method of Chen and Liu [22] to detect outliers (i.e., out-of-control observations) in wastewater treatment data. This data consists of 527 daily measurements of 38 different sensor readings (variables). These variables are shown in table 1. The wastewater plant manager identified 13 different states of performance; these are shown in table 2 and include such conditions as normal operations, storms, solids overload, etc. Of these states, only states 1, 5, 9 and 11 are normal. The objective of the research was to determine if the out-of-control observations (i.e., abnormal states) could be detected by JE in the period when they first occurred. It is of considerable importance to determine that an out-of-control situation exists on the day when it first occurs rather than several days later. Clearly the environmental and health risks involved necessitate early detection, perhaps even at the cost of som e false alarms.The joint estimation method is appealing because it performs well over a wide variety of both seasonal and non-seasonal ARIMA models. The user must specify the model type for the series prior to using the JE routine. This method is proprietary, the details of its algorithms are limited. The JE subroutine is available on the XUTS Software from Scientific Computing Associates (SCA), Oak Brook, IL. In addition, it is possible to use the JE method as an online process control technique through a communication protocoldeveloped between the online data collection unit and the SCA system. Wright et al. [24] describe the method in detail. A brief summary of the method is included here.The joint estimation method involves three stages. The first stage obtains maximum likelihood estimates of parameters and residuals. Then, outliers are sought and their effects are removed from the residuals. After all outliers have been detected, model parameter estimates are revised. In the second stage, multiple regression is utilized to jointly estimate the effect of the outliers and model parameters. Then the estimated t-values are compared with the critical value, C. If the t-value of a suspected outlier is smaller than C, the outlier is deemed not significant. Next, an adjusted series is obtained by removing significant outlier effects. Maximum likelihood estimates of model parameters are found based on the adjusted series. In the third stage, outliers are sought based on final parameter estimates found in stage two. Residuals are computed using these estimates. These residuals are used as the procedure iterates through the first two stages.Chen and Liu [22] have shown that the JE method is extremely effective for detecting outliers in autocorrelated time series data with a large number of observations. They did not, however investigate the ability of the method to identify outliers when they are the last observation in a time series. Wright et al.[24], through a simulation experiment, show that the JE method is very effective for identifying outliers when they are the last observation in short autocorrelated times series.C. Wright,D. Booth / Water treatment control 79Table 1Waste water treatment process variables.Variable Category Description of variable1 Influent to plant Flow to plant2 Influent to plant Zinc to plant3 Influent to plant pH to plant4 Influent to plant Biological demand of oxygen to plant5 Influent to plant Chemical demand of oxygen to plant6 Influent to plant Suspended solids to plant7 Influent to plant Volatile suspended solids to plant8 Influent to plant Sediments to plant9 Influent to plant Conductivity to plant10 Input to primary treatment pH to primary settler11 Input to primary treatment Biological demand of oxygen to primary settler12 Input to primary treatment Suspended solids to primary settler13 Input to primary treatment Volatile suspended solids to primary settler14 Input to primary treatment Sediments to primary settler15 Input to primary treatment Conductivity to primary settler16 Input to secondary treatment pH to secondary settler17 Input to secondary treatment BOD to secondary settler18 Input to secondary treatment Chemical demand of oxygen to secondary settler19 Input to secondary treatment Suspended solids to secondary settler20 Input to secondary treatment Volatile suspended solids to secondary settler21 Input to secondary treatment Sediments to secondary settler22 Input to secondary treatment Conductivity to secondary settler23 Effluent from pHplant24 Effluent fromplantBiological demand ofoxygen25 Effluent fromplantChemical demand ofoxygen26 Effluent fromplant Suspended solids27 Effluent fromplantVolatile suspendedsolids28 Effluent fromplant Sediments29 Effluent fromplant Conductivity30 Performance Input BOD in primary settler31 Performance Input suspended solids to primary settler32 Performance Input sediments to primary settler33 Performance Input BOD to secondary settler34 Performance Input COD to secondary settler35 Globalperformance Input biological demand of oxygen36 Globalperformance Input chemical demand of oxygen37 GlobalperformanceInput suspendedsolids38Globalperformance Input sedimentsTable 2Wastewater treatment process conditions.Condition Status Condition Number of daysnumber in this state1 Normal Normal operations 1 2752 Abnormal Secondary settler problems 1 13 Abnormal Secondary settler problems 2 14 Abnormal Secondary settler problems 3 45 Normal Normal operations, above mean 1166 Abnormal Solidsoverload 1 37 Abnormal Secondary settler problems 4 18 Abnormal Storm conditions 1 19 Normal Normal operations with lowinfluent 6910 Abnormal Storm conditions 2 111 Normal Normal operations 2 5312 Abnormal Storm conditions 3 113 Abnormal Solidsoverload 2 1When using JE, the critical value, C, is specified by the user. The critical value is compared with the t-value of a suspected outlier. The outliers ranged from day 60 to day 467.This implies that the time series studied ranged from 60 observations to 467 observations. A critical value of C=4.0 was utilized because Chen and Liu [22] recommend C of 3.0 for series between 101 and 200 observations; C > 3.0 for series greater than 200 observations. The wastewater data contains 14 outliers. The locations of these outliers are days 60, 61, 62, 98, 128, 186, 213, 244, 421, 424, 427, 465, 466 and 467.6. ResultsJE is not a multivariate method. Therefore, the concern was to seek outliers for a ll 38 sensor readings. If at least one outlier was detected within the day’s 38 readings, that day was determined to be out-of-control. JE was utilized to consider each of the 38 sensor readings in such a manner that days 60, 61, 62, 98, 128, . . . were the last day in the time series under consideration. This replicates the results that would be available to the user on the particular days when out-of-control situations occurred. Table 3 summarizes the results of the JE method in detecting the outlier when it was known to be the last observation in the time series. All abnormal days were detected except day 467.The JE method was also tested to determine the false alarm rate. Of specific concern was whether the method would identify the last observation as an outlier when it was known to be not an outlier. Thirty days were randomly chosen to determine, if they were the last day in the time series, would they be misidentified as outliers? For example, the 51st day is known to be a normal (state 1) day. The JE method was used to analyze the data up to and including day 51, where day 51 data was the last observation in the time series. The JE method reported, as shown in table 4, that day 51 is not out-of-control (not an outlier). The results for all thirty randomly selected days are shown in table 4 along with their states and the variables determined to be outliers. The false alarm rate seems a bit high. However, when weighed against the cost of loss of human life or environmental damage, the false alarm rate is of less importance than the high outlier detection rate of 92.86%. In addition, our count of false alarms in table 4 may be overly pessimistic. If, for example, a surge of increased solids en-Table 3Detection results of JE for days known to be out-of-control.Day State Number of OOC variablesvariables OOC60 2 9 24,25,26,28,33,35,3 6,37,3861 3 4 24,26,37,3862 4 4 25,28,35,38 98 7 3 28,32,38 128 6 4 6,8,12,14 186 10 3 19,20,32 213 8 1 29244 12 5 6,7,12,13,31 421 13 3 6,7,13424 6 4 6,8,12,14 427 6 2 6,12465 4 7 2,25,26,33,35,36,3 7466 4 1 29467 5 0 Nonetered the system, we might obtain more out of control observations than actuallyexist. Further, one of the reviewers suggests that if the false alarm observationsare linked in the treatment process then they may be counted more than once. Ineither case, our counts for false alarms would be definitely conservative.The results reported in table 4 may also be viewed in another light. Chen and Liu [22] and Wright et al. [24] show false alarm rates of 1% or less for simulated time series. Wright et al. [24] simulated time series and knew with certainty where the outliers were and were not located. Their false alarm rate for ARMA(1, 0) time series ranged from 0.79 to 0.10% and for ARMA(0, 1) ranged from 1.27 to 0.27%. The data used in this research is ARMA(1, 0) data. Given the results found by Wright et al.[24], one might wonder about the absolute classification of some days as “normal” or incontrol. The plant manager of the plant where this data originated categorized the wastewater data when it was recorded. These categories or operating conditions are, therefore, assigned based on the judgment of the plant manager (i.e., the 13 conditions mean something to the plant manager but would mean nothing to other plant managers elsewhere). This leads to the question, given the low false alarm rates in previous research with this method, is the false alarm rate as high as reported in table 4, or weremany days were out-of-control on at least one variable and this condi-tion was not recognized by the plant manager?Table 4False alarm results of JE for days known to be not out-of-control.Day State Number of OOCvariables OOC variables51 1 0 –65 1 0 –71 1 0 –90 1 0 –104 5 5 6,11,12,17,33117 5 0 –122 5 0 –139 5 0 –144 1 0 –153 1 0 –180 5 1 22 209 5 0 –234 9 0 –269 1 1 2 285 11 0 –306 11 0 –318 11 1 28 331 1 0 –351 5 2 6,21 362 11 0 –374 1 0 –380 1 0 –390 1 0 –415 1 0 –422 9 0 –432 1 0 –435 1 0 –497 9 1 35504 5 0 –521 1 0 –Wright et al. [24] considered twenty-two real industrial time series that were not necessarily normally distributed; the simulated time series were normally distributed (0,1). Even when the normal distribution was not assumed, false alarm rates using JE were 8.52% for ARMA(1, 0) and 4.98% for ARMA(0, 1). Thus we might conclude, given that the wastewater data may not be normally distributed, that it is unlikely that this particular data would yield such a large false alarm rate when compared with all previous research using this method. Because all classifications of “normal” data were made somewhat judgmentally, this leads to the conclusion that this method may help wastewater plant op-erators identify out-of-control days when they first occur and require less need to classify days by various judgmental titles of normal or abnormal.7. ConclusionsAcknowledgementsThe authors would like to thank David West, Ph.D., East Carolina University and Paul Mangiameli, Ph.D., University of Rhode Island, for their assistance in securing and under-standing the wastewater treatment data.Appendix: A description of the joint estimation methodThe escape of pollution into the environment by leakage or misidentification presents a serious problem, as it does for any chemical production process. Clearly, this method may be useful in monitoring and identifying out-of-control situations in various environmental data.The results reported in table 3 indicate that, at least for this data, some variables were more helpful for detecting outlying days than others. Table 3 shows that only twenty-one of the thirty-eight variables were useful in determining which days were out-of-control; these variables were 2, 6, 7, 8, 12, 13, 14, 19, 20, 24, 25, 26, 28, 29, 32, 33, 35, 36, 37 and 38.In summary, this research has combined manufacturing, chemical, and statistical methods in order to improve our ability to detect pollutants before they become a serious problem. Further, as indicated in the introduction, the importance of these techniques to decision and policy makers cannot be overemphasized.The requirement of their use by decision makers and policy makers will allow polluting facilities to be detected more quickly, thus decreasing the total amount of pollution to the environment.8. Policy relevanceIn addition to making the pollution control methods along with the associated safeguards systems more powerful, and thus being able to detect a polluting facility sooner, this method has decision making and policy implications. There are two special groups for which the results of this research are targeted. First, appropriate managers in charge of the potentially polluting facility. These decision makers need t o know as soon as possible that a problem exists so that they can decide whether a quick fix is possible or whether the fa-cility needs to be shut down for more extensive repairs to stop any potential pollution of the environment. Of course, the sooner such a decision is made the less pollution to theenvironment results. The second target group is policy mak-ers. As new methods for pollution detection are developed, policy makers can take advantage of them by requiring their use by potential polluters and regulatory agency investiga-tors. Thus, as indicated previously, the amount of pollution can be minimized. It should be noted however that policy makers must keep up to date on current methods so that the best possible pollution detection methods are being required for use.A.1. Joint estimation – stage oneThe first stage involves estimation of parameters and de-tection of outliers. First, the method obtains the maximum likelihood estimates of the parameters and the residuals. Then, the procedure searches for an outlier. If it discovers an outlier, the procedure removes the effect of the outlier from the residual. Then the method seeks additional outliers. Af-ter the procedure finds all outliers, it revises the estimates of the model parameters. If no outliers are found, the procedure stops.A.2. Joint estimation – stage twoThe procedure jointly estimates the effect of the outliers and the parameters of the model. First, it jointly estimates the outlier effects, w j’s, using multiple regression for j=1, . . . , meˆt=w jπ(B)L j (B)I t (t j ) + a t ,where eˆt is the output variable, w j indicates the magni-tude of the outlier and L j(B)I t(t j)are the input variables. When the outlier is an IO, L j(B)=θ (B)/{φ(B)α(B)},L j (B) =1 for AO, L j (B) =1/(1− B) for LS, L j (B) =1/(1 −δB) for TC at t=t j [22]. Lastly, a t is a sequence of random errors that are iid and are from a normal distribution with mean of zero and variance independent of time [25]. Next, the procedure computes the estimated t-values of the estimated weights (t j=w j/(std(w j)), j= 1, . . . , m). The t-values are compared with the critical value,C. If the t-value of a suspected outlier is less than or equal to C, the outlier is determined to be not significant and is removed from the set of identified outliers. The procedure contin-ues to jointly estimate the weights using multiple regression and compare the t-values with the critical value until there are no remaining outliers. Next, the procedure obtains the adjusted series by removing significant outlier effects.。